A DIRECT THRUST MEASUREMENT SYSTEM FOR A WATERJET-

PROPELLED, FREE RUNNING USV

by

John A. Grimes

A Thesis Submitted to the Faculty of

the College of Engineering and Computer Science

in Partial Fulfillment of the Requirements for the Degree of

Master of Science

Florida Atlantic University

Boca Raton, Florida

December 2013

iii

ABSTRACT

Author: John Grimes

Title: A Direct Thrust Measurement System for a Waterjet Propelled, Free Running USV

Institution: Florida Atlantic University

Thesis Advisor: Dr. Karl von Ellenrieder

Degree: Master of Science

Year: 2013

The relationship between cross-flow at a waterjet inlet and delivered thrust is not

fully understood. A direct thrust measurement system was designed for a waterjet

propelled, free running USV. To induce sway velocity at the waterjet inlet, which was

considered equivalent to the cross flow, circles of varying radii were performed at

Reynolds Numbers between 3.48 x 106 and 8.7 x 106 and radii from 2.7 to 6.3 boat

lengths. Sway velocities were less than twenty percent of mean forward speed with slip

angles that were less than 20°. Thrust Loading Coefficients were compared to sway as

a percent of forward speed. In small radius turns, no relationship was seen, while in

larger radius turns, peaks of sway velocity corresponded with drops in thrust, but this

was determined to be caused by reduced vehicle yaw in these intervals . Decoupling of

thrust and yaw rate is recommended for future research.

iv

A DIRECT THRUST MEASUREMENT SYSTEM FOR A WATERJET-

PROPELLED, FREE RUNNING USV

LIST OF FIGURES ..................................................................................................................... vii

LIST OF TABLES ....................................................................................................................... ix

NOMENCLATURE ...................................................................................................................... x

1 INTRODUCTION ................................................................................................................. 1

1.1 Problem Statement ........................................................................................................ 1

1.2 Background ................................................................................................................... 1

1.2.1 Momentum Flux Method ....................................................................................... 3

1.2.2 Direct Thrust Method ............................................................................................ 3

1.2.3 Cross Flow ............................................................................................................. 4

2 APPROACH .......................................................................................................................... 8

2.1 Platform Identification .................................................................................................. 8

2.2 Design of propulsion system ......................................................................................... 9

2.2.1 Waterjet ............................................................................................................... 10

2.2.2 Motor Controller.................................................................................................. 10

2.2.3 Motors ................................................................................................................. 11

2.2.4 Battery ................................................................................................................. 11

2.2.5 Electrical Design ................................................................................................. 12

v

2.2.5.1 Kill Circuit ........................................................................................................... 13

2.2.6 Structural Design ................................................................................................. 15

2.2.7 Cooling System ................................................................................................... 18

2.3 Control System and Data Collection ........................................................................... 20

2.3.1 Force Transducer Data Collection ........................................................................... 21

2.4 Force transducer calibration ........................................................................................ 22

2.5 Experimental Approach ............................................................................................... 23

3 PROPULSION SYSTEM TESTING .................................................................................. 26

3.1 Motor Pod Testing ....................................................................................................... 26

3.1.1 Hull Seal Testing ................................................................................................. 26

3.1.2 Magnetic Coupling Test ...................................................................................... 26

3.1.3 Run Time Estimation Test ................................................................................... 27

4 EXPERIMENTAL TESTING ............................................................................................. 28

4.1 Experimental Testing .................................................................................................. 28

4.1.1 Testing - June 14, 2013 ....................................................................................... 28

4.1.2 Testing: June 26, 2013 ........................................................................................ 29

4.1.3 Testing: September 19, 2013 .............................................................................. 30

4.1.4 Testing: September 27, 2013 ............................................................................... 31

5 DATA PROCESSING ........................................................................................................ 33

6 RESULTS ............................................................................................................................ 41

7 CONCLUSIONS ................................................................................................................. 48

vi

APPENDIX A - DATA SORTING CODE ................................................................................. 51

A.1 Test Sorter Function .................................................................................................... 51

A.2 Data Splitting Code ..................................................................................................... 52

A.3 Force Transducer Data Splitter .................................................................................... 53

A.4 Data Splitting Code for Straight Line Tests ................................................................ 56

A.5 Force Transducer Data Splitting Code for Strait Line Tests ....................................... 57

APPENDIX B - DATA PROCESSING CODE .......................................................................... 61

APPENDIX C - MOTOR CONTROLLER CODE .................................................................... 72

APPENDIX D - FIGURES ......................................................................................................... 73

APPENDIX E - DESCRIPTION OF MOMENTUM FLUX METHOD .................................. 113

APPENDIX F - WIRING DIAGRAMS ................................................................................... 116

APPENDIX G - CENTER OF GRAVITY CALCULATIONS AND VERIFICATION ......... 118

REFERENCES .......................................................................................................................... 122

vii

LIST OF FIGURES

Figure 1-1: Usage of Reversing Bucket and Nozzle[3] .................................................................... 2

Figure 1-2: Representation of the Intake of a Flush Inlet Waterjet [6] ............................................ 5

Figure 1-3: USV-12 Wave Adaptive Modular Vehicle [7] .............................................................. 6

Figure 1-4: Experimental Setup from 2010 Tests [7]. ...................................................................... 7

Figure 2-1: Planing Hull Platform Considered ................................................................................. 8

Figure 2-2: Roboteq Motor Controller ........................................................................................... 10

Figure 2-3: Motor Pod Block Diagram .......................................................................................... 13

Figure 2-4: Pod Cross Section ........................................................................................................ 15

Figure 2-5: General Arrangements and Side view of Motor Pod ................................................... 16

Figure 2-6: Detail View of Interface and Force Transducer Cable ................................................ 17

Figure 2-7: Cooling System Components ...................................................................................... 18

Figure 2-8: Control and Data Collection Block Diagram .............................................................. 20

Figure 2-9: Force Transducer Calibration Data – FZ Channel ....................................................... 23

Figure 2-10: North Hollywood Finger Lake ................................................................................. 24

Figure 3-1: Battery Discharge Curve at 75% Throttle ................................................................... 27

Figure 5-1: Circle Test 1 - Vehicle Velocities, Waterjet Inlet Local Velocities ............................ 36

Figure 5-2: Circle Test 2 - Frequency Analysis of 1 kHz Force Signal ......................................... 37

Figure 5-3: Circle Test 2 -Frequency Analysis of 10 Hz Force Signal .......................................... 38

Figure 5-4: Circle Test 1 - Two Components of Thrust ................................................................. 39

Figure 6-1: Circle Test 1 - Primary Frequency Thrust Compared to Sway ................................... 42

Figure 6-2: Circle Test 1 - Secondary Frequency Thrust Compared to Sway ............................... 42

viii

Figure 6-3: Circle Test 1 - Normalized Cross-Correlation for Thrust and Sway Velocity ............ 43

Figure 6-4: Circle Test 6 - GPS Path .............................................................................................. 44

Figure 6-5: Circle Test 6 - Primary Frequency Thrust Compared to Sway ................................... 45

Figure 6-6: Circle Test 6 - Normalized Cross-Correlation for Thrust and Sway Velocity ........... 46

Figure 6-7: Circle Test 6 - Slip Angle ........................................................................................... 47

ix

LIST OF TABLES

Table 1-1: Momentum Flux vs. Direct Thrust [5] ............................................................................ 4

