wamit moses

WAMIT-MOSES Hydrodynamic Analysis Comparison Study

J. Ray McDermott Engineering, LLC July 20001

WAMIT-MOSES Hydrodynamic AnalysisComparison Study

JRME, July 2000

Prepared byHull Engineering Department



Table of Contents

Summary

1. Introduction .......................................................................................................................4

2. Test Models ........................................................................................................................5

3. Results and Discussion.......................................................................................................8

4. References ........................................................................................................................30

List of Tables

TABLE 2.1 GEOMETRY AND NUMBER OF PANELS....................................................................................... 5TABLE 3.1 NORMALIZATION ........................................................................................................................... 8

List of Figures

FIGURE 2.1 SIMPLE BOX ................................................................................................................................... 5FIGURE 2.3 GENERAL SHIP FORM ................................................................................................................... 6FIGURE 2.4 TLP................................................................................................................................................... 7FIGURE 2.5 SEMI-SUBMERSIBLE (MOB) ......................................................................................................... 7FIGURE 3.1 ADDED MASS COEFFICIENTS FOR BOX................................................................................... 10FIGURE 3.2 DAMPING COEFFICIENTS FOR BOX.......................................................................................... 11FIGURE 3.3 WAVE EXCITING FORCES AND MOMENTS FOR BOX............................................................ 12FIGURE 3.4 MOTION RAO FOR BOX .............................................................................................................. 13FIGURE 3.5 ADDED MASS COEFFICIENTS FOR CYLINDER........................................................................ 14FIGURE 3.6 DAMPING COEFFICIENTS FOR CYLINDER .............................................................................. 15FIGURE 3.7 WAVE EXCITING FORCES AND MOMENTS FOR CYLINDER................................................. 16FIGURE 3.8 MOTION RAO FOR CYLINDER ................................................................................................... 17FIGURE 3.9 ADDED MASS COEFFICIENTS FOR SHIP................................................................................... 18FIGURE 3.10 DAMPING COEFFICIENTS FOR SHIP ....................................................................................... 19FIGURE 3.11 WAVE EXCITING FORCES AND MOMENTS FOR SHIP.......................................................... 20FIGURE 3.12 MOTION RAO FOR SHIP ............................................................................................................ 21FIGURE 3.13 ADDED MASS COEFFICIENTS FOR TLP.................................................................................. 22FIGURE 3.14 DAMPING COEFFICIENTS FOR TLP......................................................................................... 23FIGURE 3.15 WAVE EXCITING FORCES AND MOMENTS FOR TLP ........................................................... 24FIGURE 3.16 MOTION RAO FOR TLP.............................................................................................................. 25FIGURE 3.17 ADDED MASS COEFFICIENTS FOR MOB ................................................................................ 26FIGURE 3.18 DAMPING COEFFICIENTS FOR MOB....................................................................................... 27FIGURE 3.19 WAVE EXCITING FORCES AND MOMENTS FOR MOB ......................................................... 28FIGURE 3.20 MOTION RAO FOR MOB............................................................................................................ 29



SummaryThe global motion analysis and related installation procedures are very important tasks forfloating offshore platforms. As new deep-water oil and gas production systems such as a SPAR,FPSO and TLP are introduced these tasks have become more important since the performance ofthese floating platforms might be decided by them. For the global motion analysis WAMIT is themost widely used and well-proven 3-D diffraction and radiation computer program in thefrequency domain. For the combined work such as a global motion analysis, installationsimulation and fatigue analysis MOSES may be the most popular computer program in this area.Since MOSES has the same 3-D diffraction and radiation computer module one may use it as thetool for the global motion analysis. However, it may be necessary to examine the softwareperformance before applying it to the floating production platforms.

In this study the hydrodynamic analysis using MOSES and WAMIT were carried out toinvestigate the performance of the two computer programs. Five models which can representmost of the floating platforms currently installed or under development were selected and theresults were compared for a wide range of wave periods and wave heading angles.

The mathematical formulation and theoretical background for the two computer programs can befound in Ref [1] and Ref [2] or http://www.wamit.com and http://www.ultramarine.com.



1. IntroductionThe use of MOSES to analyze the global motion and related installation procedures for floatingplatforms has increased since installation engineering and related work has become morecomplicated as new hull forms are introduced.

