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OrcaFlex Manual

Orcina Ltd.DaltongateUlverstonCumbriaLA12 7AJUK

Telephone: +44 (0) 1229 584742Fax: +44 (0) 1229 587191E-mail: software@orcina.comWeb Site: www.orcina.com

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CONTENTS

1 INTRODUCTION 91.1 Introduction 91.2 Installing OrcaFlex 91.3 Running OrcaFlex 111.4 Demonstration Version 131.5 Frequently Asked Questions 131.6 Validation and QA 141.7 Orcina 151.8 Terms and Conditions 171.9 References and Links 20

2 TUTORIAL 242.1 Getting Started 242.2 Building a Simple System 242.3 Adding a Line 242.4 Adjusting the View 252.5 Static Analysis 262.6 Dynamic Analysis 262.7 Multiple Views 272.8 Looking at Results 272.9 Getting Output 282.10 Input Data 28

3 EXAMPLES 293.1 Introduction 293.2 A - Riser Systems - simple models 32

3.2.1 A01 Catenary Riser 323.2.2 A02 Lazy Wave Riser 343.2.3 A03 Steep Wave Riser 343.2.4 A04/A05 Lazy S Riser 353.2.5 A06 Steep S Riser 363.2.6 A07 Pliant Wave Riser 373.2.7 A08 Pliant S Riser 38

3.3 B - Riser Systems - more complex 383.3.1 B01 Jumper to High Tower 383.3.2 B02 Riser to Low Tower 393.3.3 B03 Multiple Towers 403.3.4 B04 Releasable Turret 413.3.5 B05 Detailed Pliant Wave 423.3.6 B06 Full Field Layout 42

3.4 C - Steel Catenary Risers 43

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3.4.1 C01 Catenary SCR 433.4.2 C02 Lazy SCR 433.4.3 C03 Steep SCR 44

3.5 D - Tensioned Risers, TLPs, SPARs 453.5.1 D01 Drilling Support 453.5.2 D02 SPAR 463.5.3 D03 Tension Leg Platform 47

3.6 E - Mooring Systems 473.6.1 E01/E02 Buoyed Moorings 473.6.2 E03 Released Mooring Buoy 483.6.3 E04 Branched Mooring 48

3.7 F - Buoy Systems 493.7.1 F01 CALM Buoy 493.7.2 F02 Chinese Lantern 503.7.3 F03 Current Meter Mooring 503.7.4 F04 Deep Water Mooring 51

3.8 G - Installation 523.8.1 G01 Pipelay 523.8.2 G02 Lay on Tower 533.8.3 G03 Crane Lower 533.8.4 G04 Pull Up Line End into Moonpool 543.8.5 G05/G06 Midline Pull Up 553.8.6 G07 Pipe Lift 563.8.7 G08 Snag Pull-in 573.8.8 G09 Anchor-last Deployment 583.8.9 G10 Lower with Bend Limiter 59

3.9 H - Offloading Systems 603.9.1 H01 Stowed Line 603.9.2 H02 Floating Line 613.9.3 H03 Jacket to Semisub 62

3.10 I - Towed Arrays 633.10.1 I01 Streamer Array 633.10.2 I02 Deployment with Sub 64

3.11 J - Pre and Post Processing 653.11.1 J01 Batch Script 653.11.2 J02 Results 653.11.3 J03 Stress Analysis 663.11.4 J04 Fatigue analysis 67

3.12 K - Line on Line Contact 683.12.1 K01 Line on Line Impact 683.12.2 K02 Line on Line Slide 69

3.13 L - RAO Import 703.13.1 Example RAO Text File 70

4 USER INTERFACE 724.1 Introduction 72

4.1.1 Program Windows 724.1.2 The Model 724.1.3 Model Browser 73

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4.1.4 Libraries 744.1.5 Model States 764.1.6 Using Model States 784.1.7 Toolbar 784.1.8 Status Bar 794.1.9 Mouse and Keyboard Actions 80

4.2 Menus 824.2.1 Menus 824.2.2 File Menu 834.2.3 Edit Menu 844.2.4 Model Menu 854.2.5 Calculation Menu 864.2.6 View Menu 874.2.7 Results Menu 894.2.8 Tools Menu 894.2.9 Window Menu 904.2.10 Help Menu 90

4.3 3D Views 914.3.1 3D Views 914.3.2 View Parameters 924.3.3 View Control 924.3.4 Zooming Views 934.3.5 How Objects are Drawn 934.3.6 Selecting Objects 954.3.7 Creating and Destroying Objects 954.3.8 Dragging Objects 954.3.9 Connecting Objects 954.3.10 Printing, Copying and Exporting Views 96

4.4 Replays 964.4.1 Replays 964.4.2 Replay Parameters 974.4.3 Replay Control 984.4.4 Superimpose Times 984.4.5 Multiple File Replays 99

4.5 Data Forms 1004.5.1 Data Forms 1004.5.2 Data Fields 1014.5.3 Data Form Editing 1024.5.4 Variable Data 1044.5.5 Data in Time History Files 105

4.6 Results 1064.6.1 Results 1064.6.2 Selecting Variables 1074.6.3 Summary and Full Results 1084.6.4 Statistics 1084.6.5 Linked Statistics 1084.6.6 Offset Tables 1094.6.7 Time History and XY Graphs 1094.6.8 Range Graphs 1104.6.9 Offset Graphs 111

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4.6.10 Presenting OrcaFlex Results 1124.7 Graphs 113

4.7.1 Graphs 1134.7.2 Modifying Graphs 114

4.8 Spreadsheets 1154.8.1 Spreadsheets 115

4.9 Text Windows 1154.10 Comparing Data 1164.11 Preferences 1164.12 Printing and Exporting 119

5 BATCH AND POST-PROCESSING 1205.1 Introduction 1205.2 Batch Processing 120

5.2.1 Batch Processing 1205.2.2 Script Files 1215.2.3 Script Syntax 1225.2.4 Script Commands 1225.2.5 Handling Script Errors 1245.2.6 Obtaining Variable Names 124

5.3 Fatigue Analysis 1255.3.1 Fatigue Analysis 1255.3.2 Load Cases 1265.3.3 Commands 1265.3.4 Data 1275.3.5 S-N Curve Data 1305.3.6 Results 1315.3.7 Fatigue Points 1315.3.8 How Damage is Calculated 132

5.4 Post-processing Results 1345.4.1 Post-processing Results 1345.4.2 Results Spreadsheet 1345.4.3 Instruction Format 1365.4.4 Pre-defined Commands 1375.4.5 Tips and Tricks 1385.4.6 Error Handling 1395.4.7 Stress Spreadsheet 139

6 THEORY 1416.1 Coordinate Systems 1416.2 Direction Conventions 1426.3 Object Connections 1436.4 Interpolation Methods 1446.5 Static Analysis 146

6.5.1 Static Analysis 1466.5.2 Statics of Lines 1466.5.3 Statics of Buoys and Vessels 150

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6.5.4 Multiple Statics for Vessels 1516.6 Dynamic Analysis 151

6.6.1 Dynamic Analysis 1516.6.2 Calculation Method 1526.6.3 Ramping 154

6.7 Buoyancy Variation with Depth 1546.8 Current Theory 1556.9 Waves 155

6.9.1 Wave Theory 1556.9.2 Kinematic Stretching 1566.9.3 Ochi-Hubble Spectra 1576.9.4 Non-linear Wave Theories 1586.9.5 Stokes' 5th 1586.9.6 Dean's Stream Function Theory 1596.9.7 Fenton's cnoidal theory 1606.9.8 Ranges of Applicability 1606.9.9 Breaking waves 1616.9.10 Particle velocities and accelerations 1616.9.11 Currents 1616.9.12 Seabed Slope 1626.9.13 Physically implausible solutions 162

6.10 Seabed Theory 1626.11 Line Theory 163

6.11.1 Overview 1636.11.2 Structural Model Details 1656.11.3 Calculation Stages 1666.11.4 Line End Orientation 1706.11.5 Line Local Orientation 1716.11.6 Morison's Equation 1716.11.7 Treatment of Compression 1736.11.8 Contents Flow Effects 1736.11.9 Line Pressure Effects 1756.11.10 Pipe Stress Calculation 1776.11.11 Pipe Stress Matrix 1786.11.12 Hydrodynamic Loads 1796.11.13 Drag Chains 1816.11.14 Line End Conditions 1836.11.15 Line Interaction with the Sea Surface 1836.11.16 Seabed Touchdown and Friction 1846.11.17 Interaction with Seabed and Shapes 1866.11.18 Clashing 187

6.12 Vessel Theory 1896.12.1 RAOs and Phases 1896.12.2 RAO Quality Checks 1906.12.3 Drag Loads 1926.12.4 Added Mass and Damping 1956.12.5 Wave Drift Loads 196

6.13 3D Buoy Theory 1986.14 6D Buoy Theory 199

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6.14.1 6D Buoy Theory 1996.14.2 Lumped Buoy Theory 2006.14.3 Spar Buoy and Towed Fish Theory 201

6.15 Shape Theory 2056.16 Winch Theory 207

7 SYSTEM MODELLING - DATA AND RESULTS 2107.1 Introduction 2107.2 General Data 212

7.2.1 General Data 2127.2.2 Statics 2127.2.3 Statics Convergence 2147.2.4 Dynamics 2147.2.5 Logging 2157.2.6 Target Damping 216

7.3 Environment 2167.3.1 Environment 2167.3.2 Sea Data 2177.3.3 Current Data 2207.3.4 Wind Data 2217.3.5 Wave Data 2227.3.6 Drawing Data 2267.3.7 Data for Ochi-Hubble Spectra 2277.3.8 Data for Time History Waves 2277.3.9 Wave Preview 2297.3.10 Setting up a Random Sea 2307.3.11 Results 233

7.4 Shapes 2347.4.1 Shapes 2347.4.2 Shape Data 2357.4.3 Blocks 2367.4.4 Cylinders 2377.4.5 Planes 2387.4.6 Drawing 2387.4.7 Results 239

7.5 Vessels 2397.5.1 Vessels 2397.5.2 Vessel Data 2407.5.3 Vessel Types 2487.5.4 Modelling Vessel Slow Drift 2617.5.5 Vessel Results 262

7.6 3D Buoys 2647.6.1 3D Buoys 2647.6.2 Data 2647.6.3 Results 265

7.7 6D Buoys 2667.7.1 6D Buoys 2667.7.2 Wings 2677.7.3 Common Data 268

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7.7.4 Applied Load 2707.7.5 Wing Data 2707.7.6 Wing Type Data 2717.7.7 Lumped Buoy Properties 2737.7.8 Lumped Buoy Drawing Data 2747.7.9 Spar Buoy and Towed Fish Properties 2757.7.10 Results 2777.7.11 Buoy Hydrodynamics 2797.7.12 Hydrodynamic Properties of a Rectangular Box 2807.7.13 Modelling a Surface-Piercing Buoy 283

7.8 Lines 2867.8.1 Lines 2867.8.2 Line Data 2887.8.3 Attachments 3007.8.4 Line Types 3037.8.5 Line Results 3087.8.6 Drag Chain Results 3207.8.7 Line Type Wizard 3207.8.8 Modelling Mooring Chains 3227.8.9 Modelling Lines with Floats 3277.8.10 Modelling Ropes 3327.8.11 Modelling Homogeneous Pipes 3367.8.12 Modelling Hoses and Cables 3387.8.13 Modelling Line Ends 3417.8.14 Modelling Compression in Flexibles 344

7.9 Links 3467.9.1 Links 3467.9.2 General Data 3467.9.3 Connections 3477.9.4 Properties 3477.9.5 Results 348

7.10 Winches 3487.10.1 Winches 3487.10.2 Winch Data 3507.10.3 Wire Properties 3517.10.4 Control 3517.10.5 Drive Unit 3527.10.6 Results 353

8 VIV TOOLBOX 3548.1 VIV Toolbox 354

9 TECHNICAL NOTES 3569.1 Modelling Bend Restrictors 3569.2 Modelling Design Waves 3579.3 Modelling Guide Tubes 3599.4 Modelling Mid-water Arches 3599.5 Typical Line Type Properties 361

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1 INTRODUCTION

1.1 INTRODUCTIONWelcome to OrcaFlex (version 8.2a), a marine dynamics program developed by Orcina for staticand dynamic analysis of flexible pipeline and cable systems in an offshore / marineenvironment. OrcaFlex is widely used in the offshore industry for analysis of flexible risers fromoffshore production platforms and tanker loading buoys, cable lay, installation of subseaequipment, oceanographic moorings, pull-in analysis, etc.

OrcaFlex provides fast and accurate analysis of catenary systems such as flexible risers andumbilical cables under wave and current loads and externally imposed motions. OrcaFlexmakes extensive use of graphics to assist understanding. The program can be operated inbatch mode for routine analysis work and there are also special facilities for post-processingyour results.

OrcaFlex is a fully 3D non-linear time domain finite element program capable of dealing witharbitrarily large deflections of the flexible from the initial configuration. A simple lumped masselement is used which greatly simplifies the mathematical formulation and allows quick andefficient development of the program to include additional force terms and constraints on thesystem in response to new engineering requirements.

Other applications include oceanographic systems, aquaculture and non-marine systems.OrcaFlex is fully 3D and can handle multi-line systems, floating lines, line dynamics afterrelease, etc. Inputs include ship motions, regular and random waves. Results output includesanimated replay plus full graphical and numerical presentation.

If you are new to OrcaFlex then please see the tutorial and examples.

For further details of OrcaFlex and our other software, please contact Orcina or your Orcinaagent.

Copyright notices

• Copyright Orcina Ltd. 1987-2002. All rights reserved.

• OrcaFlex contains Formula One from Visual Components. Copyright 1994-1997. All rightsreserved.

• OrcaFlex uses LAPACK for certain linear algebra calculations.

1.2 INSTALLING ORCAFLEXHardware Requirements

OrcaFlex can be installed and run on any PC compatible computer that has:

• Windows 95, 98, ME, NT 4, 2000, XP or later versions,

• At least 32 Mb of memory,

• At least 40 Mb of free disk space.

• A screen resolution of at least 800 x 600 (small fonts),

However, OrcaFlex is a very powerful package and to get the best results we wouldrecommend:

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• The fastest possible processor. This is the most important factor since OrcaFlex is acomputation-intensive program and simulation run times can be long for complex models.

• At least 128 Mb of memory. This is less important but some aspects of OrcaFlex do performbetter when more memory is available.

• As much disk space as you require to store simulation files. Simulation files vary in size, butcan be 10's of megabytes each for complex models.

• A screen resolution of 1024 x 768 (or higher) and a 16-bit colour palette.

Installation

To install OrcaFlex:

• If you are using Windows NT, 2000 or XP then first log on with Administrator privileges.

• If installing from CD, insert the OrcaFlex CD and run the Autorun.exe program on the CD(on many machines this program will run automatically when you insert the CD). Thenselect 'Install'.

• If you have received OrcaFlex by e-mail or from the web you should have the OrcaFlexinstallation program Setup.exe. You will also need licence files (*.lic) for each dongle thatyou want to use (if you have not received them you might be able to use the licence file(s)from your previous OrcaFlex CD). Place the licence files and the file Setup.exe together ina directory on your machine and then run the Setup.exe program.

• You will also need to install the OrcaFlex dongle supplied by Orcina when you purchased orleased OrcaFlex. See below for details.

For further details, including information on network and silent installation, see the ReadMe fileon the OrcaFlex CD. If you have any difficulty installing OrcaFlex please contact Orcina or yourOrcina agent.

Orcina Shell Extension

When you install OrcaFlex you are asked whether you also want to install the Orcina ShellExtension. Installing this tells Windows about the OrcaFlex data and simulation file types (.datand .sim) and associates them with OrcaFlex. You can then start OrcaFlex and open anOrcaFlex file by simply double-clicking the file. The shell extension also provides file propertiesinformation in Explorer, such as which version of OrcaFlex wrote the file and the Comments textfor the model in the file. For details see the file CD:\OrcShlEx\ReadMe.htm on the OrcaFlexCD.

Installing the Dongle

OrcaFlex is supplied with a dongle, a small hardware device that must be attached to themachine, or else to the network to which the machine is attached.

Note: The dongle is effectively your licence to run one copy (or more, if the dongle isenabled for more copies) of OrcaFlex. It is, in essence, what you havepurchased or leased, and it should be treated with appropriate care andsecurity. If you lose your dongle you cannot run OrcaFlex.

Warning: Orcina can normally resupply disks or manuals (a charge being made to covercosts) if they are lost or damaged. But we can only supply a new dongle inthe case where the dongle has failed and the old dongle is first returned to us.

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Dongles labelled 'Hxxx' (where xxx is the dongle number) must be plugged into the machine onwhich OrcaFlex is run. Dongles labelled 'Nxxx' can be used in the same way as ‘Hxxx’ dongles,but they can also be used over a computer network, allowing several used to share theprogram. In the latter case the dongle should be installed by your network administrator;instructions can be found in the Dongle directory of the OrcaFlex CD.

Types of Dongle

Dongle are available for two types of connector - for connection to the parallel port or to a USBport. The two types have exactly the same facilities (the difference is simply whether they areconnected to a parallel port or a USB port) but there are pros and cons of the two types:

• The new USB port dongles may not suit if you are using older machines or operatingsystems. This is because some older machines may not have a USB port. Also, WindowsNT4 and early versions of Windows 95 (prior to OSR 2.1) do not support USB deviceswithout modification. Windows 98, ME and 2000, XP all support USB devices (as will futureversions of Windows).

• On the other hand USB ports are a more modern and better technology and are taking overfrom the old parallel port. All recent machines we have seen have USB ports and indeedsome portable/laptop computers now have a USB port and no parallel port.

• USB ports are designed to be capable of having multiple devices attached to one port, soyou can plug in the USB dongle and other devices (printers, plotters, etc.) and they won'tinterfere with each other. The parallel port, on the other hand, wasn't originally designedwith multiple devices in mind, so dongle suppliers had to use non-standard interfacingmethods to try to make the dongle transparent to other devices. This is not alwayssuccessful and we have seen a few cases where a printer could not be used on the sameparallel port as the dongle. This problem will not arise with USB dongles.

Parallel Port Dongles

By default we send parallel port dongles, which have 25-pin connectors. The computer side ofthe dongle has a 25-pin male connector which plugs into the standard PC parallel port, whichhas a female connector. Please take care not to insert the dongle into a serial port, which issometimes a 25-pin male connector on the back of the computer; no harm should occur, but theprogram will not be able to run. If the parallel port is also needed for another device such as aprinter, then the dongle should be plugged into the computer and the printer then plugged intothe back of the dongle. The dongle is transparent and should not interfere with signals passingthrough it to other devices.

If you have any difficulties fitting the dongle, please double check that it is fitted to the right portand that it is the correct way round.

Dongle Troubleshooting

We supply, with OrcaFlex, a dongle utility and troubleshooting program called OrcaDong.exe. IfOrcaFlex cannot find the dongle then you can use this program to check various things andhopefully find the cause of the problem. For details see the file OrcaDong.hlp. The OrcaDongprogram and its help file can be found in the OrcaFlex installation directory. They are also inthe Dongle directory on the OrcaFlex CD, together with other less commonly needed donglefiles. If you need further help then please contact Orcina.

1.3 RUNNING ORCAFLEXA shortcut to run OrcaFlex is set up on the Start menu when you install OrcaFlex (seeStart\Programs\Orcina Software\OrcaFlex).

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This shortcut passes no parameters to OrcaFlex so it gives the default start-up behaviour; seebelow. If this is not suitable you can configure the start-up behaviour using command-lineparameters, for example by setting up your own shortcuts with particular parameter settings.

Default Start-up

OrcaFlex has two basic modules: full OrcaFlex and statics-only OrcaFlex. A full OrcaFlexlicence is needed for dynamic analysis. There is also an additional VIV Toolbox, which isoptional and which requires a VIV licence.

When you run OrcaFlex it looks for an Orcina dongle from which it can claim an OrcaFlexlicence (either a full licence or a statics-only licence). By default, it first looks for a licence on alocal dongle (i.e. one in local mode and connected to the local machine) and then if none isfound then it looks for a licence on a network dongle (i.e. one in network mode and accessedvia a licence manager over the network). This default behaviour can be changed by command-line parameters.

If OrcaFlex finds a network dongle and there is a choice of which licences to claim from it, thenOrcaFlex displays a Choose Modules dialog to ask you which modules you want to claim. Thishelps you share the licences with other users of that network dongle. For example if thenetwork dongle contains both a full licence and a statics-only licence then you can choose touse the statics-only licence, if that is all you need, so that the full licence is left free for others touse when you do not need it yourself. The Choose Modules dialog can be suppressed usingcommand-line parameters.

Command Line Parameters

OrcaFlex can accept various parameters on the command line to modify the way it starts up.The syntax is:

OrcaFlex.exe Filename Option1 Option2 ... etc.

Filename is optional. If present it should be the name of an OrcaFlex data file (.dat) orsimulation file (.sim) and after starting up OrcaFlex will automatically open that file.

Option1, Option2 etc. are optional parameters that allow you configure the start-up behaviour.They can be any of the following switches. For the first character of an option switch, thehyphen character '-' can be used as an alternative to the '/' character.

Dongle Search Switches

By default the program searches first for a licence on a local dongle and then for a licence on anetwork dongle. The following switches allow you to modify this default behaviour.

• /LocalDongle Only search for licences on a local dongle. No search will be made fornetwork dongles.

• /NetworkDongle Only search for licences on a network dongle. Any local dongle will beignored. This can be useful if you have a local dongle but want to use a network dongle thathas licences for more modules.

Module Choice Switches

These switches are only relevant if you the dongle found is a network dongle and there is achoice of licences to claim from that dongle. You can specify some or all of your choices usingthe following command line switches.

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• /DisableDynamics Choose the statics-only basic licence. This is sometimes useful whenusing a network dongle since it allows you to leave full licences free for other users whenyou only need a statics-only licence.

• /Disable<Module> Choose not to claim a licence for the additional module with name<Module>. For example /DisableVIV tells the program to choose not to claim a VIV Toolboxlicence, which may be useful if you are sharing a VIV licence on a network dongle.

If you do not specify all the choices then the program displays the Choose Modules dialog toask for your remaining choices. You can suppress this dialog using the following switch.

• /DisableInteractiveStartup Do not display the Choose Modules dialog. The programbehaves the same as if the user clicks OK on that dialog without changing any modulechoices.

1.4 DEMONSTRATION VERSIONFor an overview of OrcaFlex, see the Introduction topic and the tutorial.

The demonstration version of OrcaFlex has some facilities disabled - you cannot calculatestatics or run simulation, and you cannot save files, print, export or copy to the clipboard. Butotherwise the demonstration version is just like the full version, so it allows you to see howexactly the program works.

In particular the demonstration version allows you open any prepared OrcaFlex data orsimulation file. And if you open a simulation file then you can then examine the results, seereplays of the motion etc. There are numerous example files provided on the demonstrationCD.

If you have the full version of OrcaFlex then you can use the demonstration version to showyour customers your OrcaFlex models and results for their system. To do this, give them thedemonstration version and copies of your OrcaFlex simulation files. The demonstration versioncan be found on your OrcaFlex CD - see CD:\Demo_CD\ReadMe.

1.5 FREQUENTLY ASKED QUESTIONSWhat do I do if OrcaFlex cannot find my dongle?

See the Dongle directory on your OrcaFlex CD. In that directory you will find a special dongleutility program called OrcaDongle that allows you to check your dongle. See the OrcaDonglehelp file for details. If you still have difficulty, then please contact Orcina.

Can I share my OrcaFlex licence(s) with other users over a network?

Yes. Your dongle can be installed on one machine on the network and be put into "networkmode" and run under a special licence manager program on that machine. You can then installand use OrcaFlex on that or any other machine on the network. You will then be able to useOrcaFlex on any machine on which it has been installed, but within the limit that no more than Ncopies can be run simultaneously, where N is the number of licences you have in the dongle.For details see the OrcaDongle help file on your OrcaFlex CD (CD:\Dongle\OrcaDong.hlp).

Is there any QA documentation for OrcaFlex?

Yes. For more details refer to Validation and QA.

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Can OrcaFlex automate repetitive tasks like setting up multiple load cases and producingreports?

Yes. OrcaFlex has advanced automation features. Multiple load cases based on a single basecase can be specified using batch script files. In addition OrcaFlex is supplied with post-processing spreadsheets written in Excel. The spreadsheets allow you to automate the transferof results from OrcaFlex simulations to your report. The great benefit of this automation is whenyou need to re-run simulation files with changed data. Once the script files and thespreadsheets have been setup this process is reduced to just changing the data in the base file.

Does OrcaFlex have facilities for Fatigue Analysis of homogeneous pipes?

A Fatigue Analysis for homogeneous pipes module is built into OrcaFlex. For details seeFatigue Analysis.

What are the values plotted at the ends of range graphs for Effective Tension, BendMoment and Curvature?

These values are End Tension, End Bend Moment and End Curvature respectively. For moredetails see Range Graphs.

Does "mass" in OrcaFlex means mass in air or mass in water?

The mass of an object is the object's inherent resistance to acceleration, so it does not dependon whether an object is in air or water. (The extra hydrodynamic resistance to accelerationwhen in water is a separate property called added mass.) Mass is numerically the same asweight in air (providing the same units are used).

How do I make statics converge for my Lines?

If there are a lot of lines in the model then you can make investigation of the problem easier bydragging the line up to the top of the list in the model browser. OrcaFlex will then analyse thatline first.

The default statics settings are statics method "Catenary" with Full Statics set to "Yes". Thecatenary statics method sometimes struggles with complicated cases, such as when there arebuoyant sections or tethers connection to the Line. If the Line statics is not converging withthese default settings try setting statics method to "Quick" and Full Statics to "Yes". If you stillhave problems please refer to Which Line Statics method to use.

How do I include an OrcaFlex replay in my presentations?

When the replay is running right click on the 3D View windows and select Export Video. Thiswill save the replay as a video in AVI format which can then be included in your presentation.See also Presenting OrcaFlex Results.

Can OrcaFlex model Guide Tubes?

Yes. There are two standard methods of modelling a pipe or line sliding through a guide. Thefirst is to use two Links to eliminate motion in the X and Y directions. Alternatively a SolidCylinder can be used to model the guide. For more details see Modelling Guide Tubes.

1.6 VALIDATION AND QAOrcina software is developed under a formal QA system that includes rigorous testing to confirmcorrect operation. Testing takes place at a series of levels: desk checks (for example against

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hand calculations for specific cases); comparisons with analytical solutions where these exist;comparisons with other, independently developed, software packages; and finally comparisonswith data from model tests and measurements on real systems.

Desk checks are too many and too detailed to deal with here but are of the greatest importancein ensuring a satisfactory product. Suffice to say that we keep full and detailed records of suchtests, and that all new features of Orcina programs are extensively tested in this way beforerelease.

In addition each new version of an Orcina program is checked in detail against its immediatepredecessor.

OrcaFlex has been validated against published analytical and numerical results such as thosegiven by Roark (1965) and Timoshenko (1955). Various towed fish cases have been checkedagainst results given by Pode (1951) with good agreement being achieved. OrcaFlex results forthe case of a fish being towed by a vessel following a circular path, have been confirmed bycomparison with theoretical results (Chapman, 1984).

Comparisons have been made with other flexible riser programs by Orcina and by independentusers. Comparisons known to us include the following:

Comparison carried out by Software used for comparisonOrcina/Seaflex FENRISBP RiflexDunlop FlexriserBrasnor Fenris, Flexriser and othersNOS/Orcina Flexcom 3DWellstream/Orcina Flexcom 3D, FlexriserClose agreement has been obtained in all cases.

Orcina took part in a major comparison of flexible riser programs initiated by the ISSC (Larsen,1991). The published results show good agreement between OrcaFlex and the otherestablished programs.

A related Orcina program, OrcaRiser, has been derived from OrcaFlex and accurately checkedagainst it. It has then been compared with the published results of the API tensioned riserprogram inter-comparison (API Bulletin 2J). The API report shows results from a number oftensioned riser programs: OrcaRiser results fall in the middle of the scatter band of results fromthe other programs.

As regards comparisons with model and full scale systems, a major validation exercise wascarried out to compare OrcaFlex with model test results obtained from a joint industry project(Hartnup et al, 1987). Good agreement was obtained.

A large-scale test has been carried out in Lake Pend Oreille (1998) under a joint industry projectmanaged by PMB. Preliminary results show satisfactory correlation with OrcaFlex.

OrcaFlex predictions for a towed fish case have been successfully compared with full scalemeasurements from sea trials.

1.7 ORCINAOrcina is a creative engineering software and consultancy company staffed by mechanicalengineers, naval architects, mathematicians and software engineers with long experience insuch demanding environments as the offshore, marine and nuclear industries. As well asdeveloping engineering software, we offer a wide range of analysis and design services withparticular strength in dynamics, hydrodynamics, fluid mechanics and mathematical modelling.

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Contact Details

Orcina Ltd.DaltongateUlverstonCumbriaLA12 7AJUK

Telephone: +44 (0) 1229 584742Fax: +44 (0) 1229 587191E-mail: software@orcina.comWeb Site: www.orcina.com

Orcina Agents

North America

MMI Engineering, Inc.11490 Westheimer RoadSuite 150HoustonTexas 77077USA

Telephone: +1 (281) 920 4600Fax: +1 (281) 920 4602Email: orcina@mmiengineering.com or pjacob@mmiengineering.com

Stewart Technology Associates5619 Val VerdeHoustonTexas 77057USA

Telephone: +1 (713) 789-8341Fax: +1 (713) 789-0314E-mail: info@stewart-usa.com

Scandinavia

borgen•eckey INGENIØRVERKSTEDET ASSkur 35AkershusstrandaN-0150 OsloNorway

Telephone: +47 22 33 11 31Fax: +47 22 33 11 32Email: jeb@inocean.no

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Malaysia, Indonesia and Singapore

Zencomp Consultants Sdn Bhd882, Block A1, Pusat Dagang SetiajayaNo. 9, Jalan PJS 8/946150 Petaling JayaSelangor Darul EhsanMalaysia

Telephone: +60 3-7877 8001/7877 9001Fax: +60 3-7877 2008E-mail: zencom@tm.net.my

South America

Suporte Consultoria e Projetos LtdaRua Visconde de Inhauma 134, Suite 505-512CEP: 20091-000Rio de JaneiroBrazil

Telephone: +55 21 2253 4126Fax: +55 21 2253 1023Email: suporte@suporte-cp.com.br

1.8 TERMS AND CONDITIONS1. Definitions

In these conditions the following words shall have the following meanings:

a) "The Company" shall mean "Orcina Ltd".

b) "The Software" shall mean the computer software supplied under this Agreement.

c) "The Proposal" shall mean the written proposal for the supply of computer software.

d) "Agents" shall mean the Company's appointed representatives.

e) "The Client" shall mean the purchaser and its Affiliates.

f) The term "Affiliate", when used with respect to one of the parties hereto, shall mean any ofthe following:

(i) the Parent Company thereof.(ii) any company directly or indirectly controlled by, controlling, or under common controlwith that party. For the purpose of this definition, "control" shall mean owning 50% ormore of the stock, equity or property of such company.

2. General

a) The conditions set out below together with the Proposal and any Special Conditionsreferred to therein shall constitute the terms of the Contract. These conditions may not bevaried or added to without the agreement in writing of both parties.

b) The Contract shall be subject to the non-exclusive jurisdiction of the English courts and shallbe interpreted according to English law.

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3. Validity

The Proposal is valid for a period of sixty days from date of issue unless otherwise stated in theProposal or extended by the Company in writing.

4. Multisite Use

Under these conditions the Client shall be free to use the Software at any location and to moveany copy or copies of the Software from one location to another at his discretion.

5. Charges and Terms of Payment

a) Charges shall be as set out in the Proposal. Maintenance charges are subject to reviewannually.

b) Initial lease charges and charges for Software purchase shall be payable in advance unlessotherwise agreed in writing.

c) Invoices for software maintenance and for lease extensions will be submitted in advanceand are due immediately.

6. Duration and Termination of Lease

a) Unless otherwise stated in the Proposal, the minimum period of lease shall be one monthand the lease period shall be extended automatically one month at a time thereafter until theCompany receives notice of termination.

b) The lease may be terminated by either party at 7 days written notice. All invoicesoutstanding at the date of termination shall be payable immediately. On termination, theClient will return to the Company all computer disks, manuals and hardware security devicessupplied for the purposes of the lease and will delete all copies of the Software from hiscomputer systems.

7. Intellectual Property Rights and Terms of Use of Computer Software

All intellectual property rights (including copyright) in the Software and documentation willremain in the ownership of the Company and one or more non-exclusive licences will begranted to the Client to use the Software upon the following terms:

a) Each licence entitles the Client to use the Software on one machine at any one time. TheClient must not use the Software simultaneously on more machines or terminals than heholds licences for.

b) If the Client is in breach of these terms, immediately upon request by the Company he shalldelete all copies of the Software from all computer systems under his control and return tothe Company all copies of documentation and any security devices provided for use with theSoftware.

c) The Company shall indemnify the Client against any claim that the Software infringes theIntellectual Property Rights of any third party provided that the Company is given immediateand complete control of any such claim and the Client does not prejudice Company'sdefence and that the Client gives the Company all reasonable assistance in relation to anysuch claim.

The Company warrants that it has the right to grant this licence

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8. Warranty and Liability

a) The Company warrants that the Software will comply with the specifications as set out in thedocumentation supplied to the Client and will be free from defects in materials andworkmanship under normal use for a period of 90 days from the date of delivery to theClient. If within such period the Software fails to perform correctly, the Company will at itsdiscretion rectify any defects free of charge or refund the original price on return of theSoftware. In no event shall the Company or its Agents be liable for loss of profits, loss of ordamage to data, indirect, special, incidental or consequential damages or losses arising outof the use or inability to use the Software. The total joint liability of the Company and itsAgents for direct loss caused by breach of this Agreement or its proven negligence shall berestricted to the price paid for the Software.

b) The express terms of this contract are in lieu of all warranties, conditions, terms,undertakings and obligations implied by statute, common law, custom, trade usage orotherwise, all of which are hereby excluded to the fullest extent permitted by law save to theextent that the Company shall be liable for any death or personal injury arising as a result ofthis agreement and which results from its proven negligence.

9. Maintenance, Upgrades and Technical Support

a) It is the Company's policy continually to develop its software products in response to marketrequirements. When new versions are released, program upgrades will be supplied free ofcharge to those customers having a current maintenance contract.

b) For all software packages covered by a current maintenance contract or lease agreementthe Company provides full technical support by telephone, fax or e-mail without furthercharge. Limited support may be available for earlier versions of the Software at theCompany's discretion but this cannot be guaranteed.

c) An annual MUS fee will be chargeable based on the total number of copies of the Softwarefor which the Client holds licences at the renewal date. The fees for second andsubsequent copies will be discounted relative to the single copy fee at the same rates asshown in Clause 2 above.

d) MUS will be provided for all copies of the Software in the Client's possession, or for none atall at the Client's discretion. If the Client chooses not to continue MUS, then the Companyreserves the right to charge an additional fee should the Client wish to reinstate MUS at alater date.

10. Administration

The Client will nominate a single point of contact for administrative and invoicing purposes.

11. Transfer of Ownership

The Client shall be free to transfer ownership of any copy or copies of the software betweenAffiliates of the Client, but ownership shall not be transferred to another party without the writtenagreement of the Company. Where transfer of ownership to another party is agreed, theCompany may charge a fee.

Specifically, and for the avoidance of doubt, on termination of a joint venture or disposal of ashareholding in a company jointly owned with others, any copy or copies of the Softwaresupplied under this Agreement shall revert to the Client or one of its Affiliates unless theCompany has given its agreement in writing to the transfer of ownership to another party.

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12. Confidentiality

The Client undertakes to treat as confidential and keep secret all information contained in theSoftware and documentation. The Client shall not without the prior written consent of theCompany divulge any part of such information to any person except its employees, agents andconsultants. The Client shall notify the Company should it become aware of any breach of suchconfidence by any person to whom the Client divulges all or any part of such information.

13. Arbitration

Any dispute or difference arising out of the contract shall be referred to the arbitration of aperson to be mutually agreed upon or failing agreement to some person nominated by thePresident of the Institution of Mechanical Engineers.

1.9 REFERENCES AND LINKSReferences

API, 1993. API Recommended Practice 2A-WSD (RP 2A-WSD). American PetroleumInstitute.

API. Comparison of Analyses of Marine Drilling Risers. API Bulletin. 2J.

Barltrop N D P, and Adams A J, 1991. Dynamics of fixed marine structures. ButterworthHeinemann for MTD. 3rd Edition.

Batchelor G K, 1967. An introduction to fluid dynamics. Cambridge University Press.

Carter D J T, 1982. Prediction of Waveheight and Period for a Constant Wind Velocity Usingthe JONSWAP Results, Ocean Engineering, 9, no. 1, 17-33.

Casarella M J and Parsons M, 1970. Cable Systems Under Hydrodynamic Loading. MarineTechnology Society Journal 4, No. 4, 27-44.

Chapman D A, 1984. Towed Cable Behaviour During Ship Turning Manoeuvres. OceanEngineering. 11, No. 4.

CMPT, 1998. Floating structures: A guide for design and analysis. Edited by Barltrop N D P.Centre for Marine and Petroleum Technology publication 101/98, Oilfield Publications Limited.

Dean R G, 1965. Stream function representation of non-linear ocean waves. J. Geophys. Res.70, 4561-4572.

DNV, 1991. Environmental Conditions and Environmental Loads Classification Notes 30.5.March.

ESDU, 1971. Fluid forces, pressures and moments on rectangular blocks. ESDU 71016ESDU International, London.

Falco M, Fossati F and Resta F, 1999. On the vortex induced vibration of submarine cables:Design optimization of wrapped cables for controlling vibrations. 3rd International Symposiumon Cable Dynamics, Trondheim, Norway.

Faltinsen O M, 1990. Sea loads on ships and offshore structures. Cambridge UniversityPress.

Fenton J D, 1979. A high-order cnoidal wave theory. J. Fluid Mech. 94, 129-161.

Fenton J D, 1985. A fifth-order Stokes theory for steady waves. J. Waterway, Port, Coastal &Ocean Eng. ASCE. 111, 216-234.

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Fenton J D, 1990. Non-linear wave theories. Chapter in "The Sea - Volume 9: OceanEngineering Science", edited by B. Le MeHaute and D. M. Hanes. Wiley: New York. 3-25.

Fenton J D, 1995. Personal communication - preprint of chapter in forthcoming book oncnoidal wave theory.

Gregory R W and Paidoussis M P, 1996. Unstable oscillation of tubular cantilevers conveyingfluid: Part 1:Theory. Proc. R. Soc. 293 Series A, 512-527

Hartnup G C, Airey R G and Fraser J M, 1987. Model Basin Testing of Flexible Marine Risers.OMAE Houston.

Hoerner S F 1965. Fluid Dynamic Drag, Published by the author at Hoerner Fluid Dynamics,NJ 08723, USA.

Isherwood R M, 1987. Applied Ocean Research, Vol 9, No. 1 (January), pp 47-50.

Iwan W D, 1981. The vortex-induced oscillation of non-uniform structural systems. Journal ofSound and Vibration, 79, pp 291-301.

Iwan W D and Blevins R D, 1974. A Model for Vortex Induced Oscillation of Structures. Journalof Applied Mechanics, September 1974, pp 581-586.

Larsen C M, 1991. Flexible Riser Analysis - Comparison of Results from Computer Programs.Marine Structures, Elsevier Applied Science.

Maddox S J, 1998. Fatigue strength of welded structures. Woodhead Publishing Ltd, ISBN 185573 013 8.

Morison J R, O’Brien M D, Johnson J W, and Schaaf S A, 1950. The force exerted by surfacewaves on piles. Petrol Trans AIME. 189.

Mueller H F, 1968. Hydrodynamic forces and moments of streamlined bodies of revolution atlarge incidence. Schiffstechnik. 15, 99-104.

Newman J N. 1974. Second-order, slowly-varying forces on vessels in irregular waves. ProcInt Symp Dynamics of Marine Vehicles and Structures in Waves, Ed. Bishop RED and PriceWG, Mech Eng Publications Ltd, London.

Newman J N, 1977. Marine Hydrodynamics, MIT Press

NDP, 1995. Regulations relating to loadbearing structures in the petroleum activities.Norwegian Petroleum Directorate.

Ochi M K and Hubble E N, 1976. Six-parameter wave spectra; Proc 15th Coastal EngineeringConference, 301-328.

Oil Companies International Marine Forum, 1994. Prediction of Wind and Current Loads onVLCCs, 2nd edition, Witherby & Co., London.

Paidoussis M P, 1970. Dynamics of tubular cantilevers conveying fluid. J. MechanicalEngineering Science, 12, No 2, 85-103.

Paidoussis M P and Deksnis E B, 1970. Articulated models of cantilevers conveying fluid : Thestudy of a paradox'. J. Mechanical Engineering Science, 12, No 4, 288-300.

Paidoussis M P and Lathier B E, 1976. Dynamics of Timoshenko beams conveying fluid. J.Mechanical Engineering Science, 18, No 4, 210-220.

Pode L, 1951. Tables for Computing the Equilibrium Configuration of a Flexible Cable in aUniform Stream. DTMB Report. 687

Principles of Naval Architecture. Revised edition, edited by J P Comstock, 1967. Society ofNaval Architects and Marine Engineers, New York.

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Puech A, 1984. The Use of Anchors in Offshore Petroleum Operations. Editions Technique

Rawson and Tupper, 1984. Basic Ship Theory 3rd ed, 2: Ship Dynamics and Design, 482.Longman Scientific & Technical (Harlow).

Rienecker M M and Fenton J D, 1981. A Fourier approximation method for steady waterwaves. J. Fluid Mech. 104, 119-137.

Roark R J, 1965. Formulas for Stress and Strain. 4th edition McGraw-Hill.

Sarpkaya T, Shoaff R L, 1979. Inviscid Model of Two-Dimensional Vortex Shedding by aCircular Cylinder. Article No. 79-0281R, AIAA Journal, 17, no. 11, 1193-1200.

Sarpkaya T, Shoaff R L, 1979. A discrete-vortex analysis of flow about stationary andtransversely oscillating circular cylinders. Report no. NPS-69SL79011, Naval PostgraduateSchool, Monterey, California.

Rychlik I, 1987. A new definition of the rainflow cycle counting method. Int. J. Fatigue, 9, No2, 119-121.

Skjelbreia L and Hendrickson J, 1961. Fifth order gravity wave theory. Proc. 7th Conf. CoastalEng. 184-196.

Sobey R J, Goodwin P, Thieke R J and Westberg R J, 1987. Wave theories. J. Waterway,Port, Coastal & Ocean Eng. ASCE 113, 565-587.

Sparks C, 1980. Le comportement mecanique des risers influence des principaux parametres.Revue de l'Institut Francais du Petrol, 35, no. 5, 811.

Sparks C, 1983. Comportement mecanique des tuyaux influence de la traction, de la pressionet du poids lineique : Application aux risers. Revue de l'Institut Francais du Petrol, 38, no. 4,481.

Taylor R and Valent P, 1984. Design Guide for Drag Embedment Anchors, Naval CivilEngineering Laboratory (USA), TN No N-1688.

Thwaites, 1960. Incompressible Aerodynamics, Oxford, 399-401.

Timoshenko S,1955. Vibration Problems in Engineering, van Nostrand.

Triantafyllou M S, Yue D K P and Tein D Y S, 1994. Damping of moored floating structures.OTC 7489, Houston, 215-224.

Tucker et al, 1984. Applied Ocean Research, 6, No 2.

Tucker M J, 1991. Waves in Ocean Engineering. Ellis Horwood Ltd. (Chichester).

Wichers J E W, 1979. Slowly oscillating mooring forces in single point mooring systems.BOSS79 (Second International Conference on Behaviour of Offshore Structures).

Wichers J E W, 1988. A Simulation Model for a Single Point Moored Tanker. Delft UniversityThesis.

Young A D, 1989. Boundary Layers. BSP Professional Books, 87-91.

Links

Atlantia Offshore Limited1177 West Loop South, Suite 1200Houston, TX 77027, USAAttention: Dr. S. LeveretteEmail: stevel@atlantia.comTel: 713 850 8885Fax: 713 850 1178

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David Tein Consulting Engineers, Ltd.11777 Katy Freeway, Suite 434 SouthHouston, TX 77079Phone: (281) 531-0888Fax: (281) 531-5888Email: dtcel@dtcel.com

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2 TUTORIAL

2.1 GETTING STARTEDThis short tutorial gives you a very quick run through the model building and resultspresentation features of OrcaFlex. On completion of the tutorial we suggest that you also lookthrough the pre-run examples - see Example Files.

On starting up OrcaFlex, you are presented with a 3D view showing just a blue line representingthe sea surface and a brown line representing the seabed. At the top of the screen are menus,a tool bar and a status bar arranged in the manner common to most Windows software. Asusual in Windows software, nearly all actions can be done in several ways: here, to avoidconfusion, we will usually only refer to one way of doing the action we want, generally using themouse.

2.2 BUILDING A SIMPLE SYSTEMTo start with, we will build a simple system consisting of one line and one vessel only.

Using the mouse, click on the new vessel button on the toolbar. The cursor changes fromthe usual pointer to a crosshair cursor to show that you have now selected a new object andOrcaFlex is waiting for you to decide where to place it. Place the cursor anywhere on thescreen and click the mouse button. A "ship" shape appears on screen, positioned at the seasurface, and the cursor reverts to the pointer shape. To select the vessel, move the cursorclose to the vessel and click the mouse button - the message box (near the top of the 3D view)will confirm when the vessel has been selected. Now press and hold down the mouse buttonand move the mouse around. The vessel follows the mouse horizontally, but remains at the seasurface. (To alter vessel vertical position, or other details, select the vessel with the mouse,then double click to open the Vessel data window.)

2.3 ADDING A LINE

Now add a line. Using the mouse, click on the new line button . The crosshair cursorreappears - move the mouse to a point just to the right of the vessel and click. The line appearsas a catenary loop at the mouse position. Move the mouse to a point close to the left hand endof the line, press and hold down the mouse button and move the mouse around. The end of theline moves around following the mouse, and the line is redrawn at each position. Release themouse button, move to the right hand end, click and drag. This time the right hand end of theline is dragged around. In this way, you can put the ends of the lines roughly where you wantthem. (Final positioning to exact locations has to be done by typing in the appropriate numbers- select the line with the mouse and double click to bring up the line data form.)

Move the line ends until the left hand end of the line is close to the bow of the ship, the righthand end lies above the water and the line hangs down into the water.

At this point, the line has a default set of properties and both ends are at fixed positions relativeto the Global origin. For the moment we will leave the line properties (length, mass, etc.) attheir default values, but we will connect the left hand end to the ship. Do this as follows:

1. Click on the line near the left hand end, to select that end of the line; make sure you haveselected the line, not the vessel or the sea. The message box at the left hand end of thestatus bar tells you what is currently selected. If you have selected the wrong thing, tryagain. (Note that you don't have to click at the end of the line in order to select it - anywhere

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in the left hand half of the line will select the left hand end. As a rule, it is better to choose apoint well away from any other object when selecting something with the mouse.)

2. Release the mouse and move it to the vessel, hold down the CTRL key and click. Themessage box will confirm the connection and, to indicate the connection, the triangle at theend of the line will now be the same colour as the vessel.

Now select the vessel again and drag it around with the mouse. The left hand end of the linenow moves with the vessel. Leave the vessel positioned roughly as before with the line in aslack catenary.

2.4 ADJUSTING THE VIEWThe default view of the system is an elevation of the global X-Z plane - you are lookinghorizontally along the positive Y axis. The view direction (the direction you are looking) isshown in the Window Title bar in azimuth/elevation form (azimuth=270; elevation=0). You canmove your view point up, down, right or left, and you can zoom in or out, using the view control

buttons near the top left corner of the window. Click on each of the top 3buttons in turn: then click again with the SHIFT key held down. The SHIFT key reverses theaction of the button. If you want to move the view centre without rotating, use the scroll bars atthe bottom and right edges of the window. By judicious use of the buttons and scroll bars youshould be able to find any view you like.

Alternatively, you can alter the view with the mouse. Hold down the ALT key and left mousebutton and drag. A rectangle on screen shows the area which will be zoomed to fill the windowwhen the mouse button is released. SHIFT+ALT+left mouse button zooms out - the existing viewshrinks to fit in the rectangle.

Warning: OrcaFlex will allow you to look up at the model from underneath, effectivelyfrom under the seabed! Because the view is isometric and all lines are visible,it is not always apparent that this has occurred. When this has happened, theelevation angle is shown as negative in the title bar.

There are three "hot keys" which are particularly useful for controlling the view. For exampleCTRL+P gives a plan view from above; CTRL+E gives an elevation; CTRL+Q rotates the viewthrough 90° about the vertical axis. (CTRL+P and CTRL+E leave the view azimuth unchanged.)

Now click the button on the 3D View to bring up the Edit View Parameters form. Thisgives a more precise way of controlling the view and is particularly useful if you want to arrangeexactly the same view of 2 different models - say 2 alternative configurations for a particularriser system. Edit the view parameters if you wish by positioning the cursor in the appropriatebox and editing as required.

If you should accidentally lose the model completely from view (perhaps by zooming in tooclose, or moving the view centre too far) there are a number of ways of retrieving it:

• Press CTRL+T or right click in the view window and select Reset to Default View.

• Press the Reset button on the Edit View Parameters form. This also resets back to thedefault view.

• Zoom out repeatedly until the model reappears.

• Close the 3D View and add a new one (use the Window|Add 3D View menu item). Thenew window will have the default view centre and view size.

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2.5 STATIC ANALYSISNote: If you are running the demonstration version of OrcaFlex then this facility is

not available.

To run a static analysis of the system, click on the Static Analysis button . The messagebox reports which line is being analysed and how many iterations have occurred. When theanalysis is finished (almost instantly for this simple system) the Program State message in thecentre of the Status Bar changes to read "Statics Complete", and the Static Analysis buttonchanges to light grey to indicate that this command is no longer available. The appearance ofthe line will have changed a little. When editing the model, OrcaFlex uses a quickapproximation to a catenary shape for general guidance only, and this shape is replaced withthe true catenary shape when static analysis has been carried out. (See Static Analysis formore details).

We can now examine the results of the static analysis by clicking on the Results button .This opens a Results Selection window.

You are offered the following choices:

• Results in numerical and graphical form, with various further choices which determine whatthe table or graph will contain.

• Results for all objects or one selected object.

Ignore the graph options for the moment, select Summary Results and All Objects, then clickTable. The Results window then shows a summary of the static analysis results.

Use the scroll bar at the right hand side to view all the information in the summary table. Toview more static analysis results repeat this process: click on the Results button and select asbefore.

2.6 DYNAMIC ANALYSISWe are now ready to run the simulation. If you are running the demonstration version ofOrcaFlex then you cannot do this, but instead you can load up the results of a pre-runsimulation - see Examples.

Click the Run Simulation button . As the simulation progresses, the status bar reportscurrent simulation time and expected (real) time to finish the analysis, and the 3D view showsthe motions of the system as the wave passes through.

After the simulation has been run (or loaded), the Object icons are replaced by four Replay

Control buttons . Click the Start Replay button . An animated replay of the simulation isshown in the 3D view window. Use the view control keys and mouse as before to change theview.

The replay consists of a series of "frames" at equal intervals of time. Just as you can "zoom" inand out in space for a closer view, so OrcaFlex lets you "zoom" in and out in time. Click on the

Replay Parameters button , edit Interval to 0.2s and click OK. The animated replay is nowslower (because more frames are being shown) but the motion is much smoother than before.Now click again on Replay Parameters, set Replay Period to Whole Simulation and click on theContinuous box to deselect. The replay period shown is the whole of the simulation period.You will now see the simulation start from still water, the wave building and with it the motions of

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the system. Simulation time is shown in the Status bar, top left. Negative time means the waveis still building up from still water to full amplitude. At the end of the simulation the replaypauses, then begins again.

Now click on the Replay Step button to pause the replay. Clicking repeatedly on thisbutton steps through the replay one frame at a time - a very useful facility for examining aparticular part of the motion in detail. Click with the SHIFT key held down to step backwards.

To exit from "single frame" mode click on the Stop Replay button . You can then restartthe animation by clicking on 'Start Replay' as before. To slow down or speed up the replay,click on 'Replay Parameters' and adjust the speed.

2.7 MULTIPLE VIEWS

You can add another view of the system if you wish by clicking on the View button . Clickagain to add a third view, etc. Each view can be manipulated independently to give, say,simultaneous plan and elevation views. To make all views replay together, click on ReplayControl and check the All Views box. To remove an unwanted view simply close its viewwindow. To rearrange the screen and make best use of the space, click Window and chooseTile Horizontal, Tile Vertical (F4) or Cascade (SHIFT+F4). Alternatively, you can minimisewindows so that they appear as small icons on the background, or you can re-size them ormove them around manually with the mouse. These are standard Windows operations whichmay be useful if you want to tidy up the screen without having to close a window downcompletely.

2.8 LOOKING AT RESULTS

Now click on the Results button . This opens a Results Selection window.

You are offered the following choices:

• results as Tables or Graphs, with various further choices which determine what the table orgraph will contain.

• results for all objects or one selected object.

Select Time History for any line, then select Effective Tension at End A and click the Graphbutton. The graph appears in a new window. You can call up time histories of a wide range ofparameters for most objects. For lines, you can also call up Range Graphs of effective tension,curvature, bend moment: and many other variables: these show maximum, mean and minimumvalues of the variable plotted against position along the line. Detailed numerical results areavailable by selecting Summary Results, Full Results and Statistics.

Time history and range graph results are also available in numerical form - select the variableyou want and press the Values button. The results can be exported as Excel compatiblespreadsheets for further processing as required. Further numerical results are available in textform by selecting Summary Results, Full Results and Statistics.

Windows displaying system views or graphs can be automatically arranged (Tiled or Cascaded)on screen as they appear by selecting Window|Auto Arrange (this is the default setting onstart up). Windows displaying text are not automatically arranged on opening, but are includedin any subsequent rearrangement of the screen.

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Results Post-Processing

Extra post-processing facilities are available through Excel spreadsheets.

2.9 GETTING OUTPUTYou can get printed copies of data, results tables, system views and results graphs by means ofthe File|Print menu. Output can also be transferred into a word processor or other application,either using copy+paste via the clipboard or else export/import via a file.

Note: Printing facilities are not available in the demonstration version of OrcaFlex.

2.10 INPUT DATATake a look through the input data forms. Start by resetting the program: click on the Reset

button and answer 'Yes' to the warning prompt. This returns OrcaFlex to the reset state,in which you can edit the data freely. (While a simulation is active you can only edit certain non-critical items, such as the colours used for drawing.)

Now click on the Model Browser button . This displays the data structure in tree form in theModel Browser.

Select an item and double click with the mouse to bring up the data form. Many of the dataitems are self explanatory. For details of a data item, select the item with the mouse and pressthe F1 key. Alternatively use the question mark Help icon in the top right corner of the form.Have a look around all the object data forms available to get an idea of the capabilities ofOrcaFlex.

End of Tutorial

We hope you have found this tutorial useful. To familiarise yourself with OrcaFlex, try buildingand running models of a number of different systems. The manual also includes a range ofexamples and technical notes which expand on particular points of interest or difficulty.

Finally, please remember that we at Orcina are on call to handle your questions if you are stuck.

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3 EXAMPLES

3.1 INTRODUCTIONOrcaFlex comes with a tutorial and a comprehensive collection of example files. The full set ofexample files are on the OrcaFlex CD (see CD:\Demo_CD\OrcaFlex\Examples), and whenOrcaFlex is installed some or all of the examples (depending on your installation options) arecopied into the OrcaFlex installation directory.

There are a lot of examples, so they are listed twice below. The first list is organised by type ofapplication and the second list by OrcaFlex feature.

Most examples include both data files (*.dat) and pre-run simulation files (*.sim). Open thesimulation file and then reset to the default view for that example (see the right-click popupmenu on the 3D view or use the CTRL+T shortcut).

Note that the examples have been chosen to illustrate the capability of OrcaFlex and are notnecessarily examples of good engineering practice. In fact, one of the great advantages ofOrcaFlex is that you can try out a wide range of ideas very quickly, and filter the good ones fromthe not so good.

Examples Listed by Type of Application

Riser Systems - Simple Models

A01 Catenary RiserA02 Lazy Wave RiserA03 Steep Wave RiserA04 Lazy S Riser - detailedA05 Lazy S Riser - simpleA06 Steep S RiserA07 Pliant Wave RiserA08 Pliant S Riser

Riser Systems - more complex

B01 Jumper to High TowerB02 Riser to Low TowerB03 Multiple TowersB04 Releasable TurretB05 Detailed Pliant WaveB06 Full Field Layout

Steel Catenary Risers

C01 Catenary SCRC02 Lazy SCRC03 Steep SCR

Tensioned Risers, TLPs, SPARs

D01 Drilling SupportD02 SPARD03 TLP

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Mooring Systems

E01 Buoyed Mooring (No Waves)E02 Buoyed Mooring (Waves)E03 Released Mooring BuoyE04 Branched Mooring

Buoy Systems

F01 CALM BuoyF02 Chinese LanternF03 Current Meter MooringF04 Deep Water Mooring

Installation

G01 PipelayG02 Lay on towerG03 Crane LowerG04 End Pull-upG05 Midline Pull-upG06 Midline LocalG07 Pipe LiftG08 Snag Pull-inG09 Anchor-last DeploymentG10 Lower with Bend Limiter

Offloading Systems

H01 Stowed LineH02 Floating LineH03 Jacket to Semisub

Towed Arrays

I01 Streamer ArrayI02 Deployment with Sub

Pre and Post processing

J01 Batch ScriptJ02 ResultsJ03 Stress AnalysisJ04 Fatigue Analysis

Line-on-line Contact

K01 Line on Line impactK02 Line on Line slide

Examples Listed by OrcaFlex Feature

Topic Examples

GeneralUnits C01

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Simulation stages B04

EnvironmentSloped seabeds A01/C03Profiled seabed B05

VesselDrawing vessel type vs vessel D01Vessel sides using solids H01Using a vessel to model a stationary object H03Vessel forward speed vs current I01Vessel forward motion B04/I02

Line typesLine Types Wizard: Smearing A02/C02/C03Line Types Wizard: Chains A04/A05Line Types Wizard: Wires F03Limit compression A04/A05/E04Stress diameters C02Variable/non-linear properties A01/G10

Line endsLine end orientation A01Lay azimuth A01Use of different pens A07Encastré ends B01Line end stiffness values C03Slip joints D01

LinesClumps F02/G04/H01Alternative first stage static methods F02/G08Prescribed shape G04/G05/G06Branched lines A08/E04/H01/I01Vertical cantilevers B01Replacing lines with winches G04/G05Replacing lines with buoys I02

BuoysGenerating buoy/seabed friction G03Wings I01

WinchesIdentifying winch initial length G04/G05/G07

LinksLinks for contact force G01Links:- non-linear stiffness D01

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Modelling guides D02Restraining with links B04/G09

SolidsSolids for visualisation A03/B02/F03/G01/G03/G08/I02

StaticsMultiple buoy convergence E01/E02/I01Winch or spring to assist statics convergence H02

ResultsCoarse segmentation problems A01/C01Rectified curvature A02

ClashingSolid/line interaction control in statics A06Line/line clashing G08/H03Line/line vs line/solid contact G08 / H03

TethersTethers as links A07/A08Tethers as lines B05

Midwater archRiser connected to midwater arches - options A04/A05

OthersMarking structures for clearance checks D01Trapped water D02/G04Use of global and local models G04/G05

3.2 A - RISER SYSTEMS - SIMPLE MODELS

3.2.1 A01 Catenary RiserSee the A directory in the OrcaFlex Examples.

Introduction

This is the simplest riser configuration. Two lines descend from a vessel to the seabed.Although close to vertical when they leave the vessel, they are parallel with the seabed attouchdown.

The example also shows OrcaFlex ability to model a sloped seabed, non-linear axial stiffnessand variation of drag coefficient with Reynolds Number.

Building the model

To slope the seabed, the angle of slope from horizontal needs to be defined, as does itsheading. In this example the slope is 5º up from horizontal and has a heading of 180º, i.e. alongthe -X axis. In the view +X is to the right, therefore the slope rises to the left. The settings areshown on the 'Seabed' tab on the Environment Data form.

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The catenary is very simple to build. Add a line. Attach End A to the vessel and anchor End B,giving it a Z coordinate of zero so it is exactly on the seabed. The default catenary convergenceoption is best.

To assist the convergence routine, specify the end orientations and the lay direction. In thisexample the line ends have an azimuth of 0º, i.e. the line runs from End A to End B along the+X axis.

At End A declination is 153º, i.e. the line leaves the vessel 27º from vertically downwards. AtEnd B declination is 95º, i.e. parallel to the seabed (in the more usual case of a horizontalseabed, declination would be 90º). Note that in each case the orientation is given with respectto the local axes of the attached structure. For End A this is the vessel, for End B the slopedseabed.

Friction would have had an effect on the line position when it was being installed on the seabed.The lay azimuth, the heading of the line as it was laid on the seabed, allows this friction effect tobe included when determining the static position. For this catenary we assumed End B was laidfirst, then moving to End A. Therefore the lay azimuth is 180º.

For the second line, copy and paste in the model browser, then offset the ends along Y.

From the Model Browser, select Variable Data and look at the 'Drag Coefficients’ section. Atable called ‘Re vs Cd’ is presented relating Reynolds Number to Drag Coefficient. SelectProfile to see it as a curve. Note that the relationship here is specific to one OD and surfaceroughness. It cannot be applied for all lines.

Now look at axial stiffness. It has been set so there is a different slope when in compressionthan tension. One of the lines will use constant axial stiffness, the other will use variable.

From the Model Browser, select Line Types and look at the Hydrodynamics section. TheNormal x Drag Coefficient selected is ‘Re vs Cd’. At each time step OrcaFlex will calculate theReynolds Number at the node and apply the appropriate Cd value. This will also be applied forthe y direction as ‘~’ has been selected. See axial stiffness for details.

A catenary needs refined segmentation at the touchdown point. If noise occurs in the tensiontime histories it may be due to too coarse segmentation about the touchdown point. Note thatthe natural period of the line may also reduce as a result, requiring smaller step sizes.

A catenary is also prone to compression at the seabed in deep water. If a wave is beinggenerated in the line ahead of touchdown it may be due to coarse segmentation, see above.However if the compression remains the same after refinement, it is probably real.

From the Model Browser, select '10" Cat' and double click to open its 'Line Data' form. Selectthe 'Structure' tab and look at the segmentation for the line. The lengths are as short as 0.5m atthe touchdown point.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave.

Look at the range graph of the line x-Drag Coefficient in the latest wave. Note how it variesbetween 0.4 and 1.2.

Look at the range graph of effective tension for both lines. Zoom in from 100m (abouttouchdown point) to the end. Note the difference in compressive load distribution betweenresults for constant and variable tension. These are not great in this example but could besignificant in a deep water system.

Look at the range graph of curvature for both lines. Zoom in from 100m to 140m, abouttouchdown. Note that the constant axial stiffness results in slightly higher curvature at thetouchdown. The second, far smaller peak occurs in the length on the seabed and is due to the

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umbilical curving out of plane to relieve compression. Look at the animation in plan view(CTRL+P).

3.2.2 A02 Lazy Wave RiserSee the A directory in the OrcaFlex Examples.

Introduction

A lazy wave formation is similar to a catenary but has support provided at about midwater bydistributed buoyancy modules. 'Lazy' means that the riser centreline is parallel with the seabedon contact while 'Wave' describes the line shape as a result of the buoyancy modules.

Building the model

The line is built in the same manner as for a catenary, see Catenary Riser. However, at leasttwo line types are applied. The first has the properties of the bare line. The second has thecombined properties of the line and the buoyancy modules.

Each module can be modelled individually in OrcaFlex. However it is more efficient andconvenient to smear the properties of the modules over the buoyed length of the riser, as shownin this example. This can be achieved quickly using the Line Type Wizard facility, if the riserand module properties are known.

The Line Type Wizard is only fully accessible when the program is in the Reset state. Press the'Reset' button or F12. Open the Line Types data form, select '10" + Floats' and then press theWizard button. You are now in the Wizard routine. Step through it to see how the '10"+Floats'properties were built. This facility allows you to easily experiment with module properties andpitch (spacing) to get the configuration you wish.

Now open the 10" Wave data form and select the Structure tab. This example has 110m ofbare riser descending from the vessel, followed by 50m of riser with modules then 60m of bareriser again before finishing at the seabed.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave.

Look at the curvature range graph through the latest wave. Note the sudden change incurvature at 110m and 160m where the buoyed length begins and ends. The other suddendrop is at about 190m, the touchdown point.

Look at the curvature time history at an arc of 110m. This is the resultant curvature and isrectified, i.e. always positive, so the curve trough has been reflected to become a peak. Nowlook at the curvature about the line local Y-axis, within the XZ plane. This is called y-curvature.This has not been rectified so shows that the line reverses in curvature through the wave cycle.

Now look at the y-curvature range graph through the latest wave and compare it to the one forthe resultant curvature.

3.2.3 A03 Steep Wave RiserSee the A directory in the OrcaFlex Examples.

Introduction

A steep wave formation has support provided at about midwater by distributed buoyancymodules and has a vertical connection at the seabed. 'Steep' means that the riser centreline is

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vertical at the lowest end while 'Wave' describes the line shape as a result of the buoyancymodules.

This model also shows the OrcaFlex facility to input multiple wave trains.

Building the model

The line is built in a similar manner as for a Lazy wave, see Lazy Wave Riser. However thelower end is vertical rather than horizontal when it reaches the seabed. The end declination istherefore 180º, indicating the line is heading vertically down, rather than 90º indicatinghorizontal.

In this example End B is anchored 5m above the seabed on top of a terminal. The terminal isrepresented by a solid block. As it is only there for visual purposes, it has no contact stiffness.

From the Model Browser, select ‘Environment’ and go to the Waves form. There are two wavetrains specified. The first is a random wave train called 'Local', representing local wind-drivenseas. The second is a long regular wave train called 'Swell', representing a swell from a distantstorm. When you select one of the wave train names, the data for that wave train appears.

To see the sea surface when the waves are superimposed, go to 'Waves: Preview' and select'View Profile'. There is a wave peak just after time zero, so the simulation start time has beenset to 5 seconds. This helps the build-up transients dissipate before the first wave peakexcitation occurs.

Note the headings for the two wave trains differ by 10º. You can see this is a plan view(CTRL+P), since the axis symbol in the top right shows both wave headings.

Results

Go to the default view (CTRL+T) and look at the animation through stage 1.

Look at the for effective tension time history graph at End A for the whole simulation, and at they-curvature range graph for stage 1. The y-curvature is the curvature about the line local Y-axis, i.e. within the XZ plane. Note how it shows the sag and hog of the line as well as thecurvature just above the seabed termination. As this is an in-plane case, curvature about thelocal X-axis is negligible.

3.2.4 A04/A05 Lazy S RiserSee the A directory in the OrcaFlex Examples.

Introduction

A lazy S formation is similar to a catenary but has support provided at about midwater by anarch structure. 'Lazy' means that the riser centreline is parallel with the seabed on contact while'S' describes the line shape as a result of the arch.

Building the model

The riser is modelled as two lines. The upper line descends from the vessel to the arch whilethe lower line descends from the arch to the seabed.

The arch is modelled using an OrcaFlex 6D lumped buoy model. It is important to get thephysical and hydrodynamic properties of the arch as accurate as possible as they have asignificant effect on the system behaviour. See Modelling Mid-Water Arches.

The lines are usually protected from over bending at the arch by a trough structure. Twoexamples of modelling this are shown.

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The detailed model has the trough as two cylindrical solids attached to the arch. The solidsmust have stiffness specified, so they can push the lines out, and the segmentation of the linelengths in contact must be fine enough to allow them to curve around the solids. This takeslonger to set up but gives the best representation of riser/trough interaction as it allows therisers to roll on and off the arch.

The upper lines have End A at the vessel, descending at 10º from vertical. End B is at the archtop and is horizontal i.e. 90º. Note that end orientations are with respect to the local axes of theobjects to which they are attached. The lower lines have End A at the arch top and End B onthe seabed. Both ends are horizontal with respect to the arch and seabed axes.

Note that if weather loads are to be applied out of the riser plane, it is advisable to make theconnections at the arch Encastré, i.e. apply infinite bend stiffness. This will prevent the lines atthese ends rotating freely out of the plane, which would not occur in the real world due to theend fittings.

The simple model shows the lines are pinned at either side of the arch. The mass and volumeof line and its contents between the pinned connections is then included in the arch model.Note that the line length either side of the arch has been reduced by 6.5m, the length of linefrom the pin to the arch top.

The other main difference between the two models is the tether arrangement. Most archeshave the tethers connected via bridles, i.e. two short chains (bridles) either side of the archconnected to the tether top via a tie plate to form a 'Y' shape. In the simple model the tethersare attached directly to the arch with the bridles shown as part of the arch drawing only. In thedetailed model the bridles are included as lines attached to the arch while the tethers areattached to the bridles via 3D buoys. A 3D buoy can be used as chains have no bend stiffness,so rotational moments do not need to be transferred.

The Line Type Wizard routine quickly builds chain properties for you. Select '2" Chain' on theLine Types data form then press the Wizard button. You are now in the Line Type Wizardroutine. Step through it to see how the '2" Chain' properties were built. Wire properties canalso be generated with Wizard by selecting the Rope category.

Note that, unlike the risers, the chain properties have the 'Limit Compression' option turned on.This is as chains go slack rather than resisting compression. The maximum compressionpossible is therefore zero.

The simpler model is easier to set up and gives quicker runs. However it will not give thedetailed riser/arch interaction due to the line lifting off and dropping onto the arch. It will also notshow the loads on the bridles such as snatch loads.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave for bothcases. Zoom in on the arch and observe its motion.

Look at the motion of the arch in the global X direction, surge in this case, through the wholesimulation. Note how quickly it settles into a cyclic motion.

3.2.5 A06 Steep S RiserSee the A directory in the OrcaFlex Examples.

Introduction

A steep S formation is supported at about midwater by an arch structure and has a verticalconnection at the seabed. 'Steep' means that the riser centreline is vertical at the lowest endwhile 'S' describes the line shape as a result of the arch.

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Building the model

The line is built in a similar manner as for a Lazy S, see Lazy S Riser. However the lower end isvertical rather than horizontal when it reaches the arch anchor base. The end declination istherefore 180º, indicating the line is heading vertically down, rather than 90º indicatinghorizontal.

In this example the lower line End B is anchored 5m above the seabed on top of the archgravity base, represented by a solid block. As it is only there for visual purposes, the block hasno contact stiffness.

Note also that the lower line convergence routine is now a spline. A solid acts by pushing anode towards its nearest surface. If 'Catenary' or 'Quick' options were selected, the line wouldbegin nearly vertically but slightly towards the vessel due to the current heading in this example.The solid would therefore push it out towards the nearer vessel side of the arch. Try it and see.

The line must therefore be forced to remain on the right hand side of the arch and this isachieved by a spline. It does not need to be very precise, as the static analysis will refine theline position. It just needs to be enough to hold the line to the right of the arch at the start of thestatic analysis.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave. Zoom in onthe arch and observe its motion.

3.2.6 A07 Pliant Wave RiserSee the A directory in the OrcaFlex Examples.

Introduction

A pliant wave formation is a lazy wave with the addition of a tether restraining the touchdownpoint.

Building the model

The line is built in the same manner as for a lazy wave, see Lazy Wave Riser. In this examplethree line types are applied. The first has the properties of the bare line. The second has thecombined properties of the line and the buoyancy modules. While the third has the pitch(spacing) of the modules halved.

The second set of buoyed properties was generated by copying the first set and using LineType Wizard to halve the pitch. OrcaFlex then generates the new properties for you.

Also look at the pen setting in line types data form. Each property has a different colour andpen thickness so they can be identified easily in the view. Note that '10" Prod 1' needs to have'Use Line Types Pen' in the Drawing tab selected for these settings to show.

The system is made pliant by the addition of a tether. This example has the tether modelled asan OrcaFlex link '10"Prod#1'. This is the simplest way of modelling the tether and is sufficientfor most cases. Note that the link has no mass or hydrodynamic properties.

The 9.9m long link is anchored at 1.8m above the seabed, allowing for the height of an anchor.It is then attached to the line at an arc length of 176m from End A. The link can only beattached to a node. Therefore segments must be sized so that a node is present at the requiredposition. In this example the second '10"Product' section ends at this arc length.

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Results

Go to the default view, CTRL+T, and look at the animation through the latest wave.

Look at the y-curvature range graph in the latest wave. The y-curvature is the curvature aboutthe line local Y-axis, i.e. within the XZ plane. Note how it shows the sag and hog of the line aswell as the curvature at the tether and touchdown.

3.2.7 A08 Pliant S RiserSee the A directory in the OrcaFlex Examples.

Introduction

A pliant S formation is a lazy S with the addition of a tether restraining the touchdown point.

Building the model

The line is built in the same manner as for a lazy S, see Lazy S Riser.

This system has several risers attached to a communal arch. Instead of modelling the troughstructure, the lines are pinned at either side of the arch. The mass and volume of the lengthson the arch are then incorporated into the arch model.

This is the simplest way of modelling the risers on the arch. It is easy to set up and givesquicker runs. However a better representation is given by the more detailed model, whichallows the lines to lie on solids representing the troughs. See the Lazy S Riser examples for acomparison.

The arch in this example is held in place by a tether and bridle arrangement. As lines cannot bedirectly linked to each other, the tethers and bridles are joined via simple 3D buoys, 'Bridle E'and 'Bridle W'. These are given negligible properties, as they are simply a means of joining thelines and do not contribute to the behaviour of the system. See Links.

The system is made pliant by the addition of tethers to the lines. This example has the tethersmodelled as OrcaFlex links. This is the simplest way of modelling the tether and is sufficient formost cases. Note that the link has no mass or hydrodynamic properties. As they connect tonodes on the lines, the line segments must be arranged so a node is present at the required arclength.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave. Observe howclose the lines get to the semi-submersible structure.

Look at the tension time history of any of the lines through the whole simulation. Note howquickly the transient noise is damped out.

Plot time histories of the arch motion through the whole simulation. The trends show that thearch has not yet settled into a fully cyclic motion. A longer run is required.

3.3 B - RISER SYSTEMS - MORE COMPLEX

3.3.1 B01 Jumper to High TowerSee the B directory in the OrcaFlex Examples.

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Introduction

This example has jumpers connected from a vessel to the top of a high tower, i.e. the tower topis close to the surface. The lines then descend to the seabed as rigid structures within thetower. An installation of this type can be found in the Girassol field.

As this is a deep water system, the tower top will flex under the weather and jumper loads. Ithas therefore been modelled as a very stiff line with one end fixed, i.e. a vertical cantilever.

As the motion may be dependent on loads from the jumpers as well as the waves and current,all attached jumpers need to be modelled.

If the tower motions are known, it can be modelled as a vessel with the motions specified. Thiswould mean that individual jumpers could be analysed, if required, as they would have no effecton the modelled motion of the tower.

Building the model

The eight jumpers extend from the vessel side to the top of the deep water tower. They areheading vertically downwards relative to the vessel when they leave it and are restrained in thisposition by applying infinite bend stiffness at the end. They are then heading 30º from verticallyupwards relative to the tower top when they arrive there. Again bending stiffness at the line endrestrains it in this position.

Note that a fully restrained end, often called an Encastré, is only required if it is expected toaffect the behaviour of the line or the attached structure. In this case the lines are short somore sensitive to end effects. Also the line connection loads may affect the tower topbehaviour.

Try running the model with pin joints, by setting the connection stiffness to zero, to see how thebehaviour changes.

The tower is basically a very long, thin, vertical cantilever with a mass on the free endrepresenting the attachment structures. As the ratio of tower diameter to length is very small,1e^-3, it can be considered a very stiff riser that will move under environmental and systemloads. It has therefore been modelled as a line, anchored at the seabed and attached to a 6Dspar buoy at the top. Infinite bend stiffness has been applied at both ends.

The spar buoy is the simplest of the 6D buoys available. It is therefore convenient for modellingthe mass of structures at the top of the arch and for connecting lines. Remember that linescannot be directly connected to each other so an intermediate buoy is required. As the towerrotations need to be considered, a 6D buoy is used.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave. The towerappears to hardly move. A time history graph of 'X' motion (surge) and 'rotation 2' (pitch) for 'topbuoy' show some motion is occurring.

3.3.2 B02 Riser to Low TowerSee the B directory in the OrcaFlex Examples.

Introduction

This example has risers connected from a vessel to the deep water tower, i.e. the tower top isclose to the seabed. The risers are protected from over bending at the tower by a trough

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structure, as with a lazy S configuration, see Lazy S Riser. An installation of this type can befound in the Troll C field.

Building the model

The risers are modelled in two halves. The upper catenary extends from the vessel down to thetower top. The lower catenary extends from the tower top to the seabed.

The trough structure is modelled as a cylindrical solid, allowing the riser to lift off and drop backon. See Lazy S Riser for a more detailed description of this arrangement. Note that making theends fixed at the arch, Encastré ends, means that the lines do not rotate freely whenenvironmental loads are applied out of the riser plane. Instead they are held in the riser plane,as would be the case with the real clamps on the tower.

A vertical cylinder represents the tower. This has no stiffness as it is for visualisation only.However, if clashing is to be considered, stiffness can be applied. See Line Clashing.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave. Apart fromthe vessel roll, not much appears to be happening. Now zoom in to the umbilical near theseabed. The sag can be seen to rise and fall with the motion of the vessel above.

Look at a range graph of tension in 'Umb Up 1' through the latest wave cycle. Note thatalthough there is a significant tension variation near the surface, End A, it is nearly negligiblenear the tower top, End B. The same plot for 'Umb Down 1' shows no tension variation alongthe arc length from the tower top to the seabed. This indicates environmental loads areinsignificant at this depth, as would be expected.

3.3.3 B03 Multiple TowersSee the B directory in the OrcaFlex Examples.

Introduction

This system shows a field of risers and jumpers distributed from a single vessel via three towerstructures. An installation of this type can be found in the Girassol field.

Building the model

The examples Jumper to High Tower and Riser to Low Tower show how each component partis constructed. The main difference is that the high and low towers are now one structure withthe jumpers at the top and the risers at the sides, near the base.

To manage this, the tower is split into two lines joined by a 6D lump buoy with nominalproperties. A 3D buoy cannot be used in this example, as rotations of the ends are important.

The OrcaFlex model only shows line centrelines. In this case cylindrical solids have beenadded to the lower parts of the tower to represent the outer diameters. This means thatinterference between the risers and the lower part of the tower can be observed in theanimation.

If the effect of clashing needs to be modelled then this would be set up between the riser andthe line representing the lower tower, see Jacket to Semisub for an example.

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Results

Go to the default view, CTRL+T, and look at the animation through the latest wave. Look inelevation as well.

3.3.4 B04 Releasable TurretSee the B directory in the OrcaFlex Examples.

Introduction

This model represents an FPSO system with a releasable turret. The simulation shows theturret falling away and the FPSO moving off station. An installation of this type can be found inthe Terra Nova field.

Building the model

The mooring lines and pliant wave risers are connected to a 6D spar buoy that has the physicaland hydrodynamic properties of the real buoy. Note that these values need to be as accurateas possible to effectively model this system when the buoy is released from the vessel.

A solid cylinder has also been attached to give a better visual representation of the buoy shape.The cylinder has been assigned a non-zero stiffness so that interaction with the attached lines ismodelled if clashing occurs. The buoy is attached to the vessel by three vertical and fourhorizontal links. These links are linear spring/dampers that have been set up to fully restrain thebuoy.

You can split your analysis into as many stages as you like. For a simple case only, Stage 0,build-up, and 1, simulation, are required. However if a number of events are occurring, as inthis example, then the analysis will need to be split into more stages.

During the build-up stage wave amplitudes are gradually increased up to the required value.This prevents the generation of transient loads due to the sudden application of environmentalconditions. Full simulation begins at the start of Stage 1. Therefore OrcaFlex refers to thispoint as 0sec. See Figure: Time and Simulation Stages.

In this example the stages can be summarised as shown below.Stage 0 Build up of Waves -8.25sec to 0secStage 1 Full Waves applied 0 sec to 5secStage 2 Links released at start and

vessel moves forward5sec to 35sec

If you look at the data for 'VertLatch1' you will see that it will release at the start of stage 2, aswill the other tethers. The buoy will then be free to drop deeper into the water.

After release of the buoy, the vessel will move forward, i.e. to the left of the view as it has aheading of 180º. Look at the data page for 'FPSO'. Prescribed motion shows that it movesforward with a velocity of 2m/s during Stage 2.

Results

Go to the default view (CTRL+T) and look at the replay through the whole simulation. Note thebuoy dropping away at 8.25sec and the vessel starting to move forward.

Look at the proximity of the buoy to the underside of the vessel.

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3.3.5 B05 Detailed Pliant WaveSee the B directory in the OrcaFlex Examples.

Introduction

This pliant wave model has more detail in the tether and touchdown is on the edge of a ridge,the vessel being in deeper water. The ridge top and side profiles are included in the model. Aninstallation of this type can be found in the Buffalo field.

Building the model

The general pliant wave model is described in the example Pliant Wave Riser. The maindifference is in the modelling of the tie-down tether. In the simple version it was represented bya simple spring link. In this version the riser and tether are modelled as three lines, the upperlength from FPSO to the clamp, the lower from the clamp to the anchor and the chain tether.

They are joined together at the clamp, which is a 6D spar buoy. This has the properties of theclamp itself and allows transfer of bending moments from the riser at one end to the one at theother.

This more detailed model takes longer to set up and run but includes the physical andhydrodynamic properties of the clamp and chain.

The model also shows the OrcaFlex Seabed Profile facility. The seabed, ridge wall and topneed to be modelled to ensure no clashing occurs. Simple profiles could be modelled withsolids but, as friction is not included in solid/line interaction, its applicability would be limited.Instead the seabed profile can be defined by a series of points and a smooth cubic spline fit.Beyond the defined points the seabed is assumed horizontal.

Look at the Seabed tab on the Environment data form for the profile applied here.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave. Note how theriser remains clear of the ridge and seabed throughout the wave cycle.

Plot the range graph of seabed clearance through the latest wave for the 'Umb Up'. Note that ittakes account of the seabed profile, as shown by the trough at an arc of about 200m where theseabed rises locally and at an arc of about 400m where the ridge edge juts out.

3.3.6 B06 Full Field LayoutSee the B directory in the OrcaFlex Examples.

Introduction

The model contains 2 ships, 22 lines and various other items, and is modelled in a random sea.In practice, it would be unusual to model the whole of a system at once, but this example servesto demonstrate that OrcaFlex can readily handle very complicated systems. OrcaFlex imposesno limits on the number of lines, ships, buoys etc. which can be modelled.

Building the model

This is made up of a number of configurations. Descriptions of how to build them are in theexamples listed below:

Pliant Wave Riser

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Lazy S Riser

Buoyed Mooring (Waves)

If the configurations have been built in separate OrcaFlex models, they can be placed into onemodel using the OrcaFlex Library routine. This allows you to open one file then access asecond to copy the data across.

Results

Go to the default view, CTRL+T, and look at the animation through Stage 1.

3.4 C - STEEL CATENARY RISERS

3.4.1 C01 Catenary SCRSee the C directory in the OrcaFlex Examples.

Introduction

This example has a SPAR buoy with three steel pipes (SCRs) descending from it in a catenaryformation.

Building the model

Note that this example has been set up with user defined units. OrcaFlex allows you to use SI,US or user defined (customised) unit combinations. If the units are changed, OrcaFlexautomatically converts all the input data for you. See units for further details.

The SPAR is modelled as a vessel with its motions defined by RAOs. SPAR buoys that are talland thin can be modelled as buoys, though there are limitations to the model, see exampleSPAR.sim.

The pipes are catenaries. The example Catenary Risers gives more information on how togenerate this configuration.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave.

Look at the curvature range plot of 'SCR 0º' through the latest wave. This shows the maximum,minimum and mean values experienced along the arc length from the SPAR to the anchor. Ifthere is sufficient segmentation in the model in areas of high curvature, the curve will be smoothat the top, i.e. more than one point near the apex as here. Beware if a spike is seen with onlyone point at the apex. This can indicate that the segment length is too long to follow the curveand the line model has kinked.

Remember you may need to zoom in on the apex to see its shape if segment lengths are verysmall.

3.4.2 C02 Lazy SCRSee the C directory in the OrcaFlex Examples.

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Introduction

Just as for flexible risers, steel risers can be supported in a lazy wave formation. The line isgiven support at about midwater by a series of buoyancy modules along its length. 'Lazy'means that the riser centreline is parallel with the seabed on contact while 'Wave' describes theline shape as a result of the buoyancy modules.

Building the model

Each module can be modelled individually in OrcaFlex. However it is more efficient andconvenient to smear the properties of the modules over the buoyed length of the riser, as shownin this example. This can be achieved quickly using the Line Types Wizard facility, if the riserand module properties are known.

To analysis the system with an alternative module size or pitch (spacing), modify the propertieswith the Wizard and re-analyse.

Pipe effective diameters are given in the Geometry tab on the Line Types data form. Outsidediameter is used for buoyancy and hydrodynamic drag calculations, internal diameter forcontents mass. Separate stress diameters can be defined on the Stress tab on the Line Typesform. We have done this for the 'Buoyed' line type since the outer diameter of this line has beenincreased to represent the buoyancy modules.

Note that the stress values have no effect on the simulation. They are used in post-processingto obtain the stress results.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave. Note that theSCR moves very little.

Look at the maximum von Mises stress range plot for the SCR through the latest wave. Thisshows the maximum, minimum and mean values experienced along the arc length from thevessel to the anchor. The increase in stress along the buoyed length can clearly be seen.

3.4.3 C03 Steep SCRSee the C directory in the OrcaFlex Examples.

Introduction

As with flexible risers, a steel riser steep wave formation has support provided at aboutmidwater by distributed buoyancy modules and has a vertical connection at the seabed. 'Steep'means that the riser centreline is vertical at the lowest end while 'Wave' describes the lineshape as a result of the buoyancy modules.

Building the model

To slope the seabed, the angle of slope from horizontal needs to be defined, as does itsheading. In this example the slope is 3.03º up from horizontal and has a heading of 0º, i.e.along the +X axis. In the view +X is to the right, therefore the slope rises in this direction. Thesettings are shown in the Seabed tab on the Environmental Data form.

The riser ends have been restrained. The lower end has an infinite bend stiffness applied whichmeans that it is prevented from bending. The upper connection is a flex joint. It has a bendstiffness applied greater than zero but less than infinity. This allows some flexing of the endconnection structure.

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Each buoyancy module can be modelled individually in OrcaFlex. However it is more efficientand convenient to smear the properties of the modules over the buoyed length of the riser, asshown in this example. This can be achieved quickly using the Line Type Wizard facility, if theriser and module properties are known.

To analyse the system with an alternative module size or pitch (spacing), modify the propertieswith the Wizard and re-analyse.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave. Note that theconfiguration moves far less than a flexible riser would, as is to be expected.

Look at the direct tensile stress range plot for the SCR through the latest wave. This shows themaximum, minimum and mean values experienced along the arc length from the vessel to theanchor. Note how the pipe goes into compressive stress about midwater.

Look at the time history of wall tension at an arc length of 500m. Note that the compressive loadis small and is not applied suddenly.

3.5 D - TENSIONED RISERS, TLPS, SPARS

3.5.1 D01 Drilling SupportSee the D directory in the OrcaFlex Examples.

Introduction

A tensioned drilling riser descends from a platform to the seabed.

Building the model

The platform drawing is defined in the Drawing tab on the Vessel Types data form except for thetensioner support structure. This is defined in the Drawing tab on the 'Platform' data form. Thisallows a general representation to be stored with the vessel type and then customised for eachvessel using the type. Go to the 'Platform' and change the line type colour. What happens inthe view?

The slip joint at the top end is modelled as a single segment with very low axial stiffness buthigh bend stiffness, similar to that of the riser itself (arguably it should be stiffer). The 4tensioners, in the usual cruciform arrangement, are modelled using four Links ofspring/dampers type. In this case their stiffnesses are non-linear but their damping is linear withvelocity (a non-linear option is available).

The moonpool edges are modelled as dummy lines 'MP FWD', 'MP PORT', 'MP AFT' and 'MPSTBD' attached to the platform. They have negligible properties and need only be one segmentlong as they are markers. Making their lengths slightly shorter than the distance between theirend connections makes convergence quicker.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave.

Zoom in on the riser top end. Look at the tension time histories of the four links and theeffective tension in the riser. They all vary evenly. Is this what you would expect?

Look at the line clearance range graph for the riser through one wave cycle. This reports howclose the riser centreline got to any of the dummy lines marking the moonpool edge. Double

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click on the graph to reset the axes. Set X as 0 to 50 in 10 steps, Y as 0 to 50 in 5 steps. Zoomin further by dragging a box around the curve minimum.

The riser centreline approaches to 2.725m of the moonpool edge. As the riser has a diameterof 0.65m, this means the minimum clearance is 2.4m.

3.5.2 D02 SPARSee the D directory in the OrcaFlex Examples.

Introduction

A riser descends from the SPAR to the seabed via a guide down the middle of the spar. Aconstant tension device is at the top of the riser.

Building the model

The spar is modelled as a vessel with its response to wave loads given as RAOs. It has twosolids attached. One is a representation of the SPAR top. As it is for visual purposes only, ithas no contact stiffness.

The second solid represents the trapped water in the central moonpool of the SPAR. Thetrapped water facility is used here to model hydrodynamic shielding of the SPAR body so thatwave and current effects are suppressed in the moonpool. See Shapes for further information.

Fixed guides are fitted in the moonpool. These restrain the riser in the buoy X and Y directionsbut allows free motion in the Z direction (we neglect friction between the riser and the guides).Three pairs of links spaced vertically, i.e. along the riser centreline, model the guides.

These links are hidden in the view window using the OrcaFlex 'hide' option. Open the modelbrowser and click on Guide 1X with the mouse right hand button. You will see an option to'show' the link. If this is selected, the link will appear in the view window. Hiding is carried outthe same way.

The links are specified as Spring/Dampers, not Tethers, so that the spring can takecompression. Note that the ends of the links are attached to and move with the SPAR. Notealso that each link is made very long so that vertical movement of the node to which it isattached makes very little difference to the force in the link, and the link remains near-normal tothe riser.

Look at 'Guide 1X'. The stiffness profile has resistance to compression when the link length is0m to 304.5m and resistance to tension when the length is 305.1m to 609.6m. From 304.5m to305.1m, a gap of 600mm, the link has no action as the riser is within the guide - i.e. the guidehas a "rattle space" of 600mm.

It is not generally necessary to give the link the true contact stiffness between a riser and a steelguide tube. The important criterion is that the riser should not penetrate the guide so much asto invalidate the model; in practice this usually means that a few millimetres penetration is quiteacceptable. If you have some idea what contact force you are expecting, this will enable you toset an acceptable stiffness. If not, then a preliminary trial run will give you some idea of whatyou need. In general, it is not a good idea to set the stiffness too high as this may lead to noisein the results and possibly to integration instability and the need to re-run with a shortertimestep.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave. The motionappears gentle.

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Look at the time history of winch length. This is varying to keep the tension constant. It showsthat a greater tension is required to keep the line taut as with the present value it is extending.

3.5.3 D03 Tension Leg PlatformSee the D directory in the OrcaFlex Examples.

Introduction

A small TLP is modelled with its moorings and an attached umbilical.

Building the model

The recommended method of modelling a large TLP is as a vessel with RAO data or prescribedmotions. However for this small control buoy we have used the OrcaFlex Spar buoy option.Hydrodynamic loads on the buoy are modelled using Morison's equation. See 6D Buoy Theory.

In this case there are four mooring tethers plus an umbilical. The umbilical is constrained by asystem of cross-ties to prevent clashing with the tethers and a subsea structure.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave. The motionappears gentle. Look at the time histories of TLP motion.

3.6 E - MOORING SYSTEMS

3.6.1 E01/E02 Buoyed MooringsSee the E directory in the OrcaFlex Examples.

Introduction

In fields where there is limited space, mooring lines often pass over other structures. Toprevent contact, they are sometimes held up by attaching buoys at intervals along their lengths.

This example shows a single mooring line that has had two buoys attached. Each is modelledas a 6D spar buoy attached by a link.

Building the model

This model has a single line representing the mooring while the two buoys are attached withlinks. This is the simplest means of connecting buoys to lines. The links are springs with nomass or hydrodynamic properties.

Each buoy is modelled as a 6D spar buoy. These have the physical and hydrodynamicproperties of the real buoys.

With a system containing multiple buoys, the degrees of freedom of the whole model are greatlyincreased. Convergence to a static equilibrium position can therefore be difficult to find. Onesolution is to reduce the degrees of freedom of each buoy. OrcaFlex allows you the option foreach buoy to restrain all rotations in the static analysis.

However, in some systems, the convergence is still difficult to achieve, as here. Therefore asolution is to carry out a dynamic analysis with no waves applied, the 'No Waves' case here.

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This allows the system to settle dynamically. The static position can then be updated using theUse Calculated Positions button.

Static analysis can then be run using these settled positions to get a final definitive position.The static stage can still take some time, this system taking 433 iterations.

If the static results are not required then the settled positions from the 'No waves' model can beused as the starting point for dynamic analysis. Dynamic wave loading will quickly damp outany transients due to the static position not being fully converged. This is the option used in the'Waves' model.

Results

Load the waves case and go to the default view, CTRL+T. Look at the animation through thewhole simulation. This will show the response to the passing random wave train.

Zoom in on the upper buoy and see how it responds to the passing waves.

3.6.2 E03 Released Mooring BuoySee the E directory in the OrcaFlex Examples.

Introduction

This example shows how to model the effect on a mooring line of one of its attached buoysbreaking free.

Building the model

The model is the same as seen in the example Buoyed Mooring.sim. The difference is that thesimulation has been split into stages, as listed below.Stage 0 Build-up of Waves -5sec to 0secStage 1 Full Waves applied 0sec to 10secStage 2 Buoy Released at start 10sec to 35secDuring the build-up stage wave amplitudes are gradually increased up to the required value.This prevents the generation of transient loads due to the sudden application of environmentalconditions. Full simulation begins at the start of Stage 1. Therefore OrcaFlex refers to thispoint as 0sec. See Time Origins in Dynamic Analysis.

If you look at the data for link 'BotPendant' you will see that it will release at the start of Stage 2.The buoy is then free to rise to the surface.

Results

Go to the default view, CTRL+T, and look at the animation through the whole simulation. Notethe lower buoy breaking free at 10 seconds.

Look at the Z time history of the mooring at an arc of 550m, the attachment point of the lowerbuoy. See how it drops deeper in the water after the 10 seconds. Also observe the Z motion ofthe lower buoy and how its momentum throws it out of the water. This is also shown in theanimation.

3.6.3 E04 Branched MooringSee the E directory in the OrcaFlex Examples.

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Introduction

This is a 3-leg "branched" mooring. The three mooring legs and the rising leg are joinedtogether by a coupling modelled as a buoy. The rising leg is then attached to a vessel.

Building the model

As the chains have no bend stiffness, it is sufficient to connect them to each other with 3Dbuoys (translation only). 6D buoys would have been required if there were bend moments totransfer.

Note that the chain and wire properties have the 'Limit Compression' option turned on. This isas they go slack rather than resisting compression. The maximum compression possible istherefore zero.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave.

3.7 F - BUOY SYSTEMS

3.7.1 F01 CALM BuoySee the F directory in the OrcaFlex Examples.

Introduction

A CALM buoy is held in place by six equally spaced mooring lines. It is attached to the vesselby a hawser and a transfer hose.

Building the model

The CALM buoy is modelled as a 6D spar buoy in which the object is represented as a stack ofco-axial cylinders. See Spar Buoys. In this case we have used a total of 5 cylinders of whichthe top one (Cylinder 1) represents the turntable and pipework on the deck of the buoy, andCylinder 5 represents the projecting skirt.

It is important to ensure that the physical and hydrodynamic properties of the buoy are as closeas possible to the real CALM buoy properties. See Modelling a Surface Piercing Buoy forfurther discussion of data preparation for CALM buoys and the like.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave.

The replay shows that the CALM buoy follows the wave surface quite closely, as expected.

Look also at the tension results for one of the moorings - say the 6th Mooring, which is the up-wave leg. The range graph of effective tension for the latest wave shows that tension in the linegoes to zero over part of its length at some point during the wave cycle. It is interesting to findout where in the wave cycle the tension goes to zero (by looking at tension time histories forvarious points along the line) then try to understand why. Is it, for example, caused by the buoypitch motion, or by direct wave loading on the mooring chain, or a combination of these andother effects? And how might we modify the system to prevent the moorings going slack?