Table 2-1: Design Criteria for Electric Pods .................................................................................... 9

Table 2-2: Components of New Propulsion System ........................................................................ 9

Table 2-3: Motor Power and RPM Comparison............................................................................ 11

Table 2-4: Battery Specifications ................................................................................................... 12

Table 2-5: Heat Sink Temperature Test ......................................................................................... 14

Table 2-6: Data Logged on Laptop ................................................................................................ 22

Table 2-7: Expected Yaw Induced Sway Velocities in m/s ........................................................... 24

Table 4-1: Test Run Waypoints Distances ..................................................................................... 31

x

NOMENCLATURE

ITTC International Towing Tank Conference

USV Unmanned Surface Vehicle

DGPS Differential Global Positioning System

LiNiMnCo Lithium Nickel Manganese Cobalt (Lithium Polymer Battery Chemistry)

HDPE High-Density Polyethylene

LCM Lightweight Communications and Marshaling

IMU Inertial Measurement Unit

UA Velocity of location A

UG Velocity of center of gravity

� Rotation rate of vehicle

��� Distance vector between vehicle center of gravity and location A

��� Thrust Loading Coefficient

� Density

Forward Vehicle Speed

�� Nozzle Area

1

1 INTRODUCTION

1.1 Problem Statement

Waterjet propulsion is used for many types of marine vehicles. Currently the

most common method of predicting the thrust of a waterjet involves integrating the

momentum flux through a control volume surrounding the waterjet system[1]. This

method (referred to as the momentum flux method) assumes that the flow enters the

waterjet longitudinally, while non-longitudinal flow, such as what might be encountered

in high speed turns or in certain hull configurations, is not considered. The effects of

non-longitudinal flow, sometimes called cross-flow, on the delivered thrust are not well

understood. The purpose of this thesis is to design a testing platform capable of directly

measuring the thrust delivered by a waterjet propulsion system while simultaneously

recording vehicle behaviors for comparison to the thrust. Of particular interest is the

velocity and yaw rate of the vehicle which will be used to determine a local sway

velocity at the location of the waterjet inlet. This sway velocity will be assumed to be

proportional to the cross-flow ingested by the water jet.

1.2 Background

Waterjet propulsion has been successfully used in marine craft since the 1950’s.

There are three main categories of waterjets. Centrifugal waterjets are primarily used

for low speed operations and axial flow waterjets are used in high speed. A mixed jet,

which incorporates both axial and rotational flows, has been used for mid-range speeds.

2

In addition to describing the jet by the type of flow, jets are also described by their inlet.

One of the most commonly used forms is the flush inlet waterjet. In this form of

waterjet, the inlet is incorporated into the hull as opposed to in a separate pod as might

be used in hydrofoils [2].

Waterjets have many advantages over traditional propeller designs in certain

performance regimes. For example, the elimination of appendages reduces drag and

allows for vessels to be operated in shallow water. Reversing the thrust is accomplished

using a bucket to redirect the flow leaving the nozzle, which allows the vehicle to be

able to apply full thrust in a reverse direction quickly without needing a reversing gear,

making waterjet propelled vehicles very maneuverable. Maneuvering is accomplished

by changing the direction the nozzle points as opposed to using a rudder (see Figure

1-1), or in the case of catamaran style vehicles, a differential thrust approach can also be

used.

Figure 1-1: Usage of Reversing Bucket and Nozzle[3]

3

1.2.1 Momentum Flux Method

Currently, the standard methodology for predicting the performance of a

waterjet, as defined by the International Towing Tank Conference (ITTC), is a modified

momentum flux method [4]. In this approach, the thrust delivered by the waterjet on

the hull is calculated based on the change in momentum flux between the inlet and

nozzle of the waterjet. This method requires having accurate measurements of the

velocity and volume flow rate at both the inlet and nozzle of the waterjet [1]. A brief

summary of the momentum flux method as described by the ITTC can be found in

APPENDIX E.

1.2.2 Direct Thrust Method

An alternate method of determining the thrust produced by a waterjet is the

Direct Thrust Method. This method requires isolating the propulsion system from the

main hull of the vehicle without losing hull integrity. A force transducer is then placed

between the propulsion system and the hull. At the 22nd ITTC, it was stated that the

preferred method would be the momentum flux method, but further development of the

direct thrust method was deemed important, as measurement of the forces and moments

imparted on the hull by the waterjet could provide insight into waterjet-hull

interactions [1]. As of the 24th ITTC, no institution had reported efforts to conduct

direct thrust measurements. It was assumed that this was due to the inherent

complexities involved and the ITTC developed its procedure based solely on the

momentum flux method.

4

Table 1-1: Momentum Flux vs. Direct Thrust [5]

Momentum Flux Method Direct Thrust Method

Advantages: No complicated watertight sealing boundary between waterjet and hull needed.

Disadvantages Accuracy highly dependent on accurate velocity measurements

Advantages: Jet system performance need not be measured separately.

Disadvantages: Requires separation between waterjet and hull.

1.2.3 Cross Flow

One question that the direct thrust method can be used for is to investigate the

effects of ingestion of non-longitudinal flows by a waterjet on its delivered thrust. This

is still an emerging area of research and there is little published research on the topic.

There are a few circumstances where non-longitudinal flow, or cross-flow, might

develop. One situation is maneuvering in a seaway at speed where any vehicle sway

velocity would be combined with a sway velocity imparted by the vehicle's yaw rate. If

there is substantial sway velocity at the inlet location, a cross-flow may develop,

depending on the hull geometry.

Another situation where a cross-flow might develop is with surface effect ships

(SES). An SES uses an air cushion entrained within catamaran style hulls through the

use of fore and aft skirts. The pressure differential between the air cavity and

atmospheric pressure can cause a cross-flow to develop around the catamaran hulls.

This cross-flow could then affect the performance of the waterjet by inducing cavitation

or flow separation within the waterjet inlet [3].

While little research has been done on this specific topic, a survey of related

topics can provide some insight. When water enters a waterjet inlet longitudinally, it

flows up a changing curve that starts out tangent to the hull surface, and then curves up

5

toward the impeller. This curve guides the flow up smoothly, hopefully preventing

significant flow separation. The slope of the side of the inlet is much steeper.

Figure 1-2: Representation of the Intake of a Flush Inlet Waterjet [6]

The steepness of the slope of the sides varies from one manufacturer to the next,

but if we assume it to be significant, then we can imagine the flow entering the waterjet

from the sides as that flowing over a step, which is a well documented problem that can

lead to the formation of helical flow and eddy currents.

If the flow over the step causes significant flow separation, it could potentially

cause a significant portion of the flow to "skip" over the inlet, reducing the ingested

momentum. Another possible outcome of the problem is the formation of an helical

flow within the waterjet, thus affecting its efficiency. In other types of pumps,

ingestion of swirling flow has been shown to adversely affect pump efficiency.

One reference on the topic of experimental measurement of cross flow came

from previous research at Florida Atlantic University (FAU)[7]. In an effort to better

understand the effect of cross-flow on the delivered thrust of a waterjet, an experiment

was derived using a platform of opportunity. The USV-12 (see Figure 1-3 below) is a

6

waterjet propelled Unmanned Surface Vehicle currently being worked with at FAU.