The object of this study is to compare the hydrodynamic analysis results from MOSES andWAMIT. WAMIT is the most widely used 3-D computer program for the diffraction andradiation problem and is a well-proven computer program. MOSES also has the same capabilityand since both programs use conventional 3-D constant panel method and mathematicalformulation one should have the same results. However, MOSES results have never beensystematically compared with WAMIT results. In order to compare the results one must choosevarious offshore floating structures and a wide range of wave periods. Different wave headingangles should also be considered to investigate the performance of both programs.

In this study two simple geometries (rectangular box and vertical cylinder) and three offshorefloating structures (ship, TLP, semi-submersible) are chosen with the proper number of panels.These five models can represent or simulate most offshore floating structures currently installedor under development such as a FPSO, SPAR, TLP and Semi-submersible.Using MOSES and WAMIT, added mass and damping coefficients, wave exciting forces andmoments and motions were calculated for the wide range of wave periods and heading angles.

The version of each program used in this study was WAMIT 5.4PC and MOSES 5.09.027



2. Test ModelsIn order to compare the effectiveness of the programs, five models were selected to cover mostof the floating structures used for oil and gas production. By selecting the rectangular box,vertical cylinder, general ship form, TLP and semi-submersible type of structures one canexamine the performance of the two computer programs for most floating structures currentlyinstalled or under development. For example, the box can represent a FPSO or Tanker that has alarge block coefficient and the vertical cylinder can be regarded as a simplified SPAR platform.The TLP and MOB can represent a typical semi-submersible. The following table shows thebasic dimension and characteristics of the five selected models, which were used in thenumerical calculations.

TYPE Length(meter)

Beam orDiameter(meter)

Draft (meter)

Displacement(Metric-Tons)

Center ofGravity(KG)

Numberof Panels

Box 200.0 40.0 28.0 229,645.0 28.0 1264Cylinder 200.0 40.0 200.0 256,011.0 200.0 1120

Ship 275.4 27.7 9.6 43,698.0 13.9 430TLP 51.6 51.6 35.0 52,761.0 35.0 512MOB 260.0 138.0 39.0 328,894.0 26.9 1120

Table 2.1 Geometry and number of panels

The three-dimensional mesh for each model used for both methods is shown in Figures 2.1-2.5.

Figure 2.1 Simple box



Figure 2.2 Simple Vertical cylinder

Figure 2.2 General ship form



Figure 2.3 TLP

Figure 2.4 Semi-Submersible (MOB)



The nodal and panel input data used for both programs (WAMIT and MOSES) is actually thesame since all MOSES geometry files were directly converted from WAMITs geometry inputfiles. Since definition of the normal vector on the panel for the two programs is different, caremust be taken when converting the WAMIT geometry file to MOSES. By using the samenumber of panels and geometry more consistent comparison between the two programs isachieved.The wave periods used in the numerical calculation were selected from 4 seconds to 42 seconds(total 20 periods by increments of 2 seconds) which covers a wide range of waves. Three wave-heading angles (head, quartering, and beam) were also studied.

3. Results and DiscussionHydrodynamic coefficients (added mass and damping coefficients), wave exciting forces and allmotion response amplitude (RAO) were extracted and compared from both numerical outputs.All outputs are normalized by mass, frequency and wave amplitude. Table 3.1 shows thenormalization of each parameter. All units are based on the metric system.

Resulting components Units Normalized variableAdded mass coefficient Mass Aij/Mass

Damping coefficient Mass/Time SQRT(Bij/Mass)Wave exciting forces Tons Tons/A

Wave exciting moments Tons*Meter Tons*Meter/ALinear motion RAO Meter Meter/A

Angular motion RAO Degree Degree/A* A : Wave amplitude

Table 3.1 Normalization

Hydrodynamic coefficients, wave exciting forces and motion RAOs for 45 degree wave headingare plotted in Figures 3.1-3.20. Although the other two wave direction computations werecompleted, the results are not presented here.

For all five models, results show very good agreement between two programss. This wasexpected since both programs use the same constant panel method.From this study the following statements can be made.

1. Results show very good agreement between the two computer programs.2. For the magnitude near the resonance period, there are some differences. These differences

near the resonance wave period are known to be normal for the different numerical methods.Near the resonance period the RAO calculation is very sensitive so that the small numericaldifference can cause relatively large differences. According to the results from this study the



differences are not that significant for the simple geometry like box, cylinder, ship and TLP.But complicate geometry like MOB has more pronounced difference than the simplegeometry.