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3.7.2 F02 Chinese LanternSee the F directory in the OrcaFlex Examples.

Introduction

This system consists of risers descending from the underside of a buoy to its base on theseabed in a chinese lantern configuration. As they are fixed at the buoy and its base, theremust be sufficient length to prevent the risers going taut due to buoy motions. This excesslength is accommodated by encouraging the risers to bulge outwards beneath the buoy, hencethe name.

Building the model

The risers are forced to bend outwards by angling their end orientations and fitting buoyancymodules. Press CTRL+Y to turn the local axes view on. Note the heading of the Z-axis at eachend. This shows the line heading on leaving End A, at the buoy, and arriving at End B, at thebase. Open the Line data form for Riser 1; the Attachments tab shows where buoyancy isattached.

The selected method for the riser static analysis is 'spline'. This configuration has a number ofstatic solutions for the line position, not all of which are stable. Using the spline option, we canforce the risers into the correct static shape. Try changing to 'Quick' and see what positions therisers form. Note that both 'Quick' and 'Spline' are the first stage static solutions only - in bothcases, the Full statics solution then takes over and calculates the true equilibrium shape.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave.

In elevation view, the default, it appears that the risers contact the mooring lines. However ifyou switch to plan view, CTRL+P, then it can be seen that the risers remain between themoorings.

Look at the surge, X, heave, Z, and pitch, rotation 2, of the CALM buoy. This has not settledafter eight wave cycles. The wave period is 3sec while the buoy has a natural frequency ofabout 2.7sec so the wave excitation is near resonance.

Look at the tension time history of 'Riser 1' through the whole simulation. It shows that the risergoes into compression of up to 20kN.

3.7.3 F03 Current Meter MooringSee the F directory in the OrcaFlex Examples.

Introduction

To obtain information on current velocity at a location, the meters need to be spaced out atdifferent water depths and should ideally have negligible motion due to wave loads. This isachieved by attaching them on a tether beneath a buoy. The buoy needs to be positioned closeenough to the surface so that all required metering depths are available, while deep enough thatwave loads have little effect.

This example shows several current meters evenly spaced along a tether that is held in placeby a buoy.

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Building the model

The buoy is modelled as a 6D spar buoy with properties as for the real buoy. It is held in placeby a line with the properties of a wire rope. The Line Type Wizard was used to generate thesevalues. Select 'Wire' in the Line Types data form and press the Wizard button to see how thiswas done.

The current meters are modelled as clumps attached to the tether. A clump is a concentratedattachment that is connected to a node on a Line. It is a small body that experiences forces(weight, buoyancy, drag etc.) exactly as for a 3D buoy. But instead of being free to move it isconstrained to move with the node and the forces acting on it are transferred to that node. SeeAttachments: Clumps.

A rectangular solid with no stiffness represents the system anchor.

Results

Load the data file and run statics. See how the buoy equilibrium position is located. Go to thedefault view, CTRL+T, and see how the buoy equilibrium position is located.

Load the simulation file and look at the animation through the latest wave. Not much appears tobe happening. This is confirmed by looking at the time history of the buoy motion and thetension range graph for the tether. What happens if the buoy is raised closer to the seasurface?

3.7.4 F04 Deep Water MooringSee the F directory in the OrcaFlex Examples.

Introduction

The example shows a buoy positioned at the sea surface in deep water. It is held in place by along mooring line anchored at the seabed. A regular wave train has been applied.

Building the model

There are two buoys in this model. The first buoy is surface piercing and, in this case, itsmotion at the surface is of interest. Therefore it has been modelled as a 6D spar buoy. SeeModelling a Surfacing-Piercing Buoy. The second buoy is at midwater, connecting two lines aswell as applying buoyancy. As the attached lines have insignificant bend stiffness and theapplied wave loads are not great, it can be modelled as a 3D lumped buoy.

The mooring is made up of a number of different lines and intermediate structures such asshackles. Rather than building up a complex model requiring many lines and buoys, the upperand lower lines have sections with different line types and the structures have been modelled asattached clumps. This is sufficient for most mooring cases.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave. The surfacebuoy is moving with the wave as expected. However its pitch does not vary much due to therighting load from the mooring. Have a look at the time histories of the buoy motion. Note thatthe buoy is still moving forward with each wave cycle.

Zoom out and look at the whole system. On this scale any motion appears negligible.

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3.8 G - INSTALLATION

3.8.1 G01 PipelaySee the G directory in the OrcaFlex Examples.

Introduction

Pipe lay over the stern in 60m water depth from a 100m long ship. The support rollers arespaced out along a rigid stinger projecting from the stern, and the lay operation is beingmodelled in head seas and current.

This example also shows one method of modelling a prescribed shape in the length alreadylaid.

Building the model

The stinger is shown as a series of rectangular solids attached to the ship. These are shownhere to help visualisation only - they have no effect on the analysis. Similarly, the rollers areshown as small diameter circular cylinders. However the supporting force on the pipe, whichthe rollers provide, is actually modelled by links. These provide a more reliable way ofachieving the required pipe shape. In the present model, the links are hidden. To see them,open the Model Browser (press F2), select each Link in turn, right click the mouse and select'Show'.

Note that line segmentation is arranged so there is a node present at the precise point where aroller support is required. A link is then attached to each of these nodes.

The links are specified as Tethers. They extend normal to the pipe and are made very long sothat axial movement of the attached node makes very little difference to the force in the link, andthe link remains near-normal to the pipe. Note that they are attached to the vessel so movewith it.

If the pipe lifts off a roller, the link goes slack so no force is applied. If the pipe contacts theroller, the link is taut, applying a restraining force so the pipe does not fall through.

This model has a length beyond the touchdown point forming an ‘S’ shape on the seabed (lookat the model in plan view, using CTRL+P). There are two methods of achieving this. One is touse the prescribed shape facility in OrcaFlex; this is discussed in more detail in the G04example. However the geometry can be tricky when one end lifted up as the projected shapeon the seabed needs to be specified.

This example uses an alternative method, which is to hold the line in its required shape usingvery short links during statics. They are then released when dynamics starts. See the links'Prescribed 1' to 'Prescribed 10', which are holding it in place during statics.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave. Zoom in onthe roller positions and see how the line lifts off and on the last two rollers, Rollers 2 and 3.Look at the time history of tension for each tether. This confirms that the line lifts off Rollers 2and 3, i.e. they go slack.

Look at the effective tension range graph for the pipe during the Latest Wave. It showsmaximum, mean and minimum tension plotted against arclength along the pipe from the stern ofthe ship. All points along the line arclength experience compression at some point through thewave cycle.

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Look at the tension time history at an arclength of 280m, just ahead of the touchdown point. Asthe compression is applied gradually, it indicates that it is a real condition. To confirm it is realand not due to the coarseness of the model, halve the segment lengths in this region and see ifthe compression reduces. This is discussed in more detail in the Catenary Riser.sim example.

3.8.2 G02 Lay on TowerSee the G directory in the OrcaFlex Examples.

Introduction

This is an example of installing a riser over a subsea tower in 300m water. The riser is beingpaid out from the moonpool of the installation vessel, and is supported from an auxiliary winchat the stern of the ship. There is a clamp about 10m above the attachment point of the winch,which has to be placed in the centre of the support tower.

Building the model

A series of static "snapshot" analyses may be sufficient. It is a case which presentsconsiderable difficulties in static analysis, but which can be handled quite readily in OrcaFlex.In the case shown, we have used two winches to represent the main riser handling winch in themoonpool and the auxiliary winch at the stern. The critical phase of the installation is modelledin calm water. The main winch pays out 3m of line and the auxiliary winch then hauls in 3m ofline, payout of -3m, to settle the clamp into place.

The winches are active in different stages to enable the required order. The stages are as listedbelow.Stage 0 Main Winch pay-out -8sec to 0secStage 1 Main Winch pull-in 0sec to 16secStage 0, the wave build-up stage, can be used here as no waves are applied. Remember tolook at the full simulation though when replaying the animation.

Results

Go to the default view, CTRL+T, and look at the animation through the whole simulation. Notehow the flowline lowers onto the tower before the clamp is pulled into position. Also look at theflowline time history of heave, Z, and surge, X, at node 35 (clamp) for the full simulation.

3.8.3 G03 Crane LowerSee the G directory in the OrcaFlex Examples.

Introduction

This is an example of modelling the lowering of a template structure from the sea surface to theseabed using two cranes. In practice it would be more usual to look at a series of "snapshots"rather than the complete lowering operation.

Building the model

The template being lowered and the two spreader bars have been modelled as 6D buoysbecause rotations are important. The Towed Fish option is convenient for the spreaders, simplybecause a Towed Fish is a horizontal stick.

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The template has been modelled as a spar buoy so that sudden changes in profile can be takenaccount of as it enters the water, the spar buoy being built up of a series of stacked cylinders.Note that the buoy drawing has been turned off and instead solids attached to the buoyrepresent the template shape.

There is no friction interaction of solids or buoys with the seabed. Therefore dummy lines havebeen attached to the bottom of the template. These have negligible properties but will generatea friction force when they are pushed onto the seabed by the buoy.

The shackles at the top of the bridles are 3D buoys because their rotation need not beconsidered.

The bridle structures are modelled as Links, but Lines could be used equally well. Note that thelinks to the spreaders have been attached slightly off axis - if they are put all on the axis, thenthe bar would have no unique orientation and the static analysis would probably fail toconverge.

Note that slamming loads and the changes in water particle motion due to the presence of thehulls are not included in the model.

The winches have the following payout rates:Stage 0 Settle time -8sec to 0secStage 1 Both winches payout 20m 0sec to 20secStage 2 Both winches payout 65m 20sec to 60secStage 3 1st winch pays out 20m, other 22m 60sec to 100secThe 2nd winch pays out more than the 1st so that one edge of the template will contact theseabed before the other.

Note that in Stage 1 and Stage 3 the payout rate is slow. In these stages discrete events occur.In Stage 1 the template becomes fully submerged. In Stage 3 it contacts the seabed. If thepayout is too fast, the analysis step size is insufficient to cope with the changes due to theseevents and the analysis becomes unstable.

An alternative solution would be to reduce the step size but this would slow all the simulationinstead of just the relevant stages.

Results

Go to the default view, CTRL+T, and look at the animation through the whole simulation. Zoomin on the template at the seabed. Run the animation for Stage 3 only to see one side of thetemplate hitting the seabed before the other.

3.8.4 G04 Pull Up Line End into MoonpoolExample of a line end being lifted up from the seabed into a moonpool. See the G directory inthe OrcaFlex Examples.

Introduction

A line is lying on the seabed. One end is then pulled up into the moonpool of the vessel.

Building the model

The line is positioned on the seabed using a prescribed shape. Look in plan view to see how itappears. End B will be pulled up to the vessel so is free and has its pullhead attached as aclump weight at End B, i.e. the arc length of 200m.

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A cylindrical solid represents the trapped water in the vessel moonpool. The trapped waterfacility is used here to model hydrodynamic shielding of the vessel so that wave and currenteffects are suppressed in the moonpool.

A winch on the vessel is attached to End B of the line. It is used to pull in the line while thevessel moves to keep the moonpool approximately above the line end.

The analysis is carried out with the following stages:Stage 0 Wave build up -3.5sec to 0secStage 1 Vessel accelerates to 1.6m/s. Winch pull-in 60m 0sec to 14secStage 2 Vessel moves at 1.6m/s. Winch pull-in 50m 14sec to 28secStage 3 System settles 28sec to 35secIf you look at the data for 'Winch1' you will see that an initial length of 120m has been defined.This is the distance from the winch to the attachment point. The easiest way to determine thedistance is to run statics with the winch mode set at a specified tension of zero. Statics resultsfor the winch will then report the distance to the attachment point. The winch mode can then beupdated to Specified length and that distance input.

A settle time has been allowed at the end of the analysis, as there is usually a lag in someareas of a system's response to a load. Stopping too soon can result in some behaviour beingmissed.

Results

Go to the default view, CTRL+T, and look at the animation through the whole simulation. Notehow the vessel moonpool remains above the line end during the process.

Look at the time history of riser tension at the pullhead, End B. The operation has beenmodelled in a much shorter time than would really be taken, and the results show somespurious dynamic effects in consequence. Notably, the top tension drops briefly to zero at t =28s when the winch pull-in abruptly ceases. We could reduce these false effects by carryingout the pull more slowly.

3.8.5 G05/G06 Midline Pull UpSee the G directory in the OrcaFlex Examples.

Introduction

A long line is laid on the seabed. The middle is then pulled up a short distance to allowmaintenance or to position the line in a plough.

Building the Global model

The line is positioned on the seabed using a prescribed shape. This is the easiest way ofdefining a straight line on the seabed.

The line has both ends free but they need to be sufficiently far away from the middle that theyexperience negligible loading during the lift.

The analysis is carried out with the following stages:Stage 0 System settles -0.5sec to 0secStage 1 Winch pulls in 4m 0sec to 10secStage 2 System settles 10sec to 15sec

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In Stage 1 a winch raises the middle of the line 4m, i.e. payout is -4m. The initial length ofwinch wire has been set to 100m. This is the distance from the winch to the attachment pointon the line. The easiest way to determine the distance is to run statics with the winch mode setat a specified tension of zero. Statics results for the winch will then report the distance to theattachment point. The winch mode can then be updated to 'Specified length' and that distanceinput.

Results

Go to the default view, CTRL+T, and look at the animation through the whole simulation.

The winch tension time history shows a drop in tension when it stops pulling in at 10 seconds.This is a dynamic effect causing the line to overshoot. In practice, the lift would be slower andthe overshoot smaller.

Look at the curvature range plot through Stage 2, the settle period. This reports maximum,mean and minimum curvature through the stage. Zoom in on the section near 550m arc length.The graph is very angular, indicating that there is insufficient segmentation to define thecurvature accurately. This model gives a good indication of lift force and tension in the line buta poor representation of maximum curvature.

Local model

This is a local model of the high curvature region only. Since the system is symmetrical wehave modelled a short section to one side of the lift point only and treated the cable as built inhorizontally at the lift point. The winch has been used to apply a tension of 23kN at an angle ofabout 8° below horizontal. Tension and angle are estimated from the global system model. Inpractice a static analysis of this local model would be sufficient. This is very fast and can berepeated with increasing number of segments until the curvature at the built-in end converges toa value that no longer varies with segment length.

3.8.6 G07 Pipe LiftSee the G directory in the OrcaFlex Examples.

Introduction

A steel pipe is laid on the seabed. The front section is then pulled up by a series of winchesuntil it is alongside a vessel. It is shown as a dynamic lift including wave effects, but a staticanalysis of the final configuration would often be sufficient.

Building the model

The line is positioned on the seabed using a prescribed shape. This is the easiest way ofdefining a straight line on the seabed. End A is free and is to be pulled up alongside the vessel.

Three winches are equally spaced on the vessel side and attached at End A and arc lengthsalong the pipe. They are used to pull up the line.

The analysis is carried out with the following stages:Stage 0 Wave build up -2sec to 0secStage 1 Winches pull-in 97m 0sec to 32secStage 2 System settles 32sec to 40secIf you look at the data for 'Winch A' you will see that an initial length of 112m has been defined.This is the distance from the winch to the attachment point. The easiest way to determine thedistance is to run statics with the winch mode set at a specified tension of zero. Statics results

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for the winch will then report the distance to the attachment point. The winch mode can then beupdated to 'Specified length' and that distance input.

A settle time has been allowed at the end of the analysis, as there is usually a lag in someareas of a system's response to a load. Stopping too soon can result in some behaviour beingmissed.

Results

Go to the default view, CTRL+T, and look at the animation through the whole simulation.

Look at the tension time history through the simulation for all three winches. Note that only'Winch C', furthest from the pipe free end, is in tension for the whole simulation. Why is this?

Look at the tension and curvature range plots of the pipe for the whole simulation. These plotthe maximum, mean and minimum values along the arc length from the free end to the anchor.

The tension range plot confirms that the greatest load is taken by 'Winch C', attached at an arclength of 60m. The curvature range plot also shows the greatest peak at the attachment of'Winch C'.

3.8.7 G08 Snag Pull-inSee the G directory in the OrcaFlex Examples.

Introduction

A line is pulled in to a wellhead funnel by a winch. Snag catchers ahead of the funnel controlthe pipe entry.

Building the model

The snag catchers are modelled as two lines of the required diameter. They and the pipe aregiven contact stiffness values and the clashing option found on the Structure tab of the dataform is turned on. Two cylindrical Shapes, Snag1Shape and Snag2Shape, are used to showwhere the snag catcher is located. In principle, these cylinders could have been used to controlthe line movements, but the segmentation of the pipe would have to have been very fine assolids only make contact with lines at line nodes. This would have resulted in very small stepsizes and so a very long run. Line/line contact occurs between line segments so that coarsersegmentation can be used. This model uses line/line contact, so the cylinder shapes are givenzero stiffness.

For line/line contact to be modelled, the lines concerned require a contact stiffness in theirproperties, 10MN/m in this example. Accurate contact stiffness values are rarely known forpipes: in this case, all we require is that the snag catcher effectively constrains the pipe, so anarbitrary value can be applied. See Line Clashing for interpretation of the clash forces.

To turn the clashing routine on, say 'yes' to Clash check in 'Pipe A', 'Snag 1' and 'Snag 2' pages.Note that the Clash check will result in slower runs so should only be applied where required.For 'Pipe A' it has only been selected for the first 30m of the pipe, i.e. the length expected tocontact the snag catchers.

The analysis is carried out with the following stages:

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Stage Time Winch Payout Pipe End A

'to Snag' 'to Hub'

0 -1sec to 0sec Hold Relax Settle

1 0sec to 46sec -87.84m Relax To Snag Catcher

2 46sec to 66sec Release -15m Into Funnel

3 66sec to 71sec - Hold Settle

Note that 'Relax' means the winch length varies to keep the tension at 0kN.

The winch 'to snag' has three points. It is attached to End A of the pipe, on the seabed betweenthe snag catchers then 2m vertically above the snag catchers. In Stage 1 it pulls the pipe to thepoint between the snag catchers, it then releases it.

Note that having three points for the winch and only pulling into the second ensures the winchlength is never zero. The minimum length will be 2m.

The distance required to pull in is given in the winch static results. Remember to deduct 2m forthe minimum distance.

The winch 'to hub' also has three points, again to prevent the length reducing to zero. It isattached to End A of the pipe, the far end of the funnel on the seabed and 2m vertically above it.

In Stage 2 the 'to hub' winch pulls the pipe from the snag catchers to the funnel far end. Thedistance from snag catcher to funnel end, i.e. the distance the winch must pull-in, should beknown.

The pull-in is carried out with two winches, as there is no interaction between winch wires andother structures. Therefore if one winch were used, it would pull the line straight to the funnelend, ignoring the snag catchers.

A settle time has been allowed at the end of the analysis, as there is usually a lag in someareas of a system's response to a load. Stopping too soon can result in some behaviour beingmissed.

Results

Go to the default view, CTRL+T, and look at the animation through the whole simulation.

Watch the line being pulled to between the snag catchers then into the funnel. Zoom in on thesnag catchers and funnels. Watch the line curve around one of the snag catchers.

Look at the time histories of tension in both winches through the whole simulation. Both graphsshow tension overshoots and oscillations. These are a consequence of speeding the operationto save time - the actual pull-in operation would probably take an hour or more compared toabout 1 minute here. Slowing the rate of winch pull-in will reduce the overshoots and oscillationamplitudes.

3.8.8 G09 Anchor-last DeploymentSee the G directory in the OrcaFlex Examples.

Introduction

This model shows the deployment of a typical deep water oceanographic mooring. Thesemoorings are often streamed out behind a moving vessel, with the top end buoy as the firstobject in the water, furthest from the vessel. When the whole length of the mooring has been

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deployed, the anchor is tied off at the vessel fantail, and the vessel proceeds to the correctmooring position. Without stopping the vessel, the anchor is cut free, and the whole mooringfree-falls until the anchor hits the seabed.

The simulation is used to determine the final position of the anchor relative to the vessel'sposition when the anchor ties are cut. It is also used to determine the tensions in the line.

Note that the mooring line may go slack when the anchor strikes the seabed. If the line is notperfectly torque balanced, it is possible for loops and kinks to form in the line, and these willlead to early failure of the mooring.

Building the Model

The mooring is represented by a single Line, attached between the Buoy and the Anchor, eachmodelled for simplicity as 3D buoys. (A more detailed model would use 6D buoys allowing us tostudy the pitch and roll motions of these objects). The Anchor is attached to the Vessel using aLink, which is released as soon as the simulation starts (see the Link data file). This representsthe action of cutting the anchor free.

We find an initial static position for the mooring catenary, with the Buoy at a pre-selectedposition - i.e. it is not included in the static calculation. The Vessel motion is specified in theVessel data: initially it accelerates to a steady forward velocity of 2 m/s (about 4 kts), thencontinues forward at constant velocity.

Results

Go to the default view, CTRL+T, and look at the animation for the Whole Simulation. Choose arefresh interval of 1 second, and a target speed of, say, 500%. See how the catenary shapedevelops, pulling the top end buoy down from the surface.

Look at the time histories of Effective tension at End A (the Buoy) and End B (the Anchor). Youwill be able to identify the point where the buoy submerges, and the impact forces occurringwhen the anchor strikes the seabed.

Look also at the time history of the Buoy Z coordinate. The buoy maximum depth is about 64m,compared with the static depth of about 42m. This is important when choosing the depth ratingof the buoyancy unit.

3.8.9 G10 Lower with Bend LimiterSee the G directory in the OrcaFlex Examples.

Introduction

This example shows the use of non-linear bending to represent a bend limiter on an umbilicaltermination.

A seabed template is being lowered to the seabed, with an umbilical hanging in a loose bight.When the template has landed, the top end of the umbilical is paid out, laying the umbilical onthe seabed.

Building the model

For illustration, the umbilical is attached to the top of the template. Without a bend limiter itwould suffer severe overbending. The limiter protects against this over the first 12 m of theumbilical.

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Look at the Model Browser and select Variable Data / Structure / Bending Stiffness, and pressthe Profile button. This will show you the non-linear stiffness characteristic used to model theumbilical+bend limiter combination. It has the following characteristics:

• Up to a curvature of 0.25 rad/m the bend stiffness is just that of the umbilical, since thelimiter has not yet ‘locked out’. Bend moment = bend stiffness x curvature, so at 0.25 rad/mthe moment due to the umbilical alone is 0.25 x (Umbilical Bend Stiffness) = 2.531 kN.m.

• At the 0.25 rad/m curvature limit the limiter locks and the stiffness rises sharply. This ismodelled by the steep step in the bend moment profile. It is usually sufficient to model thiswith an arbitrary large stiffness, but if the limiter is a rigid plastic material then it may beworth getting an estimated figure for its stiffness to include in the model.

• The step goes up to a bend moment of 200 kN.m and then the slope reduces again. Thishelps the static analysis to converge, since it reduces the likelihood of extremely large out-of-balance forces arising during iteration towards the static solution. It does not affect thesolution itself since the bend moment will not be anything like that high in the solution.

The non-linear stiffness is used in the Line Type Data for the Line Type called Bend Limiter.Look in the Stiffnesses tab to see where a Name has been substituted for the numerical valueof stiffness.

Finally, look at the Line Data for the Line called ‘Umb’, and choose the Structure tab. You willsee that the Bend Limiter applies over a 12 m length at the termination.

Results

Run the replay for the whole simulation and see the whole operation on screen (press CTRL T toget the pre-set default view). If you press CTRL P you will get the plan view and see how theumbilical lays out on the seabed.

Look at a range graph of umbilical curvature for the full simulation. The bend limiter is presentfor the first 12m, but there is overbending in the umbilical just beyond the end of the limiter.This indicates that the bend limiter is not long enough to protect the umbilical.

3.9 H - OFFLOADING SYSTEMS

3.9.1 H01 Stowed LineSee the H directory in the OrcaFlex Examples.

Introduction

A floating hose, which is attached to the stern of an FSU (Floating Storage Unit), is stowed bycurling it around and attaching the free end to the vessel side. Interaction with the vessel sidesneeds to be considered.

Building the model

The vessel sides are modelled as solids so that clashing can be considered. However note thatthe complex loads due to turbulence and water trapped between the vessel side and theapproaching hose are not considered. The hull is modelled as a simple rectangular blockattached to the vessel.

The hose is attached to the stern of the vessel and on the port side, near the bow. It ismodelled as three lines: Hose Top runs from the vessel stern to a clamp where a 'hold back'

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chain is attached. Hose Mid runs from the clamp to a Mid-line Connector (MBC). Hose Botruns from the MBC to the vessel side.

The clamp and MBC are modelled as 6D spar buoys, as bending moments need to betransferred between the hose lines. Note that this means the lines are attached to the buoyswith Encastré ends, i.e. infinite bend stiffness, and line headings at the ends must be defined.

At intervals, clump weights are attached representing flange connections. These are attachedto nodes so the segment lengths must be arranged so that a node is present at each flangelocation.

As the lines are not in a catenary shape and 'quick' statics would start off with the lines insidethe solid, the best starting point for statics is a spline. Look in plan view, CTRL+P, to see theshape. It need only be approximate, as full statics convergence will refine the shape.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave.

The range graphs of solid contact force during the latest wave show that the first and lastlengths, 'Hose Top' and 'Hose Bot', both contact the hull of the vessel.

Looking at the time history of contact force at an arclength of 15m for 'Hose Top' and 35.7m for'Hose Bot' shows more detail of the contact loads.

3.9.2 H02 Floating LineSee the H directory in the OrcaFlex Examples.

Introduction

The same hose as in the previous example is now modelled trailing free from the FSU stern.During the analysis, the protective chain at the FSU breaks.

Building the model

The basic model structure is described in the example Stowed Line.sim. However in this caseEnd B is free and the line extends behind the vessel.

To assist in static convergence of the free-ended floating hose, a winch is attached. Thisapplies a small tension to encourage the hose into a straight line. This winch releases at thestart of dynamic analysis.

The analysis is carried out with the following stages:Statics Winch applies 0.1kN tensionStage 0 Winch releases and wave builds up -6sec to 0secStage 1 Simulation 0sec to 18secStage 2 Chain releases 18sec to 36secIf you look at 'Temp Winch' data you will see it releases at the start of Stage 0. End B of 'Chain'releases at the start of Stage 2.

Results

Go to the default view, CTRL+T, and look at the animation through the whole simulation. Look atthe transverse waves being generated along the line due to compression.

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At 18 seconds the chain releases and can be seen hanging free. Look at the time history oftension in the chain and the hose at End A, the vessel. The chain protects the hose by taking150kN of load in the first wave cycle. However after 18 seconds the chain is no longerconnected and the hose connection must take the entire load itself, shown as a tensionincrease.

3.9.3 H03 Jacket to SemisubSee the H directory in the OrcaFlex Examples.

Introduction

A cable catenary is suspended between a semi-submersible rig and fixed jacket. It is analysedin a random sea.

Building the model

Both the jacket and the semi-submersible are modelled as vessels. Although the jacket doesnot move, being a vessel allows the drawing facilities to be applied and objects to be attachedto it. To ensure it does not move, the 'Jacket' RAOs are all set to zero. Circular symmetry isapplied so the values are valid for all wave headings.

From the Model Browser, select ‘Cable’. Note that the Semisub connect has the EndOrientation Gamma angle set at 90º. When torsion is not applied, gamma can be used todefine the orientation of End x and y about z. This is convenient if you want all x axes to benormal to the vessel side and all y axes to be parallel, so that result presentation follows oneconvention.

In this example, setting gamma to 90º makes the x axis of the end connection normal to thesemisub side, and y parallel to it. This matches the x and y orientations at the Jacket End.Select the view and press CTRL+Y. The end axes will appear in the view. Press CTRL+Y again toturn them off.

The main concern in this example is clashing between the cable and the jacket structure. Thisis best assessed visually. A jacket strut has been made from a line. It has dummy propertieswith the diameter set to that for the strut. It has then been attached to the jacket. As it is toremain straight, it can be modelled as one segment. Keeping the length slightly shorter than thedistance between End A and End B just makes the statics convergence a bit easier.

A line is preferable to a solid for this clashing model. Solids only contact line nodes. The cablecould slide and allow the solid to fall between nodes. This does not occur with line/line contact.

For line/line contact to be modelled, the lines concerned require a contact stiffness in theirproperties. We have used 100 kN/m in this example, and have applied damping of 1 kN/(m/s).

Contact stiffness values are rarely known for pipes so an arbitrary value can be applied. For aviolent impact the contact impulse will be insensitive to contact stiffness. For a low speedcontact the contact force will be insensitive. See Line Clashing.

To turn the clashing routine on, say 'yes' to Clash check on the Structure tab in the data formsfor the lines 'Structure' and 'Cable'. Note that the Clash check will result in slower runs soshould only be applied where required. For 'Cable' it has only been selected for the last 100mof the line, i.e. the length expected to contact the jacket.

A random wave train has then been applied. For details see Setting Up a Random Sea.

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Results

Time histories and range graphs are available as usual but in these cases the view gives theanswers we need. Go to the default view, CTRL+T and look at the full simulation. Note how thecable curves around the strut in the larger waves.

3.10 I - TOWED ARRAYS

3.10.1 I01 Streamer ArraySee the I directory in the OrcaFlex Examples.

Introduction

This is an example of a seismic streamer model. The model represents the Port half of thesystem only i.e. two hydrophone streamers plus one air gun towed from a ship.

Building the model

The diverter is modelled as a 6D buoy with wings attached. These generate the directional liftand drag from the diverter being towed through the water. See 'Prandtl199' on the Wing Typesdata form. Pressing the Graph button will show you the lift and drag coefficients versus incidentangle. Select any item on the Wing Types data form and press F1 to get more details from theon-line help.

Lines cannot be connected directly to lines in OrcaFlex. Branching is therefore achieved using3D buoys. These are acceptable, as transfer of bending moment between lines is not importantfor this example.

Rather than modelling the two streamers in full, most of each length is represented by a "seaanchor", a 3D buoy with area and drag coefficient set to generate a drag force equivalent to thatof the streamer length it represents. Look at 'StrmTail A' data.

Getting the initial static position for this type of system can be difficult. There are many buoysso the system has a large number of degrees of freedom. However OrcaFlex allows you to lockindividual buoys in place during static analysis. Therefore as each buoy static location is found,it can be held in place and does not have to be recalculated in subsequent static analyses asyou determine other buoy positions.

The motion of the whole system through the water can be modelled within OrcaFlex in twoways. The vessel can be given a constant forward velocity. However this means that thesystem origins are constantly moving in relation to the global origin. Also the system will keepmoving out of the view window.

Alternatively, as the system is moving in a straight line, it can stay put and a current can beapplied in the opposite direction of the same velocity and through the full water depth. In bothmethods the water velocity and heading relative to the system is the same. However applyingthe current is more convenient for analysis of results. This is the method applied here.

Remember to take account of any actual current applied when using this method.

Results

Go to the default view, CTRL+T, and look at the animation through the latest wave. Look inelevation view, CTRL+E, as well as the default plan.

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Plot time histories of the lift, drag and incident angle for the diverter wings. To access these youneed to select 'Diverter' for Object on the results page then turn on 'Results for wings'. Notehow the lift is far greater than the drag and that the incident angle only varies by 3.5º.

3.10.2 I02 Deployment with SubSee the I directory in the OrcaFlex Examples.

Introduction

A submarine tows a sensor array. It releases components in turn to position them on theseabed.

Building the model

The system is to be installed using a submarine. This is modelled as a vessel with a slightresponse to the wave loading, see the RAO data. The shape is generated using solids attachedto the vessel. A line extends behind the vessel with a 6D towed fish, best for horizontalcylinders, attached at the far end to represent the deployer.

Lines connect each float to an anchor while, for towing, a short link holds each float close to itsanchor. A line also connects the anchors together so that a required maximum separation isnot exceeded. The anchors are then each attached to the deployer by a short link.

The two floats are modelled as 3D buoys, i.e. translations only, as the detailed motions of thefloats are not of interest. The two anchors are modelled as 6D buoys to better model interactionwith the seabed, for example if one edge will contact first.

The analysis is carried out in the following stages:

Stage Vessel Links Time

0 Accelerates to 1.5m/s - -10sec to 0sec

1 Proceeds at 1.5m/s 1st anchor released so anchorand float sink towards seabed

0sec to 5sec

2 Proceeds at 1.5m/s 1st float released so rises up 5sec to 30sec

3 Proceeds at 1.5m/s 2nd anchor released so anchorand float sink towards seabed

30sec to 35sec

4 Proceeds at 1.5m/s 2nd float released so rises up 35sec to 75sec

Note that the vessel is allowed to accelerate to 1.5m/s during Stage 0, the build-up stage, seethe Prescribed Motion tab on the 'Submarine'data form. At the same time the wave height isincreasing to the required maximum. This means that the system has a gentler start, reducingor avoiding transient responses.

Results

Go to the default view, CTRL+T, and look at the animation through the whole simulation. Notehow the deployer sinks at the start of the analysis unit then rises as it gets lighter, due to therelease of the anchors. Look at the animation in plan view, CTRL+P, see how the line has movedout of plane as it falls, slack, onto the seabed.

Look at the full tension time history for 'Sensor1' at any point. This is the line supported by the1st float. You will need to amend the Y-axis scale to -1kN to 6kN as transient tension at thevery start of the model has resulted in a large scale. Note the snatch load at 10sec as the floatrises to the full extent of the line.

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3.11 J - PRE AND POST PROCESSING

3.11.1 J01 Batch ScriptA simple example batch script is shown below. In addition the J01 directory in the OrcaFlexExamples contains some simple ready-to-run example batch script files.

//Example batch script file to run 3 variations//on a pre-prepared base data file.load BaseData.dat

select seaselect wavetrain Primary WaveTrainHeight = 10 WaveTrainDirection = 150run H10_D150.sim

select seaselect wavetrain Primary WaveTrainHeight = 12 WaveTrainDirection = 180run H12_D180.sim

select seaselect wavetrain Primary WaveTrainHeight = 15 WaveTrainDirection = 210run H15_D210.sim

3.11.2 J02 ResultsSee the J02 directory in the OrcaFlex Examples.

Introduction

System optimisation is often achieved by running a set of OrcaFlex analyses varying one ormore parameters systematically. As a simple example, we take a lazy wave riser configurationwith distributed buoyancy. A batch script file is used to carry out a series of increases to thebuoyed length of the riser and to generate simulation files. The results of these runs are thencompared using an OrcaFlex Results spreadsheet within Excel. An optimum buoyed length canthen be identified.

Building the model

Two files are needed.

a) Basecase.dat: This is a standard OrcaFlex model of a lazy wave configuration. It is set upfor one of the permutations to be considered. Modifying this file with Script.txt will generatethe other cases.

b) Script.txt: This is a text file containing instructions on what to do with the base case. Firststep is to load basecase.dat. It is then run to generate the first set of results, 70.sim. Notethat saving of simulation files is automatic. The second section of 'Riser A' then has itslength modified to 80m and is run and saves as 80.sim. This is then repeated for two furthercases.

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The file Script.txt is run as an OrcaFlex batch. Open OrcaFlex and go to the Calculation menu.Select 'Batch Processing' then 'Add File'. The script file can be selected just as a data orsimulation file would. See Batch Processing for further information.

Results

Open the spreadsheet Results.xls. This is an OrcaFlex Results spreadsheet that has been setup to automatically extract and summarise results from the simulation files generated by thebatch script.

The spreadsheet has six worksheets - an instructions worksheet, one worksheet for the resultsfrom each simulation file, and a worksheet giving a summary of all the results.

The 'Instructions' worksheet has an instructions table that specifies which results to extract, plustwo buttons that trigger macros to obey those instructions. The instructions in the table are ingroups (highlighted using Excel formatting, but this is optional), each of which consists of aLoad command to open one of the simulation files, followed by a series of other commands toretrieve various results from that file and place them in the appropriate worksheet.

When you press the Process button the spreadsheet executes a macro that reads and obeysthe instructions in order. The first group of instructions consists of a 'Load' command to openthe simulation file 70.sim, followed by a series '70'. There are then similar blocks of instructionsto extract the corresponding results from the other simulation files.

Instructions are only carried out when you press one of the process buttons at the top of the'Instructions' sheet. If any simulation files are modified, the button can be pressed again togenerate updated results.

Look at sheet '70' and 'Summary' to see how the results can be presented and an example ofwhat can be done with them.

3.11.3 J03 Stress AnalysisSee the J03 directory in the OrcaFlex Examples.

Introduction

The stresses in steel risers due to wave loads are usually required. OrcaFlex obtains these inthe post processing stage, using a Stress spreadsheet in Excel.

This example obtains stress results for a simple steel catenary suspended from a vessel in twodifferent wave conditions.

Building the model

An OrcaFlex model is set up with a steel riser hanging down from a vessel in a simple catenary.

The riser properties are generated using the Line Type Wizard routine. Reset the simulation sothe datafile can be accessed and open the Line Types data form. Select 'Pipe' then press theWizard button and step through the pages to see how the properties were built.

Note that OrcaFlex can cope with the load bearing wall thickness being less than the total wallthickness, due to linings and coatings. Look at the Stress tab on the Line Types data form. Theouter and inner diameters to be used for stress analysis can be input here if they are differentfrom the overall diameters. See Stress Diameters for details.

If wall tension and maximum stress results are required then an internal pressure at End A ofthe line must be specified. See the Riser data form where pressure is set at 23.2x10^3 kN/m^2(23.2MPa) for this case. See Line Pressure Effects for more details.

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For a comparison of results, the cases need the same segmentation. This means node 5 inExample1 is at the same arc length as node 5 in Example2.

Similarly, they must have a sufficient simulation period. If you want results from 26sec to 39sec,both cases must have results to at least 39sec.

The system is then analysed in two different wave conditions, generating two simulation filesExample1.sim and Example2.sim.

Results

OrcaFlex comes with an Excel template called 'Stress'. This allows you to set up Excelspreadsheets that can access OrcaFlex simulation files and retrieve results. The results canthen be manipulated on standard Excel sheets in the usual manner.

Open the spreadsheet, Stress.xls, from the Examples directory using Excel and look at thethree sheets. The first is the instruction sheet. This has been generated using the Stresstemplate. The other two are where the retrieved results from the two simulation files have beenplaced. They have been generated by pressing the 'Add Load Case Sheet' button and inputtingthe filename and line name.

Look at the first worksheet called 'Main Sheet'. In this example the spreadsheet will reportradial, hoop and axial stress at an arc of 60m from End A. As only two theta values are to bereported, results will be at 0 degrees and 180 degrees about the inner circumference.

Instructions are only carried out when the 'Collect Results' button is pressed on the first sheet.If any simulation file is modified, the spreadsheet can be run again to generate updated results.

Look at the Case1 worksheet to see how the results are presented. The pathname for thesimulation file needs to be input, as does the line name. This case will open Example1.sim andobtain the results for the line 'Riser'.

To see the stress results being collected, check that the pathnames are correct for the Examplelocations on your machine then press 'Collect Results'.

3.11.4 J04 Fatigue analysisSee the J04 directory in the OrcaFlex Examples.

Introduction

Rigid pipes are vulnerable to fatigue. OrcaFlex has a post-processing routine that extracts lineload results from a series of pre-run regular simulation files, calculates the resulting pipe stressranges and then calculates the fatigue damage. See Fatigue Analysis and related topics.

This example is a steel catenary riser suspended from a semi-submersible FPSO as usedoffshore Brazil. The model contains three risers suspended from two semisubs so that each filegenerates results for Near, Far and Transverse cases using waves and current from 0 deg.

Building the model

A base case is built consisting of three steel risers suspended from two semisubs in simplecatenaries. They are configured so that the Near, Far and Transverse results are generatedfrom one wave and current heading (0 degrees); see Base.dat.

As maximum stress results are required, an internal pressure at End A of the line must bespecified, see any line page. See Line Pressure Effects for more details.

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Six simulations at different wave heights are then carried out using the OrcaFlex batch fileFatigue.txt (see example J01: Batch Script for information on batch language). This generatesCase#02.sim, Case#04.sim, Case#06.sim, Case#08.sim, Case#10.sim and Case#12.sim.

Note that the line segmentation must be the same for all the cases in the fatigue analysis.

Results

Open the fatigue analysis tool by selecting Fatigue Analysis on the Results menu. Open theexample fatigue file Case#01.ftg. This shows a typical fatigue analysis, using the simulationfiles generated above.

The Load Cases tab defines the pathname for each case, the line to get results for andspecifies the number of wave cycles, of this particular set of load conditions, that the line willexperience. These data are usually extracted from a wave scatter diagram for the area.

The Analysis Data tab specifies the units to use in the analysis. These need not match thoseused in the simulation files. Note that a user-defined combination is used in our example.

It will collect data over two arc lengths, End A to 80m (the top of the riser) and 400m to 800m(the touchdown zone). For each arc length a different stress concentration factor and S-N curvecan be defined.

In this example it will report results every 2m over the specified arc length at eight points aroundthe pipe circumference, i.e. every 45 degrees. It will also highlight any total damage thatexceeds the specified critical value of 0.02.

The settings can be retained by selecting Save on the File menu. They are then saved as a*.ftg file.

Before carrying out the analysis, it is advisable to perform a preliminary check of the fatigueanalysis data, using Analysis / Check or the icon at the top of the window. This checks that allthe specified load case simulation files exist and that the named line and the specified arclength intervals exist in each load case.

To carry out the analysis, select Analysis / Calculate from the top menu or the icon at the top ofthe window. The fatigue analysis can take a long time if there are many load cases, or if thereare many log samples in the load case simulations, or finally if there are a lot of segments in thearc length intervals specified. A progress window is displayed and you can cancel the analysisif desired.

When the calculation is complete the results are displayed in a spreadsheet window. Thisneeds to be exported to an Excel spreadsheet if they are to be saved. Either copy and pasteinto an open spreadsheet or click with the right mouse key and export into a *.xls file.

Check the file pathnames are correct for your machine then run this example or look at theexcel file, Damage.xls, which contains the results. Note that generating the results may takesome time.

3.12 K - LINE ON LINE CONTACT

3.12.1 K01 Line on Line ImpactSee the K directory in the OrcaFlex Examples.

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Introduction

OrcaFlex allows you to prevent lines passing through each other in the dynamic analysis.When the option is selected on both lines it generates a resistive force when one line contactsthe other. This routine also takes account of line outer diameters when assessing contact.

In this example a line free at one end is swung to hit a second held at both ends in a curve.

Building the model

Two lines are generated called 'Anvil, the line that is hit, and 'Hammer', the one that swings tohit the first. 'Hammer' is made to swing simply by releasing End A at the start of Stage 1, i.e.after the build-up period.

To prevent one line passing through the other, both require contact stiffnesses to be set andclash check to be selected.

Contact stiffness is specified in the Line Types data form on the 'Friction and Clashing' tab. Thisis rarely known for pipes so an arbitrary value can be applied. The stiffness should besufficiently high that one line cannot push through the other. In this case 5MN/m is applied.

Variations in stiffness will vary the magnitude of the contact force reported but the contactenergy will be unchanged and can be derived from the results. See Line Results: Clashing.

To turn the clashing routine on, say 'yes' to Clash check on the Structure tab in the data formsfor both lines 'Anvil' and 'Hammer'. Note that the Clash check will result in slower runs soshould only be applied where required. In this case it is applied along the full arc length for bothlines but it can be applied to individual sections of the line. See the examples Jacket toSemisub and Line on line slide.

Results

Go to the default view, CTRL+T, and look at the animation through Stage 1, i.e. from the moment'Hammer' is released. It swings across to 'Anvil' which it pulls with it before it swings back andaway.

Plot a range graph of Line Clash Force for 'Anvil' through the whole simulation. The maximumclash force occurs at an arc length of 52.5m. Look at time histories of Line Clash Force andClearance at this arc length. They are in the Clashing variable set.

Note the noise in the clash force plot where the lines have bounced against each other after theinitial impact.

Also notice that the clearance plot does not go to zero. Clearance is reported betweencentrelines. As clashing takes account of the outer diameters, clashing occurs when clearanceis less than or equal to the total of each lines radius.

3.12.2 K02 Line on Line SlideSee the K directory in the OrcaFlex Examples.

Introduction

The line clashing routine can be used to model one line sliding over another. Howeverremember that friction is not included and this will only occur in dynamics. A fun example of thisis given below.

A boy scout slides down an aerial ropeway by holding onto the ends of a short rope wrappedover it. He then flies off the end to hit the ground.

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Building the model

The system is submerged but the seawater density has been set at 1.28kg/m³, the density ofair. A solid fixed in space makes the platform that the scout stands on at the start of theanalysis.

The scout is modelled as a 6D buoy, which is fixed in statics. Properties for a typical 10 yearold scout have been applied but drag and added mass are ignored as he is moving in air, sogenerated loads will be negligible. The arms and legs are then drawn using the buoy drawingfacilities.

Solids are attached to the buoy to make the head and body shapes. Lines are attached alongthe spine and across the bottom to give a friction force when the scout hits the ground. Byapplying mass to these lines, the weight distribution is varied so that the scout will land on hisback.

The ropeway is a simple line inclined and held at both ends. The hanger is also a simple rope,however to model the effect of line/line friction, the central section in contact with the ropewayhas a large normal drag coefficient applied.

Both the ropeway and the central section of the hanger have a contact stiffness and clashingcheck running so they cannot pass through each other. See the Clashing example for moreinformation on this.

To prevent one line passing through the other, both require contact stiffnesses and 'ClashCheck' selected. Contact stiffness is specified in the Line Types data form. It should besufficiently high that one line cannot push through the other.

To turn the clashing routine on, say yes to Clash check on the Structure tab in the data formsfor both lines 'Ropeway' and 'Hanger'. Note that the Clash check will result in slower runs soshould only be applied where required. In this case it is only applied along middle section forthe hanger.

Links A and B hold the hanger up above the ropeway during statics then release at the start ofStage 0. This is required as the statics needs to be told on which side of the ropeway thehanger is, and because the clashing routine only operates in dynamic analysis.

Results

Go to the default view, CTRL+T, and look at the animation through the whole simulation. Thescout slides along the line then flies off the end to somersault on the ground.

Look at the time history of line clash force on the hanger middle. Note how the hanger bounceson the ropeway as it slides down. Look at the Z time history for the boy scout. Note how heflies up after leaving the ropeway before descending to bounce on the ground.

3.13 L - RAO IMPORT

3.13.1 Example RAO Text FileA simple example RAO text file is shown below. In addition the L directory in the OrcaFlexExamples contains a ready-to-import example file.

***OrcaFlex RAO Start Data***Draught TransitDirection 0WP XA XP YA YP ZA ZP RXA RXP RYA RYP RZA RP0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

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7.0 0.1 5.0 0.0 0.0 0.3 -20 0.0 0.0 0.7 46 0.0 0.08.0 0.3 75 0.0 0.0 0.3 +80 0.0 0.0 1.2 90 0.0 0.0Infinity 1.0 90 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0***OrcaFlex RAO End Data***

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4 USER INTERFACE

4.1 INTRODUCTION

4.1.1 Program WindowsOrcaFlex is based upon a main window that contains the Menus, a Status Bar, a Tool Bar andusually at least one 3D view of the model. The window caption shows the program version andthe file name currently in use for either data (.DAT) or simulation files (.SIM).

Within this main window, you can place a selection of subordinate windows which may be:3D View Windows showing 3D pictorial views of the modelGraph Windows showing results in graphical formSpreadsheet Windows showing graph results in numerical formText Windows showing results in numerical formYou can arrange windows as desired - they can be laid on top of each other (cascaded), orside-by-side (tiled), but are restrained within the bounds of the main window.

Additional temporary windows are popped up, such as Data Forms for each object in the model(allowing data to be viewed and modified) and Dialogue Boxes (used to specify details forprogram actions such as loading and saving files). While one of these temporary windows ispresent you can only work inside that window - you must dismiss the temporary window beforeyou can use other windows, the menus or toolbar.

The actions that you can perform at any time depends on the current Model State.

Arranging Windows

3D Views, Graphs and Text Windows may be laid on top of each other (cascaded), or side-by-side (tiled), but are restrained within the bounds of the main window. There is always at leastone 3D View window but you may arrange other windows as desired, using commands from themenu and tool bar to build and run models, and then view the results.

If Auto-Arrange is selected then the program rearranges the windows using the current schemeevery time a new window is created. Otherwise you can pull the window borders to anylocations that you desire.

Tip: After creating or closing a window, press F4 or SHIFT+F4 for a quick tidy-up ofyour screen.

You may drag windows around using the caption bar, and may even slide them off the edges ofthe screen - a scroll bar appears so that you can reach them. In this way you can lay evenlarge windows out side-by-side.

4.1.2 The ModelOrcaFlex works by building a mathematical computer model of your system. This modelconsists of a number of objects that represent the parts of the system - e.g. vessels, buoys,lines etc.

Each object has a name, which can be any length. Note that the names are case-sensitive, soRiser and riser are two different names.

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The model always has two standard objects:

• General: contains general data, such as title, units etc.

• Environment: represents the sea, seabed, waves, current etc.

You can then use the Model Browser or the toolbar to add other objects to represent the partsof you system. There is no limit, other than the capacity of your computer, to the number ofobjects you can add to the model.

At any time, you can save your model to a data file - you can then reopen it at a later date tocontinue work.

4.1.3 Model BrowserAt any time you can use the Model Browser to see what objects you have in your model. To

display the model browser, use the model browser button or the Model|Model Browsermenu item, or use the keyboard shortcuts (F2 to open the model browser and ESC to close it).

The Model Browser consists of a list of all the objects in the model, arranged into categoriesaccording to object type. Several symbols are used in the list of objects:

Categories can be opened, to show their contents, or closed, tosimplify viewing a complex model.

Objects. Use double click to view or edit the object’s data.

Types such as the Line Types, Vessel Types. Use double click toview or edit the data.

Locked

You can navigate the list and select the object required by clicking with the mouse, or using thearrow keys and return. If the list is longer than the window then you can either enlarge thewindow or use the scroll bar.

Model Browser Facilities

The model browser menus, and its pop-up menu, provide the following model managementfacilities. For details of keyboard shortcuts see Keys on Model Browser.

Add Add a new object to the model.

Delete Delete the selected object from the model.

Cut/Copy Cut or Copy the selected object to the clipboard.

Paste Paste an object from the clipboard into the model. If the object is the Variable Datathen all the variable data tables are pasted in, with tables being renamed ifnecessary to avoid clashing with existing variable data names.

Note: You can use Cut/Copy and Paste to transfer objects between two copies ofOrcaFlex running on the same machine. You can also use it to transferobjects between two OrcaFlex data files (open the source file and copy theobject to the clipboard, then open the destination file and paste the objectback from the clipboard), but the Library facility (see below) provides aneasier way of achieving the same thing.

Locate Finds and highlights the object, by briefly flashing it on the currently selected 3Dview. This is useful in complex models where many objects are on the 3D view.

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Edit Open the object's data form.

Rename Rename the selected object. You can also rename by single-clicking the selectedobject.

Lock/Unlock Lock or unlock the selected object.

Hide/Show Control whether the selected object is drawn on 3D views.

Reorder You can use drag+drop with the mouse to reorder objects in the model. This isuseful if you are working on the static position of one particular line - you can dragit up to the top of the list of lines, so that it will be tackled first when OrcaFlex doesthe static analysis.

Library The Library menu facilities allow you to open a second data file. You can thenImport objects from that second file into the current model, or Export objects fromthe current model into the second file. You can also do Import/Export usingdrag+drop with the mouse. For details see Libraries.

Notes: The second data file is referred to as the library model, but in fact it can be anyOrcaFlex data file. The library facilities therefore provide an easy way to moveobjects between different OrcaFlex data files.

If the object being imported or exported is the variable data then all thevariable data tables are transferred, with tables being renamed if necessary toavoid clashing with existing variable data names.

Switch The browser's Window menu enables you to switch focus to the main form withoutclosing the browser window. A corresponding command on the main form'sWindow menu switches focus back.

4.1.4 LibrariesLibrariesAn OrcaFlex Library is a collection of OrcaFlex objects (line types, lines, buoys etc.) stored inan ordinary OrcaFlex data file. For example, a library may contain all the standard Line Typesthat you use regularly. Once such a library file has been built you can quickly build new modelsusing the library - this gives faster model building and can make QA procedures safer.

To open a library file, use the File|Libraries menu or the Library menu on the Model Browser.Note that any OrcaFlex data file can be opened as a library file, and this makes it easy to usethe model browser to copy objects from one model to another.

Building a LibraryTo build a library file run OrcaFlex and select Libraries|New Library from the File menu. Themodel browser appears and looks like:

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The left hand pane is the model currently open in OrcaFlex and the right hand pane is thelibrary. The library is simply another OrcaFlex model, except that instead of being a model ofan actual system, it usually contains just a collection of objects.

Note: Because they are OrcaFlex models, libraries contain General andEnvironment data, but these would not usually be used, except perhaps forthe model title, which can act as a title for the library.

To build up the library model, use the File|Open menu to open an existing data file that containsobjects you want to add to the library. This model then appears in the left pane and you cannow export objects from it into the library. To do this, select the object in the left pane (single-click) and then use the Export button (>>). Alternatively, you can simply drag the object fromthe current model (left pane) and drop it into the library model (right pane). After adding therequired objects, the model browser might look like:

You can now open other data files and export objects from them to the library. When you havefinished building up the library, you can save it to a library file using the Library|Save menuitem.

Note: Because the library file is just an ordinary OrcaFlex data file, it can also beopened using File|Open. This allows you to edit the data of the objects in thelibrary.

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You can set up as many library files as you wish. For example you might have separatelibraries for Line Types, Attachment Types, Vessel Types etc., or you may choose to use justone library for everything. The model browser's Library menu contains a list of the mostrecently used libraries.

Using LibrariesOnce you have set up your library, you can very quickly import objects from it into your currentmodel. To do this, use the Library menu to open the library, then select the object you want toimport and click the Import button (<<). Alternatively, you can simply drag and drop the objectfrom the library model (right pane) to the current model (left pane). When you have finishedwith the library file, close it using the Library|Close menu item.

Finally, here are some other points about using library files.

• Because library files are simply ordinary OrcaFlex data files, you can temporarily treat anyOrcaFlex data file as a library. This allows you to easily import objects from one OrcaFlexdata file to another.

• You can re-size the Model Browser by dragging its border. You can also control the relativesizes of its two panes, by dragging the right border of the left pane.

• You can view, but not edit, the data for a library model object, by double clicking it in theModel Browser or by selecting it and using the pop-up menu.

• You can rename objects in the current model or in the library model. To do this, either usethe pop-up menu, or else single click the object twice.

• When an object is imported from or exported to a library, the destination model may alreadyhave an object of that name. In this case OrcaFlex automatically gives the object a newname based on the old name; you may wish to alter this name.

• If the object being imported or exported uses a type - e.g. a line type or vessel type - thenOrcaFlex automatically imports or exports all the types that the object uses. If the names ofany of those types match names already in the destination model, then OrcaFlex needs toknow which ones to use - the ones already in the destination model or the ones in thesource model. If this situation arises then OrcaFlex warns you and gives you the followingoptions:

Use Existing: The type is not transferred. Instead, the transferred object will use the type,of that name, that already exists in the destination model.

Rename: This option transfers the used type, giving it a new name, and the transferredobject uses the transferred type.

Use All Existing: This option applies the Use Existing option to all remaining types usedby the object. So for all remaining types used by the object, the types already in thedestination model are used, whenever their names match the types used.

Rename All: This option applies the Rename option to all remaining types used by theobject. So all the remaining types used by the object are transferred, using new nameswhere needed, and the transferred object uses the transferred types.

4.1.5 Model StatesOrcaFlex builds and analyses a mathematical model of the system being analysed, the modelbeing built up from a series of interconnected objects, such as Lines, Vessels and Buoys. Formore details see Modelling and Analysis.

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OrcaFlex works on the model by moving through a sequence of states, the current state beingshown on the status bar. The following diagram shows the sequence of states used and theactions, results etc. available in each state.

RESET

CalculatingStatics

Simulating

STATICS COMPLETE

SIMULATIONPAUSED

or STOPPED

CalculateStaticPosition

Reset

Reset

Edit orReset

Run

Pause Run

Figure: Model States

The states used are as follows:

Reset

The state in which OrcaFlex starts. In Reset state you can freely change the model and edit thedata. No results are available.

Calculating Statics

OrcaFlex is calculating the statics position of the model. You can abort the calculation byCLICKING the Reset button.

Statics Complete

The statics calculation is complete and the static position results are available. You are allowedto make changes to the model when in this state but if you make any changes (except for veryminor changes like colours used) then the model will be automatically reset and the staticsresults will be lost.

Simulating

The dynamic simulation is running. The results of the simulation so far are available and youcan examine the model data, but only make minor changes (e.g. colours used). You cannotstore the simulation to a file while simulating - you must pause the simulation first.

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Simulation Paused

There is a simulation active, but it is paused. The results so far are available and you canexamine the model data. You can also store the part-run simulation to a file.

Simulation Stopped

The simulation is complete. The simulation results are available and you can store the resultsto a simulation file for later examination. You must reset the model, by CLICKING on the Resetbutton, before significant changes to the model can be made.

4.1.6 Using Model StatesTo illustrate how model states work, here is an example of a typical working pattern:

1. In Reset state, open a new model from a data file or use the current model as the startingpoint for a new model.

2. In Reset state, add or remove objects and edit the model data as required for the newmodel. It is generally best to use a very simple model in the early stages of design and onlyadd more features when the simple model is satisfactory.

3. Run a static analysis (to get to Statics Complete state) and examine the static positionresults. Make any corrections to the model that are needed - this will automatically reset themodel. Steps (2) and (3) are repeated as required.

4. Run a simulation and monitor the results during the simulation (in Simulating state).

5. If further changes to the model are needed then Reset the model and edit the modelaccordingly. Steps (2) to (5) are repeated as required.

6. Finalise the model, perhaps improving the discretisation (for example by reducing the timestep sizes or increasing the number of segments used for Lines). Run a final completesimulation (to reach Simulation Stopped state) and generate reports using the results.

4.1.7 ToolbarThe toolbar holds a variety of buttons that provide quick access to the most frequently usedmenu items. The selection of buttons available varies with the current Program State.

Button Action Equivalent Menu ItemOpen File | Open

Save File | Save

Model Browser Model | Model Browser

New Vessel Model | New Vessel

New Line Model | New Line

New 6D Buoy Model | New 6D Buoy

New 3D Buoy Model | New 3D Buoy

New Winch Model | New Winch

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New Link Model | New Link

New Shape Model | New Shape

Calculate Statics Calculation | Statics

Run Simulation Calculation | Run Simulation

Pause Simulation Calculation | Pause Simulation

Reset Calculation | Reset

Start Replay View | Start Replay

Stop Replay View | Stop Replay

Step Replay Forwards View | Step Replay Forwards

Edit Replay Parameters View | Edit Replay Parameters

Add New 3D View Window | Add 3D View

Examine Results Results | Select Results

Help Contents and Index Help | Contents and Index

4.1.8 Status BarThe Status Bar is divided into three fields:

The Message Box

At the left hand end. It shows information about the progress of the current action, such as thename of the currently selected object, or the current iteration number or simulation time. Errormessages are also shown here.

When a statics calculation is done messages showing the progress of the calculation are shownin the message box. To see all the messages from the statics calculation CLICK on themessage box - the Statics Progress Window will then be opened.

CLICKING here outside a statics calculation displays the Session Log.

The Program State Indicator

In the centre and shows which state the program is in (see Model States).

The Information Box

This is on the right. It shows additional information, including:

• The global coordinates of the position of the cursor, in the current view plane.

• Distances when using the measuring tape tool.

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4.1.9 Mouse and Keyboard ActionsAs well as the standard Windows mouse operations such as selection and dragging OrcaFlexuses some specialised actions. Clicking the right mouse button over a 3D View, Graph or TextWindow displays a pop-up menu of frequently used actions, such as Copy, Paste, Export etc.For 3D Views and Graph Windows the mouse can be used for zooming. Simply hold the ALTkey down and using the left mouse button, drag a box over the region you want to view.

All of the menu items can be selected from the keyboard by pressing ALT followed by theunderlined letters - this is described in your Microsoft Windows Manual.

Example: To exit from the program (menu: File | Exit) press ALT+F then X, or ALT then Fthen X

A number of frequently used menu items may also be accessed by "hot keys", such as CTRL+Rto start a replay. See the tables below. We suggest that as you become more familiar with theoperation of OrcaFlex that you memorise some of the hot keys for actions that you usefrequently.

Keys on Main WindowHelp F1

Print F7

Show Model Browser F2

Switch between Model Browser and Main Window SHIFT+F2

Calculate static position F9

Run simulation F10

Pause simulation F11

Reset simulation F12

Open results selection form F5

Go to next window CTRL+F6

Go to previous window SHIFT+CTRL+F6

Tile windows F4

Cascade windows SHIFT+F4

Close selected window CTRL+F4

Close program ALT+F4

Keys on Model BrowserRename object F2

Lock object CTRL+L

Cut object CTRL+X

Copy object CTRL+C

Paste object CTRL+V

Delete object DEL

Close browser ESC

Keys on Data FormsHelp F1

Go to next data form F6

Go to previous data form SHIFT+F6

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Display batch script names for currently selecteddata item or table.

F7

Close form ALT+F4

Data Selection KeysGo to next data item or table TAB

Go to previous data item or table SHIFT+TAB

Go to data item or table labelled with underlined letter ALT+LETTER

Move around within a table ← → ↑ ↓

Select multiple cells in table SHIFT + ← → ↑ ↓SHIFT+HOMESHIFT+END

Go to first or last column in table HOME, END

Go up or down table several rows at a time PGUP, PGDN

Data Editing KeysEnter new value for selected cell Type new valueEdit current value of selected cell F2

Move around within new data value being entered ←, →, HOME, END

Accept edit RETURN

Accept edit and go to adjacent cell in table ↑, ↓

Cancel edit ESC

Cut selected cell(s) to clipboard CTRL+X

Copy selected cell(s) to clipboard CTRL+C

Paste from clipboard CTRL+V

Fill selection from top (copy top cell down) CTRL+D

Fill selection from left (copy leftmost cell to right) CTRL+R

Fill selection from bottom (copy bottom cell up) CTRL+UCTRL+SHIFT+D

Fill selection from right (copy rightmost cell to left) CTRL+LCTRL+SHIFT+R

Insert new row in table INSERT

Delete selected row of table DELETE

3D View Control KeysElevation view CTRL+E

Plan view CTRL+P

Rotate viewpoint up (increment view elevation angle) CTRL+U

Rotate viewpoint down (decrement view elevationangle)

CTRL+N

Rotate viewpoint right (increment view azimuthangle)

CTRL+J

Rotate viewpoint left (decrement view azimuth angle) CTRL+H

Rotate viewpoint +90º CTRL+Q

Rotate viewpoint -90º CTRL+SHIFT+Q

Zoom In CTRL+I

Zoom Out CTRL+O

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Move view centre - fine adjustment ← → ↑ ↓

Move view centre - coarse adjustment CTRL + ← → ↑ ↓

Edit view parameters for current 3D view CTRL+W

Reset to default view CTRL+T

Show / Hide local axes CTRL+Y

Undo most recent drag CTRL+Z

Lock/Unlock selected object CTRL+L

Place new object SPACE OR RETURN

Edit selected object CTRL+F2

Cut selected object to clipboard CTRL+X

Copy selected object, or view if none selected, toclipboard

CTRL+C

Paste object from clipboard (followed by mouse clickor RETURN to position the new object)

CTRL+V

DELETE

Measuring tape tool CTRL+SHIFT+DRAG

Replay Control KeysStart / Stop replay CTRL+R

Replay faster CTRL+F

Replay slower CTRL+S

Step forwards one frame in the replay and pause CTRL+A

Step backwards one frame in the replay and pause CTRL+B

Edit replay parameters CTRL+D

4.2 MENUS

4.2.1 MenusOrcaFlex has the following menus:

• The File menu has the file opening and saving commands, plus commands for printing orexporting data or results and managing libraries.

• The Edit menu has data and object editing facilities.

• The Model menu gives access to the model building facilities.

• The Calculation menu provides commands for starting and stopping analyses, includingbatch processing.

• The View menu provides view and replay control.

• The Results menu leads to the results facilities.

• The Tools menu allows you adjust preferences and to lock or unlock objects.

• The Window menu gives access to the various windows that are available, and allows youto adjust the layout of your windows.

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• The Help menu leads to the various help documentation that is available.

4.2.2 File Menu

New

Deletes all objects from the model and resets data to default values.

Open

Open a data or simulation file. You are offered the data files (.DAT) and simulation files (.SIM)in the latest directory used in OrcaFlex.

You can also open an OrcaFlex file by dragging and dropping it onto the OrcaFlex window. Forexample if you have Windows Explorer running in one window and OrcaFlex running in anotherthen you can ask OrcaFlex to open a file by simply dragging it from Explorer and dropping itover the OrcaFlex window.

If you open a data file then OrcaFlex reads in the data, whereas if you select a simulation filethen OrcaFlex reads in both the data and the simulation results. To read just the data from asimulation file, you can use the Open Data menu item.

If you load a partially-run simulation then it can be completed by usingCalculation | Run Simulation.

OrcaFlex can read files that were written by previous Windows versions of the program. It caneven read files written by more recent version of the program. If the file requires a facility that isnot available in the version reading it then a warning is given.

OrcaFlex cannot read files written by the old DOS version of OrcaFlex (version 5), but there areconversion utility programs available that convert the data from such files to the format nowused by OrcaFlex. See the Convert directory on the OrcaFlex CD.

Save

Save the data, plus the simulation results if a simulation is active, to the currently selectedfilename, using extension .DAT (if there are no simulation results) or .SIM (if there aresimulation results). If a file of that name already exists then it is overwritten.

Note: You cannot save the simulation while it is running - you must pause thesimulation first.

Save As

This is the same as Save but allows you to specify the filename to save to. If a file of that namealready exists then you are asked whether to overwrite the file.

Open Data

Read the data from an existing data file (.DAT) or simulation file (.SIM), replacing the existingmodel. If a simulation file is specified then OrcaFlex reads just the data from it, ignoring thesimulation results in the file.

Note: To select a simulation file you first need to set "File of Type" to be "All Files(*.*)".

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Save Data

Save the data into the currently selected filename, using extension .DAT. If a file of that namealready exists then it is overwritten.

Save Data As

This is the same as Save Data but allows you to specify the filename to save to. If a file of thatname already exists then you are asked whether to overwrite the file.

Compare Data

Compares the data of 2 OrcaFlex models. See Comparing Data for details.

Libraries

You can create new libraries of OrcaFlex objects, or open existing libraries. You can thenimport objects from the library into your existing model, or export objects from your existingmodel to the library.

Export

Display the Export Dialogue box, allowing you to export Data, 3D Views, Graphs, Spreadsheetsor Text Windows. See also Copy.

Print

Display the Print Dialogue box, allowing you to print Data, 3D Views, Graphs, Spreadsheets orText Windows. See Printing.

Selected Printer

Allows you to change the selected printer.

Printer Setup

Calls up the Printer Setup dialogue. This standard Windows dialogue is used to select whichprinter to use, and allows you to control the way that it is used - the details vary from printer toprinter, and depend on the printer manufacturer's device driver currently installed. Please referto the manuals for your printer as well as the Microsoft documentation.

Most Recent Files

List of the most recently used files. Selecting an item on the list causes the file to be loaded.The size of the list can be adjusted from Preferences.

Exit

Close OrcaFlex.

4.2.3 Edit Menu

Undo Drag

Undo the most recent drag. This is useful if you accidentally drag an object.

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Cut

Copies the current selection to the clipboard and then deletes it.

Copy

If there is a currently selected object (see Selecting Objects), then that object is copied to theclipboard. You can then use Edit | Paste to create duplicate copies of the object. The data forthe object is copied to the clipboard in text form, from where it can be pasted into a wordprocessor document.

Note: After pasting into a word processor, you will probably need to put the text intoa fixed space font since much of the data is in tables.

If there is no currently selected object then the currently selected 3D view, text window, graph orspreadsheet is copied to the clipboard.

Paste

Insert object from clipboard. This can be used to duplicate an object several times within themodel. After selecting Paste, the object is inserted at the next mouse CLICK position in a3D view.

If the current window is a Spreadsheet then the contents of the clipboard are pasted into thespreadsheet.

Delete

If the active window is a 3D View then the currently selected object is deleted. Before the objectis deleted, any connected objects are disconnected, and any graphs associated with the objectare closed.

If the active window is a Spreadsheet then the selected cells are cleared.

Select All

Selects all the text in a Text Window or all the cells in a Spreadsheet.

Copy All Data

Copy the whole model to the clipboard. The model data is copied to the clipboard in text form,from where it can be pasted into a word processor document.

4.2.4 Model Menu

Model Browser

The Model Browser button opens the Model Browser from which you can choose which objectto edit or examine. Double click, press return or use the browser Edit menu to view the dataform for that object. Data is drawn in grey if it cannot currently be changed (because asimulation is active, for example). You can move to other objects' data forms by CLICKING onthe Next button on each data form (SHIFT+CLICK the Next button to go to the previous dataform).

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New Vessel

New Line

New 6D Buoy

New 3D Buoy

New Winch

New Link

New Shape

Create new objects. The mouse cursor changes to the New Object symbol . The object isplaced at the position of the next mouse CLICK within a 3D view. A three dimensional position isgenerated by finding the point where the mouse CLICK position falls on a plane normal to theview direction and passing through the Default View Centre. Vessels are always placed initiallyat the sea surface, that is with their origin at Z = Sea surface Z (see Vessel Data).

Truncate Object Names

Old versions of OrcaFlex (before 7.4b) cannot read files that contain long object names, i.e.longer than 10 characters. This menu item truncates any long object names in the model. Youshould do this if you wish to send a file to another user whose version of OrcaFlex is older than7.4b.

Delete Unused Types

Deletes any types (e.g. Line Types, Clump Types etc.) that are not in use. This is sometimesuseful to simplify a data file, or to find out which types are in use.

4.2.5 Calculation Menu

Single Statics

Start the single statics calculation (see Static Analysis). Progress and any error messages thatoccur are reported in the Statics Progress Window, which is shown as a minimised windowicon. The statics calculation can be interrupted by CLICKING the Reset button.

Multiple Statics

Starts the multiple offset statics calculation (see Multiple Statics). Progress and any errormessages that occur are reported in the Statics Progress Window, which is shown as aminimised window icon. The statics calculation can be interrupted by CLICKING the Resetbutton.

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Run Simulation

Start a full dynamic simulation (see Dynamic Analysis). If necessary, OrcaFlex willautomatically do a statics calculation first.

During the simulation, the Status Bar shows the current simulation time and an estimate of thetime that the simulation will take, and all 3D View windows and Graphs are updated at regularintervals. The update interval is set in the Tools | Preferences dialogue box. The simulationcan be interrupted by CLICKING the Pause button.

Note: Documents and Results Tables are not updated and their contents becomeinvalid.

Pause Simulation

Pause the simulation. To save the results of a part-run simulation you need to pause it first.The simulation can be restarted by CLICKING the Run button.

Reset

Reset the model, discarding any existing results. The model can then be edited or a new modelloaded.

Extend Simulation

Adds another stage to the current simulation, without having to reset. You are asked to specifythe length of the new stage. Other properties of the new stage (e.g. winch control) are set tothe same as for the previous stage. You can then continue the simulation, without having torestart it from scratch. This is particularly useful if you have a simulation that has not been runfor long enough.

This facility is only available when the current simulation is either paused or completed.

Batch Processing

Run a batch of simulations automatically while the program is unattended. SeeBatch Processing for details. A Batch Mode dialogue box is presented, allowing you to selectthe data files to be included in the batch run and then start the batch run. The results areautomatically written to simulation files with the same names as the data file, for laterinspection. While running in batch mode the program does not require user input and does notrequest confirmation before overwriting simulation files.

4.2.6 View Menu

Edit View Parameters

Adjust the View Parameters for the highlighted 3D View. You can adjust the view centreposition, view size and direction. See View Parameters.

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Rotate Up / Down / Left / Right

Change the view direction, for the highlighted 3D View, by the view rotation increment (seePreferences).

Plan

Set the highlighted 3D View to a plan view (Elevation = +90º).

Elevation

Set the highlighted 3D view to an elevation view (Elevation = 0º).

Rotate 90 / Rotate -90

Increase (or decrease) the view azimuth by 90º, for the highlighted 3D view.

Zoom In / Zoom Out

Click the zoom button to zoom in (decrease view size) or SHIFT+CLICK it to zoom out (increaseview size). Applies only to the currently highlighted 3D View.

Reset to Default View

Reset the currently highlighted 3D view back to the default view for this model.

Set as Default View

Set the default view for this model to be the currently highlighted 3D view.

Axes

This submenu gives you control of the 3D View Drawing Preferences.

Superimpose Times

Allows model configurations for different times of the simulation to be superimposed in 3DViews. See Superimpose Times.

Current Position

Draws the model at the latest time.

Edit Replay Parameters

Adjust the Replay Parameters, such as the period of simulation to replay, the time intervalbetween frames, the replay speed etc. For more information see Parameters.

Start / Stop Replay

Starts or stops the Replay.

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Step Replay Forwards, Step Replay Backwards

Step the replay forwards or backwards one frame at a time. Click the button to step forwards;CLICK with SHIFT held down to step backwards.

Replay Faster / Slower

Increase/Decrease frame repetition rate (Replay speed).

Export Video

Exports the replay as a video clip in AVI file format. See Replays for more details.

4.2.7 Results Menu

Select Results

Display Results Selection dialogue box (see Results). This allows you to choose from thecurrently available selection of graphs and results tables. Graphs such as Time Histories, XYGraphs and Range Graphs may be created before a simulation has been run, thus allowing youto watch the variables during a simulation.

Fatigue Analysis

Opens the Fatigue Analysis form.

Modal Analysis

Opens the modal analysis form.

4.2.8 Tools Menu

Lock / Unlock Selected Object

Locking an object prevents it from being accidentally dragged or connected using the mouse on3D views, for example if you nudge the mouse slightly while trying to DOUBLE CLICK. Lock /Unlock Selected Object toggles the lock on the currently selected object. If the lock is on, it willbe switched off. If the lock is off, then it will be switched on. Locked Objects may still have theirpositions edited in the data Edit Forms. The status of the object locks is shown by symbols inthe Model Browser.

Lock / Unlock All Objects

Locks or unlocks all objects in the model.

Preferences

Allows you to control various program settings so that you can customise the program to theway you prefer to work. See Preferences.

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4.2.9 Window Menu

Add 3D View

Add another 3D View Window. Having multiple views on screen allows you to watch differentparts of the system simultaneously, or to see different views at the same time (for example aplan and an elevation).

Tile Horizontal / Vertical, Cascade

Arrange windows in a stack, one above the other, or side-by-side. Using these commands is agood way of reorganising your screen after creating or deleting view or graph windows. Thepreviously selected method is shown with a check mark.

Auto Arrange

If this is checked then the program automatically tiles or cascades windows every time a newwindow is created or deleted.

Switch to Model Browser

This command, and the corresponding command on the model browser's Window menu, enableyou to switch focus between the main form and the model browser window.

Session Log

Displays the Session Log.

Statics Progress

Displays the Statics Progress Window.

Window List

This is a list of all currently open windows. If a window is hidden under others it can be selectedeasily from this list.

4.2.10 Help Menu

Contents and Index

Open the Contents / Index / Find in the on-line help.

What's New

Gives a list of recent improvements and alterations to OrcaFlex.

Tutorial and Examples

Displays an introduction to using OrcaFlex and descriptions of the example files.

Keyboard Shortcuts

Lists the keyboard shortcuts used by OrcaFlex.

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Technical Notes

Displays the technical notes in the help file.

Frequently Asked Questions

Displays help giving common questions and answers about OrcaFlex.

About OrcaFlex

Displays a window giving the program version and details about Orcina Ltd. In addition, thewindow reports the amount of disk space, memory and Windows resources that are currentlyfree.

4.3 3D VIEWS

4.3.1 3D Views3D Views are windows showing isometric projections of the three-dimensional model, and theymay be rotated, zoomed and panned to allow any aspect of the system to be viewed. The viewis controlled by a number of View parameters - see View Parameters - and the caption of a 3DView window shows the current View Azimuth and View Elevation values, while a scale bar inthe view indicates the current View Size.

Multiple view windows may be placed side-by-side so that you can view different parts of thesystem simultaneously or view from different angles (for example a plan and elevation view).This allows you to build non-in-plane models on screen with the mouse. Further 3D Viewwindows are added by using the Window | New 3D View menu item or by CLICKING on the New3D View button on the tool bar. Windows may be arranged by dragging their borders or usingthe Window | Tile and Window | Cascade menu items. 3D Views may be deleted by DOUBLECLICKING the control box at the top left-hand corner.

The objects in a 3D view are "live" in the sense that you can use the mouse pointer to selectobjects, drag them around in the view and make connections between objects. See SelectingObjects, Creating and Destroying Objects, Dragging Objects, Object Connections, for details.If you DOUBLE CLICK on an object then the data form for that object appears, so that you canexamine or edit its data.

After running a simulation, or loading a simulation file, a dynamic replay (animation) can beshown in one or more 3D View windows. A replay shows a sequence of snapshots of themodel taken at specified intervals throughout part or all of the simulation. Replays may beplayed in just one 3D View window, or in all of them simultaneously - see Preferences.

Finally, 3D Views may be printed by selecting the view desired and using the print menu. Also,the picture may be exported to a file or the windows clipboard.

Measuring Tape Tool

You can measure distance on a 3D view using the measuring tape tool. Hold down the SHIFTand CTRL keys and then drag a line between any two points - the distance between them isdisplayed on the status bar. Note that this is the distance in the plane of the 3D view.

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4.3.2 View ParametersThe view shown in a 3D view window is determined by the following parameters, which can beadjusted using the view control buttons or the Edit View Parameters item on the View menu.

View Centre

Defines the 3D global coordinates of the point that is shown at the centre of the window.

View Size

The diameter of the view area. It equals the distance represented by the smaller of the 2 sidesof the view window. This parameter must be greater than zero.

Example: If the window on screen is wider than it is high, and View Size = 100.0 then anobject 100 units high would just fill the height of the window.

View Elevation and View Azimuth

These determine the direction (from the view centre) from which the model is being viewed.The azimuth angle is measured from the global X direction towards the global Y direction. Theelevation angle is then measured upwards (downwards for negative elevation angles) fromthere. The view shown is that seen when looking from this direction - i.e. by a viewer who is inthat direction from the view centre.

Example: View Elevation +90º means looking in plan view from above, and ViewElevation = 0º, View Azimuth = 270º (or -90º) means a standard elevationview, looking along the Y axis.

Default View

Each model has its own Default View Parameters that are saved with the model data.Whenever a new 3D view is created, it starts with this default view. You can set an existing 3Dview to the default view by using the Reset to Default View command (on the view menu or pop-up menu).

To set the default view parameters, first set up a 3D View to the default view that you want andthen use the Set as Default View command (on the view menu or pop-up menu).

Window Size

You can adjust the size of a 3D view window either by dragging the window border, or by settingits window size on the view parameters form. The latter is sometimes useful when exporting aview or a exporting a replay video, since it makes it easier to export two different cases and getmatching sizes.

4.3.3 View ControlYou can adjust the view in a 3D view window using the view control buttons:

Button Action Equivalent Menu ItemIncrease view elevation View | Rotate Up

Increase view azimuth View | Rotate Left

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Zoom in View | Zoom In

Edit View Parameters View | Edit View Parameters

CLICKING these buttons while holding the SHIFT key down causes the action to be reversed.

You can also use the mouse wheel button to change view. Turn the wheel to scroll the 3D viewup and down. Turn it with the CTRL key held down to zoom in or out on the point that the mouseis currently pointing at. Note that this mouse wheel facility is not available in Windows 95.

For more precise control you can set the view parameters explicitly using the View Parametersdialogue.

Finally, 3D views can also be controlled using the View menu and various hotkeys - see Mouseand Keyboard Actions.

Note: The view control keys only affect the currently selected 3D view window - theone with its caption highlighted. They have no effect if there is no currentlyselected 3D view window. To select a 3D view simply CLICK on it.

4.3.4 Zooming ViewsYou can zoom in or out using the mouse wheel button with the CTRL key held down (notavailable in Windows 95).

Also you can zoom in on a particular region of interest in a 3D view by defining a rectanglearound it on screen using the mouse. To do this, hold the ALT key down, place the mouse inone corner of the desired rectangle and press down the left mouse button while dragging themouse to the opposite corner. When you release, the region selected will be expanded to fillthe window.

To zoom out, repeat the operation holding down the SHIFT and ALT keys - the region shown inthe window will shrink to fit into the rectangle drawn.

You can also zoom in and out by a fixed amount, keeping the same view centre, by usingALT+CLICK and SHIFT+ALT+CLICK.

4.3.5 How Objects are DrawnEach object in the model is drawn as a series of lines using the Pen Colour, Line Width andStyle (solid, dashed etc.) defined in the drawing data for that object. You can change the pencolours etc. used at any time by editing the drawing data for that object. To change the pencolour, select and CLICK the colour button on the data form and then CLICK on the new colourwanted.

You can also exclude (or include) individual objects from the 3D view, by opening the modelbrowser, selecting the object and then using the Hide (or Show) command on the browser's Editor pop-up menu.

Notes: In Windows, a line width of zero does not mean "don't draw" - it means drawwith the minimum line width.

On some machines the display driver cannot draw the dashed or dotted penstyles and instead draws nothing. So on such machines only the solid andblank pen styles work.

Warning: If you use thicker lines to draw objects, then the speed of drawing will bereduced. This may slow down the speed of replays.

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The various objects are drawn as follows:

• The various coordinate systems can be drawn as small triplet of lines showing their originand the orientation of their axes. Also, the wave, current and wind directions can be drawnas arrows in the top right hand corner of 3D views. You can control both what is drawn (see3D View Drawing Preferences) and the drawing data used.

• The Seabed is drawn as a grid using the seabed pen.

• The Sea Surface is drawn as a grid or as a single line. This is controlled by the user'schoice of Surface Type as specified on the drawing page on the Environment data form. Ifthe Surface Type is set to Single Line then one line is drawn, aligned in the wave direction.If the Surface Type is set to Grid then a grid of lines is drawn. This line or grid is drawnusing the sea surface pen.

The density of the grid is specified in terms of the length of the scale bar on the 3D view; adensity of d means that there are d lines per scale bar length, so higher density values givea finer grid (but takes longer to draw).

• Shapes are drawn either as wire frames (Blocks and Cylinders) or as a grid (Planes). Aswell as controlling the pen colour, width and style, for shapes you can also control thenumber of lines used to draw the shape.

• Vessels are drawn as a wire frame of edges and vertices defined by the user on the Vesseland Vessel Types data forms.

• 3D Buoys are drawn as a single vertical line of length equal to the height of the buoy.

• 6D Buoys are drawn as a wire frame of edges and vertices. For Lumped Buoys, thevertices and edges are defined by the user on the buoy data form. For Spar Buoys thevertices and edges are automatically generated by OrcaFlex to represent the stack ofcylinders that make up the buoy.

• Lines are drawn as a series of lines, one for each segment, joining points drawn at eachnode. Separate pens are used for the segments and nodes, so you can, for example,increase the pen width used for the nodes to make them more visible. There is also, on theLine Data form, a choice of which pen to use to draw the segments.

• Clumps are drawn as a thin vertical bar.

• Drag Chains are drawn using the colour and line style specified on the drag chain typesform. The hanging part of the chain is drawn as a line, of length equal to the hanging lengthand at the angle calculated using the above theory. The supported part of the chain (if anyis supported) is separately drawn as a blob at the seabed, directly beneath the node. Thedrag chain drawing therefore directly reflects the way in which the chain is modelled.

• Links are drawn as a single line joining the ends of the link.

• Winches are drawn as a line representing the winch wire.

Lines, Links and Winches and Shapes are special slave objects that can be connected to othermaster objects - see Connecting Objects. To allow these connections to be made, each slaveobject has a joint at each end that you can connect to a master object or else leave Free. Whenthe program is in Reset or Statics Complete state these joints are drawn as follows:

The joint at end A of a line or end 1 of a Link or Winch is drawn as a small triangle. The otherjoints are drawn as small squares. This distinguishes which end of a Line, Link or Winch iswhich.

If the joint is connected to a master object, then it is drawn in the colour of the master object towhich it is connected. If the joint is Free, then it is drawn in the colour of the Line, Link or Winchto which it belongs.

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4.3.6 Selecting ObjectsA single CLICK on or near an object in a 3D View selects it ready for further operations. Thecurrently selected object is indicated in the Status bar. All objects have a "hot zone" aroundthem, the width of which is set in the Preferences dialogue box (see Preferences). If severalobjects have overlapping hot zones at the mouse position, they will be selected in turn atsubsequent CLICKS.

To deselect the object (without selecting another object) CLICK on the 3D view away from allobjects. CLICK on an object to open its data form.

4.3.7 Creating and Destroying ObjectsWhen the model is in Reset or Statics Complete state then you can create and destroy objectsusing the mouse.

To create a new object, CLICK on the appropriate new object button on the tool bar or select theModel | New Object menu item. The mouse cursor changes to show this. A new object of thattype is created at the position of the next CLICK on a 3D View.

You can also create a new object by copying an existing one. To do this select the object andpress CTRL+C to take a copy of it. You can now press CTRL+V (more than once if you want morethan one copy) - again the mouse cursor changes and the copy object is pasted at the positionof the next mouse CLICK in a 3D view. This method of creating a new object is particularlyuseful if you want an almost identical object - you can create a copy of it and then just changethe data that you want to differ.

To destroy an object, simply select it and then press the DELETE key. You will be asked toconfirm the action.

4.3.8 Dragging ObjectsAn unlocked object may be dragged to relocate it by pressing the mouse button down andholding it down while moving the mouse. When the mouse button is released, then the objectwill be positioned at the new location. The current coordinates of the object are shown in theStatus Bar during the drag operation.

Note: Objects must be dragged a certain minimum distance (set in the Preferencesdialogue box - see Preferences) before the drag operation is started. Thisprevents accidental movement of objects when DOUBLE CLICKING etc. Thedrag operation is denoted by the mouse cursor changing to

Objects may be locked to prevent unintended drag operations moving them (see Locking anobject). Their coordinates may still be edited on their data form.

Note: Slave objects that are connected are moved relative to their master's localorigin. Other objects are moved in the global coordinate frame.

Dragging is only available in Reset or Statics Complete states, and when the object is notlocked.

4.3.9 Connecting ObjectsUnlocked slave objects (e.g. Lines, Links, etc.) can be connected to master objects using themouse in a 3D View (see Object Connections). First select the end of the slave that you want toconnect by CLICKING on or near its end joint. Then hold down the CTRL key while CLICKING on

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the master object - the two will then be connected together. This operation is only permitted formaster-slave object pairs, for example connecting a line to a vessel. The connection isindicated in the Status Bar and the joint connected is drawn in the colour of the master object toshow the connection.

To Free a joint - i.e. to disconnect it - select it and then CTRL+CLICK on the sea surface.

To connect a joint to a Fixed Point, select it and then CTRL+CLICK on the global axes.

To connect an object to an Anchor (a fixed point with a coordinate relative to the seabed), selectit and then CTRL+CLICK on the seabed grid. If the object is close to the seabed then the programsnaps it onto the seabed. This allows an object to be placed exactly on the seabed. If yourequire an anchor coordinate close to, but not on the seabed, connect it to the seabed at adistance and then drag it nearer or edit the coordinate in the Data Form.

Note: At present you cannot connect a slave object to a shape.

4.3.10 Printing, Copying and Exporting Views3D Views may be printed, copied to the windows clipboard, or exported to a windows graphicsmetafile, so that the pictures may be used in other applications such as word processors andgraphics packages.

First select the view and adjust the viewpoint as desired. Then to print the view click the rightmouse button and select Print (if needed, you can first adjust the printer setup using theFile|Printer Setup menu item). To copy or export the view, ensure no object is selected (byclicking on the 3D view away from all objects) and then to copy to the clipboard press CTRL+C(or click the right mouse button and select Copy) and to export to a file click the right mousebutton and select Export.

If you are printing the view on a black and white printer (or are transferring the view into adocument which you intend to print on a black and white printer) then it is often best to first setOrcaFlex to output in monochrome (use the Tools|Preferences|Output menu item). This avoidslight colours appearing as faint shades of grey.

After a 3D view has been transferred to another application you should be careful not to changeits aspect ratio, since this will produce unequal scaling in the vertical and horizontal directionsand invalidate the scale bar. In Word you can maintain aspect ratio by dragging the corners ofthe picture, whereas if you drag the centres of the sides then the aspect ratio is changed.

4.4 REPLAYS

4.4.1 ReplaysA Replay is a sequence of 3D views shown one after another to give an animation. A replay istherefore like a short length of film, with each frame of the film being a snapshot of a model as itwas at a given time.

There are various controls and parameters that allow you to control a replay. You can also viewa series of snapshots all superimposed onto a single view - see Superimpose Times.

There are two types of replay:

• Active Simulation Replays show the model as it was at regularly spaced times during thecurrently active simulation. This type of replay is therefore only available when a simulationis active and can only cover the period that has already been simulated. If you have a time

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history graph window open when the replay is run, then the replay time is indicated on thegraph by a vertical line that moves across the graph in time with the replay.

• Multiple File Replays are replays where each frame can be from a separate data orsimulation file. See Multiple File Replays for details.

Export Video

Replays can be exported as a video clip in AVI file format, using the Export Video button on thereplay parameters form. An AVI file is generated containing the replay using the most recentlyselected 3D view window and using the same period, frame interval and speed as the replay.

AVI is a standard video format, so the file can then be imported into other applications, forexample to be shown in a presentation.

Notes: AVI files can be very large if the window size is large or there are a lot offrames in the replay. Also, re-sizing video clips (after pasting into yourpresentation) will introduce aliasing (re-digitisation errors), so it is often best toset the 3D View window size to the required size before you export the video.

4.4.2 Replay Parameters

The replay can be controlled by the following parameters that can be set in theReplay Parameters dialogue window, accessed using the Replay Parameters button.

Replay Period

The part of the simulation that the replay covers. You can select to replay the whole simulation,just one simulation stage (an asterisk * denotes an incomplete stage), the latest wave period orelse a user specified period. If you select User Specified then you can enter your own Startand End Times for the replay period.

Interval

The simulation time step size between frames of the replay. Using shorter intervals means thatyou see a smoother animation (though the extra drawing required may slow the animation).

Example: For a simulation with stages of 8 seconds each, selecting stage 2 and a replaytime step of 0.5 seconds causes the replay to show 16 frames, correspondingto t=8.0, 8.5, 9.0 ... 15.5.

Target Speed

Determines how fast the replay is played. It is specified as a percentage of real time, so 100%means at real time, 200% means twice as fast etc. As a special case, the fastest allowabletarget speed (10000% at the moment) is taken to mean "as fast as possible".

Note: The specified target speed is not always achievable because the computermay not be able to draw each frame quickly enough. When this happens, thereplay will be played as fast as possible. Replays may be slow if you specifythick lines (line width>1) for objects in the model, since this can increase thedrawing time.

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Continuous

Continuous means replaying like an endless film loop, automatically cycling back to the firstframe after the last frame has been shown; this is suitable for replays of whole cycles of regularcyclic motion. Non-continuous means that there will be a pause at the end of the replay, beforeit starts again at the beginning; this is more suitable for non-cyclic motion.

All Views

If this is selected, then the replay is shown in all 3D Views simultaneously, allowing motion to beviewed from several different viewpoints. Otherwise the replay is played in the currentlyselected view window only.

Note: Replaying in several 3D views simultaneously may be slow on somemachines.

Show Trails

If this is selected, then when each frame of the replay is drawn the previous frame is firstoverdrawn in grey - this results in grey 'trails' showing the path of each object.

4.4.3 Replay ControlThe replay can be controlled using the following menu items, toolbar buttons and theircorresponding hot keys.

Button Menu Item Hot Key ActionView | Start Replay CTRL+R Start replay

View | Stop Replay CTRL+R Stop replay

View | Step Replay Forwards CTRL+A Step to next frameand pause

+ SHIFTView | Step Replay Backwards CTRL+B Step to previous

frame and pauseView | Replay Faster CTRL+F Speed up replayView | Replay Slower CTRL+S Slow down replayView | Replay Parameters CTRL+D Edit replay

parameters

4.4.4 Superimpose TimesAllows model configurations for different times of the simulation to be superimposed in 3DViews. Use View | Current Position to undo the superimposed view. The data items are:

List of Times

The simulation times which will be superimposed. The times listed may be slightly different fromthose entered. This is because the only times that can be drawn are at log samples. If youneed finer resolution then you may have to increase the number of log samples.

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Add Time

Adds a simulation time to the list.

Remove

Removes the selected time from the list.

Clear

Removes all times from the list.

All Views

If this box is checked then the superimposed view is drawn in all 3D View windows. If not thenit is drawn in the selected 3D View.

4.4.5 Multiple File ReplaysA multiple file replay is a replay in which each frame can be from a separate OrcaFlex file.Each frame of the replay can be either the static position for a specified data file, or a snapshotof a specified time in a specified simulation file. The former allows you to string together aseries of static analyses 'snapshots' to give an animation of an installation procedure, forexample. The latter allows you to create replays where the frames are from one or moresimulations, and control in detail the time intervals between frames.

Replay Specification File

A multiple file replay is specified by setting up a replay specification file. This is a text file thatcan have any name, but which has the structure of Windows .INI files (files that are commonlyused to store program configuration information).

Here is an example replay specification file:

; Example Replay Specification File

[General]Interval = 0.3

; Frame 1[Starting Point]File = Case#01.dat

; Frame 2[Intermediate position]File = Case#02.simTime = 27.5

; Frame 3[Final Position]File = Case#03.sim

The structure of the file is that it contains a number of 'sections', each section being a line of theform

[<SectionName>]

followed by a number of 'value' lines of the form

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<ValueName> = <Value>

The section ends at the beginning of the next section, or at the end of the file. So, in the aboveexample there are 4 sections, called 'General', 'Starting Point', 'Intermediate Position' and 'FinalPosition'.

General section

The General section, if present, must be called 'General'. It can contain a 'value' line of the form

Interval = 0.3

that specifies the real time interval (in seconds) between drawing successive frames of thereplay. If this Interval value line, or the whole General section, is not present then the defaultinterval is 0.1s. Note that you can adjust the actual replay speed relative to this nominal realtime speed.

Frame Sections

All other sections in the file are assumed to specify the individual frames in the replay. You canchoose the names of the frame sections yourself, but they must be distinct and not equal to'General'. When you run the replay the frame section names are displayed in the OrcaFlexstatus bar, to identify the current frame.

Each frame section must contain a value called File that specifies the name of the file for thatframe. This is the filename of an OrcaFlex data or simulation file. If a full path is not specifiedthen the filename is assumed to be relative to the directory containing the replay specificationfile.

If the file is a data file then the frame is a static position frame - it calculates and displays thestatic configuration of that model. If the file is a simulation file then the frame is a simulationsnapshot frame - it displays the configuration of that model at the simulation time specified bythe Time value.

Each frame section may optionally also contain a value named Time. This value is only used ifthe File value specifies a simulation file. It specifies, in seconds, the simulation time to be usedfor this frame. If the value is not specified then the frame displays the configuration of themodel at the end of the specified simulation.

Comments

You can put comment lines in a replay specification file by starting the comment line with asemi-colon character. Such lines are ignored, as are any blank lines in the file.

Running the Multiple File Replay

Whenever the replay is started OrcaFlex first has to prepare all the frames of the replay. Forstatic position frames this involves opening the specified data file and calculating the staticposition of the model. For simulation snapshot frames the simulation file is opened and read tofind the position of the model at the specified simulation time.

4.5 DATA FORMS

4.5.1 Data FormsEach object in the model has data items that define its properties. The data are examined andedited in the object's Data Form, which can be accessed by various methods:

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• use the Model Browser

• DOUBLE CLICK the object in a 3D view

• RIGHT CLICK the object in a 3D view and use the pop-up menu.

If a simulation is active then most data items cannot be changed since they affect thecalculation, but you can change things like the object's colour.

Control Buttons

OK

Accepts the data changes made and then closes the form.

Cancel

Cancels the data changes made and then closes the form.

Next

Accepts the data changes made and then displays the next form in sequence. Holding theSHIFT key down while CLICKING the Next button accepts the changes and then displays theprevious data form in sequence.

Pop-up Menu

The pop-up menu on a data form provides various facilities, including:

• The data form can be printed, copied to the clipboard or exported to a file. The data for thewhole model may be printed using the File | Print menu item.

• Access to the next and previous data form and to the Variable Data form.

• The batch script names for the currently-selected block of data items.

• On data forms of some model objects, a report of the properties of that object. The reportdisplays properties like weight in air, displacement, weight in water etc.