Figure 1-3: USV-12 Wave Adaptive Modular Vehicle [7]

One feature of the USV12 that is helpful for implementing a direct thrust

measurement system is that the propulsion sections of the vehicle are located in

enclosed pods that and are only pin connected to the main vehicle body. This allowed

for an interface unit to be placed between the engine pod and the vehicle which

contained a force transducer so that the thrust of the engine pod could be measured

directly.

One of the early tests performed was to determine the drag of one of the pods

and compare that to the drag of the craft. An open water tow test was conducted in

which the force transducer module was installed and the waterjet inlets covered. A

tension-link load cell between the tow vehicle and the USV-12 measured the tow force

which is equivalent to the drag of the vehicle. As can be seen in Figure 1-4, the load

cell assembly sits between the demi-hull and the propulsion unit. The force transducer

held within the load cell assembly measured the relative force between the engine pod

and the main hull. This data was then used to determine the drag of the engine pod [8].

7

A series of tests were then performed to induce a sway velocity at the waterjet

inlet. This sway velocity was then assumed to be equivalent to the cross flow. The

vehicle’s motions were measured using a Differential GPS (DGPS) and both the vehicle

motions as well as the force data were logged.

Figure 1-4: Experimental Setup from 2010 Tests [7].

A series of experiments were conducted, but as the vehicle was remote operated,

there was a large amount of deviation between the planned maneuver and the actual

vehicle motion. It was determined that the implementation of a control system would

limit this variability. Another problem identified related to propagation of noise. In the

data analysis, the rate of turn was calculated by differentiating the heading of the

vehicle. The calculated rate of turn was then used in the calculation of the sway

velocity. Signal noise in the heading data created amplified noise in the sway velocity

measurements which then needed to be filtered out. A better approach would be to

include a sensor which would directly measure the yaw rate[7].

8

2 APPROACH

2.1 Platform Identification

As a first step, it was necessary to choose a vehicle to base the testing platform

on. There were two vehicles available to work with. The first was an 80 inch long.

deep-V planing hull. Study of the work necessary to separate the waterjet from the main

hull revealed no simple solution. Additionally, the vehicle was payload-limited.

Figure 2-1: Planing Hull Platform Considered

Another vehicle considered was the USV-12. The USV-12 is a round hulled

catamaran that had previously been used, as described above, to conduct remote

controlled direct thrust measurements. This vehicle had the advantage of already

having the propulsion section separated from the main hull, and had a payload capacity

that was significantly larger than that of the planing hull. After consideration of the

requirements, the USV-12 was chosen for its ease of integration of the force transducer

and its payload capacity.

9

2.2 Design of propulsion system

Previous experience with the USV-12 revealed that in order to have a reliable

vehicle with predictable responses, the original two stroke gasoline engines needed to

be replaced. New propulsion units with electric motors were designed to provide a

solution to the performance issues identified. The criteria used for design decisions can

be seen in Table 2-1.

Table 2-1: Design Criteria for Electric Pods

• Components and replacement parts should be readily available

• Total thrust should be comparable to that of the existing pods

• Maximize runtime while attempting to maintain waterline

• Allow for incorporation of the force transducer into the design

After researching their availability and applicability to the system requirements,

components were chosen (see Table 2-2) to meet the above criteria.

Table 2-2: Components of New Propulsion System

Water Jet Motor

Motor Controller

Battery

Manufacturer Graupner Neumotors Roboteq Battery Space Model Jet Booster 5 2224/24/1Y MBL1650C 36V 30Ah Criteria:

Replacement parts available

Similar impeller size to current pods

RPM/power similar to the existing

Company that is easy to work with.

Controlled either with RC or serial

Feedback on serial lines

Similar to other controllers in use at FAU

LiNiMnCo chemistry gives high energy density.

90A current limit sufficient for motors

10

2.2.1 Waterjet

The Graupner Jet Booster 5 water jet is a model scale axial flow waterjet. The

jet ducting is made of cast Aluminum and the impellor is made of fiber reinforced

plastic. This jet and all replacement parts are available commercially in the US. It is

designed to use either electric motors, or the same Zenoah engine that the previous pods

used. The jet has an impeller diameter of 49mm which is similar to the size of the

impellers in the previous engine pods. Unfortunately, no documentation is available on

the performance or design criteria for this water jet, but the same was also true for all

other model scale jets that were looked at.

2.2.2 Motor Controller

Figure 2-2: Roboteq Motor Controller

The Roboteq MBL1650C (see Figure 2-2) was chosen as the motor controller

for the new system. This motor controller is designed to drive a single brushless DC

motor. This allowed for the motor controller to be located in the pod, minimizing the

length of power transmission lines. One significant advantage to using this motor

controller is that it allows for control the motor speed using an RC control line while

11

simultaneously obtaining feedback from a RS232 serial line. This motor controller also

placed some additional requirements on the design. It has a maximum allowable

voltage of 50 V and requires the motor to have Hall Effect sensors, which can be used

to measure the speed of the motor shaft. The voltage limit drove the decision to have a

36 V operating voltage for the new pods.

2.2.3 Motors

Motors were chosen to match the performance characteristics of two stroke

gasoline engines used in the previous propulsion system. The motor chosen is the

Neumotors 2224/24/1Y manufactured by Neutronics. This motor was operates in the

desired RPM range at the chosen operating voltage, while still providing power similar

to that of a Zenoah engine (see Table 2-3 for a side by side comparison). The company

was also willing to install Hall Effect sensors on the motors, as required for the use of

the Roboteq motor controller.

Table 2-3: Motor Power and RPM Comparison

Waterjet

requirements Zenoah

G260PUM Chosen Motor

Power 700 W electric

or Zenoah Engine

2.2kW 1.8 kW

RPM Not specified 12,500 RPM 15,000 RPM

2.2.4 Battery

One of the biggest design considerations for the choice of battery was energy

density. It was desirable to have the maximum amount of run time with the minimum

amount of extra weight. Lithium based batteries have some of the highest energy

densities of standard battery packs and of lithium batteries the LiNiMnCo batteries have

12

one of the highest densities. Given our operating voltage, and power requirements, a

battery was chosen.

Table 2-4: Battery Specifications

Battery Chemistry: LiNiMnCo Charge density: 160 wh/kg (approximate) Working Voltage: 36V Maximum Voltage: 42V Cutoff Voltage: 27V Capacity: 30 Ah (1080 wh) Discharge Rate: 90 A max Weight: 14 lbs 11.8 oz

The battery selected consists of 30 LiNiMnCo cells arrange in a 3S-10P

configuration (see Table 2-4 for battery specifications). A protection circuit module

(PCM) was installed in the batteries which monitors the charge and discharge of each

cell and balances the current load on the cells accordingly. The PCM also provides

over-discharge protection and will stop discharging the battery if the voltage of the cells

drops below a safe threshold.

2.2.5 Electrical Design

Communication lines, including both RC control and RS232 lines are brought

into the pod through a cord grip on the forward face of the pod. The battery provides

the voltage source to the motor controller which then distributes it to the motor.

Additionally, an RC line is also connected to a servo mounted to the aft bulkhead which

articulates the reversing bucket. By time of testing, the reversing bucket and servo had

not been installed as the ability to control them had not yet been integrated into the

control system.