3. Both programs give very effective computing time when a moderate number of panels areused. But WAMIT is more effective in the computing time when one uses the symmetryoption.

From this study we can conclude that the MOSES 3-D diffraction code can be used as ahydrodynamic analysis tool. The comparison with WAMIT, which is a widely used and well-proven code, shows good agreement. As a further study, it is suggested to use larger number ofpanels for both programs to get more accurate results.



Figure 3.1 Added Mass Coefficients for BOX

Added Mass Coefficient(Surge,A11)

0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

2.50E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass

MOSESWAMIT

Added Mass Coefficient(Heave,A33)

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

1.40E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass

MOSESWAMIT

Added Mass Coefficient(Pitch,A55)

3.00E+01

3.50E+01

4.00E+01

4.50E+01

5.00E+01

5.50E+01

6.00E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass

MOSESWAMIT

Added Mass Coefficient(Sway,A22)

0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass

MOSESWAMIT

Added Mass Coefficient(Roll,A44)

0.00E+00

2.00E+00

4.00E+00

6.00E+00

8.00E+00

1.00E+01

1.20E+01

1.40E+01

1.60E+01

1.80E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass

MOSESWAMIT

Added Mass Coefficient(Yaw,A66)

0.00E+00

1.00E+01

2.00E+01

3.00E+01

4.00E+01

5.00E+01

6.00E+01

7.00E+01

8.00E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass

MOSESWAMIT



Figure 3.2 Damping Coefficients for BOX

Damping Coefficient(Surge,B11)

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

7.00E-02

8.00E-02

9.00E-02

1.00E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT

Damping Coefficient(Heave,B33)

0.00E+00

2.00E-02

4.00E-02

6.00E-02

8.00E-02

1.00E-01

1.20E-01

1.40E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT

Damping Coefficient(Pitch,B55)

0.00E+00

2.00E+00

4.00E+00

6.00E+00

8.00E+00

1.00E+01

1.20E+01

1.40E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT

Damping Coefficient(Sway,B22)

0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

7.00E-01

8.00E-01

9.00E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT

Damping Coefficient(Roll,B44)

0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

6.00E+00

7.00E+00

8.00E+00

9.00E+00

1.00E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT

Damping Coefficient(Yaw,B66)