4.5.2 Data FieldsData items on each Data Form are displayed in Fields, generally with related fields organisedinto Groups or Tables. You can select a field with the mouse, or use the keyboard to navigatearound the form. TAB moves from group to group, and the arrow keys move across the fields ina group.

Where data are complex the form has pages of a tab index that choose between a number ofdistinct sections of the data.

Where tabular data are shown on the data form, there is usually a separate field that specifiesthe number of entries in the table, and if necessary scroll bars are shown - use these tonavigate through the whole table. Please note that if scroll bars are present, then only part ofthe data is currently being displayed.

The following types of fields are used:

Text

A general string of text, used for example for titles and comments.

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Name

Each object is given a name, which you can edit. Object names must be unique - you can nothave two objects with the same name. Certain names are reserved for special purposes:Fixed, Anchored and Free (see Connecting Objects).

Numeric

Numbers can be entered in a number of formats such as 3, 3.0, 0.3, .3 or 3.0 E6. It is possibleto enter more digits than those shown in the field, but beware that it will not be possible to seethem again without editing again and using the arrow keys to examine the rest of field.

For some numeric data items the value '~' is permitted. For example this is sometimes used tomean 'default value'. Details are given in the descriptions of the relevant data items.

Spin Buttons

These are small buttons with up and down arrows, used for incrementing and decrementing theassociated field (such as the number of entries in a table). Using the mouse, CLICK on theupper or lower parts of the button to increment or decrement the associated counter.

Multi-choice Buttons

These are used when a number of options are available. Activate the button to step on to thenext available option.

Check Boxes

These show a tick, meaning selected, or are blank, meaning not selected. CLICK or pressRETURN to change.

Colour Selection

These show as a block of colour. DOUBLE CLICK or press RETURN to open the Colour Selectiondialogue box. The desired colour may now be selected.

List Boxes

These show the current selection, such as the name of another object that this object isconnected to. DOUBLE CLICK or press RETURN to show a List Box, and then select another itemand RETURN to accept the new choice.

4.5.3 Data Form EditingThe TAB, SHIFT+TAB, HOME, END and ARROW keys and the mouse can be used to navigatearound the Edit Form.

Editing mode is entered by DOUBLE CLICKING a cell with the mouse, or by starting to typealphanumeric characters, which are entered into the field as they are typed. The charactersthat have been typed can be edited by using the arrow keys to move around (now within thefield) and the BACKSPACE and DELETE keys.

Editing mode is ended, and the new value takes effect, when you press RETURN or selectanother field or button on the form. To end editing mode but reject the edit (and so keep the oldvalue) press ESC.

Many numeric fields have limits on the range of values that can be entered, for example anobject's mass must always be greater than zero. Warnings are given if invalid values are typed.

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Input can also be from the Windows clipboard. CTRL+C copies the selected field or block offields to the clipboard whilst CTRL+V pastes from the clipboard into the selected field. In this waydata can be easily transferred to and from Spreadsheets, Word Processors, etc.

Mouse ActionsCLICK Select FieldCLICK+DRAG,SHIFT+CLICK

Select a block of fields

DOUBLE CLICK Start Edit Mode in this field (please also see Data Fields)SECONDARYBUTTON CLICK

Context sensitive pop-up menu for copying, exporting andprinting the form and, for some model objects, viewing additionalproperties

Group MovementTAB Next GroupSHIFT+TAB Previous GroupALT+... Move to the group with this letter underlined in its heading

Field Movement←↑↓→ Go to adjacent row or columnHOME Go to leftmost columnEND Go to rightmost columnPAGE UP Go to top rowPAGE DOWN Go to bottom row

Table EditingINS, DEL Insert or delete a row of a table

Start Editing0..9, A..Z Edit (replace)

During Editing←→,HOME,END Move within field

End EditingESC Cancel edit↑↓ Accept edit and move to previous/next rowRETURN Accept edit

Copy / PasteCTRL+C Copy selected field/block to clipboardCTRL+V Paste from clipboard into selected fieldCTRL+D Fill selection from top (copy top cell down)CTRL+R Fill selection from left (copy leftmost cell to right)CTRL+UCTRL+SHIFT+D

Fill selection from bottom (copy bottom cell up)

CTRL+LCTRL+SHIFT+R

Fill selection from right (copy rightmost cell to left)

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4.5.4 Variable DataMost OrcaFlex data is constant - i.e. its value, y say, is a fixed specified value. But for somenumerical data items you can choose to instead specify variable data. The data item's value yis then specified as being a function of some other value x, and the actual value y(x) used byOrcaFlex then depends on the value of x at the time. If x varies during the simulation then yvaries accordingly.

As an example consider the drag coefficient of a line. In the real world this isn't a fixed constantvalue - it depends on the Reynolds number. For many application this variation is not significantso a fixed constant drag coefficient is sufficient. But sometimes the Reynolds number variationis important, so you can then specify the drag coefficient to be a function of Reynolds number.Then, each time the drag coefficient is needed OrcaFlex will first calculate the Reynolds number(the x in the above description) and then derive and use the corresponding drag coefficient y(x).

Note that for some data items use variable data in a slightly different way. For example theaxial stiffness of a line type is the slope of the tension-strain curve, so in this case constant dataspecifies dy/dx, rather than y, where y is tension and x is axial strain. In this context 'constant'means constant slope, i.e. linear, and the constant value you specify is dy/dx, whereas 'variable'means non-linear and you specify y as a function of x. Cases like this are documented in thedescription of each data item.

Using Variable Data

Variable data can only be used for certain data items. These are the numerical data items thathave a small down-arrow button to the right of the data item value. For these you can eitherspecify a fixed constant numerical value in the usual way. Or you can specify the name of avariable data set, either by typing the name in or by selecting it using the down-arrow button.The named data set must already have been set up - see the next section.

Setting Up Variable Data

All the variable data tables are specified on the Variable Data form. This form can be openedusing the model browser or using the pop-up menu on any data form.

Each table on the Variable Data form is given a name and the tables are grouped according tothe type of data they contain. For example data for drag coefficients is kept separate from datafor axial stiffness.

This structure is indicated by the layout of the form, which is designed to be used from left toright. So first select the type of data you want, using the tree view in the left hand section of theform.

The centre section of the form then shows how many tables have already been defined for thatselected type of data, and their names. To add a new table, increment the Number of DataSets. To edit the name of a table double click the name or select the name and then press F2.To delete a data set select it and press the DELETE key.

The right hand section of the form displays the variation of y against x for the data set currentlyselected in the centre section. It is specified by giving a table of corresponding values (x1,y1),(x2,y2), .., (xn,yn), where the table's left hand column is the independent variable x and its righthand column is the dependent variable y. The data will be automatically sorted into order ofincreasing x when the data is used or when you use the Profile button.

For intermediate values of x OrcaFlex interpolates. For values of x outside the range specifiedOrcaFlex either extrapolates or else truncates. Truncation means that OrcaFlex uses y1 for allx <= x1 and yn for all x >= xn (the table already having been sorted so that x1 is the lowest x-

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value specified and xn is the highest). The variable data form reports the method ofinterpolation and whether extrapolation or truncation is used.

Profile Graph

The Profile button displays a graph of the currently-select data. This is useful for data checkingpurposes. Where appropriate, log scales are used.

4.5.5 Data in Time History FilesFor certain data you can use time history files to specify time-varying values. This is availablefor wave elevation, wind speed and vessel motion, and it allows you full control over how thevariable changes with time.

If you want to specify time-varying data for more than one object (e.g. for both the wave andwind, or for the wave and a vessel) then you can either put all the data in one file (using multiplecolumns in a single table) or you can use separate time history files for the different objects.

To use a time history file you must specify the following information.

Input File

This is the name of the Time History input file that contains the data. The filename can eitherbe typed in or else set by using the Browse button. If you type it in you can either specify thefull path or a relative path.

Columns

You must tell OrcaFlex which columns in the time history file contain the relevant data. To allowyou to do this OrcaFlex provides an Import Wizard that displays the time history data in aspreadsheet window that has list boxes at the top of each column. The list boxes allow you tospecify what data is in each column, or alternatively that a column is not used (i.e. contains datathat is not relevant). The import wizard is automatically opened when you select a new timehistory file; or you can open it yourself by clicking the button provided.

Time Origin

The time origin data item gives you control of how the times given in the time history file relateto the times in OrcaFlex. The time origin is specified relative to the OrcaFlex global time origin,so it specifies the global time that corresponds to zero time in the time history file. Thesimulation time origin is also specified relative to global time, so you can simulate differentperiods of the time history by adjusting either the time history origin or the simulation time origin.

So, for example, if the time history file's time origin is set to 100s and the simulation time originis set to 400s, then a simulation consisting of 40s of build-up (i.e. simulation time -40 to 0)followed by 200s of simulation (simulation time 0 to 200) will cover time history time from 260sto 500s. Note that the time history file must contain data to cover the whole of the simulation.

Note: If you are using more than one time history file (e.g. one for a wave train andone for motion of a vessel) then they each have their own time origins, whichyou can use to time shift each time history independently of the others.

Time History File Format

Time History files must conform to the following formatting rules:

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• The file must be a tab-delimited text file; in other words it must be a text file in which the timehistory data columns are separated by single tab characters. Files of this format can easilybe produced with commercial spreadsheet programs by using "Save As" and selecting tab-delimited text form.

• The data values must be in standard decimal or scientific form.

• One column must contain the time values and these must be given in ascending order.

• The data must be given in the same units as used in the OrcaFlex model.

• For a wave time history the time values must be equally spaced (since a fast Fouriertransform is used). But for wind velocity or vessel motion time history files variable timeintervals can be used (since cubic spline interpolation is used).

The data is assumed to start at the first numeric entry in the time column and blank rows are notallowed once the data has started. This means that textual information about the file (titles etc.)can precede the data but once the data begins it cannot be interrupted with any more text.

4.6 RESULTS

4.6.1 Results

You can access results by either CLICKING on the Results button on the toolbar or byusing the Select Results menu item; the Select Results form then appears.

There is a Keep Open switch on the form's context menu, which allows you to choose whetherthe form automatically closes when you select a result, or alternatively stays open (and on top)until you explicitly close it.

The Select Result form allows you to select the results you want by specifying:

• The type of results required. Results are available as text tables (summary results, fullresults, offset tables, statistics or linked statistics) or as graphs (time histories, range graphs,offset graphs or XY graphs). The types of results available depend on the current programstate.

• The object for which you want results (selected in the same way as in the Model Browser)and for some objects which point in the object. For the Environment you must specify theglobal X,Y,Z coordinates of the point for which you want results. For 6D Buoys that havewings attached, results for the buoy and for each wing are available separately. For linesyou must specify the arc length along the line - see Line Results.

• For time histories, XY graphs and range graphs you must specify the period of thesimulation to be included. This can be one of the stages of the simulation, the WholeSimulation or a User Specified Period. If the wave is regular then you can select the LatestWave Period. For Range Graphs you can also select Static State - this option is onlyavailable after a statics calculation.

• The desired variable(s).

Graphs and Tables can be sent straight to the printer by CLICKING the Print button. If the valuesof a graph are required in text form then CLICK the Values button - this give the values in aSpreadsheet window, which can handle multiple variables if desired.

The summary and full results are taken directly from the current state of the model. All the otherresults are derived from a temporary simulation log file which OrcaFlex creates automaticallywhen a simulation is run. As the simulation progresses, OrcaFlex samples the variables for

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each object at regular intervals and stores the sampled values in the log file. All time histories,statistics and range graphs are derived from this simulation log file.

You can control the number of samples taken during the simulation, and hence the timeresolution of the results, by setting the Number of Log Samples data item on the general dataform. This must be done before the simulation is started. Increasing the number of samplestaken will improve the time resolution of the results, but will both slow the program down a bitand use more disk space for the simulation log and for any simulation files that are created.

Note: A special algorithm is used for logging tensions (and other results that mightvary rapidly) to ensure that any spikes that may occur between samples arerecorded.

Compression Warning

If any lines have, during the simulation, gone into greater compression than their segment Eulerload then a warning note is added to the Results form. Such lines are also marked with thesymbol § in the Model Browser. See Line Compression.

Offset Warning

If any of the multiple statics calculations have failed then a warning note is added to the Resultsform.

4.6.2 Selecting VariablesEach object has associated with it:

• A currently selected variable that will be used for graphs.

• A set of statistics variables that will be included in statistics reports.

For the currently selected object, the currently selected variables are shown in a list on theresults selection form.

If Statistics results are selected, then the list shows the set of variables that will be included inthe statistics report and you can add or remove variables by CLICKING on them in the list.

If a Time History is selected, the list shows the (single) currently selected variable and you canselect a different variable by CLICKING on it in the list.

You can also multi-select variables, using: CLICK select one variable DRAG select a range of variables SHIFT+CLICK select a range of variables CTRL+CLICK add / remove one variable CTRL+DRAG add / remove range of variablesIf more than one variable is selected, then the Values button will give a single SpreadsheetWindow with a time history column for each selected variable, and the Graph button will give aseparate Graph Window for each variable.

New columns can be appended to existing time history spreadsheet windows, as follows:

• Select the spreadsheet window to which you want to append, by clicking on it.

• Then open the Select Results form and select the variables that you want to append.

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• Then hold the CTRL button down and click the Values button.

• Provided that the selected spreadsheet window is a time history values table and that thetime periods for both sets of histories match, then the new time histories will be appended tothe active window. This allows you to have a single window containing results from differentobjects.

4.6.3 Summary and Full ResultsThese spreadsheet windows give the current state of an object or of the whole model. Forexample, in Statics Complete state the full results tables show the position of objects in theirstatic position. If a simulation is active, then they show the positions of objects at the latest timecalculated.

To obtain one of these results tables:

• Select Summary Results or Full Results on the Results form.

• Select the object require.

• Click the Table button.

The summary results are simply an abbreviated form of the full results, in which the results forlines only include the end nodes, not all of the intermediate nodes.

The summary and full results include estimates of the shortest natural periods of objects or ofthe whole model. These can be used to determine suitable simulation time steps. Thesimulation inner time step should normally be no more than 1/20th of the shortest natural periodof the model - this is given at the top of the summary results or full results report for All Objects.

4.6.4 StatisticsThe Statistics report provides, for each statistics variable:

• The minimum and maximum values and the simulation times when they occurred

• The mean and standard deviation (i.e. the root mean square about the mean).

These statistics are reported for each of a number of periods of the simulation. If Statistics byWave Period is selected then these periods are successive wave periods; otherwise they arethe stages of the simulation.

To obtain a Statistics report:

• Select Statistics.

• Select the object and the variables of interest (see Selecting Variables).

• CLICK the Table button.

The report is presented in a Spreadsheet.

Warning: The samples in a time history are not independent. They have what is called'serial correlation', which often affects the accuracy of statistical results basedon them.

4.6.5 Linked StatisticsThe Linked Statistics table relates a group of variables for a given object. For a specified groupof variables and a specified period of simulation, OrcaFlex finds the minimum and maximum of

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each variable and reports these extreme values, the times they occurred and the values that allthe other variables took at those times.

To obtain a Linked Statistics report:

• Select Linked Statistics.

• Select the required object and period.

• Select the variables of interest (see Selecting Variables).

• CLICK the OK button.

The report is presented in a Spreadsheet.

4.6.6 Offset TablesThese Text Windows are available only after multiple statics calculations and only for vessels.For a given offset direction they report the total load on the vessel and show how it varies withoffset distance. The worst tension in any segment of any line connected to the vessel is alsoreported for each offset.

To obtain an Offset Table:

• Select Offset Table on the Results form.

• Select the offset vessel.

• Select the offset direction required.

• CLICK the Table button.

The report is presented in a Text Window.

4.6.7 Time History and XY GraphsTime History graphs are of a single variable against time. XY graphs are of one time dependentvariable against another.

The period of simulation covered by the graph is chosen from a list.

To obtain a Time History or XY Graph:

• Select Time History or XY Graph on the Results form.

• Select the object required.

• Select the variable required (see Selecting Variables). More than one variable can beselected for time histories.

For XY graphs the above 2 steps need to be done for both axes. Do this by CLICKING on one ofthe options labelled X-axis or Y-axis, which are located at the bottom of the results form, andthen repeating the above 2 steps.

• Select the period required.

• CLICK the Graph button.

Time history and XY graphs are displayed in Graph Windows and they are "live" - i.e. they areregularly updated during the simulation. You can therefore set up one or more graph windows

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at the start of a simulation and watch the graphs develop as the simulation progresses. If youreset the simulation then the curves will be removed but the graphs will remain, so you canadjust the model and re-run the simulation and the graphs will then be redrawn. Graphs areautomatically deleted if the object that they refer to is removed, for example by loading a newmodel.

Range Jump Suppression

For time histories of some angles OrcaFlex chooses the angle's range so that the time history iscontinuous.

For example consider vessel heading, which is normally reported in the range -180 to +180degrees. If the vessel's heading passes through 180 then without range jump suppression thetime history would be:

.., 179, 180, -179, ..

i.e. with a 360 degree jump. To avoid this jump OrcaFlex adds or subtracts multiples of 360degrees to give the best continuation of the previous value. So in this example it adds 360 tothe -179 value and hence reports:

.., 179, 180, 181, ..

This addition is valid since 181 and -179 are of course identical headings.

Note that this means that angle time history results can go outside the range -360 to +360.

Empirical Cumulative Distribution

From any time history graph you can use the pop-up menu to obtain the empirical cumulativedistribution graph for that time history. This graph shows what proportion of the samples in thetime history are less than or equal to a given value.

These graphs are sometimes referred to as an 'Exceedence Plots' since they can sometimes beused to estimate the probability that the variable will exceed a given value.

Warning: The samples in a time history are not independent. They have what is called'serial correlation', which often affects the accuracy of statistical results basedon them.

4.6.8 Range GraphsRange graphs are only available for a selection of variables and they are only available forLines. They show the values the variable took, during a specified part of the simulation, as afunction of arc length along the Line. In particular:

• Range graphs show the minimum, mean and maximum values that the variable took duringthe specified part of the simulation with the exception that the Line Clearance range graphsonly shows the minimum value.

• Effective tension range graphs have extra curves showing the segment Euler load and theMaximum Tension value (as specified on the Line Types data form).

• Bend Moment range graphs have an extra curve showing the maximum permitted bendmoment (EI / Minimum Bend Radius specified on the Line Types data form).

• Curvature range graphs have an extra curve showing the maximum permitted curvature (thereciprocal of the Minimum Bend Radius specified on the Line Types data form).

• Stress range graphs show the Allowable Stress (as specified on the Line Types data form).

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• A Standard Deviation curve can also be added to a range graph - to do this edit the graph’sproperties (by double clicking on the graph) and set the Standard Deviation curve's visibleproperty (by default the curves are not visible). Two curves are then drawn, at Mean ± xσ,where x is a user chosen value and σ is the standard deviation. The standard deviation iscalculated from all the samples that lie in the simulation period chosen for the graph.

Warning: Be careful not to assume that 95% of the data lie in the interval Mean ± 2σ.This common guideline is based on the assumption that the data are sampledfrom a Normal (i.e. Gaussian) distribution.

To obtain a Range Graph:

• Select Range Graph on the Results form.

• Select the object required.

• Select the variable required (see Selecting Variables).

• Select the period required.

• CLICK the Graph button.

Range graphs are displayed in Graph Windows and they are "live" - i.e. they are regularlyupdated during the simulation. You can therefore set up one or more graph windows at thestart of a simulation and watch the graphs develop as the simulation progresses. If you resetthe simulation then the curves will be removed but the graphs will remain, so you can adjust themodel and re-run the simulation and the graphs will then be redrawn. Graphs are automaticallydeleted if the object that they refer to is removed, for example by loading a new model.

4.6.9 Offset GraphsThese graphs are available only after a multiple statics calculation has been done and only forthe offset vessel. The following variables are plotted against offset distance:

Restoring Force

The magnitude of the horizontal component of the total force applied to the vessel by theattached Lines or other objects. Note that this force is not necessarily in the offset direction.

Vertical Force

The vertically downwards component of the total force applied to the vessel by the attachedLines or other objects.

Yaw Moment

The moment, about the vertical, applied to the vessel by the attached Lines or other objects.

Worst Tension

The largest tension in any segment of any Line connected to the vessel.

To obtain an Offset Graph:

• Select Offset Graph on the Results form.

• Select the offset vessel.

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• Select the offset direction required.

• Select the variable required.

• CLICK the Graph button.

4.6.10 Presenting OrcaFlex ResultsOrcaFlex users often wish to show their OrcaFlex results in a slide presentation prepared usinga presentation program such as Microsoft PowerPoint. Here are some tips on how this can bedone.

Graphs

Graphs can be transferred from OrcaFlex to presentation programs by simple copy + paste.

Note: In PowerPoint, instead of using Paste, it is better to use Paste Special (fromthe Edit menu) and then select the Enhanced Metafile. This gives betterresolution.

Replays

Replays can be transferred by exporting to an AVI file and then importing that video clip file intothe presentation program.

Note: Resizing video clips (after pasting into your presentation) will introducealiasing (re-digitisation errors) so it is best to set the OrcaFlex 3D Viewwindow to the required size before you export the video.

Video Clips of OrcaFlex in Use

Your presentation can even show video clips of OrcaFlex in use, illustrating how the program isused. However, it is rather harder to generate the required AVI files. Here is a method that wehave used successfully at Orcina.

• The process uses HyperCam, a shareware program for capturing and manipulating videosequences. This program writes video clips in AVI format which can then be imported intoyour presentation. For details of how to obtain HyperCam see internet websitehttp://www.hyperionics.com.

• Run OrcaFlex and set it up to be ready for the first frame of the video you want.

• Run HyperCam and define the screen area in OrcaFlex that you want to record. To do thisuse either the Select Region or Select Window button on HyperCam's Screen Area form.The HyperCam window disappears and you have either a cross hair cursor with which todefine the corners of the recording area (Select Region) or a blinking frame around theselected window (Select Window). If necessary use ALT+TAB to bring up OrcaFlex, thenmake your selection. The HyperCam menu reappears automatically.

• On HyperCam's AVI File tab, set the file name and path where you want the recorded AVIfile to be stored.

• Press HyperCam's Start Paused button. This prepares to record, but waits for a key pressbefore starting.

• In OrcaFlex, ensure it is ready for the first frame and move the cursor out of the recordingarea. Then press F4 to record a single video frame. Allow a short interval for recording(typically ½ -1 second) before proceeding.

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• Set up OrcaFlex for the next frame, press F4 to record it and allow recording time again.Continue in this way until you have recorded the last frame and then press F2 to stop.

• You should now have an AVI file of the OrcaFlex sequence you want which can be importedinto and replayed by packages such as PowerPoint.

The recording process is quite quick and easy, but some practice may be required to get exactlythe result you want. Specific problems we have encountered include:

• Aliasing where the final screen area in the presentation differs from the screen area used forrecording - this can result in continuous lines appearing broken on replay.

• Recording of unwanted parts of the screen, cursors, Help bubbles, etc. If you don’t want thecursor to appear, then move it out of the recording area before pressing the F4 key. If youare recording the full OrcaFlex window including control buttons, then move the cursor offthe screen edge. Leaving the cursor over a button may bring up the help bubble which willthen be recorded with everything else.

4.7 GRAPHS

4.7.1 GraphsWhen you request results in graphical form, they are presented in Graph Windows. You canopen several simultaneous graph windows, showing different results, and tile them on thescreen together with 3D views and text results windows. To adjust the graph's properties(range of axes, colours, etc.) see Modifying Graphs.

Graphs have a pop-up menu that provides the following facilities.

• Undo Zoom (only available after using Zoom) returns the graph axes to their original rangesof values.

• Copy copies the graph to the clipboard, from where you can paste it into other applications.

• Values displays a spreadsheet containing the numerical values on which the graph isbased.

• Spectral Density (only available for time history graphs) opens a new graph showing thefrequency spectrum of the time history. The function shown on the graph is the one-sidedpower spectral density per unit time of the sampled time history, obtained using a Fouriertransform. Note: the sampling inevitably introduces 'noise' to the spectrum and this is oftenvery noticeable on the graph.

• Export enables you to export the graph to a metafile or bitmap file.

• Print facilities and the Monochrome Output preference.

• Properties opens the graph properties form (which can also be opened by double clickingthe graph).

Graphs of simulation results are "live" - i.e. they are updated automatically as the simulationprogresses. Also, they are kept even if you reset the simulation, so once you have set up a setof interesting graphs you can edit the model and re-run the simulation to see the effect ofchanging the model. You can also set up results graphs when in reset state, prior to running asimulation - the graph will be empty initially and will grow as the simulation progresses. Notethat we do not recommend this for graphs of line clearance, however, since updating them cansignificantly slow down the simulation.

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To print a graph, use the File | Print menu item. You can also copy a graph to the clipboard -simply select the graph window by CLICKING on it and then using the Edit | Copy menu item.From the clipboard you can then paste it into another application, for instance into a wordprocessor document. Graphs can also be exported as Windows metafiles, use the File | Exportmenu item. Metafiles can be imported into many Windows programs, such as word processors,spreadsheets, graphics packages etc.

When copying a graph to the clipboard, the size of the graph on screen has an effect on howthe fonts appear when the graph is pasted into another application. For example, if you arecopying a graph to a Word Processor and want the graph to be full page size then the graphshould be made large on screen (i.e. maximised). If you are wanting a number of graphs onone page of a document then the graph should be smaller on screen - try tiling or cascading thewindows (use the Window menu). By experimenting with various differently sized graphs itshould be possible to arrange for the fonts to appear as you wish.

Note: You will get the best results when printing to a monochrome printer by settingthe Monochrome Output preference - this is set by default when the programis first installed.

4.7.2 Modifying GraphsYou can zoom in a graph by holding down the ALT key and dragging a box around the area thatyou want the graph to display. When you release the mouse button the region selected will beexpanded to fill the graph. If you want to reverse this process then right click the mouse andchoose "Undo Zoom" from the pop-up menu.

You can also change the appearance of a graph by double clicking on the graph or by selectingproperties from the graph's pop-up menu. A dialogue box then appears, allowing you to changevarious aspects of the graph, as follows:

Axes

You can set the range, the tick spacing and the number of small ticks.

Labels

You can alter the text and fonts of the axis and tick labels.

Curves

You can control the line properties and visibility for each curve on the graph.

Legend

The legend is a key showing which curve is which. It only appears on graphs that have multiplecurves, e.g. range graphs. You can control whether the legend is shown and if so where andusing what font. Note that the legend includes all the curves, even if some of them may not bevisible at the time.

Intercepts

Intercepts are lines, like the axes, that go right across the graph. In fact the X and Y axesthemselves are considered to be intercepts. You can add more intercepts, for example to markthings like stage start times, and you can control their position and style.

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Save As Default

Changes to a graph’s properties normally only apply to that graph. But for general settings(fonts etc.) you can also click the Save As Default button. OrcaFlex then remembers thecurrent settings for use with future graphs.

4.8 SPREADSHEETS

4.8.1 SpreadsheetsSome numerical results (e.g. obtained with the Values button on the Results form) appear in anExcel compatible spreadsheet.

All the usual spreadsheet operations are provided (including all the standard floating pointfunctions), so you can easily do simple post-processing calculations without having tocopy+paste the results over to your full spreadsheet program. Formula entry is identical to thatof Excel and all the standard mathematical formulae are available. The more sophisticatedspreadsheet facilities (for example cell formatting, graphs, multiple sheets) are not provided, butof course when you need these you can easily use export of copy+paste to get the results intoyour favourite spreadsheet program.

Printing, Copying and Exporting Spreadsheets

To print the spreadsheet right click and select Print, but remember that OrcaFlex time historiesare normally quite long and will therefore produce many pages. If necessary, you can firstadjust the printer setup using File|Printer Setup.

You can also easily transfer the results to other applications by either:

• Copy and paste via the Windows clipboard. Select the block to be transferred and pressCTRL+C.

• Saving to file. Right click the mouse and choose Export.

Note: When copying to the clipboard only the values of the cells are copied. If youhave entered any formulae and want these transferred you must save to file(using Excel format) and then load into your spreadsheet application.

4.9 TEXT WINDOWSSimple text windows are used for some reports - see below. To print a text window, use theFile | Print menu. You can also copy text to the clipboard - simply select a region of text andthen use the Edit | Copy menu item (or press CTRL+C). From the clipboard you can then paste itinto another application, for instance into a word processor document. Alternatively, you canexport the text to a file by using the File | Export menu item. The resulting text file can then beimported into your word processor.

Statics Progress Window

During a Statics Calculation, the progress of the calculation is shown in the message box on thestatus bar. However the messages are also sent to a text window that is normally minimised.This window may be viewed by clicking on the message box during statics, or by selecting theWindow | Statics Progress menu item if you wish to watch the process more closely. Like othertext windows it may be printed, copied or exported, as described above.

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Session Log

This is a text window giving details of file actions, calculations etc. It can be viewed from theWindow | Session Log menu or by clicking the message box. It is particularly useful for batchcalculations. If one of the simulations of a batch run fails then information about the failure iswritten to the Session Log and can be displayed when the batch run is complete.

4.10 COMPARING DATAThe Compare Data menu item opens the Compare Data form, which allows you to finddifferences between the data in 2 OrcaFlex files.

The comparison is done using a user-provided compare program, so when you first use thisfacility you need to configure OrcaFlex to tell it which compare program that you want to use;see Configuration below.

You can then compare files as follows:

• On the Files tab, specify the 2 files that you wish to compare. These can be data orsimulation files.

• Click the Compare button.

• OrcaFlex then saves the data from the 2 files to 2 temporary text files and then runs theuser-specified compare program to compare those 2 text files.

Configuration

On the Configuration tab you need to tell OrcaFlex the text file compare program that you wantto use, and how to use it. The compare program must be a program that can compare 2 textfiles passed to it through the command line. Various such programs are available on the web;examples are WinDiff, Compare It! and Araxis Merge.

Compare Program

This is the compare program's executable filename. You can specify either the full path, or justthe filename if the executable file resides in a directory which is on your system path.

Command Line Parameters

This defines the command line parameters that are passed to the compare program. OrcaFlexreplaces the special strings %1 and %2 with the filenames of the temporary text files. For mostcompare programs the default setting of "%1 %2" will be sufficient. Otherwise you will need toconsult the documentation of your compare program.

4.11 PREFERENCESOrcaFlex has a number of settings that can be customised to suit the way that you work. Themajority of settings can be adjusted in the Preferences dialogue box, which is accessed byusing the Tools | Preferences menu item.

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3D View Preferences

Mouse Selection Zone

This is the distance (in pixels) of the "hot zone" around each object. Larger values require lessaccuracy in pointing at objects with the mouse, but increase the chance of selecting a nearbyobject instead.

Minimum Drag Distance

Object positions are not updated until the mouse has been dragged at least this distance (inpixels). This prevents accidental changes to object positions. To make a small movement,drag away and then back again, or edit the coordinate directly in the object's Edit Form.

View Rotation Increment

The default is 5º. Each CLICK on a Rotate View button increments or decrements ViewAzimuth or Elevation by this amount.

Refresh Rate

During a simulation calculation all 3D View and Graph windows are updated at this rate.Selecting a faster rate allows you to see the behaviour of the simulation more clearly at theexpense of performance. Set a slow Refresh Rate to give the numerical calculation moreprocessor time.

Background Colour

This sets the background colour of all 3D View windows.

3D View Drawing Preferences

Draw View Axes

The view axes show the same directions as the global axes, but are drawn in the top right handcorner of 3D views, rather than at the global origin.

Draw Scale Bar

Determines whether a scale bar is drawn in 3D views.

Draw Global Axes

Determines whether the global axes are drawn, at the model's global origin (0,0,0).

Draw Environment Axes

Determines whether the wave, current and wind directions are drawn in the 3D view. Whenmultiple wave trains are present the first wave train is taken to be the dominant one and isdrawn using sea surface pen, whereas the other wave trains' directions are drawn in thesecondary wave direction pen.

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Draw Local Axes

Determines whether the local axes for vessels, buoys and lines are shown. Drawing the localaxes on the 3D view helps you check the orientations of these objects. Can also be set fromthe View menu or by pressing CTRL+Y.

Draw Out Of Balance Forces

If selected, then in the static analysis (not during the simulation) there are extra lines drawn onthe 3D view, representing the out of balance force acting on each vessel and buoy. Thispreference is sometimes useful for static analysis, since it enables you to see how far a buoy orvessel is from being in equilibrium.

The force is drawn as a line, starting at the force’s effective point of application, and whoselength represents the size of the force. The scaling is piecewise linear and based on the ViewSize of the 3D view. Lines up to ViewSize/2 long mean forces up to 10 force units and linesfrom ViewSize/2 to ViewSize mean forces from 10 to 1000 force units.

Video Preferences

Codec

This specifies the method used to encode and compress exported video. You can choosebetween the following options. We recommend using Run Length Encoding unless you haveproblems playing the AVI files it produces.

• Run Length Encoding: This is the default and is usually the best choice. This codec offersgood compression rates for OrcaFlex video. The AVI files produced using this codec can beplayed on most Windows PCs.

• Uncompressed: This codec stores each frame of the video as an uncompressed bitmap.This means that the AVI file produced can be extremely large.

• Other: Should you wish to use a different codec you must also specify the four charactercode which identifies the codec. For more details see the documentation of the particularcodec you wish to use.

Output Preferences

Printer Margins

These set the Left and Top margins used on printouts.

Monochrome Output

If this is checked then external output (copying to the clipboard, exporting metafiles and printing)is in black and white. This is useful with black and white printers, since otherwise pale coloursmay be drawn in very light grey and may be hard to see.

General Preferences

Auto Backup Batch Runs

If this is switched on then simulations run in batch mode are automatically stored to simulationfiles at the specified regular Auto Backup Interval. This is useful if your computer is prone tofailure (for example because of overnight power failures) since the part-run simulation file canbe loaded and continued, rather than having to re-run the whole simulation from scratch. The

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Auto Backup Interval should be neither too short, since then the program will then waste a lot oftime repeatedly storing away the results, nor too long, since then a lot of simulation work will belost if a failure occurs.

Number of Recent Files

The number of recently used files displayed in the File menu. Set this to 0 if you want to disablethis feature.

4.12 PRINTING AND EXPORTINGThe Print / Export dialogue is accessed using either the File | Print or the File | Export menuitem and allows you to choose one or more of the following items to be printed or saved to file:

• The model data. Vessel Types often have very large amounts of data, much of which maynot apply to the current model, so OrcaFlex offers you the option of printing all the vesseltype data or only the data that is in use.

• Any 3D Views, Graphs, Spreadsheets and Text Windows currently on display.

Note: Spreadsheets cannot be printed directly from OrcaFlex. To print aspreadsheet you must first export as an Excel spreadsheet and then print fromExcel.

Note: Graphs are printed as large as possible whilst maintaining aspect ratio.

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5 BATCH AND POST-PROCESSING

5.1 INTRODUCTIONOrcaFlex provides several important facilities for automating and post-processing work:

• The Batch Processing facility enables you to run a set of simulations in unattended mode,for example as an overnight job. The simulations can either be of pre-prepared data files, orelse can be specified by a batch script file that specifies the simulation as variations on abase data file.

• The fatigue analysis tool provides in-built fatigue analysis for pipes.

• OrcaFlex is supplied with two special Excel spreadsheets which enable you to automate theextraction of simulation results into your own spreadsheet. You can then use the normalExcel calculation facilities to do your own customised post-processing and graphing.

• OrcaFlex includes a programming interface. This is a Windows dynamic link library (DLL)called OrcFxAPI (short for OrcaFlex Application Program Interface) and it is installed whenyou install OrcaFlex. The interface includes facilities for setting data, calculating staticpositions and extracting results from those calculations or from pre-run simulation files. Forexample you can write programs to automate post-processing or that use OrcaFlex as a'statics calculation engine'. One important example application of this is for real-timemonitoring of pipe, moorings etc. For details of the OrcFxAPI programming interface seethe file OrcFxAPI.hlp (this help file can be found in the OrcaFlex directory on the OrcaFlexCD). For further information or to discuss possible applications of OrcFxAPI, please contactOrcina.

5.2 BATCH PROCESSING

5.2.1 Batch ProcessingSimulations, script files and fatigue analyses can all be run in unattended mode, by using theCalculation|Batch Processing menu item. This command opens a form that allows you to set upa list of files that are to be run. Then, when you run the job, OrcaFlex opens and runs each filein turn.

The list of files can include any number and mixture of the following types of file:

1. Pre-prepared OrcaFlex data files (*.dat). OrcaFlex opens the data file, runs the staticanalysis followed by the simulation, and then saves the results in a file with the same nameas the data file, but with a .SIM extension.

2. Part-run OrcaFlex simulation files (*.sim). OrcaFlex opens the part-run simulation file,finishes the simulation and then saves the completed simulation results back to the samefile.

3. A batch script file (*.txt). This is a text file which contains OrcaFlex script commands thatspecify what OrcaFlex should do. OrcaFlex opens the script file and obeys the commandsin turn. A common use of script files is to run a number of variations on a base data file.

4. A fatigue analysis file (*.ftg). OrcaFlex performs the fatigue analysis and saves the resultsto an Excel compatible spreadsheet of the same name but extension *.xls.

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Note: You can also ask OrcaFlex to store the partial results to file at regular intervalsduring the batch job. This is useful if your computer is prone to failure (forexample because of overnight power failures) since the part-run simulation filecan be loaded and continued, rather than having to re-run the wholesimulation from scratch. See Preferences.

Batch Form Buttons

Close

Dismisses the Batch form.

Add File

Files are added to the file list by CLICKING on the Add button. The Open File dialogue box isdisplayed, where you select one or more files to be entered in the Batch File list. To select agroup of files, use SHIFT+CLICK and CTRL+CLICK. You can add data files, batch script files, orpart-run simulation files.

Remove File

This button removes any files highlighted in the file list.

Check Files

OrcaFlex opens each file in the batch list in turn, checks that they contain valid OrcaFlex data orscript commands, and reports any errors. The files are not changed, and no calculations areperformed. The Check Files command does not take long, so we recommend you use it beforestarting your batch job.

Run Batch

Start running the listed files. Each file is opened and run in turn, and the file that is currentlybeing run is highlighted in the file list. If any file fails due to errors then that file is abandonedand the batch job continues with the next file. Errors are recorded in the Session Log (whichcan be viewed from the Session Log item on the Window menu) and are also reported at theend of the batch job.

Stop Batch

Terminate the batch job.

Note: Calculations run faster if there are fewer 3D View windows and Graphs open,and if the Refresh Rate in the Preferences dialogue box is set to a slowervalue. So to optimise performance consider closing all windows.

5.2.2 Script FilesOrcaFlex provides special facilities for running a series of variations on a base data file, using ascript file. This contains a sequence of commands to read a data file, make modifications to it,and run the modified file, storing the results for later processing. The file can also includecomments. The syntax for the instructions is described in the next topic. For examples see theBatch Script Examples.

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To run a batch script file, specify the script file name in an OrcaFlex batch files list. To add ascript file to the list, click the "Add File" button on the OrcaFlex batch form and then click on"Files of Type" and select *.txt, and then select your script file.

When OrcaFlex processes the files included in the batch list, it checks the type of each file inturn: OrcaFlex data and .sim files are loaded and the simulation run and stored, text files areread in and expected to contain batch script commands. You can therefore run a single batchjob containing several script files, or you can even mix 'ordinary' simulations and scripts in thesame batch job.

5.2.3 Script SyntaxAn OrcaFlex batch script is made up of commands, which are obeyed sequentially, andcomments, which are ignored. A comment is a line that is either blank or on which the firstnon-blank characters are "//". A command can be:

1. A directive followed by one or more arguments, optionally separated by white space (oneor more spaces or tabs). For example: load c:\temp\test.dat where load is thedirective and c:\temp\test.dat is the argument.

2. An assignment of the form VariableName=value, again with optional white spaceseparators. For example: Length = 55.0.

Note that:

• Directives and variable names are case independent.

• Model object names are case dependent, so tanker and Tanker are not the same objectin an OrcaFlex model.

• If your script includes a relative filename then it is taken to be relative to the directory fromwhich the script was loaded.

• Filenames, arguments, variables or values containing spaces or non-alphanumericcharacters must be enclosed in single or double quotes and they must not contain the samequote character as is used to enclose them. For example '6" pipe' and"200' riser" are valid, but the following are not valid:

6 inch pipe - contains spaces, so needs to be enclosed in quotes;

6"pipe - contains a double quote, so needs to be enclosed in single quotes;

'6' pipe' - contains a single quote, so needs to be enclosed in double quotes instead ofsingle.

5.2.4 Script CommandsThe following batch script commands are currently available. You need to put quotes roundfilenames or other parameters that include spaces or non-alphanumeric characters.

Load <FileName>

Opens an OrcaFlex data file. The model defined in the data file becomes the current model.

Run <FileName>

Run the current model and save the resulting simulation to <FileName>.

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Save <FileName>

Save the current model (data only) to <FileName>.

Note: In the Load, Run and Save commands, if <FileName> is a relative path then itis taken to be in the directory from which the script file was loaded.

Select [<Object Type>] <ObjectName>

Specify the model object to which subsequent assignment commands will apply. It will onlyremain selected until the next non-assignment command is encountered.

The <ObjectType> argument is optional, and by default is 'object', meaning select the namedmodel object. <ObjectName> must then be either the name of an object that exists in thecurrent model or one of the reserved names 'General' (for the General data form) or'Environment' or 'Sea' (for the Environment data form).

Other <ObjectType> values only need to be specified in the following special cases:

• If the sea has been selected and there is more than one wave train, then before you canspecify any wave train data you must give another select command to select the wave train.This second select command has the form

Select wavetrain <WaveTrainName>

So for example:

Select Sea Select wavetrain Primary WaveDirection = 30.0

Note that you must also give this extra select command if you alter the number of wavetrains in a script file.

• If a vessel type has been selected and it has more than one draught, then before specifyingany draught-dependent data you must give another select command that selects thedraught. This second select command has the form

Select draught <DraughtName>

Similarly, before specifying vessel type data for a given wave direction you must giveanother select command to select that direction. This takes the form

Select direction <Direction>

So for example:

Select "VType A" Select draught "Transit" Select direction 22.5 RAOYawAmplitude[2] = 0.1

Note that you must also give these extra select commands if you alter the number ofdraughts or directions in a script file.

See the file Example2.txt for a more extensive example. Note that indentation with spacesor tabs is optional, but makes scripts more readable.

Warning: In general, selecting a model object in a script is equivalent to opening thatobject's data form. The only exception to this rule is that wings on 6D Buoysare model objects in their own right, but are edited via the 6D Buoys dataform: to set their data in a batch script you must select the wing you wish toedit, not the buoy to which it is attached.

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Assignment

Assignment commands take the form

VariableName = Value

The VariableName on the left hand side must be one of the recognised variable names and thenamed variable must exist in the currently selected model object.

The Value on the right hand side must be in the appropriate form for that variable (i.e. numericor text) and it must be given in the same units as used in the current model. For example:

select 'Vessel A' length = 100 draught = 'Operating'

If VariableName is the name of a variable that appears in a check box in OrcaFlex then theValue should be True or False. For example:

select Sea CurrentRamp = True

If VariableName is the name of a variable that appears in a table in OrcaFlex, then its rownumber must be given. The row number is given as an index enclosed by either square orround brackets (don't mix them on the same line), and is always 1-based - i.e. [1] is the first rowof the table. Note that this sometimes requires care, since in OrcaFlex the table might not be 1-based. For example, when setting the prescribed motion for a vessel, the command

PrescribedMotionVelocity[2] = 4.8

sets the velocity in the 2nd row of the table, but in this case the first row of the table is stage 0(the build-up stage) so this command (slightly confusingly) sets the velocity for stage 1.

5.2.5 Handling Script ErrorsAs with other computer programs, OrcaFlex batch script files can easily contain errors. It istherefore wise to check your script file for errors before running it as a batch job. To check forerrors in your scripts, use the "Check Files" button on the OrcaFlex batch form. This will readand obey all the commands in the script files except those that perform calculations or writefiles. It will then report any errors it finds, including the line number on which the error occurs.You can then correct the problem before running the script. Example3.txt is an examplecontaining various errors, so to see how errors are reported use the "Check Files" button withthis example.

Warning: If you misspell a variable name in an assignment statement then "Check Files"will report an error. But if you incorrectly specify a variable name which isnevertheless valid then OrcaFlex cannot detect the error. So you need to bevery careful that you use the correct variable names for the data items thatyou want to change.

5.2.6 Obtaining Variable NamesEach OrcaFlex data item has its own name that is used to specify it in a script file. The namesof the data items are based on the corresponding labels used on the data form. To find out thename of a data item, open the appropriate data form, select the data item, and then open (e.g.by right click) the pop-up menu and select the Batch Script Names command. This displays thevariable name of the selected data item and you can select and copy+paste the name directlyinto your batch script.

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If the data item is in a table (or group) of data items then the Batch Script Names form displaysthe names of all the data items in the table. The different columns in the table each have theirown names; you then need to add an index to specify which row you want. The exceptions tothis are the 'Connections' data controls for Lines and Links, which consist of two rows, one forEnd A and one for End B. For these, the Batch Script Names form lists the names for End Aonly: those for End B may be obtained by simply replacing 'EndA' with 'EndB' in the name.

Finally, note that Batch Script Names are not available for an empty table - e.g. if you want thenames for the attachments table on the line data form, but there are currently no attachments.In this case you must add a row to the table before you can use the Batch Script Names form.

5.3 FATIGUE ANALYSIS

5.3.1 Fatigue AnalysisThe OrcaFlex fatigue analysis carries out a deterministic fatigue analysis based on regular orirregular wave simulations. It extracts line load results from a series of pre-run simulation files,calculates the resulting pipe stresses and then calculates the fatigue damage.

Warning: The fatigue analysis uses the stress results which assume a pipe made of auniform, homogeneous, linear material.

Two types of analysis can be performed - simple regular wave analysis or irregular waveanalysis using the rainflow cycle counting method.

The fatigue analysis tool is run by selecting the Fatigue Analysis command from the OrcaFlexResults menu. It is essentially a self-contained sub-program within OrcaFlex, with its ownmenus, data and results. Any OrcaFlex process active in the main window is paused until theFatigue Analysis data form is closed. The Fatigue Analysis has no effect on existing OrcaFlexdata.

The steps involved in doing a fatigue analysis are:

1. Use the normal OrcaFlex facilities to set up and run simulations that model the various loadcases that the line will experience.

2. Open the fatigue analysis tool and set up the data. This fatigue analysis data is heldseparately from the other OrcaFlex data and can be saved in a separate Fatigue AnalysisFile (.ftg).

Note: An example file can be found in the PostProc sub-directory of the OrcaFlexinstallation directory. The filenames in this example data may need editing,since they assume that OrcaFlex has been installed to the default installationdirectory.

3. Check the data for errors.

4. Calculate the stresses and damage.

Note: The Calculate stage of a fatigue analysis can take a long time , especially arainflow analysis using a lot of large simulation files. To help with this there isan Estimate Calculation Time facility and fatigue analyses can be run in batchmode.

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5.3.2 Load CasesBefore the Fatigue Analysis can be performed you must first prepare a set of OrcaFlexsimulation files that model the same system but under the various load conditions that thesystem will experience in its lifetime.

The approach is to divide the range of sea states that the system will experience into a numberof wave classes. A typical way of doing this is to use a wave scatter diagram.

One OrcaFlex simulation file can then be created for each wave class. For regular analysis thesimulation should use a regular wave representative of the wave class and for rainflow analysisthe simulation should use an irregular wave representative of the wave class. This simulation isthen one Load Case. Each load case is assigned an exposure level. For regular load casesthis is the total number of occurrences of waves within the class and for rainflow load cases thisis the total time exposed to waves within the class.

Warning: The included arc lengths must be the same in each load case, so the line tobe analysed should have the same number and distribution of segments ineach of the load case simulations.

5.3.3 CommandsFile Menu

The file menu commands use the latest directory used in OrcaFlex, but you can browsedirectories as required.

New

Clears previously entered Fatigue Analysis data and results, and, where relevant, resets data todefault values.

Open

Open a Fatigue Analysis file (.ftg) from the current directory.

Save

Save the data to the currently selected filename (shown in title bar of the window) If a file ofthat name already exists then it is overwritten.

Save As

This is the same as Save, but allows you to specify the filename to save to. If a file of thatname already exists then you are asked whether to overwrite the file.

Most Recent Files List

List of the most recently used files. Selecting an item on the list causes the file to be loaded.The size of the list can be adjusted from the Preferences form.

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Analysis Menu

Estimate Calculation Time

Gives an estimate of how long it will takes to do the fatigue analysis and present the results.This is useful for long analyses, e.g. rainflow analyses involving a lot of cases or longsimulations.

Check

The Check command performs a preliminary check of the fatigue analysis data. For example itchecks that all the specified load case simulation files exist and that the named line and thespecified arc length intervals exist in each load case.

The Check command is generally much quicker that the fatigue analysis itself, so werecommend that the Check command is used before the Fatigue Analysis is run, since thecheck can often detect data errors that would otherwise only be found part way through whatmay be quite a long fatigue analysis. It is particularly important to use the Check commandwhen a new fatigue analysis has been first set up or when significant changes have been madeto the data.

Calculate

The Calculate command starts the Fatigue Analysis. The fatigue analysis can take a long timeif there are many load cases, or if there are many log samples in the load case simulations, orfinally if there are a lot of segments in the arc length intervals specified. A progress window isdisplayed and you can cancel the analysis if desired.

When the calculation is complete the results are displayed in a spreadsheet window.

5.3.4 DataTitle

Used to label all output of the fatigue analysis.

Analysis Type

Two types of fatigue analysis are available:

• A Regular analysis must be based on a series of regular wave simulations that representthe various load cases that will occur. For each of these load cases a single-occurrencedamage value is calculated based on the last wave cycle in the simulation. This damagevalue is then scaled up by the specified number of cycles expected to occur during thestructure's life, and this gives the total load case damage value. Finally these total loadcase damage values for each load case are then summed to give the overall total damage.

• A Rainflow analysis is normally based on a series of random wave simulations. It uses acycle counting technique to break down each random wave case into a series of half cycles,and then sums the damage from each half cycle according to the Palmgren-Miner law (fordetails see the book by Maddox and the paper by Rychlik). This gives the single-occurrencedamage value for that load case, which is then scaled up to the specified total exposure timefor that load case, and this gives the total load case damage value. Finally these total loadcase damage values for each load case are then summed to give the overall total damage.

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Units

The units to be used for the fatigue analysis, for both the fatigue analysis data and for itsresults. The units are specified in the same way as elsewhere in OrcaFlex.

Note that the units specified for the fatigue analysis need not match the units that were used inthe various load case simulation files. If they do not match, then the stress results from thatsimulation file will automatically be converted to the units specified for the fatigue analysis. Thisis useful, since it allows the fatigue analysis to be done using mm and N as the length and forceunits (giving stresses in N/mm^2 = MPa), for example, even if the simulation load cases use mand kN (which corresponds to stresses in kN/m^2 = kPa). Similarly, in US units, the fatigueanalysis can use inches (giving stresses in ksi) even if the simulation files use feet as the lengthunit.

If you change units, then all existing fatigue analysis data is automatically changed to match thenew units. This is useful if you want to enter data in some other set of units, since you cansimply change to the units of the new data, then enter the new data, and then change back tothe original units again.

Load Case Data

Add Load Case

The Add Load Case button is used to add load cases to the Fatigue Analysis; it adds an extrarow in the load case table.

Remove Load Case

Removes the currently-selected load case from the load case table.

Simulation File Name

The name of the load case simulation file. The filename can either be typed in or else set byusing the Add Load Case button. If you type it in you can either specify the full path or arelative path.

Line Name

The name, in this load case simulation file, of the line to be analysed.

Note: Normally the line name will be the same in all of the load cases (though this isnot necessary). However the named lines in the various load cases must, ofcourse, all represent the same physical line. And they must also have thesame segmentation in the areas being analysed.

Number of Cycles (regular analysis only)

The number of wave cycles, of this particular set of load conditions, that the line will experience.

Simulation Period and Exposure Time (rainflow analysis only)

Simulation Period specifies the period of the pre-run simulation file that defines the load case.The exposure time is the total time the system is exposed to this load case.

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Analysis Data

The Analysis Data page contains the following data items, which specify the parts of the line tobe analysed, and their stress properties.

Critical Damage

Is a warning level. If the total damage at any fatigue point exceeds the Critical Damage thenthat damage figure will be highlighted in the results.

Number of Thetas

The number of theta values around the pipe circumference, at which fatigue analysis will beperformed. There will be Number of Thetas fatigue points uniformly distributed around the pipeouter circumference, and the same number similarly distributed around the inner circumference.A larger number of thetas gives a more comprehensive analysis, but takes a little longer.

Arc Length Intervals

You define the parts of the line that are to be analysed by specifying a number of non-overlapping Arc Length Intervals in the form of From and To arc length values. OrcaFlex willanalyse cross-sections at each line end and mid-segment whose arc length S is in the rangeFrom <= S < To. Note that OrcaFlex therefore won't a line end or mid-segment whose arclength S that exactly equals To; to include it specify an arc length a little beyond.

For simple cases you can use just one arc length interval covering the whole line. However it isoften clear which part, or parts, of the line are liable to fatigue problems, and it is then useful tobe selective and only analyse those parts of the line. This both speeds up the analysis and alsoreduces the quantity of results that you need to examine.

Warning: The included arc lengths must be the same in each load case, so the line tobe analysed should have the same number and distribution of segments ineach of the load case simulations.

Stress Concentration Factor (S.C.F.)

When the maximum stress range is used with the S-N curve to calculate damage, thatmaximum stress range is first scaled by the Stress Concentration Factor. If no stressconcentration is required then the S.C.F. should be set to 1.

This factor enables you to allow for special situations, where the assumption that the line is asimple pipe made of a homogeneous material does not hold. For example, at weld joints thestress tends to be more concentrated than for the rest of the pipe and so fatigue failure is morelikely in such areas. The default value is 1.

Notes: The stresses reported in the results have not been scaled by the S.C.F. Thisfactor is only applied when the maximum stress range S is used with the S-Ncurve to calculate damage.

To use different stress concentration factors for different parts of the line, youwill need to specify separate arc length intervals for those parts.

S-N Curve

Specifies which S-N curve is used for damage calculations in this arc length interval.

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5.3.5 S-N Curve DataAn S-N curve defines the number of cycles to failure, N(S), when a material is repeatedly cycledthrough a given stress range S. OrcaFlex uses the S-N curve to calculate the damage in afatigue analysis.

If needed you can define a number of different S-N curves and use them at different arc lengthsalong a line. This enables you to handle cases where different parts of the line are made up ofdifferent materials.

With each S-N curve you must also specify an associated stress fatigue limit, FL, which is thestress range below which no damage occurs. This is sometimes referred to as the endurancelimit.

The S-N curve itself can be specified either by parameters or by a table.

When the curve is defined by parameters the user specifies two parameters, A and b, and thecurve is then given by either of the following equivalent formulae:

N = 10^A / S^bLog10(N) = A - b Log10(S)

When the curve is specified by a table the user gives a table of corresponding values of S andN. For other values of S we use log linear interpolation or extrapolation to find the value of N.

The Graph button displays the selected S-N curve on a log-log graph.

S-N Curve Units

The S-N curve parameters entered must be consistent with the fatigue analysis units. S-Ncurve parameters are typically quoted with respect to stresses in Mpa, but you might be doingthe fatigue analysis using some other stress units. You can handle this problem as follows.First change the fatigue analysis units and set the units system to be 'User', the length units tobe 'mm' and the force units to be 'N'. This corresponds to stresses in Mpa, so you can thenenter the S-N parameters in terms of Mpa. Finally, restore the units to those that you want forthe fatigue analysis. The parameters will automatically be converted to allow for the change inunits.

Note: The way the S-N curve parameters A and b alter when you change units is notintuitively obvious. If you need to know the formulae, then recall that the S-Ncurve for deriving N (the number of cycles to failure) is given by:

Log10(N) = A - b.Log10(S) (1)

If we now change units then the stress value S changes to S' = c.S, where c ishow many new stress units equal one old stress unit. Let A' and b' be the newS-N curve parameters, using the new units. Then equation (1) becomes:

Log10(N) = A' - b'.Log10(S').

which leads to:

Log10(N) = A' - b'.Log10(c.S) = [A' - b'.Log10(c)] - b'.Log10(S) (2)

Comparing equations (1) and (2) we see that b'=b and A'=[A+b.Log10(c)].

For details of how the S-N curve is used to calculate the damage see How Damage isCalculated.

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5.3.6 ResultsThe Fatigue Analysis results are presented in a spreadsheet that has one Damage Tablesworksheet, plus one Load Case worksheet for each load case. There is also a worksheetechoing the S-N curve data.

Load Case Worksheets

The Load Case worksheets contain the derived stress results for each fatigue point that hasbeen analysed, together with general information such as the environmental data that applied tothat load case.

There is one table of stress results for each arc length covered by the specified arc lengthintervals. Each such table contains a row of results for each fatigue point in that arc lengthcross-section. These results are the stress ranges (for each of the stress components), themaximum stress range and the resulting single-occurrence load case damage values.

The maximum von Mises stress is also reported, but note that this value has no effect on thedamage calculation.

Damage Table Worksheet

The Damage Tables worksheet starts with an Excessive Damage table, which lists any fatiguepoints at which the overall total damage has exceeded the specified critical damage value(which is displayed in the table title).

There then follows a table summarising the Other Stresses table, which reports the maximumand minimum direct stress (i.e. any of the diagonal terms in the stress matrix) and the maximumand minimum shear stress (i.e. the off-diagonal terms) at any of the fatigue points. The largestoff-diagonal stress values should be checked to ensure that they are small compared to thedirect (i.e. diagonal) stresses - see the note in How Damage is Calculated. This table alsoreports the maximum von Mises stress.

Finally, the Damage Tables worksheet provides damage tables for each arc length cross-section analysed. These report, for each fatigue point in the cross-section, the total exposuredamage value from each load case and the overall total damage.

In all of the damage tables, overall total damage values that exceed the specified criticaldamage value are highlighted in red.

Printing and Exporting

To save the results you will need to export the spreadsheet as an Excel worksheet. If you wantto print the results then for best results you should first export them and then use Excel to dothe printing.

Note: There is no facility to print the fatigue analysis data, but the data is echoed inthe fatigue results spreadsheet.

5.3.7 Fatigue PointsFatigue is analysed at a number of line end and mid-segment cross-sections along the line, asspecified by defining Arc Length Intervals in the Analysis Data.

Each included arc length defines a cross-section through the pipe. Each such section is thendiscretised, in polar coordinates (R, Theta), using a user-specified Number of Theta angles, andusing two r-values - one at the line's stress ID and one at the line's stress OD. Theta is

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measured from the line's local x-axis towards its y-axis, as indicated in the figure below, whichshows the fatigue points that will be analysed when the number of theta angles is set to 8,giving fatigue points at theta = 0, 45, 90, 135, 180, 225, 270 and 315 degrees.

x (Theta=0)

y

Stress ID

Stress OD

Theta

R

FatiguePoints

C

Figure: Fatigue Points at an arc length cross-section

This therefore defines a total of

(Number of included arc lengths) x (Number of Theta Angles) x 2

fatigue points at which the damage will be analysed.

5.3.8 How Damage is CalculatedFor each fatigue point OrcaFlex calculates damage values that are reported in the fatigueresults. Here is a summary of how the calculation is done:

• For each of the 3 principal stress directions (axial, radial and circumferential), OrcaFlexcalculates the time history of the stress component that occurred in that principal direction,at that fatigue point, in that load case. See Principal Stress Calculation below for details.

• OrcaFlex then calculates the damage values that correspond to each of these 3 principalstress component time histories. See Component Damage Calculation below for details.

• OrcaFlex then chooses the largest of those 3 principal damage values and this is taken tobe the damage value at that fatigue point due to one occurrence of that load case. The loadcase worksheets in the fatigue results report these single-occurrence load case damagevalues for each fatigue point.

Note: This worst damage is usually due to the axial stress, since that includes theeffects of both tension and bending.

• OrcaFlex then scales the above single-occurrence load case damage values to allow for theexposure associated with that load case. For regular analysis this means multiplying by thenumber of cycles specified for this load case. For rainflow analysis this means multiplyingby the exposure time divided by the simulation period analysed for that load case. Thisgives the total exposure damage value from that load case at this fatigue point. These total-exposure load case damage values appear in the Damage Tables worksheet in the fatigueresults.

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• Finally, OrcaFlex then sums these total-exposure load case damage values to obtain thegive the final total damage value at that fatigue point. These total damage values are againreported in the Damage Tables worksheet in the fatigue results.

Principal Stress Calculation

At each fatigue point, and for each load case, OrcaFlex calculates the stress matrix RRStress RCStress RZStress RCStress CCStress CZStress RZStress CZStress ZZStressfrom the various loads that acted on the pipe during the load case simulation. See Pipe StressCalculation.

Here the 3 diagonal entries RRStress, CCStress and ZZStress are the principal radial,circumferential (or hoop) and axial (or longitudinal) stresses, respectively, and the 3 off-diagonalterms are the shear stresses.

Note: Strictly speaking, the principal stresses are the eigenvalues of this matrix. Butin practice the principal axes of stress are almost always very close to thenatural axes of the pipe, in which case the diagonal terms are very goodestimates of the principal stresses. The fatigue analysis assumes that thisholds and therefore treats the diagonal terms as being the principal stresses.The validity of this assumption can be confirmed by checking that the peakvalues of any of the shear stresses are small compared to the peak values ofthe diagonal terms. All these peak values are reported in the fatigue analysisresults.

Component Damage Calculation

The S-N curve defines the number of cycles to failure, N(S), for a given stress range S, and alsodefines a fatigue limit, FL, below which no damage occurs. OrcaFlex uses these to calculate adamage value given by:

D(S) = 1/N(S) if S > FL

D(S) = 0 if S <= FL

This damage value can be thought of as the proportion of the fatigue life that is used up by 1cycle of stress range S.

Note: If the S-N curve is defined by parameters then for S > FL we have Log10(N) = A - b Log10(S) so D(S) can be expressed in the following form: D(S) = 10^-(A - b Log10(S)) = (10^-A) x (S)^b.

OrcaFlex uses this damage definition to calculate the component damage value that isassociated with a given principal stress component in a given load case. This calculationdepends on whether a Regular or Rainflow fatigue analysis is done, as follows:

• For regular analysis the minimum and maximum values that the stress component tookover the last simulated wave cycle are used to give a stress range S. The associatedsingle-occurrence load case damage value is then given by D(κS) where κ is the stressconcentration factor specified in the fatigue analysis data.

• For rainflow analysis the stress component time history is analysed using the rainflow cyclecounting method. This gives a number of stress ranges for half cycles, say S(i) where i runsfrom 1 to the number of stress ranges. The associated single-occurrence load case

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damage value is then given by 0.5*(Sum of D(κS(i)) where the summation is over allthe half cycles and κ is the stress concentration factor. Note that the factor 0.5 is presentbecause the rainflow algorithm counts half cycles.

5.4 POST-PROCESSING RESULTS

5.4.1 Post-processing ResultsOrcaFlex users often use spreadsheets to post-process their OrcaFlex results. This can bedone manually by transferring the results from OrcaFlex into the spreadsheet using copy +paste. However, this is laborious and error prone if a lot of results need transferring, so wehave developed special facilities to automate the process.

This automation is done by creating a special Excel spreadsheet that has special buttons thattrigger automatic extraction of specified results from one or more OrcaFlex files into nominatedcells in the spreadsheet. You can then use the normal spreadsheet facilities to calculate otherpost-processed results from those OrcaFlex results.

Note: The post-processing spreadsheets work with Excel 97 or later and requireOrcaFlex to be installed on the machine.

Creating Post-Processing Spreadsheets

You can create post-processing spreadsheets from Excel templates that are supplied withOrcaFlex. There are two types available:

• Results.xlt is a general purpose spreadsheet template for extracting results from OrcaFlexsimulation files.

• Stress.xlt is a more specialised spreadsheet template, for extracting detailed stress resultsfrom OrcaFlex simulation files.

You should base your own post-processing spreadsheets on these templates, which areinstalled in the OrcaFlex installation directory when you install OrcaFlex is on your machine. Tocreate your own post-processing spreadsheet, open the Windows Start menu, selectPrograms|Orcina Software and then select New Results Spreadsheet or New StressSpreadsheet. (These are convenient shortcuts to the above template files and when usedExcel starts up and creates a new spreadsheet based on that template.)

Before you try to use the new spreadsheet you need to save it to a file; it can be given any validfilename. It is usually most convenient to save it to the directory containing the OrcaFlex filesfrom which you want to extract results, since you can then specify the names of those files inthe spreadsheet using relative paths. This makes it easier if you later need to rename thedirectory or move the spreadsheet and OrcaFlex files to some other directory.

For example post-processing spreadsheets, see J02 Results and J03 Stress Analysis.

5.4.2 Results SpreadsheetA Results spreadsheet is a post-processing spreadsheet that enables you to automate theextraction of results from OrcaFlex files into Excel. For an example see J02 Results. To createyour own see Creating Post-Processing Spreadsheets.

Note: For extracting detailed stress results a Stress spreadsheet may be suitable.

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A Results spreadsheet consists of an Instructions worksheet, plus other worksheets to receivethe OrcaFlex results and for any derived results.

The Instructions worksheet consists of an instructions table and two buttons that run Excelmacros that read and obey those instructions. Do not change the name of the Instructionsworksheet, since the macros use that name to find that worksheet.

Instructions Table

Each row in the instructions table is a separate instruction. Each instruction has 2 parts - thefirst part specifying a label cell to be written and the second part specifying some associatedresults cells to be written. Each part is optional, so you can have an instruction that has a blankcommand cell and so only writes a label, or one that has a blank label cell and so only writesresults.

The end of the table is taken to be the first row that has both its label and command columnsblank, so you cannot have an instruction that has no label and no command. In particular, youcannot have a blank row in the middle of the instruction table. Also, the macros assume thatthe first instruction is row 5 of the worksheet, so do not insert or delete rows above this.

The macros ignore the formatting of the spreadsheet, so you can use things like bold, italic,background colours etc. to make the worksheets easy to read, and you can also re-sizecolumns or rows to suit. This applies to all the worksheets, including the Instructions worksheet.

Process Buttons

The Process All button runs a macro that obeys all the instructions in the table, starting at thetop of the table and working down. The Process Selected button tells the spreadsheet toprocess only the instructions in the currently selected cell or block of cells, again in top tobottom order. If the currently selected cell(s) are not in the table then this button does nothing.

The example instruction table illustrates how the instructions work:

• Click the Process All button. You should see the Example1 worksheet being filled in andthen a new worksheet called Example2 being created and filled in. If you look at theinstructions table on the Instructions sheet then you will see how this was specified.

• The first block of instructions in the table specifies that the simulation file Example1.simshould be loaded and then various results extracted from it and written to various cells in aworksheet called Example1. Note that the example instructions are set up to work withexample simulation files that are installed with the Results.xls spreadsheet.

• The Example1 worksheet already existed, and it was already set up with suitable columnwidths and cell properties (e.g. a larger font size, right alignment for some cells). So theinstructions simply "filled in" various cells in that sheet.

• The second block of instructions in the table specifies that the simulation file Example2.simshould be loaded and then various results extracted from it and written to a worksheet calledExample2. No such sheet existed, so one was created.

• Because the worksheet Example2 was newly created it has default properties and so it notyet properly formatted. You can now format it (resize the columns, change cell font sizesetc.) as you wish. Next time you click the Process All button the worksheet will retain theformatting you set up.

• Now go back to the Example1 worksheet and try setting a new cell to calculate a "derived"result. For instance you could calculate the tension range by setting cell H4 to "=G4-F4".

• Now delete the contents of cells G4 and F4 on the Example1 worksheet - cell H4 willbecome zero. Now go back to the Instructions worksheet and in the top half of the

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instruction table select the block of 6 cells in the column headed 'Command' that contain Minor Max. Now click the Process Selected button - this button obeys just the instructions inthe currently selected block, so cells G4 and F4 on the Example1 worksheet will berewritten and your derived cell H4 will be automatically updated (assuming you have re-calculation switched on in Excel).

You should now have a good idea of how the spreadsheet works and you can now modify thespreadsheet to suit your own purpose. To do this, delete the example instructions from thetable and set up your own instructions to specify the results you want and where you want them.Details of the instruction format follow.

5.4.3 Instruction FormatIn the results spreadsheet, each instruction consists of the following cells. See also Tips andTricks.

Sheet

Specifies the name of the worksheet in which cells are to be written. If a worksheet with thisname already exists then the specified label and output cells will be overwritten, but other cellswill be left unchanged. If no sheet of that name exists then one will be created.

Label Cell

Specifies the cell, in the specified worksheet, to which the label (if not null) will be written.

Label

Specifies the label string to be written to the label cell. This cell can be left empty, in whichcase the label cell is ignored.

Output Cell

Specifies the cell, in the specified worksheet, to which results should be written. Somecommands specify multiple-value results - for example a time history consists of a column ofresults. In this case the Output Cell specifies the top left cell of the block of cells to be written.

Note: The Output Cell (or Label Cell) can be specified directly, e.g. B7, but can alsobe specified indirectly - see Tips and Tricks.

Command

This should be one of the pre-defined commands or else empty. If the command cell is emptythen the output cell is ignored. One pre-defined command, Load, is special - it causes asimulation file to be loaded, ready for subsequent commands to extract results from thatsimulation.

Object Name

The name of the object, in the OrcaFlex simulation file, for which results are wanted.

Node Number, Arc Length

These are only used if Object Name specifies a Line in the simulation file. In this case youmust specify the position on the line for which results are wanted. You can either specify theposition in either the Node Number column or in the Arc Length column but not both. In theNode Number column you can specify an actual node number, but alternatively you can specify

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'A' or 'B' (meaning end A or B) or 'Touchdown' (meaning the touchdown point). The results aregiven for the nearest appropriate result point; see Line Results for details.

For the Range Graph and Range Graph Summary commands you can specify a range of arclengths, e.g. "20 to 50".

Simulation Period

The period of simulation for which results are wanted. This can be Whole Simulation, LatestWave or a stage number (0 for the build-up, 1 for stage 1 etc.).

It can also be a specified period of simulation, given in the form "t1 to t2" where t1 and t2 arenumeric time values that are in the simulation and Simulation Start Time <= t1 <= t2 <=Simulation End Time. For example "20 to 30" or "-12.5 to +35.7".

Note: This specified period format can be used to extract results at a single timepoint; for example the period "27.4 to 27.4" will give the results at the nearestlog sample to time 27.4.

Variable

The results variable that you want. This should be set to the same name (not case sensitive) asis used for the results variable in OrcaFlex. For example Effective Tension, curvature, surge,etc.

5.4.4 Pre-defined CommandsIn the results spreadsheet, the Command Cell can contain one of the following commands:

LOAD <FILENAME>

This command tells OrcaFlex to open the specified simulation file. Subsequent resultsextraction commands then apply to that file.

You can either specify the full path of the file, for example:

Load c:\Project100\Case1.sim

or else use a relative path (relative to the directory containing the spreadsheet). The latter isoften more convenient. For example if the file Case1.sim is in the same directory as thespreadsheet then you can use the command:

Load Case1.sim

and this has the advantage that there is no need to alter the spreadsheet if the directory isrenamed or the files are moved to a different directory.

SAMPLE TIMES

Returns the time values that apply to the time history results. This command returns a columnof N numbers, where N is the number of OrcaFlex log samples that are in the specifiedSimulation Period. So if Output Cell is set to G5 and there are 500 log samples in theSimulation Period, then the time values for those log samples will be written to cells G5..G504.

TIME HISTORY

Returns the time history values of the specified variable. This command returns a column of Nnumbers, as with the Sample Times command.

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MIN, MAX, MEAN and STANDARD DEVIATION

Min return a single number, equalling the minimum value of the specified time history variableduring the specified simulation period. Similarly for Max, Mean and Standard Deviation (whichcan be abbreviated to Std Dev).

LINKED STATISTICS

The Linked Statistics command outputs the same information as the Linked Statisticscommand on the OrcaFlex results form. In the Variable column of the instruction you shouldspecify two or more results variable names, separated by commas. The command outputs atable of statistics for those variables, occupying 2N+3 rows by N+2 columns, where N is thenumber of variables specified.

RANGE GRAPH and RANGE GRAPH SUMMARY

These commands output tables containing either the full set of range graph results, or asummary, for the specified variable of a line. They are available for any line variable for which arange graph is available in OrcaFlex.

The Range Graph command gives a table having 7 columns, containing Arc Length, Minimum,Maximum, Mean, Standard Deviation, Upper Limit, and Lower Limit. For each point on the linea row is generated in the table containing the statistics of the values that occurred at that pointduring the specified simulation period.

The Range Graph Summary command gives a table having two rows, one for the overallminimum and one for the overall maximum. Each row has 4 cells; two are label cells and theother two contain the overall minimum (or maximum) value that occurred at any point on the lineduring the specified simulation period, and the arc length at which it occurred.

To use these commands you must specify, in the Simulation Period column of the instruction,the period of simulation for which you want results.

If the Arc Length column in the instruction is left blank then the results will apply to the wholeline. Alternatively, you can restrict these commands to only cover part of the line, by specifyinga range of arc lengths, e.g. "20 to 50", in the Arc Length column. The table will then onlyinclude results for points whose arc length is within the specified range. The length units usedmust be the same as those used in the OrcaFlex simulation file.

Note that the Node Number column of the instruction is not used for either of these commands.

5.4.5 Tips and TricksHere are some useful tips for setting up the instructions table of a Results spreadsheet.

Use Excel's "=" facility

If you have several instruction table cells that are equal to some other cell, A9 say, then setthem to "=A9". That way when you alter A9 then the other cells will automatically alter to match.For example if you have a block of 10 instructions that all output their result to sheet "Load Case3" then set the first instruction's Worksheet cell, cell A9 say, to "Load Case 3" and then set theother Worksheet cells to "=A9". You can now change the destination sheet for all theinstructions by simply altering cell A9.

Use OffsetCell to specify output cells indirectly

You can do a similar thing with the Output Cell (and Label Cell) by using the specialspreadsheet function OffsetCell(PointerCell, ColOffset, RowOffset).

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Suppose that, on your instruction sheet, the output cell D9 contains the address "C12"; i.e. D9points to C12 (on the output sheet). Then you can now use C12 as an Origin and set up someother output address relative to it. To do this set the other output cell to "=OffsetCell(D9, 3, 4)",which means "the cell 3 columns right and 4 rows down from the cell referenced in D9". Theoutput will therefore be placed in cell F16 on the output sheet.

The advantage of this is that you can now easily redirect the output of a whole set ofinstructions by simply changing the first one's output cell. The other instructions' outputdestinations stay fixed relative to the first's.

Here's the formal definition of OffsetCell. It takes 3 parameters: PointerCell is the address of acell that contains the address of an OriginCell, and ColOffset & RowOffset are integersspecifying an offset from that OriginCell. The function returns the address of the cell that isColOffset columns right and RowOffset rows down from the cell that PointerCell points at.

5.4.6 Error HandlingIn the results spreadsheet, errors in instructions are handled by either displaying an errormessage window or by writing an error message to the specified output cell. So when settingup new instructions:

• Check carefully that you have set all the instruction cells correctly.

• Then test the instructions by selecting them and using the Process Selected button.

• Then check that the specified Label Cells and Output Cells have been set correctly.

5.4.7 Stress SpreadsheetThe file Stress.xls is an Excel spreadsheet for extracting detailed stress components fromOrcaFlex simulation files. You can then add your extra worksheets to it to do whatever post-processing of results you require.

The stress spreadsheet consists of one main worksheet, called Main Sheet, and then a numberof load case worksheets into which the OrcaFlex stress results will be written. Each load caseworksheet corresponds to one Line in one OrcaFlex simulation file, so if you want to extractresults from 3 simulation files then you need to set up 3 load case worksheets.

To create a new stress results worksheet click the Add Load Case Sheet button on the mainworksheet. The load case worksheets are characterised by the fact that their top-left cellcontains "Stress results for single case", so do not alter this cell. However, on each load caseworksheet there are two cells that you must set up - the simulation file name (including its path)and the name of the line for which results are to be extracted. You must not alter any othercells on the load case worksheets, but you can rename the load case worksheets with suitablenames.

When you have set up the load case worksheets that you require you must then set up, on themain worksheet, the following cells specifying the points and the stress results required. Again,you should not alter any other cells on the main worksheet.

• Simulation Period is the period of simulation for which time history stress results arewanted.

• The points for which results are wanted are specified using cylindrical polar coordinates (r,theta, z), where:

z is the unstretched line length from end A to the point r is the radial distance from the centreline to the point

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theta is the circumferential angle, measured positive clockwise from the local line Lxdirection towards the Ly direction.

• Arclength is the arc length, z, from end A, to the points (r, theta, z) on the line for whichstress results are wanted. The results will be for the mid-segment point of the OrcaFlexsegment that contains that arclength.

• Radial Positions specify whether results are wanted at the line's StressID or StressOD, orboth.

• Number of Theta values is the number of points, around the line circumference, for whichresults are wanted. So if 4 theta values are requested then results will be extracted fortheta=0, 90, 180 and 270 degrees.

• Stress Components specify which components of the stress tensor are required. Thestress tensor is a 3 by 3 matrix of stress components, with respect to a local RCZ set ofright-handed Cartesian axes at the result point. R points radially outwards from the point, Cis circumferential and Z points axially along the line towards end B. So "RR Stress" is theradial stress, "CC Stress" is the hoop stress and "ZZ Stress" is the axial or longitudinalstress.

When you have set up the load case worksheets you require and set up the main worksheet tospecify the stress results you want then you are ready to extract results. To do this simply clickthe Collect Results button on the main worksheet. For each load case worksheet, thespecified stress results are then read from the specified OrcaFlex simulation file and time historycolumns containing the results are created on the load case worksheet.

When the Collect Results button is clicked the results are extracted from the OrcaFlexsimulation files and written into the load case worksheets. If the OrcaFlex cases are later re-run, for example because of a change in the model, then your spreadsheet can simply be re-opened and the Collect Results button clicked to refresh the spreadsheet with the new results.

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6 THEORY

6.1 COORDINATE SYSTEMSOrcaFlex uses one global coordinate system GXYZ, where G is the global origin and GX, GYand GZ are the global axes directions. In addition, there are a number of local coordinatesystems, generally one for each object in the model. All the coordinate systems are righthanded, as shown in the following figure, which shows the global axes and a vessel with its ownlocal vessel axes Vxyz. In general we use Lxyz to denote a local coordinate system. Anothercoordinate system that we make widespread use of is the Line End orientation which we denoteExyz.

z

Sea Surface

Z

Y

XG

V

yx

Vessel Axes

Global Axes

Figure: Coordinate Systems

The global frame of reference must be a right-handed system and its Z-axis GZ must bepositive upwards, but otherwise it is chosen by the user. You can therefore choose the positionof the global origin G and the horizontal direction GX according to what suits the problem beinganalysed.

The local coordinate systems for each type of object are described in the section about thatobject, but typically the origin is at a selected fixed point on the object and the axes are inspecial fixed directions, such as the surge, sway and heave directions for a vessel. The seabedalso has its own seabed origin and local axes, with respect to which the seabed shape isdefined.

The local axes are distinguished from the global axes by using lower case; for example the localobject direction is referred to as the "x-direction" whereas the global direction is referred to asthe "X-direction". Whenever data or results are coordinate system dependent, they are referredto as being either global-relative (and are labelled in upper case) or object-relative (and arelabelled in lower case).

You can ask OrcaFlex to draw the local axes on the 3D view. This enables you to see the localaxes and check that they are as wanted.

Most of the data and results are given relative to the global axes, including:

• data defining the sea, such as the mean sea surface Z level and the current and wavedirection.

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• the positions of objects; for example the position of the vessel is defined by giving the globalcoordinates of the vessel origin V

The most common object-relative items are:

• the coordinates of points that move with the object, such as the vertices of a vessel or theconnection point when something is connected to a buoy

• the direction-dependent properties of objects, such as drag and added mass coefficients,moments of inertia, etc.

6.2 DIRECTION CONVENTIONSDirections and Headings

Wave, current and wind directions are specified in OrcaFlex by giving the direction in which thewave (or current or wind) is progressing, measured positive from the global X-direction towardsthe global Y-direction, as shown in the following figure:

GY

GX 0

30150

330

180

270

90

210

Direction relativeto global axes

Figure: Directions and Headings

This convention is also used when specifying vessel headings and slope directions:

• The vessel heading is the direction in which the vessel Vx-axis is pointing.

• The slope direction for the seabed or a shape is the direction that points up the slope. Forthe slope of a plane shape that is connected to another object, the slope direction isspecified relative to that object's axes.

Vessel response to waves (similarly for current and wind) depend on the wave direction relativeto the vessel, so vessel type properties are given for a specified relative wave direction(= Wave Direction - Vessel Heading). So a relative wave direction of 0 means a wave comingfrom astern and a relative direction of 90 means one coming from starboard.

Azimuth and Declination

Directions are defined in OrcaFlex by giving two angles, azimuth and declination, that arebroadly similar to those used in navigation, gunnery, etc. As with positions, directions aresometimes defined relative to the global axes and sometimes relative to the local object axes.

For directions defined relative to the object axes Oxyz, the azimuth and declination angles aredefined as follows:

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• Azimuth is the angle from the x axis to the projection of the direction onto the xy plane. Thepositive x axis direction therefore has Azimuth = 0, and the positive y axis direction hasAzimuth = 90 degrees.

• Declination is the angle the direction makes with the z axis. Therefore Declination is 0 forthe positive z-direction, 90 degrees for any direction in the xy plane, and 180 degrees for thenegative z-direction. When Declination is 0 or 180 degrees, Azimuth is undefined (OrcaFlexreports Azimuth = 0 in these cases).

Directions relative to the global axes are defined in just the same way, simply replacing the localxyz directions above with the global XYZ directions. A global declination of 0 therefore meansvertically upwards, 90 means horizontal and 180 means vertically downwards.

When a direction is being defined, the "sign" of the direction must also be defined. For example"vertical" does not fully define a direction - it must be either "vertically up" or "vertically down"before the azimuth and declination angles can be derived. The "sign" conventions used inOrcaFlex for directions are:

• For Lines, axial directions are always defined in the A to B sense, in other words from end Atowards end B. Thus a vertical line with end A at the top has declination 180 degrees.

• For Winches and Links, axial directions are defined in the sense 'from first end towardssecond end'. Thus a link with end 1 directly above end 2 has declination 180 degrees.

6.3 OBJECT CONNECTIONSLines, links, winches and shapes are special objects that can be connected to other objects.First consider connecting a line to another object. To enable connections to be made each linehas two joints, one at each end, which are drawn as small blobs on the ends of the line, whenthe model is in Reset state. To distinguish the two ends, the joint at end A is drawn as atriangle and the joint at end B as a square.

Each of these line end joints can either be Free or else be connected to a Vessel, 3D Buoy, 6DBuoy, the Global Axes or the seabed. Lines cannot be connected to themselves, to other lines,nor to a Link or Winch. When a line's joint is Free, that end of the line is free to move and this isindicated by the joint being drawn in the same colour as the line. When the joint is connected toanother object, that end of the line becomes a slave and the object to which it is connectedbecomes its master. The connection is then indicated by the joint being drawn in the colour ofits master.

Links and Winches also have joints at each end (winches can also have extra intermediatejoints) and these are connected to other objects in the same way as with lines, but with thefollowing exceptions.

• Link and winch joints cannot be Free - they must always be connected to some master.

• Link and winch joints can be connected to nodes on a line, as well as to Vessels, 3D Buoys,6D Buoys, the Global Axes or the seabed. This allows, for example, a winch to be attachedto the end node of a line so that winching in or out can be modelled.

Shapes have a single joint which can be connected to Vessels, 3D Buoys, 6D Buoys, the GlobalAxes or the seabed.

When a joint is connected to a master, the connection is made at a specified master-relativeposition and the master object then determines the position of its slave - the slave is draggedaround by its master as the master moves. In response the slave applies forces and momentsto its master - for a line these are simply the end force and moment applied by the line.

Because neither the Global Axes nor the seabed move, a joint connected to either of them issimply fixed in one position. The difference between them lies in how the connection point is

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specified. For a connection to the Global Axes, the X, Y and Z coordinates of the connectionpoint are specified relative to those axes and the joint is called Fixed. For a connection to theseabed the X and Y coordinates are specified relative to the global axes, but the Z coordinate isspecified relative to the seabed Z level at that X,Y position; the joint is then referred to as beingAnchored. So for an Anchored joint, Z=0 means that the connection is exactly on the seabedand Z=1 means it is 1 unit above the seabed. By using anchored joints you can therefore avoidthe need to calculate the seabed Z level at the given X,Y position (not simple with slopingseabeds).

6.4 INTERPOLATION METHODSOrcaFlex use a number of different methods for interpolating data. These methods aredescribed below:

• Linear. The data is assumed to follow a straight line between each (X,Y) pair. Linearinterpolation is said to be piecewise linear. Curves that are linearly interpolated arecontinuous but their first derivative is discontinuous at each X data point.

• Cubic spline. Cubic spline interpolation fits a cubic polynomial over each interval in thedata - that is the fitted curve is piecewise cubic. These cubics are chosen so that both firstand second derivatives are continuous at each X data point.

• Cubic Bessel (also known as Parabolic Blending). Cubic Bessel interpolation is similar tocubic spline in that it is also piecewise cubic. However, for this method the cubics arechosen so that the first derivative at each data point equal to the unique parabola passingthrough 3 consecutive data points. The fitted curve has continuous first derivative butdiscontinuous second derivative.

Choosing interpolation method

Sometimes OrcaFlex provides a choice of interpolation method. In general we wouldrecommend that you use the default interpolation method, but in some cases it may beappropriate to use a different method. To decide you need to take into account what theinterpolated data is used for and the different properties of the interpolation methods.

If continuity of first derivative is not required then linear interpolation is often appropriate. It hasthe advantage that it is very simple.

The other 2 methods are piecewise cubic and they produce smooth curves, but they cansometimes produce curves that have overshoots. For example the following graphs show howeach method interpolates a particular set of data. Although the greatest Y value in the data is 8,the interpolated curves for cubic spline and cubic Bessel both exceed this value (although theeffect is much smaller for cubic Bessel). How serious this overshoot is depends on the data - itcan be much more serious than illustrated here or sometimes there can be no problem at all.

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If you are using either of the piecewise cubic interpolation methods then you should alwayscheck whether the interpolated curve gives an appropriate fit to the data. If it does not then youusually need to supply more data points. The main difference between the two is that cubicspline interpolation has a continuous second derivative whereas cubic Bessel does not.However, in many cases this is not important, and one attractive feature of cubic Besselinterpolation is that it is less prone to overshoot than cubic spline.

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6.5 STATIC ANALYSIS

6.5.1 Static AnalysisThere are two objectives for a static analysis:

• to determine the equilibrium configuration of the system under weight, buoyancy,hydrodynamic drag, etc.

• to provide a starting configuration for dynamic simulation.

In most cases, the static equilibrium configuration is the best starting point for dynamicsimulation and these two objectives become one. However there are occasions where this isnot so and OrcaFlex provides facilities for handling these special cases. These facilities arediscussed later.

Static equilibrium is determined by a series of linked iterative calculations. At the start of thecalculation, the initial positions of the vessels and buoys (3D and 6D) are defined by the data:these in turn define the initial positions of the ends of lines connected to them. The equilibriumconfiguration for each line is then calculated, which determines the forces applied by the lines tothe other free bodies. The out of balance force vector acting on each free body (3D or 6D buoy)is then calculated together with the associated stiffness matrix, and a new position for the bodyis estimated by a Newton-Raphson technique. The calculation is then repeated from this newstarting position. The process is repeated until the net force vector on each free body is zero(within a small tolerance). For details see Statics of Buoys and Vessels.

For simple systems, the static analysis process is very quick and reliable. For very complexsystems with multiple free bodies and many inter-connections, however, convergence may bedifficult to achieve. To help overcome this problem, OrcaFlex provides facilities for the user tosuppress some of the degrees of freedom of the system and approach the true equilibrium by aseries of easy stages. See Statics of Buoys and Vessels.

Finally, the static analysis can also be turned into a steady state analysis by specifying non-zerostarting velocity on the General Data form. This is useful when modelling towed systems orother systems that have a steady velocity.

6.5.2 Statics of LinesStatics of LinesWhen you do a static analysis OrcaFlex does a static analysis of each line in the model.

Note: The lines are analysed in the order they appear in the model browser. So ifyou are having a problem with the static analysis of a particular line, and thereare a lot of lines in the model, then you can make investigation of the problemeasier by dragging the line up to the top of the list in the model browser.

The static analysis of a given line has two stages:

• The first stage calculates an initial position of all the nodes on the line, using the StaticsMethod specified on the line data form.

• The second stage, which is optional, is called Full Statics. If Full Statics is included, then itcalculates the true equilibrium position of the line, starting from the initial position found bystage 1. If Full Statics is not included, then the line is simply left in the initial position foundby stage 1, which (depending on the Statics Method chosen) may not be an equilibriumposition.

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Catenary StaticsThe Catenary method calculates the equilibrium position of the line, but it ignores the effects ofbending and torsional stiffness of the line or its end terminations.

The Catenary method also ignores contact forces between the line and any solid shapes in themodel, but it does include all other effects, including weight, buoyancy, axial elasticity, currentdrag and seabed touchdown and friction.

Note: For technical reasons, seabed effects are only included if end B is exactly onthe seabed - see Seabed Touchdown.

Because bend stiffness (and other) effects are not included in the Catenary method, the positionfound is not, in general, an equilibrium position. Therefore Full Statics. should normally beincluded unless it is known that the omitted effects are unimportant. Nevertheless, the Catenaryposition is often quite close to the true equilibrium position, especially when bend stiffness is nota major influence.

The Catenary algorithm is robust and efficient for most realistic cases but it cannot handlecases where the line is in compression. This is because, when bending stiffness is ignored,compression means the line is slack and there is no unique solution.

The algorithm is an iterative process that converges on the solution. If necessary; you cancontrol the maximum number of iterations that are attempted, as well as other aspects of theconvergence process - see Catenary Convergence.

Spline StaticsThe Spline method gives the line an initial shape that is based on a user-defined smooth Bezierspline curve. It is therefore not, in general, an equilibrium position, and so when it is used FullStatics should be included if you want the equilibrium position to be found.

The Bezier curve is specified by the user giving a series of control points - it is a curve that triesto follow those control points - and the Bezier curve and its control points (marked by +) can beseen on the 3D view when in Reset state. The smoothness of the spline can be controlledusing the spline order.

The Spline method puts the line into a position that, as far as possible, follows the Bezier curve.However the Bezier curve may often have the wrong length (depending on how accurately youhave set up the control points), so the Spline method scales the Bezier spline curve up or downuntil the resulting line shape has the correct pre-tension, as specified on the line data form.

Quick StaticsThe Quick method simply leaves the line in the position that it was drawn when in Reset state.This is a crude catenary shape that (for speed reasons) ignores most effects, includingbuoyancy, drag, bending and torsional stiffness, and interaction with seabed and solids. In factthe position set by the Quick method only allows for the line's average weight per unit lengthand axial elasticity, so it is not usually an equilibrium position (though for simple cases it may bequite close). The Quick method should usually be used only as a preliminary to Full Statics.

Prescribed StaticsThe Prescribed method is intended primarily for pull-in analyses. It provides a convenient wayof setting the line up in the as laid (i.e. pre pull-in) starting position, ready for a time simulation ofthe pull-in. The starting shape of the line is specified by defining a track on the seabed (seeTrack Data). The track is defined as a sequence of track sections each of which is a circular arcof user-specified length and angle of turn and the line is laid along this track. See Laying Outthe Line.

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Y

XStartof track

End AAzimuth = 10°

Track Section 1Length = 150Turn = 0 Track section 2

Length = 100Turn = -90

Track section 3Length = 100Turn = 90

Track Section 4Length = 150Turn = 0

Continuation oflast track section

10°

Figure: Plan View of Example Track

Full StaticsThe Full Statics calculation is a line statics calculation that includes all forces modelled inOrcaFlex. In particular it includes the effects of bend stiffness and interaction with shapes.These effects are omitted from the Catenary calculation, and this sometimes results insignificant shock loads at the start of the simulation, when the effects of bend stiffness andshapes were introduced. Because the Full Statics calculation includes these effects, no suchshock loads should occur when it is used. We therefore recommend using Full Statics for mostcases.

To use Full Statics set the Full button on the Line data form to "Yes". Full statics needs astarting shape for the line, and it uses the specified Statics Type to obtain this; it then finds theequilibrium position from there. You must therefore also set the Statics Type to give areasonable starting shape, choosing from one of the four other statics methods: Catenary,Prescribed, Quick or Spline.

Which Statics Type you should choose for the starting shape depends on the model in question.In general you should choose the statics type that gives the best initial estimate of the line'sstatic position. For lines with no buoyant sections and no interaction with shapes or the seabed,the Quick statics type may well suffice. If there is seabed interaction or a buoyant section thenCatenary might be better. For lines that interact with a shape, the Spline starting shape isperhaps best since it enables you to ensure that the line starts on the correct side of the shape.

Which Line Statics method to useThe settings to use for the line data items Statics Method and Full Statics depend on the type ofsystem being modelled and the type of static position wanted.

The default settings (for a new line) are the Catenary method followed by Full Statics. This isoften a good choice, since the Catenary method is fast and in many case gives a good initialestimate of the equilibrium position. It therefore often provides a good starting point for the FullStatics calculation, which then refines the position to take into account the effects that theCatenary omits, such as bending and torsional stiffness and interaction with solids.

There are situations where you may need to use other settings. Some specific cases aredescribed below, but first here are some general points to bear in mind.

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Full Statics should be included if you want the true equilibrium position to be found.

When Full Statics is included, the first stage Statics Method is only used to give the initialstarting shape for the Full Statics. The choice of Statics Method is then, in principle, notimportant, since the final position found will be the equilibrium position, irrespective of the initialstarting position. However it is normally best to choose the Statics Method that gives the bestinitial estimate of the desired equilibrium position, since this will give the best starting positionfor the Full Statics to work from.

There are some cases where the choice of Statics Method is important. Firstly, in cases wherethere may be more than one equilibrium position, the Full Statics calculation will tend to find theone that is closest to the initial starting position found by the Statics Method. Secondly, the FullStatics calculation is iterative and may have difficulty converging if the initial Statics Methodposition from which it starts is a long way form the true equilibrium position. In both thesesituations, it is generally best to choose the Statics Method that gives the best initial estimate ofthe desired equilibrium position.

Catenary convergence failure

The Catenary method is iterative and may fail to converge. It may be possible to solve this byadjusting the Catenary Convergence Parameters on the line data form. If this proves difficult,then an alternative is to use one of the other statics methods. The Quick method may suffice,or alternatively the Spline method may be needed. Providing Full Statics is included then thefinal static position found will be the same.

Full Statics Convergence Failure

Full Statics is also an iterative calculation and may sometimes fail to converge. Theconvergence process is controlled by the Full Statics Convergence Parameters on the line dataform so it may be possible to obtain convergence by adjusting some of those parameters.

However, the problem may be due to the initial starting position obtained by the specified staticsmethod being a long way from the equilibrium position. In this case it may be necessary for theuser to specify the Spline statics method and specify control points that give a good startingshape for the Full Statics.

Note: When setting up the spline control points, it is often useful to first set FullStatics to "No". This allows you to examine and refine the spline shape, byrunning the static analysis and adjusting the control points until the splineshape is close to the desired shape. You can then set Full Statics back to"Yes" in order to find the true equilibrium position.

Contact With Solids

The Catenary and Quick methods both ignore contact with solids and so they may well give apoor initial position for the Full Statics to work on. As a result the Full Statics calculation mayfail to converge, or else converge to the wrong equilibrium position (e.g. one in which the line ison the wrong side of the solid). In both these cases it may be better for the user to select theSpline method and then specify control points that give an initial shape that is close to thedesired equilibrium position.

Pipeline Pull-In

For a pipe lying on the seabed there are usually many equilibrium positions, since seabedfriction will often be able to hold the pipe in the shape it was originally laid. For pull-in analysisthis originally-laid shape is generally known, and the Prescribed method can be used to definethis shape.

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It is then optional whether Full Statics is included or not. Normally, it would not be included. If itis included then it will have no effect if the Prescribed position is already in equilibrium - i.e. iffriction is sufficient to hold the pipe in that position. But if friction is not sufficient then FullStatics will tend to find a nearby position that is in equilibrium.

6.5.3 Statics of Buoys and VesselsEach buoy and vessel can be either included or excluded form the static analysis. This iscontrolled by the data item Included in Static Analysis on the object's data form.

Notes: You can also use the Buoy Degrees of Freedom Included In Static Analysis.data item, on the General data form, to include or exclude all buoys with asingle setting.