13

Figure 2-3: Motor Pod Block Diagram

2.2.5.1 Kill Circuit

The system is designed to kill the power to the motor controller if any of several

conditions occurs, including low control system voltage, processor fault, or human

intervention by means of a switch on the vehicle remote. This is accomplished by

placing a pair of 60V, 100A relays between the battery and the motor controller. These

relays are mounted on a heat sink with a fan to dissipate the heat generated from the

relay when it is in a closed position.

The efficiency of the heat sink was tested by placing load resistors of a known

resistance on the heat sink and adjusting the power dissipated though them. For this

test, the heat sink was mounted in a sealed motor pod on a worktable. The temperature

14

rise of the heat sink was measured using a thermocouple connected to a volt meter.

This allowed us to estimate the thermal resistance of the heat sink. As can be seen in

Table 2-5 below, the thermal resistance of the heat sink was found to be approximately

1.9 degrees Celsius per Watt. When examining the datasheet for the relays it was

determined additional cooling was recommended so a cooling fan was incorporated.

This cooling fan draws power from the motor battery.

Table 2-5: Heat Sink Temperature Test

Elapsed Time (min)

Target Power (W)

Target Voltage

(V)

Actual Voltage

(V)

Actual Power

(V)

Starting Temp (°C)

Ending Temp (°C)

Temp Change

(°C) °C /W

0:46 10 4.47 4.51 10.17 24.7 46.7 22 2.16 1:54 15 5.48 5.54 15.35 28.4 56.5 28.1 1.83 1:33 20 6.32 6.3 19.85 26.3 62.6 36.3 1.83 2:06 30 7.75 7.76 30.11 24.9 78 53.1 1.76

15

2.2.6 Structural Design

Figure 2-4: Pod Cross Section

The physical design of the new pods was performed with an eye towards ease of

use and repair. A U-shaped cross-section with lid was used (see Figure 2-4). This

allows access to all of the components from above. Aluminum was chosen for the outer

shell due to its ability to be worked with along with its durability. The lid, as well as

fore and aft bulkheads are made from Starboard and the keel liner is made from high-

density polyethylene (HDPE).

The battery, which is by far the heaviest of the loads in the pods, has been

located slightly forward of the longitudinal center of the pod to accommodate the space

required for the motor and waterjet (see Figure 2-5). The battery is mounted in a

module consisting of fiber two fiber reinforced bulkheads, a tray, and a pair of

cylindrical lifting rails. The battery sits in the tray and is held in place by a restraining

strap. The bulkheads, in addition to raising the battery up off of the bottom of the pod

(to minimize damage that might be caused by small leaks), provide convenient

mounting points for the motor controller, the shut off relay, and cooling system.

16

Figure 2-5: General Arrangements and Side view of Motor Pod

One problem identified with the design is the increased weight from the

aluminum hull and battery. However, the shape of the new pods give increased

reserved buoyancy as compared to the original cylindrical design. Also, the diameter

was increased from 8.25 inches to 8.5 inches and the pods were lengthened from 29

inches to 34.5 inches. These factors increased the buoyancy of the new pods to attempt

to maintain the existing waterline without putting excessive downward force on the

superstructure of the vehicle.

The interface between the pod and the hull has also been revised. In the old pod,

a pin went through the forward end of the pod connecting it to the hull and a strap kept

the pod from having a greater than 30 degree downward pitch relative to the vehicle. In

the previous force transducer experiments, an aluminum insert was placed between the

pod and the hull with the force transducer. The new design includes the force

transducer as part of the configuration and a steel blank of the same size will be used

when not performing thrust measurements.

17

Figure 2-6: Detail View of Interface and Force Transducer Cable

The pin which holds the pods to the hull will go through an interface plate.

Attached to the aft of this plate will be a foam ring which will surround the force

transducer to help provide continuity of flow. The other end of the force transducer will

be mounted to forward bulkhead of the pod. The force transducer’s data cable will run

into the pod, and then back out through a port on the forward bulkhead. This was done

to allow for a shorter overall interface section.

A design constraint imposed by the force transducer is that the transducer is

moment limited to 1000 in-lbs. This is greater than the moment caused by the mass of

the pod in air, pivoting around the transducer. To prevent damage to the force

transducer, a lockout ring has been design which prevents motion between the interface

plate and the pod. This ring will be removed after the vehicle has been placed in the

water and before any testing begins. At the time of testing, the lockout ring had not yet

been manufactured, so the pods were installed after the vehicle body was already in the

water to minimize the torque inducing loads exerted on the pod.

Thrust Direction

18

2.2.7 Cooling System

Originally, the pressure tap that comes preinstalled on the side of the waterjet

was going to be used to provide a flow of water to cool the motor. The water would

then flow up through a tube on the outside of the stern of the pod to a hull penetration

which was located near the top of the pod to make sure that the penetration was far

above waterline. Upon initial testing, it was determined that the waterjet didn't produce

a high enough pressure for the water to reach the hull penetration until the throttle was

greater than 80%. Once the system was "primed" it only had sufficient flow above 50%

throttle. At full speed, the flow rate was determined to be 100 mL per min. This was

determined to be insufficient as the motor still got quite warm at midrange throttle

settings.

Figure 2-7: Cooling System Components

To increase the flow rate, a standalone cooling system was designed to circulate

water through a coil wrapped around the motor (see Figure 2-7 above). The motor that

was chosen was a peristaltic pump. This type of pump is designed for passing fluids

Pump

Coil

Intake

Exhaust

External Pickup

19

through tubing and is known for its self priming capabilities. The specific pump that

was chosen can self prime up to 7.5 meters of pressure head and has a flow rate on the

order of 200 mL per minute. One other feature of this style of pump is its ability to be

able to run dry without causing damage to the pump. This feature makes it easy to both

prime and purge the system.

The pump is powered by a standalone 12V 2400 mAh Nickel Cadmium battery

pack. This should allow the cooling pumps to be run for up to 90 minutes, making it

advisable to change the cooling system batteries at the same time as the main batteries.

The cooling system is activated by turning on either one of two switches that are

placed in parallel in its circuit. The main switch is a voltage controlled solid state relay.

This switch is tied into the kill circuit of the pod making it possible to turn on and off

the cooling system remotely. The second switch is a manual switch. This switch is

designed so that the cooling system can be turned on and off manually to facilitate the

flushing of the system. Please refer to the appendix for a wiring diagram of the cooling

system's electrical components.

20

2.3 Control System and Data Collection

Figure 2-8: Control and Data Collection Block Diagram

Motor throttle was controlled using a control system that has been developed for

use with several of FAU’s autonomous surface vehicles including the USV-12, DUKW

model, USV-14, and the AVUSI Roboboat student competition vehicle. This control

system uses data from a compass, IMU, and GPS to determine what corrections need to

be made to the vehicle motions and then sends the appropriate signals to the motor

controllers. The sensors used by the control system include an OS5000 tilt

compensated compass and an MTI-G IMU. The MTI-G has several sensors of its own

including gyro, accelerometer, magnetometer, barometer, and GPS receiver. The GPS

receiver is capable of obtaining ground based corrections to improve its accuracy.