0.00E+00

5.00E+00

1.00E+01

1.50E+01

2.00E+01

2.50E+01

3.00E+01

3.50E+01

4.00E+01

4.50E+01

5.00E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT



Figure 3.3 Wave exciting forces and moments for BOX

Surge Wave Exciting ForceWave Heading=45 Deg

0.00E+00

2.00E+02

4.00E+02

6.00E+02

8.00E+02

1.00E+03

1.20E+03

1.40E+03

1.60E+03

1.80E+03

2.00E+03

0 4 8 12 16 20 24 28 32 36 40 44

Period

F/A MOSES

WAMIT

Sway Wave Exciting ForceWave Heading=45 Deg

0.00E+00

1.00E+03

2.00E+03

3.00E+03

4.00E+03

5.00E+03

6.00E+03

0 4 8 12 16 20 24 28 32 36 40 44

Period

F/A MOSES

WAMIT

Heave Wave Exciting ForceWave Heading=45 Deg

0.00E+00

1.00E+03

2.00E+03

3.00E+03

4.00E+03

5.00E+03

6.00E+03

7.00E+03

8.00E+03

0 4 8 12 16 20 24 28 32 36 40 44

Period

F/A MOSES

WAMIT

Roll Wave Exciting MomentWave Heading=45 Deg

0.00E+00

1.00E+04

2.00E+04

3.00E+04

4.00E+04

5.00E+04

6.00E+04

0 4 8 12 16 20 24 28 32 36 40 44

Period

M/A MOSES

WAMIT

Pitch Wave Exciting MomentWave Heading=45 Deg

0.00E+00

2.00E+04

4.00E+04

6.00E+04

8.00E+04

1.00E+05

1.20E+05

0 4 8 12 16 20 24 28 32 36 40 44

Period

M/A MOSES

WAMIT

Yaw Wave Exciting MomentWave Heading=45 Deg

0.00E+00

5.00E+04

1.00E+05

1.50E+05

2.00E+05

2.50E+05

3.00E+05

3.50E+05

4.00E+05

0 4 8 12 16 20 24 28 32 36 40 44

Period

M/A MOSES

WAMIT



Figure 3.4 Motion RAO for BOX

Surge RAOWave Heading=45 Deg

0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

7.00E-01

8.00E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT

Sway RAOWave Heading=45 Deg

0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

7.00E-01

8.00E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT

Heave RAOWave Heading=45 Deg

0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

1.40E+00

1.60E+00

1.80E+00

2.00E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT

Roll RAOWave Heading=45 Deg

0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

2.50E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT

Pitch RAOWave Heading=45 Deg

0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT

Yaw RAOWave Heading=45 Deg

0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

2.50E-01

3.00E-01

3.50E-01

4.00E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT



Figure 3.5 Added Mass Coefficients for CYLINDER


0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass

MOSESWAMIT


0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass

MOSESWAMIT


0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

6.00E-02

7.00E-02

8.00E-02

9.00E-02

1.00E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass

MOSESWAMIT


0.00E+00

2.00E+01

4.00E+01

6.00E+01

8.00E+01

1.00E+02

1.20E+02

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass

MOSESWAMIT


0.00E+00

2.00E+01

4.00E+01

6.00E+01

8.00E+01

1.00E+02

1.20E+02

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass

MOSESWAMIT


0.00E+00

1.00E-03

2.00E-03

3.00E-03

4.00E-03

5.00E-03

6.00E-03

7.00E-03

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass

MOSESWAMIT



Figure 3.6 Damping Coefficients for CYLINDER


0.00E+00

2.00E-02

4.00E-02

6.00E-02

8.00E-02

1.00E-01

1.20E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0.00E+00

2.00E-02

4.00E-02

6.00E-02

8.00E-02

1.00E-01

1.20E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0.00E+00

1.00E-04

2.00E-04

3.00E-04

4.00E-04

5.00E-04

6.00E-04

7.00E-04

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0.00E+00

2.00E+00

4.00E+00

6.00E+00

8.00E+00

1.00E+01

1.20E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0.00E+00

2.00E+00

4.00E+00

6.00E+00

8.00E+00

1.00E+01

1.20E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0.00E+00

5.00E-05

1.00E-04

1.50E-04

2.00E-04

2.50E-04

3.00E-04

3.50E-04

4.00E-04

4.50E-04

5.00E-04

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT



Figure 3.7 Wave exciting forces and moments for CYLINDER


0.00E+00

2.00E+02

4.00E+02

6.00E+02

8.00E+02

1.00E+03

1.20E+03

1.40E+03

1.60E+03

1.80E+03

2.00E+03

0 4 8 12 16 20 24 28 32 36 40 44

Period

F/A MOSES

WAMIT


0.00E+00

2.00E+02

4.00E+02

6.00E+02

8.00E+02

1.00E+03

1.20E+03

1.40E+03

1.60E+03

1.80E+03

2.00E+03

0 4 8 12 16 20 24 28 32 36 40 44

Period

F/A MOSES

WAMIT


0.00E+00

1.00E+02

2.00E+02

3.00E+02

4.00E+02

5.00E+02

6.00E+02

7.00E+02

8.00E+02

9.00E+02

0 4 8 12 16 20 24 28 32 36 40 44

Period

F/A MOSES

WAMIT


0.00E+00

2.00E+04

4.00E+04

6.00E+04

8.00E+04

1.00E+05

1.20E+05

0 4 8 12 16 20 24 28 32 36 40 44

Period

M/A MOSES

WAMIT


0.00E+00

2.00E+04