Also, for 6D buoys, you can include just the translational degrees of freedom(X,Y,Z) and exclude the rotational degrees of freedom. This is sometimesuseful as an aid to convergence.

If a buoy is excluded from the static analysis, then when the static analysis is done OrcaFlex willsimply place the buoy in the Initial Position specified on the buoy data form. This will not, ingeneral, be the equilibrium position. The same applies to vessels.

If any buoys or vessels are included in the static analysis, then the static analysis finds theequilibrium position of those buoys and vessels, using an iterative procedure, as follows:

1. OrcaFlex first places all of the buoys and vessels in their Initial Position, as specified on theirdata forms. Buoys or vessel that are excluded from the analysis are then simply left in thatposition.

2. OrcaFlex then calculates the forces and moments acting on each of the buoys and vesselsthat are included in the analysis. This takes into account weight, buoyancy, drag, appliedload etc., and also loads from any attached links, winches or lines. The calculation thereforeinvolves calculating the statics of any lines that are attached, which is often itself an iterativecalculation.

3. Next, OrcaFlex moves the included buoys and vessels by an amount that is aimed atbalancing the forces and moments acting on them. Note that this movement and loadbalance is only done with the degrees of freedom that are included in the analysis. Forvessels these are surge, sway and yaw only. For 6D buoys you can specify whether toinclude just the translational degrees of freedom or the rotational degrees of freedom aswell.

4. Steps 2 and 3 are then repeated until all included buoys and vessels are in equilibrium.

This iterative procedure usually converges successfully, but in some cases there can bedifficulties. To give the best chance of convergence you should specify buoy and vessel initialpositions that are good estimates of the true equilibrium position. Often you can obtain goodestimates by running static analyses of a simplified model and then using the buoy positionsfound as the initial positions for the more complex model. There is a button on the general dataform for this purpose - see Use Static Positions.

Note: As an aid to static analysis, the out-of-balance forces on buoys and vesselscan be drawn on the 3D view.

If necessary, you can also control the buoy convergence process using the statics convergenceparameters on the general data form.

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6.5.4 Multiple Statics for VesselsYou can use the Multiple Statics command on the Calculation menu to perform a series of staticanalyses for an array of different position of a vessel. This feature is mainly intended for use inmooring analyses.

The user specifies a series of regularly spaced positions for one vessel in the model andOrcaFlex then carries out separate static analyses for each of the these vessel positions. Keyresults, for example load-offset curves, are then made available in the form of tables and graphsas a function of the offset distance.

The vessel positions are specified by a series of offsets about the vessel's initial position (seeVessel Multiple Statics Data).

Note: If the offset vessel has "Included in Static Analysis" set to "Yes" then inMultiple Statics this setting will be ignored (for the offset vessel only) and thevessel will be placed as specified by the offsets. See Vessel Data.

If the static calculation fails to converge for a particular offset then this is noted in the StaticsProgress Window and the program continues to the next offset. No results are given for offsetswith failed statics.

When the calculation is completed the program enters Multiple Statics Complete state.Results can only be viewed in this state and are lost upon Reset. Results cannot be saved. Adynamic simulation cannot be carried out after multiple statics - you must Reset first.

6.6 DYNAMIC ANALYSIS

6.6.1 Dynamic AnalysisThe dynamic analysis is a time simulation of the motions of the model over a specified period oftime, starting from the position derived by the static analysis.

The period of simulation is defined as a number of consecutive stages, whose durations arespecified in the data. Various controlling aspects of the model can be set on a stage by stagebasis, for example the way winches are controlled, the velocities and rates of turn of vesselsand the releasing of lines, links and winches. This allows quite complex operational sequencesto be modelled.

Before the main simulation stage(s) there is a build-up stage, during which the wave andvessel motions are smoothly ramped up from zero to their full size. Ramping of current isoptional (see Current Data). This gives a gentle start to the simulation and helps reduce thetransients that are generated by the change from the static position to full dynamic motion. Thisbuild-up stage is numbered 0 and its length, which is specified in the data, should normally be atleast one wave period. The remaining stages, simply numbered 1, 2, 3..., are intended as themain stages of analysis.

Time is measured in OrcaFlex in seconds. To allow you to time-shift one aspect of the modelrelative to the others, different parts of the OrcaFlex model have their own user-specified timeorigins. See the diagram below.

For example, simulation time is measured relative to the simulation time origin, which isspecified on the Wave tab on the environment data form. The simulation time origin is at theend of the build-up stage, so negative simulation time is the build-up stage and the remainingstages are in positive simulation time. The figure below shows a simulation using a build-up of10 seconds, followed by two stages of 15 seconds each.

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Each wave train also has its own time origin, and similarly for time-varying wind and any timehistory files that you use. All of these time origins are defined relative to the global time origin(which is not user-specified), so if necessary you can use the time origins to time-shift oneaspect of the model relative to the others.

By default all of the time origins are zero, so all of the time frames coincide with global time. Formost cases this simple situation is all you need, but here is an example where you might wantto adjust a time origin.

• You might want to arrange that a wave crest, or a particularly large wave in a random sea,arrives at your vessel at a particular point in the simulation. If you use the View Profilefacility and find that the wave arrives at the vessel at global time 2590s, then you canarrange that this occurs at simulation time 10s (i.e. 10 seconds into stage 1) by either settingthe simulation time origin to 2580 or else setting the wave train time origin to -2580. Theformer shifts the simulation forwards to when the wave occurs, whereas the latter shifts thewave back to the period the simulation covers.

SimulationTimeOrigin

End ofSimulation

Stage 2Stage 1

Static StartingPosition

30-10 0 15

SimulationTime t

Build-up

Global Time TT=0

GlobalTimeOrigin

Time-historyTimeOrigin

Time-history Time0

Wave Train Time0

Wave TrainTimeOrigin

Figure: Time and Simulation Stages

6.6.2 Calculation MethodThe OrcaFlex dynamic analysis is a time-domain simulation that uses an explicit Eulerintegration technique with a constant timestep that is specified in the data. At the start of thetime simulation, the initial positions and orientations of all objects in the model, including allnodes in all lines, are known from the static analysis. The forces and moments acting on eachfree body and node are then calculated. Forces and moments considered include:

• weight

• buoyancy

• hydrodynamic drag

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• hydrodynamic added mass effects, calculated using the usual extended form of Morison'sequation with user-defined coefficients

• tension and shear

• bending and torque

• seabed reaction and friction

• contact forces with other objects

• forces applied by links and winches

The equation of motion (Newton's law) is then formed for each free body and each line node:

{M}.{x"} = {F}

where {M} is the mass matrix for the node or body, including added mass terms, {x"} is theacceleration vector, and {F} is the total force vector. The equation is solved for the accelerationvector which is then integrated. At the end of each timestep, the positions and orientations of allnodes and free bodies are again known and the process is repeated.

The timestep required for stable integration is very short - typically around 0.001s. OrcaFlexgives guidance on an appropriate timestep. Hydrodynamic forces typically change little oversuch a short time interval, and are time-consuming to compute. To save computing time,hydrodynamic loads are updated only over a longer "outer" timestep. Both time steps are user-defined (see Inner and Outer Time Steps) and may be set equal for critical cases.

Simulation time is further reduced by the use of a build up time at the beginning of thesimulation. During the build-up time the wave amplitude and vessel motions are increasedsmoothly from zero to the full amplitude specified in the data. This gives a gentle start to thesimulation which reduces transient responses and avoids the need for long simulation runs.The build-up time is specified in the data, and normally should be at least one wave period.Negative time is shown during the simulation to indicate the build-up time; so time before timezero is build up time, time after time zero is normal simulation with the full specified excitation.

Since the system geometry is recomputed at every timestep, the simulation takes full account ofgeometric non-linearities, including the spatial variation of both wave loads and contact loads.Note that the method of solution does not involve the construction and inversion of a stiffnessmatrix for any part of the system. An important consequence is that the program has nodifficulty in dealing with the transition between tension and compression in lines, e.g. at seabedtouchdown.

Of the various objects available in OrcaFlex, Lines are the most computationally demanding.For most models that include lines, the length of time required for dynamic analysis isapproximately proportional to the total number of nodes used multiplied by the total number ofinner time steps in the whole simulation. If the time step is maintained at the maximum levelrecommended value (see Inner and Outer Time Steps) and nodes are distributed uniformlyalong the lines, then the run time is approximately proportional to the square of the number ofnodes.

The simulation can be interrupted using the Pause button. OrcaFlex will pause when it reachesthe end of the current outer time step, so if the outer step size is long you will have to wait a fewseconds. Whilst the simulation is interrupted, you can use most of the normal commands. So,for example, you can examine the results obtained so far and examine the data.

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6.6.3 RampingDuring the build-up stage of the simulation the wave dynamics, vessel motions and optionallythe current (see Current Data) are built up smoothly from zero to their full level. The rampingfactor is calculated as follows:

Ramping Factor = 3r² -2r³

where r is the proportion of the build-up stage completed, given by:r = (Time + Length of Stage 0) / (Length of Stage 0)

Note: Time is negative throughout the build-up stage.

6.7 BUOYANCY VARIATION WITH DEPTHThe buoyancy of an object is normally assumed to be constant and not vary significantly withdepth. But the buoyancy is equal to ρ.V.g, where ρ is the water density, V is the volume and gis the acceleration due to gravity. So in reality the buoyancy does vary with depth, due to twoeffects:

• Firstly, if the object is compressible then its volume V will reduce with depth due to theincreasing pressure.

• Secondly, the water density ρ can vary with depth, either because of the compressibility ofthe water, or else because of temperature or salinity variations. Normally the densityincreases with depth, since otherwise the water column would be unstable (the lowerdensity water below would rise up through the higher density water above).

For buoys and lines these effects can be modelled in OrcaFlex.

Compressibility of Buoys and Lines

All things are compressible to some extent. The effect is usually not significant, but in somecases it can have a significant effect on the object's buoyancy. To allow these effects to bemodelled, you can specify the compressibility of a 3D Buoy, 6D Buoy or Line Type by giving thefollowing data on the object's data form.

Bulk Modulus

The bulk modulus, B, specifies how the object's volume changes with pressure, according to thefollowing formula.

Volume at pressure P = V0.(1 - P/B)

where V0 is the uncompressed volume at atmospheric pressure, and P is the pressure excessover atmospheric pressure.

The bulk modulus has the same units as pressure (F/L²) and the above formula can be thoughtof as saying that the volume reduces linearly with pressure, and at a rate that would see theobject shrink to zero volume if the pressure ever reached B. For an incompressible object thebulk modulus is infinity, and this is the default value in OrcaFlex.

Note: The above formula breaks down when P ≥ B and would become inaccuratewell before that pressure was reached. However, B is normally very large, sothe object normally only experiences pressures that are small compared to B.

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6.8 CURRENT THEORYExtrapolation

In the presence of waves, the current must be extrapolated above the still water level; inOrcaFlex we adopt the convention that the surface current applies to all levels above the stillwater level.

If a sloping seabed is specified, the boundary is inconsistent with a horizontal current. Thiseffect is not usually important and is uncorrected in OrcaFlex. The current at the greatest depthspecified is applied to all greater depths.

Interpolated Method

Horizontal current is specified as a full 3D profile, variable in magnitude and direction withdepth. The profile should be specified from the still water surface to the seabed. Linearinterpolation is used for intermediate depths. If the specified profile does not cover the fulldepth then it is extrapolated (see Extrapolation above).

Power Law Method

Current direction is specified and does not vary with depth. Speed (S) varies with position(X,Y,Z) according to the formula:

S = Sseabed + (Ssurface - Sseabed) x ((Z-Zseabed) / (Zsurface-Zseabed)) ^(1/Exponent)

where

Ssurface and Sseabed are the current speeds at the surface and seabed,Exponent is the power law exponent,Zsurface is the water surface Z level, all as specified in the data,Zseabed is the Z level of the seabed directly below (X,Y).

Note: If Z is below the seabed (e.g. has penetrated the seabed) then the currentspeed is set to Sseabed and if Z is above the surface (e.g. in a wave crest)then current speed is set to Ssurface.

6.9 WAVES

6.9.1 Wave TheoryEach wave train can be a regular wave, a random wave or specified by a time history file.

Regular Waves

OrcaFlex offers a choice of a long-crested, regular, linear Airy wave (including seabed influenceon wave length) or nonlinear waves using Dean, Stokes' 5th or Cnoidal wave theories (seeNonlinear Wave Theories). Waves are specified in terms of height and period, and direction ofpropagation.

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Random Waves

OrcaFlex offers three standard spectra, JONSWAP (see below), ISSC (based on Pierson-Moskovitz) and Ochi-Hubble. The program synthesises a wave time history from a user-determined number of wave components, whose amplitudes and periods are selected by theprogram to match the specified spectrum. The phases associated with each wave componentare pseudo-random: a random number generator is used to assign phases, but the sequence isrepeatable, so the same user data will always give the same train of waves. Different wavesfrom the same spectrum can be obtained by shifting the simulation time origin relative to thewave time origin.

OrcaFlex provides special facilities to assist in selecting an appropriate section of random sea.The first lists all the waves in a selected time interval whose height or steepness is large bycomparison with the reference wave Hs, Tz. The second allows the wave elevation for aselected period to be drawn to screen.

JONSWAP Spectrum

Five parameters are required for a complete definition. Two of these, the spectral widthparameters Sigma 1 and Sigma 2, are set to standard values of 0.07 and 0.09 respectively.Alpha, fm and gamma are then calculated by the program for the given values of Hs and Tz(using the formulae given by Isherwood, Applied Ocean Research, September 1987). You mayselect a different value of gamma if required. The program then recalculates alpha and fm tocorrespond to the required Hs and Tz.

6.9.2 Kinematic StretchingKinematic stretching is the process of extending linear Airy wave theory to provide predictions offluid velocity and acceleration (kinematics) at points above the mean water level. It only appliesto Airy waves and to random waves (which are made up of a number of Airy waves).

Linear wave theory in principle only applies to very small waves, so it does not predictkinematics for points above the mean water level since they are not in the fluid. The theorytherefore needs to be 'stretched' to cover such points, and OrcaFlex offers a choice of threepublished methods: Vertical Stretching, Wheeler Stretching and Extrapolation Stretching (seebelow).

Consider, for example, the horizontal particle velocity u. In Airy wave theory the formula for u atposition (x,z) at time t is:

u = E(z) a ω cos(ωt - φ + kx) ........................ (1)

where a, ω, φ and k are the wave amplitude, angular frequency, phase lag and wave number,respectively, and z is measured positive upwards from the mean water level.

The term E(z) is a scaling factor given by E(z) = cosh(k(d+z))/sinh(kd), where d = mean waterdepth. It is an exponential decay term that models the fact that the fluid velocity reduces as thepoint goes deeper. However for z>0 (i.e. above the mean water level) E(z) is greater than 1 soit amplifies the velocity. This can give particle velocity predictions that are unrealistically large(the problem being worst for high frequency waves). The various stretching methods deal withthis problem by replacing E(z) with a more realistic term.

Note that all the stretching methods apply not only to the scaling factor E(z) in the horizontalvelocity formula (1), but also to the scaling factors in the corresponding Airy wave theoryformulae for the vertical velocity and the horizontal and vertical acceleration.

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Vertical Stretching

This is the simplest of the 3 methods. E(z) is left unchanged for z<=0, but for z > 0 (i.e. abovethe mean water level) E(z) is replaced by E(0). This has the effect of setting the kinematicsabove the mean water levels to equal those at the mean water level.

Wheeler Stretching

This method stretches (or compresses) the water column linearly into a height equivalent to themean water depth. This is done by replacing E(z) by E(z') where

z’ = d.(d+z)/(d+ζ) - d

and ζ is the z-value at the instantaneous water surface. This formula for z' essentially shifts zlinearly to be in the range -d to 0.

Extrapolation Stretching

This method extends E(z) to points above the mean water level by using linear extrapolation ofthe tangent to E(z) at the mean water level. In other words, for z<=0 equation (1) is leftunchanged, but for z>0, E(z) is replaced by E(0) + z.E'(0), where E' is the rate of change of Ewith z.

6.9.3 Ochi-Hubble SpectraThe Ochi-Hubble Spectrum allows 2-peaked spectra to be set up, enabling you to represent seastates that include both a remotely generated swell and a local wind generated sea.

Example of Ochi-Hubble Spectrum

0

1

2

3

4

5

6

0 1 2 3 4

Relative Frequency r

S(r)

[m^2

]

The Ochi-Hubble wave spectrum is the sum of 2 separate component spectra - the examplegraph shows the 2 components and their sum. The component spectrum with the lowerfrequency peak corresponds to the remotely generated swell and the one with the higherfrequency peak corresponds to the local wind generated sea. This is why the Ochi-Hubblespectrum is often called a 2-peaked spectrum; however in practice, the resulting total spectrumtypically has only one peak (from the remotely generated swell) plus a ‘shoulder’ of energy fromthe local wind generated sea.

The two component spectra are each specified by a set of three parameters - Hs1, fm1,Lambda1 for the lower frequency component and Hs2, fm2, Lambda2 for the higher frequencycomponent. See Data for Ochi-Hubble Spectra.

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In OrcaFlex you can either specify all these 6 parameters explicitly, or you can simply specifythe overall significant wave height Hs and tell OrcaFlex to automatically select the mostprobable 6 parameters for that value of Hs. In the latter case, OrcaFlex uses ‘most probable’parameters based on formulae given in the Ochi-Hubble paper (table 2b).

6.9.4 Non-linear Wave TheoriesOrcaFlex models two types of waves, periodic regular waves and random waves. A regularwave is a periodic wave with a single period. A random wave in OrcaFlex is a superposition ofa number of regular linear waves of differing heights and periods. We shall not discuss randomwaves here.

For very small waves in deep water, Airy wave theory (also know as linear wave theory) is valid.Many waves in practical engineering use do not fall into this category, hence the need for non-linear wave theories. These include Stokes' 5th order theory, Dean's stream function theoryand Fenton's cnoidal theory which are all available in OrcaFlex. We shall give an outline ofthese theories here in the form of concise abbreviations of the relevant papers. For an overviewof all the theories considered here see Sobey R J, Goodwin P, Thieke R J and Westberg R J,1987.

To fix notation we use the following conventions throughout. These conventions are differentfrom those used in OrcaFlex but we use them here in order to agree with the literature. Weassume that the wave is long-crested and travels in the x direction and we shall work only in the(x,z) plane. The seabed has z = 0 and the mean water level is given by z = d, where d is thewater depth (at the seabed origin). The wave is specified by wave height (H) and wave period(T) and the wavelength (L) will be derived. The horizontal and vertical particle velocities aredenoted by u and v respectively. We assume a moving frame of reference with respect towhich the motion is steady and x = 0 under a crest.

See Stokes' 5th, Dean's stream function theory and Fenton's cnoidal theory for a brief overviewof each of the non-linear wave theories available in OrcaFlex and for guidance on how to decideon which wave theory to use in practice.

6.9.5 Stokes' 5thThe engineering industry's standard reference on 5th order Stokes' wave theory is Skjelbreiaand Hendrickson (1961). This paper presents a 5th order Stokes' theory with expansion termak where a is the amplitude of the fundamental harmonic and k = 2π / L is the wave number.The length a has no physical meaning and by choosing ak as expansion parameter,convergence for very steep waves cannot be achieved. Fenton (1985) gives a 5th order Stokes'theory based around an expansion term kH/2 and demonstrates that it is more accurate thanSkjelbreia and Hendrickson's theory. Thus it is Fenton's theory which we recommend, althoughboth theories have been implemented in OrcaFlex. It is worth noting that the linear theory ofAiry is a 1st order Stokes' theory.

Assuming that the user supplies wave train information comprising water depth, wave heightand wave period then the wave number k must be computed before the theory can be applied.In order to do this a non-linear implicit equation in terms of k is solved using Newton's methodwith derivative calculated by perturbation. This equation is known as the dispersionrelationship. Once k is known, a number of coefficients are calculated and these are used forpower series expansions in order to find surface profile and wave kinematics.

Accuracy of method

Inherent in the method is a truncation of all terms of order greater than 5. Thus if the termswhich are discarded are significant then this theory will give poor results. See Ranges of

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applicability for the waves for which Stokes' 5th theory is valid, but essentially this is a deepwater, steep wave theory.

6.9.6 Dean's Stream Function TheoryA typical approach to wave theory makes use of the idea of a velocity potential. This is a vectorfield φ (x,z) whose partial derivatives are the particle velocities of the fluid. That is:

∂φ / ∂x = u and ∂φ / ∂z = v.

Chappelear devised a wave theory based on finding the best fit velocity potential to the definingwave equations. This was quite complicated and Dean's idea was to apply the same idea to astream function. A stream function is a vector field ψ(x,z) which satisfies

∂ψ / ∂x = -v and ∂ψ / ∂z = u.

Dean's original paper (1965) was intended to be used to fit stream functions to waves whoseprofile was already known, for example a wave recorded in a wave tank. For the purpose ofOrcaFlex the user provides information on the wave train in the form of water depth, waveheight and wave period and we wish to find a wave theory which fits this data. Thus Dean'stheory in its original form does not apply and we choose to follow the stream function theory ofRienecker and Fenton (1981). This method is also known as Fourier approximation wavetheory.

The problem is to find a stream function which:

• satisfies Laplace's equation ∂²ψ / ∂x² +∂²ψ / ∂z² = 0, which means that the flow is irrotational

• is zero at the seabed, that is ψ( x,0 ) = 0

• is constant at the free surface z = η( x ), say ψ( x , η ) = -Q

and

• satisfies Bernoulli's equation ½ [ (∂ψ / ∂x)² + (∂ψ / ∂z)² ] + η = R, where R is a constant.

In these equations all variables have been non-dimensionalised with respect to water depth dand gravity g.

By standard methods, equations (a) and (b) are satisfied by a stream function of the form

ψ(x,z) = B0 z + Σ Bj [sinh (jkz) / cosh (jk)] cos (jkx)

where k is the wave number which is as yet undetermined, and the summation is from j = 1 toN. The constant N is said to be the order of the stream function. The problem now is to findcoefficients Bj and k which satisfy equations (c) and (d).

Implementing stream function theory requires numerical solution of complex non-linearequations. The number of these equations increases as N increases and there is a short pausein the program while these equations are solved. The default value is 10 and for most purposesit is not necessary to alter this. However, for nearly breaking waves the solution methodsometimes has problems converging. If this is the case then it might be worth experimentingwith different values.

Accuracy of method

Because the method is a numerical best fit method it does not suffer from the truncationproblems of the Stokes' 5th and cnoidal theories. For these methods, power series expansionsare obtained and then truncated at an arbitrary point. If the terms which are being ignored arenot small then these methods will give inaccurate answers. In theory, Dean's method shouldcope well in similar circumstances as it is finding a best fit to the governing equations. This

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means that stream function wave theory is very robust. However for finite waves in deep water,Stokes' 5th is preferred as the ignored terms are indeed small and the computation is fasterthan that for Dean. In very shallow water Fenton believes that his high order cnoidal wavetheory is best, although we would recommend stream function theory here. It is possible that,by their very nature, Stokes' 5th and the cnoidal theories may give inaccurate results if appliedto the wrong waves. In all circumstances the stream function method, if it converges, will givesensible results. Hence it can be used as a coarse check on the applicability of other theories.That is if your preferred wave theory gives significantly different results from Dean's, applied tothe same wave, then it is probably wrong!

6.9.7 Fenton's cnoidal theoryThis is a steady periodic water wave theory designed to be used for long waves in shallowwater. The Stokes' 5th order theory is invalid in such water as the expansion term is large andthe abandoned terms due to truncation are significant. The high-order cnoidal theory of Fenton(1979) has been regarded as the standard reference for many years but it gives unsatisfactorypredictions of water particle velocities. This work has been superseded by Fenton (1990 and1995).

Fenton's original paper gave formulae for fluid velocities based on a Fourier series expansionabout the term ε = H / d In his later works Fenton discovered that much better results could beobtained by expanding about a "shallowness" parameter δ. We follow this approach.

A 5th order stream function representation is used but instead of terms involving cos theJacobian elliptic function cn is used, hence the term cnoidal. The function takes twoparameters, x as usual, and also m which determines how cusped the function is. In fact whenm = 0, cn is just cos and the Jacobian elliptic functions can be regarded as the standardtrigonometric functions. The solitary wave which has infinite length corresponds to m = 1 andlong waves in shallow water have values of m close to 1. Fenton shows that the cnoidal theoryshould only be applied for long waves in shallow water and for such waves m is close to 1.

The initial step of the solution is to determine m and an implicit equation with m buried deepwithin must be solved. As in the Stokes' theory this equation is the dispersion relationship. Thesolution is performed using the bisection method since the equation shows singular behaviourfor m ≈ 1 and derivative methods fail.

After m has been determined Fenton gives formulae to calculate surface elevation and otherwave kinematics. In practice m is close to 1 and Fenton takes advantage of this to simplify theformulae. He simply sets m = 1 in all formulae except where m is the argument of an elliptic orJacobian function. This technique is known as Iwagaki approximation and proves to be veryaccurate.

6.9.8 Ranges of ApplicabilityRegular wave trains are specified in OrcaFlex by water depth, wave height and wave period.Which wave theory should one use for any given wave train? For an infinitesimal wave in deepwater then Airy wave theory is accurate. For finite waves a non-linear theory should be used.In order to decide which wave theory to use one must calculate the Ursell number given by

U = HL² / d ³

See Non-linear Wave Theories for notation conventions used.

If U < 40 then the waves are said to be short and Stokes' 5th may be used. For U > 40 we havelong waves and the cnoidal wave theory can be used. The stream function theory is applicablefor any wave. The boundary number 40 should not be considered a hard and fast rule. In factfor Ursell number close to 40 both the Stokes' 5th theory and the cnoidal theory have

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inaccuracies and the stream function method is recommended. In regions well away fromUrsell number 40 then the relevant analytic theories (Stokes' 5th or cnoidal) perform very well.

Our recommendations are:

Ursell number Recommended wave theory<< 40 Dean or Stokes' 5th~ 40 Dean>> 40 Dean or CnoidalIn general then, we would recommend the stream function wave theory in most cases. Ifanother theory is being used then it should be compared against the stream function theory tocheck its validity. This is a very important point. OrcaFlex has no way of telling if a theory hasbeen misapplied, other than giving warnings for obvious abuses - it is up to the user to makesure they are using an applicable theory. By comparing with the stream function theory areliable check can be made - and if two theories give the same answers then one should befilled with confidence!

6.9.9 Breaking wavesAll the regular wave theories are suspect for breaking or near breaking waves. In shallow waterthen the height of a breaking wave, HB, is around 0.8d and for deep water HB = 0.14L. Anexpression which covers all depths, due to Miche, is

HB = 0.88k¯¹ tanh ( 0.89 kd )

where k is the local wave number as calculated by Airy wave theory. OrcaFlex reports awarning if the wave height exceeds HB.

6.9.10 Particle velocities and accelerationsAn important consideration for computing the wave kinematics is whether to use apparent orreal quantities. That is, do we compute velocities and accelerations relative to a fixed point inthe fluid (Eulerian) or relative to an individual water particle (Lagrangian). For velocities there isno confusion as the two concepts coincide but there is an issue for accelerations.

The accelerations are used by OrcaFlex in relation to Morison's equation in order to computepressure gradients which in turn result in forces being applied to objects. Tucker (1991) givesan example of a Venturi tube with zero apparent acceleration throughout the tube but a nonzero pressure gradient! For the linear theory of Airy, which is based on the assumption that thewave is very small, then apparent and real accelerations are effectively equal and OrcaFlexcomputes apparent accelerations for Airy wave theory. For the non-linear theories, realaccelerations are used in all cases.

6.9.11 CurrentsEach of the theories implemented allows for a uniform Eulerian current but none is designed todeal with current profiles. Because we are dealing with non-linear waves it is not possible toanalyse the wave assuming zero current and then add in the current afterwards, as we do forAiry waves. So we have to reach some compromise. The convention chosen is as follows:

The current profile is defined as usual and the current used to analyse the wave is taken to bethe component of current in the wave direction at the mean water level. Call this currentcomponent CW. To calculate the fluid velocity V at any given point in time we must take intoaccount the fluid velocity VW containing uniform current CW together with the current C at thepoint in question, as specified by the current profile. The formula is:

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V = VW - CW + C

A similar formula is used during the build up. If the wave factor is λ then

V = λ (VW - CW ) + C

6.9.12 Seabed SlopeIn the case of a sloping seabed in OrcaFlex, we adopt the following convention for wavetheories. We assume that the water depth is that at the seabed origin for the purpose ofderiving the wave information (wave number, stream function etc.) We define the fluid motionfor a point (x,y,z) where z < 0 to be the fluid motion for the point (x,y,0).

6.9.13 Physically implausible solutionsThe non-linear wave theories implemented in OrcaFlex each have their own ranges andlimitations as previously discussed. However, it is sometimes possible to obtain a solution for aparticular wave train which is physically implausible. For example if the stream function orStokes' 5th theories are misapplied then they may predict wave profiles with multiple crests.Whilst these are valid solutions to the mathematical problem, they are not realistic. Also it issometimes predicted by each theory that the horizontal fluid velocities under a crest increasewith depth. This also is physically implausible. OrcaFlex warns if such unrealistic solutionsoccur. It is then up to the engineer to judge the validity of the results.

It has not been possible to guard against all such anomalies, in particular the Stokes' 5th theorycan predict wave profiles with points of inflection other than at crest and trough.

6.10 SEABED THEORYThe seabed is modelled as a sprung surface whose properties are specified in the seabeddata.

Objects Affected

Only 3D buoys and 6D buoys, lines and drag chains interact with the seabed; other objects arenot affected by it.

A line interacts when one of its nodes penetrates the seabed. The node then experiences theseabed stiffness force and damping force, applied at the node centre. The node may alsoexperience a friction force - see Seabed Friction.

A 3D buoy interacts when the buoy origin penetrates the seabed. The seabed stiffness anddamping forces are then applied at the buoy origin. No seabed friction force is applied.

A 6D buoy interacts when its vertices penetrates the seabed. (A 6D buoy with no vertices istreated as if it had one vertex at the buoy origin.) Each penetrating vertex experiences theseabed stiffness and damping forces, applied at the vertex. No seabed friction force is applied.

Drag chain interaction with the seabed is slightly different; see drag chain seabed interaction.

Seabed Stiffness Force

The seabed reaction force is in the outwards normal direction and has magnitude R = K.A.dwhere

K is the seabed stiffnessA is the area of contact

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d is the depth of penetration into the seabed.

For details on how the area of contact values are calculated see 3D Buoy Theory, 6D BuoyTheory and Line Interaction with Seabed and Solids.

Seabed Damping Force

The seabed damping force is only applied when the object is travelling into the seabed, notwhen it is coming out of the seabed. It is in the outwards normal direction and has magnitude Dgiven by:

D = λ.2√(M.K.A).Vn if Vn > 0D = 0 if Vn <= 0

where

λ is percentage of critical seabed damping / 100M is the mass of the objectK is the seabed stiffnessA is the area of contactVn is the component of velocity normal to the seabed, +ve when travelling into theseabed and -ve when coming out.

We recommend using 100% critical damping for seabeds.

6.11 LINE THEORY

6.11.1 OverviewOrcaFlex uses a finite element model for a line as shown in the figure below.

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Segment 1

Segment 2

Segment 3

Node 3

Actual Pipe Discretised Model

End A

End B

Node 2

Segment 2

Segment 3

Node 1

Segment 1

Figure: OrcaFlex Line model

The line is divided into a series of line segments which are then modelled by straight masslessmodel segments with a node at each end.

The model segments only model the axial and torsional properties of the line. The otherproperties (mass, weight, buoyancy etc.) are all lumped to the nodes, as indicated by the arrowsin the figure above.

Nodes and segments are numbered 1,2,3,... sequentially from end A of the line to end B. Sosegment n joins nodes n and (n+1).

Nodes

Each node is effectively a short straight rod that represents the two half-segments either side ofthe node. The exception to this is end nodes, which have only one half-segment next to them,and so represent just one half-segment.

Each line segment is divided into two halves and the properties (mass, weight, buoyancy, dragetc.) of each half-segment are lumped and assigned to the node at that end of the segment.

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Forces and moments are applied at the nodes - with the exception that weight can be applied atan offset. Where a segment pierces the sea surface, all the fluid related forces (e.g. buoyancy,added mass, drag) are calculated allowing for the varying wetted length up to the instantaneouswater surface level.

Segments

Each model segment is a straight massless element that models just the axial and torsionalproperties of the line. A segment can be thought of as being made up of two co-axialtelescoping rods that are connected by axial and torsional spring+dampers.

The bending properties of the line are represented by rotational springs+dampers at each endof the segment, between the segment and the node. The line does not have to have axialsymmetry, since different bend stiffness values can be specified for two orthogonal planes ofbending.

This section has given only an overview of the line model. See structural model for full details.

6.11.2 Structural Model DetailsThe following figure gives greater detail of the line model, showing a single mid-line node andthe segments either side of it. The figure includes the various spring+dampers that model thestructural properties of the line, and also shows the xyz-frames of reference and the angles thatare used in the theory below.

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Node

Torsion spring+ damper

Bending springs+ dampers

Axial spring+ damper

Nx

Ny

Nz (axial direction)

End B

Sy1

Sx2

Sz

Sx1

Sz Sx1

τ

α2

α1

Sy2

Figure: Detailed representation of OrcaFlex Line model

As shown in the diagram, there are 3 types of spring+dampers in the model:

• The axial stiffness and damping of the line are modelled by the axial spring+damper at thecentre of each segment, which applies an equal and opposite effective tension force to thenodes at each end of the segment.

• The bending properties are represented by rotational spring+dampers either side of thenode, spanning between the node's axial direction Nz and the segment's axial direction Sz.

• If torsion is included (this is optional) then the line's torsional stiffness and damping aremodelled by the torsional spring+damper at the centre of each segment, which appliesequal and opposite torque moments to the nodes at each end of the segment. If torsion isnot included then this torsional spring+damper is missing and the two halves of the segmentare then free to twist relative to each other.

6.11.3 Calculation StagesWe now describe the calculation sequence that OrcaFlex uses to calculate the forces andmoments on the mid-node shown in the diagram Line Model Detail.

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Stage 1: Tension Forces

Firstly the tensions in the segments are calculated. To do this, OrcaFlex calculates the distance(and its rate of change) between the nodes at the ends of the segment, and also calculates thesegment axial direction Sz, which is the unit vector in the direction joining the two nodes.

The tension in the axial spring+damper at the centre of each segment can then be calculated; itis the vector in direction Sz and whose magnitude is given by:

Te = EA . [(L - L0)/L0+ (e . dL/dt)/L0)]

where

Te = effective tensionL = instantaneous length of segmentL0 = unstretched length of segmentdL/dt = rate of increase of lengthEA = axial stiffness of line, as specified on the line types form (= effective Young'smodulus x cross-section area)e = damping coefficient of the line, in seconds.

Note that the effective tension Te can be negative, indicating compression. For the relationshipbetween effective tension and pipe wall tension see Line Pressure Effects.

The damping coefficient e represents the structural damping in the line. It is calculatedautomatically based on the Axial Target Damping value specified on the general data form.

e = e(critical) . (Target Axial Damping) / 100

where

e(critical) = √ (2.SegmentMass.L0 / EA) is the critical damping value for a segment

and SegmentMass includes the mass of any contents but not the mass of any attachments.

This tension force vector is then applied (with opposite signs) to the nodes at each end of thesegment. Each mid-node therefore receives two tension forces, one each from the segmentson each side of it.

Stage 2: Bend Moments

The bend moments are then calculated. There are bending spring+dampers at each side of thenode, spanning between the node's axial direction Nz and the segment's axial direction Sz, andeach of these spring+dampers applies to the node a bend moment that depends on the angle αbetween the segment axial direction Sz and the node's axial direction Nz.

These axial directions are associated with the frames of reference of the node and segment.The node's frame of reference Nxyz is a Cartesian set of axes that is fixed to (and so rotateswith) the node. Nz is in the axial direction and Nx and Ny are normal to the line axis andcorrespond to the end x- and y-directions that are specified by the Gamma angle on the linedata form (see End Orientation).

The segment has two frames of reference - Sx1 y1 z at the end nearest end A, and Sx2 y2 z atthe other end. These two frames have the same Sz-direction, which was calculated in step 1above, so the bend angle α2 between Nz and Sz can now be calculated. The effectivecurvature vector C is then calculated - it is the vector whose direction is the binormal direction,which is the direction that is orthogonal to Sz and Nz, and whose magnitude is α2 / (½ L0),where L0 is the unstretched length of segment.

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The bend moment, M2, generated by the bending spring+damper is then calculated. If the bendstiffnesses for the x and y-directions are equal then it is the vector in the binormal directionwhose magnitude is given by -

M2 = EI.|C| + D.d|C|/dt

where

EI = bending stiffness, as specified on the line types form

D = (λ/100).Dc.

Dc = the bending critical damping value for a segment = L0.√(SegmentMass.EI.L0)

λ = target bending damping, as specified on the general data form.

If the bend stiffnesses for bending about the x and y-directions are different, then the aboveequation is separated into its components in the Sx2 and Sy2 directions, giving -

component of M2 is the Sx2 direction = EIx.Cx + Dx.dCx/dtcomponent of M2 is the Sy2 direction = EIy.Cy + Dy.dCy/dt

where

EIx, EIy = bending stiffnesses of segment, as specified on the line types formCx, Cy = components of the curvature vector C in the Sx2 and Sy2 directions

Dx = (λ/100).L0.√(SegmentMass.EIx.L0)

Dy = (λ/100).L0.√(SegmentMass.EIy.L0).

The curvature used in the calculation of bending moments is the value in the true plane ofbending, taking full account of the 3D motions of the adjacent nodes. The bending dampingterm D represents the effect on bending of the structural damping in the line; its level is set bythe Target Bending Damping data item on the general data form.

The bend angle (α1) and bend moment vector (M1) on the other side of the node are calculatedsimilarly, so the node experiences two bend moments, one each from the segments on eachside of it.

Stage 3: Shear Forces

Having calculated the bend moments at each end of the segment, the shear force in thesegment can be calculated.

Each model segment is a straight stiff rod in which the bend moment vector varies from M1 atone end (the end nearest end A of the line) to M 2 at the other end, where these bend momentsare calculated as described in Step 2 : Bend Moments above.

Because the model segment is stiff in bending, the bend moment varies linearly along thesegment and the shear force in the segment is the constant vector equal to the rate of changeof bend moment along the length. The shear force is therefore given by:

Shear Force Vector = (M 2 - M1) / L

where L is the instantaneous length of the segment. Note that M1 and M2 are vectors, so this isa vector formula that defines both the magnitude and direction of the shear force.

This shear force vector is applied (with opposite signs) to the nodes at each end of thesegment.

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Stage 4: Torsion Moments

The torsion is then calculated (providing torsion has been included). To do this, the directionsSx1, Sy1, Sx2 and Sy2 must first be calculated, since so far only the segment axial direction Szhas been found.

The directions Sx2 and Sy2 at the end of the segment are determined from the orientation Nxyzof the adjacent node, by rotating Nxyz until its z-direction is aligned with Sz. This rotation istherefore through angle α2 and it is a rotation about the binormal direction (i.e. the direction thatis orthogonal to both Nz and Sz). (Note that rotations about the binormal direction are bendingrotations only - i.e. they involve no twisting.) The directions Sx1 and Sy1 at the other end of thesegment are derived in the same way, but starting from the orientation of the node at that otherend of the segment.

The twist angle τ in the segment can then be calculated - it is the angle between the directionsSx1 and Sx2. Note that this twist angle is also the angle between Sy1 and Sy2 - in other wordsthe orientations Sx1 y1 z and Sx2 y2 z, at the two ends of the segment, differ by just a twistthrough angle τ.

The torque generated by the torsion spring+damper can then be calculated - it is a momentvector whose direction is the segment axial direction Sz and whose magnitude is given by:

Torque = K.τ / L0 + C.(dτ/dt) + A.Te

where

K = torsional stiffness, as specified on the line types form

τ = segment twist angle (in radians), between directions Sx1 and Sx2

L0 = unstretched length of segment

dτ/dt = rate of twist (in radians per second)

C = torsional damping coefficient of the lineA = torque per unit tension, as specified on the line types formTe = effective tension in the segment

The damping coefficient C represents the torsional effect of structural damping in the line. It iscalculated automatically based on the Target Torsional Damping value specified on the generaldata form using the formula

C = C(critical).(Target Torsional Damping) / 100

where C(critical) is the critical damping value for a segment, given by

C(critical) = √ (2.Iz.K/L0).

Here, Iz is the rotational moment of inertia of the segment about its axis, allowing only for thestructural mass of the line, not the mass of any contents (since the contents are assumed to nottwist with the pipe).

This torque moment vector is then applied (with opposite signs) to the nodes at each end of thesegment.

Stage 5: Total Load

As described above, each mid-node experiences two tension forces, two bend moments, twoshear forces and two torque moments (one each from the segments either side of the node).These loads are then combined with the other non-structural loads (weight, drag, added massetc.) to give the total force and moment on the node. OrcaFlex then calculates the resulting

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translational and rotational acceleration of the node, and then integrates to obtain the node'svelocity and position at the next time step. See Calculation Method.

6.11.4 Line End OrientationAt line ends, we usually need to define not only the axial direction of the end fitting but also thetwist orientation about that axial direction. This is done by first specifying the azimuth anddeclination of the axial direction and then specifying the twist orientation by giving a third anglecalled gamma. See End Orientation.

Together, the 3 angles azimuth, declination and gamma fully define the rotational orientation ofthe end fitting. To define how this is done we need to define a frame of reference Exyz for theend fitting, where:

• E is at the connection point.

• Ez is the axial direction of the fitting, using the "A to B" convention - i.e. Ez is into the line atend A, but out of the line at end B.

• Ex and Ey are perpendicular to Ez.

The 3 angles, Azimuth, Declination and Gamma, specify the orientation of Exyz relative to thelocal axes Lxyz of the object to which the end is connected, as follows. (If the line end is notconnected to another object, then it is either Fixed, Anchored or Free. In these cases theangles define Exyz relative to the global axes GXYZ.)

• Start with Exyz aligned with Lxyz.

• Then rotate Exyz by Azimuth degrees about Ez (= Lz at this point).

• Now rotate by Declination degrees about the resulting Ey direction.

• Finally rotate by Gamma degrees about the resulting (and final) Ez direction.

In all these rotations, a positive angle means rotation clockwise about the positive directionalong the axis of rotation, and a negative angle means anti-clockwise.

Three-dimensional rotations are notoriously difficult to describe and visualise. When setting theazimuth, declination and gamma, it is best to check that the resulting Exyz directions are correctby drawing the local axes on the 3D view.

Here are some examples of the effect of various values of (Azimuth, Declination, Gamma) for aFixed end. For ends connected to other objects, replace GXYZ by Lxyz in these examples.

• (0,0,0) sets Exyz to be aligned with GXYZ.

• (0,30,0) sets Ex at 30° below GX (in the GXZ plane), Ey along GY, Ez at 30° to GZ, towardsGX.

• (0,180,0) sets Ex along -GX, Ey along GY, Ez along -GZ.

• (90,90,0) sets Ex along -GZ, Ey along -GX, Ez along GY.

• (90,90,90) sets Ex along -GX, Ey along GZ, Ez along GY.

End Direction Results

If the end orientation Exyz is defined, then OrcaFlex offers various results relative to those axes.For a given vector V (such as the end force) these include the components of V relative to Exyzand the angles that V makes with the various axes of Exyz (see Line Results: Angles). Theangles offered are as follows:

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• The "Ez-Angle" is the angle between V and the Ez-direction (i.e. axial direction). Thismeasures how far V is away from the end fitting axial direction.

• The "Ezx-Angle" is the angle from Ez to the projection of V onto the Ezx plane (measuredpositive from Ez towards Ex). This is the angle V makes with Ez when viewing the zx-plane.

• The "Ezy-Angle" is the angle from Ez to the projection of V onto the Ezy plane (measuredpositive from Ez towards Ey). This is the angle V makes with Ez when viewing the zy-plane.

• The "Exy-Angle" is the angle between the Ex-direction and the projection of V onto the Exyplane (measured positive from Ex towards Ey). This is the angle V makes with Ex whenviewing the xy-plane.

6.11.5 Line Local OrientationAt any point P, the line orientation is defined by its local axes Pxyz. Pz is in the axial direction,towards end B, and is reported by the azimuth and declination angles. Px and Py are normal tothe line axis.

At the ends of the line, these local axes are referred to as the end axes Exyz, and theirdirections are specified by the end orientation angles on the line data form.

At other points on the line the calculation of the local orientation depends on whether torsion isincluded:

• If torsion is included then the local Pxyz directions are calculated using the specifiedtorsional properties of the line.

• If torsion is not included then the local directions at P are calculated by assuming that notwisting occurs anywhere along the line between end A and P. In more detail, OrcaFlexcalculates the local orientation at P by starting with the orientation at end A (as specified byits end orientation angles) and then stepping along the line from node to node, using theno-twist assumption at each step to calculate the next node's local orientation. Note thatthis method is not used if end A is free (or if it is released), so currently for such lines torsionmust be included if the line has non-isotropic properties, in order to properly calculate thelocal orientation.

6.11.6 Morison's EquationOrcaFlex calculates hydrodynamic loads on lines, 3D buoys and 6D buoys using an extendedform of Morison's Equation. See Morison, O'Brien, Johnson and Schaaf.

Morison’s equation was originally formulated for calculating the wave loads on fixed verticalcylinders. There are two force components, one related to water particle acceleration (the‘inertia’ force) and one related to water particle velocity (the ‘drag’ force). For moving objects,the same principle is applied, but the force equation is modified to take account of themovement of the body.

The extended form of Morison’s equation used in OrcaFlex is:

Fw = (∆.aw + Ca.∆.ar) + ½.ρ.Vr|Vr|.CD.A

where

Fw is the wave force

∆ is the mass of fluid displaced by the body

aw is the fluid acceleration relative to earthCa is the added mass coefficient for the body

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ar is the fluid acceleration relative to the body

ρ is the density of water

VR is the fluid velocity relative to the bodyCD is the drag coefficient for the bodyA is the drag area

The term in parentheses is the inertia force, the other is the drag force. The drag force isfamiliar to most engineers, but the inertia force can cause confusion.

The inertia force consists of two parts, one proportional to fluid acceleration relative to earth (the‘Froude-Krylov’ component), and one proportional to fluid acceleration relative to the body (the‘added mass’ component).

To understand the Froude-Krylov component, imagine the body being removed and replacedwith an equivalent volume of water. This water would have mass ∆ and be undergoing anacceleration aw. It must therefore be experiencing a force ∆.aw.

Now remove the water and put the body back: the same force must now act on the body. Thisis equivalent to saying that the Froude-Krylov force is the integral over the surface of the bodyof the pressure in the incident wave, undisturbed by the presence of the body. (Note theparallel with Archimedes’ Principle: in still water, the integral of the fluid pressure over thewetted surface must exactly balance the weight of the water displaced by the body.)

The ‘added mass’ component is due to the distortion of the fluid flow by the presence of thebody. A simple way to understand it is to consider a body accelerating through a stationaryfluid. The force required to sustain the acceleration may be shown to be proportional to thebody acceleration and can be written:

F = (m + Ca.∆).a

where

F is the total force on the bodym is the mass of the body

(Ca.∆) is a constant related to the shape of the body and its displacement

a is the acceleration of the body.

Another way of looking at the problem is in terms of energy. The total energy required toaccelerate a body in a stationary fluid is the sum of the kinetic energy of the body itself, and thekinetic energy of the flow field about the body. These energies correspond to the terms (m.a)and Ca.∆.a respectively.

Trapped Water

The term (Ca.∆) has the dimensions of mass and has become known as the ‘added mass’. Thisis an unfortunate name which has caused much confusion over the years. It should not beviewed as a body of fluid trapped by and moving with the body. Some bodies are so shapedthat this does occur, but this trapped water is a completely different matter. Trapped wateroccurs when the body contains a closed flooded space, or where a space is sufficiently closelysurrounded to prevent free flow in and out. Trapped water should be treated as part of thebody: the mass of the trapped water should be included in the body mass, and its volumeshould be included in the body volume.

For a more complete description of Morison’s equation and a detailed derivation of the addedmass component see Barltrop and Adams, 1991 and Faltinsen, 1990.

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6.11.7 Treatment of CompressionA segment is said to experience compression if the effective tension is negative. OrcaFlex hastwo modes for handling this, depending on the setting of the Limit Compression data item on theline types form.

Limit Compression: No

The segment is treated as a strut which can support unlimited elastic compression. This is thepreferred model except where the bend stiffness is insignificant.

Limit Compression: Yes

The segment is treated as an elastic Euler strut; the compression is limited to the segment Eulerload value for the segment π²EI/L0², where EI is the bending stiffness of the pipe and L0 issegment unstretched length. This correctly models a chain or very flexible rope, which cansupport little or no compression. In the case of a chain, the bending stiffness is set to zero, andthe segment Euler load limit is also zero.

The segment Euler load provides a check on the ability of the model to represent compressiveloads and the deformations which result. Compression causes the line to deform laterally, thedeformation being controlled by bending. Given adequate segmentation, OrcaFlex will correctlyrepresent this deformation. If compression exceeds the segment Euler load of an individualsegment, this indicates that the wavelength of deformation is shorter than can be representedby the chosen segmentation and the results may be unreliable. The model should be re-runwith shorter segments in the affected area. The segment Euler load is shown on tension rangegraphs and infringement warnings are given on the result form and in the statistics tables.

For more details see Modelling Compression in Flexibles and "Limit Compression" Switch.

6.11.8 Contents Flow EffectsIntroduction

Contents flow effects are normally neglected when modelling pipes in OrcaFlex. However forpipes carrying high contents density at rapid flow rates the flow effects can be significant. Thepublished literature show that there are three extra forces introduced by contents flow - acentrifugal force, a Coriolis force and a flow friction force.

OrcaFlex includes the facility to specify the contents mass flow rate on the line data form. If thisis non-zero then the resulting centrifugal and Coriolis effects are included. Note that the flowfriction effects are not included in OrcaFlex.

Note that these flow effects apply only to the dynamic simulation, not to any of the staticcalculations performed by the program. The mass flow rate is increased smoothly through thebuild-up period of the simulation, using the same algorithm employed for 'ramping' wave height.Since the duration of the build-up period is under the user's control, this feature can be used todetermine the transient effect of different start-up rates.

Theory

This section documents the theory behind the modelling of the centrifugal and Coriolis forces inOrcaFlex. This theory is technical and specific to the way pipes are modelled in OrcaFlex.

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Notation

ρ contents density

r mass flow rate

a internal cross-sectional area

l segment length

p position of node relative to fixed axes

v velocity of node relative to fixed axes

u unit vector in downstream direction of line

ω angular velocity of moving frame relative to fixed frame

dx/dt rate of change of any variable x relative to fixed axes

x' rate of change of any variable x relative to moving axes

The contents mass per unit length is aρ so the flow velocity is r/(aρ).

Centrifugal force on a node due to flow through a node

First consider a node with flow arriving from one direction, uin say, and leaving in anotherdirection, uout. For a mid-node uin and uout are simply the unit vectors in the directions of thesegments before and after the node. For the first node uin is the end direction - this is taken tobe the same as uout if the end is free and otherwise is taken to be the no-moment direction.Similar treatment is applied to uout at the last node.

Similarly let ain and aout denote the internal cross sectional areas on the input side and outputside, respectively. ain for the first node, and aout for the last node, are taken to be the same asthe internal cross section area of the end segment - i.e. we assume no change in internal crosssectional area at the line ends.

Then contents flow into the node at mass flow rate r and velocity r/(ainρ)uin so the rate of inputof momentum is r²/(ainρ)uin. The output mass flow rate is also r but the output velocity isr/(aoutρ)uout so the rate of output of momentum is r²/(aoutρ)uout. The force on the contents that isrequired to achieve this change in flow direction must therefore be the rate of output ofmomentum minus the rate of input of momentum, i.e.

r²/(aoutρ)uout - r²/(ainρ)uin

The resulting centrifugal force on the node must be equal and opposite to this, so

Centrifugal Force on Node = (r²/ρ)( uin / ain - uout / aout ).

We can check this result in two ways. Firstly, it has the correct units:

Units = [(M/T)² ] / [(M/L³).(L²)] = ML/T² = F.

Secondly, it matches the centrifugal term included in equation 10 - see Gregory & Paidoussis,1996.

Coriolis force due to movement of a segment

Now consider a segment between two nodes n1 and n2 and consider two frames of reference - afixed global frame and a moving local frame whose origin moves with node n1 and whose z-axisalways points in direction u = unit vector from n1 towards n2.

Consider the contents of a segment. Its velocity relative to the moving axes is

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p' = (r/aρ)u

So its velocity relative to the fixed axes is

v1 + dp/dt

= v1 + p' + ω x p

Therefore its acceleration relative to fixed axes is

d( v1 + p' + ω x p) )/dt

= (v1 + p' + ω x p)' + ω x (v1 + p' + ω x p)

= 0 + 0 + ω' x p + ω x p' + ω x v1 + ω x p' + ω x (ω x p)

= ω' x p + 2ω x p' + ω x v1 + ω x (ω x p)

and of these terms the only new one, i.e. that is dependent on the rate of flow p' rather than p, isthe term 2ω x p' = 2ω x (r/aρ)u. When multiplied by the mass of contents in the segment, laρ,this gives the Coriolis force on the segment, i.e. 2lr (ω x u).

But ω is given by

ω = u x (v2 - v1) / l

so the Coriolis force is given by

2r (u x (v2 - v1)) x u= 2r ( (u.u)(v2 - v1) - (u.(v2 - v1))u )= 2r ( (v2 - v1) - (u-direction component of (v2 - v1)) )= 2r . (component of (v2 - v1)) normal to u).

We then apportion this total Coriolis force on the segment into two equal parts - i.e. a force of

r . (component of (v2 - v1)) normal to u)

on each of the two nodes at the ends of the segment.

Note: A mid node therefore receives two Coriolis force contributions - one each fromthe segments either side - but an end node only receives one suchcontribution.

The above result has the correct units:

Units = (M/T) . (L/T) = ML/T² = F.

and it agrees with the Coriolis term included in equation 10 - see Gregory & Paidoussis, 1996.

Other references:

Paidoussis M P, 1970

Paidoussis M P & Deksnis E B, 1970.

Paidoussis M P & Lathier B E, 1976.

6.11.9 Line Pressure EffectsOrcaFlex reports two different types of tension - the effective tension (Te) and the wall tension(Tw). These two tensions are related by the formula

Tw = C1.(Te + Pi.Ai - Po.Ao)

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• Pi = internal pressure. Pi at end A is the Contents Pressure specified in the data and it isassumed to remain constant during the simulation. Internal pressure elsewhere in the line iscalculated from this value by allowing for the static pressure head due to the current heightdifference between the point and end A.

• Po = external (i.e. surrounding fluid) pressure. Po is assumed to be zero at and above themean water level. Below there it is calculated allowing for the static pressure head due tothe current height difference between the point and the mean water level.

• Ai, Ao = internal and external stress cross section areas, respectively. Ai = π.StressID²/4and Ao = π.StressOD²/4, where StressID, StressOD are the stress diameters.

• C1 = tensile stress loading factor. By default this equals 1.

Explanation of Wall Tension Formula

To understand this formula and the difference between effective tension and wall tension,consider the forces acting axially at the mid-point of a segment. The nodes either siderepresent a length of pipe plus its contents. More importantly, the forces on them are calculatedas if the length of pipe represented had end caps which hold in the contents and which areexposed to the internal and external pressure. The diagram below illustrates this and shows thetension and pressure forces present; the equation above is simply the force balance equationfor this diagram.

Pi.AiPo.Ao

TeTwPi.Ai

Po.Ao

TeTw

segment mid-pointnode n node n+1

Figure: Tension and Pressure forces

This is the standard method of handling internal and external pressure when modelling pipes.The effect is that the spring tension calculated by OrcaFlex is the effective tension, rather thanthe wall tension. OrcaFlex then derives the wall tension, using the above equation, and offersboth effective and wall tension in the results.

This method of modelling lines introduces a small error, since the axial stiffness specified by theuser is being stretched by the effective tension Te, rather than by the wall tension Tw. But if theaxial stiffness is high then the resulting change in extension is negligible, and this is so for mostpractical applications. To reduce this error further, we recommend that the unstretched lengthyou specify for the line is the unstretched length at normal working pressure.

Notes: Both effective tension and wall tension are relevant to the question of pipebuckling. For buckling of the pipe as an Euler strut, effective tension is thegoverning parameter - when it is negative the strut is in compression. On theother hand, local buckling of the pipe wall is determined by wall tension. (Notethat OrcaFlex does not model local buckling, which depends critically ondetails of the pipe construction and is therefore beyond the scope of theprogram.)

For cables, umbilicals and ropes, the internal pressure term PiAi does notapply. However, the external pressure term PoAo is still applicable, and theactual tension in the cable is the wall tension as defined above.

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For chains, which are inherently discontinuous, the pressure terms do notapply and the effective tension is the true tension in the chain.

6.11.10 Pipe Stress CalculationOrcaFlex provides stress results that apply only to simple pipes. More precisely, the stresscalculation assumes that the loads on the line are taken by a simple cylinder whose inside andoutside diameters are given by the stress diameters specified on the line-types form. It alsoassumes that the cylinder is made of a uniform material. The pipe stress results are thereforeonly valid for things like steel or titanium pipes - they do not apply to composite structureflexible pipes. Note that the fatigue analysis uses the pipe stresses, so these restrictions alsoapply to the fatigue analysis.

Consider a cross-section through a mid-segment point, as shown in the following diagram. Thediagram shows the frame of reference used for the cross-section, which has origin O is at thepipe centreline, Oz along the pipe axis (positive towards end B) and Ox and Oy normal to thepipe axis (and so in the plane of the cross-section).

x (Theta=0)

y (Theta=90)

Stress ID Stress OD

r

z

P

y

Theta

Cross-SectionSide View

End A O

C

R

O

Figure: Frame of Reference for Stress Calculation

The OrcaFlex simulation calculates the following loads that are acting at the cross-section:

• Internal and external pressures, Pi and Po respectively.

• Effective tension and resulting wall tension. These are both vectors in the z-direction, withmagnitudes Te and Tw respectively.

• Bend Moment, which is a vector in the xy-plane, with magnitude M and components Mx andMy in the Ox and Oy directions, respectively.

• Shear force, which is also a vector in the xy-plane, with magnitude S and components Sxand Sy in the Ox and Oy directions, respectively.

• Torque, which is a vector in the z-direction with magnitude τ.

In addition we define the following terminology:

• StressOD and StressID = stress diameters, as specified on the line types form.

• A = cross-sectional stress area = (π/4).(StressOD² - StressID²)

• Ixy = 2nd moment of stress area about Ox (or Oy) = (π/64).(StressOD^4-StressID^4)

• Iz = 2nd moment of stress area about Oz = 2.Ixy

• C1, C2, C3, C4 = stress loading factors (C1 = tensile, C2 = bending, C3 = shear, C4 =torsional), as specified on the line types form.

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The stress generated by the above loads varies across the cross-section. Consider the point Pin the cross-section shown as a black dot in the diagram, which can be identified by its polarcoordinates (r, θ). At P, we define a local set of axes (R,C,Z) where R is radially outwards, C isin the circumferential direction (positive in the direction of Theta increasing) and Z is parallel toOz.

With respect to these axes, the stress at P is a symmetric 3x3 matrix of stress components (seePipe Stress Matrix). OrcaFlex calculates this matrix and then derives stress results from it.

6.11.11 Pipe Stress MatrixThe pipe matrix at point P (see Pipe Stress Calculation) can be written as:RRStress RCStress RZStressRCStress CCStress CZStressRZStress CZStress ZZStressThese stress components are calculated as follows. For terminology see Pipe StressCalculation.

Diagonal Terms

The 3 diagonal entries of the stress matrix, RRStress, CCStress and ZZStress, are the radial,circumferential (or hoop) and axial (or longitudinal) stresses, respectively.

Radial and Hoop Stresses

RRStress and CCStress are due to the internal and external pressure. They are calculatedusing Lame's equation for a thick-walled cylinder whose internal and external diameters areStressID and StressOD, as specified on the line types form. This gives:

RRStress = Radial Stress = a - b/r²CCStress = Hoop Stress = a + b/r²

where a and b are the values that satisfy

a - b / (StressID/2)² = -Pia + b / (StressOD/2)² = -Po.

Notes: StressID and StressOD are by default equal to the ID and OD specified on theline type form. However, they can be set to be different to ID and OD. In thiscase the above calculation is equivalent to assuming that the material inbetween ID and StressID, and between StressOD and OD, is transparent topressure. The internal pressure therefore applies right through to the StressIDand the external pressure applies right through to StressOD.

If StressID is zero, then OrcaFlex assumes that external pressure appliesthroughout the structure - i.e. that RRStress = CCStress = -Po.

Axial Stress

ZZStress is the axial stress and is given by:

ZZStress = Direct Tensile Stress + Bending Stress

where the Direct Tensile Stress is the contribution due to wall tension and Bending Stress is thecontribution due to bend moment. The wall tension is assumed to be uniformly distributedacross the stress area, so its contribution is given by:

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Direct Tensile Stress = Tw / A

The bend moment contribution varies across the cross-section and is given by:

Bending Stress = (C2.Mx.r.sinθ - C2.My.r.cosθ) / Ixy

Off-Diagonal Terms

The 6 off-diagonal terms are the shear stresses, but there are in fact only 3 independent terms,since the matrix is symmetric. They are given by:

RCStress = 0

RZStress = (C2.Sx.cosθ + C2.Sy.sinθ) / A

CZStress = C3.τ.r / Iz + (C2.Sy.cosθ - C2.Sx.sinθ) / A

The contribution C3.τ.r / Iz in the above equation is the shear stress contribution due to torque.If torsion is not included in the model, then it is zero. The other contributions are both due to theshear force, which is assumed to be uniformly distributed across the stress area.

Finally, for two useful references on this subject, see Sparks (1980) and Sparks (1983).

6.11.12 Hydrodynamic LoadsDrag

The drag forces applied to a line are calculated using the "cross flow" principle. That is, the fluidvelocity relative to the line is split into its components Vn normal to he line axis, and Vz parallelto the line axis. The components of drag force normal to the line axis are then based on Vn,and its x and y-components Vx, Vy. The component of drag force parallel to the line axis isbased on Vz.

The drag force formulae use drag coefficients, Cdx, Cdy and Cdz (specified on the line typedata form) and the drag areas appropriate to each direction.

For the directions normal to the line axis (x and y) the drag area is taken to be the projectedarea D.L where D is the outside diameter and L is the length of line represented by the node.For the axial direction (z) the drag area is taken to be the skin surface area π.D.L.

If Cdx or Cdy vary with Reynolds number then OrcaFlex calculates the Reynolds number usingthe normal component of relative velocity, Vn. This Reynolds number is then used to find Cdxor Cdy (or both) using the specified variable data table. OrcaFlex uses linear interpolation forReynolds numbers between those specified in the table, and truncation for Reynolds numbersbeyond those specified in the table.

There is a choice of the following three possible drag formulations for the drag forcecomponents (Fx, Fy, Fz) in the local line directions. The formulations differ in how the dragforce components vary with the incidence angle φ between the flow and the line axial direction.The formulations are reviewed in Casarella and Parsons.

In the formulae below, ρ is the sea water density and PW is the proportion wet.

Standard Formulation

Fx = PW.( ½.ρ.(D.L).Cdx.Vx.|Vn| )

Fy = PW.( ½.ρ.(D.L).Cdy.Vy.|Vn| )

Fz = PW.( ½.ρ.(πD.L).Cdz.Vz.|Vz| )

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This formulation is the most commonly-used and was the formulation used by versions ofOrcaFlex before a choice of formulation was introduced. It has been proposed or used byvarious authors, including Richtmyer, Reber and Wilson. It is appropriate for general flowconditions.

Pode Formulation

Fx = same as standard formula for Fx, aboveFy = same as standard formula for Fy, above

Fz = +/- PW.( ½.ρ.(πD.L).Cdz.|V|² )

where the sign of Fz, i.e. whether it is towards end A of the line or towards end B, is the sameas the axial component of the relative flow vector.

This formulation is preferred by some analysts for systems with near-tangential flow.

Warning: The Pode formula for Fz is discontinuous at φ = 90, since then the axialcomponent of the flow vector is zero and so the direction of Fz is undefined.In this case OrcaFlex sets Fz to zero.

Eames Formulation for bare cables

Fx = PW.( ½.ρ.(D.L).Cdx.Vx.|Vn| + ½.ρ.(πD.L).Cdz.Vx.(|V| - |Vn|) )

Fy = PW.( ½.ρ.(D.L).Cdy.Vy.|Vn| + ½.ρ.(πD.L).Cdz.Vy.(|V| - |Vn|) )

Fz = PW.( ½.ρ.(πD.L).Cdz.Vz.|V| )

Drag Force Variation with Incidence Angle

The above formulae for the drag force components can be re-written in a form that highlightshow the drag force varies with incidence angle.

Consider the case where the line is axially symmetric, i.e. Cdx = Cdy = Cdn say, and let φ bethe incidence angle between the flow vector V and the line axis. Then Vz = V.cosφ and Vn =V.sinφ. Also, let:

R = PW.( ½.ρ.(D.L).Cdn.|V|² )

µ = π.Cdz/Cdn.Fn = the normal component of the drag force.

Then the formulations can be expressed as follows.

Standard: |Fn| = R.sin²φ |Fz| = R.µ.cos²φ

Pode: |Fn| = R.sin²φ |Fz| = R.µ

Eames: |Fn| = R.( (1-µ).sin²φ + µ.sinφ ) |Fz| = R.µ.cosφ

Added Mass

The added mass effects on a line are calculated separately for the local x, y and z-directions.For each of these directions, the line is subject to two added mass effects:

1. Its effective mass is increased by

Ca.(Displaced Mass)

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where Displaced Mass is the mass of the fluid displaced (taking into account the proportionwet) and Ca is the added mass coefficient specified for that direction. As a result, if the lineaccelerates then it experiences an extra inertial force (due to added mass) given by

-Ca.(Displaced Mass).AL

where AL is the component (in that direction) of the acceleration of the line (relative to theearth).

2. If the fluid is accelerating then the line experiences a fluid acceleration force given by

(1+Ca).(Displaced Mass).AF

where AF is the component (in that direction) of the acceleration of the fluid (relative to theearth).

Note: The fluid acceleration force is sometimes written as

Cm.(Displaced Mass).AF

where Cm = 1 + Ca. It can also be split into two terms:

(Displaced Mass).AF + Ca.(Displaced Mass).AF

where the first term is called the Froude Krylov force and the second term iscalled the added mass force.

Fluid Flow

If the mass flow rate of the Line is non-zero then the centrifugal and Coriolis effects due to thisflow are included.

6.11.13 Drag ChainsA drag chain is an attachment to a line that applies a force to the node to which it is attached.The force consists of the tension in the drag chain and so is in the direction in which the chain ishanging. This direction is determined by the relative velocity of the water past the chain - thefaster the flow then the greater the angle of the drag chain to the vertical. This is now describedin more detail.

θ Vn

Va

V

W

WnWa

180-θ

Drag Chain

α =θ-90Connectionto Line

A

Figure: Drag Chain

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Consider the drag chain shown in the above diagram.

Let

D = drag chain effective diameterL = drag chain length

θ = drag chain declination from vertical

V = horizontal relative velocity = (horizontal fluid velocity at A) - (horizontal node velocityat A).

Then the incidence angle α between the horizontal relative velocity vector V and the drag chainis α = θ - 90 and the normal and axial drag forces are given by:

Fn = normal drag force = 0.5.ρ.L.D.Cdn(α).Vn.|Vn|

Fa = axial drag force = 0.5.ρ.π.L.D.Cda(α).Va.|Va|

where

Vn = normal component of relative velocity = |V|.sin(α)

Va = axial component of relative velocity = |V|.cos(α)

ρ = water density

Cdn(α), Cda(α) = normal and axial drag coefficients for this incidence angle.

The inertia of the drag chain is assumed to be small enough to be neglected, so we assumethat the drag chain is always in equilibrium under the action of 3 forces:

• the chain's wet weight (W)

• the fluid drag on the chain

• the tension being applied by the line at the top of the chain.

Because the tensile force being applied by the line is axial to the chain, the components of wetweight and drag normal to the chain must balance. In other words, the direction in which thedrag chain hangs is that in which the chain is in force balance in the direction normal to thechain. The remaining net force on the chain in the axial direction, Fa, is then applied to the line.

OrcaFlex therefore hangs the chain in the same vertical plane as the relative velocity vector Vand at angle θ to the vertical. OrcaFlex calculates the angle θ by iterating until the sum of thenormal components of drag force and wet weight is zero.

Drag Chain Seabed Interaction

Drag chains, in OrcaFlex, interact with the seabed in a fairly simplistic way that is designed toachieve the following two primary effects of seabed interaction:

• Firstly, that as the chain is lowered down onto the seabed, the wet weight of the chain issteadily reduced as the chain becomes supported by the seabed.

• Secondly, that if the chain is dragged across the seabed then an opposing friction force µRis generated, where µ is the friction coefficient and R is the seabed reaction.

The seabed interaction model used is as follows:

• At any given time, OrcaFlex first calculates how much of the drag chain would be supportedby the seabed if the chain hung straight vertically down from the line. The drag chain is then

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considered as being made up of two parts - the supported part and the remaining hangingpart.

• The hanging part of the chain is then analysed as described above.

• The supported part of the chain is modelled as if it lying on the seabed directly beneath thenode to which the chain is attached. As the node moves laterally, the supported chain alsomoves laterally (but below the node) and so generates a friction force that is then applied tothe node.

Note that the division of the drag chain into a hanging length and a supported length is donebefore the hanging length is analysed, and so is done with the chain vertical. This means that ifcurrent drag causes the chain to hang at an angle to the vertical then the supported length willgenerally have been overestimated and the hanging length correspondingly underestimated.This is an inaccuracy that cannot easily be avoided at the moment.

6.11.14 Line End ConditionsExcept for Free Ends, the connection at the line end is modelled as an isotropic 'ball-joint' with arotational stiffness and a preferred 'no-moment' direction. A rotational stiffness of zerosimulates a freely rotating end, and a value of Infinity simulates a clamped end.

The inclusion of end stiffness allows the program to calculate the curvature and bendingmoment at the termination. If the curvature is large, the calculated value is accurate only ifsufficiently short segments have been used to model the line near its end.

OrcaFlex reports a value for End Force and End Ez-Angle. These are the magnitude of the endforce, and the magnitude of the angle between the end force vector and the no-momentdirection. Vessel motion is automatically accounted for. The end force and angle valuesprovide the basis for the design of end fittings such as bend stiffeners. See Modelling LineEnds.

6.11.15 Line Interaction with the Sea SurfaceOrcaFlex Lines are subdivided into segments, and the various forces are attributed to nodes ateach end. For a partially submerged segment, the hydrostatic and hydrodynamic forces areproportioned depending on how much of the segment is submerged - the Proportion Wet. (TheProportion Wet is available as a line result variable.)

For a segment whose axis is normal to the surface, the Proportion Wet could be calculated fromthe intersection of the segment centreline axis with the free surface. However, this simpleapproach breaks down when the segment is tangent to the surface.

For this reason, OrcaFlex uses a simple but effective modification of this concept. Instead ofusing the centreline axis, we use the diagonal line joining the highest point on the segmentcircumference, at the 'dry' end, with the lowest point at the 'wet' end; see the diagonal line in thefigure below. As the segment passes through the tangent position, the diagonal line switchescorners but the proportion wet varies continuously. The intersection of the diagonal line withthe surface continues to give the appropriate Proportion Wet result, and the hydrostatic anddynamic forces are attributed to the appropriate node.

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B

A

Proportion Wet = B / (A+B)

Figure: Proportion Wet for a surface-piercing segment

This surface-piercing model enables OrcaFlex to model systems such as floating hoses,containment booms and wave suppression systems. However please note the following pointswhen modelling such systems:

• A consequence of this model is that a hose floats in still water as a wall-sided body; in otherwords OrcaFlex does not take account of the variation in water plane area with draft thatarises from the circular cross-section. For cases of practical dynamics, this simplification isof minor importance, but it does mean that if you check the immersion depth of a hose in stillwater you may find the answer slightly wrong if the hose is very buoyant, or just awash.

• When modelling floating hoses, it is important to have enough segments to model the localcurvature. If your hose is flexible, and the waves are short, then you will need at least tenand preferably twenty segments per wave to model the curvature properly. However a stiffhose tends to bridge the wave troughs, and fewer segments are required.

• The program uses constant drag and added mass coefficients for the floating hose, and theuser has to select appropriate values based on the average immersion depth.Unfortunately the literature is of limited help - if you know of any good data source, we wouldbe very pleased to hear of it.

6.11.16 Seabed Touchdown and FrictionSeabed Touchdown

The Catenary algorithm for calculating the static position of a line has facilities for includingseabed touchdown, but for technical reasons it has the following limitations:

• Seabed touchdown can only be included at end B of the line, not at end A. Therefore, if youwant touchdown then you should arrange it to be at end B.

• Touchdown is only included if end B is anchored exactly on, or else below, the seabed. Ifend B is above the seabed, even if only by a small amount, then no touchdown will bemodelled and the line may hang below the seabed. This will be corrected when thesimulation starts, since the nodes below the seabed will be pushed back up by the seabedreaction forces. Alternatively, you should use the Full statics option, which can handle thiscase.

• If end B is below the seabed, then the Catenary algorithm models touchdown by assumingthat the line 'levels out' at the level of end B. This will result in part of the line being belowthe seabed, but again this will be corrected when the simulation starts, since the nodesbelow the seabed will be pushed back up by the seabed reaction forces.

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Seabed Friction

OrcaFlex provides a simple friction model that can give an approximate representation ofseabed interaction. In reality seabed interaction is much more complicated than simple friction -it involves effects such as the soil being displaced by the line as it moves, accumulation of soilin front of the line, etc. To model seabed interaction accurately would require much moreinformation about the soil structure and would involve modelling the soil itself. This is beyondthe scope of OrcaFlex.

Statics

Friction can be included in the static analysis only if the Statics Method specified is Catenary orif Full Statics is used.

There is a problem in deriving a static position for a line with seabed friction present, since ingeneral a range of static solutions exist, depending on how the line was originally laid and on itssubsequent loading history.

The particular approach we have chosen in OrcaFlex is to apply friction so that the resultingstatic position is as near as possible to an assumed "originally laid" position. This is done byapplying, to each node in contact with the seabed, a friction force with:

• Magnitude less than or equal to µR, where µ is the friction coefficient and R is the normalcomponent of the reaction force.

• Direction chosen so that the resulting static position of the node is as near as possible to the"originally laid" position.

• If the Statics Type is Prescribed, then the originally laid position is taken to be the positiongiven by the Prescribed track, allowing for the specified Pre-Tension. Otherwise, the line isassumed to have originally been laid, with the specified Pre-Tension, leading away from endB in the Lay Azimuth direction. See Line Data:Statics.

Dynamics

Seabed friction is modelled as Coulomb friction in the seabed plane. If a node is stationary andin contact with the seabed then the friction force opposes the in-plane component, Fi, of theresultant force on the node. The value of the friction force is set equal to Fi or µ.R, whichever isthe less, where R is the seabed reaction force on the node and µ is the friction coefficient in thedirection Fi.

If the node is sliding across the seabed, the friction force has magnitude µ.R, where µ is thefriction coefficient in the direction of sliding. The direction of the applied friction force dependson the specified friction coefficients and bias power (see Friction Coefficients and Bias Power).If the normal and axial friction coefficients are equal then the friction force is applied directlyopposing the direction of sliding. But if the normal and axial friction coefficients differ then thebias power can be used to bias the friction direction towards the direction of larger coefficient.For example if µn > µa then the larger the bias power the more the friction direction is turnedtowards opposing sliding in the normal direction.

Note: This friction direction bias is not (yet) available with profile seabeds.

Friction Model

We now give the friction model in detail. Consider one node of a line that is lying on the seabed. Denoting vectors by underline, we let:

µn, µa = normal and axial friction coefficients, as specified on the line types form

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C = friction bias power, as specified on the line types form R = magnitude of the sea bed reaction force D = unit vector in the plane of the sea bed, in the direction of motion Dn, Da = the vector components of D in the normal and axial directions

F = magnitude of the vector (µn.Dn + µa.Da).R

V = - { (µn^C).Dn + (µa^C).Da }

Then for a moving node the friction force applied by OrcaFlex has magnitude F and is applied inthe direction of vector V. For a stationary node the friction force has magnitude up to F and isapplied in the direction directly opposing the force attempting to move the node.

This model has the following characteristics:

• For pure axial motion the friction force is µaR axially and for pure lateral motion it is µnRlaterally, as required.

• As D varies from the axial to the normal direction, the friction force varies smoothly andmonotonically from µaR to µnR.

• For a moving node the friction direction (given by the vector V) varies from axial when D isaxial, to normal when D is normal, but in between its direction is "biased" towards thedirection of the larger friction coefficient.

• For moving nodes, the model described above "biases" the direction of the friction forcetowards the direction of the larger friction coefficient. So, for example, if µn > µa (and C>0)then motion at an angle to the line axis is resisted by an opposing force at a larger angle tothe line axis, tending to make the line move axially, as expected.

The amount of direction bias for a moving node depends on the ratio (µn/µa)^C, so the frictionbias power C provides a way of controlling the amount of direction bias in the model. Note thatC only affects the direction in which friction is applied for moving nodes. It has no effect on themagnitude of the friction force, nor on its direction for a stationary node.

The direction bias in this model has the following properties:

• If µn = µa then there is no direction bias and a standard isotropic friction model results. Inthis case C has no effect.

• If C=0 then again there is no direction bias - the friction force on a moving node then simplyopposes the direction of motion.

• If µn > µa and C>0 then C controls the amount of direction bias. Increasing C increases thedirection bias and hence increases the tendency of the line to slide axially.

6.11.17 Interaction with Seabed and ShapesNodes are also subjected to reaction forces from the seabed and any Shapes with which theycome into contact, given by:

Reaction = K A d

where

K is the Stiffness of the seabed or shaped is the depth of penetrationA is the contact area, which is taken to be Outside Diameter multiplied by the length ofline represented by the node.

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In addition, nodes experience a damping force. For details see Seabed Theory and ShapesTheory.

6.11.18 ClashingOrcaFlex includes the capability to model clashing between lines. To include clash modellingbetween two lines, you must set Clash Check to "Yes" and set the Contact Stiffness to a non-zero value, for both lines. You can also specify the Contact Damping value.

The facility to suppress clash modelling (by setting Clash Check to "No") has been includedbecause the clashing algorithm is time consuming. It is therefore best to suppress clashmodelling on all sections that will never clash with other lines, or if you are not interested in theeffects of clashing.

OrcaFlex assumes constant spring stiffness and damping values, and neglects friction. Theforce algorithm is described below. It pushes lines apart again if they try to pass throughanother, and it permits lines to separate again after contact. Multiple contact points along theline length are allowed for, but clashes of one part of a line with another part of the same lineare not modelled at present.

Clashing behaviour can be difficult to understand and it is not always obvious what the resultsmean and how they should be used in practice. This is a developing area and we wouldappreciate feedback from users. The following notes expand on the way the calculations arecarried out by the software and give our suggestions on interpretation.

Calculating the Clash Force

OrcaFlex checks for clashing between each line segment and every segment in every other linein the OrcaFlex model (providing check checking is enabled and the contact stiffness is non-zero, for both segments involved). Note that OrcaFlex does not check for clashing between twosegments of the same line, so it does not model clash contact of a line with itself.

The clash check between segment S1 (on line L1) and segment S2 (on a different line L2) isdone as follows. Let the radii of the two segments be r1 and r2 (as defined by the line typeouter diameter). First OrcaFlex calculates the shortest separation distance, d, between thecentrelines of the two segments. If d >= (r1 + r2) then the lines are not in contact and nocontact force is applied.

If d < (r1 + r2) then the lines are in contact. In this case OrcaFlex applies equal and oppositeclash contact forces to the 2 segments to push them apart, as follows. Let p1 and p2 be the twopoints of closest proximity - i.e. p1 is on the centreline of segment S1 and p2 is on the centrelineof segment S2, and these are the two points that are minimum distance d apart. Also, let u bethe unit vector in the direction from p1 towards p2. Then the magnitude of the clash contactforce applied is given by:

F = (Stiffness Term) + (Damping Term)

where the two terms on the right are documented below. A force of this magnitude F is appliedto segment S1, at p1, in direction -u. And the equal and opposite force is applied to segmentS2, at p2, in direction +u.

The stiffness term is given by:

Stiffness Term = k.(d - [r1 + r2])

where k = 1 / (1/k1 + 1/k2) is the combined contact stiffness of the segments. Here k1 and k2are the contact stiffnesses of the two segments, as specified in the Line Types data.

The damping term is based on the rate of penetration, v, which is the u-direction component ofp1's velocity relative to p2. If v <= 0 then the two segments are moving apart and then no

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damping force is applied. If v>0 then the penetration is increasing and the damping term isthen given by:

Damping Term = c.v

where c is the combined contact damping value of the two segments, which is given by:

c = 0 if c1=0 or c2=0c = 1 / (1/c1 + 1/c2) otherwise.

Here c1 and c2 are the contact damping values of the two segments, as specified in the LineTypes data.

How the Clash Force is Applied and Reported

In general, clashing will take place between one segment of one line and one segment ofanother (the probability of a clash occurring exactly at a node is very small unless you takespecial measures to make it happen). OrcaFlex determines the force as just described, andreports the force as a segment variable - i.e. when you ask for the clash force at a particular arclength along the line, the force reported is the clash force for the segment which contains thespecified point.

If multiple clashes occur simultaneously on the same segment then the Line Clash Forcereported is the magnitude of the vector sum of the clash forces involved.

In the OrcaFlex model, all forces act at the nodes, so the clash force has to be divided betweenthe two nodes at the ends of the segment in which the force acts. The force is divided in such away that the moments of the two forces about the contact point are equal and opposite.

Interpreting the Results

Clashing between lines can be a violent impact at high relative velocity, or a gentle drift of oneline against another, or anything in between. We need to view the results in different ways fordifferent sorts of clash.

Impact

In the case of a violent impact, the contact forces arrest the relative movement of the lines overa very short time interval. Kinetic energy is extracted from the system and transformed intostrain energy at the point of contact, with some energy loss to damping. This sort of clash isprobably best quantified in terms of the clash impulse rather than the clash force. Numericalexperiments show that the clash impulse is relatively insensitive to changes in contact stiffnessor model discretisation.

Since the line contact formulation is based on a linear spring, then if the damping is low theenergy of impact can be estimated from the peak clash force:

Estimated Contact Energy = Fmax²/(2.k)

where Fmax is the peak clash force and k is the combined contact stiffness.

Note that in the case of an exactly symmetric collision with a line node, the reported clash forcewill be shared between the two adjacent segments. In this case, the energy should becalculated using the clash force reported for the other line involved in the collision.

Low Speed Contact

Where one line drifts quite slowly against another as a result of weight or drag forces, then theenergy of impact is negligible, and the clash force at the point of contact is the best measure ofwhat is happening, and will be insensitive to changes in modelling.

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6.12 VESSEL THEORY

6.12.1 RAOs and PhasesVessel motions in waves are defined by Response Amplitude Operators (RAOs). Each RAOconsists of a pair of numbers that define the vessel response, for one particular degree offreedom, to one particular wave direction and period. The two numbers are an amplitude, whichrelates the amplitude of the vessel motion to the amplitude of the wave, and a phase, whichdefines the timing of the vessel motion relative to the wave.

Example: A surge RAO of 0.5 in a wave of height 4m (and hence wave amplitude 2m)means that the vessel surges to and fro -1m to +1m from its static position; apitch RAO of 0.5° per metre in the same wave means that the vessel pitchesfrom -1° to + 1°.

The vessel has 6 degrees of freedom: 3 translations (surge, sway, heave) and 3 rotations (roll,pitch, yaw), so the RAO data consist of 6 amplitude+phase pairs for each wave period anddirection. The RAO amplitude and phase vary for different types of vessel, and for a givenvessel type they vary with draught, wave direction, forward speed and wave period (orfrequency). It is important to obtain accurate values for the RAO amplitude and phase if thedynamics of the system are to be correctly modelled.

RAOs can be obtained either from model tests or from specialist computer programs. The datamay be presented in tabular or graphical form: tables of numbers are better for our purposessince they can be imported directly into OrcaFlex (see Import RAOs from Text Files).

There are many different conventions for defining RAOs. There have been attempts atstandardisation but these have not been successful so there remain differences between themain computer programs and model basins: some establishments even use differentconventions for reporting model and computed data. The only safe course is to obtain acomplete description of the system used for the data in each case.

The Orcina convention is to use the amplitude of response (in length units for surge, sway,heave, in degrees for roll, pitch, yaw) per unit wave amplitude, and to use the phase lag fromthe time the wave crest passes the RAO origin until the maximum positive excursion is reached(in other words, the phase origin being at the RAO origin). Mathematically, this is given by:

x = R.a.cos (ωt - φ)

where

x is the vessel displacement (in length units for surge, sway, heave, in degrees for roll,pitch, yaw)

a, ω are wave amplitude (in length units) and frequency (in radians/seconds)t is time (in seconds)

R, φ are the RAO amplitude and phase.

However, OrcaFlex can accept RAO data using a wide range of different conventions - seeConventions Data - so you can input your RAO data in its original form and simply tell OrcaFlexwhat conventions apply to that data.

In addition to the actual RAO data you therefore also need to know:

• The coordinates of the RAO origin and of the phase origin.

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• The system used to define wave direction. In OrcaFlex 0° means waves approaching thevessel from astern and 90° means waves coming from the starboard side, but if a differentconvention applies to your data then you must allow for this when entering the data.

• The coordinate system used to define vessel motions and, in particular, which direction ispositive (e.g. is surge positive forward or aft? is heave positive up or down? is pitch positivebow up or bow down?). OrcaFlex allows the RAO input data to use a wide range ofsystems, but all OrcaFlex results use a right-handed system in which the positivemovements are as follows:

Surge: positive Forward

Sway: positive to Port

Heave: positive Up

Roll: positive Starboard Down

Pitch: positive Bow Down

Yaw: positive Bow to Port

• Whether the rotational RAO data are in degrees (or radians) of rotation per metre (or foot) ofwave height, or in degrees (radians) per degree (radian) of wave slope or wave steepness.

• The reference time for phase angles, and the reporting convention used (e.g. whetherphases are reported as lags or leads). Again, OrcaFlex allows a range of options.

6.12.2 RAO Quality ChecksRAOs (particularly the phases) are difficult, abstract concepts for which few users have anatural, intuitive understanding. This makes them difficult to check, but it also makes it all themore important to check them, since the same difficulty applies to the people who derived thedata in the first place. RAOs and phases, even from the most respected sources, arenotoriously error-prone!

Fortunately, there are a few natural points of reference where we know what must be going on.The most obvious and useful ones are response at very short and very long wave periods. Invery short period waves, the vessel inertia suppresses response, so the expected RAOamplitudes are zero (and phase is then irrelevant).

In very long waves (typically wave periods over 20 seconds for ships or 30 seconds forsemisubmersibles) the vessel will move like a raft on the wave surface. The tables below givethe expected RAO amplitudes and phases (using the Orcina standard conventions) for a free-floating vessel in very long waves.

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Expected RAOs for a vessel in very long waves

From ahead(180º)

From astern(0º)

From port(270º)

From starboard(90º)

Amp. Phase Amp. Phase Amp. Phase Amp. Phase

Surge 1 -90º 1 +90º 0 ~ 0 ~

Sway 0 ~ 0 ~ 1 -90º 1 +90º

Heave 1 0º 1 0º 1 0º 1 0º

Roll 0 ~ 0 ~ 1 -90º 1 +90º

Pitch 1 +90º 1 -90º 0 ~ 0 ~

Yaw 0 ~ 0 ~ 0 ~ 0 ~

Towards direction θθθθ

Amp. Phase

Surge | cos(θ) | +90º if cos(θ)>0-90º if cos(θ)<0

Sway | sin(θ) | +90º if sin(θ)>0-90º if sin(θ)<0

Heave 1 0

Roll | sin(θ) | +90º if sin(θ)>0-90º if sin(θ)<0

Pitch | cos(θ) | -90º if cos(θ)>0+90 if cos(θ)<0

Yaw | ½ sin(2θ) | 180º if sin(2θ)>00º if sin(2θ)<0

Warning: The expected yaw RAOs given in the above table only apply to slender ships.

Notes: In these tables, the translational amplitudes are non-dimensionalised againstwave amplitude and the rotational amplitudes are non-dimensionalised againstmaximum wave slope.

The phases given are lags relative to the wave crest. I.e. +90 means that themaximum positive motion occurs 90 degrees after the wave crest passes thevessel (where positive surge is forward, positive sway is to port, positiveheave is up, positive roll is starboard down, positive pitch is bow down andpositive yaw is bow to port.

When the amplitude is zero the phase value is irrelevant; this is indicated inthe tables by '~' .

You can check RAOs in two ways. First, OrcaFlex provides RAO graphs that help spot errorssee Checking RAOs. Second, you can run quick simulations with only the vessel in the modeland then check that the motions you see are sensible.

Consider a ship in waves coming from ahead. Set up a simple OrcaFlex model with the vesselonly - nothing else - and run a short simulation (say 10 seconds build up plus 2 wave periods).Use a large wave height (20m) and long time step - say 0.05 seconds for both inner and outer

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time steps. When the run is finished (a few seconds only for such a trivial case) replay the lastwave period and watch to see whether the motion of the ship is realistic. The best viewdirection is horizontal, normal to the direction of travel of the waves. With the waves comingfrom the right on screen, then in the wave crest the ship should be at maximum heave up andmoving to the left, and vice versa in the trough. At the point of maximum wave slope as thecrest approaches, the ship should be at maximum surge forwards into the wave and maximumpitch angle with the bow up. If the phase convention has been misunderstood (e.g. leads havebeen read as lags) then the motion is obviously wrong and you should go back and re-examinethe data, or confirm your interpretation with the data source.

This is an excellent check for phases, which are usually the most troublesome to get right. It isnot quite so good for amplitudes, but it is nevertheless worth pursuing. If the wave is very longcompared to the ship, then the ship should move like a small particle in the water surface.Heave amplitude should be equal to wave amplitude and pitch motion should keep the deck ofthe ship parallel to the water surface. Surge amplitude should also be equal to wave amplitudein deep water, but will be greater in shallow water in which the wave particle orbits are elliptical.

The check can be extended to other wave directions. Broadly speaking, we may expect themotion to be predominantly in the wave direction, with the phasing of surge and sway such thatthe components in the wave direction reinforce each other. Similarly, roll and pitch phasingshould be such that the components of rotation about an axis normal to the wave directionreinforce each other. Yaw phasing for a ship in seas off the bow should be such that the shipyaws towards the broadside on position as the wave crest passes: this is easiest to see in anear-plan view. Generally speaking, if it looks right in long waves, it probably is right. If not,then think again!

6.12.3 Drag LoadsDrag loads on a vessel are an important source of damping when modelling vessel slow drift.For a discussion of the various damping sources see Damping Effects on Vessel Slow Drift.

The hydrodynamic and aerodynamic drag loads on a vessel are calculated using the dataspecified on the Hydrodynamic and Wind Drag tabs on the vessel type data form. The dragloads are split into those due to translational relative velocity and those due to yaw rate.

Drag Loads due to Translational Relative Velocity

The drag loads due to translational velocity of the sea and air past the vessel are calculatedusing the standard OCIMF method, which is outlined below. For further details see OilCompanies International Marine Forum, 1994.

The OCIMF method is for calculating the surge, sway and yaw drag loads on a stationaryvessel. OrcaFlex extends the method to cover a moving vessel by replacing the current (orwind) velocity used in the OCIMF method by the relative translational velocity of the current (orwind) past the vessel.

More precisely, the relative velocity used is the current (or wind) velocity, relative to the primarymotion of the vessel, at the specified current (or wind) load origin. In other words the relativevelocity includes the current but not the waves, and it includes the primary motion of the vessel,but not the superimposed motion.

Note that the OCIMF method does not include any drag due to yaw angular velocity of thevessel, since there are none for a stationary vessel. OrcaFlex's extension of OCIMF does notadd these yaw rate drag terms, since the OCIMF method has no framework for them. They aretherefore calculated separately in OrcaFlex - see Drag Loads due to Yaw Rate below.

Note: The OCIMF method is intended for tankers, but could be applied to othervessel types providing suitable data is obtained.

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Warning: The current and wind loads are based on theory for surface vessels and arenot suitable for submerged vessels.

The drag loads due to surge and sway relative velocity are calculated as given by the followingOCIMF formulae.

Surge Force = ½.C(surge).ρ.V².A(surge)

Sway Force = ½.C(sway).ρ.V².A(sway)

Yaw Moment = ½.C(yaw).ρ.V².A(yaw)

where

A(surge), A(sway) and A(yaw) are the surge and sway areas and the yaw area moment,as specified in the data. For current these correspond to the exposed areas below thewaterline, and for wind to the exposed areas above the waterline.C(surge), C(sway) and C(yaw) are the surge, sway and yaw coefficients for the actualcurrent or wind direction relative to the vessel.

ρ is the water density (for hydrodynamic drag) or air density (for wind drag).V is the magnitude of the relative velocity of the sea or air past the vessel. For windloads, V is based on the wind velocity specified in the data (i.e. the wind velocity at 10mabove mean water level). For hydrodynamic drag, V is based on the current velocityrelative to the vessel at the instantaneous position of the load origin (if this is above thewater surface, then the current velocity at the surface is used). In both cases V includesallowance for the translational velocity of the load origin due to any primary motion of thevessel, but does not include any superimposed motion.

These surge force, sway force and yaw moment act at the current or wind load origin. Thesurge and sway forces act in the vessel Vx and Vy-directions, respectively, and the yawmoment acts about the vessel Vz-direction.

Notes: The OCIMF standard method uses L² x D for the yaw area moment forcurrent loads, and L x A(sway) for the yaw area moment for wind loads,where L is the length between perpendiculars and D is the draught. Forcurrent loads (not wind loads) the OCIMF standard method uses L x D forboth the surge and sway areas.

Drag Loads due to Yaw Rate

A vessel rotating in yaw will generate a drag moment resisting the yaw rate, but the OCIMFmethod described above does not include this drag load (since the OCIMF method is designedfor stationary vessels).

For wind drag these yaw rate terms are insignificant and so are omitted by OrcaFlex. But forhydrodynamic drag they are important, so OrcaFlex models them using the following formulae.

Surge Force = (½.ρ.ω²).SurgeFactor

Sway Force = (½.ρ.ω²).SwayFactor

Yaw Moment = (½.ρ.ω²).YawFactor .................. (1)

where

SurgeFactor, SwayFactor, YawFactor are the yaw rate drag factors (specified on theHydrodynamic Drag tab on the vessel type data form).

ω is the vessel yaw rate, in radians per second, due to any primary motion of the vessel

ρ is the water density.

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These yaw rate drag loads are then applied at the hydrodynamic load origin.

Estimating the Yaw Rate Drag Factors

The above formulae (1) are based on a simple strip theory estimate of the drag loads on ayawing vessel, as given by Wichers (1979). Consider the simplest situation where the vesselcentre is stationary but the vessel is yawing at rate ω about that centre. Let us also assume thatthe area exposed to sway drag is a simple rectangle of height D (the draught) and length L (thelength between perpendiculars), and that for simplicity we choose to put the load origin at thecentre of that area.

We now divide the drag area into vertical strips of width dx and consider the sway drag load onthe strip at distance x forward of the centre. The strip's area is D.dx and its sway velocity due tothe yaw rate is ω.x, so we can estimate the sway drag load on it by ½.ρ.Cd.D.dx.(ω.x).|ω.x|.where Cd is the drag coefficient, which we assume to be the same for all the strips.

These sway drag loads from each strip, and their moments about the centre, are then integratedto give the total sway force and a contribution to yaw moment. When we do this integral thesway forces from corresponding strips forward and aft of centre have the same magnitude butopposite direction, so they cancel and the total sway drag force is therefore zero. However theyaw moment terms from forward and aft of centre have the same magnitude and samedirection, so they reinforce, giving a significant yaw drag moment. In fact the integral gives thefollowing yaw moment.

Yaw Moment = (½.ρ.ω²).(Cd.D.L^4/32) ................. (2)

The same argument can be applied to the drag forces in the surge direction, with length L beingreplaced by width W. But for a slender vessel W is much less than L, so the surge forcecontribution to yaw moment is generally negligible.

Comparing equations (1) and (2) we see that the YawFactor corresponds to the bracketed term(Cd.D.L^4/32) in equation (2). This is in fact a combination of a drag coefficient and the 3rdmoment of drag area about the centre.