21

At the heart of the control system is a TS7800 microprocessor board with an

ARM9 CPU. The TS7800 is mounted on an interface board. This board has RC

outputs that can be used to control RC Servos as well as the motor controllers. Several

serial ports are available for various sensors, depending on the platform being used and

the experiments being conducted.

Lightweight Communications and Marshaling (LCM) is used to facilitate

communication on the platform. LCM utilizes a publish/subscribe message passing

system to improve communication between system components [9]. In this application,

signals received from the IMU and motor controllers were announced by the TS7800

over a vehicle based local area network. A laptop was connected to this network

wirelessly for data logging which allowed for significantly increased storage space.

This laptop was also able to be remotely logged into using Windows Remote Desktop,

allowing for real time viewing of the data.

2.3.1 Force Transducer Data Collection

The force transducer used is a MC2.5-2K-SP manufactured by AMTI. It has 6

channels (3 force and 3 moment) and is rated for underwater use. In this experiment,

the unit is situated so that the Z-axis of the force transducer, which has a range of ±

2000 lbs, is aligned with the thrust axis of the pod. The transducer requires that power

be provided by a separate amplifier and signal conditioning module. This module

allows the user to select the excitation voltage and gains used. The amplifier outputs

analog voltages in the ±10V range.

22

The analog outputs of the amplifier were connected to a National Instruments

cDAQ equipped with two modules. The first module use was a 14 bit analog to digital

converter. This module converted the ±10V into a 14 bit digital signal, giving a

resolution of 0.00122V, which equates to 0.348 N of thrust under maximum excitation

voltage and gain.

The second module used was a digital output module. This module is used to

zero the amplifier remotely. This was performed in between each individual test run,

after letting the vehicle come to rest, as it had been noticed that under cyclical loading

the signal from the amplifier does not always return to its zero condition.

The cDAQ was controlled by a laptop running Signal Express. The laptop used

for this was the same as the data logging laptop mentioned above (see Table 2-6 below).

This permitted all data points to be time stamped using the same system clock to make

comparing the data easier in post processing.

Table 2-6: Data Logged on Laptop

Sensor: MTI-G IMU Motor

Controller Force

Transducer Parameters: Velocity (X,Y,Z)*

Rate of Turn (x, y, z) Acceleration (x, y, z)

Pitch Roll Yaw

Latitude Longitude Heading

Battery Voltage Motor Current

Motor Command Motor RPM

Fx Fy Fz Mx My Mz

* Velocities are relative to a North-East-Down Earth-fixed coordinate system

2.4 Force transducer calibration

The force transducer used in this experiment was manually calibrated in an

23

effort to verify that the output of the force transducer was accurate. A series of

calibration tests were performed in which all six channels of the force transducer (three

forces and three moments) were tested in both compression and tension. This data was

then used to determine the actual sensitivity of the sensor. The data (see Figure 2-9)

showed that there was good correspondence between the manufacturer specifications

for the force channels, but a small DC offset was observed at no load. This will be

compensated for in post processing.

Figure 2-9: Force Transducer Calibration Data – FZ Channel

2.5 Experimental Approach

To determine the if cross-flow at the inlet of a waterjet has an effect on its

delivered thrust, a set of tests were conducted to induce varying amounts of sway

velocities, as it was assumed that the primary contributor to cross-flow in this type of

vehicle is due to sway velocities at the waterjet inlet.

0 50 100 150 200 250 300 350 400 450 500-0.5

0

0.5

1

1.5

2

Load (lbs)

Out

put

Vol

tage

(V

)

y=0.0039x-0.0648

R2=0.9998

24

First, the testing location was identified as the North Hollywood Finger Lake

(see Figure 2-10 below). This lake is a relatively calm body of water in close proximity

to the SeaTech Campus of Florida Atlantic University.

Figure 2-10: North Hollywood Finger Lake

Preliminary vehicle testing showed that the minimum turning radius of the

USV-12 with the new motor pods was approximately 10 meters, and the maximum

forward velocity was around 2.5 meters per second. After collecting this information, a

Matlab code was developed to predict how much yaw induced sway velocity could be

anticipated at different speeds and circle diameters (see Table 2-7 below).

Table 2-7: Expected Yaw Induced Sway Velocities in m/s

Speed (m/s) R=10 m 15 m 20 m 25 m 2 0.32 0.21 0.16 0.13

2.5 0.40 0.27 0.20 0.16

Hollywood Sailing Club Boat Ramp

Center of Turning Circles

25

It was determined that these speeds and circle diameters would give a wide

range of induced sway velocities from which a conclusion should be able to be drawn.

To that end, a set of waypoints was derived using the given turning circle radii.

26

3 PROPULSION SYSTEM TESTING

3.1 Motor Pod Testing

During and after construction of the new motor pods, testing was conducted to

determine functionality and reliability of the platform.

3.1.1 Hull Seal Testing

One of the first tests performed was a hull integrity test. During this series of

tests, after assembling the shell of the pod, and installing the waterjet, the pod was

weighted and placed in fresh water to test the integrity of the watertight seals. Initial

tests showed a problem with leakage through some hull penetrations.

It was determined through testing that the root cause of the leaks was that the

silicone adhesive that had been used was not adhering to the starboard and HDPE parts.

Several solutions were considered and the ultimate solution was to place coil type

threaded inserts into the bolt holes that surrounded any watertight seal. This increased

the compression between the materials. Silicone was used to provide a compliant seal,

but not for adhesion.

3.1.2 Magnetic Coupling Test

The magnetic shaft coupling used to connect the motor to the waterjet is

designed to operate with a small air gap between the two halves. To determine what the

appropriate gap distance was, an initial estimate was made and then refined during

27

testing. Testing of the gap involved running the motor throttle at various positions. If

any slippage of the shaft was noted, the distance was adjusted. After testing, the

appropriate air gap was determined to be approximately 1 millimeter.

3.1.3 Run Time Estimation Test

One of the motor pods was tested to determine how long the system would run

for, and to observe the system under operation. The results of the test showed that at

75% throttle, the batteries should provide 77 minutes of run time (see Figure 3-1

below).

Figure 3-1: Battery Discharge Curve at 75% Throttle

0 10 20 30 40 50 60 70 8028

30

32

34

36

38

40

42

Run Time (Minutes)

Bat

tery

Vol

tage

(V

)

28

4 EXPERIMENTAL TESTING

4.1 Experimental Testing

After confirming that the propulsion system and control system both were

working, the experimental tests were performed. Experiments were conducted on

several days with varying success.

4.1.1 Testing - June 14, 2013

Initial testing revealed problems with the logging of the IMU data, and

significant holes were reported in the data. The problem was identified as being caused

by the motor controller signals overloading the system and causing dropouts of the IMU

signal. To solve this several steps were undertaken, the first of which was to change the

format of the telemetry strings from the motor controller.

After consulting with the manufacturer, it was determined that the default

telemetry option, which sends out each parameter in a separate string, was not the ideal

situation. This caused the data to be transmitting much faster than any other device.

Each motor controller was transmitting four types of information (battery voltage,

motor current, RPM, and motor command) with each one being sent out ten times a

second. This made a total of 80 messages being sent between the two motor controllers

each second. To limit this, a script was created in MicroBasic and loaded on the motor

controllers (see APPENDIX C). This code compiled all four pieces of data into a

29

single, tab separated string which was then sent out at 5 Hz. One problem that was

found with this was that the version of MicroBasic supported by the motor controller

does not allow for creation of a checksum value.