4.00E+04

6.00E+04

8.00E+04

1.00E+05

1.20E+05

0 4 8 12 16 20 24 28 32 36 40 44

Period

M/A MOSES

WAMIT


0.00E+00

1.00E-03

2.00E-03

3.00E-03

4.00E-03

5.00E-03

6.00E-03

7.00E-03

0 4 8 12 16 20 24 28 32 36 40 44

Period

M/A MOSES

WAMIT



Figure 3.8 Motion RAO for CYLINDER


0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0.00E+00

2.00E+00

4.00E+00

6.00E+00

8.00E+00

1.00E+01

1.20E+01

1.40E+01

1.60E+01

1.80E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

3.00E-02

3.50E-02

4.00E-02

4.50E-02

5.00E-02

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

3.00E-02

3.50E-02

4.00E-02

4.50E-02

5.00E-02

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0.00E+00

1.00E-06

2.00E-06

3.00E-06

4.00E-06

5.00E-06

6.00E-06

7.00E-06

8.00E-06

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT



Figure 3.9 Added mass coefficients for SHIP


0.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

3.00E-02

3.50E-02

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT


0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT


0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00

3.00E+00

3.50E+00

4.00E+00

4.50E+00

5.00E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT


0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

6.00E+00

7.00E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT


0.00E+00

2.00E+01

4.00E+01

6.00E+01

8.00E+01

1.00E+02

1.20E+02

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT


0.00E+00

1.00E+01

2.00E+01

3.00E+01

4.00E+01

5.00E+01

6.00E+01

7.00E+01

8.00E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT



Figure 3.10 Damping coefficients for SHIP


0.00E+00

1.00E-03

2.00E-03

3.00E-03

4.00E-03

5.00E-03

6.00E-03

7.00E-03

8.00E-03

9.00E-03

1.00E-02

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


-5.00E-01

0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00

3.00E+00

3.50E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0.00E+00

1.00E+01

2.00E+01

3.00E+01

4.00E+01

5.00E+01

6.00E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0.00E+00

1.00E+01

2.00E+01

3.00E+01

4.00E+01

5.00E+01

6.00E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT



Figure 3.11 Wave exciting forces and moments for SHIP


0.00E+00

5.00E+01

1.00E+02

1.50E+02

2.00E+02

2.50E+02

3.00E+02

3.50E+02

0 4 8 12 16 20 24 28 32 36 40 44

Period

F/A MOSES

WAMIT


0.00E+00

1.00E+02

2.00E+02

3.00E+02

4.00E+02

5.00E+02

6.00E+02

7.00E+02

8.00E+02

0 4 8 12 16 20 24 28 32 36 40 44

Period

F/A MOSES

WAMIT


0.00E+00

1.00E+03

2.00E+03

3.00E+03

4.00E+03

5.00E+03

6.00E+03

7.00E+03

0 4 8 12 16 20 24 28 32 36 40 44

Period

F/A

MOSESWAMIT


0.00E+00

1.00E+03

2.00E+03

3.00E+03

4.00E+03

5.00E+03

6.00E+03

0 4 8 12 16 20 24 28 32 36 40 44

Period

M/A

MOSESWAMIT


-2.00E+04

0.00E+00

2.00E+04

4.00E+04

6.00E+04

8.00E+04

1.00E+05

1.20E+05

1.40E+05

1.60E+05

1.80E+05

2.00E+05

0 4 8 12 16 20 24 28 32 36 40 44

Period

M/A MOSES

WAMIT


0.00E+00

1.00E+04

2.00E+04

3.00E+04

4.00E+04

5.00E+04

6.00E+04

0 4 8 12 16 20 24 28 32 36 40 44

Period

M/A

MOSESWAMIT



Figure 3.12 Motion RAO for SHIP


0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

7.00E-01

8.00E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

7.00E-01

8.00E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0.00E+00

2.00E+00

4.00E+00

6.00E+00

8.00E+00

1.00E+01

1.20E+01

1.40E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

7.00E-01

8.00E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

2.50E-01

3.00E-01

3.50E-01

4.00E-01

4.50E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT



Figure 3.13 Added mass coefficients for TLP


0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT


0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT


0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

7.00E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT


0.00E+00

5.00E+00

1.00E+01

1.50E+01

2.00E+01

2.50E+01

3.00E+01

3.50E+01

4.00E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT


0.00E+00

5.00E+00

1.00E+01

1.50E+01

2.00E+01

2.50E+01

3.00E+01

3.50E+01

4.00E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT


0.00E+00

1.00E+01

2.00E+01

3.00E+01

4.00E+01

5.00E+01

6.00E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT



Figure 3.14 Damping coefficients for TLP


0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

2.50E-01

3.00E-01

3.50E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0.00E+00

5.00E-02

1.00E-01

1.50E-01

2.00E-01