This strip theory argument therefore concludes that for a slender ship, with the hydrodynamicdrag load origin at the centre, then we can estimate the yaw rate drag factors by:

SurgeFactor = SwayFactor = 0YawFactor = (Cd.D.L^4/32)

where Cd is some appropriate drag coefficient. However, there are a lot of questionableassumptions in the strip theory argument. Indeed Wichers (1979) found that the strip theoryresults significantly underestimated the actual yaw drag measured in model tests, unless the Cdvalue was increased to about 5, which is rather high for a drag coefficient. So if more specificdata is available, e.g. from model test, then we recommend setting the yaw rate drag factors tovalues that best fit your data.

Interaction with sway rate

Further complications arise if the vessel is swaying as well as yawing. In this case the integralin the above strip theory argument turns out to give an extra term involving v.ω. This is aninteraction between sway velocity and yaw rate and its effect is to significantly increase the yawmoment.

OrcaFlex does not yet include this interaction effect. The reason for this is that it is difficult tomodel. Wichers (1979) included them in his strip theory model, but as described above themodel's results did not match experimental results particularly well. He returned to the problemin his PhD thesis (Wichers, 1988) and developed a more accurate empirical approach based on

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model test data. However the method has some theoretical difficulties, since the formulaebreak down when ω is zero.

Orcina is studying this, with a view to implementing a more accurate yaw rate drag model in afuture release of OrcaFlex. In the meantime we recommend that you specify yaw rate dragfactors that are appropriate to the conditions prevailing in the case being modelled. See thepapers by Wichers for further information.

6.12.4 Added Mass and DampingThe added mass and damping loads are calculated using the formulae given below. Wave-related fluid motion is not included in the damping load, since wave frequency motion isassumed to be completely prescribed by the vessel RAOs.

Damping Load

The damping loads are calculated by multiplying the damping matrix by the primary velocity ofthe vessel centre of gravity, using the formulae:

Surge damping force = - (C[surge,surge].V[surge] + C[surge,sway].V[sway] + C[surge,yaw].V[yaw])Sway damping force = - (C[sway,surge].V[surge] + C[sway,sway].V[sway] + C[sway,yaw].V[yaw])Yaw damping moment = - (C[yaw,surge].V[surge] + C[yaw,sway].V[sway] + C[yaw,yaw].V[yaw])where:C is the damping matrix, specified on the vessel type data form. For example C[surge, yaw] is theentry in the surge row and yaw column of that matrix.V[surge/sway] are the components, in the primary x/y axes directions, of the primary velocity ofthe vessel CG relative to global axes.V[yaw] is the primary yaw angular velocity of the vessel, in radians/sec, relative to global axes.The units of the damping matrix elements are therefore as follows:

surge sway yaw

surge F/(L/T) F/(L/T) F/(1/T)

sway F/(L/T) F/(L/T) F/(1/T)

yaw (F.L) / (L/T) (F.L) / (L/T) (F.L) / (1/T)

where F, L and T denote the units of force, length and time, respectively.

Added Mass Load

The added mass load is calculated by multiplying the added mass matrix by the primaryacceleration of the vessel CG, using the formulae:

Surge added mass force = - (M[surge,surge].A[surge] + M[surge,sway].A[sway] + M[surge,yaw].A[yaw])Sway added mass force = - (M[sway,surge].A[surge] + M[sway,sway].A[sway] + M[sway,yaw].A[yaw]Yaw added mass moment = - (M[yaw,surge].A[surge] + M[yaw,sway].A[sway] + M[yaw,yaw].A[yaw])whereM is the added mass matrix, specified on the vessel type data form. For example M[sway, surge]is the entry in the sway row and surge column of that matrix.A[surge/sway] are the components, in the primary x/y axes directions, of the primary accelerationof the vessel CG relative to global axes.

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A[yaw] is the primary yaw angular acceleration of the vessel, in radians/sec^2, relative to globalaxes.The units of the added mass matrix elements are therefore as follows:

surge sway yaw

surge M M M.L

sway M M M.L

yaw M.L M.L M.L^2

where M and L denote the units of mass and length, respectively.

6.12.5 Wave Drift LoadsThe wave drift load on a vessel is only calculated if the vessel's primary motion is set toCalculated. For a detailed description of the theory see Faltinsen's book. Here we give asummary and the formulae used in OrcaFlex.

The wave loads on a vessel can be expressed as a sum of first order, second order and evenhigher order terms. The linear first order terms are the largest. The second order terms arenon-linear effects that are much smaller, but they can be significant in some cases. The higherorder terms are even smaller and are neglected.

The first order terms generate the vessel's first order motion and this is modelled in OrcaFlex bythe vessels RAOs. The first order wave loads are therefore not calculated by OrcaFlex.

The second order terms are quadratic terms and they are made up of three terms:

• Difference frequency terms, which have frequencies given by the differences betweencombinations of different wave component frequencies.

• A constant term, called the mean wave drift force. This term is really the limiting case of thedifference frequency term when the two frequencies are equal.

• Sum frequency terms, which have frequencies given by the sums of combinations of wavecomponent frequencies.

The constant and difference terms are collectively known as the wave drift loads; these are bothincluded in OrcaFlex. The constant term is called the mean wave drift load and this is applied inOrcaFlex in both the static and dynamic analyses; it can cause significant mean offset. Thedifference frequency terms are only included in the dynamic analysis; they can cause significantslow drift motion if their frequencies are near to a vessel surge, sway or yaw natural frequency.The sum frequency terms are not included in the OrcaFlex calculation, since they are highfrequency terms whose effect on a massive moored vessel is normally negligible.

Wave Drift Load Theory

Wave drift loads are calculated based on the Quadratic Transfer Functions (QTFs) specified inthe user's wave drift data. QTFs are similar to RAOs in so far as they are scaling factors thatare applied to wave components. But whereas an RAO is applied to a single component andgives a displacement, a QTF is applied to a pair of wave components and gives a wave driftforce or moment.

The full QTF is a complex-valued function Q(ω1, ω2) of a pair of wave angular frequencies ω1and ω2. There are separate QTFs for each of the 6 vessel degrees of freedom, so we use thefollowing notation:

Q1(ω1, ω2) = Surge QTF

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Q2(ω1, ω2) = Sway QTF

Q6(ω1, ω2) = Yaw QTF

where the digits 1, 2 and 6 refer to the surge sway and yaw degrees of freedom. OrcaFlex doesnot calculate slow drift for heave (3), roll (4) and pitch (5), since those degrees of freedom areconstrained by buoyancy effects.

Consider a vessel exposed to a pair of wave components, of angular frequencies ω1 and ω2,and let the wave elevation at the vessel's QTF origin due to those components be:

Z1 = A1.Cos(ω1.t - φ1) = Real part of A1.Exp[ω1.t - φ1]

Z2 = A2.Cos(ω2.t - φ2) = Real part of A2.Exp[ω2.t - φ2]

Then the wave drift load due to the difference term from those 2 components is given by:

Surge force = Real part of (ρ.g.L).Q1(ω1, ω2).A1.A2.Exp[(ω1-ω2).t - (φ1-φ2)]

Sway force = Real part of (ρ.g.L).Q2(ω1, ω2).A1.A2.Exp[(ω1-ω2).t - (φ1-φ2)]

Yaw moment = Real part of (ρ.g.L^2).Q6(ω1, ω2).A1.A2.Exp[(ω1-ω2).t - (φ1-φ2)]

The first bracketed term on the right hand side of each equation is a dimensionalising factor thatgives a non-dimensional definition of Q. The factors involve the water density ρ, theacceleration due to gravity g, and the vessel type length L.

The total wave drift load is then the sum of these loads, over all pairs of frequencies (ω1, ω2)present in all the wave trains specified. This terms involved in this sum can be viewed as beingmade up of two types:

• The 'diagonal' terms (i.e. those where ω1 and ω2 are equal) each give a constant load. Thesum of these terms is the mean wave drift load, and this is applied in both the static anddynamic analysis in OrcaFlex.

• The off-diagonal terms (i.e. those where ω1 and ω2 differ) each give a harmonically time-varying load. The sum of these terms is the dynamic wave drift load and this is onlycalculated and applied in the OrcaFlex dynamic analysis. These terms are not included inthe static analysis since their time-average value is zero.

OrcaFlex uses Newman's Approximation to Calculate the Wave Drift Loads

There are 2 significant implementation problems with the above theory.

The first problem is that it is not practical for the user to specify the QTF values for all possiblepairs of frequencies (ω1, ω2). Instead, in the OrcaFlex QTF data, the user only specifies the'diagonal' values of the function, Q(ω, ω), for a range of discrete frequencies ω = ω1..ωn. Forintermediate frequencies OrcaFlex uses linear interpolation to obtain the diagonal QTF value.

These diagonal values must be real and they are the terms that give the constant term - i.e. themean wave drift load. However we also need to calculate the difference terms that arise fromthe off-diagonal terms. To do this, Newman approximated the off-diagonal terms from thediagonal terms by taking the off-diagonal term Q(ω1, ω2) to equal the geometric mean of the 2diagonal terms Q(ω1, ω1) and Q(ω2, ω2).

The justification for this approximation is twofold. Firstly, the important difference terms arethose with low frequency, which arise from the near-diagonal terms in Q. The far-from-diagonalvalues give much higher frequency difference terms which have little effect of a vessel ofsufficiently large inertia. Secondly, on theoretical grounds, the function Q should be continuousin both ω1 and ω2, so the near-diagonal term Q(ω1, ω2) should be well-approximated by themean of Q(ω1, ω1) and Q(ω2, ω2).

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The second implementation problem is the amount of computation required to do the fullcalculation. To calculate and sum the difference terms due to each pair of frequencies is adouble summation that requires computation time proportional to N^2, where N is the number ofwave components. When N is large this double summation calculation is much too slow to bepractical. To reduce the computation Newman therefore proposed a further approximation inwhich the double sum is estimated by a difference of squares of single sums; see Newman'spaper for details.

OrcaFlex uses Newman's 'difference of squares' formula to calculate the wave drift loads fromthe QTF data specified by the user. The formula incorporates the geometric meanapproximation (described above) to estimate the off-diagonal terms. It also introduces spurioushigh-frequency terms that have no physical basis. However numerical tests confirm that thesehigh frequency terms have little effect on the vessel providing the vessel's inertia is largeenough.

6.13 3D BUOY THEORYThe effects included for a 3D Buoy are weight, buoyancy, drag, added mass and reactions fromshapes. All of the fluid related effects are calculated allowing for what proportion of the buoy iscurrently immersed in the sea. This is done by calculating a proportion wet, PW, and thenscaling all of the fluid related forces by this proportion. In the following equations, the waterdensity is denoted by ρ.

The forces applied are:

Weight = Mass . g vertically downwards

Buoyancy = ρ . g . PW . Volume vertically upwards

Drag forces are calculated separately for each of the global X, Y and Z directions. For the Xdirection (and similarly for the Y and Z directions) the drag force applied is

PW . ½ . ρ . CdX . AX . VrX . |Vr|

where

CdX and AX are the Drag Coefficient and Drag Area, respectively, specified in the datafor the X directionVr is the velocity vector of the fluid relative to the buoy and |Vr| is its absolute magnitudeVrX is the component of Vr in the X direction.

Fluid acceleration force = (1+Ca) . ρ . PW . Volume . A, in each of the global axes directions

where

Ca is the Added Mass Coefficient specified in the data for that directionA is the acceleration of the fluid in that direction.

This force is often considered as being made up of two parts:

1. The Froude-Krylov force: ρ . PW . Volume . A

2. The added inertia force: Ca . ρ . PW . Volume . A.

In addition, the inertia of the buoy in each of the global axes directions is increased by:

Added mass = ρ . Ca . PW . Volume

where

Ca is the Added Mass Coefficient specified in the data for that direction.

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Finally, 3D Buoys are also subjected to a reaction force from the seabed and any elastic solidwith which they come into contact, given by:

Reaction = K . A . d

where

K is the Stiffness of the seabed or elastic solidA is the contact area, which is taken to be Volume/Heightd is the depth of penetration of the buoy origin B.

In addition to this reaction force, 3D Buoys receive a damping force. For details see SeabedTheory and Solids Theory.

6.14 6D BUOY THEORY

6.14.1 6D Buoy TheoryHydrodynamic Loads

Hydrodynamic loads are calculated using Morison's equation with additional components asdiscussed below.

Hydrodynamic Damping (linear)

For Lumped Buoys, additional damping forces and moments may be applied which are directlyproportional to the fluid velocity and angular velocity relative to the buoy. The main use of theseterms is to represent wave radiation damping for surface buoys. Values may be obtainedtheoretically from a 3D diffraction model of the body or, more commonly, from empirical resultssuch as a roll decay test.

Hydrodynamic Moments

Rotation of the body relative to the fluid generates hydrodynamic moments which are analogousto the hydrodynamic forces given by Morison’s equation. OrcaFlex includes facilities forcalculating these moments.

For Lumped Buoys, rotational hydrodynamic properties are included for damping, drag andadded inertia components. For Spar Buoys, drag moment data only are included.

In all cases, the fluid moments are calculated by reference to the local angular velocity andacceleration of the fluid, defined as the angular velocity and acceleration of the local waterisobar. The resulting moments are correct for rotational motions of the body itself, and give agood representation of moments due to waves where the moments derive from vertical-facingareas, e.g. discus buoys. However, the formulation gives a poor representation of wave-induced moments which derive from horizontally-facing areas. The difficulty arises becausethere is no unique definition of fluid angular velocity and angular acceleration at a point.

If you are in any doubt as to the correctness of the model, then we recommend setting themoment terms to zero. Hydrodynamic moments will then be omitted completely for a LumpedBuoy. For a Spar Buoy represented by several cylindrical sections, moments will be generatedautomatically as a result of the distribution of hydrodynamic forces along the buoy axis.

Estimation of Hydrodynamic Properties

See technical note Buoy Hydrodynamics.

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Interaction with Shapes

Interactions with shapes and the seabed are calculated as if the buoy consists of a series oflumps, one at each vertex.

Notes: For a lumped buoy you can specify the number and location of the vertices. Ifyou specify none then, for seabed and solid contact purposes, OrcaFlexbehaves as if there was just one vertex, located at the buoy origin.

For a spar buoy or towed fish, OrcaFlex automatically generates the verticesand edges that are visible on the 3D view. There are eight vertices percylinder, placed at the extremities of a box whose length, width and centre areall the same as the cylinder.

Whenever a vertex penetrates a shape, it then experiences a reaction force from the shapegiven by

Reaction = K . A . d

Because the vertices are (in general) offset from the buoy origin, this reaction force gives areaction moment about the buoy origin. Here K is the Stiffness of the Solid, A is the contactarea associated with each vertex and d is the depth of penetration of the vertex into the solid.The contact area associated with each vertex is derived by assuming that the total contact areafor the buoy is (Volume/Height) and then dividing this equally between all the vertices.

A damping force is also included - see Solids Theory for details.

Note: For a lumped buoy with no vertices

Interaction with the Seabed

Interaction with the seabed is treated in exactly the same way as with shapes. The seabedreacts to penetration by the vertices of the buoy and applies a reaction force at the vertex,giving a moment about the buoy origin. See Seabed Theory for details.

6.14.2 Lumped Buoy TheoryWeight and Buoyancy

The weight and buoyancy forces applied to the buoy are given by:

Weight Force = g . Mass

Buoyancy Force = PW . ρ . g . Volume

where PW is the proportion wet for the buoy, g is the acceleration due to gravity and ρ is thewater density.

Damping

The damping force applied in each local axis direction is given by:

Force = PW . UnitDampingForce . Vr

where UnitDampingForce is the Unit Force specified in the data for that direction and Vr is thecomponent, in that direction, of the water velocity relative to the buoy.

Similarly, the damping moment applied about each local axis direction is given by:

Moment = PW . UnitDampingMoment . Wr

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where UnitDampingMoment is the Unit Moment specified in the data for rotation about thatdirection and Wr is the component in that direction, of the angular velocity of the local waterisobar relative to the buoy.

Drag

The drag force applied in each local axis direction is given by:

Force = PW .½ .ρ . Cd . A .Vr.|Vr|

where A and Cd are the Drag Area and Drag Coefficient specified in the data for that directionand Vr is the component, in that direction, of the water velocity relative to the buoy.

The drag moment applied about each local axis direction is given by:

Moment = PW . ½ .ρ . Cd . AM . Wr.|Wr|

where AM and Cd are the Moment of Area and drag coefficient specified in the data for rotationabout that axis and Wr is the component, in that direction, of the angular velocity of the localwater isobar relative to the buoy.

Fluid Inertia Loads

The fluid inertia force applied in each local axis direction is given by:

Force = PW . Cm . HydroMass . A

where HydroMass and Cm are the reference hydrodynamic mass and Cm coefficient specifiedin the data for that direction, and A is the component, in that direction, of the local water particleacceleration.

The fluid inertia moment applied about each local axis direction is given by:

Moment = PW . Cm . HydroInertia . B

where HydroInertia and Cm are the reference inertia and Cm coefficient specified in the data forrotation about that direction, and B is the component, in that direction and in radians/s², of therotational acceleration of the local water isobar.

Added Mass and Inertia

The buoy inertia for translational motion is increased, for each local axis direction, by:

Added Mass = PW . Ca . HydroMass

where HydroMass and Ca are the reference hydrodynamic mass and added mass coefficientspecified in the data for translations in that direction.

The buoy inertia for rotational motion is increased, for each local axis direction, by:

Added Inertia = PW . Ca . HydroInertia

where HydroInertia and Ca are the reference hydrodynamic inertia and added mass coefficientspecified in the data for rotations about that direction.

6.14.3 Spar Buoy and Towed Fish TheoryThe fluid related loads on Spar Buoys and Towed Fish are calculated and applied separately foreach cylinder. The loads on each cylinder are calculated as follows (the proportion wet, PW, iscalculated for each cylinder according to its level of immersion).

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Drag Forces

The drag forces are calculated using the "cross-flow" assumption. In the local x and ydirections, i.e. normal to the cylinder axis, the drag forces are given by:

x Drag Force = PW . ½ . ρ . Cdn . An . Vrx. |Vrxy|

y Drag Force = PW . ½ . ρ . Cdn . An . Vry. |Vrxy|

where

An is the drag area specified in the data for the normal directionCdn is the drag coefficient specified in the data for the normal directionVrx and Vry are the x and y-direction components of the water velocity relative to thebuoy| Vrxy | is the absolute magnitude of the relative velocity in the x-y plane.

And in the z direction, i.e. parallel to the cylinder axis, the drag force is given by:

z Drag Force = PW . ½ . ρ . Cda . Aa . Vrz .|Vrz|

where

Aa is the drag area specified in the data for the axial directionCda is the drag coefficient specified in the data for the axial directionVrz is the z direction component of the water velocity relative to the buoy|Vrz| is its absolute magnitude.

Drag Moments

Drag moments are also calculated using the cross-flow assumption.

About the local x and y directions the drag moments are given by:

x Moment = PW . ½ . ρ . Cdn . An . Wrx .|Wrxy|

y Moment = PW . ½ . ρ . Cdn . An . Wry .|Wrxy|

where

An is the drag area moment specified in the data for the normal direction.Cdn is the drag moment coefficient for the normal directionWrx and Wry are the x and y components of the angular velocity of the local water isobarrelative to the buoy|Wrxy| is the absolute magnitude of the component in the xy plane of the angular velocityof the local water isobar relative to the buoy.

And about the local z direction the drag moment is given by:

z Moment = PW . ½ . ρ . Cda . Aa . Wrz .|Wrz|

where

Aa is the drag area moment specified in the data for the axial direction.Cda is the drag moment coefficient specified for the axial directionWrz is the z component of the angular velocity of the local water isobar relative to thebuoy

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|Wrz| is its absolute magnitude.

Drag Area Moments

The drag area moments in the above equations are the rectified 3rd moments of drag areaabout the axis of rotation. I.e. drag area moment = Sum(A.|r|^3) where A is an element of dragarea at an (absolute) distance |r| from the axis of rotation. The modulus |r| arises from the dragterm in Morison's equation. The area moment should have dimensions L^5. Note that the axialArea Moment is about the cylinder axis, and the normal Area Moment is about the normal tothat axis through the cylinder centre.

We have derived the following results for simple bodies:

• For a rectangle of length L and width W, the 3rd moment of area about the line in the planeof the rectangle and through its centre in the length direction is (L.W^4) / 32. And the 3rdmoment of area about the line in the plane of the rectangle and through its centre in thewidth direction is (W.L^4) / 32.

• For a circular disc of diameter D, the 3rd moment of area about a line in the plane of the discand through its centre = (D^5) / 60.

• We can use the two results above to calculate reasonable Drag Area Moment values to usefor a cylinder in a spar buoy. Let L be the length of the cylinder and D be the diameter, andfirst consider the Area Moment for the Normal direction, i.e. about a line through the cylindercentre and normal to the cylinder axis. If the curved surface of the cylinder is exposed todrag then we can account for its contribution to the Area Moment by using its projection ontothe plane made by the line and the cylinder axis. This projected area is a rectangle of lengthL and width D and the line crosses it in the width direction, so the contribution to the AreaMoment is (D.L^4) / 32. If either of the end discs of the cylinder are also exposed to dragthen we also need to account for their contribution to the Area Moment.

Calculation of Sea Angular Velocity

In order to calculate the relative angular velocity, OrcaFlex has to determine a local angularvelocity for the water. This is not defined by standard wave theory, so OrcaFlex uses theangular velocity of the local isobar (at the surface this is the angular velocity of the watersurface). The resulting drag moments due to waves are approximately correct for a buoy withlarge horizontal extension - e.g. a discus shape.

For a long vertical SPAR buoy, the calculated pitch/roll drag area moment is actually in thewrong direction. Instead the buoy should be divided into several cylinders and the requiredmoments are generated by distributing the hydrodynamic loading between them. The drag areamoments for the individual cylinders should be set to zero.

For an object which has significant dimensions both vertically and horizontally, the drag areamoments are a mix of roughly correct and incorrect parts. The problem relates only to dragmoments due to waves - moments resulting from body angular velocity in still water arecorrectly calculated.

Added Mass

The components, relative to buoy axes, of the added mass force and moment applied to acylinder are given by:

x Force = PW . (DM . Ax + Can . DM . Arx) y Force = PW . (DM . Ay + Can . DM . Ary) z Force = PW . (DM . Az + Caa . DM . Arz)

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x Moment = PW . (DIn . Wx + AIn . Wrx) y Moment = PW . (DIn . Wy + AIn . Wry) z Moment = PW . (DIa . Wz + AIa . Wrz)

where

PW is the proportion wet for this cylinder DM is the displaced mass of the cylinder when it is fully submerged(= WaterDensity . (π/4 . CylinderDiameter² . CylinderLength)) DIn and DIa are the normal and axial moments of inertia of the displaced mass of thecylinder, when fully submerged Can and Caa are the normal and axial added mass coefficients (specified in the data) AIn and AIa are the normal and axial added moments of inertia (specified in the data) Ax, Ay, Az are the components, in buoy axes directions, of the local water particleacceleration relative to global axes Arx, Ary, Arz are the components, in buoy axes directions, of the local water particleacceleration relative to the buoy Wx, Wy, Wz are the components (in buoy axes directions) of the angular acceleration ofthe local water isobar relative to global axes Wrx, Wry, Wrz) are the components (in buoy axes directions) of the angular accelerationof the local water isobar relative to the buoy.

Notes: In the above equations, the first term is known as the Froude Krylov force (ormoment) and the second term is the added mass force (or moment).

If the added inertia (AIn or AIa) is zero, then the Froude Krylov moment term isomitted for that direction, so no moment is applied about that direction. Thisdoes not apply to the Froude Krylov force terms - they are still applied even ifthe added mass coefficient for that direction is zero.

Damping Forces and Moments

The components, relative to buoy axes, of the damping force and moment applied to a cylinderare given by:

x Damping Force = PW .UDFn. Vrx y Damping Force = PW .UDFn. Vry z Damping Force = PW .UDFa. Vrz x Damping Moment = PW .UDMn. Wrx y Damping Moment = PW .UDMn. Wry z Damping Moment = PW .UDMa. Wrz

where

PW is the proportion wet for this cylinder UDFn and UDFa are the Unit Damping Forces specified in the data for the normal andaxial directions, respectively UDMn and UDMa are the Unit Damping Moments specified in the data for the normaland axial directions, respectively Vrx, Vry and Vrz are the components (in local buoy axes directions) of the water velocity

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relative to the buoy Wrx, Wry and Wrz are the components (in local buoy axes directions) of the angularvelocity of the local water isobar, relative to the buoy.

Munk Moment

Slender bodies in near-axial flow experience a destabilising moment called the Munk moment.This emerges from potential flow and is distinct from (and additional to) any momentsassociated with viscous drag. It is only well defined for a fully submerged body.

Newman (1977, page 341) derives the term and points out that it "acts on a non-lifting body insteady translation". Thwaites (1960, pages 399-401) gives an alternative derivation andprovides numerical values for spheroids.

Note that for bluff bodies the flow tends to separate over the afterbody. This has the effect ofreducing the Munk moment to a value less than the potential flow theory would suggest. SeeMueller (1968).

The Munk moment effect can be modelled in OrcaFlex by specifying a non-zero Munk momentcoefficient for a Spar Buoy or Towed Fish. OrcaFlex then applies a Munk moment given by:

Munk Moment = Cmm . M . ½ . sin(2α) . V²

where

Cmm is the Munk moment coefficient M is the mass of water currently displaced. If the buoy is surface-piercing then thisallows for the proportion of the buoy that is in the fluid. However, note that the value ofCmm is ill defined for a partially submerged body. Moreover, the true effects of breakingsurface, for instance planing and slamming, are much more complex than this and arenot modelled. V is the flow velocity relative to the buoy, at the point on the stack axis that is half waybetween the ends of the stack.

α is the angle between the relative flow velocity V and the buoy axis.

The moment is applied about the line that is normal to the plane of the buoy axis and therelative flow vector, in the direction that tries to increase the angle α.

6.15 SHAPE THEORYElastic Solids

The reaction force on an object penetrating an elastic solid is in the direction of the outwardnormal of the nearest surface of the shape with magnitude equal to K.d.A where

K = stiffness of the material,d = depth of penetration,A = contact area.

Also there is a damping force D, in the same direction, given by:

D = λ.2√(M.K.A).Vin

where

λ is percentage of critical damping / 100,M is the mass of the object,

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Vin is the normal component of object velocity.

The damping force is only applied when the object is travelling into the shape (i.e. when Vin ispositive).

For details of the way the contact area is calculated, see: Line Interaction with Seabed andSolids, 3D Buoy Theory and 6D Buoy Theory.

Care is needed when using elastic solids - some of the issues involved are listed below:

• Elastic solids are only taken into account in the static analysis for those lines with the FullStatics calculation.

• Elastic solids are intended only for modelling the overall limitation on movement that aphysical barrier presents; they are not intended to model an object's interaction with thebarrier in detail. For example no friction forces are included and the calculation of thecontact area and penetration depth are very simplistic and do not allow for the detailedgeometric shape of the object. The value given for Stiffness is therefore not normallyimportant, providing it is high enough to keep penetration small. On the other hand,although the actual stiffness of real barriers is usually very high, the Stiffness should not beset too high since this can introduce very short natural periods which in turn require veryshort simulation time steps.

• Friction is not calculated for elastic solids in the current version, so you must check that aphysically realisable configuration is modelled.

• Lines only interact with elastic solids by their nodes coming into contact, so elastic solidsthat are smaller than the segment length can "slip" between adjacent nodes. The segmentlength in a line should be therefore be small compared with the dimensions of any elasticsolid with which the line may make contact.

• Where elastic solids intersect with each other, it is sometimes necessary to "overlap" them.If the overlap is zero or small, a line may slip along the interface.

Trapped Water

Inside a trapped water shape the fluid motion is modified as follows:

• The fluid translational velocity and acceleration are calculated on the assumption that thetrapped water moves and rotates with the shape. So if the trapped water shape is Fixed orAnchored then no fluid motion occurs inside the shape. But if the shape is connected to amoving vessel, for example, then the trapped water is assumed to move and rotate with thevessel.

• The fluid angular velocity and acceleration of the local water isobar are both taken to bezero. (These angular motions are only used for calculating moments on 6D buoys.)

Notes: If the shape intersects the water surface then the surface is assumed to passthrough the shape unaltered. Thus a wave in the open sea also appearsinside the shape. We make this assumption because of the difficulty inpredicting, for realistic cases, how the surface will behave inside the trappedwater volume.

For example, a moonpool with an open connection at the bottom will suppressmost of the wave and current action. However there will be some flow in andout of the moonpool, depending on the size of the opening to the sea,pressure difference effects and the local geometry. The surface elevation inthe moonpool therefore does respond to the wave outside, but it is attenuatedto some extent and lags behind the surface outside.

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6.16 WINCH THEORYStatic Analysis

If the Statics winch control mode is set to Specified Length then for the static analysis theunstretched length of wire paid out, L0, is set to the Value specified, the wire tension t is then setto:

Equation (1)

t = (L-L0) . (Wire Stiffness)/L0

where

L is the total length of the winch wire path,Wire Stiffness is specified in the data,the winch drive force f is set to equal t.

Alternatively, if the Statics winch control mode is set to Specified Tension then for the staticanalysis the winch drive force f and the wire tension t are both set to the given Value, and theunstretched length paid out, L0, is then set to match this wire tension according to equation (1)above.

Dynamic Analysis

If Specified Payout is specified (length control mode) for a stage of the simulation, then theunstretched length of winch wire paid out, L0, is steadily increased or decreased during thatstage so that the total change during the stage is the Value specified. Positive Value meanspay out, negative Value means haul in.

The winch wire tension t (which is applied to each point on the wire) is then given by

Equation (2)

t = [(L-L0) + (Wire Damping).(dL/dt - dL0/dt)]. (Wire Stiffness) / L0

where

L i the total length of the winch wire pathWire Damping and Wire Stiffness are as specified in the data.

Note: The winch wire is not allowed to go into compression, so if the value for t givenby equation (2) is negative then the winch wire is considered to have goneslack and t is set to zero.

If Specified Tension mode is specified for a stage of the simulation, the Value specified in thedata is used as a target nominal constant tension that the winch drive attempts to achieve.

In Simple winches the winch drive is always assumed to achieve the target tension, so theValue specified is used for the actual winch wire tension.

In Detailed winches the winch drive tries to achieve the target tension by applying a drive forceto one side of the winch Inertia, opposing the wire tension being applied to the other side. Thedrive force f applied is then given by:

Equation (3)

if dL0/dt < 0: f(V) = f(0) - Deadband + A.V - C.V²

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if dL0/dt = 0: f(V) = f(0)if dL0/dt > 0: f(V) = f(0) + Deadband + B.V + D.V²

where

V = rate of payout = dL0/dtDeadband = the winch drive deadband data itemA, B = the winch drive damping term data itemsC, D = the winch drive drag term data items.f(0) = Value + Stiffness.(L0 - L00)Value = the nominal constant tension Value givenStiffness = the winch drive stiffness data itemL00 = original value of L0 at the start of the simulation (set by the static analysis)

Drive Force f

Payout Speed V(-ve = hauling in)

Deadband

Deadband

0

f(V) = f(0) - Deadband + A.V - C.V2

f(V) = f(0) + Deadband + B.V + D.V2

f(0) = Nominal Tension + Stiffness × (Payout since simulation started)

Figure: Force Control Mode for Detailed Winches

If the winch Inertia is non-zero, then the winch wire tension is set as in equation (2) above andthe winch inertia reacts by paying out or hauling in wire according to Newton's law:

d²(L0)/dt² = t - f

so the wire tension therefore tends towards the winch drive force and is hence controlled by thegiven Value.

If the winch inertia is set to zero, then the winch is assumed to be instantly responsive so that

Equation (4)

f = t at all times.

Given the current value of L0, the common value of f and t is then found by solving thesimultaneous equations (2), (3) and (4) for the payout rate dL0/dt. The unstretched length ofwinch wire out, L0, is then altered at the calculated rate dL0/dt as the stage progresses.

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Note: If the winch inertia is set to zero then at least one of the damping and dragterms A, B, C, D should be non-zero, since otherwise the simultaneousequations (2), (3) and (4) may have no solution. A warning is given if this isattempted.

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7 SYSTEM MODELLING - DATA ANDRESULTS

7.1 INTRODUCTIONTo analyse a marine system using OrcaFlex, you must first build a mathematical model of thereal-world system, using the various modelling facilities provided by OrcaFlex. The modelconsists of the marine environment to which the system is subjected, plus a variable number ofobjects chosen by the user, placed in the environment and connected together as required.The objects represent the structures being analysed and the environment determines thecurrent, wave excitation, etc. to which the objects are subjected.

The following types of objects are available in OrcaFlex. (Detailed descriptions of each type ofobject are given later.)

Vessels

are used to model ships, floating platforms, barges etc. They are rigid bodies whosemotions are prescribed by the user. The motion can be specified either by a time historymotion data file, or else by specifying Response Amplitude Operators (RAOs) for eachof 6 degrees of freedom (surge, sway, heave, roll, pitch and yaw). They can also bedriven around the sea surface, at user specified velocities and headings, during thecourse of the simulation.

3D Buoys

are simple point bodies with just 3 degrees of freedom - the translational degrees offreedom (X,Y and Z). Unlike a vessel, whose response to waves is defined by the data,the motion of a buoy is calculated by OrcaFlex. 3D buoys are not allowed to rotate andare intended only for modelling objects that are small enough for rotations to beunimportant.

6D Buoys

are much more sophisticated than 3D buoys - they are rigid bodies with the full 6degrees of freedom. That is, OrcaFlex calculates both their translational and rotationalmotion. Several different types of 6D Buoy are available, for modelling different sorts ofmarine object.

Note: Although called buoys, 3D and 6D buoys do not need to be buoyant and socan readily be used to model any rigid body whose motion you want OrcaFlexto calculate.

Lines

are catenary elements used to represent pipes, flexible hoses, cables, mooring lines,etc. Line properties may vary along the length, for example to allow a buoyant section tobe represented. Line ends may be fixed or free, or attached to other objects such asVessels or Buoys, and ends can be disconnected in the course of a simulation.Each line can also have a number of attachments. These are elements attached to linesat user-specified locations, and provide a convenient way of modelling items such asfloats, clump weights, or drag chains.

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Links

are mass-less connections linking two other objects in the model. Two types areavailable: Tethers are simple elastic ties, Spring / Dampers are combined (linear ornon-linear) spring + damper units.

Winches

are also mass-less connections linking two (or more) objects in the model. Theconnection is by a winch wire, which is fed from and controlled by a winch drivemounted on the first object. The winch drive can be operated in either constant speedmode, in which it pays out or hauls in the winch wire at a user-specified rate, or else inconstant tension mode, in which it applies a user-specified tension to the winch wire.

Shapes

are geometric shapes and two types are available - Solids or Trapped Water. TrappedWater Shapes can be used to model parts of the sea, such as moonpools, that areshielded from the waves. Solids can be used to act as physical barriers to restrict themovement of the other objects in the system; they are made of an elastic material andso apply a reaction force to any object that penetrates them. However, by specifyingzero stiffness, you can also use a solid purely for drawing purposes, for example to seeon the 3D view the position of a piece of equipment.Several different elementary shapes (cuboids, planes and cylinders) are available and anumber of shapes may be placed together to build up more complex compound shapes.They may be fixed or attached to other objects such as Vessels or Buoys.

Of these various object types, the lines, links and winches have the special property that theycan be used to connect together other objects. Assembling the model therefore consists ofcreating objects and then using the lines, links and winches to connect the other objectstogether, as required. See Object Connections for details.

The number of objects in the model is only limited by the memory and other resources availableon the computer being used. Similarly, there are no built-in limits to the number of lines, links orwinches that are attached to an object. As a result very complex systems can be modelled,though of course the more complex the model the longer the analysis takes. Example files areprovided with OrcaFlex.

Computer programs cannot exactly represent every aspect of a real-world system - the dataand computation required would be too great. So when building the model you must decidewhich are the important features of the system being analysed, and then set up a model thatincludes those features. The first model of a system might be quite simple, only including themost important aspects, so that early results and understanding can be gained quickly. Later,the model can be extended to include more features of the system, thereby giving moreaccurate predictions of its behaviour, though at the cost of increased analysis time.

Once the model has been built, OrcaFlex offers three types of analysis:

Modal Analysis

is only available for lines. It calculates and reports the undamped natural modes of aline.

Static analysis

in which OrcaFlex calculates the static equilibrium position of the model; current dragloads can be included but not waves.

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Dynamic analysis

in which OrcaFlex carries out a time simulation of the response of the system to waves,current and a range of user-defined inputs.

7.2 GENERAL DATA

7.2.1 General DataThe General Data form gives data that applies to the whole model.

Comments

A free form multi-line text field that can be used to store notes about the model. OrcaFlex doesuse this text.

Units Data

This may be SI, US or User Defined (multiple choice). Units are defined for length, mass,force, time and temperature.

Selecting SI gives length in metres, mass in tonnes, force in kN, time in seconds andtemperature in Celsius. Selecting US gives length in feet, mass in kips, force in kips, time inseconds and temperature in Fahrenheit.

If neither of these systems meets your requirements then select User Defined. You may thenselect individually from the length, mass, force, time and temperature units on offer. Theprogram displays the units selected and the corresponding value of g (gravitationalacceleration).

If the units are changed, then OrcaFlex converts all the data in the model into the new units.

7.2.2 StaticsBuoy Degrees of Freedom Included in Static Analysis

Buoys can either be included or excluded from the static analysis. When a buoy is includedOrcaFlex calculates the static equilibrium position of the buoy; when it is excluded OrcaFlexsimply places the buoy at the position specified by the user.

Which buoys are included in the static analysis is determined by the data item "Buoy Degrees ofFreedom Included in Static Analysis" on the General Data form, together with individual settingson each buoy's data form.

This data item should normally be set to All, in which case the static analysis will attempt to findthe static equilibrium position of all the buoys in the model, as well as finding the staticequilibrium position of the other objects.

When this data item is set to None, OrcaFlex does not find the true static equilibrium position ofthe buoys in the model, but instead simply places the buoys at the initial starting positionspecified in the data.

The final option for this data item is Some. In this case you can specify individually for eachbuoy, on the buoy data form, whether that buoy should be included in the static equilibriumcalculation. For 6D Buoys you can also choose whether the rotational degrees of freedom areincluded or excluded.

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There are several cases where this data item should be set to None. The first is if the you arenot using Catenary Statics or Full Statics for any lines in the model (see Static Analysis). Inthis case, the line is not in true static equilibrium and so OrcaFlex cannot find the staticequilibrium position of any buoy to which such lines are attached. If any such lines exist then allthe buoys must be excluded from the static analysis by setting this data item to None.

The second case where this item may need to be set None is if the model is staticallyindeterminate, for example a free floating buoy, or if the static analysis fails to converge. Thestatic analysis is an iterative calculation and for some complex systems this calculation may failto converge, especially if the initial estimated position given in the data is far from being anequilibrium position. If this happens you can exclude some or all buoys (or, for 6D buoys, justthe rotational degrees of freedom) from the static analysis; this simplifies the static analysis andshould enable convergence. Although the simulation then starts from a non-equilibriumposition, it does allow the simulation to proceed and the initial non-equilibrium errors willnormally be dissipated during the build-up stage of the simulation, provided a reasonable lengthbuild-up stage is specified. In fact the simulation can then often be used to find the true staticequilibrium position, by running a simulation with no waves; once it is found, the true staticequilibrium positions of the buoys can then be input as their starting positions for subsequentruns.

Finally, you may specifically want the simulation to start from a non-equilibrium position. Oneexample of this is to use the simulation to determine the damping properties of the system, byrunning a simulation with no waves and starting from a non-equilibrium position.

Use Calculated Positions

This button is available after a successful static iteration or when the simulation is finished orpaused.

If the model is in the statics complete state then clicking the button sets the initial positions ofbuoys, vessels and free line ends to be the calculated static position. This can be desirablewhen setting up a model, since the positions found are likely to be good estimates for the nextstatics calculation.

If the model is in the simulation paused or stopped state, then clicking the button sets the initialpositions of buoys and free line ends to be the latest position in the simulation. This is usefulwhen the statics calculation is failing to converge and you are using dynamics with no wavemotion to find the static equilibrium position.

Use Static Line End Orientations

This button is only available after a successful static analysis. Clicking the button sets the lineend orientation data, for all line ends in the model that have zero connection stiffness, to theorientations found in the static analysis. This is done as follows.

• For any line end with zero bend connection stiffness, the end azimuth and end declinationwill be set to the azimuth and declination of the end node, as found by the static analysis.

• If the line includes torsion and the line end connection twist stiffness is zero, then the endgamma will be set to the gamma of the end node, as found by the static analysis.

This button can be useful if you want to set the line end orientation to that which gives zero endmoments when the line is in its static position. To do this first set the end connection stiffnessvalues to zero, then run the static analysis and then click the Use Static Line End Orientationsbutton. You can then set the end connection stiffness to their actual values.

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Starting Velocity

Specifies the velocity of the whole model for the static analysis and for the start of thesimulation. It is defined by giving the speed and direction.

Normally the starting speed is zero. If a non-zero speed is specified (e.g. for modelling a towedsystem) then the static analysis becomes a steady state analysis that finds the steady stateequilibrium position in which the whole model is moving with the specified velocity. The staticposition is therefore then referred to as a steady state position, and the calculation of thisposition allows for any drag loads due differences between the starting velocity and the currentvelocity.

Note: The model will start the simulation from the calculated steady state; i.e. withthe specified starting velocity. So you should normally ensure that eachvessel in the model has its prescribed motion for stage 0 (the build up stage)set to match the specified starting velocity. Otherwise the simulation will startwith a sudden change in vessel velocity, which will cause a "kick" which maytake some time to settle down.

7.2.3 Statics ConvergenceConvergence

When buoys or vessels are included in the static analysis, their equilibrium positions arecalculated using an iterative algorithm that is controlled by the convergence parameters on theGeneral data form. They do not normally need to be altered. However if the static calculationfails to converge it is sometimes possible to improve the behaviour by adjusting theconvergence parameters.

The Set To Default button restores the parameters to their default values.

For further details contact Orcina or your Orcina agents.

7.2.4 DynamicsInner and Outer Time Steps

For efficiency of computation, OrcaFlex uses 2 integration time steps in the dynamic simulation,an Inner time step and a larger Outer time step. Most calculations during the simulation aredone every Inner time step, but some parameters (the more slowly-varying values such as waveparticle motion and most hydrodynamic forces) are only recalculated every Outer time step.This reduces the calculations needed and so increases the speed of simulation.

Both time steps must be short enough to give stable and accurate simulation. Experienceindicates that the inner step should not exceed 1/20th of the shortest natural period of motion ofthe model, the value of which is reported in the Static Analysis results.

The outer step can usually be set to 100 times the inner time step; this gives a good saving incomputing time without risking instability. Occasionally it may be necessary to use a shorterouter time step, for example where the velocity of part of the system changes very rapidly(perhaps as part of a transient during build-up). The outer time step should generally not bemore than 1/40th of the wave period (or 1/40th of the zero crossing period for a wavespectrum).

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Note: When a simulation is started OrcaFlex checks the time steps specified. If thecriteria outlined above are infringed OrcaFlex gives you the option of settingthe time steps automatically - according to these criteria. You are free todisregard the warnings if desired, but if either time step (though especially theinner step size) is set too large there is danger of instability or inaccuracy inthe simulation.

See also the effects of seabed stiffness.

The usual effect of setting one of the time steps too large is that the simulation becomesunstable, in the sense that very large and rapidly increasing oscillations develop, usually verynear the start of the simulation. OrcaFlex detects and reports most such instabilities; the timesteps can then be reduced and the simulation retried. However, it is generally worth repeatingimportant simulations with smaller step sizes to ensure that no significant loss of accuracy hasoccurred.

Note: Seabed stiffness will shorten the natural period of parts of the system lying onit, and this in turn requires a smaller simulation inner time step. Beware thatthe shorter natural periods will not be reported in the statics results table iftouch-down does not occur until dynamics are run.

Simulation Stages

The simulation proceeds in a Number of Stages each of a given Duration. See Figure: Timeand Simulation Stages in Dynamic Analysis.

Before the first stage is a Build-Up Period during which the sea conditions are slowly ramped upfrom zero in order to avoid sudden transients when starting a simulation. Time during the buildup stage is reported by the program as negative, so that the first stage proper starts at time t=0.

When using regular waves, it is usual to define the whole simulation as a single stage andresults are presented on a cycle-by-cycle basis. In random waves there is no meaningful "wavecycle". By dividing the simulation time into stages you are free to collect results for specific timeperiods of interest.

7.2.5 LoggingOrcaFlex stores the results of a simulation by sampling at regular intervals and storing thesamples in a temporary log file. When you save the simulation OrcaFlex writes the data to thesimulation file, followed by a copy of the log file, so that the sampled values can be read back inagain at a later date.

You can control the time interval between log samples by setting the Target Sample Intervalon the general data form. The Actual Sample Interval will be the nearest whole multiple of theinner time step. You can obtain more information about the logging by using the Propertiescommand on the pop-up menu on the general data form. This reports the number of logsamples that will be taken and the size of the resulting simulation file.

Logging Precision

You can also control the Precision with which samples are logged.

Single precision uses 4 bytes to represent each value and gives about 7 significant figures,which is quite accurate enough for almost all applications. Double precision uses 8 bytes pervalue, giving about 16 significant figures but uses twice as much disk space.

Double precision logging is usually only needed in certain cases. We therefore recommend thatyou use single precision logging unless you see signs of precision problems in the results. The

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typical signs of precision problems are that the curvature or bend moment time histories for aline look more like a step function than a smooth curve. If you see such results then try usingdouble-precision logging to see if precision is the cause.

The typical case where precision problems can occur is where the model contains a pipe orriser that has an extremely high bend stiffness and which experiences large displacementsduring the simulation. The reason is that OrcaFlex logs the positions of each node but in orderto save space in the simulation file it does not log the curvature, bend moment etc. InsteadOrcaFlex recalculates results like curvature and bend moment from the node positionswhenever you request these results. When both the bend stiffness and the node displacementsare very large then this calculation can greatly amplify the small steps in node position (8thsignificant figure) that are present in a single precision log, giving a bend moment graph thathas steps rather than being smooth.

7.2.6 Target DampingTarget Damping

The percentage of critical damping to be assumed for tension, bending and torsion in allLines.

All practical systems include some internal (structural) damping, but how much is rarely known,even approximately. Within broad limits, this damping has little influence on the results of asimulation unless the system is subject to very rapid variations in tension or bending, forexample when snatch loads occur. A value between 5% and 50% of critical damping is usuallyassumed. For details on the use of this data, see the documentation of tension, bending andtorsion in the Line Theory: Calculation Stages section.

7.3 ENVIRONMENT

7.3.1 EnvironmentThe environment defines the conditions to which the objects in the model are subjected; itconsists of the sea, current, waves and seabed.

Wave Direction

G

Still watersurface

Z

Y

XGlobal Axes

Seabed Origin

Datum CurrentDirection

Seabed Directionof Slope

SurfaceZ-level

WaterDepth

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Figure: Environment

As shown above, the environment is defined relative to the global axes. So for example theseabed and the current and wave directions are specified relative to the global axes.

7.3.2 Sea DataSea Surface Z

Specifies the global Z coordinate of the mean (or still) water level.

Kinematic Viscosity

This data is used to calculate the Reynolds number. The viscosity can either be a constant orvary with temperature. In the latter case the user can either input their own table of viscosityvariation against temperature, or else use one of the tables supplied in the OrcaFlex defaultdata.

The tables supplied in the OrcaFlex default data are for 0% (freshwater) and 3.5% salinity, asgiven on page 337 of the book Principles of Naval Architecture (PNA). For other salinity valuesthat book recommends using interpolation between the freshwater and 3.5% salinity tables.

If variation with temperature is specified then OrcaFlex uses linear interpolation fortemperatures between those specified in the table, and truncation for temperatures beyondthose specified in the table.

Temperature

The temperature of the water can either be constant or vary with depth below the mean waterlevel.

If variation with depth is specified then OrcaFlex uses linear interpolation for depths betweenthose specified in the table, and truncation for depths beyond those specified in the table.

The temperature can affect the viscosity (if that is specified as varying with temperature), whichin turn affects the Reynolds number, which in turn can affect the drag coefficient used for a line(if the drag coefficient is specified as varying with Reynolds number).

Sea Density

Water Density Variation specifies whether, and how, the water density varies with depth. It isnormally set to Constant, allowing you to specify a single density value that applies everywherein the sea. This is the most common value to use, since in most models the effects of densityvariation with depth are not significant.

For some systems, however, density variation with depth is important because it causesbuoyancy variation with depth. For such cases, two other settings for Water Density Variationwith depth are available:

Interpolated allows you to specify a density profile as a table giving the density at a series ofdepth levels. Linear interpolation is used to obtain the density at intermediate levels, and atlevels beyond the ends of the table the density value at the end of the table is used.

Bulk Modulus specifies that the density varies with depth purely because of the compressibilityof the water. You must specify the water's Surface Density and Bulk Modulus. The water's bulkmodulus specifies how a given mass of water shrinks under pressure, using the same volumeformula as for buoys and line types - see Bulk Modulus. OrcaFlex then derives the density

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variation with depth on the assumption that the water column has the given bulk modulus and isat uniform temperature and salinity.

For the Interpolated and Bulk Modulus options, you can check that the density variation is asexpected by using the View Profile button to display a graph showing the density variation thatwill be used.

Note: Density variation with depth only affects the buoyancy of objects. OrcaFlexdoes not allow for density variation with depth when calculating hydrodynamiceffects such as drag and added mass. For these effects the water densityvalue at the still water surface is used.

A dry land system can be modelled by using Constant density and setting the density to zero.

Seabed Data

Seabed Type

Two types of seabed shape are available. A Flat seabed is a simple plane, which can behorizontal or sloping. A Profile seabed is one where the shape is specified by a 2D profile in aparticular direction; normal to that profile direction the seabed is horizontal.

Seabed Origin and Depth

The seabed origin is a point on the seabed and is the point to which the seabed data refer. Itcan be chosen by the user and is specified by giving its coordinates with respect to global axes.For a profile seabed the seabed origin Z-coordinate is not specified directly, but is determinedby the Z values specified in the profile table.

The seabed origin Z-coordinate and the specified Sea Surface Z together determine the waterdepth at the seabed origin, which is displayed on the data form (but cannot be edited directly).The seabed origin Z-coordinate must therefore be less than the specified Sea Surface Z.

Warning: The depth at the seabed origin is used for all the wave theory calculations, soif the water is shallow and the depth varies then the seabed origin shouldnormally be chosen to be near the main wave-sensitive parts of the model.

Direction

The direction in which the depth varies, measured positive anti clockwise from the global X-axiswhen viewed from above.

For a flat seabed the direction specified is the direction of maximum upwards slope. Forexample, 0 degrees means sloping upwards in the global X direction and 90 means sloping upin the in the global Y direction.

For a profile seabed the direction specified is the direction in which the 2D profile is defined.

Slope (flat seabed only)

The maximum slope, in degrees above the horizontal. The flat seabed is modelled as a plane,inclined at this angle, passing through the seabed origin. The model is only applicable to smallslopes. The program will accept slopes of up to 45 degrees but the model becomesincreasingly unrealistic as the slope increases because the bottom current remains horizontal.

Profile (profile seabed only)

The profile table defines the seabed shape in the vertical plane through the seabed origin in theseabed direction. The shape is specified by giving the seabed Z coordinate, relative to global

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axes, at a series of points specified by their Distance From Seabed Origin, which is measuredfrom the seabed origin in the seabed direction (negative values can be given to indicate pointsin the opposite direction). The resulting depths at the points are reported in the table. Theseabed also has its own seabed origin and local axes, with respect to which the seabed shapeis defined.

Seabed Z-values in between profile points are obtained by smooth cubic spline interpolation,and beyond the ends of the table the seabed is assumed to be horizontal. The seabed isassumed to be horizontal in the direction normal to the seabed profile direction.

Interpolation Method (profile seabed only)

Determines how OrcaFlex interpolates between values in the specified profile.

Warning: Linear interpolation can cause difficulties for static and dynamic calculations.If you are having problems with static convergence or unstable simulationsthen you should try one of the other interpolation methods.

Note: You cannot model a true vertical cliff by entering 2 points with identicalDistance from Seabed Origin but different Z coordinate - the second point willbe ignored. However you can specify a near-vertical cliff. If you do this, notethat to avoid interpolation overshoot you may need to specify several extrapoints just either side of the cliff, or else use linear interpolation. SeeChoosing Interpolation Method.

View Profile

The View Profile button provides a graph of the seabed profile. The specified profile points areshown, together with the interpolated shape in between profile points. The seabed is horizontalbeyond the ends of the graph.

You should check that the interpolated shape is satisfactory, in particular that the interpolationhas not introduced overshoot - i.e. where the interpolated seabed is significantly higher or lowerthan desired. Overshoot can be solved by adding more profile points in the area concerned andcarefully adjusting their coordinates until suitable interpolation is obtained.

Seabed Stiffness and Damping

The seabed is normally modelled as a sprung and damped surface with a spring reaction forcethat is proportional to the depth of penetration and the contact area, plus a damping force that isproportional to the rate of penetration. See Seabed Theory.

The seabed stiffness is the constant of proportionality of the spring force and equals the sprungreaction force per unit area of contact per unit depth of penetration. A high value models asurface such as rock; a low value models a soft surface such as mud. The seabed damping isthe constant of proportionality of the damping force, and is percentage of critical damping.

Warning: A high seabed stiffness will shorten the natural periods of parts of the systemlying on it, which may require the use of a smaller simulation time step.Beware that the shorter natural periods will not be reported in the staticsresults table if touchdown only occurs during the simulation.

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7.3.3 Current DataCurrent Method

Can be Interpolated or Power Law. The Interpolated method uses a full 3D profile withvariable magnitude and direction. The Power Law method uses an exponential decay formula.This enables modelling of boundary layer effects.

Ramp During Build-Up

If selected then the static position will be calculated without the effects of current and during thebuild-up stage of dynamics the current is ramped up to its full value. If not selected (the default)then the current is used in calculating the static position and full current is applied throughout.

This facility to omit current effects from the static calculation and introduce them during the buildup is useful where the current may cause lines to come into contact. For example, consider acase where a flexible line is to the left of a stiff pipe but current pushes the flexible up againstthe pipe. Since the OrcaFlex static analysis does not include the effects of contact betweenlines, if current was included in the static analysis then it would find a static position where theflexible line was to the right of the pipe. The simulation would then start with the flexible on thewrong side of the pipe.

This problem can be overcome by setting the current to ramp during build up and setting clashchecking for the two lines. The static position will exclude the effect of current and so will leavethe flexible to the left of the pipe. The build-up stage will then introduce the current effects butwill also include the effect of contact between the two lines.

View Profile

Draws a graph of current speed against depth.

Data for Interpolated Method

Speed and Direction

The magnitude and direction of a reference current, generally taken as a surface current. Theactual current at a given Z level is then defined relative to this reference current by a currentprofile.

The direction specified is the direction the current is progressing - for example, 0 and 90degrees mean currents flowing in the X and Y directions, respectively.

The speed and direction can either be fixed or vary with simulation time. If they are variablethen linear interpolation is used for times between those specified in the variable data table, andtruncation is used for times beyond those specified in the table.

Profile

A current profile may be defined by specifying factors and rotations at various depths, relative toreference. At each Depth in the table the current speed is the reference current speedmultiplied by the Factor for that depth; the Direction is the reference direction plus the rotationspecified. Current speed and direction are interpolated linearly between the specified levels.The current at the greatest depth specified is applied to any depth below this, for example whena sloping seabed is specified. Similarly, the current at the least depth specified is applied to anydepth above this.

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If you prefer to enter current speeds and directions directly, rather than using a referencecurrent and reference-relative profile, simply set the reference current speed to 1 and thereference direction to 0.

Data for Power Law Method

Speed at Surface and at Seabed

The current speed at the still water level and at the seabed level.

Note: Speed at Seabed cannot be greater than Speed at Surface.

Direction

When using the power law current method, the current direction is the same at all levels. Thedirection specified is the direction the current is progressing, measured positive from the globalX-axis towards the global Y-axis. For example, 0 and 90 mean currents flowing in the X and Ydirections, respectively.

Exponent

This determines how the current decays. With a smaller value, the decay is spread moreevenly across the water depth. With a higher value, the decay mostly occurs close to theseabed.

7.3.4 Wind DataThe Wind tab on the Environment data form contains the following data for modelling wind.Note that this wind data is only currently used to calculate the wind loads on vessels - seeVessel Theory: Drag Loads.

Air Density

The air density is assumed to be constant and the same everywhere.

Wind Direction

The direction specified is the direction in which the wind is progressing - see Direction andHeadings. In all cases the wind is unidirectional.

Wind Speed

Wind speed is assumed to be the same everywhere. The speed specified should be the valueat an elevation of 10m (32.8 ft) above the mean sea surface, since that is the height used by theOCIMF vessel wind load model. If you have the wind speed V(h) at some other height h (inmetres), then the wind speed V(10) at 10m can be estimated using the formula: V(10) = V(h)(10/h)^(1/7).

You can choose to specify wind speed in various ways, by setting the Wind Type to one of thefollowing.

Constant

The wind speed is then constant in time.

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Random

The wind speed varies randomly in time, using a choice of either the American PetroleumInstitute spectrum (API) or the Norwegian Petroleum Directorate spectrum (NPD).

In both cases:

• The spectrum is determined by specifying the Mean Speed and the spectrum thendetermines the statistical variation about that mean. The View Spectrum button shows agraph of the spectrum.

• The wind speed is modelled by a sum of a number of components. The components aresinusoidal functions of time whose amplitudes and frequencies are chosen by OrcaFlex tomatch the spectral shape. OrcaFlex uses a 'equal energy' algorithm to choose theamplitudes and frequencies. This gives all the components the same energy, and thereforethe same amplitude, but their frequencies are chosen so that the components are moreclosely spaced where the spectral energy density is high, and more widely spaced wherethe spectral energy is low.

• You can specify the Number of Components to use. You should specify enough to give areasonable representation of the spectrum.

• The phases of the components are chosen using a pseudo-random number generator thatgenerates phases which are uniformly distributed. The phases generated are repeatable -i.e. if you re-run a case with the same data then the same phases will be used - but you canchoose to use different random phases by altering the Seed used in the random numbergenerator. This can be any integer in the range -2^32 to +2^32-1.

• The View Components button gives a report of the components that OrcaFlex has chosen.

• The View Profile button shows the resulting wind speed time history, as a function of globaltime. If you want to simulate a particular section of that time history then you can use thewind Time Origin to time shift that section into the simulation period. See Time Origins fordetails.

Time History

The wind speed variation with time is then specified explicitly in a file. For details see Data inTime History Files. Linear interpolation is used to obtain the wind speed at intermediate times.

View Profile

The View Profile button displays a time history graph showing the wind speed that will be used.The graph covers the specified Duration, starting at the specified Start time. This Start time,and the graph's time axis, are both global times.

7.3.5 Wave DataNumber of Wave Trains

You can define a number of different wave trains and the overall sea conditions are thesuperposition of the wave trains. In most cases a single wave train is sufficient, but multiplewave trains can be used for more complex cases, such as a crossing sea (i.e. a superpositionof locally generated waves in one direction and distant storm-generated swell in a differentdirection).

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Each wave train can be given a name and a specified direction. And each wave train can beeither a regular wave (with a choice of wave theory) or a random wave (with a choice ofspectrum), or else be specified by a time history file.

Simulation Time Origin

The simulation time origin allows you to control the period of time that the dynamic simulationcovers. It defines the global time that corresponds to simulation time t = 0, so changing thesimulation time origin allows you to shift the period of global time that is simulated. Altering thesimulation time origin shifts the simulation time relative to all of the wave trains; alternatively,you can also time shift an individual wave train by altering its wave time origin. See DynamicAnalysis for details of the time frames used in OrcaFlex.

Data for a Wave Train

Each wave train is specified by the following data.

Wave Direction

For both regular and random waves, the wave Direction is the direction that the wave isprogressing, measured positive anti-clockwise from the global X-axis when viewed from above.So, for example, 0 degrees means a wave travelling in the positive X-direction, and 90 degreesmeans a wave travelling in the positive Y-direction.

With multiple wave trains the direction of the first wave train is taken to be the primary directionand this is reflected in both the way the sea is drawn and the Sea Axes.

Wave Type

Each wave train can be any of the following types:

• Airy, Dean, Stokes' 5th or Cnoidal. These are various different wave theories for regularwaves. See Data for Regular Waves.

• JONSWAP, ISSC (also known as Pierson-Moskowitz), Ochi-Hubble, or User DefinedSpectrum. These are various different spectra for random waves.

• Time History allows you to specify the wave in the form of a time history input file. SeeData for Time History Waves.

For regular waves we recommend the Dean wave - this is a nonlinear wave theory using aFourier approximation method and it is suitable for all regular waves. The Airy wave theory is asimple linear wave theory that is only suitable for small waves. The Cnoidal wave theory is onlysuitable for long waves in shallow water. The Stokes' 5th wave theory is only suitable for shortwaves in deep water.

There are two Stokes' 5th order theories implemented in OrcaFlex which we have called Stokes'5th (SH) and Stokes' 5th. The former is the standard method of Skjelbreia and Hendricksonwhilst the latter theory is due to Fenton. We consider Fenton's work to be an improvement onthe original, primarily because it deals with currents more accurately.

If the specified wave is not suitable for the selected wave theory, OrcaFlex will give a warning ormay report that the wave calculation has failed. If this happens please check that the wavetheory selected is suitable. For further details see Ranges of Applicability.

Kinematic Stretching Method

Kinematic stretching is the process of extending linear Airy wave theory to provide predictions offluid velocity and acceleration (kinematics) at points above the mean water level. OrcaFlex

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offers a choice of three methods: Vertical Stretching, Wheeler Stretching and ExtrapolationStretching. For details see Kinematic Stretching Theory.

Note: Random waves are modelled by combining a number of linear Airy waves, sokinematic stretching also applies to random waves.

The Horizontal Velocity preview graph can be used to see the effect of the different kinematicstretching methods.

Wave Time Origin

Each wave train has its own Wave Time Origin, which is specified relative to the global timeorigin. The wave train's data specify the wave train relative to its own time origin, so you cantime-shift a given wave train, independently of the other wave trains, by adjusting its wave timeorigin.

For a regular wave train the wave time origin is the time at which a wave crest passes the globalorigin. You can therefore use the Wave Time Origin to arrange that a wave crest passes aparticular point at a particular time during the simulation.

For a random wave train, the phases of the wave components that make up the wave train arerandomly distributed, but they are fixed relative to the wave time origin. You can thereforearrange that the simulation covers a different piece of the random wave train by changing thewave time origin. This can be useful for two purposes:

• You may want to select a particularly significant event in the wave train, such as a largewave. OrcaFlex has special facilities to make this easy - see Wave Preview.

• Secondly, you may want to do a series of runs with the same wave train data but differentrandom phases for the wave components. This can be done by specifying randomly chosenwave time origins for the different runs, since randomly selecting different periods of thewave train is statistically equivalent to choosing different random phases for the wavecomponents.

Stream Function Order

For the Dean wave theory only, you can set the order of stream function to be used. Thedefault value is 10 and for most purposes it is not necessary to alter this. However, for nearlybreaking waves the method sometimes has problems converging. If this is the case then itmight be worth experimenting with different values.

Data for Regular Waves

A regular wave is a single wave component defined by wave Direction, Height and Period.Wave height is measured from trough to crest.

Data for Random Waves

Random waves are specified by giving the energy spectrum of the random sea. The WaveType specifies the type of spectrum and the spectral data then defines the actual spectrumwithin that type. You can use the View Spectrum button to view a graph of resulting energyspectrum.

For the JONSWAP and Ochi-Hubble spectra (see Data for Ochi-Hubble spectra) you have achoice of using Auto or User settings for some of the spectra data.

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Number of Components and Seed

Random wave trains are represented by a user-defined number of component waves, all in thespecified wave direction, whose amplitudes and periods are selected by the program to give asea state having the specified spectrum and spectral parameters.

The phases associated with each wave component are pseudo-random. OrcaFlex uses arandom number generator and the used-defined seed to assign phases. The sequence isrepeatable, so the same seed will always give the same phases and consequently the sametrain of waves.

For a given spectrum, sea state and simulation time origin, different wave conditions can beobtained by shifting the wave time origin. For more information, see Setting up a Random Sea.

You can use the View Wave Components command (on the Waves tab of the environmentdata form) to get a spreadsheet that gives details of the wave components that OrcaFlex hasused to represent a random or time history wave train.

For a random wave train the spreadsheet also reports the spectrum's:

• Mean period T1. This equals m0/m1 where mi denotes the i'th moment of the spectrum.

• Peak period and frequency Tp and Fm. These are the period and frequency at which thespectrum has the highest spectral density.

Spectral Data for JONSWAP and ISSC Spectra

The following spectral parameters are available. For the JONSWAP spectrum you have achoice of using Auto or User settings. Auto sets standard spectral parameter values, basedonly on the specified Hs and Tz. User allows you to specify individual parameters of thespectrum.

Hs, Tz, fm, Tp

Hs is the significant wave height. Tz is the zero crossing period. Tp and fm are the spectralpeak period and peak frequency, i.e. those with largest spectral energy.

Note that Tz, Tp and fm are tied together, so setting any one of them sets the other two tomatch. If you change some other parameter that affects the relationship between Tz, Tp andfm, then Tz is taken as the master data and Tp and fm are updated accordingly.

Gamma

The peak enhancement factor. For the ISSC spectrum Gamma is determined by Hs and Tz.For the JONSWAP spectrum you have the choice of Auto setting or User setting for Gamma. IfAuto is selected then Gamma is automatically calculated by the program using formulae givenby Isherwood, 1987. If User is selected then you can specify the value.

Sigma1 and Sigma2

The spectral width parameters are reported. These only apply to the JONSWAP spectrum andare fixed at the standard values of 0.07 and 0.09 respectively.

Alpha

Alpha is the spectral energy parameter. It is calculated by the program to give a sea state withthe specified Hs and Tz.

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Spectral Data for Ochi-Hubble Spectrum

The Ochi-Hubble formulation allows 2-peaked spectra to be set up, enabling you to representsea states that include both a remotely generated swell and a local wind-generated sea. SeeData for Ochi-Hubble Spectra.

Spectral Data for User-Defined Spectrum

A user defined spectrum is specified by giving a table of values of S(f), where S(f) is the spectralenergy as a function of frequency f in Hertz.

The values of f specified do not need to be equally spaced. For intermediate values of f (i.e.between those specified in the table) OrcaFlex uses linear interpolation to obtain the spectralordinate S(f). And for values of f outside the range specified in the table OrcaFlex assumes thatS(f) is zero. Your table should therefore include enough points to adequately define the shapeyou want (important where S(f) is large or has high curvature) and should cover the full rangeover which the spectrum has significant energy.

OrcaFlex reports on the data form the significant wave height and zero-crossing period thatcorrespond to the user-defined spectrum specified.

7.3.6 Drawing DataThis data allows you to control the drawing of the various components which make up theOrcaFlex Environment. For a more general discussion of drawing in OrcaFlex see How ObjectsAre Drawn.

Sea Surface Pen

Determines how the sea surface, current direction arrow and wave direction arrows are drawn.The current direction arrow is an arrow next to the view axes which points in the direction of thecurrent. This arrow is only drawn if the current speed is not zero and if the Draw EnvironmentAxes preference is ticked. The wave direction arrows are explained below.

Secondary Wave Direction Pen

When the Draw Environment Axes preference is ticked a wave direction arrow is drawn in thedirection of the wave. If there are multiple wave trains whose directions are not equal then awave direction arrow is drawn in the direction of each wave train. The first wave train uses thesea surface pen since it is regarded as the dominant one for drawing purposes. All subsequentwave trains' direction arrows are drawn in the Secondary Wave Direction Pen.

Wind Direction Pen

Determines how the wind direction arrow is drawn. This is an arrow next to the view axes whichpoints in the direction of the wind. This arrow is only drawn if the wind speed is not zero and ifthe Draw Environment Axes preference is ticked.

Seabed Pen

The seabed grid is drawn in this pen.

Seabed Profile Pen

If you are using a profile seabed then an extra grid line is drawn along each data point used tospecify the profile. This can be used to emphasise the seabed profile data.

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7.3.7 Data for Ochi-Hubble SpectraThe Ochi-Hubble formulation allows 2-peaked spectra to be set up, enabling you to representsea states that include both a remotely generated swell and a local wind generated sea.

Hs and Tz

Hs is the significant wave height and Tz is the zero crossing period. Their values depend onwhether you specify Auto or User.

Auto: In this case Hs is specified by the user and the program selects the most probablespectral parameters for that value of Hs. The resulting Tz is then derived and displayed, butcannot be edited.

User: In this case the user specifies the spectral parameters explicitly. The resulting Hs and Tzvalues are displayed, but neither can be edited.

Hs1, fm1, Lambda1, Hs2, fm2 and Lambda2

The Ochi-Hubble spectrum is the sum of 2 component spectra, each of which is specified by aset of three parameters: Hs1, fm1, Lambda1 for the lower frequency component and Hs2, fm2,Lambda2 for the higher frequency component.

Parameters Hs1 and Hs2 are the significant wave heights of the component spectra; the overallsignificant wave height Hs is given by Hs = √(Hs1² + Hs2²). Parameters fm1 and fm2 are themodal frequencies of the two components. Finally, Lambda1 and Lambda2 are shapeparameters that control the extent to which the spectral energy is concentrated around themodal frequency - larger values give more concentrated component spectra.

You can specify these spectra parameters in two alternative ways:

Auto: In this case the program calculates the parameters of the most probable spectrum,based on the overall significant wave height Hs that you have specified. The parameters usedare as given in the Ochi-Hubble paper, table 2b.

User: In this case you must specify all 6 parameters. The program then derives and displaysthe corresponding overall Hs and Tz values.

Notes: The modal frequency of the first component, fm1, must be less than that of thesecond, fm2. It is also recommended that fm2 is greater than 0.096.

The significant wave height of the first component, Hs1, should normally begreater than that of the second, Hs2, since most of the wave energy tends tobe associated with the lower frequency component.

7.3.8 Data for Time History WavesData for Time History Waves

A time history wave train is defined by a separate text file that contains the wave elevation as afunction of time. To use this you need to do the following:

• Create up a suitable time history text file defining the wave elevation as a function of time.The time values in the file must be equally spaced and in seconds. The elevation valuesmust be the elevation at the global origin used in the OrcaFlex model, measured positiveupwards from the still water level specified in the OrcaFlex model, and using the same unitsas those in the OrcaFlex model.

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• Set the Input File to refer to your time history file. See Data in Time History Files.

• Set the Minimum Number of Components. This affects the number of Fouriercomponents that will be used to model the time history wave. It should be set high enoughto give desired accuracy, but note that using a very large number of components maysignificantly slow the simulation. See How Wave Time History Data is Used for details.

• Set the Wave Time Origin to position the required section of wave time history within thesimulation period. You can use the View Profile button (on the Waves Preview tab on theenvironment data form) to see the wave elevation as a function of situation time.

How Wave Time History Data is Used

Briefly, OrcaFlex uses a Fast Fourier Transform (FFT) to transform the data into a number offrequency components. Each component is then used to define a single Airy wave and theseAiry waves are then combined to give the wave elevation and kinematics at all points. TheView Wave Components and View Spectrum buttons on the data form show (in tabular andpower spectral density graph form respectively) the Airy wave components that OrcaFlex willuse to model the waves.

Here are the steps in more detail.

1. OrcaFlex first selects the elevation values that cover the simulation period

To do this OrcaFlex searches the time history file and selects the time samples that cover thesimulation period. These will be the time samples from time

(T0 - BuildUpDuration) to (T0 + SimulationDuration)

where BuildUpDuration is the length of the build-up stage of the simulation, SimulationDurationis the length of the remaining stages and T0 = SimulationTimeOrigin - WaveTimeOrigin. Thesetime origin settings allow you, if you want, to shift the simulation relative to the time history.

2. OrcaFlex then includes more samples, if necessary

Let n be the number of samples selected in step 1. In order to achieve the specified minimumnumber of components, m say, OrcaFlex needs at least 2m samples. So if n is less than 2mthen OrcaFlex selects more samples from the file (taken equally from earlier and later in the file)until it has 2m samples. If OrcaFlex runs out of samples in the file while doing this then an errormessage is given; you must then either provide more samples in the time history file or elsereduce the minimum number of components requested.

However OrcaFlex also needs the number of samples to be a power of 2, since that is neededin order to use a fast Fourier transform. So if 2m is not a power of 2 then OrcaFlex againselects more samples from the file (taken equally from earlier and later in the file) until thenumber of selected samples is a power of 2. If OrcaFlex runs out of samples in the file whiledoing this then it zero-pads (i.e. it adds extra samples of value zero); you will be warned if thishappens.

3. OrcaFlex uses a fast Fourier transform to obtain Fourier components

The selected time history samples, N of them say, are converted into frequency domain formusing a Fast Fourier Transform (FFT). This gives N/2 sinusoidal Fourier components. TheView Wave Components button reports their numerical values and the View Spectrum showstheir spectrum.

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4. OrcaFlex models the time history wave as the superposition of Airy waves

N/2 Airy waves are created, with periods, amplitudes and phases that match the Fouriercomponents. The time history wave is then modelled as the superposition of these Airy waves.

Warning: This last step effectively uses Airy wave theory to extrapolate from the globalorigin, where the surface elevation has been defined, to derive surfaceelevation at other points and to derive fluid kinematics from the surfaceelevation readings. This extrapolation introduces errors, which become worsethe further you go from the global origin. It is therefore recommended that theglobal origin (= the point the time history file data applies to) is placed close tothe main wave-sensitive parts of the model.

7.3.9 Wave PreviewWhen using a random wave or a time history wave, OrcaFlex provides two preview facilities toaid selection of the wave, namely List Events and View Profile. These are provided on theWaves Preview tab on the environment data form and are documented below.

Notes: These commands work in terms of global time, rather than simulation time.This enables you to search through a period of global time looking for aninteresting wave event and then set the time origins so that the simulationcovers that event.

If you are using multiple wave trains then these commands report thecombined sea state from all of the wave trains.

See also Setting up a Random Sea.

Position

This is the point to which the List Events, View Profile and Horizontal Velocity commands apply.Since wave trains vary in space as well as time you should normally set this point to be close toa system point of interest, such as a riser top end position.

View Profile

This plots a time history of wave elevation at the specified Position over the specified interval ofglobal time.

An example of the use of these commands is to use List Events to scan over a long period ofglobal time (e.g. 10000 seconds or more), look for large waves and then use View Profile tolook in more detail at short sections of interest. Having decided which part of the wave train touse, the simulation time origin can then be set to just before the period of interest, so that thesimulation covers that period.

Horizontal Velocity

This plots how the water horizontal velocity (due to current and waves) varies with depth, at thespecified (X,Y) Position and specified global time.

List Events

This command lists all "severe" wave events in the specified interval of global time and at thespecified Position. "Severe" here means that either there is a rise or fall that exceeds thespecified height H, or (providing there is only a single wave train) that the wave steepnessexceeds the specified steepness S.

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Note: The steepness criterion S is not used if there is more than one wave trainspecified. This is because steepness is measured in the wave direction andwhen multiple wave trains are present there is not necessarily a unique wavedirection.

For each event, the height (total rise or fall) is given and an equivalent period is derived from thetime interval between the peak and trough. These are then used to calculate, for this waterdepth, an Airy wave of the same height and period, and the length and steepness of thisequivalent Airy wave are given.

If there is only one wave train then, for comparison purposes, a reference wave is reported atthe top of the table. This reports the Airy wave whose height and period match the Hs and Tz ofthat single wave train.

Finally, various wave elevation statistics are reported for the position and period of timespecified. These include the largest rise and fall, the highest crest and lowest trough, thenumber of up and down zero-crossings and the sample's estimated Hs and Tz values. Thesestatistics enable you to measure how "typical" this wave elevation sample is, compared with theoverall parent spectrum.

7.3.10 Setting up a Random SeaSetting up a Random SeaThis section gives information on how to set up a random sea using OrcaFlex's modellingfacilities. For a detailed description of these, see Wave Data.

The most common requirement is to produce a realistic wave train which includes a "designwave" of specified height Hmax and period Tmax. However alternative requirements are possibleand it is sometimes useful to impose additional conditions for convenience in resultspresentation, etc.

The height and period of the maximum design wave may be specified by the client, but onoccasion we have to derive the appropriate values ourselves, either from other wave statistics(for example a wave scatter diagram, giving significant wave heights Hs and average periodsTz) or from a more general description of weather (such as wind speed). See Wave Statisticsfor guidance.

Having decided what values of Hmax and Tmax are required, we select an appropriate wavetrain as follows, using the facilities available in OrcaFlex.

• Set the significant wave height (Hs) and average period (Tz) for the design storm, and thewave spectrum - ISSC, JONSWAP and Ochi-Hubble options are available. See Setting theSea State Data for details.

• Set the number of wave components (typically 100). See Setting the Number ofComponents for details.

• Search through the time history of wave height and looking for a particular wave rise (troughto crest) or fall (crest to trough) which has the required total height and period. If no wave ofthe required characteristics can be found, then adjust Hs and Tz slightly and repeat. SeeFinding a Suitable Design Wave Event for details.

• When the required design wave has been located, you can set the simulation time originand duration so that the design wave occurs within the simulation time, with sufficient timebefore and after to avoid starting transients and collect all important responses of thesystem to the design wave. A typical random sea simulation may represent 5 or 6 averagewave periods (say 60-70 seconds for a design storm in the North Sea) plus a build up period

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of 10 seconds. If the system is widely dispersed in the wave direction, then the simulationmay have to be longer to allow time for the principal wave group to pass through the wholesystem. Since short waves travel more slowly than long ones, this affects simulations ofmild sea states more than severe seas.

Setting the Sea State DataThe ISSC spectrum is a generalised form of the Pierson-Moskowitz spectrum and is appropriatefor fully-developed seas in the open ocean. The JONSWAP spectrum is a variant of the ISSCspectrum in which a "peak enhancement factor", γ, is applied to give a greater concentration ofenergy in the mid-band of frequencies. The Ochi-Hubble spectrum enables you to representsea states that include both a remotely generated swell and a local wind generated sea.

JONSWAP is commonly specified for the North Sea. 2 parameters are sufficient to define anISSC spectrum - we use Hs and Tz for convenience. For the JONSWAP spectrum, 5parameters are required, Hs, Tz, γ, and 2 additional parameters σa and σb, (denoted σ1 and σ2 inOrcaFlex), which define the band width over which the peak enhancement is applied. If youchoose JONSWAP then you can either specify γ or let the program calculate it (see formulaegiven by Isherwood (1987). The 2 band width parameters are set automatically to standardvalues). For the North Sea it is common to set γ = 3.3. If you have to do a systematic series ofanalyses in a range of wave heights, there are advantages in keeping γ constant. Note that aJONSWAP spectrum with γ = 1.0 is identical to the ISSC spectrum with the same Hs and Tz.

Choice of wave spectrum can cause unnecessary pain and suffering to the beginner. Forpresent purposes, the important point is to get the "design wave" we want embedded in arealistic random train of smaller waves. The spectrum is a means to this end, and in practice itmatters little what formulation is used. The one exception to this sweeping statement may be 2-peaked spectra (e.g. Ochi-Hubble).

Setting the Number of ComponentsOrcaFlex generates a time history of wave height by dividing the spectrum into a number ofcomponent sine waves of constant amplitude and (pseudo-random) phase. The phasesassociated with each wave component are pseudo-random. OrcaFlex uses a random numbergenerator and the used-defined seed to assign phases. The sequence is repeatable, so thesame seed will always give the same phases and consequently the same train of waves. Thewave components are added assuming linear superposition to create the wave train. Shipresponses and wave kinematics are also generated for each wave component and addedassuming linear superposition. OrcaFlex currently allows you to specify the number of wavecomponents to use; more components give greater realism but a greater computing overhead.

The time history generated is just one of an infinite number of possible wave trains whichcorrespond to the chosen spectrum - in fact there are an infinite number of wave trains whichcould be generated from 100 components, a further infinite set from 101 components and so on.

Strictly speaking, we should use a full Fourier series representation of the wave system whichwould typically have several thousand components (the number depends on the requiredduration of the simulation and the integration time step). This is prohibitively expensive incomputing time so we use a much reduced number of components, as noted above. However,this does involve some loss of randomness in the time history generated. For a discussion ofthe consequences of this approach, see Tucker et al (1984).

Finding a Suitable Design WaveA frequent requirement is to find a section of random sea which includes a wave correspondingin height and period to a specified "design wave". OrcaFlex provides "preview" facilities for thispurpose. If you are looking for a large wave in a random sea, say Hmax = 1.9Hs, then use the

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List Events command (on the Waves Preview tab of the environment data form) to ask for alisting of waves with height > H=1.7Hs, say. It is worth looking over a reasonably long period oftime at first - say t = 0 to 50,000 or even 100,000 seconds. OrcaFlex will then search that timeperiod and list wave rises and falls which meet the criterion you have specified.

Suppose that the list shows a wave fall at t = 647s which is close to your requirement. Thenyou can use the View Profile command to inspect this part of the wave train, by asking OrcaFlexto draw the sea surface elevation for the period from t = 600 to t = 700s, say. You will then seethe large wave with the smaller waves which precede and follow it.

Note that when you use the "preview" facility you have to specify both the time and the location(X,Y coordinates). A random wave train varies in both time and space, so for waves going inthe positive X direction (wave direction = 0°), the wave train at X = 0 differs from that at X =300m.

You can use the "preview" facility to examine the wave at different critical points for yoursystem. For example, you may be analysing a system in which lines are connected betweenShip A at X = 0 and Ship B at X = 300m. It is worth checking that a wave train which gives adesign wave at Ship A does not simultaneously include an even higher wave at Ship B. If youwant to investigate system response to a specified design wave at both Ship A and Ship B, thenyou will usually have to do the analysis twice, once with the design wave at Ship A and once atShip B.If necessary, adjust Hs and Tz and repeat.If no wave of the required characteristics can be found, then adjust Hs and Tz slightly andrepeat. As we noted above, the important point is to get the "design wave" we want embeddedin a realistic random train of smaller waves. This is often conveniently done by smalladjustments to Hs and Tz. We need make no apology for this. In the real world, even in a"stationary" sea state, the instantaneous wave spectrum varies considerably and Hs and Tz withit. For further discussion see Tucker et al (1984).

If you are using an ISSC spectrum, or a JONSWAP spectrum with constant γ, then you canmake use of some useful scaling rules at this point. In these 2 cases, provided the number ofwave components and the seed are held constant, then:

• For constant Tz, wave elevation at any time and any location is directly proportional to Hs.For example, if you have found a wave at time t which has the period you require but is 5%low in height, increasing Hs by 5% will give you the wave you want, also at time t.

• For constant Hs, the time between successive wave crests at the origin (X = 0, Y = 0) isproportional to Tz. For example, if you have found a wave at the origin at time t which hasthe height you require but the period between crests is 5% less than you want, increasing Tzby 5% will give you the wave you want, but at time 1.05t.

Note: This rule does not apply in general except at the origin of global coordinates.

These scaling rules can be helpful when conducting a study of system behaviour in a range ofwave heights. We can select a suitable wave train for one wave height and scale to each of theother wave heights. This gives a systematic variation in wave excitation for which we mayexpect a systematic variation in response. If the wave trains were independently derived, thenthere would be additional scatter.

Wave StatisticsThe following is based on Tucker (1991).

Deriving Hmax from Hs

Hmax/Hs = K.√[(loge N)/2]

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where N is the number of waves in the period under consideration and K is an empiricalconstant. Since wave statistics are usually based on measurements made every 3 hours, N isusually taken as the number of waves in 3 hours:

N = 10800/Tz

For extreme storms, K may be taken as 0.9, but for moderate wave conditions as used forfatigue analysis, K = 1 is usually assumed.

In extreme storm conditions, it is common to assume a "significant wave steepness" of 1/18, i.e.

S = (2π.Hs)/(g.Tz²) = 1/18

hence

Tz = √[(2π.Hs)/(g.Ss)] = 3.39√(Hs)

for

Ss = 1/18 ( Hs in metres, Tz in seconds.)

Deriving Tmax from Tz

Generally, it can be assumed that

1.05Tz < Tmax < 1.4Tz

A common assumption is

Tmax = 1.28Tz

7.3.11 ResultsSummary and Full Results

Results tables are available for the Environment reporting Wave length, Wave number, Ursellnumber and theoretical Breaking wave height.

Time History, Statistics and Linked Statistics

For details on how to select results variables see Selecting Variables.

For Environment results you must specify the global X,Y,Z coordinates of the point for whichyou want results. Note that the results given are for the sea conditions that apply during thesimulation - they therefore include the build-up of wave motion that is done during the build-upstage.

The available variables are as follows.

Elevation

The global Z-coordinate of the sea surface at the specified global X,Y position.

Velocity, X, Y, Z-VelocityAcceleration, X, Y, Z-Acceleration

The magnitude and global X,Y and Z components of the water particle velocity (due to currentand waves) and acceleration (due to waves) at the specified global X,Y,Z position. If thespecified Z position is above the water surface then zero is reported. If the specified Z is belowthe seabed then the value applicable at the seabed is given.

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Current Speed and Current Direction

The speed and direction of the current at the specified global X,Y,Z position.

Wind Speed

The wind speed. Note that this does not depend on the specified global X,Y,Z position.

Static Pressure

The pressure due to the static head of water at the specified global X,Y,Z position.

7.4 SHAPES

7.4.1 ShapesShapes are simple 3 dimensional geometric objects that can be used to model two distinctthings:

1. elastic solids to model physical obstacles,

2. trapped water to model moonpools or other areas where fluid motion is suppressed.

Note: In older versions of OrcaFlex elastic solids were referred to simply as solids.

You may choose between a number of different basic geometric shapes and several shapescan then be placed together to defined more complex shapes. The basic shapes available areplanes, blocks and cylinders.

Elastic solids

An elastic solid represents a physical barrier to the motion of lines and buoys. It is made of amaterial of a specified stiffness and resists penetration by applying a reaction force normal tothe nearest surface of the elastic solid and proportional to the depth and speed of penetration ofthe object into the elastic solid.

Note: Elastic solids do not resist penetration by Vessels, Links, Winches or otherShapes.

Each elastic solid has an associated stiffness, which determines the rate at which the forceapplied to an object increases with the area of contact and depth of penetration into the elasticsolid. The stiffness is the force per unit area of contact per unit depth of penetration.

Where an object interacts with more than one elastic solid simultaneously, the force acting on itis the sum of the individual forces from each elastic solid.

Note: A elastic solid with zero stiffness has no effect on the rest of the model. Suchshapes can be useful for drawing reference marks on the 3D views, withoutaffecting the behaviour of the model.

Trapped water

Trapped water can be used to model hydrodynamic shielding - i.e. areas such as moonpools,the inside of spars or behind breakwaters, where wave and current effects are suppressed.

Inside a trapped water shape the fluid motion is calculated as if the fluid was moving with theshape. So if the trapped water shape is fixed then no fluid motion occurs in the shape - thiscould be used to model a breakwater. But if the shape is connected to a moving vessel, for

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example, then the trapped water is assumed to move with the vessel - this could be used tomodel a moonpool.

Note: Objects ignore any trapped water shapes which are connected to thatparticular object. If this wasn't done then if you connected a trapped watershape to a buoy and part of the buoy was in the trapped water shape then afeedback would occur (the buoy motion determines the motion of the shape,which in turn would affect the fluid forces on the buoy and hence its motion).Such feedback is undesirable so the buoy ignores any trapped water shapesthat are connected to it.

7.4.2 Shape DataName

Used to refer to the shape.

Type

Either Elastic Solid or Trapped Water.

Shape

Can be one of Block, Cylinder or Plane.

Connection

Can be Fixed, Anchored or connected to another object (Vessels, 3D Buoys or 6D Buoys).

Pens and Number of Lines

Each surface of the solid is drawn as a wire frame using one the specified pens. To aidvisualisation, the Outside pen is used if the surface is being viewed from the outside of thesolid, and the Inside pen is used if it is being viewed from the inside.

The Number of Lines determines how many lines are used in the wire frames - a larger valuegives a more realistic picture, but takes a little longer to draw.

Data for Elastic Solids

Stiffness

This is the reaction force that the solid applies per unit depth of penetration per unit area ofcontact. Stiffness may be set to zero, giving a solid that is drawn but which has no effect on theother objects in the system.

Damping

The percentage of critical damping for the elastic solid.

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7.4.3 Blocks

Block Position Bx

y

z

y-sizex-size

z-size

A Block shape is a rectangular cuboid, defined by giving:

Origin

This is the position of one of the block's vertices, defined relative to the connection. This pointis taken as the origin of the block's local x,y,z axes.

For Fixed connections this is the global position of the point.

For Anchored connections the object-relative x,y coordinates given are the global X,Ycoordinates of the anchor point, and the z-coordinate is the distance of the anchor above(positive) or below (negative) the seabed at that X,Y position.

For connections to other objects, the coordinates of the connection point are given relative tothe object local frame of reference.

Size

This defines the block's dimensions in its local x, y and z directions. With respect to its localaxes, the block occupies the volume x=0 to Size(x), y=0 to Size(y), z=0 to Size(z).

Orientation

This is defined by giving three rotation angles, Rotation 1, 2 and 3, that define its orientationrelative to the object to which the block is attached, or else relative to global axes if it is notattached to another object. For example, if the block is attached to an object with local axesLxyz, then the 3 rotations define the orientation of the block axes Bxyz as follows. First alignthe block with the local axes of the object to which it is attached axes, so that Bxyz are in thesame directions as Lxyz. Then apply Rotation 1 about Bx (=Lx), followed by Rotation 2 aboutthe new By direction, and finally Rotation 2 about the new (and final) Bz direction.

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7.4.4 Cylinders

r

r = Inner RadiusR = Outer Radius

R

End 1 Position

End 2 Position

A cylinder shape is a thick walled hollow pipe defined by giving:

• Inner and Outer Radii.

• Length.

• Object-relative coordinates of one end point of the axis.

For Fixed connections the coordinates are relative to global axes.

For Anchored connections the object-relative x,y coordinates given are the global X,Ycoordinates of the anchor point, and the z-coordinate is the distance of the anchor above(positive) or below (negative) the seabed at that X,Y position.

For connections to other objects, the coordinates of the connection point are given relativeto the object local frame of reference.

• Azimuth and Declination of the axis.

The azimuth and declination define the direction of the axis relative to the local axes of theobject to which the end is connected. For objects that rotate, such as vessels and 6D buoys,the axis direction therefore rotates with the object. For Fixed or Anchored ends it is definedrelative to global axes.

Cylinders are drawn using circles to represent the end faces and a number of rectangular facetsto represent around the curved surfaces. The number of facets used is the Number of Linesspecified; 2 gives a very simple wire frame profile of the cylinder, whilst a very large numbergives a pseudo-opaque cylinder at the expense of drawing speed.

If the Inner Radius is zero then a solid disc is formed. If the Outer Radius is very large then it istreated as infinite.

If the cylinder is an elastic solid then reaction forces are applied:

• radially inwards if an object comes into contact with the inner curved surface,

• radially outwards if an object comes into contact with the outer curved surface,

• normally outwards if an object comes into contact with one of the end faces.

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7.4.5 Planes

Direction ofMaximum Slope

Slope

Point on Plane

A plane shape is an infinite plane surface - one side of the plane is outside and the other isinside. The position of the plane is defined by specifying a Point on Plane through which itpasses. The coordinates are object-relative.

• For Fixed connections the point is relative to global axes.

• For Anchored connections the object-relative x,y coordinates given are the global X,Ycoordinates of the anchor point, and the z-coordinate is the distance of the anchor above(positive) or below (negative) the seabed at that X,Y position.

• For connections to other objects, the coordinates of the connection point are given relativeto the object local frame of reference.

• The angle of the plane is then specified by giving its (maximum) Slope Angle and SlopeDirection, relative to the object to which it is connected.

Consider for the moment a Fixed or Anchored shape.

The angle of the plane is specified by giving its (maximum) Slope Angle relative to horizontal(90° is therefore a vertical plane) and Slope Direction. The Slope Direction is the azimuthdirection of the line of maximum slope upwards, relative to global axes. For example a planehaving a Slope Angle of 30° and a Slope Direction of 90° slopes upwards in the positive Ydirection at 30° to the horizontal.

A plane with zero slope angle is horizontal with the inside underneath. For a sloping plane, todetermine the position and which side is which, begin with a horizontal plane through the Pointon Plane. The inside is then on the under side of the plane. Now turn to look along thespecified Slope Direction and tilt up to the maximum Slope Angle.

Now consider shapes connected to other objects.

In this case the Slope Angle and Slope Direction are relative to the object's local x,y plane. Forexample a plane having a Slope Angle of 30° and a Slope Direction of 90° slopes upwards inthe positive y direction at 30° to the object's local x,y plane.

Planes are drawn as a rectangular grid, with the specified Number of Lines, centred on thereference point and with a spacing determined by the 3D View Size. Only a part of the infiniteplane local to the View Centre is shown.

7.4.6 DrawingRepresentation of shapes in full on the screen can give a confusing display. OrcaFlex does notprovide hidden-line removal as it would be too slow for practical use of the program, so objectsare displayed by simple wire-frame drawings. You may exercise control over the display by

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selecting the number of lines drawn for each object, and the sequence in which they are drawn.For pen details, see How Objects Are Drawn.

Where it is necessary to keep the display simple you should set Number of Lines to 2 for blocksand cylinders, 5 or 7 for planes. If the number of lines is set large for blocks or cylinders theyappear as solid objects, although they may take a long time to draw.

Please note also that the Number of Lines only affects the drawing, and not the calculations(which are correctly performed with curved geometry). Planes and Blocks are drawn first, andthen Cylinders, but otherwise the solids in the model are drawn in the sequence that they werecreated. You can sometimes take advantage of this, by defining background shapes beforeforeground ones, to obtain a pseudo-hidden line effect. You are encouraged to experiment, butsimplicity is best.

Hint: Although the program provides 'depth clues' to the eye by drawing rear facesin a different colour, the eye can sometimes be fooled by the picture - tryrotating the view back and forth a few times.

7.4.7 ResultsFor details on how to select results variables see Selecting Variables.

Contact Force

The magnitude of the total force applied by an elastic solid to other objects in the model. Thisvariable is only available for elastic solids.

7.5 VESSELS

7.5.1 VesselsA Vessel is used to model a ship, floating platform, barge, or any other rigid body whose motioncan either be prescribed by a Time History file or else by a set of Response AmplitudeOperators (RAOs) or other harmonic motions, superimposed on prescribed motion.

vertex 3

vertex 5

edge joining3 to 5

pitch

z (heave)

y (sway)

x (surge)V

yaw

roll

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Figure: Vessel Model

Each vessel has a Vessel Type that determines its RAO and drawing data. To illustrate this,consider a model of a pipe being towed by two identical tugs. This is modelled by creating avessel type called ‘Tug’ and then creating two vessels, each of type ‘Tug’. The drawing data(defining the tug outline) are data of the Tug vessel type, since they apply to both tugs.Similarly, the RAOs are data of the vessel type, since again they are the same for both tugs.On the other hand the two tugs differ in their positions and prescribed motion, so these areproperties of the individual vessel objects.

Note: The vessel also has extra drawing data - this is to allow you to set up vessel-specific drawing. For example the lead tug may have a special tow-pointfitting that you want to draw. When the vessel is drawn, OrcaFlex first drawsthe vessel type wire frame and then draws the vessel wire frame. These twowire frames can have different colours, so you can highlight application-specific drawing.

The vessel is defined relative to a right-handed system of local vessel axes Vxyz, where:

• V is the vessel origin for this vessel type. This is chosen by the user when the vessel type isset up. However note that if you specify that the vessel type has symmetry then the vesselorigin must be placed on the plane of symmetry or at the centre of circular symmetry; seeVessel Type Data: Symmetry for details.

• Vx, Vy and Vz must be the directions of surge, sway and heave, respectively, for this vesseltype. Note that these directions must therefore be the directions to which the RAOs apply.

Points on the vessel, for example where cables or risers are connected, are then definedrelative to these vessel axes. These points then move with those axes as the vessel movesand rotates relative to the global axes, and OrcaFlex calculates these motions automatically.

The vessel is drawn, in 3D views of the model, as a "wire frame" of user-specified vertices andedges. This allows a simple visual check that amplitudes, phases etc. are consistent with theapplied wave. The vessel wire frame can also be used to do a visual check for interferencebetween lines and vessel structure. As with all points on the vessel, the vertices are definedrelative to the vessel axes Vxyz.