The second change that was made was in how the data was processed. In the

initial test run, the data for the motor controllers was being logged on the TS-7800,

while the IMU and compass information was announced on the network across an LCM

channel. To make future logging easier, and to make sure all signals had the same

timestamp, changes were made so that the motor controller data also was announced

using LCM and logged on the same computer as the IMU and force transducer.

Additionally, after looking at the data, it was revealed that the data from the

force transducer had significant noise in the channel of interest. One possible cause for

this was saturation of the moment channels. In this test, the gains and excitation

voltages for all six channels were set to their maximum values. Saturation was

observed in several of the moment channels during most of the test runs. The gains and

excitation voltage were reduced for future tests to limit the noise produced.

4.1.2 Testing: June 26, 2013

During follow-up testing on June 26, 2013 a catastrophic leak occurred in one of

the motor pods. By the time the pod was removed from the water, several inches of

water was in the pod, partially immersing the motor controller and battery, and fully

submerging the motor in salt water. Additionally, the battery leads were also

submerged. This caused serious damage to all of the electronics. The source of the leak

was identified as the shaft seal in the waterjet. The drive shaft as provided by the

30

manufacturer was not made of a corrosion resistant material and had significant

corrosion develop despite rinsing the pod in fresh water after each previous test run.

The corrosion caused sufficient shaft roughness to develop to damage the lip seal and

the sealed bearing, allowing water to penetrate the pod.

New drive shafts were manufactured out of stainless steel and new bearings and

seals were installed in both motor pods, as corrosion was identified on both shafts. The

motor and motor controller were sent back to the manufacturers for repairs. The motor

controller was damaged and needed to be replaced, while the motor only needed new

bearings and hall effect sensors. The damage to the battery was significant enough that

the manufacturer recommended that it not be repaired, as the actual extent of damage to

the cells could not be easily determined. As spare batteries were already on hand, it was

determined that replacing the damaged battery was not a high priority.

4.1.3 Testing: September 19, 2013

After repairs, further testing was conducted. During this test we had several

advances in our testing. The first of which was that this was the first day that we were

able to perform true closed loop tests. Previously, the tests were being conducted with

purely open loop control. A proportional controller was used to perform basic waypoint

following autonomy. Four waypoints were used equidistant from a common center.

This gave a very diamond shaped vehicle path, indicating the need for additional

waypoints in future tests.

Unfortunately, there was a failure of the force transducer amplifier to correctly

amplify the data from the force transducer. While the gains excitation voltages were

31

adjusted from previous test runs so that the channels did not hit saturation, a problem

was observed where zeroing the amplifier did not accurately zero the sensor, and under

no load the signal would then float around. Testing after the fact showed this problem

occurred again outside of the water, in a lab environment. After examining the

amplifier settings, and verifying that all jumpers were well seated, the problem was

corrected.

4.1.4 Testing: September 27, 2013

After the lessons learned in the previous testing days, a new set of waypoints

was created. These waypoints used a constant distance between waypoints for different

circles of different radii. This distance varied based on the speed of the vehicle (see

Table 4-1 below). Additionally, prior to going to the testing location, the functioning of

the force transducer was verified.

Table 4-1: Test Run Waypoints Distances

Circle Radii (m)

Speed (m/s)

Number of waypoints Arc Length

(m) Time between waypoints (s)

10

1.0 1.5 2.0

6 10.5 5.25

2.5 4 15.7 6.28

15 2.0 9 10.5 5.25

2.5 6 15.7 6.28

20 2.0 12 10.5 5.25

2.5 8 15.7 6.28

25 2.0 15 10.5 5.25

2.5 10 15.7 6.28

32

An additional difference to the previous days of testing was that the force

transducer data logging was performed slightly differently. Instead of having one large

data file, a separate data file was created for each test run. This was accomplished by

remotely logging into the laptop on the vehicle using a wireless network connection.

This also allowed us to re-zero the force transducer after each test run to help improve

the accuracy of the transducer.

During this day of testing several observations were made about the different

styles of test runs. In small radius turns, the vehicle frequently had trouble finding

waypoints and would circle the missed waypoint several times at maximum differential

thrust until it came within the threshold of acceptance for the waypoint. This caused

some interesting paths and also had the effect of the vehicle moving faster than planned

for some of the test runs.

Several lower speed test runs were conducted at the ten meter radius circle. This

was in an attempt to cause circles of different yaw induced sway velocity, but it became

clear that even at slower speeds, the vehicle struggled with the small radius turns.

33

5 DATA PROCESSING

Processing of the data began was performed using Matlab. The first step taken

in processing the data was the parsing of the collected data into various test runs. The

collected data was in two different file types. The data from the force transducer was

saved in separate files for each test run, and was stored using LabView Signal Express

in a TDMS file format. This was opened again in Signal Express and exported to a tab

separated text file that could be opened in Matlab. Each test run had identified the exact

start time as well as the sampling frequency. The default collection rate of 1 kHz was

used during experimentation.

The remaining data was saved on the laptop in individual text files for each

sensor (IMU, GPS, and motor controllers), each file containing data from the complete

day of testing. The individual samples were time-stamped as they were logged with a

one second resolution. As we were collecting data from these sensors at sub-second

frequencies (five and ten Hertz), this resulted in several samples having the same

timestamps. This would be addressed in later data processing.

To separate the data from the IMU, GPS and motor controllers into separate

files, a custom Matlab function was used. This function loads the data file and, using a

user specified start and end time, extracts the data points of interest and saves them into

a MAT file which can then be loaded into a different Matlab program. This function

was modified slightly to allow for the parent code to also pass a file name in addition to

34

start and end times instead of waiting for user input (see APPENDIX A).

As a first pass, the start and end times of the force transducer files were used to

parse the data. The individual data sets created from this first pass were then analyzed

to identify the time that the vehicle started and finished its turning circle and the test

sorter function was run again. As previously discussed, in some of the tight radius

turns, the vehicle's path was not circular. For data analysis purposes, circular sections

of the data were identified and extracted for further processing. These refined start and

end times were then used to separate out the force transducer reading from the same

times. Additionally, it was noticed that each time the force transducer amplifier was

zeroed, a slightly different DC bias was observed. To correctly identify this for each

test run, an average was taken of the first 100 samples of the data file. This

corresponded to the time between when the amplifier was zeroed and the test run was

actually begun. During this time, the vehicle was sitting at rest in the waters of the

finger lake.

After parsing the data, a code was written that would look at the data for

individual test runs. After loading the data for the specific test run, the pitch and roll

information from the IMU was used to correct for vehicle's pitch and roll. This allowed

for the surge, sway and heave data to be corrected to accurately reflect the orientation of

the vehicle. To perform this correction, the angle2dcm function that is part of Matlab's

aerospace toolbox was used to create a direction cosine matrix that was then multiplied

to a state space vector of the data to be corrected. This correction was performed for the

vehicle's acceleration, velocity, and gyro data.

A plot was then made showing the data before and after the angular correction

35

was applied. Review of this plot showed that there was a recorded heave velocity that

oscillated around 0.1 meters per second. While some heave velocities could be

expected, they should be oscillating around zero. Upon consultation with the sensor

manufacturer, it was revealed that the maximum accuracy of the sensor is at a vehicle

speed of 30 meters per second. At slower speeds, such as those in these tests, the

accuracy would be less than that, although no information was available to state what

the accuracy would be in this speed regime.