2.50E-01

3.00E-01

3.50E-01

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0.00E+00

2.00E-03

4.00E-03

6.00E-03

8.00E-03

1.00E-02

1.20E-02

1.40E-02

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

6.00E+00

7.00E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

6.00E+00

7.00E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0.00E+00

5.00E+00

1.00E+01

1.50E+01

2.00E+01

2.50E+01

3.00E+01

3.50E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT



Figure 3.15 Wave exciting forces and moments for TLP


0.00E+00

1.00E+02

2.00E+02

3.00E+02

4.00E+02

5.00E+02

6.00E+02

7.00E+02

8.00E+02

9.00E+02

0 4 8 12 16 20 24 28 32 36 40 44

Period

F/A

MOSESWAMIT


0.00E+00

1.00E+02

2.00E+02

3.00E+02

4.00E+02

5.00E+02

6.00E+02

7.00E+02

8.00E+02

9.00E+02

0 4 8 12 16 20 24 28 32 36 40 44

Period

F/A MOSES

WAMIT


0.00E+00

1.00E+02

2.00E+02

3.00E+02

4.00E+02

5.00E+02

6.00E+02

7.00E+02

8.00E+02

0 4 8 12 16 20 24 28 32 36 40 44

Period

F/A

MOSESWAMIT


0.00E+00

2.00E+03

4.00E+03

6.00E+03

8.00E+03

1.00E+04

1.20E+04

1.40E+04

1.60E+04

1.80E+04

0 4 8 12 16 20 24 28 32 36 40 44

Period

M/A

MOSESWAMIT


0.00E+00

2.00E+03

4.00E+03

6.00E+03

8.00E+03

1.00E+04

1.20E+04

1.40E+04

1.60E+04

1.80E+04

0 4 8 12 16 20 24 28 32 36 40 44

Period

M/A

MOSESWAMIT


0.00E+00

1.00E-01

2.00E-01

3.00E-01

4.00E-01

5.00E-01

6.00E-01

7.00E-01

8.00E-01

9.00E-01

1.00E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

M/A

MOSESWAMIT



Figure 3.16 Motion RAO for TLP


0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

1.40E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0.00E+00

2.00E-01

4.00E-01

6.00E-01

8.00E-01

1.00E+00

1.20E+00

1.40E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0.00E+00

1.00E+00

2.00E+00

3.00E+00

4.00E+00

5.00E+00

6.00E+00

7.00E+00

8.00E+00

9.00E+00

1.00E+01

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00

3.00E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0.00E+00

5.00E-01

1.00E+00

1.50E+00

2.00E+00

2.50E+00

3.00E+00

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0.00E+00

2.00E-06

4.00E-06

6.00E-06

8.00E-06

1.00E-05

1.20E-05

1.40E-05

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT



Figure 3.17 Added mass coefficients for MOB


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass

MOSESWAMIT


0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT


0

0.5

1

1.5

2

2.5

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT


0

10

20

30

40

50

60

70

80

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT


0

10

20

30

40

50

60

70

80

90

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT


0

10

20

30

40

50

60

70

80

0 4 8 12 16 20 24 28 32 36 40 44

Period

A/M

ass MOSES

WAMIT



Figure 3.18 Damping coefficients for MOB


0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


-5

0

5

10

15

20

25

30

35

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0

5

10

15

20

25

30

35

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT


0

5

10

15

20

25

30

35

40

45

50

0 4 8 12 16 20 24 28 32 36 40 44

Period

SQ

RT(

B/M

ass)

MOSESWAMIT



Figure 3.19 Wave exciting forces and moments for MOB


0

500

1000

1500

2000

2500

0 4 8 12 16 20 24 28 32 36 40 44

Period

F/A MOSES

WAMIT


0

500

1000

1500

2000

2500

3000

3500

0 4 8 12 16 20 24 28 32 36 40 44

Period

F/A MOSES

WAMIT


0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 4 8 12 16 20 24 28 32 36 40 44

Period

F/A

MOSESWAMIT


0

50000

100000

150000

200000

250000

0 4 8 12 16 20 24 28 32 36 40 44

Period

M/A

MOSESWAMIT


0

50000

100000

150000

200000

250000

300000

0 4 8 12 16 20 24 28 32 36 40 44

Period

M/A

MOSESWAMIT


0

20000

40000

60000

80000

100000

120000

140000

160000

0 4 8 12 16 20 24 28 32 36 40 44

Period

M/A

MOSESWAMIT



Figure 3.20 Motion RAO for MOB


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0

0.5

1

1.5

2

2.5

3

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0

0.05

0.1

0.15

0.2

0.25

0.3

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0

0.2

0.4

0.6

0.8

1

1.2

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT


0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 4 8 12 16 20 24 28 32 36 40 44

Period

RA

O MOSESWAMIT



4. References

1. WAMIT Version5.4 : A Radiation Diffraction Panel program for Wave-Body Interaction ,MIT, 1998.

2. MOSES Version 5.09.027 Reference Manual, Ultra Marine, 1999.

wamit moses

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