7.5.2 Vessel DataOverviewThe upper part of the vessel data form contains data that specifies the vessel type, geometryand initial position and the lower part contains various tabs containing other data.

On the Calculation tab you must choose how the vessel motion is to be obtained. Your choicethen determines which of the following other tabs of data are visible:

• Prescribed Motion.

• Harmonic Motion

• Time History

• Applied Load

• Multiple Statics

• Drawing.

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Type and Geometry

Name

Used to refer to the Vessel.

Type

Specifies the Vessel Type. The Vessel Types button allows you to view and edit the VesselType Data.

Draught

Specifies which set of RAOs to use from the specified vessel type. See Draughts.

Length

Specifies the length of this vessel. The default value '~' means that this vessel is the samelength as the vessel type. If you specify a length that differs from the vessel type length, thenOrcaFlex will scale all the vessel type's data to allow for the scaling factorVesselLength / VesselTypeLength. This is useful if you have RAO and drawing data for a 70mship, for example, but want to use a 50m ship that is otherwise very similar.

Note: The RAO scaling is done using Froude scaling (see Rawson and Tupper).

Warning: The scaling is done assuming that all dimensions are scaled by the samefactor VesselLength / VesselTypeLength. It is therefore only valid if the vesselis an exact scale model of the vessel type. If this is not the case, then scalingintroduces errors and should not normally be used. Instead, accurate dataspecific to this vessel should be obtained.

However, for ships in head and stern seas the RAO scaling errors may beacceptable, since the RAOs for these wave directions depend mainly onvessel length. For other cases the RAO scaling is likely to be poor, soOrcaFlex issues a warning if scaling is used and the wave direction is notclose to a head or stern sea.

Initial Position and Orientation

These specifies the vessel's static position relative to the global axes. The Initial Positiondefines the position of the vessel origin V. The Initial Orientation defines the orientation of thevessel axes Vxyz as three rotations, Heading, Trim and Heel. The static orientation of Vxyz isthat which results from starting with Vxyz aligned with the global axes and applying the Headingrotation about Vz, then the Trim rotation about Vy and finally the Heel rotation about Vx.

If the vessel is not included in the static analysis then this Initial Position is taken to be the staticposition of the vessel. If the vessel is included in the static analysis, then this Initial Position isused as an initial estimate of the vessel position and the statics calculation will move the vesselfrom this position iteratively until an equilibrium position is found.

Note: The vessel Z coordinate can only be changed by editing on the vessel dataform. Dragging in the Z direction with the mouse is prevented.

Warning: If you have included any harmonic motion on the vessel (see HarmonicMotion) then the phases of the harmonic motions will normally depend on thevessel Initial Position, so if you change the Initial Position you may need tochange the harmonic motion phases accordingly.

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For other vessel data see Vessel Data: Overview.

Calculation DataThe following settings (on the Calculation tab on the vessel data form) control how the vessel'sstatic position and dynamic motion are determined.

Included in Static Analysis

You can control whether the OrcaFlex static analysis calculates the static equilibrium position ofthe vessel, or simply places the vessel in the user-specified initial position.

OrcaFlex first places the vessel at the initial position and orientation specified by the user. IfIncluded in Static Analysis is set to No then OrcaFlex leaves the vessel in this user-specifiedposition. This is not necessarily an equilibrium position.

If Included in Static Analysis is set to Yes then OrcaFlex starts from the user-specifiedposition and adjusts the vessel's X, Y and Heading until an equilibrium position is reached.Note that only these 3 free degrees of freedom of the vessel (X, Y and Heading) are included inthe calculation. The other three degrees of freedom (Z, Heel and Trim) are assumed to beconstrained and so are left at the values specified by the user.

Note: If multiple statics are being performed on the vessel then no equilibriumcalculation is performed on the vessel and its placement is determined by themultiple statics data. Other vessels in the model are included in the staticanalysis as specified by their own data.

Dynamic Analysis

The motion of a vessel during the dynamic analysis can be specified in a variety of ways.OrcaFlex allows the vessel motion to be made up of two parts, called the Primary motion andthe Superimposed motion. Broadly, the Primary motion is aimed at modelling the steady orlow frequency motion of the vessel, whereas the Superimposed motion is aimed at modellingthe higher frequency motion, such as that generated by waves.

As an example, consider a ship being driven under power along a specified course. In theabsence of waves it moves steadily along its course and this would be modelled by the Primarymotion. But when waves are present the primary motion is augmented by wave-generatedmotion that would often be modelled in OrcaFlex as Superimposed motion specified by RAOs.OrcaFlex superimposes this latter motion on the primary motion to give the total combinedmotion of the vessel.

You can specify both the Primary and Superimposed motions in a choice of ways, as follows.

Primary Motion

The Primary motion determines what OrcaFlex refers to as the primary position of the vessel. Itcan be one of the following options.

• None. In this option there is no primary motion and the primary position of the vesselremains fixed at the position determined by the static analysis.

• Prescribed. This option allows you to drive the vessel around the sea surface, for exampleto model the vessel moving station during the simulation. The vessel's speed and course isspecified using the data on the Prescribed Motion tab on the vessel data form.

• Calculated. In this option the OrcaFlex calculates the wave drift loads and the vessel slowsurge, sway and yaw motion that results from these and other loads. The other loads

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included are those from hydrodynamic and wind drag, damping, applied loads and loadsfrom any lines or other objects that are attached to the vessel.

Note: If the primary motion is not Calculated, then OrcaFlex does not calculate thewave drift or damping loads, so those loads will be omitted from the vesselresults.

• Time History. In this option the user specifies the primary motion in a time history file thatdefines the vessel Primary X, Primary Y, Primary Z, Heel, Trim, Heading as a function oftime. See the vessel's Time History data.

Superimposed Motion

The Superimposed motion is applied as an offset from the position given by the primary motion.It can be one of the following options.

• None. In this option there is no offset and the vessel position is equal to the primaryposition at all times.

• RAOs + Harmonic. In this option the vessel's position oscillates harmonically about theprimary position. The harmonically varying offset comes from two sources. Firstly, if wavesare present and you specify non-zero RAOs for the vessel type, then the offset will includethe wave-generated harmonic motions specified by those RAOs. Secondly, the vessel'ssuperimposed offset also includes any harmonic motions that you specify on the HarmonicMotions tab on the vessel data form.

• Time History. In this option the user specifies the offset in a time history file that definesthe vessel Surge, Sway, Heave, Roll, Pitch and Yaw as a function of time. See the vessel'sTime History data.

Report RAOs

The Report RAOs button is only available if you set the superimposed motion to RAOs +Harmonic. It provides a spreadsheet showing the RAOs that will be used for this vessel for anygiven direction. Note that these RAOs may differ from those specified on the vessel type formsince they include any scaling and interpolation that OrcaFlex uses when deriving this vessel'sRAOs from those of its vessel type.

The spreadsheet has a highlighted cell into which you should type the wave direction (relative tothe vessel) for which you want to see the RAOs. The spreadsheet then displays the RAOs thatOrcaFlex will use, using the RAO conventions specified for this vessel's type.

The table covers the wave periods specified on the vessel type data form, plus (if appropriate)the regular wave period specified on the environment data form.

For other vessel data see Vessel Data: Overview.

Prescribed MotionThe prescribed motion data only applies if the vessel's Primary Motion is set to Prescribed. Itenables you to drive the vessel around the sea surface along a predetermined path, byspecifying how the vessel's primary position and heading change during the simulation.

The vessel is driven by specifying, for each stage of the simulation, the forward velocity of themean position and the rate of turn (the rate of change of the heading). For each simulationstage the velocity of the mean position can be either

1. set to a Constant Velocity that applies throughout the stage.

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Warning: This may cause an abrupt change at the beginning of the stage, which maycause transients in the system

or

2. specified as a Velocity Change to be applied smoothly throughout the stage. For example,an increment of 1m/s during a stage of length 10 seconds causes an acceleration of 0.1m/s² to be applied throughout the stage, so that if the vessel starts at rest then at the start ofthe next stage the vessel is travelling at 1m/s.

In addition to changing the velocity of the mean position, you can specify a Rate of Turn foreach stage. This is the angle change per second to be applied to the vessel's headingthroughout the stage.

For other vessel data see Vessel Data: Overview.

Harmonic MotionThe Harmonic Motion tab (on the vessel data form) only applies if the vessel's superimposedmotion is set to RAOs + Harmonic. It allows you to specify a number of harmonic motions ofthe vessel.

The harmonic motions are in addition to any wave-generated motion specified by the RAO data,so if you only want the wave-generated motion then you should set the number of harmonicmotions to zero.

Each harmonic motion is a single-period sinusoidal motion of the vessel, specified by giving:

• the Period of the harmonic motion; this applies to all 6 degrees of freedom,

• the Amplitude and Phase of the motion for each of the 6 degrees of freedom of the vessel.If you are modelling slow drift, then note that slow drift normally only applies to surge, swayand yaw, in which case the amplitudes for heave, roll and pitch should be set to zero.

Note: The harmonic motion amplitudes (unlike the RAO responses of the vessel) arenot specified relative to a wave amplitude - they are specified directly in lengthunits (for surge, sway and heave) or degrees (for roll, pitch and yaw).

Similarly, the phases are not specified relative to the phase of a wave - they are the phase lagsfrom the global time origin T=0 until the maximum harmonic motion occurs. More precisely, thephase that should be specified for the harmonic motion is given by

360 . ((Tmax / P) mod 1)

where P is the period of the harmonic motion and Tmax is the global time at which you want themaximum of the motion to occur.

Warning: Harmonic motions can be used to model pre-calculated vessel slow drift. Ifyou do this, then if you move the vessel’s Initial Position in the wave direction,or if you change the data for the waves (other than changing the simulationtime origin), then you will normally also then have to adjust the phases of theslow drift. This is because such changes affect the global time at which aparticular part of the wave train will reach the vessel and hence will also affectthe global time at which maximum slow drift motion is achieved.

For other vessel data see Vessel Data: Overview.

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Time HistoryThe Time History tabs (on the vessel data form) only apply if the vessel's primary orsuperimposed motion, or both, are set to Time History. It allows you to specify the motion bygiving a time history file. To do this:

• On the Calculation tab set the primary motion or superimposed motion data item (or both) toTime History.

• Create a tab-delimited text file containing the time history motion you want. See below fordetails.

• On the appropriate Time History tab, set the Input File to the name of the time history fileand specify which columns in the file contain the data. The Browse button allows you tospecify the file by finding it, and the Import Wizard button then provides a visual way ofspecifying which column is which. See Time History Files for details.

• Set the time history's time origin and the simulation time origin (on the Waves tab of theenvironment data form) so that the simulation covers the period you want.

• Choose which interpolation method you want OrcaFlex to use when it needs the vesselposition and orientation for times between those specified in the time history file.

Note: For most purposes we recommend using Cubic Spline interpolation, since itgives continuity of vessel velocity and acceleration. Cubic Bessel interpolationtypically gives step changes in acceleration at the specified time samples, andLinear interpolation gives zero acceleration between the times specified andthen an infinite acceleration when the velocity changes at a specified timesample. Such acceleration effects can manifest themselves as steps orspikes in the inertial forces on any objects attached to the vessel.

Contents of Time History File

The time history file must contain a time column and columns for all 6 degrees of freedom of thevessel. For primary motion these are Primary X, Primary Y, Primary Z, Heel, Trim and Heading,measured relative to the global axes.

For superimposed motion the degrees of freedom that must be specified are Surge, Sway,Heave, Roll, Pitch and Yaw. They are measured relative to the primary position of the vessel,as specified by the vessel's primary motion.

The time values in a vessel time history file need not be equally spaced. The units used for allthe columns must be the same as those used in the OrcaFlex model, so the time values mustbe in seconds and angles in degrees.

For further details of the file format see Time History Files.

Notes: If there is any wave-generated motion present in a vessel's time historymotion then the OrcaFlex wave data needs to match the wave that generatedthat motion. If you have suitable data for the wave elevation then you can usethat to specify the wave by time history. This can be done either in a separatetime history file for the wave or else in an extra column in the vessel's timehistory file.

The position and velocity specified by a time history file for the start of thesimulation (i.e. for SimulationTime = -BuildUpDuration) will not, in general,match the static state from which OrcaFlex starts the simulation. To handlethis OrcaFlex uses ramping during the build-up stage to smooth the transitionfrom the static state to the position and motion specified in the time history file.

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For other vessel data see Vessel Data: Overview.

Applied LoadYou can apply to the vessel an external Global Load that does not rotate if the vessel rotates.This is specified by giving the components of Applied Force and Applied Moment relative toglobal axes. These components remain constant, so if the vessel rotates then the load does notrotate with it.

In addition, you can specify an external Local Load that does rotate with the vessel. This isspecified by giving the components of Applied Force and Applied Moment relative to vesselaxes. Again these components remain constant, so if the vessel rotates then the load doesrotate with it. This is suitable for modelling thrusters, for example.

In both cases the Point of Application of the load is specified by giving its x,y,z coordinatesrelative to vessel axes.

Notes: Applied loads will only affect vessel position in the static analysis and onlywhen the vessel is included in the static analysis. Otherwise the vesselposition is determined (e.g. by RAOs) and the applied loads are simplyreported.

The vessel's heave, roll and pitch degrees of freedom are not included in thestatic analysis, so the components of these loads in these degrees of freedomare ignored.

For other vessel data see Vessel Data: Overview.

Multiple StaticsThe offsets for multiple statics calculations are specified here. Offsets are from the vessel'sinitial position and are specified by giving a range of azimuth and offset values. For example:

AzimuthsFrom (deg) To (deg) Number of Steps0.0 180.0 4

OffsetsFrom (m) To (m) Number of Steps0.0 100.0 5The Azimuths table determines which directions are to be analysed. The Offsets table specifieshow far in the given direction the vessel is to be placed. With the above data, the offsetsanalysed by the multiple statics calculation are as illustrated by the dots in the diagram below:

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0m 20m 40m 60m 80m 100m

180 deg

135 deg

90 deg

45 deg

0 deg

Vessel InitialPosition

X

Y

Figure: Example Offsets

A diagram showing the selected offsets is drawn on the Vessel Offsets data form, to helpvisualise which offsets will be analysed.

For other vessel data see Vessel Data: Overview.

DrawingVessels are drawn as wire frames defined in the data as a set of Vertices and Edges. TheVertices are defined by giving their coordinates relative to the vessel axes Vxyz. The Edges arelines drawn between two vertices.

You can define wire frame drawing data in two places - for the vessel and also for its vesseltype. The vessel is drawn by first drawing a wire frame based on the vertices, edges and penspecified for its vessel type (see the vessel types data form). Then a further vessel-specific wireframe may be drawn, using any vertices, edges and pen that you specify on the vessel's dataform.

This allows you to specify a wire frame drawing of the basic vessel type, and then optionally addto it (possibly in a different colour) a wire frame drawing of some equipment that is specific tothat vessel. If the vessel length differs from the vessel type length, then the vessel type wireframe is scaled accordingly. Note that either, or both, of these wire frames can be empty (i.e.no edges) if desired.

The drawing data do not affect the mathematical model in any way - they are purely for drawing3D views. The vertices and edges follow the motions of the vessel, and thus may be used toimprove understanding of the motion of the model. They can also be used to represent a sparor other equipment attached to the vessel, so that you can then look for clashing with otherparts of the system. For example during a simulation replay you can adjust the viewpoint tolook exactly along the edge of interest, and check visually if other parts of the model passthrough it.

For other vessel data see Vessel Data: Overview.

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7.5.3 Vessel TypesVessel TypesEach vessel has a vessel type that determines a lot of its data and which is defined on thevessel types form. You can define a number of different vessel types and each type is given aname, which is then used on the vessel data form to specify the type of that particular vessel.

Two different vessels can have the same type. To illustrate this, consider a model of a pipebeing towed by two identical tugs. This is modelled by creating a vessel type called ‘Tug’ andthen creating two vessels, each of type ‘Tug’. The RAOs, for example, are data of the 'Tug'vessel type, since they apply to both tugs. On the other hand the two tugs differ in theirpositions and any prescribed motion, so these are properties of the individual vessel objects.

You don't have to use all, or even any, of the vessel types you define. For example you can setup a data file that defines a number of vessel types but has no vessels. Such a file can then actas a library of vessel types that can be imported into other OrcaFlex data files.

Vessel Type Data

For each Vessel Type you can enter data for several different draughts, each draught having auser-specified Name. Each vessel in the model must specify (on its vessel data form) whichdraught to use. It is not possible to use different draughts at different times during the samesimulation.

Some of the vessel type data apply to all draughts, but a lot of the data is draught-dependentand so separate data is defined for each defined draught. See the following list of the mainclasses of vessel type data.

• Geometry and drawing data. Applies to all draughts.

• Conventions define the meaning of any RAO and wave drift QTF data. The conventionsapply to all draughts.

• RAO data. Separate RAOs are specified for each different draught. There is aCheck RAOs facility that provides RAO graphs that help detect errors.

• Hydrodynamic and Wind Drag data. Separate values are specified for each differentdraught.

• Wave Drift data. Separate values are specified for each different draught.

• Inertia and Damping data. The mass, moments of inertia and centre of mass apply to alldraughts, but separate added mass and damping data can be specified for each differentdraught.

Geometry and Drawing

Vessel Type Length

The length to which the vessel type RAO and drawing data apply. This may be left unspecified('~'). If a value is specified, then it may be used to scale the vessel type data to the length of thevessel. See Vessel Length for details.

Drawing Data

Each vessel of this type is drawn as a wire frame, based on vertices and representing thevessel type, plus a wire frame representing vessel-specific features. See Drawing.

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ConventionsThe conventions tab (on the vessel types form) contains settings that define the meaning ofboth the RAO and QTF data. This enables you to enter RAO and QTF data directly from manyother programs without having to convert the values into OrcaFlex conventions. Instead youcan tell OrcaFlex the conventions that apply to that data and OrcaFlex will then automaticallyallow for those conventions when it uses the data.

Although RAOs are simple enough in principle, a number of complications make themnotoriously error-prone and difficult to check in practice. The main issues are:

• Different coordinate systems.

• Different definitions of phase angle and rotational RAOs.

• Use of vessel symmetry, e.g. to obtain motions in seas from the port side given data forseas from the starboard side.

OrcaFlex provides easy ways of handling these problem areas.

The use of differing coordinate systems and conventions by different suppliers of data is themain source of confusion. It is vital that you know the conventions that apply to the RAO tablesthat you are using. Unfortunately, not all RAO tables fully document the conventions used: seeRAO data checklist for help finding out what conventions apply to your data and see CheckingRAOs to check that the conventions are set correctly.

Symmetry

You can specify symmetry of the vessel type. OrcaFlex will then use the user-specifiedRAO/QTF tables for wave directions on one side of the symmetry plane to derive tables for thereflected directions on the other side of the plane.

The Symmetry can be set to:

• None: The vessel type has no symmetry. The directions specified must cover all the wavedirections used in the simulation.

• XZ plane (or YZ plane): This specifies that the XZ (or YZ) plane through the vessel originis a plane of symmetry. For each direction given OrcaFlex uses symmetry to derive tablesfor the reflected direction on the other side of the plane.

• XZ & YZ planes: This specifies that both the XZ and YZ planes through the vessel originare planes of symmetry. For each direction given OrcaFlex uses symmetry to derive tablesfor the reflected directions in the other 3 quadrants.

• Circular: This specifies that the vessel has circular symmetry about the vessel origin.RAO/QTF tables can only be given for one wave direction, and OrcaFlex uses symmetry toderive tables for all other directions.

Warning: If you specify some planes of symmetry then your vessel origin must be on allthe planes of symmetry. Or if you specify circular symmetry then you mustplace your vessel origin at the centre of symmetry.

Rotational RAOs

Roll, pitch and yaw RAOs may be specified in degrees or radians, relative to a wave of unitamplitude (e.g. degrees/metre), or to a wave of unit steepness or unit maximum slope (e.g.degrees/degree) Wave steepness ( = Waveheight / Wavelength ) is a commonly used angularmeasure of a wave and maximum wave slope ( = π.Waveheight / Wavelength ) is the truemaximum slope of the sea surface.

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Warning: If rotational RAOs are given relative to wave slope or steepness, thenOrcaFlex (internally) converts them to be relative to wave amplitude using thedeep water wavelength, not the wavelength for the water depth specified inthe model.

Note: The translational RAOs are always non-dimensional (e.g. metres/metre orfeet/foot).

Waves referred to by

The RAO and QTF data can be specified by period in seconds, or by frequency inradians/second or Hertz (cycles per second).

Note: If you import RAO or QTF data from a text file, the setting specified here willbe overridden by that defined in the text file - see Importing RAO Data andImporting QTF Data for details.

Phases

You can specify phases as leads or lags, in degrees or radians. The phase defines the time atwhich the maximum positive value of the motion occurs, relative to the time at which the wavecrest or trough passes the phase origin.

Directions Positive

You must specify the directions that correspond to positive motion in the RAO data and positiveload in the QTF data. The most common convention is as given by the default OrcaFlex vesseltype: a right-handed system with Z upwards and clockwise rotations being positive.

RAOsThe vessel type RAOs are only used if the vessel's superimposed motion is set to "RAOs +Harmonic". In this case, in the dynamic analysis the vessel moves harmonically, in all 6degrees of freedom, about its mean position. These harmonic motions are specified by givingthe RAO (response amplitude operator) amplitudes and phases, for all six degrees of freedom,usually for a range of wave periods and directions. For further information see RAOs andPhases.

RAO Origin

The RAO origin is the point on the vessel whose motion is defined by the RAOs. The RAOorigin is specified by giving its coordinates relative to the vessel axes. It is commonly, but notalways, at the centre of gravity. Different draughts can use different RAO origins.

RAO Phase Origin

The RAO phase origin is the point on the vessel that the RAO phase values are relative to; it isspecified by giving its x and y-coordinates with respect to vessel axes. The phase values givenin the RAOs must be relative to the time that the wave crest or trough (depending on the RAOphase conventions specified) passes the specified RAO phase origin.

Often the phase origin is the same as the RAO origin, i.e. the phases are relative to the time thecrest or trough passes the point whose motion the RAOs define. In this case the phase origincan be set to '~', meaning 'same as RAO origin'. But some programs (one example beingMoses) generate RAOs where the phase origin is not necessarily the same as the RAO origin.

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RAO Data

RAOs are defined as the ratio of the motion amplitude to the wave amplitude.

RAO data can be specified for a number of different wave directions, relative to the vessel. Thisrelative wave direction is labelled on the tab at the bottom of the RAO table. It is the direction inwhich the wave is progressing, measured positive from the vessel x-direction towards thevessel y-direction.

To change the wave direction for one of the RAO tables, select that table and edit the SelectedDirection. To insert a new wave direction after an existing direction, select the existingdirection's tab and click the Insert Direction button. Similarly, the Delete Direction buttondeletes the currently selected direction.

For each direction, the RAO table covers a range of wave periods or frequencies, as specifiedin the conventions data. The periods/frequencies need not be entered in order - they will besorted before use.

In the case of a circular symmetric vessel, RAOs are specified for only one wave direction -OrcaFlex will derive RAOs for all other directions.

RAO Interpolation/Extrapolation

You must provide RAO tables that include or span the wave direction(s) involved in thesimulation. If RAOs are required for a wave direction for which an RAO table has not beensupplied, then OrcaFlex will use linear interpolation to obtain an RAO table for that direction.

For regular wave analysis, RAO data is only needed for the appropriate wave period, or forwave periods either side of that period. For random sea simulations, RAO data should bespecified for a wide enough range of wave periods to cover the spectrum. The View WaveComponents button (on the Waves tab of the environment data form) reports the wavefrequencies that OrcaFlex will use to represent the spectrum.

Note: If the vessel length differs from the vessel type length then the RAO periodsspecified on the vessel type form are Froude scaled, and it is these Froudescaled periods that must cover the actual wave period(s).

Linear interpolation is used if RAOs are required for a period that is between the periods givenin the table. We strongly recommend that your RAO tables provide data for periods that includeor span all the wave periods that will be involved in the simulation. However if RAOs arerequired for a period outside the range of periods given then OrcaFlex will use linearextrapolation; a warning is given if this occurs.

You can avoid the need for extrapolation by providing RAOs for periods zero and Infinity. TheRAOs for the zero period limit must be all zero (since no object can respond to an infinitefrequency wave). For the Infinity period limit the RAOs of a free-floating vessel can be derivedfrom the knowledge that the vessel must surface follow in a sufficiently long wave. See RAOQuality Checks for details.

Warning: Interpolation is likely to be poor if the interval involved is large. We thereforerecommend that the RAO directions defined cover all the wave directions thatwill be used and in steps of 30 degrees or less.

Note that RAO interpolation and extrapolation is done using the complex value representation ofthe RAOs, in which the RAO with amplitude A and phase lag P is represented by the complexnumber:

C(A,P) = A.(cos(P)+i.sin(P)).

So given RAOs (A1,P1) at period T1 and (A2,P2) at period T2, the interpolated RAO at period(T1+T2)/2 is (A,P) where:

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C(A,P) = ( C(A1,P1) + C(A2,P2) ) / 2

This gives better results than interpolating the amplitude and phase separately.

Drag LoadsHydrodynamic and wind drag loads on a vessel are square law loads due to the relative velocityof the fluid past the vessel. They can be modelled using the data on the Hydrodynamic Dragand Wind Drag tabs on the vessel type data form. If the length of the vessel differs from that ofthe vessel type then the vessel type data will be scaled accordingly.

Drag loads are an important source of damping when modelling vessel slow drift. For adiscussion of the various damping sources see Damping Effects on Vessel Slow Drift.

The velocity used to calculate the drag loads is the relative velocity of the fluid past the vessel.This includes any current or wind velocity and the vessel due to any primary motion. The dragforces and moments due to translational motion are modelled using the standard OCIMFmethod. The drag forces and moments due to any vessel rate of yaw are modelled using yawrate drag load factors. For details of how the loads are calculated, see Vessel Theory: DragLoads.

Warning: The current and wind loads are based on theory for surface vessels and arenot suitable for submerged vessels.

Load Origin

The coordinates (relative to vessel axes) of the point on the vessel at which the hydrodynamicor wind drag loads are calculated and at which they will be applied. This need not be at thevessel origin. It is normally best to place the load origin at the centre of the vessel.

The velocity used in the hydrodynamic drag load calculation is the relative current velocity at theload origin, allowing for any velocity of the load origin due to prescribed motion of the vessel.The velocity used in the wind load calculation is the wind velocity at 10m above mean waterlevel, minus any velocity of the wind load origin due to prescribed motion of the vessel.

Load Symmetry

Specifies what symmetry the vessel type has below (for hydrodynamic drag) or above (for winddrag) the water line. For XZ and YZ symmetry, OrcaFlex will use the symmetry to derive loadcoefficients for extra directions generated by reflection in the specified vessel axes planes. Forcircular symmetry, you must specify coefficients for one direction only and OrcaFlex will usesymmetry to derive coefficients for all other directions.

Note: The symmetry for hydrodynamic drag, wind drag and RAOs (see RAOSymmetry) need not be the same, though of course the symmetry forhydrodynamic drag would normally be the same as that for RAOs.

Areas and Area Moment

The surge and sway areas and yaw area moment that will be used to calculate the current orwind loads. For details see Vessel Theory: Drag Loads.

Coefficients

Load coefficients are specified for the vessel surge, sway and yaw directions. They depend onthe direction of the current or wind, relative to the vessel (direction 0 meaning from astern, 90meaning from starboard, etc.).

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OrcaFlex uses any symmetry specified to derive coefficients for other directions and then useslinear interpolation to derive coefficients for intermediate directions.

Note: When the symmetry is XZ and YZ the yaw moments must be zero, soOrcaFlex forces zero yaw coefficients in this case.

The View Coefficients button allows you to view the coefficients that will be used - the blobs onthe graph show the coefficients you have specified plus any that OrcaFlex has derived usingreflection, and the curve shows the interpolated coefficients that will be used for intermediatedirections. You should specify sufficient directions to define the shape of the curve and to coverthe range of directions that the vessel will experience.

Yaw Rate Drag Factors

The yaw rate drag factors only apply to the hydrodynamic load data. They determine the yawdrag moment, and any surge and sway drag forces, that result if the vessel has a non-zero rateof yaw. With wind drag this effect is insignificant.

For a slender ship, and if the load origin has been placed at the centre of the vessel, then thesurge and sway drag factors can usually be taken to be zero, and then yaw drag factor can beestimated based on the vessel length and draught. See Drag Loads due to Yaw Rate fordetails.

Wave Drift LoadsThe Wave Drift tab on the vessel type form contains the Quadratic Transfer Functions (QTFs)that OrcaFlex uses to calculate a wave drift load (sometimes called the slow drift load).

Note that the wave drift load is only calculated for a vessel that has its primary motion set toCalculated. See Modelling Vessel Slow Drift for details.

See Wave Drift Load Theory for details of how OrcaFlex calculates the wave drift loads.

QTF Origin

The QTF origin is the point on the vessel to which the QTFs apply. The wave drift loads arecalculated based on the wave conditions at this point and they are applied at this point. TheQTF origin is specified relative to the vessel axes and different draughts can use differentorigins. There is no need to specify the z-coordinate of the point since the loads are calculatedand applied only for the surge, sway and yaw degrees of freedom.

Wave Drift QTFs

The way QTF data is entered in OrcaFlex has many similarities with RAO data. In particular:

• For each draught, QTF tables are specified for each of a number of wave directions. Toinsert a new table use the Insert Direction button and to delete a table select that table'stab and then click the Delete Direction button. To change the direction associated with atable, select that table's tab and then edit the Selected Direction value.

• Some of the RAO conventions apply to the QTFs. The relevant conventions are shown onthe Wave Drift tab as a reminder, but to edit them you must go to the Conventions tab.

• If the vessel type has some symmetry (see the conventions tab) then OrcaFlexautomatically generates QTF tables for all the reflected directions implied by that symmetry.You must provide QTF tables for enough directions for OrcaFlex to have data (either user-specified or generated based on symmetry) for directions that cover the wave directions thevessel will experience.

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• Each QTF table consists of data for a range of wave periods or frequencies (depending onthe convention specified). You should provide data for periods that (after allowing forFroude scaling if the vessel length differs from the vessel type length) cover the waveperiods the vessel will experience.

Warning: The settings on the conventions tab apply to all draughts and they apply toboth the vessel type's RAOs and to its wave drift QTFs. If your RAO and QTFdata use different conventions you will therefore need to transform you QTFsinto the conventions of the RAOs (or vice versa) before using them inOrcaFlex.

QTFs are only entered for surge, sway and yaw, since OrcaFlex does not calculate wave driftloads (or vessel slow drift) for heave, roll and pitch. This is because the heave, roll and pitchwave drift loads are normally not significant when compared to the typically much largerbuoyancy restoring forces in those degrees of freedom.

The QTF amplitudes are entered in non-dimensional form. No phases are required becauseonly the diagonal terms of the full QTF matrix are entered in OrcaFlex, and these diagonalterms always have zero phase. OrcaFlex uses Newman's approximation to obtain the off-diagonal QTFs from the diagonal QTFs specified. See Wave Drift Load Theory for details.

Importing QTFs

Wave drift QTF data can be imported into OrcaFlex from text files in one of two differentformats.

Standard format is the same as the text format used to import RAOs, except of course that nophases or heave, roll or pitch data are required. Here is a simple example: *** OrcaFlex Start Data *** Draught Transit Direction 45 WP surge sway yaw 0.0 0.030 0.090 -0.006 5.0 0.030 0.090 -0.006 10.0 0.001 0.005 -0.002 15.0 0.000 0.001 -0.001 Infinity 0.000 0.000 0.000 *** OrcaFlex End Data ***

NMIWAVE format is for use with the NMIWAVE diffraction program. The file should be the textNMIWAVE output file with a new line containing the string 'NMIWAVE Wave Drift' inserted at thestart of the file. Here is an example: *** NMIWAVE Wave Drift Data *** Scaled Tanker: Lpp, B, T (m) =310.90 ,48 0.31090E+03, -0.10000E+01, 0.10250E+04 45.00 1 0.50000E+01, 0.30000E-01 0.10000E+02, 0.10000E-02 0.15000E+02, 0.00000E+00 -0.10000E+01, 0.00000E+00 2 0.50000E+01, 0.90000E-01 0.10000E+02, 0.50000E-02 etc.

Note that NMIWAVE uses the ITTC conventions, which are surge +ve forward, sway +ve tostarboard, heave +ve down, roll +ve starboard down, pitch +ve bow up, yaw +ve bow to

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starboard. If your RAOs also use these conventions then they can be set on the Conventionstab. Otherwise you will need to modify the data to allow for convention differences.

The wave heading convention used by NMIWAVE is that wave heading is measured +veclockwise when viewed from above, and zero wave heading means a stern wave. This is thesame as OrcaFlex uses, except that OrcaFlex measures +ve anti-clockwise. OrcaFlexautomatically handles this by changing the sign of the wave headings when an NMIWAVE file isimported.

Inertia and DampingThe Inertia and Damping tab (on the vessel type form) contains the following data that is onlyused if the vessel's primary motion is set to Calculated. The main use of this data is whenmodelling vessel slow drift.

Centre of gravity (CG)

The coordinates of the vessel type's centre of mass, relative to vessel axes.

Mass and Moments of Inertia

The vessel type's mass and its moments of inertia about axes through the CG in the vessel x, yand z directions. This should include the structural and contents mass and inertia, but not theadded mass.

Added Mass and Damping matrices

The damping and added mass matrices are specified with respect to axes through the CG in thevessel x, y and z directions. These matrices are multiplied by the vessel velocity andacceleration, respectively, to obtain the resulting load resisting the motion. For details of theunits of this data, and the theory used, see Vessel Theory: Added Mass and Damping.

These matrices can generally be obtained from the results of a diffraction program. They areassumed to be frequency independent over the range of frequencies involved in wave driftmotion, so you should specify values that are appropriate to the vessel motion frequency youexpect. Since the data is used by OrcaFlex in the calculation of the slow drift motion of thevessel, it is normally appropriate to enter low frequency values.

The damping matrix given by a diffraction program models wave radiation damping. Howeverthere is another, often more important, source of damping, namely wave drift damping. SeeDamping Effects on Vessel Slow Drift. Wave drift damping can be modelled in OrcaFlex byadjusting the diagonal entries in the damping matrix.

Importing RAOsThe Import RAOs button on the vessel types forms enables RAO data to be imported intoOrcaFlex from text files or from a *.rao file exported by OrcaMotion.

Import RAOS from *.rao Files

The preferred method of importing RAOs is from text files (see below) but you can also importfrom an OrcaMotion *.rao file. In this case please note the following:

• Each OrcaMotion file contains data for one wave direction, but the direction is not defined inthe file. Therefore, to import from a *.rao file, you must select the draught and direction towhich the *.rao file applies and then click the Import button. The imported data will overwritethe RAO table for the currently selected draught and direction.

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• Because the data in *.rao files always use the Orcina standard conventions, the conventionsdata in OrcaFlex will be set to these standard conventions.

Warning: These conventions apply to all RAO data for this vessel type, so any existingdata that does not conform to the standard Orcina conventions, will beinvalidated by importing a *.rao file.

Import RAOS from Text Files

You can use text files to import RAO data from some other source, for example from a shipresponse calculation program or from model test results.

Note: When you import RAOs from a text file, any RAO data previously present inOrcaFlex for the draughts given in the text file will be deleted. (Other data forthese draughts, e.g. wind and hydrodynamic drag data, will not be affected.)So for each draught you import, all the RAOs for that draught must be in asingle file. You can therefore either put all the RAOs in a single file, or elsehave separate files for separate draughts.

RAO data in a text file can be imported providing that the data appears in tabular form andmarkers are first inserted into the file to identify the data to OrcaFlex. This saves the laboriousand error prone job of typing in a large table of RAO data. The markers, described below, canbe inserted using a text editor or word processor; if using a word processor, note that the filemust be saved as an ASCII text file and not as a word processor document.

A text RAO file must contain the RAO data in the following form. It is usually easy to create asuitable file by adding a few lines to your original response data file. See the examples.

• The RAO data must appear in the file in one or more tables, each table being for onedraught and direction. To enable OrcaFlex to find the tables, each table must be precededby a line containing the string OrcaFlex RAO Start Data and must be immediately followedby a line containing the string OrcaFlex RAO End Data. There must not be any blank linesbetween these two marker lines. Any mixture of upper and lower case is accepted.

• Immediately following the line containing the OrcaFlex RAO Start Data string there must betwo lines (in either order) specifying the draught and direction that applies to that table. Theline specifying the draught must be of the form Draught DraughtName, whereDraughtName is the name of the draught (a string, without any spaces). The line specifyingthe direction must be of the form Direction n, where n is a number specifying the directionthe wave is progressing, in degrees, measured positive from forward towards the port side.So direction 0 means waves coming from astern and direction 90 means waves comingfrom the starboard side.

• Following these two lines, the first line of the table must be a set of headers defining thesubsequent columns. This headers line consists of a number of character strings,separated by spaces. The strings indicate the contents of the columns; the following headerstrings are recognised by OrcaFlex; otherwise the corresponding column is ignored. SeeHeader Strings for Text RAO Tables

• If you want OrcaFlex to ignore a column, for example because it contains irrelevant orsuperfluous data, then insert a header string, (e.g. "N/A" or "~") that is not listed in the abovetable. In particular, if the table contains both wave period and frequency you must indicatethat one of these is to be ignored, since OrcaFlex will not accept two columns specifying thesame information.

• The remaining lines in the table must contain numbers, one for each header in the headersline, separated by any string of characters that cannot appear in a number (i.e. anythingexcept 0..9,-,+,. or E). Please note that it is the order of the columns that matters, not their

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actual position across the page. Hence, although it is natural to align the headers above thecolumns of numbers, this is not in fact necessary.

• There is no provision for specifying the associated conventions (other than whether theRAOs are given by period or frequency) in the text file; the conventions data must be set tocorrespond to the imported data. Since the conventions apply to all RAO data for the vesseltype, the period/frequency convention specified by the header (WP or WFH or WFR) mustbe consistent throughout the file. Similarly, the input origin to which the RAOs apply is notread in, but must be set on the Vessel Type form.

Header Strings for Text RAO TablesWhen importing RAOs from a text file, the following strings can be used in the headers line.

Header string Column containsWP Wave period in secondsWFH Wave frequency in Hz (cycles per second)WFR Wave frequency in radians/secondXA Surge amplitudeXP Surge phaseYA Sway amplitudeYP Sway phaseZA Heave amplitudeZP Heave phaseRXA Roll amplitudeRXP Roll phaseRYA Pitch amplitudeRYP Pitch phaseRZA Yaw amplitudeRZP Yaw phase.(In these header strings X, Y and Z represent the vessel axes, 'A' denotes amplitude, 'P'denotes phase and 'R' rotation about the given axis.)

RAO Data ChecklistTo derive vessel point motions, you need to obtain data giving both RAOs and phases for thevessel for the relevant wave period. You also need to know what conventions apply to yourdata; these may be documented with the data, but sometimes you may have to deduce whatthey are. You should have answers to all the following questions:

To what point on the vessel do the data apply?

This is the RAO origin and is often the vessel centre of gravity, but you need to be sure. If it isnot specified check with your data supplier.

Are the responses in dimensional or RAO form?

RAO form is the most common; data giving dimensional form would have to also give thecorresponding wave amplitudes/heights. OrcaFlex will only accept RAO form.

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In what form are the rotational roll, pitch and yaw RAOs?

Units such as degrees/metre or radians/metre almost always mean the rotational motions arerelative to waves of unit amplitude.

Very rarely, rotational RAO amplitudes are given per unit wave height (i.e. double amplitude) -check your data source. In this case you will have to divide the RAOs by 2 manually, beforeentry to OrcaFlex.

Units such as degrees/degree, radians/radian, or no units, imply rotational RAOs relative towaves of unit steepness or maximum slope. For long wave periods in deep water, the rotationalRAOs in the wave plane (e.g. pitch in head or stern seas) should tend to 1 for RAOs relative tounit maximum slope, or to pi for RAOs relative to unit steepness.

Are the phases in degrees or radians?

Unless you only have a small amount of data, this should be obvious from the range of phasevalues.

What directions are positive for surge, sway, heave, roll, pitch and yaw?

Often they are surge positive forward, sway positive to port, heave positive up, but someauthors use heave positive downwards. Roll, pitch and yaw are usually positive when clockwiseabout the positive surge, sway and heave directions.

Most data sources use right-handed axes, but not all. OrcaFlex allows complete generality in itsdata input, but you must find out how your data are defined.

To what phase time origin are the phases relative?

OrcaFlex allows you to specify that the phases to be relative to the time the wave crest ortrough passes the phase origin. The passage of the crest passed the RAO origin is the mostcommon phase time origin, but you need to check and tell OrcaFlex - see note on phaseleads/lags below.

Are the phases leads or lags?

Phase conventions are sometimes documented by giving the formula used to represent theharmonic motion. Commonly used ones are:

• A.cos(w.t - P) or A.cos(P - w.t) imply that phase P is a lag.

• cos(w.t + P') implies that phase P' is a lead.

Using sine rather than cosine in the above formulae has no effect on whether the phases areleads or lags.

Checking RAOsThe Check RAOs button on the vessel types form allows a visual check on the RAO data. For agiven draught and wave direction, it displays graphs (one for each vessel degree of freedom)showing how the RAO and phase vary with wave period.

The graphs initially show the RAOs for the currently selected draught and direction. You canswitch to other draughts and directions, either by using the navigation buttons at the bottom ofthe form to step through the data, else or by selecting from the drop-down lists. You canchange the scale of the graphs (double click on the graph and change the ranges of the axes).This is useful if the curve does not initially fit on the graph.

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0

0

R

φ

Figure: RAO Graph for Amplitude (R) and phase (φφφφ)

The graphs depicts the RAO data specified by the user for the specified RAO origin. The graphhas two parts:

• A curve showing the RAO data specified by the user as a series of points joined in order ofincreasing period. The point at the origin represents the 'short' wave (zero period) responseand always has zero amplitude (this is enforced by OrcaFlex since no vessel can respond toinfinitely fast waves). Moving along the curve away from the origin corresponds to the waveperiod increasing from zero. For surge, sway and heave, the other end of the curve is the'long' wave RAO data specified for period 'Infinity'. For roll, pitch and yaw, the RAO data forperiod 'Infinity' cannot (for technical reasons) be included in the curve, so instead the otherend of the curve is the RAO data for the largest finite period specified.

• A solid circle representing the expected long wave response limit for a freely floating vessel.This is calculated by OrcaFlex and only applies to free-floating vessels. Also the yawresponse limit only applies to slender vessels (i.e. to vessels that are long in the x-directionand narrow in the y-direction). See RAO Quality Checks for details of the expected longwave RAOs.

Warning: The expected long wave response limits calculated by OrcaFlex only apply tofree-floating vessels. Also, the yaw response limit only applies to slendervessels (i.e. to vessels that are long in the x-direction and narrow in the y-direction).

The purpose of the graph is help you check your RAO data - the curve should normally bereasonably smooth and tend towards the expected limit shown by the solid circle. See How toCheck RAO Data for details.

The graph represents RAOs as points in polar coordinates (R,φ), where:

• R is the non-dimensional amplitude. For surge, sway and heave R is the vessel motionamplitude divided by the wave amplitude. And for roll, pitch and yaw, R is the rotationalresponse normalised with respect to maximum wave slope - i.e. it is vessel rotationamplitude divided by the maximum wave slope.

• φ is the phase lag from the time the wave crest passes the RAO origin until the maximumpositive motion occurs.

Note: Positive here means as in the OrcaFlex conventions (not necessarily the sameas the vessel type RAO conventions). So positive surge is forward, positivesway is to port, positive heave is up, positive roll is starboard down, positivepitch is bow down and positive yaw is bow to port.

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This polar coordinates way of representing RAOs is better than drawing separate graphs ofamplitude and phase, since it presents all the information on a single graph and also theresulting curves are smooth, whereas phase graphs frequently show phase jumps.

How to Check RAOsFor each draught and wave direction, you should check that the curves on the RAO graphs arereasonably smooth and approach the circle, which is the expected long-wave limit for a free-floating vessel. Note that:

• The curve may not approach the expected long wave limit if the RAO data does not includevalues for any long waves. Wave periods over 20 seconds for ships, or 30 seconds forsemisubmersibles, are considered to be sufficiently long for this purpose.

• The curve might also not approach the circle if the vessel is not free-floating. For examplethe heave RAO amplitude of a tension leg platform will not approach the usual long wavelimit of 1.

• The circle on the yaw graph only applies to slender vessels (i.e. long in the x-direction andnarrow in the y-direction).

• Smooth graphs can only be expected if the data includes RAOs for reasonably closelyspaced periods.

As examples, consider the following three example graphs:

1.510.50-0.5-1-1.5

1.5

1

0.5

0

-0.5

-1

-1.5 1.510.50-0.5-1-1.5

1.5

1

0.5

0

-0.5

-1

-1.5 1.510.50-0.5-1-1.5

1.5

1

0.5

0

-0.5

-1

-1.5

The first graph shows a typical, well-behaved set of RAO data - the curve is smooth and thelong-wave limit agrees with the expected value marked by the circle.

For a freely floating vessel, the second graph is clearly in error, since the curve does not lead tothe expected long wave limit. The RAO data for long waves (represented by the end of thecurve) has the correct amplitude, but its phase differs by 180º from the expected long-wavevalue (represented by the circle). There are two likely causes - it may be that the phaselead/lag convention data has been set wrongly (this would give a phase angle sign error) or elsethat the convention data for the direction of positive motion has been set wrongly (this wouldgive a phase error of 180º).

The curve on the third graph approaches the expected long wave limit, but then suddenly goesto zero. This suggests that the RAO data for period 'Infinity' has not been set correctly and iszero.

Common Problems

It is not unusual to be given RAO data for a vessel but not be given all the conventions apply tothe data. Below are some common problems and their symptoms. But beware that severalcommon problems have very similar symptoms, so it is not possible to be sure what the problemis unless you are sure about most of the data's conventions and only unsure about one. It istherefore important to get as much information as possible from the original RAO data supplier.

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• The quoted wave direction might be measured clockwise (viewed from above) from the x-direction, rather than anticlockwise (which is the OrcaFlex convention). The effect would bea 180 degree shift in the sway, roll and yaw phases.

• The quoted wave direction may be the direction the wave is coming from, rather than thedirection it is progressing towards (which is the OrcaFlex convention). The effect would beto negate all the phase values.

• The phases may be leads instead of lags (OrcaFlex will accept either - see RAO PhaseConventions). The effect of an error here would be to negate all the phase values.

7.5.4 Modelling Vessel Slow DriftWhen a vessel is exposed to waves it experiences wave loads that can be split into first orderand second order terms. The first order terms generate motion at wave frequency and this ismodelled in OrcaFlex using RAOs. The second order terms are much smaller but they includeloads with a much lower frequency. These low frequency terms are called the wave drift loadsand they can cause significant slow drift motions of the vessel if their frequencies are close to anatural frequency of the vessel.

One common situation where the wave drift loads can matter is with a moored vessel. Thevessel's natural frequencies in surge, sway and yaw are typically quite low and so the lowfrequency wave drift loads can generate quite significant slow drift excursions.

If you have already calculated the vessel slow drift motion then that motion can be applied inOrcaFlex using harmonic motion or a time history file. But OrcaFlex can calculate and apply theslow drift motion for you. To do this you need to do the following:

• Specify QTF data on the wave drift tab of the vessel type form. The wave drift loads arecalculated based on this data.

• Specify the vessel centre of gravity, mass, moments of inertia, added mass and dampingproperties. This data is on the Inertia and Damping tab on the vessel type form.

• Specify appropriate data for the hydrodynamic and wind drag loads, any applied load, etc.

• Set the vessel's primary motion to Calculated. This tells OrcaFlex to apply the mean wavedrift load to the vessel during the static analysis, and then in the simulation to apply the timevarying wave drift load and calculate the low frequency vessel surge, sway and yaw motionthat results from these and other loads. The 'other loads' referred to here are any specifiedhydrodynamic or wind drag, loads from added mass or damping, applied loads and loadsfrom any lines or other objects that are connected to the vessel.

• Set the vessel's superimposed motion according to whether and how you want to model firstorder wave frequency motion.

In the dynamic simulation OrcaFlex will then calculate all the loads on the vessel and theresulting slow surge, sway and yaw motion.

Damping Effects on Vessel Slow Drift

Drag and damping loads have an important effect on vessel slow drift motions. The followingdiscussion documents the various damping effects and how they are modelled in OrcaFlex.See CMPT (1998) section 3.12.

• Hydrodynamic drag and skin friction on the vessel hull. This is modelled in OrcaFlexusing a combination of the OCIMF approach plus a yaw drag moment proportional to (yawrate)^2. See the Hydrodynamic Drag data on the vessel type data form. For details of the

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theory see Vessel Theory: Drag Loads. Note that OrcaFlex does not yet have thedependency of yaw drag on sway velocity proposed by Wichers, 1979.

• Wind drag on the vessel hull. This is the aerodynamic drag due to wind and any vesselvelocity. It is modelled in OrcaFlex based on the OCIMF approach. See the Wind Dragdata on the vessel type data form. For details of the theory see Vessel Theory: Drag Loads.

• Hydrodynamic drag on the risers/moorings. This is modelled in OrcaFlex by the dragforce part of the Morison force on the lines that model the risers/moorings.

• Wave radiation damping. This is not usually very significant at low frequencies, becausethe asymptotic limit of the wave frequency damping is zero. It can be modelled in OrcaFlexusing the damping matrix on the vessel type form.

• Wave drift damping. This arises because the wave drift loads vary with vessel velocity. Itcan be modelled in OrcaFlex by including it in the damping matrix on the vessel type dataform. See CMPT (1998) page 3-78 and Faltinsen (1990) page 161.

• Material damping in the risers/moorings. This is the structural damping in the material ofthe risers and mooring lines. This can be modelled in OrcaFlex by the line target dampingvalue. However Triantafyllou et al (1994) concluded that its effect is negligible.

• Seabed soil friction on the risers/moorings. This arises from the frictional force acting onthe part of a mooring/riser that is lifting off and touching down on the seabed. It is modelledin OrcaFlex by the friction between the seabed and the line used to model the mooring/riser.However Triantafyllou et al (1994) concluded that its effect is negligible.

7.5.5 Vessel ResultsFor details on how to select results variables see Selecting Variables.

Results Tables

The results tables report the position of the vessel, plus the loads acting on it from varioussources. The loads are labelled according to their source:

• Applied load is the sum of the local and global applied loads specified on the vessel dataform.

• Current and Wind loads are those that result from the vessel type's current and windproperties.

• Connections load is the total load from all attached lines, links, winches, solids, etc. Inmooring analysis this is therefore the mooring load if only mooring lines are attached to thevessel.

Dynamic Results

For vessels the results variables available in dynamics are as follows:

Position Results

The vessel motion is split into two components called the primary and superimposed motions.To provide both components of the motion, plus the total overall motion, OrcaFlex provides thefollowing 3 sets of positions results.

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Primary X, Primary Y, Primary Z, Heel, Trim, Heading

The primary position of the vessel, as produced by any primary motion, relative to global axes.So Primary X, Primary Y and Primary Z are the global X,Y,Z coordinates of the primary positionof the vessel origin, and Heel, Trim and Heading are the primary orientation of the vessel, againrelative to global axes.

Trim is in the range -90 to +90. Range jump suppression is applied to Heel and Heading (sovalues outside the range -360 to +360 degrees might be reported).

Surge, Sway, Heave, Roll, Pitch and Yaw

The offset of the vessel, due to any superimposed motion, relative to the primary position of thevessel. They are therefore the wave-generated part of the motion, so Surge, Sway and Heaveare the offsets from the primary position to the final position and are measured in the primaryvessel axes directions. And Roll, Pitch and Yaw are the wave-generated rotations and arerelative to the primary vessel axes directions.

Pitch is in the range -90 to +90. Range jump suppression is applied to the Roll and Yaw angles(so values outside the range -360 to +360 degrees might be reported).

X, Y, Z, Rotation 1, Rotation 2 and Rotation 3

The position of the vessel, relative to global axes, due to the combination of the primary andsuperimposed motion. So X, Y and Z are the global coordinates of the final vessel originposition and Rotation 1, 2 and 3 define the final orientation relative to global axes. The 3rotations (called Euler angles) are 3 successive rotations that take the global axes directions tothe final axes directions.

Rotation 2 is in the range -90 to +90. Range jump suppression is applied to the Rotation 1 andRotation 3 angles (so values outside the range -360 to +360 degrees might be reported).

Force and Moment Results

Force, Lx-Force, Ly-Force and Lz-ForceMoment, Lx-Moment, Ly-Moment and Lz-Moment

The magnitude and components (in vessel axes directions) of the total force and momentexerted on the vessel. The moments are about the vessel origin.

These results include applied loads and drag loads and loads from any objects connected to thevessel. If the Primary Motion of the vessel is set to Calculated, then they also include the wavedrift loads and the damping loads. They do not include weight and buoyancy loads.

Multiple Static Results

For multiple statics calculations the results variables available are as follows. The loadsreported are the total loads, including those from current, wind, applied loads and attached linesand other objects.

Restoring Force

The magnitude of the horizontal component of the total force applied to the vessel. Note thatthis force is not necessarily in the offset direction.

Vertical Force

The vertically downwards component of the total force applied to the vessel.

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GZ-Moment

The total moment, about the vertical, applied to the vessel.

Worst Tension

The largest tension in any segment of any Line connected to the Vessel.

7.6 3D BUOYS

7.6.1 3D BuoysOrcaFlex 3D Buoys are simplified point elements with only 3 degrees of freedom -X,Y and Z.They do not rotate, but remain aligned with the global axes. They therefore do not haverotational properties and moments on the buoy are ignored. They should therefore be usedonly where these limitations are unimportant.

3D Buoys are able to float part-submerged at the surface, and may also be used independently,with no lines attached. Although they are much less sophisticated than 6D Buoys, 3D Buoysare easier to use and are convenient for modelling buoys at line junctions etc.

B

yz

x

height/2

height/2

Buoy Axesalways aligned

with Global Axes

Figure: 3D Buoy

7.6.2 DataName

Used to refer to the 3D Buoy.

Included in Static Analysis

Determines whether the equilibrium position of the buoy is calculated by the static analysis.See Buoys Included in Static Analysis.

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Mass

Mass or weight in air.

Volume

Used to calculate buoyancy and added mass.

Bulk Modulus

Specifies the compressibility of the buoy. If the buoy is not significantly compressible, then theBulk Modulus can be set to Infinity, which means "incompressible". See Buoyancy Variationwith Depth.

Height

Used to model floating buoys correctly, where the buoyancy, drag etc. vary according to thedepth of immersion. It also determines the height used to draw the buoy. The Height is thevertical distance over which the fluid-related forces change from zero to full force as the buoypierces the surface. It is taken to be symmetrical about the buoy's origin.

Initial Position

Specifies the initial position for the buoy origin as coordinates relative to the global axes. If thebuoy is not included in the static analysis then this initial position is taken to be the staticposition of the buoy. If the buoy is included in the static analysis, then this initial position is usedas an initial estimate of the buoy position and the statics calculation will move the buoy from thisposition iteratively until an equilibrium position is found. See Include Buoys in Static Analysis.

Drag

Drag forces are applied in each of the global axes directions OX, OY and OZ. For eachdirection you must specify a Drag Coefficient and Drag Area.

Added Mass

You must specify the added mass coefficient Ca for each global axis direction. The addedmass is set to be Ca multiplied by the mass of water currently displaced. The inertia coefficient,Cm, is set automatically to equal 1+Ca.

7.6.3 ResultsFor details on how to select results variables see Selecting Variables.

For 3D Buoys the available variables are:

X,Y and Z

Positions of the buoy origin, relative to global axes.

Surface Z

Elevation of the sea surface directly above the instantaneous position of the buoy origin.

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Dry Length

Length of buoy above the water surface, measured along the buoy z axis. For this purpose, thez-extent of a 3D buoy is assumed to be ½ Height either side of its volume centre.

7.7 6D BUOYS

7.7.1 6D Buoys6D Buoys are objects having all six degrees of freedom - 3 translational (X,Y and Z) and 3rotational (Rotation 1,2 and 3). The forces acting on a buoy are mass, buoyancy, added massand damping and drag in the three principal buoy directions. Corresponding moments areapplied for the rotational degrees of freedom. Buoys can be surface-piercing, and have anotional height; this allows the hydrostatic and hydrodynamic forces to be proportioneddepending on the depth of immersion.

6D Buoys can have wings attached to them. A wing is a rectangular surface, attached to thebuoy at a specified position and orientation, which experiences lift and drag forces, and amoment, due to the relative flow of the sea past the wing.

Lines attached to a 6D Buoy can thus experience both moment effects and translations as thebuoy rotates under the influence of hydrodynamics and applied loads. Lines can be attached toan offset position on a buoy - this allows the direct study of line clashing, including theseparation introduced by spaced attachment points.

Three types of 6D Buoy are available, the differences being the way in which the geometry ofthe buoy is defined.

Lumped Buoys

The first type, Lumped Buoys, are specified without reference to a specific geometry. Thisnecessarily restricts the accuracy with which interactions with the water surface are modelled.Where a lumped buoy pierces the surface it is treated for buoyancy purposes as a simplevertical stick element with a length equal to the specified height of the buoy (thus buoyancychanges linearly with vertical position without regard to orientation). This model does notprovide the rotational stiffness that would be experienced by most surface piercing buoys.

Interactions with the seabed and with shapes are also modelled in a fairly simple manner, andfriction effects are not included. Arbitrary hydrodynamic and physical properties are modelledby deriving equivalent terms which are applied at the centre of mass.

Spar Buoys

The second type, called Spar Buoys, are intended for modelling axi-symmetric buoys whoseaxis is normally vertical, particularly where surface piercing effects are important (such as for aCALM buoy).

Spar Buoys are modelled as a series of co-axial cylinders mounted end to end along the local z-axis (see Spar Buoy and Towed Fish Properties). This allows you to provide some informationabout the buoy geometry, by specifying the number of cylinders and their lengths anddiameters. A conical or spherical shape can be approximated as a series of short cylinders ofgradually increasing or diminishing diameter.

Spar Buoys model surface-piercing effects in a much more sophisticated way than Lumpedbuoys. Effects such as heave stiffness and righting moments in pitch and roll are determined bycalculating the intersection of the water surface with each of the cylinders making up the buoy,allowing for the instantaneous position and attitude of the buoy in the wave. However note that

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OrcaFlex does not calculate radiation damping (a linear damping term resulting from thecreation of surface waves as the buoy oscillates) or impact loads (slamming).

Because they are modelled as a stack of concentric cylinders, Spar Buoys are often not suitablefor fully submerged objects with more complex geometries.

As with Lumped Buoys, the modelling of seabed interaction is simplistic and friction effects arenot included.

Hydrodynamic loads on Spar Buoys are calculated using Morison’s equation. Added mass anddrag forces are applied only to those parts of the buoy which are in the water at the time forwhich the force is calculated. For partly immersed cylinders, added mass and drag areproportioned according to the fraction of the cylinder which is immersed. The use of Morison’sequation implies that the buoy diameter is small compared to the wavelength (usually the casefor CALM buoys and the like) but means that some load terms are not represented.

Towed Fish

The third type, called Towed Fish, are intended for modelling bodies, such as towed fish,whose principal axis is normally horizontal. Towed Fish buoys are identical to Spar Buoysexcept that the stack of cylinders representing the buoy is laid out along the x-axis of the buoy,rather than along the z-axis.

7.7.2 Wings6D buoys can have a number of wings attached; these are useful for representing lift surfaces,diverters etc. Each wing has its own data and results available.

A wing is a rectangular surface, attached to the buoy at a specified position and orientation,which experiences lift and drag forces, and a moment, due to the relative flow of the sea pastthe wing. Wings do not have any mass, added mass or buoyancy associated with them; anymass, added mass or buoyancy due to wings should be added into the properties specified forthe buoy itself.

The drag force on a wing is the force applied in the direction of relative flow. The lift force is theforce at 90º to that direction. The moment represents the moment (about the wing centre) thatarises due to the fact that the centre of pressure may not be at the wing centre. These loadsare applied at the wing centre and are specified by giving lift, drag and moment coefficients as afunction of the incidence angle α between the relative velocity vector and the wing plane.

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Wy

Wx

Span

ChordWz

PrincipalWing Axis

RelativeVelocityVector V

α

+ve lift

-ve lift

W

Figure: Wing Model

Each wing has its own set of local wing axes, with origin W at the wing centre and axes Wx, Wyand Wz. Wy is normal to the wing surface and points towards the positive side of the wing; thepositive side of a wing is the side towards which positive lift forces act. Wx and Wz are in theplane of the wing and Wz is the primary axis of the wing - it is the axis about which the wing canbe pitched. The wing is therefore a rectangle in the Wxz plane, centred on W. We refer to itslength in the Wz direction as its span and its width in the Wx direction as its chord.

If the wing is not completely submerged, then the forces and moments applied by OrcaFlex arescaled down according to the proportion of the wing area that is below the surface. However,note that the true effects of breaking surface, for instance planing and slamming, are muchmore complex than this and are not modelled.

7.7.3 Common DataAll types of 6D Buoy use a local coordinate system with the origin at the centre of gravity. Thefollowing data items are common to all types.

Name

Used to refer to the 6D Buoy.

Type

Three types of buoy are available: Lumped Buoys, Spar Buoys and Towed Fish.

Connection

A 6D Buoy can either be Free, Fixed or connected to a Vessel or a Line (provided that lineincludes torsion).

• If the buoy is Free then it is free to move in response to wave loads, attached lines etc. Inthis case the buoy's Initial Position and Attitude are specified relative to global axes.

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• If the buoy is Fixed then it cannot move. Its Initial Position and Attitude are specifiedrelative to global axes.

• If the buoy is connected to a Vessel or a Line, then it is rigidly connected to that object andso moves and rotates with it. All resulting forces and moments on the buoy are transmittedto the object. In this case the buoy's Initial Position and Attitude are specified relative to theobject to which it is connected.

Initial Position and Attitude

Specifies the initial position of the buoy origin (which must be the centre of gravity) and its initialorientation.

If the buoy is Free or Fixed then its initial position is specified by giving the X, Y and Zcoordinates of the buoy origin B, relative to the global axes. And its initial orientation isspecified by giving 3 angles Rotation 1, Rotation 2, Rotation 3, which are successive rotationsthat define the orientation of the buoy axes Bxyz, relative to global axes, as follows. First alignthe buoy with global axes, so that Bxyz are in the same directions as GXYZ. Then applyRotation 1 about Bx (=GX), followed by Rotation 2 about the new By direction, and finallyRotation 3 about the new (and final) Bz direction.

If a Free buoy is not included in the static analysis then this initial position is taken to be thestatic position of the buoy. If the buoy is included in the static analysis, then this initial positionis used as an initial estimate of the buoy position and the static analysis will move and rotate thebuoy from this position until an equilibrium position is found. See Degrees of Freedom Includedin Static Analysis.

If the buoy is connected to a Line, then the Initial Position and Attitude specify where on the lineit is connected, and with what orientation, as follows:

• The Initial Position z-coordinate specifies the arc length at which the buoy should beconnected to the line. The buoy will be connected to the nearest node to that arc length.

• The buoy will be connected to that node, but with an offset relative to that node's axes thatis given by (x, y, 0).

• The buoy orientation relative to the node axes is specified by the Initial Attitude angles.

Degrees of Freedom Included in Static Analysis

Determines which degrees of freedom are calculated by the static analysis (see Buoy Degreesof Freedom Included in Static Analysis). This data item only applies to Free buoys and it can beset to one of:

• None: the buoy position and orientation are not calculated by the static analysis - they aresimply set to the initial position and orientation specified on the buoy data form.

• X,Y,Z: the buoy position is calculated by the static analysis, but its orientation is simply setto the initial orientation set on the buoy data form.

• All: the buoy position and orientation are calculated by the static analysis.

Normally this data item should be set to All so that the static analysis calculates the trueequilibrium position and orientation of the buoy. However it is sometimes useful to fix the buoyposition or orientation, for example if the static analysis is unable to find the equilibrium positionor orientation.

Mass

Mass or weight in air.

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Moments of Inertia

The solid moments of inertia of the buoy about its local x, y and z axes.

Bulk Modulus

Specifies the compressibility of the buoy. If the buoy is not significantly compressible, then theBulk Modulus can be set to Infinity, which means 'incompressible'. See Buoyancy Variation withDepth for details.

7.7.4 Applied LoadYou can apply to the buoy an external Global Load that does not rotate if the buoy rotates. Thisis specified by giving the components of Applied Force and Applied Moment relative to globalaxes. These components remain constant, so if the buoy rotates then the load does not rotatewith it.

In addition, you can specify an external Local Load that does rotate with the buoy. This isspecified by giving the components of Applied Force and Applied Moment relative to buoy axes.Again these components remain constant, so if the buoy rotates then the load does rotate withit. This is suitable for modelling thrusters, for example.

In both cases the Point of Application of the load is specified by giving its x,y,z coordinatesrelative to buoy axes.

7.7.5 Wing Data6D buoys can have a number of wings attached, each having its own data and type.

Name

Used to refer to the wing.

Span

The length of the wing, in the local Wz direction.

Chord

The width of the wing, in the local Wx direction.

Centre of Wing

The position of the centre of area of the wing, relative to buoy axes.

Orientation

The orientation of the wing is specified by giving 3 angles - azimuth, declination and gamma -relative to the buoy axes. The angles can either be fixed or vary with simulation time. If theyare variable then linear interpolation is used for times between those specified in the variabledata table, and truncation is used for times beyond those specified in the table.

The angles define the orientation of the local wing axes relative to the buoy axes as follows:

• Start with the wing axes Wxyz aligned with the buoy axes Bxyz and then rotate Wxyz aboutBz by the azimuth angle. This leaves Wz aligned with Bz but Wx now points in the directiontowards which the declination is to be made.

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• Now rotate by the declination angle about the new direction of Wy. This declines Wz downinto its final direction, i.e. Wz now points along the direction whose azimuth and declinationangles are as specified.

• Finally rotate by the gamma angle about this final Wz direction. This is a rotation about theprincipal wing axis, so it allows you to adjust the pitch of the wing.

For each of these rotations, positive angles mean clockwise rotation and negative angles meananti-clockwise rotation, when looked at along the axis of rotation.

When setting these orientation angles, it is easiest to first set the azimuth and declination valuesto give the desired Wz-direction. This is the direction of the axis about which the wing pitch isset. Then set gamma to give the correct pitch of the wing. This process is best done with theDraw Local Axes option set on (see the View menu or the Tools|Preferences menu) since thewing axes are then visible on the 3D view and you can check that the resulting orientation iscorrect.

Wing Type

Determines the properties of the wing. You can define a number of wing types - click the "WingTypes" button to access the wing types data form.

7.7.6 Wing Type Data6D buoys can have a number of wings attached, each having its own data and type.

Name

Used to refer to the wing type.

Wing Type Properties

The properties of each wing type are specified by giving a table of lift, drag and momentcoefficients as a function of the incidence angle of the flow relative to the wing. A "Graph"button is provided - this displays a graph of the 3 coefficients so that you can visually checkyour data.

Incidence Angle

The incidence angle is the angle, α, that the relative flow vector makes to the wing surface.This equals 90º minus the angle between Wy and the relative flow vector.

The incidence angle is always in the range -90º to +90º, where positive values mean that theflow is towards the positive side of the wing (i.e. hitting the negative side) and negative valuesmean that the flow is towards the negative side of the wing (i.e. hitting the positive side).

The incidence angles in the table must be given in strictly increasing order and the table mustcover the full range of incidence angles, so the first and last angle in the table are set to -90ºand +90º and cannot be changed. Linear interpolation is used to obtain coefficients over thecontinuous range of angles.

Note: The wing lift, drag and moment are assumed to only depend on the incidenceangle, not on the angle of attack in the wing plane. OrcaFlex will therefore usethe same lift, drag and moment coefficients for flow (with the same incidenceangle) onto the front, the side or the back of the wing, even though your datamay only apply over a limited range of in-plane attack angles. You can checkthat the angle of attack in the wing plane stays within the range of your data byexamining the Beta angle result variable.

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Lift Coefficient

The lift coefficient Cl(α) defines the lift force applied to the wing, as a function of incidence angleα. The lift coefficients can be positive or negative and the lift force is given by:

Lift Force = ½.Cl(α).ρ.A.V²

where ρ is the water density, A is the area of wing that is under water at the time and V is therelative flow velocity at the wing centre. The lift force is applied at the wing centre, along theline that is at 90º to the relative flow vector and in the plane of that vector and Wy. For α= ±90ºthis line is ill-defined and the lift coefficient must be zero. Positive lift coefficients means liftpushing the wing towards its positive side.

Drag Coefficient

The drag force is defined by the drag coefficient Cd(α) using the formula:

Drag Force = ½.Cd(α).ρ.A.V²

where ρ is the water density, A is the area of wing that is under water at the time and V is therelative flow velocity. The drag coefficient cannot be negative, so the drag force is always in therelative flow direction.

Moment Coefficient

The moment coefficient Cm(α) defines a moment that is applied to the wing. This momentrepresents the fact that the position of the centre of pressure may depend on the incidenceangle α.

The moment coefficients can be positive or negative and the moment is given by:

Moment = ½.Cm(α).ρ.A.V².Chord

where ρ is the water density, A is the area of wing that is under water at the time and V is therelative flow velocity.

This moment is applied about the line that is in the wing plane and is at 90 degrees to therelative flow vector. For α = ±90º this line is ill-defined and the moment coefficient must bezero. Positive moment coefficients mean that the moment is trying to turn the wing to bring Wyto point along the relative flow direction. Negative moment coefficients mean the moment triesto turn the wing the opposite way.

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7.7.7 Lumped Buoy Properties

pitch

roll

z (heave)

y (sway)

x (surge)B(centre of gravity)

yaw

Vertices

Figure: Lumped Buoy

For a Lumped Buoy the forces and moments are calculated as follows (ρ is water density, g isacceleration due to gravity). Each degree of freedom is calculated independently.

Geometry

Volume is the total volume of the buoy, with its centre at the Centre of Volume, definedrelative to the local buoy axes Bxyz.

Height is the buoy vertical dimension, assumed equally spaced about the centre of volume.Height is assumed to be independent of buoy rotation.

To allow for interaction with the water surface "Proportion Wet", PW, is defined such that:

PW = 1.0 when the centre of volume is Height / 2 or more below the water surface,P = 0.0 when the centre of volume is Height / 2 or more above the water surface.

Between these two limits, PW varies linearly with immersion.

Wetted volume is then given by PW . Volume.Centre of wetted volume is a distance Height . (1-PW) / 2 below Centre of Volume.

Hydrostatic and hydrodynamic forces are applied at the centre of wetted volume.

Warning: For Lumped Buoys, since OrcaFlex has no information regarding the actualbody geometry, there is no contribution to roll and pitch stiffness from freesurface effects when the buoy pierces the surface. Static stability of a floatingbuoy is therefore not correctly represented.

Damping

Hydrodynamic damping forces and moments may be applied to the buoy. These are loads thatare directly proportional to the relative velocity, or angular velocity, of the sea past the buoy.For each of the local buoy axes directions, you specify the magnitude of the Unit Force that isapplied when the relative velocity is 1 length unit/second. OrcaFlex then scales thesemagnitudes according to the actual relative velocity and applies the resulting force or moment.Similarly you can specify a Unit Moment that is applied when the relative angular velocity is1 radian/second.

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Drag

Hydrodynamic drag forces and moments may be applied to the buoy. These are loads that areproportional to the square of the relative velocity, or angular velocity, of the sea past the buoy.

The drag force properties are specified by giving, for each of the local buoy axes directions, theDrag Area that is subject to drag loading in that direction and the corresponding DragCoefficient.

Drag moment properties are specified in a similar way, except that instead of specifying a dragarea you must specify a Moment of Area.

Note: Drag Area Moment is the 3rd absolute moment of drag area about the axis.Separate Cd values are given for force and moment calculations.

Fluid Inertia

Fluid inertia properties are those that are proportional to the acceleration of the sea and thebuoy. These accelerations have two main effects. Firstly, they result in forces and momentsbeing applied to the buoy - these are referred to as the fluid acceleration loads. Secondly, thebuoy experiences an increase in inertia - this is known as the added mass. These propertiesare specified separately for translational and rotational motions and also separately for eachlocal axis direction.

The translational fluid inertia properties of the buoy are specified, for each of the local buoy axisdirections, by giving a reference Hydrodynamic Mass together with the two inertia coefficients,Ca and Cm.

The translational Hydrodynamic Mass values can be set to '~', meaning equal to the fullysubmerged displaced mass.(= volume x water density). This is often a convenient referencemass to use.

Ca determines the amount of added mass that is added to the buoy in that direction - it equalsCa multiplied by the reference Hydrodynamic Mass for that direction.

Cm determines the fluid acceleration force that is applied in that direction. It equals:

Cm . Hydrodynamic Mass . Af

where Af is the component, in that direction, of the fluid acceleration at the buoy.

Just as translational relative acceleration of the sea past the buoy gives rise to added mass andfluid inertia forces, so rotational relative acceleration of the sea past the buoy gives rise toadded rotational inertia and fluid inertia moments. The rotational fluid inertia properties of thebuoy are specified in the same way as for the translational properties, except that a referencemoment of inertia is specified, instead of a reference mass.

7.7.8 Lumped Buoy Drawing DataVertices and Edges

This defines a "wire frame" representation of the buoy. The data layout and interpretation is thesame as for Vessels. The wire frame representation of the buoy is used to draw the buoy and isalso used to calculate the interaction of the buoy with shapes and the seabed.

The vertices are also used in calculating the interaction of the buoy with shapes and theseabed. See 6D Buoy Theory for details.

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7.7.9 Spar Buoy and Towed Fish Properties

Cylinder 1 Diameter

Buoy Axis

Stack Base Position

Cylinder 1 Length

pitch

z (heave)

y (sway)

x (surge)(centre of gravity) B

yaw

roll

Figure: Spar Buoy

The figure above shows the geometry of a Spar Buoy. The geometry of a Towed Fish isidentical except that the buoy axis is aligned with the x-axis of the buoy.

If you are modelling a CALM or SPAR buoy then see also Modelling a Surface-Piercing Buoy.

The following data items apply to Spar Buoys and Towed Fish.

Stack Base Centre Position

The centre of base of the stack, relative to buoy axes. Note that the centre of gravity of thebuoy must be at the origin of the buoy axes, so this data positions the stack relative to thecentre of gravity.

Munk Moment Coefficient

Slender bodies in near-axial flow experience a destabilising moment called the Munk moment.This effect can be modelled by specifying a non-zero Munk moment coefficient.

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Cylinders

The cylinders are numbered from the top downwards. So in the tables on the buoy data formthe cylinder at the base of the stack (lowest x or z) appears at the bottom of the table.

Diameter and Length

The diameter of the cylinder and its length measured along the axis.

These parameters define the buoy geometry from which buoyancy forces and moments aredetermined. When the buoy pierces the water surface, OrcaFlex allows for the angle ofintersection between the sea surface and the buoy axis when calculating the immersed volumeand centre of immersed volume, and includes the appropriate contributions to static stability.

The remaining parameters determine the hydrodynamic loads acting on each cylinder. Loadsare calculated for each cylinder individually, then summed to obtain the total load on the buoy.

Drag Forces and Moments

Drag loads are the hydrodynamic loads that are proportional to the square of fluid velocityrelative to the cylinder. For details of the drag load formulae see 6D Buoys: Spar Buoy andTowed Fish Theory. For information when modelling a SPAR of CALM buoy see Modelling aSurface-Piercing Buoy.

The drag forces are calculated on each cylinder using the "cross flow" assumption. That is, therelative velocity of the sea past the cylinder is split into its normal and axial components andthese components are used, together with the specified drag areas and coefficients, to calculatethe normal and axial components of the drag force.

The drag forces are specified by giving separate Drag Area and Drag Coefficient values forflow in the normal direction (local x and y directions) and in the axial direction (local z direction).The Drag Area is a reference area that is multiplied by the Drag Coefficient in the drag forceformula. You can therefore use any +ve Drag Area that suits your need, but you then need togive a Drag Coefficient that corresponds to that specified reference area.

The Drag moments are specified and calculated in a similar way to the drag forces, except thatthe reference drag area is replaced by a reference Area Moment. This and the DragCoefficient are multiplied together in the drag moment formula, so again you can use any +veArea Moment that suits your need, providing you then specify a Drag Coefficient thatcorresponds to the specified Area Moment.

There are two alternative methods that you can adopt when specifying the drag data. The firstmethod is to set the OrcaFlex data to get best possible match with real measured results for thebuoy (e.g. from model tests or full scale measurements). This is the most accurate method, andwe recommend it for CALM and discus buoys - see Modelling a Surface-Piercing Buoy fordetails. Because the Drag Area and Drag Coefficient data are simply multiplied together, youcan calibrate the model to the real results by fixing one of these two data items and thenadjusting the other. For example, you could set the axial Drag Coefficient to 1 and adjust theaxial Drag Area until the heave response decay rate in the OrcaFlex model best matches themodel test results. Or, you could set the axial Drag Area to a fixed value (e.g. 1 or someappropriate reference area) and then adjust the axial Drag Coefficient until the heave responsedecay rate in OrcaFlex best matches the model test results.

The second method is to set the drag data using theoretical values or given in the literature. Itis less accurate but can be used if you cannot get any real buoy results against which tocalibrate. To use this method, set the data as follows.

Set the Drag Areas to the projected surface area that is exposed to drag in that direction andthen set the Drag Force Coefficients based on values given in the literature (see Barltrop &

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Adams, 1991, Hoerner,1965 and DNV, 1991). Note that the drag area specified should be thetotal projected area exposed to drag when the buoy is fully submerged, since OrcaFlex allowsfor the proportion wet in the drag force formula. For a simple cylinder of diameter D and lengthL the total projected drag area is D.L for the normal direction and (π.D^2)/4 for the axialdirection, but if the buoy has attachments that will experience drag then their areas must also beincluded.

Set the Drag Area Moments to the 3rd absolute moments of projected area exposed to drag inthe direction concerned; see Drag Area Moments for details. And then set the Drag MomentCoefficients based on values given in the literature.

Added Mass

Translational added mass effects are calculated using the displaced mass as the referencemass for each cylinder. Separate added mass coefficients are given for flow normal (x and ydirections) and axial (z direction) to the cylinder.

Rotational added inertia is specified directly (so no reference inertia is involved). Separatevalues can be given for rotation about the cylinder axis and normal to that axis.

See Spar Buoy Theory.

Damping Forces and Moments

Damping forces and moments are the hydrodynamic loads that are proportional to fluid velocity(angular velocity for moments) relative to the cylinder. They are specified by giving the UnitDamping Force and Unit Damping Moment for the normal and axial directions. These specifythe force and moment that the cylinder will experience, in that direction, when the relative fluidvelocity (angular velocity for moments) in that direction is 1 unit. See Damping Forces andMoments for details.

7.7.10 ResultsFor details on how to select results variables see Selecting Variables.

6D Buoy Results

For 6D Buoys the available variables are:

X, Y and Z

The position of the buoy origin, relative to global axes.

Rotation 1, Rotation 2 and Rotation 3

Define the orientation of the buoy relative to global axes. They are 3 successive rotations thattake the global axes directions to the buoy axes directions. See Initial Position and Attitude forthe definition of these angles.

Rotation 2 is in the range -90 to +90. Range jump suppression is applied to Rotation 1 andRotation 3 (so values outside the range -360 to +360 degrees might be reported).

Surface Z

Elevation of the sea surface directly above the instantaneous position of the buoy origin.

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Dry Length

The length of buoy above the water surface, measured along the buoy z axis, calculated asfollows:

• For a Lumped Buoy, this is calculated by assuming that the z-extent of a Lumped Buoy is½ Height either side of its volume centre.

• For a Spar Buoy it is the sum of the dry lengths of each of its cylinders, where the dry lengthof an individual cylinder is calculated as

(cylinder length) . (submerged volume of cylinder) / (total volume of cylinder).

Connection Force, Connection Moment

Connection x-Force, Connection y-Force, Connection z-Force

Connection x-Moment, Connection y-Moment, Connection z-Moment

These connection load results are only available for buoys that are connected to other objects.They report the total force and moment applied to the buoy by the object to which it isconnected.

Connection Force and Connection Moment report the magnitudes of the connection loads(they are therefore always non-negative). The other results report the components of theconnection force and moment in the buoy axes directions.

These connection force and moment results include the inertial load on the buoy due to anyacceleration of the object to which it is attached. This means that these results can be used forsea fastening calculations, by using a 6D buoy to model the object to be fastened and thenattaching it to a vessel. The connection force and moment include the weight of the buoy andthe inertial loads due to the vessel acceleration. Note that if the vessel motion is specified by atime history then the time history interpolation method used is important since it affects thecalculation of vessel acceleration and hence affects the inertial loads.

Wing Results

If the 6D buoy has wings attached then for each wing the following results are available.

Wing X, Wing Y, Wing Z

The position of the wing origin, relative to global axes.

Wing Azimuth, Declination and Gamma

The orientation angles of the wing, relative to the buoy.

Lift

The lift force applied to the wing. This is applied at 90º to the relative flow direction and positivevalues mean a force trying to push the wing towards its positive side, negative values towardsits negative side.

Drag

The drag force applied to the wing. This is applied in the relative flow direction and is alwayspositive.

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Moment

The moment applied to the wing. This is applied about the line that is in the wing plane and at90º to the relative flow direction. Positive values are moments trying to turn the wing to bringWy to point along the relative flow direction; negative values are moments trying to turn the wingthe opposite way.

Incidence Angle

The angle, α, that the relative flow vector makes with the plane of the wing, in degrees in therange -90 to +90. Positive values mean that the flow is towards the positive side of the wing(i.e. hitting the negative side) and negative values mean that the flow is towards the negativeside of the wing (i.e. hitting the positive side).

Beta Angle

The angle of the relative flow direction, measured in the wing plane. More specifically, it is theangle between wing Wx axis and the projection of the relative flow vector onto the wing plane,measured positive towards Wz. Zero beta angle means that this projection is in the Wxdirection, 90º means it is along Wz and -90º means it is along the negative Wz direction.

Range jump suppression is applied to the Beta Angle (so values outside the range -360 to +360degrees might be reported).

7.7.11 Buoy Hydrodynamics3D and Lumped 6D buoys are generalised objects for which no geometry is defined in the dataother than a value of 'height': this is used only for proportioning hydrodynamic properties whenthe object is partially immersed, and for drawing a 3D buoy.

Since the geometry of the object is undefined, it is necessary to define properties such asinertias, drag areas, added masses, etc. explicitly as data items. This can be a difficult task,especially where a 6D buoy is used to represent a complex shape such as a midwater arch ofthe sort used to support a flexible riser system.

We cannot give a simple step-by-step procedure for this task since different objects can havewidely differing geometries. As an example, the hydrodynamic properties in 6 degrees offreedom are derived for a rectangular box. This gives a general indication of the way in whichthe problem should be approached. If a 3D buoy is used, the rotational properties are not used.

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7.7.12 Hydrodynamic Properties of a Rectangular Box

O

XY

Z

x y

z

O is the centre of the box

Figure: Box Geometry

Drag areas

In X direction: Ax = y . zIn Y direction: Ay = x . zIn Z direction: Az = x . y

Drag Coefficients for Translational Motions

These are obtained from ESDU (1971), Figure 1 which gives data for drag of isolatedrectangular blocks with one face normal to the flow. The dimensions of the block are

a in the flow directionb and c normal to the flow direction (c>b).

The figure plots drag coefficient, Cx against (a/b) for (c/b) from 1 to infinity (2D flow). Cx is inthe range 0.9 to 2.75 for blocks with square corners.

Note: ESDU (1971) uses Cd for the force in the flow direction; Cx for the forcenormal to the face. For present purposes the two are identical.

Drag Properties for Rotational Motions

There is no standard data source. As an approximation, we assume that the drag forcecontribution from an elementary area dA is given by

dF = ½.ρ.V².Cd.dA

where Cd is assumed to be the same for all points on the surface.

Note: This is not strictly correct. ESDU 71016 gives pressure distributions forsample blocks in uniform flow which show that the pressure is greatest at thecentre and least at the edges. However we do not allow for this here.

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dz

Z

O

z

X

Figure: Integration for rotational drag properties

Consider the box rotating about OX. The areas Ay and Az will attract drag forces which willresult in moments about OX. For the area Ay, consider an elementary strip as shown:

For an angular velocity ω about OX, the drag force on the strip is

dF = ½.ρ.(ωz).|ωz|.Cd.x.dz

and the moment of this force about OX is

dM = ½.ρ.(ωz).|ωz|.Cd.x.dz.z = (½.ρ.ω.|ω|.Cd).x.z³.dz

Total moment is obtained by integration. Because of the V.|V| form of the drag force, simpleintegration from -Z/2 to +Z/2 gives M = 0. We therefore integrate from 0 to Z/2 and multiply theanswer by 2. The result is

M = (½.ρ.ω.|ω|.Cd).(x.z /32)

OrcaFlex calculates the drag moment by

M = (½.ρ. ω.|ω| .Cdm).(AM)

so we set

Cdm = Cd, AM = x.z /32.

This is the drag moment contribution about OX from the Ay area. There is a similar contributionfrom the Az area. Since Cd is generally different for the 2 areas, it is convenient to calculate thesum of (Cd.AM) for both, set AM equal to this value and set Cd equal to 1.

Added Mass

OrcaFlex requires the added mass and inertia contributions to the mass matrix, plus thehydrodynamic masses and inertias to be used for computation of wave forces. For each degreeof freedom (3 translations, 3 rotations), 3 data items are required. These are HydrodynamicMass in tonnes (or Inertia in tonne.m²); and coefficients Ca and Cm. Added mass is thendefined as Hydrodynamic Mass . Ca; and wave force is defined as (Hydrodynamic mass . Cm)multiplied by the water particle acceleration, aw.

On the usual assumptions intrinsic in the use of Morison's equation (that the body is small bycomparison with the wavelength), the wave force is given by (∆ + AM) . aw, where ∆ is bodydisplacement and AM is added mass. OrcaFlex calculates the wave force as Cm . HM . awwhere HM is the Hydrodynamic Mass given in the data.

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For translational motions, set HM = ∆ for all degrees freedom. Then Ca = AM/∆, Cm = 1 + Ca.For rotational motions, set HI = ∆I, the moment of inertia of the displaced mass. ThenCa = AI/∆I, Cm = 1 + Ca where AI is the added inertia (i.e. the rotational analogue of addedmass).

Translational Motion

DNV (1991), Table 6.2, gives added mass data for a square section prism accelerating along itsaxis. The square section is of side a, prism length is b, and data are given for b/a = 1.0 andover. The reference volume is the volume of the body which is the same definition we haveadopted. We can therefore use the calculated Ca without further adjustment.

Consider the X direction: Area normal to flow = Ax.

For a square of the same area, a = √(Ax).

Length in flow direction = x.

Hence b/a = x/√(Ax).

Hence Ca can be obtained from DNV (1991) by interpolation, and then Cm = 1 + Ca.

If b/a < 1.0 this approach fails and we use the data given in DNV (1991) for rectangular flatplates. If y > z, aspect ratio of the plate = y/z. Hence CA from DNV (1991) by interpolation.The reference volume in this case is that of a cylinder of diameter z, length y. Hence:

Added mass = CA.ρ.(π/4).y.z² = AMx, say

and then Ca = AMx/∆ and Cm = 1 + Ca.

Note: If y < z, then aspect ratio = z/y and reference volume = CA . ρ. (π/4) . z . y².

Rotational Motion

DNV (1991) gives no data for hydrodynamic inertia of rotating bodies. The only data for 3Dsolids we know of is for spheroids (Newman 1977). Fig 4.8 of Newman 1977 gives the addedinertia for coefficient for spheroids of varying aspect ratio referred to the moment of inertia of thedisplaced mass. We assume that the same coefficient applies to the moment of inertia of thedisplaced mass of the rectangular block.

Rotation about X

∆I = ∆(Y² + Z²)/12

Added inertia:

Using data for spheroids from Newman 1977 :

Length in flow direction = 2a = x, so a = x/2.

Equivalent radius normal to flow, b, is given by πb² = yz, so b = √(y . z/π).

Hence Ca from Newman 1977.

For b/a < 1.6

Ca can be read from the upper figure where the value is referred to the moment of inertia of thedisplaced mass. In this case no further adjustment is required.

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For b/a > 1.6

The coefficient CA is read from the lower graph in which the reference volume is the sphere ofradius b. In this case:

Ca = CA . (2 . b³)/(a . (a²+b²))

In either case, Cm = 1 + Ca.

7.7.13 Modelling a Surface-Piercing BuoySurface-piercing buoys, such as CALM buoys, SPAR buoys or meteorological discus buoys,can be modelled in OrcaFlex using the Spar Buoy version of a 6D Buoy. Despite its name, theOrcaFlex Spar Buoy can be used to model any axi-symmetric body. See the examplesimulation file CALM Buoy.SIM.

Spar Buoys have many data items available. This enables you to model a wide range ofeffects, but it also makes setting up a Spar Buoy model more complicated. To help in this taskwe describe, in this section, the approach we adopt for setting up an OrcaFlex model of asurface-piercing buoy.

1. Create a simple model containing just a Spar Buoy

Start by modelling the free-floating behaviour of the buoy, without any lines attached. Thisallows us to get the basic behaviour of the buoy correct, before complications such as mooringsetc. are introduced. We therefore set up an OrcaFlex model containing just a Spar Buoy andwith no waves or current.

Set the buoy's Applied Load to zero. This data allows you to apply extra forces and moments tothe buoy, in addition to those from any lines that you attach to it. You can use this later tomodel the wind force on the upper part of the buoy. To do this you will need to know theprojected area (i.e. the area exposed to wind) of the pipe work etc. in the upper part of the buoy.

Set the buoy's Munk Moment Coefficient to zero. This data item is only used for slender bodiesin near axial fully-submerged flow only.

Set the number of wings to zero. Wings are normally only relevant for towed fish.

Finally, we start by setting all the buoy's drag and added mass data to zero. We will set up theactual values later.

2. Set up the geometry data

The Spar Buoy has its own local coordinate system. This must have its origin at the buoycentre of gravity (CG) and must have the local z-axis pointing upwards along the axis of thebuoy. You therefore need to know the position of the centre of gravity. The buoy manufacturershould supply this information.

Set the Stack Base Position. This is the position of the centre of the bottom of the buoy, relativeto the centre of gravity. The Stack Base Position is therefore (0, 0, -h) where h is the distancefrom the bottom of the buoy to the centre of gravity.

Now set up a number of cylinders, and their lengths and diameters, in order to model the shapeof the buoy. To do this you need the dimensions of the various parts of the buoy. The buoymanufacturer should supply this information. Set the cylinder lengths and diameters so that youget the correct length and volume for each section. You can represent tapered sections by aseries of short cylinders with diameters changing progressively from one to the next.

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We recommend using a number of short cylinders, even where the buoy diameter is constantover a long length. Using more cylinders gives more accurate results, though at the cost ofreduced computation speed.

You can check your geometry data by zooming in on the buoy in a 3d view window. Turn onthe local axes so that you can check that the buoy origin (=centre of gravity) is in the correctplace.

The Bulk Modulus data item is not relevant to a surface-piercing buoy, so it can be left at thedefault value of Infinity.

3. Set up the mass and inertia data

Now set the Mass and Moments of Inertia of the buoy. The buoy manufacturer should supplythis information.

The mass equals the weight of the buoy in air. The moments of inertia are those of the buoy (inair) about its centre of gravity, as follows:

• lz = the moment of inertia about the buoy axis

• lx and ly = the moments of inertia about axes perpendicular to the buoy axis, through thecentre of gravity. Usually it is sufficient to assume that Ix = ly.

If you cannot obtain data for the moments of inertia, then they can be approximately calculatedfrom a knowledge of the masses of the various parts of the buoy, and approximately how thatmass is distributed.

4. Check the buoy floats at the correct draught

Set the Initial Position and Initial Attitude of the buoy so that the buoy is in its expectedequilibrium position. The initial position is the position of the buoy local origin, and therefore ofthe CG, and you can calculate this point's expected equilibrium position from the buoy draught,which should be available from the buoy manufacturer.

The Initial Attitude defines the initial orientation of the buoy. Set it to (0,0,0), which orients thebuoy with its axis vertical and the buoy local x,y axes aligned with the global X,Y axes.

Set the Degrees of freedom included in statics to None and then run the simulation and look atthe time history of buoy Z. If the data has been set up correctly then the buoy should havestayed basically in its initial position and attitude, with perhaps just small oscillations about thatposition.

If the buoy Z has oscillated significantly then the model's equilibrium position does not matchthe expected equilibrium position. This means that something is wrong in the data and thisneeds tracing and correcting before you proceed. You can estimate the model's equilibriumposition by looking at the mean Z position in the time history.

5. Check that the buoy is stable

Now check that the buoy is stable - i.e. that if it is pitched over to one side and released then itrights itself. In the Initial Attitude data, set the Rotation 2 value to say 10 degrees and run thesimulation. If the buoy falls over then there is something wrong with the CG position or thevolume distribution, and this must be corrected.

Note: The buoy on its own may not be intended to be stable, e.g. stability may onlybe achieved when the moorings are attached. In this case you will need tomodel the moorings in order to check stability.

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6. Set the Added Mass data

The x and y added mass coefficients can be set to 1.0, which is the standard value for acylinder in flow normal to its axis.

Added mass in the z direction should be estimated for the buoy from the published literature(DNV rules, Barltrop & Adams, 1991) and distributed between the immersed cylinders(remember that hydrodynamic loads are only applied to the immersed parts of the model).

Ideally, this data should then be checked by comparing the heave and pitch natural periods ofthe model against values obtained from model tests or full scale measurements, andadjustments made as necessary.

7. Set the drag and damping data

The best approach depends on whether the buoy is a SPAR whose length is great bycomparison with its diameter, or a surface-following Discus shape such as an oceanographicbuoy. CALM buoys are usually closer to the Discus configuration, often with a damping skirtwhich is submerged at normal draft.

Spar Buoys

Set the Drag Areas for each cylinder to the areas, of the part of the buoy which that cylinderrepresents, that are exposed to fluid drag in the direction concerned. Note that you shouldspecify the areas that are exposed to drag when the buoy is fully submerged. OrcaFlexautomatically calculates the proportion of the cylinder that is submerged and scales all the fluidloads on the cylinder using that 'proportion wet' as a factor. So if a cylinder is not submerged, oris partially submerged, then the drag loads will be scaled accordingly for you.

For a simple cylinder, of diameter D and length L, the normal drag area is D.L since that is thearea of a cylinder when viewed normal to its axis. And the axial drag area is (π.D²)/4 since thatis the area of the cylinder when viewed along its axis. However, where a cylinder isrepresenting part of the buoy that is not in reality a simple cylinder (for example, we mayrepresent the pipework and turntable on the deck of a SPAR buoy as an equivalent cylinder) orwhere the cylinder is shielded from drag by adjacent structure, then the drag areas should beset accordingly. For example, if the cylinder is shielded below by another cylinder of diameter d(less than D) then the axial drag area should be reduced by (π.d²)/4 to model that shielding.

Set the Drag Force Coefficient based on values given in the literature. For short simplecylinders fully immersed there are standard values given in the literature (see Barltrop & Adams,1991, Hoerner,1965 and DNV, 1991). However, the standard book values do not includeenergy absorption by wave-making at the free surface. Strictly, this is a linear term (forcesdirectly proportional to velocity), but in OrcaFlex this must be done by adjusting the dragcoefficients of one or more cylinders.

The Unit Damping Force data can be set to zero. If you later find that the buoy showspersistent small amplitude oscillations then you may wish to set a non-zero value to damp thisout.

Set the Drag Area Moments, Drag Moment Coefficients and Unit Damping Moment data. Forthe normal direction these data items can usually all be left as zero, providing you havesubdivided the buoy into short enough cylinders (since these terms involve a high power of L,the cylinder length). For the axial direction these data items model the yaw drag and dampingeffects, so if this is important to you then set them to model the two main sources, namely skinfriction on the cylinder surface and form drag on any protuberances on the buoy.

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Having set up this drag and damping data, it is well worth now running simulations of heave andpitch oscillations and checking that their rate of decay is reasonable and consistent with anyreal data you have available.

Discus and CALM Buoys

These types of buoy require different treatment since they have little axial extension. Instead itis their radial extension that most affects the buoy's pitch properties. As a result the axialdiscretisation of the buoy into cylinders does not capture the important effects. For example thepitch damping is often mostly due to radiation damping, i.e. surface wave generation; this isespecially important for a CALM buoy with a skirt.