After correcting for pitch and roll, the data needed to be corrected for the

translational offset between the CG of the vehicle and the location of the sensor. To do

this, a coordinate transformation was performed using the following formula:

� = � + � × ���

This formula relates the velocity at any point A with the velocity at the center of

gravity G using the rotation rate and the distance vector between the two points. This

same formula was then used to translate the coordinate system again to the location of

the waterjet inlet (see Figure 5-1 below).

36

Figure 5-1: Circle Test 1 - Vehicle Velocities, Waterjet Inlet Local Velocities

The thrust data was collected at 1 kHz, 100 times faster than the data from the

IMU. In order to be able to compare the IMU data with the force data, the thrust data

was down-sampled. This was accomplished by averaging 100 consecutive samples into

a single sample in the down-sampled data set. In analyzing the thrust, first a frequency

analysis was performed on both on the 1 kHz data and the down-sampled data 10 Hz

data. Reviewing the spectrum of rays from the 1 kHz data set revealed two main things.

The first was a large lobe around zero Hz as well as another signal at approximately 200

Hz. This 200 Hz signal was determined to be at the same frequency as the speed of the

motor.

0 20 40 60 80 100 120-0.5

0

0.5

1

1.5

2

2.5

time (s)

Vel

ocity

(m/s

)

Vehicle SurgeVehicle Sway

Vehicle Heave

Waterjet Surge

Waterjet SwayWaterjet Heave

Heave Velocity Offset - Mean -0.113

37

Figure 5-2: Circle Test 2 - Frequency Analysis of 1 kHz Force Signal

Reviewing the 10 Hz signal showed two lobes of interest, the main lobe,

centered about zero Hertz, and a secondary lobe that varied in position, but tended to

fall between 0.5 and 2.5 Hz.

-500 -400 -300 -200 -100 0 100 200 300 400 500-5

0

5

10

15

20

25

30

Frequency (Hz)

For

ce S

pect

rum

of

Ray

s(N

)

Real Component

Imaginary Component

220 Hz SignalEquates to 13,200 RPM

38

Figure 5-3: Circle Test 2 -Frequency Analysis of 10 Hz Force Signal

To investigate these two signals and their relation to the sway velocity at the

waterjet inlet, they were isolated from each other and the rest of the background

frequencies. A low-pass filter was used for the main signal (with cutoff at 0.75 Hz),

and a band-pass filter was used to isolate the secondary frequency (0.75 Hz - 2 Hz).

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

0

5

10

15

20

25

30

Frequency (Hz)

Fo

rce

spe

ctru

m o

f ra

ys (N

)

Real ComponentImaginary Component

Main Signal

Secondary Frequency

39

Figure 5-4: Circle Test 1 - Two Components of Thrust

Some data points were observed that existed outside of the physically realistic

range (i.e. velocities faster than the speed of sound or accelerations greater than the

sensor can record). These data points were identified and excluded from further

processing.

The signals were then smoothed using the "smooth" function in Matlab. This

function uses a moving average with a span identified by the user. A span of 5 samples

was used for the velocity signal and a span of 11 samples was used for the thrust data.

One thing noticed in reviewing the motor controller data from the experiments

was that there were numerous intervals where the messages being sent by the motor

controller were not logged. This resulted in instances where the data from the motor

0 20 40 60 80 100 120-20

-10

0

10

20

30

40

50

60

70

Time (s)

For

ce (N

)

Primary Frequency Thrust Component

Secondary Frequency Thrust Component

40

controllers was good in some test runs, and lacking in others. Because of this, the data

processing and analysis did not use the data from the motor controllers.

To facilitate comparison, the thrust and sway velocity were both non-

dimensionalized. The thrust was non-dimensionalized using the Thrust Loading

Coefficient, which relates the thrust to the nozzle area and the square of the forward

velocity.

��� = ����12 ����

This was done for both the low frequency and the secondary frequency

components of the thrust. The sway velocity was non-dimensionalized using the

forward velocity in what we will call the "Sway Velocity Ratio."

The Thrust Loading Coefficient for both frequency ranges and the Sway

Velocity Ratio were then plotted, with the yaw rate in a subplot. The yaw rate was

included to be able to easily determine the intervals where the vehicle was turning and

moving strait.

In an effort to quantify the relation between the sway velocity and the thrust, the

biased cross-covariance between thrust and waterjet inlet sway velocity was calculated

and plotted. This was performed for both frequency components.

In addition to looking at the relation between thrust and sway velocity, the

relation between surge acceleration and sway velocity was compared. The same

approach was taken, except that primary frequency was excluded. This was done

because the primary effect of interest was in vibration and not the actual acceleration of

the vehicle.

41

6 RESULTS

Analysis of the data from the test runs revealed that the test runs could be

categorized into two different types of runs; those with relatively constant thrust and

those where the thrust fluctuated. The first category, those with relatively constant

thrust, consisted mainly of the circular sections of the small radius turns. In most of

these turns, the vehicle was at maximum differential thrust for most or all of the data

set. This resulted in an almost constant yaw rate.

As can be seen in Figure 6-1, there is little noticeable relation between the

delivered thrust and the sway velocity in when looking at the primary frequency.

Figure 6-2 shows a certain pulsing that appears to follow peaks of high sway velocity,

but further analysis of subsequent test runs did not show the same relationship.

42

Figure 6-1: Circle Test 1 - Primary Frequency Thrust Compared to Sway

Figure 6-2: Circle Test 1 - Secondary Frequency Thrust Compared to Sway

0 20 40 60 80 100 1200

20

40

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120-0.2

0

0.2

Vw

j / U

0

Primary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 1200.05

0.1

0.15

0.2

0.25

time(s)

Yaw

Rat

e (r

ad/s

ec)

0 20 40 60 80 100 120-2

0

2

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120-0.2

0

0.2

Vw

j / U

0

Secondary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 1200.05

0.1

0.15

0.2

0.25

time(s)

Yaw

Rat

e (r

ad/s

ec)

43

Review of the normalized cross-correlation plots (see Figure 6-3) for the two

frequency ranges showed that in the primary frequency signal, there is a moderate peak

just to the right of zero lag, indicating that the two signals do have some correlation, but

no causal relationship could be derived when plotted against time. . No significant

amplitude was observed in any of the secondary frequency signals.

Figure 6-3: Circle Test 1 - Normalized Cross-Correlation for Thrust and Sway

Velocity

-1500 -1000 -500 0 500 1000 1500-0.4

-0.2

0

0.2

0.4

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Primary Frequency Thrust

-1500 -1000 -500 0 500 1000 1500-0.02

-0.01

0

0.01

0.02

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Secondary Frequency Thrust

44

In larger radius turns, the vehicle did not have to make as sharp of a turn and

would frequently turn after passing through a way point, and then go straight for a

period of time (see Figure 6-4).