To deal with this OrcaFlex offers the rotational drag and damping data, but there is littleinformation in the literature to help in setting up this data. We therefore strongly recommendthat you set the data up by calibration against real test results from model or full scale tests.The easiest information to work with are time history graphs of the buoy heave and pitch in stillwater, starting from a displaced position. This will give the heave and pitch natural periods andthe rates of decay and you can adjust the buoy's drag and damping data until you get a goodmatch with this measured behaviour.

Here is the approach we use:

• For the normal direction, set the Drag Area, Drag Force Coefficient and Unit Damping Forceas described for Spar buoys above.

• Then set the axial Unit Damping Force to zero and run a simulation that matches theconditions that existed in the real heave time history results, i.e. with the same initial Zdisplacement.

• Then adjust the axial Drag Area and Drag Force Coefficients until the OrcaFlex buoy's Ztime history matches the real time history. These two data items are simply multipliedtogether when they are used to calculate the drag force, so you can give one of the two dataitems a fixed +ve value (e.g. 1) and then adjust the other.

• The match will probably be poor in the later parts of the time history, where the heaveamplitude has decayed to small values. This is because the square law drag term isinsignificant at small amplitude and instead the damping force takes over. Therefore wenow adjust the axial Unit Damping Force to further improve the match where the amplitudeis small. You may find that this disturbs the match in the large amplitude part, in which caseyou might need to readjust the drag data.

• For the axial direction, set the Drag Area Moment, Drag Moment Coefficient and UnitDamping Moment as described for Spar buoys above.

• Then set the normal Drag Area Moment, Drag Moment Coefficient and Unit DampingMoment to best match the real pitch time history, in a similar way to that used above tomatch the heave time history.

7.8 LINES

7.8.1 LinesLines are flexible linear elements used to model cables, hoses, chains or other similar items.Lines are represented in OrcaFlex using a lumped mass model. That is, the line is modelled asa series of lumps of mass joined together by massless springs, rather like beads on a necklace.The lumps of mass are called nodes and the springs joining them are called segments. Eachsegment represents a short piece of the line, whose properties (mass, buoyancy, drag etc.)

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have been lumped, for modelling purposes, at the nodes at its ends. See the figure below,which shows an example line spanning from a Vessel to a Buoy.

End positions and no-moment directions are definedrelative to the objects to which the ends are connectedand move with those objects.

xy

z

V

x

yz

B

End B

End A

Clump

section 1(3 segments)

section 3(9 segments)

section 2(7 segments)

Figure: Line Model

The properties of a Line are specified by dividing it up into a number of consecutive sectionsthat are chosen by the user. For each section you must define its length, the Line Type ofwhich it is made and the number of segments into which it should be divided for modellingpurposes. A Line Type is simply a set of properties (for example the diameter, mass per unitlength and bend stiffness) given a name so that they can be called by that name. The LineTypes are defined separately, on the Line Types data form. This allows the same set of lineproperties to be used for a number of different sections of the line, or for different lines. There isalso a Line Type Wizard tool that helps you set up Line Types representing common structureslike chains, ropes, etc.

In addition, a number of attachments may be specified, to represent items that are connectedto the Line. For example, attachments may be used to model clump weights, drag chains orbuoyancy bags attached to the line. Two types of attachment are available - clumps (buoyancyor heavy) and drag chains.

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Each attachment attached to the Line is specified by giving the Attachment Type and the arclength, measured from end A, at which it should be attached. The attachment is then attachedto the nearest node to that arc length. Attachment Types are similar to Line Types - they aresimply named sets of attachment properties. The properties themselves are then givenseparately, on the Attachment Types data form. This allows the same set of attachmentproperties to be used for a number of different attachments.

The two ends of a Line are referred to as end A to end B and each end can be Free, Fixed,Anchored or else connected to a Vessel or Buoy. The two ends of a line are treated basicallythe same, but some aspects of the line are dependent on which end is which. In particular thenumbering of parts of a Line is always done starting at end A.

7.8.2 Line DataLine DataFor every line in the system there is a data form defining its structure and interconnection. It ison these data forms that the system is built up by connecting lines between the objects thathave been defined.

Name

Used to refer to the Line.

Include Torsion

Torsional effects can be included or ignored, for each line in the model. If torsion is includedthen the line type torsional properties must be specified. See Torsional Stiffness.

To see the line orientation visually on the 3D views, select Draw Local Axes on the View menu.OrcaFlex then draws the node axes Nxyz at each node, and these axes allow you to see howthe line is behaving torsionally.

Notes: The node axes are drawn using the node pen, specified on the line data form.

If torsion is included for a line, you must specify the torsional orientation ateach end of the line. This is done by setting the Gamma angle of the endconnections on the line data form. The Gamma angle determines thetorsional position of the line end - for details see Line End Orientation. Tocheck visually that you have the orientation you expect, select Draw LocalAxes on the View menu.

If torsion is included for a line, the static analysis should also include the effectof torsion - otherwise the simulation will start from a position that is not intorsional equilibrium and an unstable simulation may result. Torsion is onlyincluded in the "Full" statics, so Full Statics (on the line data form) is alwaysset to Yes when torsion is included.

ConnectionsThe line end connection data specifies whether the line ends are connected to other objects, theposition, angle and stiffness of the connection, and whether the end is released during thesimulation.

You can view and edit an individual line's connection data on the line's data form. Or you canview and edit the connection data for all the lines together on the Line Ends data form.

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Connect to Object

The line spans from end A to end B and each end may be connected to another object in themodel, such as a buoy or vessel, or else Fixed, Anchored or left Free.

Object Relative Position

• If the end is connected to another object this defines the coordinates of the connection pointrelative to that other object's local axes.

• If the end is Fixed this defines the coordinates of that point relative to global axes.

• If the end is Anchored this defines the X and Y coordinates of the anchor relative to globalaxes, plus the Z-coordinate relative to the seabed level at that (X,Y) position.

• If the end is Free then this defines the coordinates of the estimated equilibrium position ofthe line end, relative to global axes.

End Orientation

When a line is connected to an object, it is connected into an end fitting that is rigidly attachedto that object and you specify the orientation of this connection by giving its Azimuth,Declination and Gamma angles.

These angles define the end fitting orientation relative to the object, so for objects that rotate(e.g. vessels and 6D buoys) the fitting rotates with the object. For Fixed or Anchored ends theend orientation is defined relative to global axes. For Free ends the end orientation is not used.

Azimuth, Declination and Gamma define the end fitting orientation by specifying the directionsof the axes (Ex, Ey, Ez) of its frame of reference, where E is the end fitting origin - the point towhich the line end is connected. See Line End Orientation.

The direction of Ez is defined by specifying its Azimuth and Declination angles. Ez is the endfitting axial direction; when the end segment is aligned with Ez then no bending moment isapplied by the joint, so Ez is sometimes called the no-moment direction. Note that Ez must bespecified using the "A to B" convention, i.e. Ez is into the line at end A, but out of the line atend B.

Ex and Ey are perpendicular to Ez and they are defined by specifying the Gamma angle, whichis a rotation about Ez. The Ex and Ey directions are used for reporting results (e.g. the 2components of shear force). And if the line has torsion included and the joint twisting stiffnessis non-zero, then Ex and Ey also define the line end orientation at which no torsional moment isapplied by the joint.

The connection at a line end is modelled as a "ball-joint" with this orientation being the preferred"no-moment" orientation, i.e. the orientation of the line end that gives rise to no moment fromany rotational stiffness of the connection.

If all of the end connection stiffness values are zero, e.g. to model a ball joint that is completelyfree to rotate, then the end orientation angles have no effect on the line behaviour. The anglesthen only serve to define the local x, y and z-directions that are used to define results (e.g.shear and bend moment components, stress components, etc.) that depend on the local axesdirections.

Bending and Twisting Stiffness

The connection at a line end is modelled as a joint with the specified rotational stiffness. Therestoring moments applied by the joint depend on the deflection angle, which is the differencebetween the end fitting orientation and the orientation of the line. The end orientation istherefore the orientation of the line that corresponds to zero moment being applied by the joint.

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The connection stiffness is the slope of the curve of restoring moment against deflection angle.

The x bending and y bending values specify the connection bending behaviour for rotationabout the end Ex and Ey directions, respectively. For an isotropic ball joint the two values mustbe equal; this can conveniently be specified by setting the y-bending value to '~', meaning 'sameas x-value'. A non-isotropic ball joint can be modelled by giving different x and y bendingvalues; in this case the line must include torsion.

The x bending and y bending behaviour can either be linear or non-linear, as follows:

• For a simple linear behaviour, specify the bending stiffness to be the constant slope of thecurve of restoring moment against deflection angle.

• For a non-linear behaviour, use variable data to specify a table of restoring moment againstdeflection angle. OrcaFlex uses linear interpolation for angles between those specified inthe table, and linear extrapolation for angles beyond those specified in the table. Therestoring bend moment must be zero at zero angle.

The Twisting Stiffness value is only relevant if torsion is included for the line. It specifies therotational stiffness about the end Ez direction. For the twisting stiffness this variation is alwaysmodelled as linear so the twisting stiffness you specify should be the slope of the linear angle-moment curve.

The bending and twisting stiffness can be set to zero (free to rotate with no resistance), non-zero (can rotate but with resistance) Infinity (a rigid connection) or variable (non-linear, forbending only). Note that Infinity can be abbreviated to ‘Inf’.

A flex joint can be modelled by setting the stiffness values non-zero (and less than infinity).

Warning: Avoid specifying large connection stiffness values (except the special valueInfinity) since they require very short simulation time steps.

Release at Start of Stage

If desired each line end can be disconnected at the start of a given stage of the simulation. If norelease is wanted then set this item to "~", meaning "not applicable".

Line Ends FormThe Line Ends form allows you to view or edit the end positions and connections for all thelines, on a single form. It can be opened using the model browser or using the pop-up menu onthe individual line data forms. Similarly, the pop-up menu on the Line Ends form provides a linkto the individual line data forms.

The Sort By box allows you choose whether the form displays the line ends in Line order (i.e.both ends of first line, then both ends of second line, etc.) or End order (i.e. end A of all lines,then end B of all lines).

Positions and Connections Tabs

The Positions and Connections tabs allow you to view or edit all the connection data for the lineends. This is exactly the same data as on the individual line data forms - the only difference isthat you can view or edit the data for all the line ends on a single form. The positions areCartesian coordinates relative to the frame of reference of the object to which the line end isconnected.

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Polar Coordinates Tab

The Polar Coordinates tab provides a way of viewing or setting the positions of the line endsusing polar coordinates, relative to a choice of frames of reference. This facility is useful forcases, for example mooring arrays, where a series of line ends need to be laid out around acircle.

The polar coordinates (R, Theta, Z) are those of the line end position relative to the polarcoordinates frame of reference chosen on the form for that line end. (The Cartesiancoordinates of the line end, relative to the same reference frame, are (R.cos(Theta),R.sin(Theta), Z) ).

On the other hand, the Object Relative Position data (on the Positions tab and on the individualline data form) are the Cartesian coordinates of the line end relative to the frame of reference ofthe object to which it is connected.

OrcaFlex keeps the two sets of coordinates synchronised, so if you change one then the otheris automatically updated to match. If you change any other data then the Cartesian ObjectRelative Position coordinates are taken to be the master data and so left unchanged, and thepolar coordinates are updated to match.

You have a quite a lot of flexibility to choose what reference frame you want for the polarcoordinates. The reference frame has its origin at your chosen Reference Origin and has itsaxes are parallel to those of your chosen Reference Axes.

For the reference origin you can choose between:

• the global origin

• if one end is anchored, then the origin for anchored ends. This is the point on the seabedthat is directly below the global origin.

• the origin of the frame of reference of any object to which that line's ends are connected.

• the position of the other end of that line.

And for the reference axes directions you can choose between:

• the global axes directions

• the axes directions of the frame of reference of any object to which that line's ends areconnected.

Example of Using Polar Coordinates

The choices of reference frame for the polar coordinates may seem complex at first sight, butthey allow various useful coordinate transformations to be done easily and accurately. Here isan example.

Consider mooring a spar with an array of 4 lines, each of which has end A connected to thespar and end B anchored. Suppose you want to place the A ends of the lines so that they areevenly spaced circumferentially around the spar, all at radius 5m from the spar axis and all 3mbelow the spar origin. To do this easily, first sort into End order so that all the A ends aregrouped together. Then, for the first line, set the reference frame origin and axes to be the sparorigin and spar axes and set its polar coordinates to be R=5, and Z=-3. You can now usecopy+paste or fill down to set all the other A ends to the same reference origin, axes and R andZ coordinates. Finally you can set the Theta coordinates for the A ends to 0, 90, 180 and 270degrees

Similarly, suppose you want the B ends to be anchored to the seabed, with the anchors againevenly spaced circumferentially, and with each line spanning 200m horizontally. The easiest

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reference frame for this is with the reference origin being End A and the reference axes beingthe spar axes. The Theta coordinates should again be set to 0, 90, 180 and 270 degrees andthe R coordinates set to 200m. But this time, to set the vertical positions of the B ends, it iseasier (especially if the seabed is sloping) to go to the Connections Tab and set Connect ToObject to be Anchored and then go to the Positions tab and set the Object Relative Positionz coordinate to zero.

Contents

Contents Density

If any section of the line is of a line type that is hollow, i.e. has non-zero inner diameter, then itsmass is increased by:

Density . Inner Cross Sectional Area . Section Length.

Mass Flow Rate

The rate of flow of mass through the line. If it is non-zero then it is used to calculate thecentrifugal and Coriolis forces due to flow of fluid in the line. Positive values mean flow fromEnd A to End B; negative values mean flow from end B towards end A. To convert betweenmass flow rate, volume flow rate and flow velocity use the following simple formulae:

Volume flow rate = Mass flow rate / ρ

Flow velocity = Mass flow rate / (ρ π d² / 4)

where ρ is the contents density and d is the internal diameter of the line.

Contents Pressure

The internal pressure in the line at End A. This value is only used for reporting the wall tensionand stress results - it does not affect any other results. The internal pressure at end A isassumed to remain constant at this value throughout the simulation. Internal pressureelsewhere in the line is calculated. See Line Pressure Effects for details of contents pressuremodelling.

Structure & HydrodynamicsEach line can be made up of up a number of sections with different properties, the sectionsbeing defined in sequence from end A to end B.

Line Type

This determines the properties of the section.

Section Length

The length of the section.

Number of Segments

The number of segments in the section.

Clash Check

Clash modelling is included when this data item set to Yes. If it is set No then the section willbe ignored for clashing purposes.

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Note: Clash checking is quite time-consuming, so you should only set this item toYes for those sections for which you need clash modelling to be included.See Line Clashing.

Drag Formulation

A number of authors have proposed formulae to model how the drag force on a line varies withthe incidence angle. OrcaFlex offers the choice of the Standard, Pode or Eames formulations.All of these use drag coefficients, which are specified in OrcaFlex on the line type data form.

For details of the formulations see the Line Theory section.

AttachmentsA number of attachments may be added to each line. Each attachment can either be of aspecified Attachment Type or else be a clone of a specified 6D buoy.

Attachment Type

Can be a Clump Type, a Drag Chain Type or an existing 6D Buoy.

If you specify a 6D buoy as the attachment type then the attachment is a clone of that 6D buoyand changing the properties of the 6D buoy also changes the properties of the attachment. The6D buoy from which the attachment is cloned cannot be deleted, without first deleting all theattachments that are clones of it.

6D buoy attachments are useful when you want a number of identical 6D buoys attached to aline. To attach 20 identical buoys to a line, for example, first create the first buoy separatelyfrom the line and then connect it to the line by setting its connection data item on the buoy dataform. This first buoy acts as the master from which all the other attachment buoys are cloned.Then, on the line data form, specify 19 attachments and set their attachment type to be the first6D buoy.

Note: 6D Buoy attachments can only be used when the Line includes torsion.

Position

The x, y and z coordinates specify the position of the attachment relative to the line.

• For Clumps and Drag Chains the x and y coordinates must be zero and the z coordinate isthe arclength. Clumps and Drag Chains are connected at the node nearest to thisarclength.

Note: If the attachment is a clump then it is also offset vertically from the node by theoffset distance specified in the clump type data. Beware that the signconvention for this offset varies depending on whether the clump is netbuoyant (positive offset is upwards) or heavy (positive offset is downwards).

• For 6D Buoy attachments the z coordinate specifies the arc length at which the buoy shouldbe connected to the line. The buoy will be connected to the nearest node to that arc length.The buoy will be connected with an offset relative to that node's axes that is given by (x, y,0). See 6D Buoy Initial Position for more details.

Orientation

For 6D Buoy attachments only. Rotation 1, Rotation 2 and Rotation 3 determine the InitialAttitude of the attached buoy.

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Name

For 6D Buoy and Drag Chain attachments only. This is the name of the attached object and isused to select results for that object.

DrawingYou can define the colour, line style and thickness of the pens used for drawing the nodes andsections of the line. See How Objects Are Drawn.

For the sections there is a choice for which pen is used, the choice being made by clicking onthe "Sections" box. You may either specify the pen explicitly on the Line Data form, in whichcase it will be used for all sections of that line. This allows you to use different pens todistinguish between different lines. Alternatively, you can choose to have the sections drawnusing the appropriate Line Type Pen defined on the Line Types table. This allows you to usedifferent pens to distinguish sections of different line types.

For Lines with Prescribed Statics Method you can control how the track is drawn. You canswitch between the options of drawing the track in the chosen pen and not drawing it at all.Similarly for the Spline Starting Shape you can switch between the options of drawing theunscaled spline in the chosen pen and not drawing it at all.

Statics

Statics Method

For lines, there is a choice of calculation methods available for the static analysis. The methodmay be set to Catenary, Spline, Prescribed or Quick.

The normal setting is Catenary, in which case the static analysis finds the equilibrium catenaryposition of the line, allowing for weight, buoyancy, drag, but not allowing for bend stiffness orinteraction with shapes. See Catenary Calculation.

The Catenary solution has some limitations and some systems, such as those with slack orneutrally buoyant lines, can be troublesome. For such lines you can instead specify Spline, inwhich case the line is instead set to a 3D spline curve based on spline control points specifiedby the user. See Spline Data.

For pull-in analysis the Prescribed option has been provided. Here the user specifies thestarting position of the line as a sequence of straight line or curved sections on the seabed.See Prescribed Starting Shapes.

Finally, you may specify Quick, in which the line is left in the rough catenary shape used in theReset state.

Full Statics

This calculation finds a full equilibrium position for the model. Unlike the Catenary method,bend stiffness and interaction with shapes are included. Full statics needs a starting shape forthe line, and it uses the specified Statics Method to obtain this; it then finds the equilibriumposition from there. You must therefore also set the Statics Method to give a reasonablestarting shape, choosing from one of the above statics methods. See Full Statics.

For more details of the Statics Calculation see Statics Analysis.

Warning: If you do not use the Catenary method or Full Statics, then the startingposition will not (in general) be an equilibrium position.

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Note: It is only possible to include buoys in the static analysis (see Include Buoys inStatic Analysis ) if either the Catenary method or Full Statics is used for alllines in the model.

Include Friction

Friction can be included in the static analysis only if the Statics Method is Catenary or if FullStatics is used.

With seabed friction present there is not, in general, a unique static position for the line, sincethe position it adopts depends on how it was originally laid and its history since then. In order todefine a unique solution, we therefore need to make some assumptions about how the line wasoriginally laid and friction is then assumed to act towards this position.

If the Statics Method is Prescribed, then this ‘originally laid’ position is assumed to be theposition defined by the Prescribed track. Otherwise, the ‘originally laid’ position is defined byspecifying the Lay Azimuth and Pre-Tension values.

Lay Azimuth

This data is only used when seabed friction is included in the static analysis and the StaticsMethod is not Prescribed. It then defines the position in which the line is assumed to havebeen originally laid, and friction is then assumed to act towards this position. When StaticsMethod is not Prescribed, it is assumed that:

• The line was originally laid, with the specified Pre-Tension, starting with end B at itsspecified position (or at the point on the seabed directly below, if end B is not on theseabed) and then leading away from there in the Lay Azimuth direction and allowing for theseabed slope at end B.

• End A was then moved slowly from that original position to its specified position.

To help set this data item, there is a button on the form marked Set. This button sets the LayAzimuth value to be the direction from End B towards End A, based on their current positions.

Notes: If a profile seabed is used then for the purposes of calculating this assumedoriginal lay position, the seabed is treated as a simple plane with slope equalto the local seabed slope at end B. In other words the assumed original laidposition does not track down into any hollows or over any hills, and the effectis that it bridges any hollows and is stretched by any hills along its path.

Whilst the program will accept any Lay Azimuth, we would expect the staticsconvergence routine to have increasing difficulty in finding a solution as theangle between the Lay Azimuth direction and the vertical plane through theline ends increases. For example, if we have a line top at X=0, Y=0, andanchor at X=100, Y=0, we would expect trouble for a Lay Direction of 90degrees.

Pre-Tension

If the Spline or Prescribed statics methods are used, then the line is laid out along the specifiedcurve with a strain determined by the axial stiffness and this Pre-Tension value.

This data item is also used if friction is included in the static analysis. It determines the strainwith which the line is assumed to have been originally laid, and this original position is used asthe target position towards which friction acts.

Otherwise, this data item is not used.

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Catenary ConvergenceIf the Catenary statics method is chosen, then an iterative catenary calculation is used todetermine the static position of the line. This calculation is controlled by a number ofconvergence parameters which can normally be left at their default values. Howeversometimes the calculation can fail to converge. If this happens, first check your data for errorsand check for the following common causes of convergence failure:

• Does the solution have a slack segment? This can happen in lines that touch down on theseabed almost at right angles or in lines that hang in a very narrow U shape. The catenarycalculation cannot handle lines with slack segments - try increasing the number of segmentsin the relevant section of the line.

• For lines that touch down on the seabed, is the Lay Azimuth value specified correctly? It isthe azimuth direction leading away from end B and it is easy to get it wrong by 180 degrees.

• Is the line buoyant, either deliberately or by mistake. The catenary calculation has problemswith floating lines - you may need to use the Spline statics method instead.

• Does the line have a surface-piercing buoyant clump attached? If the clump is short thenthe catenary calculation is more difficult.

If the calculation still fails to converge, then it is sometimes possible to obtain convergence bychanging one or more of the convergence parameters, as follows:

Max Iterations

The maximum number of iterations that OrcaFlex will make before treating the calculation ashaving failed to converge. Increasing this value can sometimes help.

Tolerance

The non-dimensional accuracy to which the calculation is done, before the calculation is treatedas having converged. Increasing the tolerance increases the chances of convergence butreduces the accuracy.

Min Damping

The minimum damping factor to be used in the calculation. Convergence can sometimes beachieved by increasing this parameter to a value greater than 1 - try values in the range 1.1 to2.0. The minimum damping should not be set to less than 1.

Mag. of Std. Error, Mag. of Std. Change

These parameters control the maximum size of the change, in the estimated solution, this isallowed in a single step. Reducing these values can sometimes help, but the calculation willthen usually require more iterations.

The remaining parameters should not normally be changed. For further information contactOrcina.

Full Statics ConvergenceThe numerical method used to solve for the static position is an iterative process in which theprogram tries to converge on the solution in a series of steps. This process is controlled by anumber of convergence parameters, found on the Line data form. These can normally be leftset to the Default values, but in some cases where the calculation fails to converge to a solutionit may be necessary to use Specified values that suit the problem being handled. If Specified

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parameters are used, the following parameters can be edited, and a command is available toreset them to the default values.

Max Iterations

The calculation is abandoned if convergence has not been achieved after this number of steps.For some difficult cases simply increasing this limit may be enough.

Tolerance

This controls the accuracy of the solution. The program accepts the line position as a staticequilibrium position if the largest out of balance force component on any node is less thanTolerance*LineDryWeight (including contents). Reducing the Tolerance value will give a moreaccurate static equilibrium position, but will take more iterations. The program may not be ableto achieve the Tolerance specified if it is too small, since the computer has limited numericalprecision.

Delta

This is a perturbation size, used to calculate the Jacobian matrix for the problem. Delta shouldalways be less than the tolerance specified.

Min / Max Damping

For some cases it is necessary to control the convergence process by damping down, i.e.reducing, the step taken at each stage. The program includes an automatic damping systemthat chooses a suitable damping factor for each iteration, but the user can set the minimumdamping and maximum damping factors that are used. Normally the default values will sufficebut for difficult cases, or to try to speed up slow cases, the default values can be altered. Fordifficult cases that appear to make the convergence unstable (e.g. giving very bad line positionson the screen) the maximum damping factor should be increased. To speed up convergencefor simple cases where damping is not necessary, the maximum damping factor can be set low,e.g. equal to 1. If this causes the convergence process to become unstable, the maximumdamping factor should be increased again. The minimum damping factor should always be leftequal to 1.

The remaining parameters should not normally be changed. For further information contactOrcina.

SplinesThe following data is only used if the Spline statics method is specified.

Order

This sets the smoothness of the spline shape; generally order 3 is reasonable. If a higher orderis chosen, a smoother curve results. The order cannot exceed the number of spline points.

Control Points

The line shape is specified by a number of Control Points. The first and last control points areautomatically placed at the line ends A and B respectively and OrcaFlex generates a smoothcurve between the first and last control points and passing near to the intermediate controlpoints. These intermediate control points may be adjusted to 'pull' the curve into the desiredshape.

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The first and last control points correspond to line ends A and B respectively. The line isstretched to the specified pre-tension and laid out following the spline curve starting at End Aand working towards End B.

For a line with a Free end the line is laid out along the curve until End B is reached. If the lengtharound the curve is not equal to the stretched line length then the end will either fall short of theend Estimated Position or lie beyond it (along the continuation of the curve along its 'final'direction).

For a line with a Fixed end, Anchor or attached to some object the curve is automaticallyexpanded or contracted to allow the end to lie at the specified end position. A warning isgenerated if this process fails.

Track DataThe Track Data is only used if the Prescribed statics method is specified. It can be found in theStarting Shape group on the line data form and can be edited in several ways:

• By editing the Length and Turn values of a track section on the line data form. OrcaFlexthen creates an arc of the specified Length and Turn, and the X and Y coordinates of theend of this section, and all subsequent sections, are automatically adjusted to match.

• By editing the X and Y coordinates of the ends of a track section on the line data form.OrcaFlex then creates the (unique) circular arc (or straight line) that is a smooth continuationof the previous section and passes through the new (X,Y) point. The Length and Turnvalues for this section, and the X and Y coordinates for subsequent sections, are thenautomatically adjusted to match.

• By dragging the end points of the track sections on a 3D view using the mouse. The trackand the track section end points are drawn on the 3D views. Dragging a track section endpoint is equivalent to editing its X and Y values, as described above.

The individual data items (see Figure: Plan View of Example Track) are as follows:

End A Azimuth

The initial direction of the track.

Track Sections

The number of sections used to define the track.

Section Length

The length of the circular arc (or straight line if Section Turn = 0).

Section Turn

The amount by which the track azimuth increases over this section. A positive value denotes aturn to the left, when viewed from above, and a negative value denotes a turn to the right. Avalue of zero can be entered to specify a straight track section.

Section Radius

The radius of curvature of the circular arc. The radius equals (180L)/(πT), where L is the sectionlength and T is the absolute value of section turn, in degrees. For straight sections (i.e. ifSection Turn = 0) the radius is reported as Infinity.

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Notes: This is a reported value, not an editable data item, and is hence always shownin grey.

With a sloping seabed the actual track on the seabed will have a slightlydifferent radius of curvature - see Laying Out the Line.

Section X and Y

The global X and Y coordinates of the end of this track section. You can either edit these X andY coordinates explicitly, on the line data form, or else by dragging the end point on a 3D view. Ifyou edit X or Y then OrcaFlex fits a circular arc (starting at the previous section's end point)through the new end point and the Section Length and Section Turn are automaticallyupdated to match this new arc.

Section Z

The global Z coordinate of the section end point on the seabed. This is a reported value, not aneditable data item, and is hence always shown in grey.

Section Arc Length

The total arc length to the end of the section. This is a reported value, not an editable dataitem, and is hence always shown in grey.

Section Azimuth

The azimuth direction at the end of the section. This is a reported value, not an editable dataitem, and is hence always shown in grey.

Track Pen

This controls how the track is drawn. You can switch between the options of drawing the trackin the chosen pen and not drawing it at all.

Laying Out the LineThe track data defines a sequence of straight lines and circular arcs in the horizontal plane,which are then projected vertically onto the seabed to define the track itself. The program thenlays the line out along the track, allowing for any pre-tension specified by the user on the linedata form.

Because the line is modelled as a series of straight segments, when the line is laid out along acurved track it will repeatedly 'cut corners' and so the length of line laid along a given curvedtrack section will be slightly shorter than the length of that section. The size of this discrepancyreduces as more segments are used.

If End A is above the seabed then the line descends linearly to the seabed, reaching the seabedat the end of the first track section. If the end of the last track section is reached before all theline has been laid out, then the rest of the line is laid out in a straight line in the direction of theend of the track.

Sloping Seabeds

The track on the seabed is obtained by projecting the specified circular arcs or straight sectionsvertically down onto the seabed. With a horizontal seabed this vertical projection has no effecton the shape of the track. But with a sloping seabed the vertical projection does not preservedistances and this causes some effects that users should note:

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• The section lengths and arc lengths that appear in the prescribed starting shape data tableare lengths in the horizontal plane, i.e. before projection down onto the seabed. With asloping seabed the true section and arc lengths on the seabed will differ, the differencedepending on the slope of the seabed. The actual arc lengths can be obtained by runningthe static analysis and looking at the Full Results table for the line.

• The section radius reported in the prescribed starting shape data table is that of the circulararc in the horizontal plane, i.e. before projection down onto the seabed. When the circulararc is projected down onto a sloping seabed the resulting track section is slightly ellipticalrather than circular, so again the actual radius of curvature will differ. The actual radii ofcurvature can be obtained by running the static analysis and looking at the Full Resultstable for the line.

7.8.3 AttachmentsAttachment TypesThe Attachment Types form defines the properties of a number of named attachment types.Attachments with these properties can then be connected to lines. Attachment Types can beeither Clump Types or Drag Chain Types.

The attachment types form must include all the attachment types referred to on all of the Linesdata forms, but it can also include other attachment types that are not currently in use in themodel. This allows you to build up a library of standard attachment types that can then beeasily used when building Lines.

ClumpsA clump is a concentrated attachment that is connected to a node on a Line. It can be buoyantor heavy and is a small body that experiences forces (weight, buoyancy, drag etc.) exactly asfor a 3D Buoy. But instead of being free to move it is constrained to move with the node andthe forces acting on it are transferred to that node. A clump therefore adds to the mass,buoyancy and hydrodynamic force of the node to which it is attached.

Clumps only have 3 degrees of freedom - X,Y and Z - which are determined by the position ofthe node to which they are attached. Clumps do not rotate - their local axes always remainaligned with the global axes directions.

Each clump is assigned a height and an offset from the node, both measured vertically. Theseare used to determine the Z coordinate of the clump for the purposes of evaluating buoyancyand hydrodynamic forces: no moment is applied to the node by the clump. Where the clumppierces the water surface, buoyancy and hydrodynamic forces are applied in proportion to theimmersed length of the clump.

Each clump is of a named clump type, from which it inherits all its properties. The clump typesare specified on the Attachment Types form and have the following data.

Clump Type Name

Used to refer to the Clump Type.

Mass

Mass or weight in air.

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Volume

Used to calculate buoyancy and added mass for each clump of this type on a line. Clumps maybe either net buoyant or heavy as desired.

Note: If a clump is net heavy in water, then it is treated as a Drag Chain. Thismeans that its length is truncated at the point where it touches the seabed,and the weight force acting on the line is reduced proportionately. Theprogram also calculates a friction force due to the part of the drag chainsupported by the seabed. This friction force acts on the node to which theclump is attached, and uses the coefficient of friction supplied for that line.

Height

Used for drawing the clump and also to determine how much of the clump is below the watersurface. A heavy clump (modelling a Drag Chain) is assumed to start at the Offset distancebelow the node, and extend downwards for its Height, or until it meets the seabed. A buoyantclump is assumed to be centred at the Offset position above the node, and extend for half itsHeight above and below this point.

Offset

A clump may be offset vertically from the line, for example to represent a line supported belowthe surface by floats. The connection is not modelled fully: the clump is always treated as beingat the specified offset vertically above (offset positive) or below (offset negative) the node towhich it is attached.

Note: The way in which Offset is used depends on whether the clump is heavy orbuoyant - see the note above.

Drag

Drag forces are calculated in global horizontal and vertical directions for each clump on a line.

drag force = ½ . Water Density . (velocity)² . Cd . Drag Area

where

Cd is Drag Coefficient as specified here,Drag Area is specified here,

velocity is the velocity of the fluid relative to the clump in the appropriate direction.

Added Mass Coefficients

Added mass in global horizontal and vertical directions are given by

added mass = Ca . Water Density . Volume

where

Ca is Added Mass Coefficient as specified here.

Pen

Defines the colour, line style and thickness of the pen used for drawing this clump type. SeeHow Objects Are Drawn.

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Drag ChainsDrag chains are attachments to a line that model straight chains that hang down from the line.They apply weight, buoyancy and drag forces to the node to which they are attached, but notany added mass effects. For details see Drag Chain Theory.

Drag chains include two facilities that can be important in modelling towed systems. Firstly, thechain's drag coefficients can vary with the incidence angle of the relative flow; this enablesmodelling the effect that as the relative flow increases the chain hangs at a greater angle to thevertical and so fluid drag generates more lift, which is applied to the line. Secondly, drag chainsinteract with the seabed (in a simple manner); if the node comes closer to the seabed than thechain length, then the seabed provides a supporting reaction force and a friction force, both ofwhich are applied to the node.

Each drag chain is of a named drag chain type, from which it inherits all its properties. Thedrag chain types are specified on the Attachment Types form and have the following data.

Name

Used to refer to the Drag Chain Type.

Length

Length of the drag chain.

Effective Diameter

Effective diameter of the drag chain. This is the diameter of the cylinder that has the samedisplaced mass per unit length.

Mass

Mass per unit length. Mass is assumed to be uniformly distributed along the length of the dragchain.

Friction Coefficient

Coefficient of friction for contact with the seabed. This coefficient is used for all directions offriction. The value can be set to '~', in which case the drag chain will instead use the axialfriction coefficient of the node to which the drag chain is attached.

Drawing

Defines the colour, line style and thickness of the pen used for drawing drag chains of this type.See How Objects Are Drawn.

Drag Coefficients

A table specifying normal and axial drag coefficients, as a function of the incidence angle of therelative velocity vector. The incidence angle is the angle between the relative velocity vectorand the drag chain. So 0 means flow axially along the drag chain and 90 means flow normal tothe drag chain.

Coefficients are specified for a range of incidence angles between 0 and 90 degrees and linearinterpolation is used to obtain coefficients for intermediate angles. The Graph button shows theresulting coefficient variation. Symmetry is used to obtain coefficients for angles outside therange 0-90.

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See Drag Chain Theory for further details.

7.8.4 Line TypesLine Type DataThe Line Types form defines the properties of a number of named line types, which can then beused to specify the structure of the Lines used in the model.

The line types form must include all the line types referred to on all of the Lines forms, but it canalso include other line types that are not currently in use in the model. This allows you to buildup a library of standard line types which can then be easily used when building Lines.

There isn't room on the screen to show all the properties of all the line types, so OrcaFlex offerstwo view modes. Individual mode shows one line type at a time, but shows you all itsproperties. All mode shows all the line types, but different types of properties are shown indifferent tables.

There is also a Line Type Wizard that helps set up line type data to represent commonly usedstructures such as chains, ropes etc.

Line Type Name

Used to refer to the Line Type.

Outer and Inner Diameter

Used to define buoyancy, drag area and mass of contents per unit length respectively.

CG Offset

The x and y coordinates of the centre of gravity (CG) relative to the centreline. These dataitems are only used when torsion is being modelled. Note that if the line has contents then thecontents CG is assumed to be at the centreline and is not affected by this CG Offset.

Bulk Modulus

Specifies the compressibility of the line type. If the line type is not significantlycompressible, then the Bulk Modulus can be set to Infinity, which means"incompressible". See Buoyancy Variation with Depth.

Mass per Unit Length

The mass of the line or pipe structure, excluding contents, per unit length. Commonly quotedas "weight in air, empty".

Axial Stiffness

The axial stiffness is the slope of the tension-strain curve. You can either specify linear or non-linear behaviour, as follows:

• For a simple linear behaviour, specify the axial stiffness to be the constant slope of thetension-strain line. This slope is the equivalent EA value for the line, where E is Young'smodulus and A is the cross section area. It equals the force required to double the length ofany given piece of line, assuming perfectly linear elastic behaviour. (In practice, of course,most lines would yield before such a tension was reached.)

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• For a non-linear behaviour, use variable data to specify a table of tension against strain.OrcaFlex uses linear interpolation for strains between those specified in the table, and linearextrapolation for strains beyond those specified in the table. The tension must be zero atzero strain.

Warning: Non-linear behaviour breaks the assumptions of the stress results and fatigueanalysis.

See Calculating Tension Forces for details of the tension model used.

Warning: The axial stiffness specified here has a major effect on how long the dynamicsimulation will take, since very large axial stiffness values lead to very smallnatural periods for the nodes and this in turn requires very small simulationtime steps. See Inner and Outer Time Steps.

Fortunately, the value of axial stiffness used is often not very important, providing it is largeenough that the axial strains produced are small. The exception to this is where snatch loadsoccur, since the axial stiffness directly affects the peak tension that results.

It is therefore normally quite acceptable to specify a much smaller axial stiffness value thanapplies to the real line, so enabling much faster simulations. We recommend that artificially lowaxial stiffness values are specified, particularly for early investigative simulations. The effect ofthis can easily be investigated later by re-running a selection of important simulations with theactual axial stiffness value.

Bend Stiffness

The bend stiffness is the slope of the bend moment-curvature curve. You can specify linear ornon-linear behaviour, as follows:

• For a simple linear behaviour, specify the bend stiffness to be the constant slope of the bendmoment-curvature line. This slope is the equivalent EI value for the line, where E is Young'smodulus and I is the section moment of area. It equals the bend moment required to bendthe line to a radius of curvature of 1 radian per length unit.

• For a non-linear behaviour, use variable data to specify a table of bend moment againstcurvature. OrcaFlex uses linear interpolation for curvatures between those specified in thetable, and linear extrapolation for curvatures beyond those specified in the table. The bendmoment must be zero at zero curvature.

Warning: Non-linear behaviour breaks the assumptions of the stress results and fatigueanalysis.

You can specify separate values for bending about the x and y-directions, but often the bendstiffness for the x and y-directions are equal. This can be specified by setting the y-bendstiffness to '~' which means 'same as x-bend stiffness'.

The bend stiffness specified may be zero, for example for chains. It can also be very largevalues, for example for steel pipes, but this will often result in short natural periods in the modeland hence require short simulation time steps. See Inner and Outer Time Steps.

See Calculating Bend Moments for details of the bending model used.

Torsional Stiffness

Each line type can have a linear torsional stiffness; it is used only if torsion is included on theline data form. The torsional stiffness is the torsional moment that results if the line is given atwist of 1 radian per unit length.

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Torque per Unit Tension

This data item defines the effect of tension on torsion; it is used only if torsion is included on theline data form. Many pipes or cables with a spiral-wound construction have the property thatwhen tension is applied a torsional moment is produced. The Torque Per Unit Tension dataitem allows you to model this effect - set it to the torque that results when 1 unit of tension isapplied to the line. If your line has no tension-torque interaction then set the data item to zero.

Contact Stiffness and Damping

The stiffness and damping values used by the clashing algorithm. See Line Clashing.

Drag Coefficients

The drag coefficients for the normal (x and y) directions and axial (z) direction are specified onthe line type data form. For the x and y directions you can either specify a fixed constant value,or else a value that varies with Reynolds number. Often the coefficients for the x and y-directions are equal and this can be specified by setting the y-coefficient to "~", which means"same as x-coefficient".

OrcaFlex also offers a choice (on the line data form) of different formulations for how the dragforce components vary with the incidence angle.

For further details see the Line Theory section.

Added Mass Coefficients

The added mass coefficients Ca for normal (x and y-directions) and axial (z-direction) flow.Often the coefficients for the x and y-directions are equal and this can be specified by settingthe y-coefficient to "~" which means "same as x-coefficient".

For each flow direction, the inertia coefficient, Cm, is automatically set to equal 1+Ca. SeeAdded Mass for details.

Friction Coefficients and Bias Power

OrcaFlex applies Coulomb friction between the line and the seabed. The friction force appliedis ≤ µR where R is the seabed reaction force and µ is the friction coefficient. See SeabedFriction Data for published friction data.

Lines lying on the seabed often move axially more readily than the move laterally. To enablethis effect to be modelled, you can specify different friction coefficients µ for motion normal (i.e.lateral) and axial to the line. For intermediate directions of motion OrcaFlex interpolatesbetween these two values to obtain the friction coefficient µ to use. If the axial frictioncoefficient is be set to '~' then the normal friction coefficient is used for µ for all directions ofmotion. This provides a convenient way of using the same friction coefficient for all directions ofmotion.

If different friction coefficients are specified for motion normal and axial to the line, then as wellas varying the magnitude of the friction force according to the direction of motion, OrcaFlex canalso bias the direction of the friction force towards the direction of the larger friction coefficient.This reflects the tendency of a line, when pulled diagonally, to slide not exactly in the directionof pull but instead to slide more in the axial direction (assuming the axial direction has the lowerfriction coefficient). You can control the strength of this direction bias by setting the BiasPower. This non-dimensional constant only affects the direction of the friction force, not itsmagnitude, and only applies when the motion is diagonal (i.e. when the line is moving bothlaterally and axially).

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If the bias power is zero, or if the normal and axial friction coefficients are equal, then no bias isapplied - the friction force is applied directly opposing the direction of motion. If the bias poweris positive, and the normal friction coefficient is greater then the axial coefficient (as is commonfor a line), then the friction force direction is changed so as to make the line move more in theaxial direction. The larger the bias power, the larger is this change in direction and so the morethe line tends to move axially.

Note: The friction direction bias is not yet available with profile seabeds.

See Seabed Touchdown and Friction for further details of the friction model used.

Stress Outer and Inner Diameter

The stress diameters are the inside and outside diameters of the load-bearing cylinder. Theyare used in the wall tension and stress results calculations, which are based on the assumptionthat the loads in the line are taken by a simple homogeneous cylinder. For simple cases, thestress diameters can be set to '~', in which case they will be taken to be the same as the pipediameters. For more complex cases, for example where the pipe outside diameter allows foradded buoyancy modules that are not load bearing, the stress diameters can be set separately.See Line Results - Forces.

Allowable Stress

The maximum allowable stress for this type of line. This value is only used to draw a limit curveon Stress Range Graphs; it does not limit the stress achieved in the line. If no limit curve iswanted then you may input the tilde character "~" (meaning not applicable) instead of a number.

Stress Loading Factors

These are used to specify what proportion of the loads (tension, bend moment, shear andtorque) are to be used when calculating wall tension and stress results. The effective tension,bend moment, shear force and torque are multiplied by the appropriate stress loading factorwhen they are used to calculate the wall tension and stress results.

For many cases, e.g. when modelling a simple homogeneous pipe that carries all the loads,these load factors should be set to 1, the default value.

In some cases, values less than 1 may be suitable. For example, consider a case where theline models a composite structure that consists of a main carrier pipe and an external piggybackpipe. You might estimate that the main pipe takes all of the tensile and torsional loads, but onlycarries 70% of the bending loads, the other 30% being taken by the piggyback pipe. Then toobtain stress estimates for the main pipe you could set the Stress Outer and Inner Diameters to'~' and set the bending and shear stress loading factors to 0.7.

Note: These data items have no affect on the simulation. They only affect the walltension results, stress results and fatigue analyses.

Maximum Tension

The maximum permitted tension for this type of line. This value is only used to draw a limitcurve on Tension Range Graphs; it does not limit the tension achieved in the line. If no limitcurve is wanted then you may input the tilde character "~" (meaning not applicable) instead of anumber.

Minimum Bend Radii

You can specify the minimum permitted radii of curvature for bending about the x and y-directions. These values are optional - they are only used to draw "allowable" curves on range

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graphs - they do not limit the bend radius of the line. If you do not want these curves then setthe x-radius to "~" (meaning "not applicable") and the y-value to "~" (meaning "same as x-value").

Often the radii for the x and y-directions are equal and this can be specified by setting the y-radius to "~" which means "same as x-radius".

The specified values are used to draw "allowable curvature" curves on the x- and y-Curvaturerange graphs, and also (if the x and y-minimum radii are equal) on the Curvature range graph.In addition, they are used (together with the specified bend stiffness) to derive "allowable bendmoment" curves which are drawn on the x- and y-Bend Moment range graphs, and also (if the xand y-values are equal) on the Bend Moment range graph.

Note: The "allowable" curve may not be visible on the range graph, since it may beoutside the range covered by the graph. To see the "allowable" curve in thiscase you will need to modify the graph to increase the range of valuescovered.

Limit Compression

The program has two modes for handling slack segments, i.e. when the distance between twoadjacent nodes becomes less than the original unstretched segment length:

No: means that the segment is treated as a strut which can support unlimited compression.This is the preferred model except where bend stiffness is insignificant.

Yes: means that the segment is treated as an elastic Euler strut - the compression is limited tothe segment Euler load. This is a better model for cases where the bend stiffness isinsignificant, such as for chains and soft ropes.

The segment Euler load is given by π².EI/L0² where EI is the bending stiffness of the pipe andL0 is the unstretched length of the segment. In all cases, whenever a segment has beencompressed to or beyond the segment Euler load, then a warning of this is given on the resultsform and in the statistics table.

For items such as mooring chain, the bending stiffness is zero, and the segment Euler load isalso zero. In this case "Limit Compression" should be set to "Yes" - this correctly models achain or very flexible rope, which cannot support any compression. The segment Euler loadwarning is then simply a warning that the line has gone slack.

For a line with non-zero bend stiffness the Euler load warning is effectively a warning that thesegments at that point are too long to accurately model the bending that is occurring.Effectively, bending is occurring at a scale that is less than the segment length, so shortersegments are needed to model it accurately. Using shorter segments in that area will give alarger segment Euler load, and to obtain an accurate solution you should, ideally, usesufficiently short segments that the resulting segment Euler load is not reached. See LineCompression and Modelling Compression in Flexibles for details.

Pen

Defines the colour, line style and thickness of the pen used for drawing this line type. See HowObjects Are Drawn. For each line there is a choice, on the Line Data form, of whether to drawthe sections of the line using these Line Types pens, or whether to define a specific pen to usefor all the sections of the line.

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Line Type PropertiesOn the line types form, you can display various properties of the currently-selected line type byright clicking and then selecting Properties. The properties displayed include weight in air,displacement, weight in water, and diameter to weight (in water) ratio.

For Line Types that have a non-zero bore you must specify the contents density to be used inthe calculation of properties, since this will affect the properties that involve weight.

The properties form also displays the names and contents densities of each line that uses thatline type.

7.8.5 Line ResultsLine ResultsThis section describes the line results that are available for the static and dynamic analyses.These results are available using the Results Selection form.

Results from the modal analysis and fatigue analysis are described elsewhere - see the ModalAnalysis and Fatigue Analysis sections.

Selecting which Categories of Line Results are Shown

For Lines there are a large number of results variables available on the Results form. SoOrcaFlex groups the results variables into the following categories.Positions X, Y, Z, Surface Z, Depth, Seabed Clearance, Arc LengthMotions Velocity, GX-Velocity, GY-Velocity, GZ-Velocity

Acceleration, GX-Acceleration, GY-Acceleration, GZ-AccelerationRelative Velocity, Normal Relative Velocity, Axial Relative Velocity

Angles Azimuth, Declination, Gamma, TwistEz-Angle, Exy-Angle, Ezx-Angle, Ezy-AngleNo-Moment Azimuth, No-Moment DeclinationEnd Force Azimuth, End Force Declination, End Force Ez-AngleEnd Force Exy-Angle, End Force Ezx-Angle, End Force Ezy-Angle

Forces Effective Tension, Wall TensionShear Force, x-Shear Force, y-Shear ForceVortex Force, GX-Vortex Force, GY-Vortex Force, GZ-VortexForce

Moments Curvature, x-Curvature, y-CurvatureBend Moment, x-Bend Moment, y-Bend MomentTorque

Clashing Line Clearance, Line Clash Force, Line Clash Impulse, SolidContact Force

Pipe Stresses Internal Pressure, External PressureDirect Tensile Stress, Max Bending Stress, Worst Hoop StressMax xy Shear Stress, Max von Mises Stress, von Mises StressRR Stress, CC Stress, ZZ Stress, RC Stress, RZ Stress, CZ Stress

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End Loads End Force, End MomentEnd GX-Force, End GY-Force and End GZ-ForceEnd GX-Moment, End GY-Moment, End GZ-MomentEnd Lx-Force, End Ly-Force and End Lz-ForceEnd Lx-Moment, End Ly-Moment, End Lz-MomentEnd Ex-Force, End Ey-Force and End Ez-ForceEnd Ex-Moment, End Ey-Moment, End Ez-MomentBend Restrictor Load

To ease results selection the Show boxes on the results form allow you to choose which ofthese categories of variables are shown in the Variable list. To get the full list of availablevariables simply select all the categories. But normally there are several categories of variablethat you do not currently need, in which case de-selecting them reduces the displayed list ofvariables to a more manageable set.

Specifying the Position on the Line

For line results you need to specify the position on the line at which you want results. This isdone by setting the entries in a row in the Position table on the results form. You are thenoffered the Variables that are available for the point specified by the currently-selected row.

Each row in the table specifies one point on the line. There are multiple rows in the table, soyou can set up rows specifying a number of different points of interest and then easily switchbetween them by choosing which row you select. In a row that you don't want to use you canset the Node or Arclength column to '~', meaning 'unspecified'.

Three rows in the table are dedicated to special arc lengths on the line:

• The first and last rows in the Position table are dedicated to the line's end points A and B.

• The next to last row in the table is dedicated to the Touchdown point. This is defined to beimmediately before the first node on the seabed (starting from End A). If the results variableselected is a segment variable (i.e. is only available at mid-segment points) then the valuereported for the touchdown point is the mid-segment valued in the segment that precedesthe Touchdown node. When there are no nodes on the seabed then the results variable isreported to be zero.

Arclength and Node Columns

The Arclength column specifies how far along the line the point is, measured from zero at endA. For information, if you set the Arclength column then the adjacent Node cell is set to thenumber of the nearest node to that arclength.

The Node column can also be used as an alternative way of setting the arclength. You can setthe Node column to the number of a node on the line. The adjacent Arclength cell will then beset to the arclength to that node. The node number must be in the range 1 (the node at end A)to N+1 (the node at end B), where N is the total number of segments in the line.

Note The actual arc length for which line results are reported may not be exactly thespecified arclength. OrcaFlex reports results for the 'nearest appropriate'result point. See Result Points below.

R and Theta Columns

For some variables (e.g. stress components) you must also specify the position of the pointwithin the cross section through the specified arclength. Whenever one of these variables isselected in the Variables list, two extra columns become visible in the Position table. These

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extra columns specify the polar coordinates (R,Theta) of the point within the cross section; seethe diagram in the Pipe Stress Calculation section. The R column can only be set to eitherInner or Outer, meaning the radii corresponding to the Stress ID or Stress OD respectively.Results are not available for points between these two radii.

Result Points

OrcaFlex uses a discretised model and so results are only available at nodes, mid-segmentpoints and line ends; we call these points 'result points'. The available result points depend onwhich variable you request, they are documented in the description of the variable.

When you ask for a variable at a specified arclength OrcaFlex gives the value for the 'nearestappropriate' result point. The phrase 'nearest appropriate' here means that OrcaFlex considersthe available result points that are in the same section as the arclength you specified and thenchooses the one that is nearest to the arclength you specified. If you specify an arclength thatis exactly at the boundary of two sections then OrcaFlex uses the section that starts at thatarclength.

OrcaFlex always labels results with the actual arclength to the result point to which they apply,so you can check to ensure that you are getting results at the result point you want.

Positions

X, Y and Z

Available at nodes only. The global coordinates of the selected node.

Proportion Wet

Available at nodes only. The proportion of the part of the line that the node represents, that issubmerged in the sea. The value is in the range 0 to 1, a value of 0 meaning no submersionand 1 meaning is completely submerged. For details see Line Interaction with the Sea Surface.

Surface Z

Available at nodes only. The global Z coordinate of the sea surface directly above theinstantaneous position of the selected node.

Depth

Available at nodes only. The depth of the node beneath the sea surface (= Surface Z - Node Z).

Seabed Clearance

Available at nodes only. The clearance is the shortest distance between the centre of the nodeand any point on the seabed. The value reported is for the node that is nearest the specifiedarclength. A negative value indicates that the node is in contact with the seabed.

For a horizontal flat seabed the clearance is simply the height of the node above the seabed.For a sloping flat seabed it is the distance in the direction normal to the seabed. For a curvedseabed it is the shortest distance, allowing for the curvature of the seabed.

Arc Length

Available at nodes only. The arc length from end A to the selected point. This is normally onlyuseful for the touchdown point, since for other points it is constant. For the touchdown point itgives the arc length from end A to the first node on the seabed, or zero if there is no touchdown.

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Motions

Velocity, GX-Velocity, GY-Velocity, GZ-Velocity

Acceleration, GX-Acceleration, GY-Acceleration, GZ-Acceleration

Available at nodes only. The magnitude and components (with respect to global axes) of thevelocity and acceleration of the node.

Warning: The velocity results are derived by numerically differentiating the loggedpositions of the node with respect to time, using the central difference scheme.The acceleration results are derived by a further such numericaldifferentiation. Because of this the accuracy of the results (especially theaccelerations) will depend on the log sample interval. If the log sampleinterval is large then the results will not show higher frequency components ofvelocity and acceleration.

Relative Velocity, Normal Relative Velocity, Axial Relative Velocity

Available at nodes only. Relative Velocity is the velocity of the fluid relative to the node,i.e. Vfluid - Vnode. The results reported are the magnitude of the relative velocity and its normaland axial components (relative to the line). For the axial component, a positive value meansthat the fluid is moving (relative to the line) towards end B.

Note: For a node that is above the water surface OrcaFlex reports a relative velocitybased on the fluid velocity at the surface.

Warning: The relative velocity results are derived using the node velocity results, so seethe accuracy warning given above.

Reynolds Number

Available at nodes only. The Reynolds number is a measure of the flow regime. It is given bythe equation:

Re = V.D / νwhere V = magnitude of the normal component of the relative velocity vector at the node

D = line outer diameter

ν = kinematic viscosity at the node.

x-Drag Coefficient, y-Drag Coefficient, z-Drag Coefficient

Available at nodes only. These are the line drag coefficients used in the calculation.

If the line's drag coefficients are constant then these results report the values given in the user'sdata, except for a node at the junction between two sections with different drag coefficients,where an effective average value is used.

If the line's drag coefficients vary with Reynolds number then these results report the computedvalue that was used.

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Angles

Azimuth, Declination and Gamma

Available at mid-segment points only. The azimuth, declination and gamma angles at the mid-segment point. These angles report the local orientation of the line relative to global axes. Thegamma angle is defined as for line ends (see Line End Orientation) and is only available if theline twist orientation is defined.

Declination is in the range 0 to 180 degrees. Range jump suppression is applied to Azimuthand Gamma (so values outside the range -360 to +360 degrees might be reported).

Twist

Available at mid-segment points only. The twist per unit length experienced by the segment.

Fluid Incidence Angle

Available at nodes only. The angle between the relative velocity direction and the line axialdirection. A value in the range 0 to 90 degrees.

Ez-Angle, Exy-Angle, Ezx-Angle, Ezy-Angle

Available at mid-segment points only. The direction angles of the mid-segment point withrespect to the end axes of the nearest line end. See End Direction Results. These results areonly available if the end orientation angles are defined.

Ez-Angle is in the range 0 to 180 degrees. Range jump suppression is applied to Exy-Angle,Ezx-Angle and Ezy-Angle (so values outside the range -360 to +360 degrees might bereported).

No-Moment Azimuth, No-Moment Declination

Available at line ends only. The azimuth and declination angles, relative to global axes, of theno-moment direction at the end, allowing for any motion of the object to which the line isattached. These results are only available if the end orientation angles are defined.

No-Moment Declination is in the range 0 to 180 degrees. Range jump suppression is applied toNo-Moment Azimuth (so values outside the range -360 to +360 degrees might be reported).

End Force Azimuth, End Force Declination

Available at line ends only. The azimuth and declination of end force vector, relative to globalaxes.

End Force Declination is in the range 0 to 180 degrees. Range jump suppression is applied toEnd Force Azimuth (so values outside the range -360 to +360 degrees might be reported).

End Force Ez-Angle, End Force Exy-Angle, End Force Ezx-Angle, End Force Ezy-Angle

Available at line ends only. The direction angles of end force vector, with respect to the frameof reference of the line end. See End Direction Results. These results are only available if theend orientation angles are defined.

End Force Ez-Angle is in the range 0 to 180 degrees. Range jump suppression is applied to theother 3 end force angles (so values outside the range -360 to +360 degrees might be reported).

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Forces

Effective Tension and Wall Tension

Available at mid-segment points and line ends only. The structural force along the line axis.Positive values denote tension and negative values denote compression. For details of thedifference between the effective tension and the wall tension see the Line Pressure Effectssection.

Shear Force, x-Shear Force, y-Shear Force

Available at mid-segment points and line ends only. The structural force normal to the line axis,and its components in the local x and y-directions.

Vortex Force, GX-Vortex Force, GY-Vortex Force, GZ-Vortex Force

The magnitude of the lift and drag force on the node, and its components in the global axesdirections. Available at nodes only and only when line uses one of the time domain VIV modelsfrom the VIV Toolbox. For details, see the documentation of the relevant time domain VIVmodel.

Moments

Torque

Available at mid-segment points and line ends only, and available only for lines with torsionincluded. The component of structural moment along the line axis. Note that Torque includesany torque generated by tension-torque interaction.

Curvature, x-Curvature, y-Curvature

Available at mid-segment points and line ends only. The curvature and the magnitude of itscomponents in the local x and y-directions.

Warning: Curvature results are accurate only if the segment length is short.

Bend Moment, x-Bend Moment, y-Bend Moment,

Available at mid-segment points and line ends only. The bend moment and the magnitude of itscomponents in the local x and y-directions.

Clashing

Line Clearance

Available at mid-segment points only. The centreline clearance from this line to any other line.More precisely, the clearance reported for a segment is the shortest distance from thecentreline of the segment to the centreline of any segment on any other line. Note that theclearance reported therefore does not allow for the radii of the lines involved. Note also that lineclearance is only available if there are at least 2 lines in the model.

The line clearance variable is useful for checking for clashing between lines. It is available inboth range graph and time history form. The range graph, for a given period of the simulation,enables you to see where on the line clashing may be a problem. You can then examine thetime history of line clearance for that point on the line, to see when closest approach occurs.You can then use the replay to examine which other line is coming closest.

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It is sometimes worth choosing carefully which line to check for clearance. An example ischecking for clashing between a single mooring line and one or more of a number of closelyspaced flowlines. The clearance graphs for the flowlines will include clearance to the otherflowlines, between which clashing may not be a concern. The mooring line clearance isprobably more useful, since it only includes clearance to the flowlines.

Line clearance only checks against other lines, not against edges of vessels, buoys, etc.However you can check clearance against part of a vessel, for example, by attaching a dummysingle-segment line to the vessel, spanning across the area of interest. The line clearancegraphs for that dummy line will then show how close other lines come to that area of the vessel.

Notes: The segment used is the one containing the selected arclength.

The clearance reported does not allow for the outer diameters of the linesinvolved.

Warning: For complex models, building and updating clearance graphs can be slow.Having "live" clearance graphs open whilst a simulation is running cansignificantly slow down the simulation.

Line Clash Force, Line Clash Impulse

Available at mid-segment points only. The Line Clash Force is the magnitude of the clashforce between this segment and other lines. Please note that this variable is only available ifclash checking has been included for the lines concerned. See Line Clashing for details.

Line Clash Force is given for the segment containing the selected arclength and results areavailable in the form of time histories and range graphs. If multiple clashes occur simultaneouslyon the same segment then the Line Clash Force reported is the magnitude of the vector sum ofthe clash forces involved.

The Line Clash Impulse is the integral of the Line Clash Force with respect to time. It istherefore a cumulative measure of the line clash force.

Solid Contact Force

Available at nodes only. The magnitude of the force per unit length due to contact with elasticsolids.

Pipe StressesStress results are available at mid-segment points and at line ends.

Note: The loads (tension, bend moment, shear and torque) which are used in stresscalculations are scaled by the stress loading factors before being used.

Warning: The stress calculation makes various assumptions - see below. In particular itis assumed that the pipe is made of a uniform, homogeneous, linear materialand that the tension and shear are uniformly distributed across the pipe wall.It is therefore only valid for pipes such as steel or titanium risers, not forcomposite flexible risers, ropes chains, etc. Also, it also does not allow for thestress concentrations that occur at joints etc.

Warning: OrcaFlex does not, and indeed cannot, allow for the complex stressconcentrations that can occur at joints or at the top and bottom of a riser. Thestress calculations included are only valid under the assumptions given below;detailed stress analysis is still necessary.

The stress calculation makes the following assumptions:

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• At each point along the line all the loads are taken by a single simple cylinder of thespecified Stress OD and Stress ID and made of a homogeneous material.

• The stresses included are those due to tension, bending, shear and hoop stress.

• Internal pressure in the line generates wall tension in the line as it would do in a sealedcylinder.

• Shear stress is assumed to be uniformly distributed across the cross section. Although thisis not strictly the case, the shear stress is normally negligible so this simplifying assumptionis reasonable.

• The hoop stress due to static internal and external pressure at the current Z-level isincluded, and is calculated using the standard Lamé equation for thick walled cylinders.However the effect of dynamic variations in pressure, for example from the passage of thewave, are not included.

For terminology see Pipe Stress Calculation.

Internal and External Pressure

Available at mid-segment points and line ends only. The internal and external static pressures,Pi and Po. See Line Pressure Effects for details.

Direct Tensile Stress

Available at mid-segment points and line ends only. This is the axial stress due to wall tension(which includes the effects of internal and external pressure). It is constant across the cross-section and equals Tw/A. A positive value indicates tension; a negative value indicatescompression.

Max Bending Stress

Available at mid-segment points and line ends only. This is the maximum value that theBending Stress takes anywhere in the section. It is given by

Max Bending Stress = (C2.M.StressOD/2) / Ixy

and this maximum occurs at the extreme fibre on the outside of the bend.

Worst Hoop Stress

Available at mid-segment points and line ends only. The Hoop Stress is due to internal andexternal pressure. It varies across the section and can be positive (tension) or negative(compression), and by the Worst Hoop Stress we mean the hoop stress of greatest magnitude.It is obtained by finding the point in the cross-section where the unsigned magnitude of theHoop Stress is largest; this must be either at the inside or outside fibre of the stress area. TheHoop Stress at this point is called the Worst Hoop Stress.

Max xy-Shear Stress

Available at mid-segment points and line ends only. The value √(RZStress² + CZStress²) iscalled the xy-Shear Stress. This varies across the cross-section, and OrcaFlex reports themaximum value that takes anywhere in the cross-section. This is the Max xy-Shear Stress andit is given by

Max xy-Shear Stress = (C4.τ.StressOD/2) / Iz + C3.S / A

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von Mises Stress, Max von Mises Stress

Available at mid-segment points and line ends only. The von Mises stress is a stress measurethat is often used as a yield criterion. It is a combination of all the components of the stressmatrix and in terms of principal stresses it is given by:

von Mises Stress = Sqrt( ( (s1-s2)^2 + (s2-s3)^2 + (s3-s1)^2 )/2 )

where s1,s2,s3 are the principal stresses, i.e. the eigenvalues of the 3 by 3 stress matrix.

The von Mises Stress varies across the cross-section, so its value is reported at a specified (R,Theta) position.

The Max von Mises Stress is an estimate of the maximum value of the von Mises Stress overthe cross-section. The way it is calculated depends on whether the line includes torsion or not,as follows.

• If torsion is not included, then OrcaFlex assumes that the torque is zero. In this case themaximum value of the von Mises stress must occur in the plane of bending. OrcaFlex alsoassumes that the maximum occurs at either the inner or outer fibre. (This is a commonly-used assumption that is almost always valid, since if the internal pressure stress contributionis dominant then the maximum will be at the inner fibre, whereas if bending stress isdominant then it will occur at the outer fibre.) OrcaFlex therefore calculates the von Misesstress at 4 points (R = ±StressID/2 and ±StressOD/2, in the plane of bending) and reportsthe largest value.

• If torsion is included, then the maximum value of the von Mises stress can, in general, occuranywhere in the pipe wall. So OrcaFlex calculates the von Mises stress at a grid of pointsacross the pipe wall and reports the largest value found. Currently, the grid consists 36Theta-values (i.e. every 10 degrees around the pipe circumference) at each of 5 R-valuesacross the pipe wall.

Warning: If torsion is included then the reported maximum von Mises stress is thereforeapproximate, since the actual maximum may not occur at a grid point.

RR Stress, CC Stress, ZZ Stress, RC Stress, RZ Stress, CZ Stress

Available at mid-segment points and line ends only. These are the individual stresscomponents at a point in the cross-section. The point is specified by its polar coordinates (R,Theta) within the cross section. See Pipe Stress Calculation and Pipe Stress Matrix for details.

End LoadsMost results variables that are available for mid-segment points are also available at the lineend points. For example to obtain the end tension at end A you can ask for the EffectiveTension (or Wall Tension) at end A. The enables you to obtain the following results at a lineend:

• Effective Tension, Wall Tension and Torque

• Shear, Bend Moment and Curvature, and their components in the local x and y-directions.

• Seabed Clearance

• Stress results.

For the forces, moments and stresses, the difference between the end value the mid-segmentvalue for the end segment is that the end value includes allowance for the loads on the last halfsegment adjacent to the end.

In addition the following extra load results are only available at line ends.

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End Force, End MomentEnd GX-Force, End GY-Force and End GZ-Force, End GX-Moment, End GY-Moment, EndGZ-MomentEnd Lx-Force, End Ly-Force and End Lz-Force, End Lx-Moment, End Ly-Moment, End Lz-MomentEnd Ex-Force, End Ey-Force and End Ez-Force, End Ex-Moment, End Ey-Moment, EndEz-Moment

The magnitude of the end force and end moment vectors, and their components in the followingdirections:

• The directions of the global axes GX, GY, GZ.

• The directions of the local axes Lx, Ly, Lz of the object to which the line end is connected.For example if the line end is connected to a vessel, the Lx, Ly, Lz are the directions of thevessel axes.

• The directions of the line end axes Ex, Ey, Ez. See Line End Orientation.

If the line end is not free, then the end force and end moment are the total load acting betweenthe end node and the object to which it is connected. If the line end is free, then the end forceand moment are the total load acting between the line end and any links or winches attached tothe end node.

When considering the sign of end load components the question arises as to whether the loadreported is that applied by the line to its connection or vice versa. The OrcaFlex convention isthat the load reported at any point is that applied by the B side of that point to the A side. So atEnd A we report the end load applied by the line to its connection (e.g. a vessel), but at End Bwe report the end load applied to the line by its connection. This is in keeping with theOrcaFlex convention for specifying no-moment direction.

Bend Restrictor Load

This is defined as Bend Restrictor Load = End Force*(1 - cos(End Force Ez-Angle)). Anothercommonly used name for this variable is "pseudo-curvature".

Modal AnalysisThe modal analysis form enables you to calculate and view the undamped natural modes of aline in the model. To open this form, see the Modal Analysis command on the Results menu.Note that the analysis is only available when the static position of the model has beencalculated.

Doing a Modal Analysis

To perform a modal analysis you need to specify the following:

• Which line you want to analyse. Note that the analysis is not yet available for lines that havetorsion included.

• Which modes you want to calculate. You can ask for All modes or a specified range ofmodes. See Modal Analysis Theory for details.

• Whether you want to calculate the mode shapes or just the natural periods. If you excludethe mode shapes then the analysis only calculates the natural periods of the line, not theshapes of the natural modes. If you include the model shapes then the analysis takeslonger.

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When you have made your selections click the Calculate button. The modal analysis will thencalculate the undamped natural periods and, if requested, the mode shapes. Each mode isnormalised to have largest offset magnitude equal to 1, i.e. the offsets vectors are scaled sothat largest offset vector is a unit vector.

Mode Table

The Table tab then displays a spreadsheet giving the results in numerical form. If you do notcalculate the mode shape then the table reports only the periods of the requested naturalmodes. If you calculate the mode shapes then the table also gives the shape in the form of thedisplacements of each free node.

Mode View

If you requested the mode shapes then the View tab displays a 3D view of the line showing oneselected mode shape superimposed on the static position of the line. The current direction isalso shown on the view, and you can control the view angle, zoom etc., as on any 3D view.

Note that if you may need to zoom out in order to see the line, and you may need to adjust theview angle to suit the mode that you are viewing. For example an out of plane mode is bestviewed by looking along the plane of the line.

You can use the Mode drop-down list to control which mode is shown on the view. Note thatwhen that drop-down list has the focus (click it to give it the focus) then you can use the arrowkeys to quickly increment or decrement the mode shape number that is displayed.

The Drawing Exaggeration value allows you to control the amplitude of the mode. (A modeshape does not define the overall amplitude of the oscillation - it only defines how the amplitudevaries along the line.)

Export SHEAR7 Mds File

This button exports a SHEAR7 .Mds file. It is only available if the VIV Toolbox is enabled.

Modal Analysis Theory

The model analysis calculates the undamped natural modes of a single line. Each free node inthe line (i.e. nodes that are mid-nodes or free end nodes) has 3 degrees of freedom (for a linewith torsion not included). A line with N free nodes therefore has 3N degrees of freedom, andas a result the discretised model of the line has 3N natural modes. These modes are given indecreasing order of period and are numbered starting from 1.

Note that the analysis calculates the natural modes of the discretised model, not those of thereal continuous line. However the discretised modes are close to the continuous ones and forany given mode number the accuracy improves as more and more elements are used to modelthe line. For any given level of discretisation the accuracy is better for the lower modes andprogressively worsens as you go to higher and higher modes. The highest numbered modesare unlikely to be realistic since they are oscillations whose wavelengths are of the same orderas the segment length.

Typically there are 3 types of natural mode - lateral in plane, lateral out of plane, and axial. Thefirst two modes are often the simple out-of-plane and in-plane 'fundamentals' - i.e. the modeswhere the whole line swings to and fro together and the graph of displacement against arclength consists of just 1 half cycle. Then follow the higher harmonics, both in-plane and out-of-plane, with progressively more and more half cycles of displacement along the line length. Theaxial modes usually have much higher frequencies and so they are usually found among thehigh number modes.

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If the line hangs in one of the global axis planes then you can often distinguish whether a modeis in-plane or out-of-plane by looking at the pattern of zeros in the table of displacements. Forexample if the line hangs in the XZ plane then the out-of-plane modes have non-zero Y-displacements but zero (or very small) X- and Z-displacements, and the in-plane modes havethe opposite pattern of zeros.

Non-Symmetric Effects

Seabed friction is a non-conservative force that introduces non-symmetric terms into the linestiffness matrix. The OrcaFlex modal analysis can only handle a symmetric stiffness matrix. Todeal with this problem OrcaFlex does the modal analysis using the symmetric part of the matrix(which is given by (K+Ktranspose)/2). This is an approximation that neglects the non-symmetriceffects of friction, so OrcaFlex warns you if this approximation is being done.

Outline Theory

Modal analysis is a standard technique that is well-documented in the literature, but here is abrief outline. First consider a single degree of freedom system consisting of a mass attached toa linear spring. The equation of motion is:

Mx''(t) = -Kx(t)

where x(t) is the offset (at time t) from mean position, x''(t) is the acceleration, M is its mass andK is the stiffness of the spring. Note that this analysis neglects damping and so the results arereferred to as the undamped modes. The effect of damping is usually small.

The solution of the equation is known to be simple harmonic, i.e. of the form x(t) = a.sin(ωt),where a and ω are unknowns to be found by solving the equation. Differentiating x(t) gives:

x''(t) = -ω^2.a.sin(ωt)

so when we substitute into the equation of motion we obtain:

-M.ω^2.a.sin(ωt) = -K.a.sin(ωt) (1)

which can be rearranged to give:

ω = sqrt (K/M).

This is the angular frequency of the oscillation and so the natural period T is given by:

T = 2.π.sqrt (M/K)

For this simple harmonic oscillator there is just a single undamped natural mode, correspondingto the single degree of freedom. For a continuous riser there are an infinite number of degreesof freedom, and hence an infinite number of undamped natural modes, but computer modelsinevitably have to use discretised models with a finite number of degrees of freedom. InOrcaFlex a line has 3N degrees of freedom, where N is the number of nodes that are free tomove, so the discretised model has 3N undamped natural modes.

In this situation the above equations still apply, but they now have to be interpreted asmatrix/vector equations. ω and T remains scalars, but a, x and x'' become vectors with 3Nelements, and M and K become matrices with 3N rows and 3N columns.

Equation (1) then turns out to have 3N solutions, the i'th solution being ωi and ai, say, where ωiis a scalar and ai is a vector with 3N components. This i'th solution is called the i'th naturalmode. It is an oscillation of the line in which all the degrees of freedom oscillate at the sameangular frequency ωi. But different degrees of freedom have different amplitudes, given by thecomponents of ai, and this amplitude variation is called the mode's shape.

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7.8.6 Drag Chain ResultsFor details on how to select results variables see Selecting Variables.

For Drag Chains the following results variables are available.

Azimuth and Declination

The azimuth and declination of the drag chain, relative to global axes.

Supported Length and Hanging Length

The supported length is the length deemed to be supported by the seabed. The hanging lengthis the length of the rest of the drag chain. The supported length plus the hanging length equalsthe total length of the drag chain. See Drag Chain Seabed Interaction for details on how thesevalues are calculated.

Drag Force

The magnitude of the drag force acting on the drag chain. This includes both the axial andnormal components of the drag force.

Axial Drag Force, Normal Drag Force

The components of drag force axial and normal to the drag chain.

Horizontal Drag Force, Vertical Drag Force

The horizontal and vertical components of the drag force. For the vertical drag force a +vevalue indicates an upwards force.

See Drag Chain Theory for details on how the drag force is calculated.

7.8.7 Line Type WizardLine Type WizardThe Line Type Wizard is a tool that helps you set up a Line Type that represents one of thefollowing commonly used structures:

• Chains: see Data for Chains and Modelling Mooring Chains

• Ropes: see Data for Ropes and Modelling Ropes

• Lines with Floats: see Data for Lines with Floats and Modelling Lines with Floats

• Homogeneous Pipes: see Data for Homogeneous Pipes and Modelling HomogeneousPipes.

• Hoses: see Data for Hoses and Modelling Hoses and Cables.

• Cables: see Data for Cables and Modelling Hoses and Cables.

What the Wizard does is ask you for the basic data of the structure - e.g. the bar diameter for achain - and then calculate for you as much of the line type data as it reasonably can forrepresenting that structure. The Wizard leaves you to set other data - e.g. friction coefficients -where there is no formula on which to base the data.

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Warning: The values generated by the Wizard are offered in good faith, but due tovariations in properties between products they cannot be guaranteed. Pleaseuse suppliers' data where this is available.

How The Line Type Wizard Works

The Wizard works on the currently selected line type on the line types form, so you should firstcreate, name and select the Line Type that you want to set up. You can then open the Wizardusing the Wizard button on the Line Types form.

The first time you use the Wizard on a given line type you must be in reset state, since you willbe setting data. You then tell the Wizard the category of structure that you want to model(chain, rope etc.) and the data for that structure (e.g. chain bar diameter). This information iscalled the Wizard data, and from it the Wizard derives line type data to correspond to thatWizard data. If necessary you can then manually adjust the derived line type data.

Once you have used the Wizard to set up data for a given line type, then the Wizard remembersthe Wizard data you gave it. If you re-open the Wizard when in reset state then you can edit theWizard data and the Wizard will calculate corresponding new derived line type data. Anymanual adjustments will need to be done again.

You can also re-open the Wizard when in other states (e.g. in static state or when a simulationis active) but only in order to view the Wizard data. You cannot edit Wizard data or re-deriveline type data except in reset state.

Note: Remember that the current line type data might not correspond to the currentWizard data, since you might have manually edited the line type data after itwas derived by the Wizard.

Using the Line Type Wizard

The Wizard has three stages, with Next and Back buttons so that you can move betweenstages to set up the data you want.

Stage 1 displays the name of the selected Line Type and asks you to specify the specialcategory that you want. You can then click Next to proceed to the second stage.

Stage 2 presents 3 frames of information. The top left frame asks you for the basic data of thespecial category you have selected. The bottom left frame displays the resulting derived LineType data - you should check that the values are reasonable.

The right hand frame displays other properties of the resulting Line Type, which are often usefulas a check. In some cases these depend on contents density, in which case you can specifythe contents density to be used for the calculation of properties. The properties includeminimum breaking load for chains and ropes. If there are any errors then a message will bedisplayed. When everything is correct you can click Next to proceed to the last stage.

Stage 3 displays all of the Line Type data. Bold text is data that has been derived for you bythe Wizard, based on the special line type data you specified. Non-bold text is data that has notbeen set by the Wizard - this data will be as you last set it. You can adjust any of the data atthis stage, overriding the values derived by the Wizard if you wish. You can also still go back toprevious stages of the Wizard if further modifications are required. When everything is correctyou can click the Finish button, in which case the new data will be written, overwriting theprevious data for that line type. Alternatively, you can Cancel to leave the line type unchanged,but then any newly entered special category data will also be lost.

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7.8.8 Modelling Mooring ChainsModelling Mooring ChainsA chain can be modelled in OrcaFlex by using a Line Type with its various properties set tosuitable values. This note derives the values to use for anchor chain of nominal (i.e. bar)diameter D, as shown in the Figure: Mooring Chain Geometry.

The properties of an equivalent line type are given below. For the derivations of these values,click the property concerned:

Studless StudlinkOD 1.80 D 1.89DID 0 0Mass/Length 19.9 D² 21.9D te/m for D in mAxial stiffness 0.854x10 D² 1.01x10 D² kN for D in mBend stiffness 0 0Limit Compression yes yesNormal drag coefficient 1.17 1.20Axial drag coefficient 0.042 0.040Normal added mass coefficient 1.0 1.0Axial added mass coefficient 0.08 0.07Stress diameters '~' '~'Allowable stress '~' '~'Friction coefficient typically 0.4 - 0.8 depending on the seabed

Reference

Puech A, 1984.

Geometry

3.35D(3.6D)

6D

3.35D(3.6D)

D = Nominal Diameter

AEDGE

AFACE

Figure: Mooring Chain Geometry

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DataChains are widely used in a variety of offshore applications, most obviously in mooring. TheLine Type Wizard helps derive a line type to represent a chain based on the following inputdata.

Bar Diameter

The diameter of the metal bar that forms the links.

Link Type

Can be either studlink or studless.

The Line Type data that are derived, and the associated underlying expressions, are detailed inModelling Mooring Chains.

Mechanical Properties

Catalogue Data

When modelling mooring chains the Line Type Wizard aims to derive data for a line type whosecharacteristics are equivalent to that of a chain.

Warning: The values generated by the Wizard are approximate only and are intendedas first estimates for preliminary use. They are offered in good faith, but dueto variations in properties between products they cannot be guaranteed.Please use suppliers' data where this is available.

In deriving these some of the available catalogue data will prove useful and we outline here therelevant aspects. The Mooring Chain figure shows the geometry of a pair of chain links. Thevalues are given in terms of the nominal bar diameter of the chain (D), assumed to be in metres,and are given for both a studless chain and, where different, for a studlink chain (in italics). Thegeometry given in the figure is based on catalogue data available from the chain manufacturerScana Ramnas (1990 & 1995), as is the following expression for mass per metre:

Studless (Studlink)Mass per metre (M) 19.9D² te/m (or 21.9D² te/m).The catalogue also gives the following value for the Young’s Modulus of the chain that has beendeduced from stress-strain relationships in which the cross-sectional area of two bars is takento be the load bearing area:

E = 5.44 x 10^7 kN/m² (or 6.40 x 10^7 kN/m²).

Minimum Breaking Loads

For information, the properties window displays minimum breaking loads that depend on thenominal diameter and chain grade. They are derived using the following relationship, whichwas obtained from the manufacturer's catalogue:

Min Breaking Load = c.D^2.(44 - 80D) kN

Here the grade-dependent constant, c, is catalogued as follows: Grade 2 -1.37e4; Grade 3 -1.96e4; ORQ - 2.11e4; R4 - 2.74e4. Studless and Studlink chains with the same nominaldiameters are stated to withstand the same break- and proof-loads.

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Derived Data

It will be useful to know the centreline length of bar needed to make a single link. We canobtain this by noting that, for a long chain, there is one chain link every 4D length of chain.Hence, the number of links per metre of chain is N = 1/(4D), and thus for a single link:

Mass per link = M / N = 79.6D³ te (or 87 6D³ te)

Assuming that the chain is made from steel, and using ρs as density of steel (= 7.8 te/m³), thisthen leads to:

Volume per link = (M / N) / ρs = 10.2D³ m³ (or 11.2D³ m³).

But, by considering the geometry of a link, we also have

Volume = L . πD²/4,

where L is centreline length of bar needed to make a single link (including the stud in the caseof the studlink chain).

Hence:

L = Volume / (πD²/4) = 13.0D m (or 14.3D m).

Outer and Inner DiameterThe Line Type Wizard sets up Outer and Inner Diameter for a chain as follows:

The effective outer diameter of the equivalent line is obtained using a similar argument to thatdeployed in obtaining the overall length of bar per link. Firstly, note that the volume per metrecan be expressed as both:

Volume per metre = M / ρs

and also as

Volume per metre = π OD² / 4

where OD is the equivalent diameter for a line with constant volume along its length. Equatingthese expressions leads to:

Outer Diameter = √ [4M / (π ρs)] = 1.80D m (or 1.89D m)

Chains do not have any contents, so the Inner Diameter is set to zero.

Axial and Bending StiffnessThe Line Type Wizard sets up Axial and Bending Stiffness and Limit Compression for a chainas follows:

Axial Stiffness

As detailed in Mechanical Properties of Mooring Chains we have values for the Young’sModulus for both studlink and studless chains from catalogue data. Taking A to be thecombined cross-sectional area of two bars, that is:

A = 2(πD² / 4) m²

leads to:

EA = 0.85 x 10^8 D² kN (or 1 x 10^8 D² kN).

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Bending Stiffness

For both studlink and studless chains the bending stiffness is set to zero as the chains areassumed to bend when subjected to very small moments.

Limit Compression

In conjunction with a zero value for bend stiffness, Limit Compression is set to 'yes'.

Axial Added Mass CoefficientThe Line Type Wizard sets up Axial Added Mass Coefficient for a chain as follows.

As for axial drag the parts attracting added mass in axial flow are the projecting lobes only - seethe figure. Each pair of lobes are simply a link with the middle sector removed and can beviewed roughly as an ellipsoid split down the centre with the following dimensions:

length 6D, width D and height 2.35D (or 2.60D).

J N Newman, 1977, (page 147, Fig 4.8) gives added mass coefficients for spheroids. Weapproximate the ellipsoid as a spheroid with mean width of 1.675D (or 1.80D), which has anaspect ratio (width/length) of about 0.3 in both cases. Newman gives Ca = 0.1 for this case, inaxial flow. Therefore, we have that:

Axial Added Mass = 0.1ρ [N . Vollobes].

However, the reference displaced volume in the expression for added mass includes wholelinks, not just the lobes as considered above. A suitable scaling of the above coefficient isneeded to reflect this. If we consider that for each link, the lobes represent approximately 11.0D(or 10.7D) effective length of a total bar length 13D (or 14.3D) we see that the lobe volume isabout 84.6% (or 74.8%) of the link volume. Hence, in reference to the total link volume:

Caa = 0.08 (or 0.07).

Axial Drag CoefficientThe Line Type Wizard sets up Axial and Drag Coefficient for a chain as follows:

Generally, axial drag is very low for smooth pipes, being due to skin friction only. However, fora chain there is some projected area present even in axial flow and we consider the drag forcedue to this effect. We ignore the effect of skin friction in the derivation outlined below.

As in the calculation for normal flow we consider two adjacent links and calculate their projectedarea. The projected area, normal to the flow, for axial flow consists of the four "lobes" only,since the central part is effectively shielded from the flow - see the figure. There is effectivelyno difference between studlink and studless links in this case. The projection of each lobe is1.30D, square at one end, rounded at the other. So the total projected area per metre (normalto the flow) is given by the following expression:

Anormal = 4 (0.8D² + πD²/8) (1/(8D)) = 0.60D.Hence, the drag force per metre length of chain as:

Drag force = ½ ρv² Cda-chain (0.60D).

Hoerner (1965), page 5-8, Fig 14c, gives Cda = 0.32 for a hemispherical rivet head projectingfrom a plane. The lobes here are similar - more elongated in the flow direction (implying a lowerCda) but on a less smooth body (implying a higher Cda). Hence, we assume Cda-chain = 0.40.

As detailed above, we also have an expression for the drag force when considering the chain interms of the equivalent line type parameters. In this case, we are only interested in the dragdue to friction on the wetted area of the equivalent line type (i.e. the circumference):

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Drag force = ½ ρv² Cda (π OD)

and equating the two expressions leads to:

Cda = Cda-chain 0.6 D / (π OD) = 0.042 (or 0.040).

Normal Drag CoefficientThe Line Type Wizard sets up Normal Drag Coefficient for a chain as follows:

We first calculate the drag force on a chain in normal flow, for which we require a value for itsprojected area (normal to the flow). To calculate this we must consider the chain as a collectionof pairs of adjacent links, one face on to the flow, with projected area AFACE, and one edge on,with projected area AEDGE - see Figure. The overall projected area per metre will be a multipleof the sum of these two areas.

AFACE = L D - 2D² = 11.0 D² m² (or 12.3D² m²)

and

AEDGE = 5D D + 2(πD²/4)/2 = 5.79 D² m².

There are 1/(4D) links per metre and hence 1/(8D) such pairs of links per metre. Hence, thetotal projected area per metre (normal to the flow) is given by the following expression:

ANORMAL = (AFACE + AEDGE) (1/(8D)) = 2.10D m (or 2.26D m).

So, we are now able to calculate the drag force per metre length of chain as:

Drag force = ½ ρv² Cdn-chain ANORMAL

for a given drag coefficient Cdn-chain, where ρ is the density of seawater and v is the flowvelocity. For irregular shaped bluff bodies such as chain links, of either type, a suitable valuefor Cdn-chain is 1.00.

However, we are actually interested in the drag coefficient for the equivalent line, Cdn,associated with the reference area of (1xOD) of a cylindrical line:

Drag force = ½ ρv² Cdn OD.

Equating these two expressions for the drag force leads to:

Cdn = ANORMAL / OD = 1.17 (or 1.20).

Normal Added Mass CoefficientThe Line Type Wizard sets up Normal Add Mass Coefficient for a chain as follows:

When a line is accelerated in water it requires an impulse in excess of that needed for the sameacceleration in air. This is due to the extra force required to displace the water in the vicinity ofthe submerged part of the line. An added mass term is used to reflect this and it is found to beproportional to the volume of displaced fluid:

Added mass = Ca . ρ . Vol

where

ρ is density of water,Vol is the displaced volume.

The parts of a line displacing the fluid are said to be attracting added mass. For asymmetricalbodies the parts attracting added mass will differ in different directions. Hence, we consider theeffect due to fluid flow exerting a force in, first, the normal and then the axial directions.

For a circular cylinder in flow normal to its axis:

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Can = 1.0.

The situation for a chain is more complicated as, for flow normal to a link, parts of the link areshielded from the flow but there is also some entrapped water within each edge-on link. Anaccurate calculation is very problematic and is unlikely to give a value for the normal addedmass coefficient far distant from 1.0. Hence we assume:

Can = 1.0.

Stress Diameters and Allowable StressThese are not relevant for chains which have no contents and so are set to '~', the defaultvalues. Any available stress or wall tension results should be ignored.

7.8.9 Modelling Lines with FloatsModelling Lines with FloatsYou can model floats or buoyancy modules attached to a line by using buoyant Clumpsattached at the relevant points. However when a number of floats are supporting a length ofline it is often easier to model the buoyancy as if it were smeared, i.e. spread out evenly, alongthat part of the line. This allows the length and segmentation of the buoyed section to be variedeasily without having to add and remove individual floats.

To use this 'smeared properties' approach you need to do the following.

• Create a new line type.

• Set the new line type's properties to be equivalent to those of the original pipe+floats. Thisis done by spreading each float's buoyancy, drag, etc. uniformly over the length of pipe fromSf/2 before the float centre to Sf/2 after the float centre, where Sf is the float pitch, ie. thespacing between float centres (see diagram below). The result is a uniform circular sectionline which will experience the same forces per unit length as the original line plus floats.The line type wizard will automatically set up this 'equivalent' line type for you.

• Set up a line section to model the length of line supported by the floats. The section's linetype should be set to the equivalent line type and its length should be N x Sf, where N is thenumber of floats and Sf is the float pitch. Note that this length is a little more than the lengthbetween the start of the first float and the end of the last one, since each float is effectivelybeing smeared equally both ways from its centre; see the diagram below, which show thesituation when N=3.

We describe below how the Line Type Wizard derives the properties of the equivalent line type.Note that this approach is also suitable for modelling a regularly weighted section of line.

Warning: The values generated by the Wizard are based on current best practice, butmore specific project data should be used where this is available.

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Dp Df

Sf SfSf

Floats

Figure: Geometry of Line and Floats

We first define the notation to represent the underlying line onto which the floats are to beattached, which we refer to as the Base Line Type - see Base Line Type Notation. We thenspecify the quantities required to represent the floats - see Float Notation.

DataAdding floats to a line to produce extra buoyancy is a common requirement. The Line TypeWizard helps you to quickly derive such a line type by specifying both the existing underlyingbase line type, onto which the floats will be added, and various properties of the floats:

Base Line Type

The line type on which the floats are mounted.

Float Diameter

The outside diameter of each float. It must be greater than the outside diameter of theunderlying base line type.

Float Length

The axial length of each float.

Float Pitch

The average distance between the centres of successive floats.

Float Material Density

The density of the material forming the floats, excluding additional items such as fixing material.

Float Hardware Mass

This accounts for the extra mass due to the addition of the floats above that due to the materialdensity and covers such items as the clamping/fixing mechanisms.

Float Normal Drag Coefficient

The drag coefficient associated with the float for flow normal to the line.

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Float Axial Skin Drag Coefficient

The drag coefficient associated with the floats, due to the floats' skin friction, for flow along theaxis of the line.

Float Axial Form Drag Coefficient

The drag coefficient associated with the float, due to the projected annulus area of the end ofthe float, for flow along the axis of the line.

Float Normal Added Mass Coefficient

The added mass coefficient for flow normal to the line.

Float Axial Added Mass Coefficient

The added mass coefficient for flow along the axis of the line.

The Line Type data that are derived, and the associated underlying expressions, are detailed inModelling Lines with Floats.

Properties of Base Line TypeFor modelling lines with floats the line without floats is referred to as the base line type and thefollowing notation is used. The line without floats is assumed to be of circular cross-section andhave the following characteristics:

• ODp - outer diameter

• IDp - inner diameter

• Mp - mass per unit length

• Cdnp - drag coefficient in normal flow

• Cdap - drag coefficient in axial flow

• Canp - Added mass coefficient in Normal flow (commonly taken as 1.0 for circular section)

• Caap - Added Mass coefficient in Axial flow (commonly taken as zero).

Properties of the FloatsFor modelling lines with floats the following notation is used for the floats. The floats areassumed to be short cylinders fitted co-axially on the line at constant spacing:Lf lengthDf diameterρf float densitySf float pitchmfh float hardware mass (e.g. fixing clamps, bolts, etc.)Cdnf drag coefficient, normal flowCdaf1 drag coefficient, axial flow due to formCdaf2 drag coefficient, axial flow due to skin frictionCanf added mass coefficients in normal flowCaaf added mass coefficient in axial flowWith the above information we can calculate the volume occupied by an individual float as:

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Vf = π/4 (Df² - ODp²) Lf

which leads to the mass of the float being calculated as follows:

Mf = Vf.ρf + mfh.

Outer and Inner DiameterThe Line Type Wizard sets up Outer and Inner Diameter for a Line with Floats as follows:

Outer Diameter

The Outer Diameter (OD) of the equivalent line is calculated by equating two equivalentexpressions for the volume per unit length of the line:

Vol per unit length = π/4.OD² (equivalent line)

Vol per unit length (V) = π/4.ODp² + Vf /Sf (line with floats)

This leads to:

Outer Diameter (OD) = √(4 V /π)

Inner Diameter

The Inner Diameter is unaffected by the addition of floats and so is set to be the same as that ofthe base line.

Mass per Unit LengthThe line type mass per unit length is calculated by allowing for the fact that there is one float forevery Sf length of the section and hence (1/Sf) floats per unit length, giving:

Mass per unit length = Mp + Mf / Sf

Axial Drag CoefficientThe Line Type Wizard sets up Axial Drag Coefficient for a Line with Floats as follows.

To derive the drag coefficient when flow is axial to the line we adopt a similar approach to thatused above for normal flow.

When considering the equivalent line, with the additional buoyancy smeared along it’s outersurface, the drag force per unit length, when flow is axial to the line, is due solely to skin frictionand can be expressed as:

Drag Forcea = ½ ρv² Cda (π OD)

in which the reference area is the circumference of the equivalent line and where r is the densityof seawater and v is the flow velocity.

As in the case for flow normal to the line, we can also express the drag force per unit lengthexperienced by the equivalent line as the sum of the drag forces experienced by the floats andthe drag forces experienced by the part of the line not hidden by the floats. However, the dragforces experienced by the floats are slightly more complicated in axial flow as there will be adrag force due to the exposed annulus on the end of each float and a drag force due to skinfriction.

Drag Forcea = Drag Forcea-FLOATS + Drag Forcea-EXP LINE

= ½ ρv² [Cdaf1.Drag Area1a-FLOATS + Cdaf2.Drag Area2a-FLOATS + Cdap.Drag Areaa-EXP LINE]

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in which the reference drag area, due to the annulus, for the floats in axial flow is given by:

Drag Area1a-FLOATS = π/4 (Df² - ODp²).1/ Sf

the reference drag area, due to the skin, for the floats in axial flow is given by:

Drag Area2a-FLOATS = πDfLf / Sf

and the reference drag area, due to the skin, for the exposed line in axial flow is given by:

Drag Areaa-EXP LINE = πODp (1-Lf/Sf).

Equating these two expressions leads to:

Cda = [Cdaf1.Drag Area1a-FLOATS + Cdaf2.Drag Area2a-FLOATS + Cdap.Drag Areaa-EXP LINE]/(πOD).

Normal Drag CoefficientThe Line Type Wizard sets up Normal Drag Coefficient for a Line with Floats as follows:

The drag force per unit length of the equivalent line when flow is normal to the line’s axis can beexpressed as:

Drag Forcen = ½ ρv² Cdn OD

in which the reference drag area per unit length, normal to the flow, is given by OD and where ρis the density of seawater and v is the flow velocity.

We can also express the drag force per unit length experienced by the equivalent line as thesum of the drag forces experienced by the floats and the drag forces experienced by the part ofthe line not hidden by the floats:

Drag Forcen = Drag Forcen-FLOATS + Drag Forcen-EXP LINE

= ½ ρv² [Cdnf.Drag Arean-FLOATS + Cdnp.Drag Arean-EXP LINE]

in which the reference drag area for the floats in normal flow is given by:

Drag Arean-FLOATS = Df Lf/Sf

and the reference drag area for the exposed line in normal flow is given by:

Drag Arean-EXP LINE = ODp (1-Lf/Sf).

Equating these two expressions leads to:

Cdn = [Cdnf.Drag Arean-FLOATS + Cdnp.Drag Arean-EXP LINE] / OD.

Added Mass CoefficientsThe Line Type Wizard sets up Normal and Axial Added Mass Coefficients for a Line with Floatsas follows:

Normal Added Mass Coefficient

Added mass coefficients are calculated in a similar way to the drag force coefficients. For flownormal to the axis of the line the added mass per unit length is given by:

Added Massn = ρ π/4 OD² Can

in which the reference volume is the volume of the equivalent line and where ρ is the density ofseawater.

We can also express the added mass term of the equivalent line as the sum of the addedmasses due to the floats and due to the underlying line:

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Added Massn = ρ (Canf AMVolFLOATS + Canp AMVolEXP LINE)

in which the reference volume per unit length for the floats (and the portion of line they cover) isgiven by:

AMVolFLOATS = π/4 Df² Lf/Sf

and the reference volume per unit length for the exposed part of the line is given by:

AMVolEXP LINE = π/4 ODp² (1-Lf/Sf)

Equating these two expressions leads to:

Can = (Canf AMVolFLOATS + Canp AMVolEXP LINE)/(π/4 OD²).

Axial Added Mass Coefficient

The added mass coefficients follow in a similar way to above. The reference volumes for theequivalent line and for the floats and exposed part of the underlying base line are taken to bethe same in axial flow as in normal flow. Hence, we can take the above expression for theadded mass coefficient in normal flow and replace the coefficients for normal flow with those foraxial flow:

Caa = (Caaf AMVolFLOATS + Caap AMVolEXP LINE)/(π/4 OD²).

Stress Diameters and Allowable StressThe stress diameter and allowable stress are set to be the values used by the base line, since itis the base line which is load bearing.

7.8.10 Modelling RopesModelling Ropes

D = Nominal rope diameter

Wire with Fibre core Wire with Wire coreFibre rope

D

Figure: Rope Geometry

Ropes have many applications in the offshore industry including towing, mooring and winching.The Line Type Wizard can be used to derive Line Type data to represent five different types ofrope: 8-strand Multiplait Nylon; 8-strand Multiplait Polyester; 8-strand Multiplait Polyethylene;6x19 Wire rope with Fibre core; and 6x19 Wire rope with Wire core.

For documentation of the formulae used by the Line Type Wizard to derive the Line Typeproperties, see the topics that follow this one. You can access these topics either via theRelated Topics link above or via the Previous Topic (<<) and Next Topic (>>) buttons.

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Most of the calculations of the derived line properties are based on data from a cataloguepublished by Marlow Ropes Ltd (1995). All quantities are expressed as a function of the rope'snominal diameter D. Note that this documentation uses the SI units system, so D is in metres inthis documentation, but the program automatically adjusts the formulae to match the unitsspecified by the user.

Warning: The values generated by the Wizard are approximate only and are intendedas first estimates for preliminary use. They are offered in good faith, but dueto variations in properties between products they cannot be guaranteed.Please use suppliers' data where this is available.

DataThe Line Type Wizard can be used to create line types representing a variety of ropes. Theinput data required consists of the following:

Rope Nominal Diameter

The overall diameter of the rope. The majority of the derived line type data are functions of thisRope Nominal Diameter.

Warning: The line type outer diameter derived by the wizard is less than this nominaldiameter, in order to give the correct buoyancy. You need to allow for thiswhen setting the line type drag and added mass coefficients, since thecoefficients correspond to the derived line type outer diameter, not the nominaldiameter.

Construction

Can be one of nylon, polyester, polyethylene, 6x19 wire with fibre core and 6x19 wire withwire core. The construction affects both the mass per unit length of the line type and thestrength of the line type.

The Line Type data that are derived, and the associated underlying expressions, are detailed inModelling Ropes.

Mass per unit lengthThe Line Type Wizard sets up Mass for a Rope as follows:

The quantity Mass per unit length is available from catalogue data for ropes. The nominal ropediameter and nominal mass are available for a variety of rope constructions. A simple statisticalanalysis of the available data leads to the following expressions:

Mass Per Metre = 0.6476 D² te/m (for Nylon ropes);Mass Per Metre = 0.7978 D² te/m (for Polyester ropes);Mass Per Metre = 0.4526 D² te/m (for Polypropylene ropes);Mass Per Metre = 3.6109 D² te/m (for Wire ropes with fibre core);Mass Per Metre = 3.9897 D² te/m (for Wire ropes with wire core).

Outer and Inner DiametersThe Line Type Wizard sets up outer and inner diameters for a Rope as follows.

The inner diameter is set to zero for all rope construction types. The line type outer diameter,OD, is set as follows:

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OD = 0.85 D (for Nylon ropes)OD = 0.86 D (for Polyester ropes)OD = 0.80 D (for Polypropylene ropes)OD = 0.82 D (for Wire ropes with fibre core)OD = 0.80 D (for Wire ropes with wire core)

where D is the specified rope diameter.

These outer diameters are effective diameters that give the line type a displaced volume perunit length that equals the estimated displaced volume per unit length of the rope. The line typethen has the appropriate buoyancy. Note that this effective diameter is less than the specifiedrope diameter, because there are gaps between the fibres and so not all of the specified ropediameter contributes to buoyancy.

The above formulae for the line type OD were derived by equating the line type displacedvolume per unit length, πOD²/4, to the rope displaced volume per metre, M/ρ, where M is therope mass per unit length and ρ is the average density of the rope material.

The following average rope material densities ρ (in te/m³) were assumed: Nylon 1.14; Polyester1.38; Polypropylene 0.91; Wire with fibre core 6.87; Wire with Wire core 7.85. The averagematerial density for the Wire with fibre core was estimated by assuming a ratio of 6:1 betweenthe wire and fibre volume, with the fibre taken to have the same density as (fresh) water.

Axial and Bending StiffnessThe Line Type Wizard sets up Axial and Bending Stiffness and Limit Compression for a Ropeas follows

Axial Stiffness

The expressions for axial stiffness are calculated in different ways for the two groups of fibreropes and wire ropes.

For Fibre Ropes we use the catalogue data. Load/extension characteristics depend onprevious load history, whether the rope is wet or dry, and the rate of application of the load. Toreflect the likely working environment of the rope we use data associated with ropes that havebeen tested under the following conditions:

• the rope has been pre-worked - loaded to 50% of breaking load and then rested for 24 hours(this causes the rope to bed down so that its elastic behaviour is more consistent andrepeatable)

• subjected to slowly varying loads (for loads varying at wave frequency, stiffness should beabout twice the value shown)

• a wet rope - pre-soaked in water (this is most significant for Nylon ropes which suffer a lossin performance when wet)

• we use figures for the average performance when the mean extension is 10% (by taking thetangent of the stress-strain curve at 10%).

Incorporating all of the factors indicated above we can produce values of axial stiffness for arange of rope diameters. Once again using simple statistical techniques we obtain the followingexpression for axial stiffness of fibre ropes:

Axial Stiffness = 1.18 x 10^5 D² kN (for Nylon ropes) Axial Stiffness = 1.09 x 10^6 D² kN (for Polyester ropes)

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Axial Stiffness = 1.06 x 10^6 D² kN (for Polypropylene ropes).

Axial stiffness for Wire Ropes is calculated directly, rather than estimated from empiricalrelationships. We assume a value for Young’s Modulus, for the 6x19 strand group, of:

E = 1.03 x 10^8 kN/m² (for Wire ropes with fibre core); E = 1.13 x 10^8 kN/m² (for Wire ropes with wire core);

and work on an assumed metallic area of:

A = 0.455 (πD²/4) m² (for both wire ropes).

Both of these quantities have been obtained from the HER Group Marine Equipment & WireRope Handbook. Note that for wire ropes with a wire core the additional axial stiffness isaccounted for in the enhanced Young's modulus. This leads to:

Axial Stiffness = 3.67 x 10^7 D² kN (for Wire ropes with fibre core); Axial Stiffness = 4.04 x 10^7 D² kN (for Wire ropes with wire core).

Bending Stiffness

For all rope construction types the bending stiffness offered by the Wizard is zero. For systemswhere bend stiffness is a significant factor you should override this value with the true valueobtained from the rope supplier.

Limit Compression

In conjunction with a zero value for bend stiffness Limit Compression is set to yes.

Stress Diameters and Allowable StressThe Line Type Wizard sets the stress diameters and allowable stress for a Rope to '~' since theOrcaFlex stress analysis is not applicable to complex structures such as ropes. Any availablestress or wall tension results should be ignored.

Minimum Breaking LoadsThe properties window in the line type wizard displays approximate minimum breaking load(MBL) values for ropes. These may be useful for setting the Maximum Tension data item forthe line type.

The MBL values displayed are calculated using the following functional formulae, where D isrope nominal diameter in metres:Nylon ropes (dry) 163950.D² kNNylon ropes (wet) 139357.D² kNPolyester ropes 170466.D² kNPolypropylene ropes 105990.D² kNWire ropes with fibre core 584175.D² kNWire ropes with wire core 633358.D² kNThese formulae were derived from manufacturer's catalogue data, which consist of minimum(dry) strength against nominal diameter for each of the five rope constructions. The formulaewere derived using least squares fitting, and they were found to give a good fit to themanufacturer's data, except that they tend to underestimate MBL for small diameter non-wireropes.

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Note: Nylon ropes lose some strength when wet; the formula given for wet nylonropes is based on the manufacturer's statement that they can lose up to 15%of their (dry) strength when wet.

7.8.11 Modelling Homogeneous PipesModelling Homogeneous Pipes

N N’

O

O’

Figure: Homogeneous Pipe

Given certain of the geometrical and material properties of a homogeneous pipe many of thenecessary Line Type data items can be derived. We outline here the calculations used by theLine Type Wizard performed to derive line type data based on:

• ρ - the density of the material

• E - the Young’s Modulus of the material

• ν - the Poisson’s Ratio of the material

• OD - the Outer Diameter of the pipe

• ID - the Inner Diameter of the pipe

Warning: The data derived by the Line Type Wizard are based on average materialproperties. Project specific data should be used where available.

The properties of the derived equivalent line type are given below.

Mass per Unit Length

Mass per unit length = ρ (π/4) (OD² - ID²) where ρ is the material density specified.

Outer and Inner Diameters

The line type outer and inner diameters are set to the pipe diameters specified by the user.

Axial Stiffness

The line type axial stiffness is given by:

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Axial Stiffness = EA

where E is the Young’s Modulus and A is the cross sectional area, hence:

Axial Stiffness = E.(π/4) (OD² - ID²).

Bending Stiffness

The line type bending stiffness is given by:

Bending Stiffness = E.I

where I is the second moment of area, about an axis in the plane of the cross-section throughthe centroid (e.g. NN’), and leads to:

Bending Stiffness = E.(π/64) (OD^4 - ID^4).

Limit Compression

As the bending stiffness is significant this is set to 'no'.

Torsional Stiffness

The line type torsional stiffness is set as follows. The torque experienced by a pipe of length lwhen twisted through an angle θ is given by:

Torque = [(G.θ)/l] J

where J is the second moment of area about the axial axis OO’ (often called the polar momentof inertia) and G is the Shear Modulus (sometimes called the modulus of rigidity). Forhomogeneous pipes J = 2*I. The quantity G is related to the Young’s Modulus (E) andPoisson’s Ratio (ν) of the material through the following relationship:

G = E / [2(1+ν)].

The Torsional Stiffness, representing the Torque resisting a twist of 1 radian, per unit length, istherefore given by:

Torsional Stiffness = G.J = [E/{2(1+ν)}] (π/32) . (OD^4 - ID^4).

Torque per Unit Tension

The line type torque per unit tension is set to zero, since tension applied to a homogeneouspipe does not generate any torque.

Stress Outer and Inner Diameters

The line type stress diameters are set to ‘~’, since they are the same as the pipe diameters.

Stress Loading Factors

These are set to one, the default value, as a simple homogeneous pipe carries all the loads.

DataThe Line Type Wizard helps build a line type to represent a homogeneous pipe, based on thefollowing data:

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Material

The Wizard provides 3 standard materials for a homogeneous pipe: Steel; Titanium and HighDensity Polyethylene. For these standard materials OrcaFlex automatically sets MaterialDensity, Young's Modulus and Poisson's Ratio.

There is also an option to enter User Defined as the Material. In this case you must setMaterial Density, Young's Modulus and Poisson's Ratio.

Material Density

This is the density of the material used in the construction of the pipe.

Outer Diameter

The Outer Diameter of the pipe and should be greater than the Inner Diameter.

Inner Diameter

The Inner Diameter of the pipe and should be less than the Outer Diameter.

Young's Modulus

The ratio of the tensile stress to the tensile strain.

Poisson's Ratio

The amount of lateral strain experienced by a material subjected to tensile strain as a negativeproportion of the tensile strain.

The Line Type data that are derived, and the associated underlying expressions, are detailed inModelling Homogeneous Pipes.

7.8.12 Modelling Hoses and CablesModelling Hoses and CablesThe Line Type Wizard estimates typical properties for hoses and cables based on project data.

Warning: The values generated by the Wizard are approximate only and are intendedas first estimates for preliminary use. They are offered in good faith, but dueto variations in properties between products they cannot be guaranteed.Please use suppliers' data where this is available.

There are three categories of hoses available:

• High pressure - which cover high pressure flexible risers and flowlines of unbondedconstruction with inside diameters in the range 2 to 15 inches (50 to 380mm).

• Low pressure - which cover low pressure floating hoses of bonded rubber construction withinside diameter from 2 to 20 inches (50 to 500 mm).

• Fold-flat - which cover low pressure, fold-flat hoses with steel reinforcement; inside diameteraround 6 inches (150 mm).

There is currently only one category of cable available:

• Umbilical - constructed with steel wire armour and thermoplastic hoses and outside diameterup to 250mm.

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The properties derived by the Wizard are obtained from empirically estimated relationships withthe diameter of the hose/cable. They have been estimated from a limited amount of datacovering only the range of diameters indicated above. For simplicity, only those relationships ofthe form:

Y = a X^b,

where b is an integer, were considered. In the details below the diameter is assumed to be inmetres and the SI units system is applied throughout.

The amount of data available for low pressure hoses and fold-flat hoses is very small.

There is quite a bit more data for high pressure hoses and umbilicals but it is found to havequite a large spread. To demonstrate this spread, the ratio of the observed value to the fittedvalue, expressed as a percentage, is calculated and the largest and smallest of these is given.

The OrcaFlex stress analysis is not applicable to complex structures such as hoses and cables.Any available stress or wall tension results should therefore be ignored.

Data for CablesThe Line Type Wizard can help build a line type to represent one type of cable - an umbilical.Umbilical cables have many applications including the carrying of electrical communicationwires and hydraulic connectors to submersibles. The Line Type data quantities that the wizardderives have been estimated from a limited amount of project data. Input data for cablesconsists of:

Cable Diameter

The outer diameter of the cable. Each derived line type property is a function of the CableDiameter.

Cable Type

The only Cable Type currently offered is Umbilical.

The Line Type data that are derived, and the associated underlying expressions, are detailed inModelling Hoses and Cables.

Data for HosesThe Line Type Wizard helps you build a line type to represent a hose, based on the followingdata. A limited amount of available project data has been collated and used to derive purelyempirical relationships between the diameter of types of hose and certain line type dataquantities. The input data consists of:

Hose Inner Diameter

Each derived line type property is a function of the hose inner diameter.

Hose Type

The Hose Type can be one of high pressure, low pressure or fold-flat. These categoriesroughly cover the available project data.

The Line Type data that are derived, and the associated underlying expressions, are detailed inModelling Hoses and Cables.

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Outer and Inner DiametersThe Line Type Wizard sets up Outer and Inner Diameters for hoses and cables as follows:

Hoses

The inner diameter (ID) is specified by the user and the outer diameter (OD) is a function of theinner diameter:

OD = 1.40 ID m (for High Pressure) [90% 150%]OD = 1.28 ID m (for Low Pressure)OD = 1.34 ID m (for Fold-Flat)

Cables

The inner diameter (ID) is set to zero and the outer diameter (OD) is specified by the user.

Mass per unit lengthThe Line Type Wizard sets up mass for hoses and cables as follows:

Hoses

For each type of hose the mass per metre has been estimated as a function of inner diametergiving:

Mass per metre = 0.7523 ID te/m (for High Pressure) [55% 145%]Mass per metre = 0.3642 ID te/m (for Low Pressure)Mass per metre = 0.1844 ID te/m (for Fold-Flat)

Cables

For the cables the mass per metre has been estimated as a function of outer diameter giving:

Mass per metre = 1.8 OD² te/m (for Umbilical) [35% 170%]

Axial and Bending StiffnessThe Line Type Wizard sets up Axial and Bending Stiffness and Limit Compression for hosesand cables as follows:

Axial Stiffness

For each type of hose the axial stiffness has been estimated as a function of inner diametergiving:

Axial Stiffness = 2.80 x 10^6 ID kN (for High Pressure) [40% 160%]Axial Stiffness = 3.40 x 10^4 ID kN (for Low Pressure)Axial Stiffness = 6.56 x 10^3 ID kN (for Fold-Flat)

For the cables the axial stiffness has been estimated as a function of outer diameter giving:

Axial Stiffness = 1.44 x 10^6 OD kN (for Umbilical) [15% 415%]

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Bending Stiffness

For each type of hose the bending stiffness has been estimated as a function of inner diametergiving:

Bending Stiffness = 3 x 10^4 ID^4 kN.m² (for High Pressure) [45% 300%]Bending Stiffness = 6 x 10^2 ID^3 kN.m² (for Low Pressure)Bending Stiffness = 1 x 10^3 ID^3 kN.m² (for Fold-Flat)

For the cables the bending stiffness has been estimated as a function of outer diameter giving:

Bending Stiffness = 3 x 10^3 OD^3 kN.m² (for Umbilical) [55% 240%]

Limit Compression

As the bending stiffness is significant this is set to ‘no’.

7.8.13 Modelling Line EndsModelling Line EndsLines in OrcaFlex run from End A to End B. Travelling from A to B, the orientation of anysegment in the line is defined in terms of Azimuth and Declination angles, relative to globalaxes. Azimuth is measured in the X-Y plane, Declination is measured downwards from the Zaxis. See No-Moment Direction.

No-Moment DirectionAssociated with each end is a stiffness, and a no-moment direction which is described in termsof azimuth and declination. This too uses the 'A to B' convention, so if we hang up a catenary ofline, and then freeze the ends, the no-moment directions are as shown below:

x

z

yDeclinationAngle

AzimuthAngle

No moment direction( Az = 0, Dec = 160 )

No moment direction( Az = 0, Dec = 45 )

End A End B

Figure: Directions

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If the line end is attached to a body which can move (a Vessel or Buoy), then the no-momentdirection is defined relative to the body axes and therefore moves with the body. Otherwise, it isdefined in global axes.

End StiffnessThe stiffness associated with the end can be used to represent an item such as a flexjoint,whose stiffness is in units of moment per unit angle, e.g. kN.m/degree. More commonly, theline end is either free to rotate or fully restrained. In the first case, the end stiffness is set tozero; in the second case, the end stiffness is set to Infinity. Note that it is never necessary (orcorrect) to 'convert' the line stiffness into an end stiffness: the program includes the line stiffnessfor you automatically.

Free-to-rotate or Fully-restrained EndsIn many practical cases, the line ends are neither completely free nor fully restrained.Nevertheless, we recommend that you should usually choose one of these conditions. Whenshould you use one rather than the other? The following notes offer a brief guide:

1. Many systems modelled using OrcaFlex consist of relatively long flexible lines where bendstiffness plays only a minor role in determining the overall forces on and movements of thesystem. In such systems, line ends may safely be modelled as free-to-rotate.

2. An exception to this rule is systems which include one or more 6D buoys. The rotationalmotions of the buoy may then be influenced by moment transfer from the ends of linesattached to it, particularly where buoy rotational inertias are small. In such cases, the endconnections to the buoy should be fully restrained.

3. A further exception is systems where the flexible lines are relatively short and stiff, e.g. alarge diameter under-buoy hose in shallow water. Bend stiffness, including end moments,may have a significant influence on overall system behaviour in such cases, and the endconnections should be fully restrained.

4. Where fully restrained ends are used, it is necessary to pay more attention to the modellingof the line close to the end. In particular make allowance for the additional stiffness of abend stiffener, if one is fitted and use shorter segments near the line ends so as to representthe moments with sufficient accuracy.

5. Roll-on/roll-off contact (e.g. stern rollers, pipelay stingers, mid-water arches for risersystems). A pinned connection at the average contact point is often sufficient. For a moreexact representation, use one or more solids to represent the supporting surface, butremember that there must be sufficient nodes at the line end to interact with the solid.

End Force and End Force Ez-AngleThe figure below shows the end connection of a flexible line fitted with a bend stiffener. The lineapplies a load (tension) T as shown. If the local loads (weight, drag, etc.) on the end part of theline, including the bend stiffener, are small by comparison with T, then the reaction force F isequal and opposite to T, and the bend moment at the end fitting is M = T.h.

OrcaFlex reports the End Force, F, and the End Force Ez-Angle, θ, as shown. The "No momentdirection" is defined in the input data. When the reaction force F acts in the no momentdirection, then the reaction moment M is zero.

It is clear from this that

1. End Force and End Force Ez-Angle are the same whether the end condition is defined asfree-to-rotate, fully restrained, or some intermediate condition;

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2. The bend moment at the end fitting, M, is a function of the lever arm, h, which depends notonly on the end condition but also on the bend stiffness distribution in the line/bend stiffener.

No moment direction

h

T

FM

θ

Figure: End connection of a flexible line fitted with a Bend Stiffener

Design Loads for End FittingsFor design of end fittings, including bend restrictors, the principal parameters provided byOrcaFlex are End Force and End Force Ez-Angle. The moment at the end can then bedetermined by a local (static) analysis which can be developed to incorporate as much detail asrequired.

This approach is usually sufficient, except where End Force is very small. This occurs when theline tension T comes close to zero. The direction of the end force is then no longer dominatedby the line tension, and other loads (shear, local drag and inertia loads etc.) which are usuallynegligible become important. In these conditions, the reported End Force Ez-Angle ismisleading and a more appropriate estimate should be made from the system geometry. Thiscan be done using the Ez-Angle results variable. Ez-Angle for any segment gives the angle ofthat segment relative to the No Moment Direction at the adjacent line end, including allowancefor the motion of line end where the line is attached to a vessel or buoy. Ez-Angle for a pointnear the end of the bend restrictor is a reasonable alternative where End Force Ez-Angle is notsuitable.

Results for Line EndsWhen examining results at line ends note that if a stiff pipe goes into compression, line tensionbecomes negative but End Force remains positive, and End Force Ez-Angle may approach180º.

Curvature is calculated in OrcaFlex by dividing the angle change at any node by the sum of thehalf-segment lengths on each side of the node: bend moment is curvature multiplied by bendstiffness. At the end, OrcaFlex takes the angle change between the end segment of the lineand the no-moment direction, and reports the corresponding curvature and bend moment basedon the half length of the end segment. Where bend stiffness at the line end is zero (pinned endor a zero stiffness line), curvature and bend moment are reported as zero.

Design Data for Bend RestrictorsWe classify bend restrictors into 3 types:

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• Bellmouths: curved surfaces which support the flexible and maintain acceptable curvature.

• Bend Limiters: articulated devices which rotate freely to a specified curvature, then stop.

• Bend Stiffeners: elastomeric devices which provide a tapered additional bend stiffness.

Different design information is required for each type:

Bellmouth

The principal design requirement is that bellmouth angle should be greater than the maximumvalue of End Force Ez-Angle. For cases where the bellmouth is not radially symmetrical,OrcaFlex reports components of End Force Angle in the local XZ and YZ planes. End ForceEzx-Angle is the component in the local xz plane; End Force Ezy-Angle is the component in thelocal yz plane.

Bend Limiter

There are two design requirements:

1. The limiter length must be not less than a*R where a is End Force Ez-Angle and R is thelimiter locking radius.

2. The limiter must be capable of withstanding the maximum bend moment M given by M =R*F*(1-cos(a)) where F, a are simultaneous values of End Force and End Force Ez-Angle.OrcaFlex reports Bend Restrictor Load P = F*(1-cos(a)) as an aid to bend limiter design. Pis sometimes called "pseudo-curvature".

Bend Stiffener

The design process is more complex and the critical design load cases are not always self-evident. An X-Y graph of F against a (End Force against End Force-Ez Angle) provides acomplete definition of the loading for one analysis case, with each (F,a) pair defining a loadcase. The bend stiffener should be designed to prevent infringement of the permitted curvaturefor any (F,a) pair. In practice, it is often sufficient to consider just the three (F,a) pairscorresponding to maximum values of End Force F, End Force Ez-Angle a and Bend RestrictorLoad P.

7.8.14 Modelling Compression in FlexiblesModelling Compression in FlexiblesWhen a flexible line experiences compression, it responds by deflecting transversely: themagnitude of the deflection is controlled by bend stiffness. Under static conditions, thebehaviour of an initially straight section of line under pure axial loading is described by classicEuler buckling theory. This defines the maximum compressive load - the "Euler load" - which aparticular length of line can withstand before transverse deflection occurs. The Euler load is afunction of the length of the straight section, the bend stiffness and the end conditions. For asimple stick of length L, bend stiffness EI, with pin joints at each end, the Euler load is π²EI/L².The Euler load is derived from a stability analysis: it tells us the value of axial load at whichtransverse deflection will occur but nothing about the post-buckling behaviour.

Under dynamic loading conditions, the transverse deflection is resisted by a combination ofinertia and bending. OrcaFlex is fully capable of modelling this behaviour provided thediscretisation of the model is sufficient, i.e. provided the segments are short enough to modelthe deflected shape properly. Another way of saying the same thing is that the compressiveload in any segment of the line should never exceed the Euler load for the segment.

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Notes: Why are these two statements equivalent? Imagine the real line replaced by aseries of rigid sticks connected by rotational springs at the joints - this isessentially how OrcaFlex models the line. Under compression, the linedeflects: the sticks remain straight and the joints rotate. Provided thewavelength of the deflection is longer than the length of the individual sticksthen the rigid stick model can approximate it: shorter sticks give a betterapproximation.

If the compressive load reaches the Euler load for an individual stick, then thereal line which the stick represents will start to deform at a shorter wavelength,and deflections within the stick length become significant. Clearly, this stickmodel is no longer adequate. By replacing each long stick by several shortones, we can make the Euler load for each stick greater than the appliedcompressive load. Each stick will then remain straight, but we now have moresticks with which to model the deflected shape.

This gives us a convenient way of checking the adequacy of our model: provided thecompressive load in each segment always remains less than the Euler load for that segment,then we can have confidence that the behaviour of the line in compression is adequatelymodelled. OrcaFlex makes this comparison automatically for all segments and reports anyinfringements in the Statistics tables. The segment Euler load is also plotted in tension rangegraphs (as a negative value - compression is negative) so that infringements are clearly visible.

If the segment Euler load is infringed during a simulation, then we have to decide what to doabout it. If infringement occurs only during the build-up period, perhaps as a result of a startingtransient, then we can safely ignore it. If it occurs during the main part of the simulation, thenwe should examine the time histories of tension in the affected areas. Where infringements aresevere and repeated or of long duration the analysis should be repeated with shorter segmentsin the affected area. However it may be acceptable to disregard occasional minor infringementsof short duration on the following grounds:

• transverse deflection caused by compression takes some time to occur because of inertia.

• the segment Euler load used in OrcaFlex as a basis for comparison is the lowest of thevarious alternatives, and assumes pinned joints with no bend stiffness at each end of thesegment. This is a conservative assumption.

• whether or not to disregard an infringement is a decision which can only be taken by theanalyst in the context of the task in hand.

Limit Compression SwitchFor each line type, the data includes a Limit Compression switch.

The usual setting is "No". This means that each segment of this line type is treated as a strutcapable of taking whatever compressive loads arise in the course of the simulation.

For some special cases, such as chains and soft ropes with little bend stiffness, this is not themost useful model and OrcaFlex offers an alternative. Lines of this sort cannot takecompression at all, so the "Limit Compression" switch can be set to "Yes". OrcaFlex then doesnot allow compressive loading greater than the segment Euler load (which is zero if the bendstiffness is zero).

Note: In either case, if the segment Euler load is reached then a Warning is given onthe result form and in the statistics table.

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7.9 LINKS

7.9.1 LinksLinks are simple spring or spring/damper connections linking two points in the model, forexample a node on a line to a vessel, or a buoy to an anchor. They pull the two points together,or hold them apart, with a force that depends on their relative positions and velocities.

Links have no mass or hydrodynamic loading and simply apply an equal and opposite force tothe two points. They are useful for modelling items such as wires where the mass andhydrodynamic effects are small and can be neglected; for example buoy ties can sometimes bemodelled using links.

Two types of Link are available:

Tethers

simple elastic ties that can take tension but not compression. The unstretched lengthand stiffness of the tether are specified. The tether remains slack and does not apply aforce if the distance between the ends is less than the unstretched length.

Spring/Dampers

combined spring and independent damper units. The spring can take both compressionand tension and can have either a linear or a piecewise-linear length-force relationship.The damper velocity-force relationship can also be either linear or piecewise-linear.

Spring-Damper:

Tether:

Figure: Types of Link

7.9.2 General DataName

Used to refer to the Link.

Type

may be either:

• Tether: a simple elastic tie having linear stiffness and no damping.

• Spring/Damper: a combined spring and independent damper, each of which can havelinear or piecewise-linear tension relationship.

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7.9.3 ConnectionsConnect to Object and Object Relative Position

Specifies the objects to be linked. A point on a Line is specified by arc length measured fromend A; the link is attached to the nearest node. For a point on a Buoy or Vessel, the specifiedcoordinates are relative to the object's origin. For a Fixed end they are relative to the globalorigin. For an Anchored end, the X and Y coordinates are relative to the global origin, but the Zcoordinate is relative to the seabed at that X,Y position.

Release at Start of Stage

The link can be released at the start of a given stage of the simulation, by setting this number tothe stage number required. Once released a link no longer applies any forces to the objects itconnects. If no release is required, then set this item to '~'.

7.9.4 PropertiesUnstretched Length

Is the unstretched length of the Tether or Spring.

Linear

Both the spring and damper in a Spring/Damper can have either simple linear forcecharacteristics or else a user-specified piecewise-linear force table.

Stiffness

For a tether the tension t depends on its strain and stiffness as follows:

t = k.(L-L0)/L0

where

k is the specified Stiffness,

L is the current stretched length between the two ends,L0 is the specified Unstretched Length.

Tethers remain slack and exert no force if L is less than L0.

For a linear spring in a Spring/Damper the tension (positive) or compression (negative) isgiven by:

t = k.(L-L0)

where

k is the specified Stiffness,

L is the current stretched length between the two ends,L0 is the specified Unstretched Length.

The linear spring does not go slack if L is less than L0, but instead goes into compression.

Warning: Please note that this is not the same formula as for tethers.

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Damping

A linear damper in a Spring/Damper exerts an extra tension of

t = c.(rate of increase of L)

where

c is the specified Damping,L is the current stretched length between the two ends.

Piecewise-Linear Force Tables

For a piecewise-linear spring (or damper) the force characteristic is specified as a table oftension against length (or velocity). The table must be arranged in increasing order of length(velocity) and a negative tension indicates compression. For a passive damper the tensionsspecified should therefore normally have the same sign as the velocities, since otherwise thedamper will apply negative damping. For lengths (velocities) between, or outside, thosespecified in the table the program will use linear interpolation, or extrapolation, to calculate thetension.

7.9.5 ResultsFor details on how to select results variables see Selecting Variables.

For links the following variables are available:

Tension

The total tension in the link.

Length

The current stretched length of the link.

Velocity

The rate of increase of the stretched length.

Azimuth and Declination

The azimuth and declination angles, relative to global axes, of the 'downstream' direction of thelink.

7.10 WINCHES

7.10.1 WinchesWinches provide a way of modelling constant tension or constant speed winches. Theyconnect two (or more) points in the model by a winch wire, fed from a winch inertia (typicallyrepresenting a winch drum) that is then driven by a winch drive (typically representing the winchhydraulics that drive the drum).

As well as connecting its two end points, the winch wire may, optionally, pass via intermediatepoints, in which case it does so as if passing over a small frictionless pulley at that point. The

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wire tension either side of the intermediate point is then applied to that point; if the point is offseton the object involved then this also gives rise to an applied moment.

Winch Drive Winch Inertia

DriveForce f t t

t WireTension t

Winch may pull viaintermediate objects

Winch wire

Figure: Winch Model

Two types of winch are available in OrcaFlex:

Simple Winches

Simple Winches model perfect constant tension or constant speed performance and areeasiest to use. It is assumed that the winch inertia is negligible and the winch drive isperfect, so that it always exactly achieves the requested constant tension or constantspeed. Because of these assumptions, no data needs to be given for the winch inertiaor winch drive.

Detailed Winches

Detailed Winches include modelling of the performance of the winch drive system - itsdeadband, stiffness, inertia, damping and drag - but therefore require more data and areharder to set up.

We recommend using Simple winches unless you know the characteristics of the winch drivesystem and believe that its performance significantly differs from the constant tension or speedideal. In particular, Simple winches are appropriate:

• at the early design stage, when the type of winch to be used has not yet been decided

• if the duty is such that the winch drive will give near to perfect constant tension or constantspeed performance

• if the winch drive data are not available

Winch Control

OrcaFlex winches allow quite complex offshore operations to be modelled. The winch drive canbe operated in either of two modes:

Length Control Mode

For modelling constant speed winches. The winch wire is paid out or hauled in at a velocityspecified in the data.

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Force Control Mode

For modelling 'Constant tension' winches. Since such winches are usually hydraulic deviceswhose performance deviates quite seriously from the constant tension ideal, OrcaFlex Winchesprovides facilities for modelling winch deadband, damping and drag forces (force decrementsproportional to velocity and velocity² respectively) and winch stiffness effects such as thosecaused by hydraulic accumulators.

The winch can be switched between these two modes at predetermined times during thesimulation and the constant velocity or target tension can also be varied.

7.10.2 Winch DataName

Used to refer to the Winch.

Type

May be either Simple or Detailed. See Winches.

Connect to Object and Object Relative Position

The (mass-less) winch wire connects at least two objects, one at each end of the winch wire.

If more than 2 are specified then the winch wire passes from the first connection point to the lastvia the intermediate points specified. When intermediate connections are specified, the winchwire slides freely through these intermediate points as if passing via small friction-less pulleysmounted there. The winch wire tension on either side then pulls on the intermediate points, soapplying forces and moments (if the points are offset) to the objects concerned.

Each connection is defined by specifying the object connected and the object-relative position ofthe connection point.

For connecting to a Line, the object-relative z coordinate specifies the arc length to theconnection point, measured from end A. The winch wire is then connected to the nearest node.The x,y coordinates are ignored.

For Fixed connections the object-relative coordinates given are the global coordinates of thepoint.

For connecting to an Anchor, the object-relative x,y coordinates given are the global X,Ycoordinates of the anchor point, and the z-coordinate is the distance of the anchor above(positive) or below (negative) the seabed at that X,Y position.

For connecting to other objects, the coordinates of the connection point are given relative to theobject local frame of reference.

Release at Start of Stage

The winch wire can be released at the start of a given stage of the simulation, by setting thisnumber to the stage number required. Once released the winch no longer applies any forces tothe objects it connects. If no release is required, then set this item to '~'.

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7.10.3 Wire PropertiesWire Stiffness

Elastic stiffness of the winch wire.

Wire Damping

Material damping value for the winch wire.

Note: The mass of the winch wire is not modelled.

Winch Inertia (Detailed Winches only)

The inertia of the winch drive, which resists changes in the rate of pay out of haul in of the winchwire if the winch is in Force Control Mode. The Winch Inertia has no effect if the winch is inLength Control Mode.

This is a linear, rather than rotational, inertia. To represent the rotational inertia of a winchdrum, set the winch inertia to

l / r²

where

I = drum rotational inertia,r = radius at which the wire is fed.

Notes: The winch inertia does not contribute to the mass of any objects to which thewinch is attached and so does not directly resist acceleration of any of theconnection points. (Such accelerations are resisted indirectly, of course,through the changes they cause to the winch wire path length and hence tothe winch wire tension.) To include the true translational inertia of the winchdrive, drum and wire it is necessary to suitably increase the masses of theobjects to which it is attached.

Setting the winch inertia to a small value to model a low inertia winch can leadto very short natural periods for the winch system. These then require veryshort time steps for the simulation, slowing the simulation. To avoid this, thewinch inertia can be set to zero, rather than to a small value; the winch systeminertia is then not modelled at all, but the short natural periods are thenavoided. See Winch Theory for full details of the algorithm used when thewinch inertia is zero.

7.10.4 ControlWinch Control

For the static analysis, the Mode of the winch drive can be set to one of Specified Length orSpecified Tension.

Specified Length

The winch drive is locked with the unstretched length of winch wire out, L0, being set to theValue specified. The winch wire tension t then depends on the stretched length L of the winchwire path.

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Specified Tension

The winch drive operates in perfect constant tension mode, the tension t being the Valuespecified. The unstretched length out L0 is then set to correspond to this tension.

During the simulation the winches are controlled on a stage by stage basis. For each stagethe winch control mode can be set to one of Specified Payout or Specified Tension.

Specified Payout

The Value specifies the unstretched length of winch wire to be paid out (positive) or hauled in(negative) at a constant rate during that stage. That is, the Value specifies the total change inunstretched length during the stage, so to keep a constant length set the Value to zero.

Specified Tension

The Value specifies the nominal constant tension for this stage. In Simple winches the winchdrive is assumed to always achieve this nominal tension, so the Value is used as the actualwinch wire tension. In Detailed winches this nominal tension is used as the target tension forthe winch drive, which then applies drive force to the winch inertia to try to achieve this targettension. The algorithm for the winch drive force is designed to model the characteristics of real-world winches that are nominally "constant tension". See Winch Theory.

Note: Changes of nominal tension are applied instantly at the start of each stage,and this can therefore apply a shock load which, if large enough, may affectthe stability of the simulation.

7.10.5 Drive UnitNote: The drive unit data applies to Detailed Winches only

Winch Drive

The winch drive controls the winch wire in one of two winch control modes - Length ControlMode ("Specified Length" for statics, "Specified Payout" for dynamics) or Force Control Mode("Specified Tension").

• Length Control Mode is for modelling a constant speed winch. The winch tension thendepends simply on the unstretched length of winch wire out, and the wire properties(Stiffness and Damping).

• Force Control Mode is for modelling a (nominally) constant tension winch. Because suchwinches often deviate quite seriously from the constant tension ideal, facilities are providedfor modelling winch Deadband, Damping, Drag and Stiffness.

Deadband

A deadband of +/- this value is applied to the winch drive force between hauling in and payingout the winch. See Winch Theory. for full details.

Stiffness

This can be used to model, for example, winch hydraulic accumulators. It is the rate at whichthe zero-velocity winch force (the drive force applied when the winch is neither hauling in norpaying out) varies with the total unstretched length of winch wire paid out. See Winch Theory.

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Damping Terms A and B

These terms can be used to model damping in a winch's hydraulic drive system. The winchdrive force is taken to vary with haul-in/payout velocity at rates A and B, respectively. SeeWinch Theory.

Drag Terms C and D

These terms can be used to model drag in a winch's hydraulic drive system. The winch driveforce is taken to vary with haul-in/payout velocity² at rates C and D, respectively. See WinchTheory.

7.10.6 ResultsFor details on how to select results variables see Selecting Variables.

For winches the available variables are:

X, Y and Z

The coordinates of the winch mount point, relative to global axes.

Tension

The tension in the winch wire.

Azimuth and Declination

The azimuth and declination angles of the 'downstream' direction of the winch wire, relative tothe global axes.

Declination is in the range 0 to 180 degrees. Range jump suppression is applied to Azimuth (sovalues outside the range -360 to +360 degrees might be reported).

Length

The unstretched length of winch wire paid out.

Velocity

The rate of pay out of winch wire. Positive value means paying out, negative value meanshauling in.

Surface Z

The elevation of the sea surface directly above the instantaneous position of the winch mount.

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8 VIV TOOLBOX

8.1 VIV TOOLBOXThe OrcaFlex VIV Toolbox provides analysis of vortex induced vibration (VIV) of lines. It offersa choice of various alternative ways of modelling VIV, including both frequency and time domainapproaches, and is the product of extensive and ongoing research in co-operation withacademics in the UK and USA.

VIV analysis is a specialised area that is not required by all OrcaFlex users. Because of this theVIV Toolbox is an optional facility and to use it you will need a VIV licence, which you canpurchase or lease from Orcina.

When OrcaFlex starts up it looks for a VIV licence on your dongle. If one is available, and thedongle is not shared with other users over a network, then OrcaFlex claims the VIV licence andthe VIV Toolbox is enabled. This is indicated by 'VIV' being included in the list of availablemodules, displayed at the top of the OrcaFlex main window.

If the dongle is shared over a network, then any VIV licences on it are shared with other usersand so may not always be available. If one is available OrcaFlex gives you the choice ofwhether to claim it, so you can choose to leave it free for other users if you do not need it.

For further information see Running OrcaFlex.

Different VIV Models

The VIV Toolbox provides facilities for using the following different VIV models:

• VIVA Interface. The VIV Toolbox provides a fully integrated link to VIVA. OrcaFlexautomatically prepares the VIVA data from the OrcaFlex data, calls VIVA and presents theresults. To use this you will need a copy of VIVA, release 2.0.3 or later.

• SHEAR7 Export. The VIV Toolbox provides facilities for exporting a SHEAR7 .mds file forthe current OrcaFlex model. This file is one of two data files needed by SHEAR7 (and is themore difficult of the two to generate manually).

• Milan wake oscillator model

• Iwan and Blevins wake oscillator model

• Vortex Tracking model.

Of all these models, VIVA and SHEAR7 are the two main programs in current use in theindustry. They are both independent non-Orcina programs written and distributed by othercompanies, so to use them you need to purchase and install them on your machine. They areboth frequency domain models, so they only analyse steady state conditions.

The other models are included in the VIV Toolbox within OrcaFlex, so no further software isneeded. They are all time-domain models, so they can analyse non-steady-state conditions.They do not yet have a track record in the industry.

For details, see Using VIV Models and the links above to the individual models, in the OrcaFlexhelp file.

Testing, Verification and Warranties

VIVA and SHEAR7 are interfaces to third party analysis packages. Orcina’s warranty is limitedto providing the data required by each package in the required format to allow the package to

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commence its analysis. We cannot accept any responsibility for the results of the analysis, orfor any failure by the third party package to complete the analysis, save insofar as the failure tocomplete results from incorrect preparation of the input data.

The other models are software implementations by Orcina of published theory. We have testedour implementations and give guidance to users on the assumptions implicit in using thesemethods for analysis of practical risers, but give no warranties that such use is valid.

Any commercial use of these VIV models is at the user’s own risk and on the understanding thatusers are aware of the assumptions involved and have taken steps to satisfy themselves thatthey are justified.

For further details contact Orcina.

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9 TECHNICAL NOTES

9.1 MODELLING BEND RESTRICTORSFirst some terminology that we use:

• A bend restrictor is any device that controls bending at a line end.

• A bend limiter is something that has no effect until a certain curvature is reached, and thencurvature is prevented from going above that value. See Modelling Bend Limiters below.

• A bend stiffener is something that provides increased bend stiffness near the line end, tomore evenly distribute the bending near the end. See Modelling Bend Stiffeners below.

Modelling Bend Limiters

Non-linear bend stiffness can be used to model a bend limiter. See example G10.

A reasonable number of segments will be needed to model the limiter and this require a shortertime step and hence longer run times. To avoid this problem you could use a global model, withthe bend limiter omitted, and then a separate local model to examine how the line behavesaround the limiter. This is valid providing the limiter only has local effects.

Modelling Bend Stiffeners

To model a bend stiffener in OrcaFlex, use a series of short sections near the end of the line, torepresent the bend stiffener. Each of these sections can then be of a different line type, andthese line types can be given different bend stiffness values, according to where it is in thestiffener - the nearer the root then the higher the bend stiffness. The bend stiffness valuesshould include both the bend stiffener stiffness at that point and the pipe bend stiffness.

The approach just described applies where a bend stiffener has already been designed, andone of the objectives of the analysis is to confirm that the stiffener provides the requiredprotection. However, in many cases the stiffener design does not yet exist and the analysis isneeded in order to define design loads. If this is the case, then run a preliminary analysis usinga pinned end (i.e. zero bending stiffness at the line end connection). The load informationrequired for bend stiffener design then consists of paired values of tension and angle at thepinned end. These can be extracted in the form of an X-Y plot showing Effective Tensionagainst Ez Angle for the first segment. In practice, it is often sufficient to consider just threepoints on this graph, corresponding to maximum tension, maximum angle and maximum bendrestrictor load: these can be extracted as linked statistics.

As an example, look at Example A01 Catenary Riser. The top end of the riser (End A) is pinnedto the ship near the bow. Turn on the Draw Local Axes option and note the direction of the linez axis at End A. The Ez Angle for the first segment is the angle between this direction and thesegment direction. A graph of Effective Tension at End A vs Ez Angle at End A gives theinformation required. Recall that Ez Angle is an absolute magnitude and is therefore alwaystakes a positive value. If a signed value is required (e.g. to define out-to-out load cycles forfatigue analysis), then use the Ezx or Ezy angle as appropriate.

It is usually necessary to combine results from several analysis runs in order to fully define thebend stiffener design loading. This is most conveniently done by exporting the EffectiveTension vs Ez Angle results as a table of values for each analysis case, combining into a singleExcel spreadsheet and using the plotting facilities in Excel to generate a single plot with allresults superimposed. A simplified set of load cases representing the overall loading envelope

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can then be selected for use in stiffener design. The export to Excel can be done manually orautomated through the Results spreadsheet.

Bend Stiffener Design - OrcaBend

The task of bend stiffener design is usually left to the manufacturer, since the actual stiffenershape selected is governed in part by the manufacturing process, availability of tooling, etc., aswell as by the load cases. The Orcina program OrcaBend has been developed to assist thisprocess. There is a demonstration version of OrcaBend on the OrcaFlex CD - seeCD:\Demo_CD\ReadMe for details. For further information contact Orcina.

9.2 MODELLING DESIGN WAVESDesign wave heights and periods are commonly provided as a design input, but this is notalways so, and the data are sometimes incomplete or in a different form from that required forOrcaFlex. For a comprehensive discussion, see Tucker (1991) on which the following notes arebased.

Maximum Storm

In the absence of measured wave data, the maximum storm can be estimated from windstatistics on the assumption that the waves are generated by the local winds. The governingparameters are fetch (i.e. the length of open water over which the wind blows), wind speed andduration. Significant waveheight, Hs, and average zero up-crossing period, Tz, can then beestimated from equations given by Carter (1982):

Fetch-limited

Hs = 0.0163 × √X × U

Tz = 0.439 × X^0.3 × U^0.4

Duration-limited

Hs = 0.0146 × D^5/7 × U^9/7Tz = 0.419 × D^3/7 × U^4/7

where X is fetch in km, U is wind speed in m/s at 10m above mean sea level, and D is durationin hours.

Maximum Individual Wave Height

Expected maximum waveheight Hmax, occurring in time T in a storm of significant wave heightHs, average zero crossing period Tz is

Hmax = k.Hs.√(½ Loge(N)), where N = T/Tz

Most wave statistics are based on measurements taken at 3 hour intervals so T shouldgenerally not be greater than 10800s. The factor k provides for the fact that the highest wavecrest and deepest trough in any given storm do not in general occur together. The maximumcrest-to-trough waveheight is generally less than the sum of the maximum crest elevation plusmaximum trough depth. Tucker recommends k = 0.9 for the maximum wave; k = 1.0 for morefrequent waves (fatigue waves).

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Period of the Maximum Wave

The period associated with the maximum wave Tass, can take a range of values. Tuckerrecommends

1.05 . Tz < Tass < 1.40 . Tz

The spectral peak period Tp is sometimes specified rather than Tz.

For the ISSC spectrum

Tp = 1.41 . Tz

For the JONSWAP spectrum, the factor varies with the peak enhancement factor γ. TheOrcaFlex random wave data form reports the spectral peak frequency fm for the selectedspectrum where Tp = 1/fm.

For the mean JONSWAP spectrum, γ = 3.3 and

Tp = 1.29 . Tz

Wave Conditions for Short Term Operations

For operations lasting from a few hours to a few days, different criteria apply. A typicalrequirement is to determine the maximum seastate in which a given operation can safely takeplace. Whilst the complete operation may take many hours or even days, critical parts such aslanding an item of equipment on the seabed may only take a few minutes. It would be tooconservative to apply 3 hour maximum conditions in such a case.

The question comes down to a balance of cost against risk. The overall risk of failure must besmall enough to be acceptable (how small - 1%, 0.01%?), but the cost rises disproportionatelyas the level of acceptable risk is reduced. The risk of encountering a large wave is only one ofmany elements to be considered in assessing overall risk. This is a big subject which is rarelyaddressed rigorously.

There is a need here for some feedback from practical experience to determine what is inpractice acceptable and what is not. Hindcasting of operations which took place successfully inwhat were judged to be marginal conditions, and of operations which were not successfulbecause of weather conditions could provide a calibrated basis for analysis of future operations.I don't know anyone who has done this. Until they do, we are left with subjective judgement -i.e. we guess.

A common guess is to combine the significant wave (a regular wave of height Hs, period Tz orTp according to preference) for the assumed seastate with a maximum tidal current, applyingboth waves and current from the worst direction. This has no objective basis, but is plausible.

Recommendations

1. Use regular waves for preliminary work. Regular waves are easier to set up, quicker to run,and easier to understand. For regular wave analysis we recommend that you use the Deanstream function theory.

2. If random sea analysis is required, determine the heights and period ranges for themaximum design waves as above, then generate suitable wave trains incorporating thesewaves following the procedures detailed in Setting up a Random Sea.

3. For analysis of permanent systems (e.g. flexible risers) use expected maximum wave heightwith the appropriate return period (commonly 50 or 100 years return period for 5 to 20 yearfield life) and a range of associated wave periods. If field specific data are not available, usethe period range recommended by Tucker.

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9.3 MODELLING GUIDE TUBESAssume we wish to model a pipe running through a vertical guide tube in the moonpool of adrilling rig. The guide tube prevents the pipe from moving more than a small distance in theship X and Y directions but allows free motion in the Z direction (we neglect friction between theriser and the guide). Example data file GUIDE.DAT shows two ways of modelling a guide.

The first option is to use two Links to eliminate motion in the X and Y directions. The linksshould be specified as Spring/Dampers, not Tethers, so that the spring can take compression.Note that the ends of the links are attached to and move with the ship: you can, of course, fixthem globally if this is appropriate. Note also that each link is made very long so that verticalmovement of the node to which it is attached makes very little difference to the force in the link,and the link remains near-normal to the pipe.

The second option is to use a cylinder shape as a guide tube. Again, this can be attached tothe ship or fixed globally. The guide must be long enough to ensure that there is always at leastone node of the pipe within it, preferably 2 or more. When using the Solid Cylinder option,OrcaFlex may find a static solution with the pipe outside the guide. If this happens, then add atemporary link to force the pipe inside. This is done in the example with the link "Temp_Tie". Itslength and end position are chosen so as to pull the riser close to the centre of the cylinder, butto be slack when static convergence is achieved (this is quite easy to arrange by trial and error).Note also that this temporary tie is arranged to release at the start of the dynamic simulation.

What stiffness values should we use for the links or the cylinder, and can we model the smallamount of clearance between the pipe and the guide?

It is not generally necessary to model the true contact stiffness between a steel pipe and a steelguide tube. The important criterion is that the pipe should not penetrate the guide so much asto invalidate the model: in practice this usually means that a few millimetres penetration is quiteacceptable. If you have some idea what contact force you are expecting, this will enable you toset an acceptable stiffness. If not, then a preliminary trial run will give you some idea of whatyou need. In general, it is not a good idea to set the stiffness too high as this may lead to noisein the results and possibly to integration instability and the need to re-run with a shortertimestep.

Clearance is easy to represent with the Solid Cylinder: remember that solid contact occurs atthe centreline of the pipe, and set the internal radius equal to the required annular clearance.Representing clearance using Links is more difficult and is not recommended.

9.4 MODELLING MID-WATER ARCHESSteep and Lazy S riser systems use mid-water arches to support groups of risers. The risersare typically clamped to the top of the arch and lie on the curved surface to either side. Thearch radius is chosen to be not less than the minimum bend radius for the risers.

There are two types of arch. Type A provides a separate flared trough for each riser; Type Buses a single curved apron plate for all the risers with dividers at the top to prevent the separaterisers slipping sideways. Type B appears to be the preferred design for most present dayprojects and is the type principally discussed here.

A typical Type B arch is shown below. The structure consists of 2 or 4 buoyancy tanks with anarched apron plate over. There is additional structure to connect the elements together, anddetails at the crown of the arch to separate the several risers: these details are omitted from thesketch.

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X

Z Z

Y

Y

X

Apron Plate

BuoyancyTank

Lz

Ly

Lx

Figure: Mid-water Arch

OrcaFlex Modelling

The arch itself, including its mass, buoyancy and hydrodynamic properties, is best representedas a 6D Buoy in OrcaFlex, using the Lumped Buoy option.

Derivation of the data items for the 6D buoy is not easy and requires close attention. Thestarting point is to decide what to include in the buoy model: in particular, are there anyenclosed or nearly enclosed volumes within the buoy which will trap water and force it to movewith the buoy? For the arch shown in Fig 1, the apron plate effectively prevents flow in the Xand Z directions, and the structure required to hold the buoy together will severely restrict flowin the Y direction. We may therefore approximate the arch as a closed box of dimensions Lx,Ly, Lz, partly full of water, and derive mass, volume and hydrodynamic properties accordingly.

Treating the arch as an "equivalent rectangular box", the volume of displacement is

V = Lx . Ly . Lz m³

If the net buoyancy of the buoy is B te, then the total mass of the buoy including trapped wateris

M = ρV - B

Moments of inertia about X, Y and Z axes through the centre of gravity can be calculated indetail, but it is usually sufficient to estimate the radii of gyration by eye. The positions of the CGand centre of buoyancy must also be estimated. Note that OrcaFlex defines the CG as theorigin of the local coordinate system for the arch.

Estimating the hydrodynamic properties of the equivalent box is described in HydrodynamicProperties of a Rectangular Box . Note, however, that we at present recommend setting allrotational hydrodynamic properties to zero for the reasons set out at the end of this note.

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Connecting Risers to the Arch

The simplest approach is to omit the length of riser in contact with the arch (the mass of whichshould be added to the arch mass), and connect the risers to either side of the arch using pinjoints. See Lazy S Riser - simple.

Alternatively, riser contact with the apron plate can be represented by attaching two cylindricalsolids to the arch Lazy S Riser - detailed. In this case, it is necessary to use sufficient nodes inway of the arch to ensure good representation of riser/arch contact.

Advantages of the Pin Joint approach are:

• It is simpler to set up.

• It is generally quicker to run because it does not demand such short segments in the risersnear the arch (short segments mean short time steps and longer runs). Note however, thatfor some systems it is necessary to use short segments at touchdown in the lowercatenaries and this may determine the time step.

• Riser exit angles in 3 planes are easily defined as a basis for determining the size of theapron plate.

Disadvantages are:

• The risers are connected at the wrong points so the moments acting on the arch are notcorrect.

Advantages of the Solid Cylinders approach are:

• It is a better representation of the real system.

• Riser exit angles in the horizontal plane at the top of the arch are readily extracted.

Disadvantages are:

• "Full" static analysis is necessary to take account of riser/cylinder interaction, probablystarting from a spline. This can be time-consuming to set up.

• Longer run time (ARCH_SB takes about 10 times as long to run as ARCH_PB).

9.5 TYPICAL LINE TYPE PROPERTIESThe physical properties of the lines are set out in the Line Types form. Where possible, specificdata provided for the project should be used, but this is not always possible. Data may beunavailable, incomplete or even incorrect. Where good quality data specific to the project arenot available, you could use typical values. Some typical values are given below. Anotheruseful resource is the Line Type Wizard.

Typical Line Hydrodynamic Data

The hydrodynamic properties suggested here apply to smooth cylindrical lines only.

Normal drag coefficients Cdx, Cdy

The drag coefficient Cd depends on the Reynolds number Re. As a first approximation, thedrag coefficient can be taken as follows:

If Re < 3.8E5 then Cd = 1.2.If Re > 4.6E5 then Cd = 0.7.

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with linear interpolation linearly between these values. The minimum Cd value of 0.7 followsDNV recommendations.

You can estimate the value of Re at the surface by taking the velocity V to be the currentvelocity plus 15% of maximum horizontal wave particle velocity. Wave particle velocities can beobtained from a preliminary OrcaFlex run for the wave alone without current. At the sea surfacein deep water, V = Vc + 0.15 . πH / T where Vc is current velocity, H is wave height and T iswave period.

If Re > 3.8E5 at the surface, then it is probably appropriate to specify variable data for thenormal drag coefficients.

The above values apply where vortex-induced vibration (VIV) is expected to be negligible. Ifsignificant VIV is anticipated, then drag coefficients may be increased significantly. If this is thecase, a more detailed VIV analysis should be carried out.

Axial drag coefficient, Ct

Axial drag results from skin friction only. In subcritical flow (Re < 3.8E5), Ct = 0.008 for asmooth cylinder, 0.011 for a rough cylinder, based on ESDU data. At higher Re, ESDU suggestthat skin friction may be neglected, i.e. Ct = 0. In practice, axial drag is often negligible and Ct =0 is often acceptable.

Normal added mass coefficient

Can = 1.

Axial added mass coefficient

Caa = 0.

Typical Seabed Friction Data

Below is information on the influence in calculations of seabed friction.

Published data are sparse. Some information is given in Puech (1984) and Taylor and Valent(1984). Both references distinguish between sliding friction and starting friction: starting frictionis greater to represent the "breakout" force. OrcaFlex does not draw this distinction. In mostcases, the sliding friction coefficient should be used; this will usually be conservative. Bothreferences are written in the context of the contribution of chains and cables to anchor holdingpower, so we assume the friction values given are axial. Transverse values will be greater,perhaps by 50% to 100%.

The values given below are recommendations from Taylor and Valent.

Line type Seabed Type Starting FrictionCoefficient

Sliding FrictionCoefficient

Chain Sand 0.98 0.74

Mud with sand 0.92 0.69

Mud/clay 0.90 0.56

Wire rope Sand 0.98 0.25

Mud with sand 0.69 0.23

Mud/clay 0.45 0.18

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INDEX— / —/Disable<Module>, 13/DisableDynamics, 13/DisableInteractiveStartup, 13/LocalDongle, 12/NetworkDongle, 12— 3 —3D buoy, 38, 49, 51, 63, 78, 94, 143, 198,

210, 264, 265added mass, 265added mass coefficient, 265drag, 265drag area, 265drag coefficients, 265inertia coefficient, 265statics, 264

3D view, 72, 79, 82, 90, 91, 92, 93, 95, 96,97, 98, 121new, 90

— 6 —6D buoy, 35, 39, 40, 41, 42, 47, 49, 51, 53,

61, 63, 64, 70, 78, 94, 143, 199, 200, 201,210, 266, 267, 268, 270, 271, 273, 274,275, 277, 283, 360added mass, 203added mass coefficient, 277drag moment, 276fluid acceleration force, 203

— A —acceleration, 152, 181, 198, 199, 233, 243,

311, 351accuracy, 215, 296added inertia, 198, 199, 201added mass, 165, 172, 179, 183, 195, 198,

201, 264, 266, 267, 274, 277, 301, 305,322, 325, 326, 329, 331, 3613D buoys, 2656D buoys, 203axial, 322, 325, 331clump, 301coefficient, 171, 181, 198, 201, 203, 264,

277, 305, 329, 3623D buoys, 2656Dbuoys, 277spar buoys, 277

floating line, 184line, 180normal, 322, 326, 331spar buoys, 203vessels, 195

address, 16air density, 193, 221air gun, 63Airy wave, 155, 223

single, 155allowable stress, 306Alpha, 156, 225amplitude, 243, 244, 250analysis, 210anchor, 30, 59anchored, 96, 144, 147, 184, 236, 237, 238,

288, 289, 298, 347, 350angle, 142, 170, 184, 217, 220, 222, 237,

246, 270, 271, 277, 288, 294, 296, 312,348, 353azimuth, 142, 170, 218, 237, 246, 270,

289, 295, 296, 312, 348, 353beta, 279declination, 142, 170, 237, 270, 289, 312,

348, 353Exy-angle, 171, 312Ez-angle, 171, 312Ezx-angle, 171, 312Ezy-angle, 171, 312gamma, 170, 270, 289, 312incidence, 271, 279, 312lay azimuth, 295, 296twist, 312

angular velocity, 202, 273animation, 96, 97API, 20, 222applied, 241, 246, 266, 270

force, 246load, 266, 270

buoys, 270vessels, 246

moment, 246apron plate, 359arc length, 106, 107, 110, 288, 292, 310,

347, 350arch, 35, 36, 38, 39, 40arch radius, 359area, 162, 186, 198, 199, 200, 205, 234,

235, 252, 273, 275, 303moment, 252moment of, 201, 274, 276, 304of contact, 162, 186, 199, 200, 205, 235

arranging windows, 72attachment, 210, 287, 293, 300, 302attachment type, 288, 300auto arrange, 72, 90auto backup, 118AVI file, 97, 112

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axes, 80, 94, 117, 141, 142, 143, 216, 239,316global, 94, 117, 141, 142, 143local, 82, 94, 117, 142, 317vessel, 240

axial, 147, 166, 175, 294, 303, 311, 322,324, 334, 336, 340relative velocity, 311stiffness, 147, 167, 175, 295, 303, 322,

324, 334, 336azimuth, 142, 170, 218, 237, 238, 246, 270,

278, 289, 295, 296, 312, 320, 348, 353end force, 312no moment, 312

— B —background colour, 117ball joint, 183, 289barge, 239Barltrop, 20barriers, 211batch, 66, 68batch processing, 66, 68, 87, 120, 121, 122,

124batch script files, 65, 121bellmouth, 344bend, 59, 110, 146, 147, 148, 163, 166,

173, 178, 183, 216, 288, 294, 303, 312,313, 316, 324, 334, 336, 340, 343, 356,359damping, 167, 216limiter, 59, 344, 356moment, 148, 178, 304, 313radius, 110, 306, 359restrictor, 183, 343, 356restrictor load, 317, 344stiffener, 344, 356stiffness, 147, 148, 165, 168, 173, 289,

294, 304, 324, 334, 337, 341, 356target damping, 167, 216

beta angle, 279bias power, 305black and white, 118Blevins, 21block, 35, 37, 236booms, 184breaking load, 323, 334, 335breakout force, 362breakwater, 234bridle, 38, 54, 359buckling, 173, 176, 344build up, 41, 48, 53, 64, 69, 151, 153, 215bulk modulus, 154, 217, 265, 270, 303buoy, 29, 35, 38, 40, 41, 42, 43, 46, 47, 48,

49, 50, 51, 53, 60, 63, 64, 69, 78, 93, 143,198, 199, 200, 201, 212, 214, 234, 264,

265, 266, 267, 268, 270, 271, 273, 274,275, 277, 279, 283, 346, 3593D, 38, 49, 51, 63, 78, 94, 143, 198, 264,

2656D, 35, 39, 40, 41, 42, 47, 49, 51, 53, 61,

63, 64, 70, 78, 94, 143, 199, 200, 201,266, 267, 268, 270, 271, 273, 274, 275,277, 283, 360

applied load, 270axis, 274axi-symmetric, 266CALM, 266, 283free floating, 213, 283hydrodynamics, 279, 283in static analysis, 214lumped, 35, 40, 51, 200, 266, 273, 274,

360spar, 29, 39, 41, 42, 43, 46, 47, 49, 51,

54, 61, 201, 266, 275, 283statics, 212, 264ties, 346towed fish, 64

buoyancy, 34, 44, 147, 154, 165, 198, 200,217, 265, 266, 267, 276, 286, 300, 303,327, 328, 329, 330, 331, 332, 359distributed, 34, 44module, 327tank, 359variation with depth, 154, 217

buoyant line, 296— C —Ca, 180, 198, 201, 265, 274, 301, 305cable, 56, 62, 210, 265, 286, 320, 338, 339,

340calculation method, 147, 151, 152, 154, 296CALM buoy, 30, 49, 50, 283cantilever, 39caption, 72Carter, 20, 357Casarella, 20cascade, 72, 90catenary, 29, 33, 34, 35, 36, 40, 43, 52, 62,

66, 67, 147, 184, 210, 294riser, 29, 32, 67statics, 147, 184, 210, 294

catenary statics, 37, 147, 162, 296Cd, 179, 201, 274, 301centre, 199, 267, 268, 270, 271, 273, 275,

303, 359of base, 275of gravity, 267, 268, 270, 271, 303, 359of pressure, 267of volume, 199, 273

centrifugal force, 173, 181, 292

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chain, 173, 205, 286, 301, 304, 320, 322,323, 324, 325, 326, 327mooring, 322studless, 323studlink, 323

Chapman, 20check box, 102chinese lantern, 30, 50chord, 268, 270clamped end, 183clash force, 187, 314clash impulse, 314clashing, 32, 40, 41, 42, 47, 57, 60, 62, 69,

113, 187, 247, 266, 313clearance, 32, 42, 45, 69, 113, 187, 310,

313clipboard, 114, 115closest approach, 113, 313clump types, 151, 215, 286, 292, 300clumps, 51, 54, 61, 94, 292, 300

added mass, 301drag, 301

Cm, 201, 265, 274, 305cnoidal wave, 155, 158, 223colour, 93, 102command line parameters, 12, 116comments, 212compare data, 116components, 228

Fourier, 228compressibility, 154, 265, 270, 303compression, 107, 173, 207, 307, 344, 347compressive force, 147connecting objects, 94, 95connections, 143, 183, 235, 277, 288, 347,

350loads, 278shapes, 235

constant, 207, 243, 348, 351, 352speed, 207, 348, 352tension, 207, 348, 352velocity, 243, 348

consultancy, 15contact, 30, 34, 36, 44, 46, 47, 50, 54, 57,

61, 62, 69, 70, 162, 186, 187, 198, 199,205, 234, 235, 239, 303area, 162, 186, 199, 200, 205, 235damping, 305energy, 62, 69, 188force, 31, 46, 61, 62, 69, 239stiffness, 35, 37, 46, 57, 62, 69, 70, 187,

305contents, 173, 175, 292, 303continuous, 98control, 11, 47, 351

buoy, 47

control mode, 207, 348, 351, 352force, 208, 350, 351, 352length, 207, 349, 351, 352

controlling views, 92conventions, 249, 257, 289convergence, 213, 214, 296

parameters, 214coordinate systems, 141copy, 81, 85, 95, 96, 114, 115Coriolis, 173Coriolis force, 181, 292Coulomb friction, 147, 185, 305crane, 30, 53creating objects, 95crest, 357critical damping, 163, 205, 216, 217, 235

seabed, 219shapes, 205, 235

cross flow, 179, 202, 276crosshair cursor, 24current, 29, 50, 155, 192, 216, 220, 233,

252direction, 220exponent, 221meter, 30, 50speed, 220speed at seabed, 221speed at surface, 221

curvature, 167, 313customisation, 116cut, 81, 85cylinder, 36, 40, 41, 55, 201, 237, 266, 276— D —damage, 132damper, 165, 346, 347damping, 45, 151, 156, 163, 166, 187, 195,

199, 200, 205, 207, 212, 216, 217, 235,261, 266, 273, 286, 296, 303, 348, 351,352bend, 167, 216clashing, 187, 305critical, 163, 205, 216, 219, 235minimum, 296moment, 200, 273properties, 199, 213seabed, 163, 205, 219structural, 169, 216target, 151, 216, 286vessels, 195, 261

data, 11, 72, 78, 82, 83, 95, 100, 101, 102,212, 217, 235, 275, 300, 303environment, 217form, 72, 95, 100, 101, 102line type, 303open, 78, 83

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save, 78, 84shapes, 235spar buoys, 275

deadband, 207, 348, 352Dean, 20, 155, 158, 159, 160, 222

wave, 155, 158, 159, 160, 223declination, 142, 170, 237, 270, 278, 289,

312, 320, 348, 353end force, 312no moment, 312

default value, 102degrees of freedom, 244, 250, 264, 266,

269Deksnis, 21delete, 85, 95density, 154, 217, 221, 292

air, 221seawater, 154, 217

deployment, 30, 58, 64depth, 162, 186, 198, 199, 201, 205, 217,

234, 235, 264, 266, 310of immersion, 201, 264, 266of penetration, 162, 186, 199, 201, 205,

235, 264seabed, 218water, 218

design wave, 230, 231, 357destroying objects, 95diameter, 43, 276, 302, 340

effective, 44differences, 116direction, 142, 170, 183, 185, 218, 220,

223, 238, 288, 295, 296, 341, 348, 353conventions, 142no moment, 183, 289, 341

disk space, 215displaced mass, 180, 277distributed buoyancy, 34, 44diverter, 267DNV, 20dongle, 10, 12drag, 93, 116, 164, 171, 179, 183, 192, 198,

201, 202, 208, 210, 212, 252, 264, 266,267, 271, 274, 275, 278, 283, 286, 300,302, 303, 311, 320, 322, 325, 326, 329,330, 331, 352, 3613D buoys, 265area, 179, 198, 201, 202, 274, 276, 301

3D buoys, 265area moment, 203, 276, 285axial, 322, 325, 330chain, 94, 210, 301, 302clump, 301coefficient, 172, 179, 198, 201, 202, 276,

301, 302, 305, 311, 329, 3613D buoys, 265

floating line, 184minimum distance, 117moment, 201, 202, 274, 276

6D buoys, 276spar buoys, 276

normal, 322, 326, 331spar buoys, 276starting velocity, 214vessels, 192, 252

drag & drop, 83dragging, 72, 91, 95, 117drawing, 31, 45, 53, 62, 93, 226, 238, 240,

247, 248, 274, 292, 294as seen in example files, 45, 54, 62data, 226, 294shapes, 238vessels, 247

drilling rig, 359dry length, 266, 278dynamic analysis, 29, 151, 152, 207dynamics data, 214— E —Eames, 180, 293edges, 93, 240, 247, 274edit, 100, 101, 102effective diameter, 44effective tension, 167, 175, 313eigenvalues, 316elevation, 81, 88, 91, 92, 117, 233e-mail, 16empirical cumulative distribution, 110Encastre, 31, 36, 39, 40, 61end bend moment, 316end curvature, 316end directions, 289end Ez-angle, 183end faces, 237end fittings, 183, 342, 343end force, 312, 317, 342, 343

azimuth, 312declination, 312Exy-angle, 312Ez-angle, 312, 342, 344Ezx-angle, 312, 344Ezy-angle, 312, 344

end loads, 143, 183, 316, 342Exyz, 143, 183, 316, 342GXYZ, 316Lxyz, 316

end moment, 317end orientation, 141, 289, 317end shear, 316end stiffness, 342end tension, 316end torque, 316

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energy, 187contact, 188

environment, 210, 216, 217, 233equilibrium, 147, 212, 264, 267, 268, 270,

271, 289, 294error message, 79ESDU, 20Euler, 110, 173, 175, 303, 344, 345

buckling, 173, 175, 344load, 110, 173, 307, 344, 345strut, 173, 307

example, 29, 32, 34, 35, 36, 37, 38, 39, 40,41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51,52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62,63, 64, 65, 66, 67, 68, 69

exit, 84export, 74, 75, 84, 96, 97extend simulation, 87Exy-angle, 171, 312Ez-angle, 171, 312Ezx-angle, 171, 312Ezy-angle, 171, 312— F —Falco, 20Faltinsen, 20FAQs, 13fastening, 278faster simulations, 304fatigue, 29, 67, 115, 125, 126, 127, 130,

131, 132, 357analysis, 30, 67, 125, 126, 127, 130, 131,

132damage, 132load case, 126, 128points, 131rainflow, 125, 133regular, 125, 133S-N curve, 130spreadsheet, 115waves, 357

fax, 16Fenton, 20, 21, 158fetch, 357FFT, 228fields, 101Fill, 81, 103finite element model, 9, 163fixed, 96, 144, 236, 237, 238, 288, 289,

298, 347, 350flex joint, 44, 290flexible, 177

pipe, 177floating hose, 61, 184floating line, 30, 61floating platform, 239

floats, 320, 327flow velocity, 173, 292flowline, 53fluid, 163, 179, 198, 200, 201, 273, 292

acceleration force, 198, 201, 2746D buoys, 203spar buoys, 203

acceleration load, 274flow, 181, 292inertia, 201, 274

fluid incidence angle, 312fm, 227fonts, 119force, 111, 116, 147, 163, 179, 187, 198,

207, 239, 241, 246, 263, 270, 273, 292,313, 316, 348, 351, 352, 361applied, 246breakout, 362centrifugal, 181, 292clash, 187, 314compressive, 147contact, 239control mode, 208, 350, 351, 352Coriolis, 181, 292end, 317fluid acceleration, 198, 274line clash, 314Lx-Ly-Lz-force, 263out of balance, 118restoring, 111, 263shear, 313solid contact, 314vertical, 111, 263

Fossati, 20Fourier, 105, 227

components, 228transform, 228

FPSO, 41, 42, 67frames, 96, 97free, 96, 143, 183, 288, 289, 298frequently asked questions, 13friction, 33, 42, 46, 54, 69, 147, 185, 266,

295, 301, 302, 305, 319, 362Froude Krylov force, 172, 181Froude scaling, 248full statics, 50, 61, 146, 148, 149, 288, 294,

296— G —g, 142gamma, 156, 170, 270, 278, 288, 289, 312general preferences, 118global, 93, 116, 141, 142, 143

axes, 94, 117, 141, 142, 143coordinates, 141origin, 141

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relative, 141graph, 72, 109, 111, 112, 113, 114, 115,

120Gregory, 21guide tube, 359GUIDE.DAT, 359GX-velocity, 311GY-velocity, 311GZ-moment, 264GZ-velocity, 311— H —hanging length, 320harmonic motion, 244, 338Hartnup, 21hauling in, 207, 352, 353hawser, 49heading, 142, 241, 243, 263heave, 141, 190, 240, 244, 263heel, 241, 263height, 155, 199, 200, 224, 229, 265, 266,

273, 300help, 15, 79, 90hide, 46, 93Hoerner, 21hollow, 292hose, 60, 61, 286, 320, 338, 339, 340

fold flat, 338high pressure, 338low pressure, 338thermoplastic, 338

hot, 80, 95, 98keys, 80, 98zone, 95

Hs, 156, 227, 357hydraulic accumulators, 350, 352hydrodynamic, 199, 200, 273

mass, 201, 274properties, 199

hydrodynamics, 171, 279hydrophone, 63— I —impact, 188import, 74, 76, 255incidence angle, 179, 271, 279include in statics, 212, 241, 264inertia, 198, 199, 201, 207, 264, 267, 268,

270, 271, 274, 305, 348, 351, 352, 359coefficient

3D buoys, 265moment of, 270, 359

information box, 79initial, 264, 268

attitude, 269position, 265, 269

inner time step, 152, 214inside diameter, 292, 303, 336instability, 46, 214, 215, 359installation, 9integration, 152, 214interaction, 32, 36, 41, 42, 54, 58, 60, 64interaction with seabed and shapes, 186intercept, 114interference, 40, 240internal pressure, 175interpolation, 104, 144, 219, 251introduction, 9Isherwood, 21, 225isometric, 91ISSC, 156, 223, 230, 231iterations, 147, 296

maximum, 296Iwan, 21— J —joint, 94, 95, 143JONSWAP, 156, 223, 230, 231, 357jumper, 29, 38, 40— K —keep open, 106keyboard actions, 80keys, 80, 98

hot, 80, 98kinematic stretching, 223— L —lambda, 227Larsen, 21Lathier, 21lay azimuth, 31, 33, 295, 296lazy, 29, 34, 35, 37, 38, 40, 42, 43, 65, 359

S riser system, 29, 35, 38, 43, 359wave, 29, 34, 65

lazy S riser system, 359legend, 114length, 173, 201, 207, 241, 248, 265, 276,

277, 310, 347, 348, 351, 352, 353arc, 310control mode, 207, 349, 351, 352cylinder, 204dry, 266, 278unstretched, 173, 207, 347, 351, 353vessel, 241

library, 74, 76, 84, 300, 303licence, 12lift, 267, 271, 278

surface, 267limit compression, 31, 36, 49, 173, 307,

325, 335, 337, 341, 345

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line, 29, 34, 35, 37, 43, 44, 50, 61, 66, 78,94, 96, 141, 143, 147, 163, 170, 171, 173,175, 179, 183, 184, 186, 187, 210, 216,264, 266, 286, 288, 290, 292, 293, 294,296, 297, 300, 303, 308, 310, 311, 312,313, 314, 316, 320, 322, 327, 332, 338,341, 361added mass, 180attached, 264, 266attachments, 293buoyancy module, 327clash force, 314clashing, 187clearance, 313connections, 170, 288contents, 292data, 288, 361direct tensile stress, 315effective tension, 175end coordinates, 141, 170end directions, 170end joints, 143end orientation, 141, 170, 171ends, 183, 288, 290, 341floating, 30, 61, 183, 296floats, 327flow in, 181, 292lay azimuth, 185max bending stress, 315max xy-shear stress, 315pressure forces, 175results, 308, 310, 311, 312, 313, 314, 316statics, 147, 294structure, 292style, 93theory, 163type data, 303type wizard, 34, 36, 37, 44, 45, 51, 66,

320, 327, 332, 338types, 287, 292, 303, 308, 320von Mises stress, 316wall tension, 175width, 93worst hoop stress, 315

linear, 152, 155, 346, 347link, 31, 37, 38, 41, 42, 45, 46, 47, 48, 52,

54, 59, 64, 70, 79, 94, 143, 211, 346, 347,348, 359

linked statistics, 108, 138load, 78, 126

case, 126local, 32, 35, 50, 80, 93, 116, 141, 142, 316

axes, 36, 94, 117, 141, 142, 317coordinates, 141

Locate, 73locking objects, 73, 89, 95

log, 107, 215file, 106, 215precision, 215samples, 215

logging tension, 107lumped, 9, 35, 40, 51, 155, 163, 200, 214,

266, 273, 274, 286, 359buoy, 35, 40, 51, 200, 266, 273, 274, 360mass model, 9, 164, 215, 286

Lxyz moment, 263Lxyz-force, 263— M —magnitude, 296

of standard change, 296of standard error, 296

main window, 72maintenance, 15margins, 118mass, 152, 164, 173, 179, 198, 200, 265,

266, 267, 269, 273, 277, 286, 292, 300,302, 303, 330, 333, 336, 340, 346, 350,351flow rate, 173, 181, 292per unit length, 303, 330, 333, 336, 340

master, 94, 95, 143master relative, 143maximum, 108, 110, 138, 296, 303, 313

iterations, 296, 297tension, 110, 306

MBL, 335mean, 108, 110, 138measuring tape, 91menus, 72, 82, 83, 84, 85, 86, 87, 89, 90message box, 79Miche, 161mid-water arches, 35, 359minimum, 108, 110, 116, 138, 296, 303

damping, 296drag distance, 117radius, 306

modal analysis, 317model, 73, 76, 78, 82, 85, 92, 210

browser, 73, 78, 85centre, 92

modelling, 173, 210compression, 173

modules, 12moment, 111, 148, 163, 178, 200, 201, 241,

246, 263, 268, 270, 273, 275, 279, 303,313, 316, 359applied, 246bend, 148, 178, 304, 313damping, 200, 273drag, 201, 202, 274, 276end, 317

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end bend, 316GZ, 264Lx-Ly-Lz-moment, 263munk, 205, 275of area, 201, 274, 276, 304of inertia, 270, 359yaw, 111

monochrome output, 118moonpool, 45, 46, 53, 54, 234, 359mooring, 41, 47, 48, 49, 50, 51, 58, 151,

291, 322chain, 322line, 41, 47, 48, 49, 50, 51

Morison, 21, 171, 199, 267Morison's equation, 153most recent files, 116mouse, 80, 95, 101, 102, 117

selection zone, 117moving objects, 74Mueller, 21multiple statics, 86, 109, 111, 151, 246, 263munk moment, 205, 275— N —name, 102, 235, 241, 264, 268, 270, 271,

288, 303, 346, 350natural modes, 317natural period, 108, 214, 219, 351neutrally buoyant, 294new, 24, 78, 82, 85, 90, 95

3D view, 90line icon, 24object, 78, 86, 95

Newman, 21, 197Newton's law, 153, 208NMIWAVE, 254no moment, 170, 183, 288, 312, 341

azimuth, 312declination, 312direction, 183, 289, 341

node, 108, 143, 162, 164, 184, 186, 286,288, 304

noise, 33, 38, 46, 69non linear, 31, 32, 104, 290, 303, 304non-linear wave theory, 155, 158normal relative velocity, 311North Sea, 231NPD spectrum, 222numbers, 102numeric, 102— O —object, 78, 82, 89, 93, 95, 100, 106, 141,

143, 210, 288, 347, 350browser, 100, 106connecting, 94, 95

connections, 143creating, 95destroying, 95locking, 89, 95new, 78, 95relative, 141, 289, 347, 350

obstacles, 234Ochi Hubble, 21, 157, 227, 230, 231OCIMF, 192offset, 109, 111, 151, 199, 246, 266, 292,

300, 348, 350graph, 111table, 109

open, 78, 83data, 83

OrcaFlex, 9OrcaFlex offers a choice of 3 methods of k,

156OrcaMotion, 255OrcaRiser, 15OrcFxAPI, 120Orcina, 9, 15orientation, 171, 236, 241, 243, 269, 270

vessel, 241origin, 141, 155, 199, 200, 216, 220, 236,

264, 265, 268, 277oscillations, 215out of balance force, 118outer time step, 153, 214output preferences, 118outside diameter, 179, 186, 303, 336— P —Paidoussis, 21Parsons, 20paste, 81, 85, 95, 113, 115pause, 78, 79, 80, 87payout, 207, 352peak enhancement factor, 225, 231, 358pen, 31, 37penetration, 162, 186, 199, 205, 219, 235

depth of, 162, 186, 199, 205, 235period, 109, 111, 155, 224, 229, 244phase, 155, 189, 244, 250, 258Pierson-Moskowitz, 155, 223, 231pin end, 39pin joints, 39, 361pinned end, 183pinned-ended line, 356pipe, 29, 52, 56, 173, 175, 177, 237, 303,

320, 336, 337flexible, 177lift, 30, 52, 56steel, 177titanium, 177

pipelay, 30, 52

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PIPELAY.SIM, 52pitch, 34, 37, 39, 49, 50, 51, 190, 244, 249,

264, 267, 268, 271plan view, 81, 88, 92plane, 238planing, 205, 268pliant S, 29, 38pliant wave, 29, 37, 41, 42Pode, 21, 180, 293point of application, 246, 270point on plane, 238polar coordinates, 291position, 108, 241post-processing, 115, 120post-processing results, 134PowerPoint, 112preferences, 89, 95, 116, 119prescribed, 146, 147, 294, 298, 299

statics, 147prescribed motion, 243presentation, 97, 112pressure, 175, 178, 233, 315

forces, 175static, 234

pre-tension, 185, 295, 299primary motion, 196, 242, 245, 263print, 80, 91, 100, 113, 115, 119print setup, 119printed output, 28profile, 32, 42, 46, 54, 105, 155, 229programming interface, 120proportion wet, 198, 200, 201, 273, 310Puech, 22, 362pull up, 30, 54, 55, 56pulley, 348, 350pull-in, 30, 53, 55, 56, 57, 147— Q —QA, 14, 74QTF, 196, 253, 261quick statics, 37, 147, 294— R —rainflow fatigue analysis, 125, 127, 133ramping, 151, 173, 220random waves, 156, 224, 251range graph, 106, 109, 110, 138, 173, 306,

313RAOs, 43, 46, 47, 62, 64, 189, 190, 210,

239, 243, 244, 249, 250, 255, 257, 258checking, 190, 258conventions, 189, 249, 257graphs, 258importing, 255origin, 250, 257phase origin, 250

report, 243rotational, 190spreadsheet, 243text files, 251, 256vessels, 251

rate of turn, 243Rawson & Tupper, 22reaction, 162, 184, 186, 198, 200, 205, 237,

274, 305Reber, 180recent files, 119rectified, 32, 34reference axes, 291reference current, 220reference origin, 291references, 20refresh rate, 117, 121regular fatigue analysis, 125, 133regular wave, 155, 224, 251relative velocity, 311releasing, 30, 41, 48, 58, 61, 64, 69, 70,

151, 290, 347, 350replay, 79, 82, 91, 96, 97, 98, 112reset, 77, 78, 79, 80, 87, 92, 110, 111, 113,

294response amplitude operators, 239, 243Resta, 20restoring force, 111, 263results, 32, 34, 35, 36, 37, 38, 39, 40, 41,

42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52,53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 65,66, 67, 68, 69, 72, 79, 89, 106, 107, 108,109, 113, 115, 119, 134, 136, 137, 139,215, 233, 239, 277, 348, 353in example files, 33, 34, 35, 36, 37, 38,

39, 40, 41, 42, 43, 44, 45, 46, 47, 48,49, 50, 51, 52, 53, 54, 55, 56, 57, 58,61, 63, 64, 66, 67, 68, 69, 70

shapes, 239spreadsheet, 134, 136, 137, 139

Reynolds number, 179, 217, 305, 311, 361Richtmyer, 180roll, 190, 244, 249, 264, 267, 268, 270, 271rope, 173, 307, 320, 332, 333, 334

fibre, 332, 333, 334nylon, 332, 333, 334

rotate view, 81, 88, 117rotation, 39, 40, 47, 50, 53, 262, 266, 277

1, 263, 266, 2772, 50, 263, 266, 2773, 263, 266, 277

rotational, 183, 189, 266RAOs, 190stiffness, 183, 266

run simulation, 79, 80, 87, 152run time, 153

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372

— S —salinity, 217Sarpkaya, 22save, 78, 83, 139

data, 84, 140scale bar, 117SCR, 29, 43, 44script files, 121scroll bars, 72, 97, 101sea, 24, 93, 154, 155, 183, 215, 216, 217,

222, 229, 233, 310, 353density, 154, 217results, 233surface, 24, 183surface and seabed, 94, 217, 233, 310,

353seabed, 29, 32, 42, 44, 53, 94, 143, 147,

155, 162, 184, 199, 200, 205, 215, 216,218, 235, 266, 274, 295, 310clearance, 310critical damping, 219damping, 163, 205, 219, 235depth, 218direction, 218friction, 31, 147, 185origin, 218profile, 31, 42, 54, 218slope, 31, 32, 44, 218slope direction, 218stiffness, 219theory, 162touchdown, 147, 184type, 218

seastate, 227, 357section, 287, 292seed, 225segment, 156, 165, 286segmentation, 32, 33, 36, 43, 52, 56, 57,

67, 68seismic, 63select, 95, 107

object, 95variable, 107

session log, 116, 121set lay azimuth, 295shape, 79, 94, 143, 148, 205, 211, 234,

235, 238, 239, 266, 274connection, 235critical damping, 205, 235data, 235drawing, 238results, 239shape, 235stiffness, 234, 235theory, 205

type, 235shear, 178, 313, 314

force, 313stress, 315

shielding, 234ship, 239short term operations, 358shortest natural period, 108, 214SI Units, 212Sigma, 156simulation, 72, 77, 79, 80, 82, 83, 86, 96,

120, 151, 214, 303, 352extend, 87open, 78run, 79, 80, 87save, 78, 83speed of, 304unstable, 215

single Airy wave, 155single statics, 146skin friction, 362Skjelbreia & Hendrickson, 22slack, 147, 294, 296, 307, 347slamming, 54, 205, 267, 268slave, 94, 95, 143sliding friction, 362slip joint, 45slope, 155, 218, 220, 238, 294slow drift, 253, 261smear, 31, 34, 44, 45S-N curve, 129, 130snag catcher, 57snatch loads, 216, 304solid, 32, 34, 35, 36, 38, 39, 40, 41, 46, 51,

52, 54, 57, 60, 62, 64, 70, 79, 94, 143,148, 205, 234, 235, 238, 239, 266, 274,313, 359block, 35, 37contact force, 61, 314cylinder, 36, 40, 41, 55, 359, 361data, 235stiffness, 205theory, 205

span, 268, 270spar buoy, 29, 39, 41, 42, 43, 46, 47, 49,

51, 54, 61, 201, 234, 275, 283added mass, 203added mass coefficient, 277data, 275drag, 276drag moment, 276fluid acceleration force, 203

Sparks, 22spectral, 113, 215, 222, 234, 357

density, 113, 215energy parameter, 225

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373

peak, 358peak frequency, 225

spectrum, 156, 157, 224speed, 97, 98, 207, 243, 303, 348, 351,

352, 357constant, 207, 348, 352of simulation, 304wind, 357

spike, 43spin buttons, 102spline, 37, 42, 50, 60, 146, 147, 294, 297

control points, 297order, 297statics, 50, 61, 147

spreadsheet, 115, 134, 139results, 134, 139stress, 139

spring, 346, 347spring/damper, 41, 45, 46, 211, 346, 347,

359stages, 31, 41, 48, 53, 54, 55, 56, 57, 61,

64, 151, 215, 290, 347, 350, 352standard deviation, 108, 138start, 98starting friction, 362starting shape, 297, 298starting velocity, 214start-up, 11state, 72, 76, 78, 79, 95statically indeterminate, 213statics, 26, 36, 50, 60, 77, 78, 79, 86, 108,

109, 111, 115, 120, 146, 147, 148, 151,162, 184, 207, 210, 212, 214, 234, 241,242, 246, 262, 264, 268, 288, 294, 296,297, 351, 359analysis, 26, 148, 151, 207, 212, 269,

294, 296, 351buoy, 212, 264catenary, 37, 147, 162, 184, 210, 294,

296covergence, 214, 359data, 212, 214full, 50, 61, 146, 148, 149, 288, 294, 296line, 147, 294method, 147, 294, 296, 297

catenary, 37, 147full statics, 148prescribed, 147quick, 37, 147spline, 147

multiple, 86, 109, 111, 151, 246, 263quick, 37, 294single, 146vessels, 242

statics only OrcaFlex, 12statistics, 106, 107, 108, 115, 232, 357

linked, 108wave, 232, 357wind, 357

status bar, 72, 77, 79, 95, 96steady state, 146steel, 177

pipe, 177steep riser system, 359steep S, 36steep wave, 29, 34, 44step replay, 89stiffness, 36, 46, 147, 162, 165, 166, 173,

175, 183, 186, 199, 200, 207, 219, 234,235, 266, 288, 294, 303, 322, 324, 334,340, 346, 347, 351, 352, 359axial, 147, 175, 295, 322, 324, 334, 340bend, 147, 165, 168, 289, 324, 334, 341contact, 37, 305rotational, 183, 266shapes, 234, 235torsional, 304twisting, 289, 304value, 359

stinger, 52Stokes' wave, 155, 158, 223stop, 78, 98storm, 357stowed line, 30, 60stream function, 158, 224streamer, 30, 63stress, 29, 44, 66, 67, 127, 132, 134, 139,

175, 178, 303, 314, 337allowable, 306analysis, 30, 66axial, 140components, 139, 140, 316concentration factor, 129, 133diameter, 31, 44hoop, 140, 178loading factor, 175, 306, 337longitudinal, 140matrix, 133, 178radial, 140shear, 315spreadsheet, 134, 139von Mises, 316

studless, 323chain, 323

studlink, 323chain, 323

style, 93superimpose, 98superimposed motion, 243, 245supported length, 320surface piercing, 183, 266, 283, 300surface Z, 265, 277, 310, 353

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374

surge, 141, 190, 240, 244, 263, 310sway, 141, 190, 240, 244, 263, 310swell, 157, 227symmetry, 249, 252— T —target damping, 151, 167, 168, 169, 216,

286technical notes, 13telephone, 16temperature, 212, 217tension, 107, 110, 167, 175, 178, 207, 303,

347, 348, 351, 352, 353constant, 207, 348, 352maximum, 110, 306

tension leg platform, 47tensioned riser, 45tensioners, 45termination, 183tether, 37, 38, 41, 42, 47, 50, 52, 211, 346,

347, 359text, 72, 101, 106, 109, 115tie-down, 42ties, 346tile, 72, 80, 90, 91, 113time, 78, 105, 106, 107, 108, 109, 137, 151,

152, 155, 214, 222, 233, 245, 257, 303,313, 351history, 105, 106, 107, 109, 137, 223,

233, 245, 313vessels, 245

history file format, 105history multiple, 107origin, 151, 156, 223, 258step, 78, 108, 151, 152, 214, 304, 351

titanium pipe, 177TLP, 29, 47tolerance, 296, 297toolbar, 72, 78torque, 179, 303, 313, 336

per unit tension, 305, 337torsion, 288torsional stiffness, 304, 337touchdown, 184, 309towed fish, 53, 64, 267towed systems, 146, 214tower, 29, 39, 40, 53track, 147, 294, 298, 299trails, 98transient, 38, 41, 48, 64, 151, 153, 214, 244trapped water, 32, 46, 55, 172, 205, 234,

235data, 235theory, 206

trim, 241, 263trough, 35, 38, 39

truncation, 104Tucker, 22, 357turn, 298turret, 29, 41tutorial, 24, 25, 26, 27, 28twist, 312twisting stiffness, 289, 304Tz, 156, 227, 357— U —umbilical, 40, 47unattended, 120undo, 84unit mass, 303, 330, 333, 336, 340units, 128unstable simulation, 215unstretched length, 173, 207, 347, 351, 353Ursell number, 160US customary units, 212use static line end orientations, 213use static positions, 213user defined spectrum, 223, 226user defined units, 212— V —values, 106, 107variable data, 31, 59, 104, 179, 217, 220,

270, 290, 304, 305variables, 107, 108, 109, 111, 233, 239,

262, 265, 277, 308, 320, 348, 353velocity, 233, 243, 311, 348, 353

axial relative, 311constant, 243, 348GY-velocity, 311GZ-velocity, 311normal relative, 311relative, 311

version, 72, 224vertical force, 111, 263vertices, 93, 200, 236, 240, 247, 274vessel, 24, 78, 94, 143, 151, 189, 190, 192,

195, 196, 201, 207, 210, 229, 239, 241,242, 243, 244, 245, 246, 247, 248, 249,250, 252, 253, 255, 257, 258, 260, 261,262, 275, 348, 351, 353added mass, 195applied load, 246axes, 240checking RAOs, 258constant velocity, 243current load, 192, 252damping, 195drag, 192draught, 241, 248drawing, 247, 248driving, 243

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harmonic motion, 244heading, 243length, 229, 241, 252motion, 189, 190orientation, 241origin, 240phases, 189prescribed motion, 243RAO conventions, 257RAO origin, 257RAOs, 250, 251, 255response, 245results, 262slow drift, 192, 196, 253, 261static analysis, 242statics, 242time history, 245type, 240, 248, 249, 250, 255, 257, 258,

260wind load, 192, 252

video, 97, 112, 118view, 80, 82, 87, 91, 92, 93, 116, 217

angle, 92area, 92centre, 92control, 92default view, 88, 92parameters, 87, 91, 92plan, 88profile, 219rotate, 81, 88, 117rotation increment, 117size, 92, 93

viscosity, 217, 311VIV, 354volume, 198, 200, 264, 273, 276, 292, 301

flow rate, 292vortex force, 313vortex induced vibration, 354vortex-induced vibration, 362— W —wake oscillator, 354wall tension, 175, 313water, 205, 216, 217, 233, 234

depth, 218level, 217particle, 233trapped, 206, 234

wave, 100, 113, 115, 155, 158, 159, 160,161, 189, 190, 196, 214, 216, 222, 227,229, 230, 232, 233, 244, 249, 250, 253,261, 357Airy, 155, 223breaking, 161cnoidal, 155, 158, 223

components, 156, 225crest, 250crest-to-trough height, 357Dean, 155, 158, 159, 160, 223design, 357direction, 190, 222, 251drift load, 196, 253, 261fatigue, 357height, 224, 227irregular, 114, 115, 155, 229, 244maximum, 357maximum height, 357period, 214, 224phase, 225random, 156, 215, 224, 229, 230, 233,

244, 251regular, 155, 215, 223, 224significant height, 357single Airy, 155slope, 249statistics, 232, 357steepness, 229, 249Stokes', 155, 158, 223theory, 158time history, 227train, 222, 223trough, 250, 357type, 223

web site, 16weight, 198, 200weight in air, 300, 303wetted volume, 273Wichers, 22, 194Wichers (1979), 192width, 93Wilson, 180winch, 31, 47, 53, 54, 55, 56, 57, 61, 78, 94,

143, 151, 207, 211, 348, 350, 351, 352,353constant speed, 207, 348, 352constant tension, 207, 348, 352constant velocity, 348control mode, 349, 351detailed, 349drive, 207, 348, 351, 352drum, 348, 351hydraulics, 348mount, 353simple, 349theory, 207type, 349, 350wire, 350, 351, 353

wind, 192, 221, 252, 357direction, 221load, 192, 252speed, 221, 357

w

376

statistics, 357window size, 92wing type, 271wings, 266, 267, 270wire, 110, 235, 237, 238, 239, 247, 248,

274, 332, 346, 348frame, 237, 238, 240, 247, 248, 274rope, 332

wizard, 31, 36, 37, 44, 45, 51, 66, 320wizard data, 321word processor, 115worst tension, 111, 264— X —X, 263, 264, 265, 266, 277, 278, 310, 353

XY graph, 109— Y —Y, 263, 264, 265, 266, 277, 278, 310, 353yaw, 111, 190, 244, 249, 262

moment, 111Young's modulus, 303— Z —Z, 263, 264, 265, 266, 277, 278, 310, 353zero crossing period, 227, 357zero up-crossing period, 357zoom, 81, 88, 91, 93, 114