Figure 6-4: Circle Test 6 - GPS Path

As the vehicle alternated between turning and not turning, a varying thrust was

observed, with times of higher thrust corresponding to times of higher yaw rate (turning

behavior) as can be seen in Figure 6-5. The time interval between turns seems to show

higher sway velocities compared to times when the vehicle is turning. Further

investigation reveals the cause. As the yaw rate drops to zero, the yaw induced

contribution to the local sway velocity also drops to zero. This yaw rate component,

during turns, subtracts from the CG based sway velocity because the waterjet of focus

180 185 190 195 200 205 210 215 220

-15

-10

-5

0

5

10

15

Meters E of Dock

Met

ers

Nor

th o

f Doc

k

Vehicle Path Waypoints

45

was the port pod, and as such, the X and Y and Z components of the waterjet inlet

position vector is negative. relative to the center of gravity. Because of this, the actual

relation between the thrust and sway velocity could not be easily determined in these

test runs. Additionally, the amplitude of the sway velocities in most of the test runs

remained less than twenty percent of the mean forward velocity.

Figure 6-5: Circle Test 6 - Primary Frequency Thrust Compared to Sway

In these larger radius turns, the cross correlation plot (Figure 6-6) shows a

significant relationship between the trust and the sway velocity, with a moderately

significant trough, in this example at a lag of 4 samples and an amplitude of -0.4. This

correlation can most likely be associated to the phenomenon previously discussed,

0 50 100 1500

20

40

Thr

ust/

0.5

ρANU

o2

0 50 100 150-0.2

0

0.2

Vw

j / U

0

Primary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 50 100 150-0.1

0

0.1

0.2

0.3

time(s)

Yaw

Rat

e (r

ad/s

ec)

TURNS

46

where the sway velocity increases during straight line motion due to the reduced yaw

rate.

Figure 6-6: Circle Test 6 - Normalized Cross-Correlation for Thrust and Sway

Velocity

For all of the test runs, the slip angle was also calculated. This was done by

looking for the angle between the total velocity vector and the surge direction. Analysis

of the plots showed that most of the slip angles ranged between -5 and 12 degrees, with

reduced slip angles being observed in larger radius turns. A Slip angles as high as 50

degrees were recorded in one test run, but this is most likely due to a sensor anomaly.

-1500 -1000 -500 0 500 1000 1500-0.5

0

0.5

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Primary Frequency Thrust

-1500 -1000 -500 0 500 1000 1500-0.1

-0.05

0

0.05

0.1

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Secondary Frequency Thrust

Lag 4 samplesAmplitude: -0.4

47

Figure 6-7: Circle Test 6 - Slip Angle

0 50 100 150-2

0

2

4

6

8

10

12

14

Time (s)

Slip

Ang

le (d

egre

es)

48

7 CONCLUSIONS

While the initial objective of designing a free running waterjet propelled USV to

perform direct thrust measurements was a success, attempting to meet the secondary

objective of investigating the relationship between cross-flow and delivered thrust

proved challenging. Review of the data collected did not conclusively show that cross-

flow at the waterjet inlet causes a noticeable effect in the thrust, but it could not

conclusively disprove it either. Further research is needed before any definitive

conclusion can be drawn about the association between cross-flow and thrust.

As it was not possible to directly observe and quantify the cross-flow, the

assumption was made that sway velocity at the waterjet would be related to the cross-

flow. While this is a logical assumption, further analysis for this platform should be

conducted to verify this., This could be done using computer modeling or experimental

tests where the actual ingested flow can be visualized and compared to the slip angle.

This experiment would most likely need to be performed in a testing tank as visualizing

the flow becomes problematic in a free running condition.

In this experiment, the sway velocities used in the data analysis are derived

solely from the data recorded from the IMU. The IMU used is designed primarily for

aerospace applications where the speed traveled is much greater. It's rated accuracy for

velocity peaks at 0.1 m/s at a velocity 30 m/s with an increasing but unknown error at

slower speeds. The majority of sway velocities recorded were less than 0.5 m/s. This

49

means that error of the senor is approximately 20% of the recorded velocity. Usage of a

sensor designed for the speed regime that the vehicle operates in should significantly

improve the quality of the sway velocity data, and as such might help to identify a

causal relationship. An additional suggestion would be to use an additional sensor

measure the sway velocity, such as a second IMU.

Another item of consideration is the noise observed in the force transducer. The

standard deviation of the recorded force before filtering was approximately 12% of the

mean force. This could possibly cause an actual effect being masked within the noise of

the sensor if it is of a low amplitude or a high frequency. One theorized effect that

cross-flow could have would be increased cavitation due to changing pressure

differentials across the impellor. The effect of this would most likely be a low

amplitude, high frequency vibration which could be missed in the current testing set up.

Additionally, to capture higher frequency signals, a faster sampling rate should be used

for the IMU data. The inclusion of an accelerometer within the pod would help to

detect increased vibration as well.

Another challenge encountered was that the thrust was the item being controlled

by the autonomous control system, so any drop in thrust would have been adjusted for

by a change in the input from the control system. For this reason, an effect in waterjet

efficiency might be easier to identify than an effect in thrust in a closed loop test such as

this, and might be worthy of consideration for future testing. Alternatively, open loop

testing might be helpful.

An additional area that should be addressed in future testing is the coupling of

thrust and yaw. The waypoint following design of the control system created a situation

50

where the vehicle would turn as it oriented on the next waypoint and then go straight for

a few meters until it passed the waypoint. The control system actuated the thrust,

causing the vehicle to yaw, which then created a sway velocity. This made it

particularly difficult to observe any effect on the thrust caused by the sway velocity.

Some suggestions here would be to do one of two things. Instead of using a closed loop

waypoint following control paradigm, it might be a better approach to focus instead on

a closed loop yaw rate control paradigm. This would hold the yaw rate constant, which

should limit the variance in sway velocity caused by a fluctuating yaw rate.

An additional idea for future research would be to completely de-couple the

orientation of the waterjet from its thrust. This could be accomplished by redesigning

the experiment to use a flow tank. The efficiency of the waterjet could be characterized

in a strait on orientation as well as at an angular offset. Another advantage to this

would be the ability to use Laser Doppler Velocimetry or another similar method to

visualize the relation between slip angle and cross-flow.

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APPENDIX A - DATA SORTING CODE

A.1 Test Sorter Function

function output = TestSorter(value, startmat, finis hmat,Run,Sens) %Ivan Bertaska %6/3/2013 % %This program parses the data collected on 5/22/13 into separate subfolders %as according to the timestamp % % INPUT = matrix to sort, start time matrix, end ti me matrix (both in Unix % Epoch) %9/30/2013 % Modified by John Grimes to accept input from prog ram for file names %determine length count = length(startmat); % disp(count); for i=1:count % %user input to determine file name % usr_string = input('Enter file name: ', 's'); % %start and finish times start = startmat(i); finish = finishmat(i); start_place = find(value(:,1) >= start, 1, 'fir st'); finish_place =find((value(:,1) >= finish & valu e(:,1) < finish + 1), 1, 'last'); values = value(start_place:finish_place, :); save([char(Run(i)), '_',Sens], 'values'); end end

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A.2 Data Splitting Code

This code was used to sort the IMU, GPS, and Motor Controller data files into separate files for

further processing.

% % Sort of compass, IMU, and GPS data from 9/27 te sts into different files % % based on the individual runs % % % % Identify the start and end times for each run % File name components RunNameArray= [... 'r10u10'; ... 'r10u15'; ... 'r10u20'; ... 'r10u25'; ... 'r15u20'; ... 'r15u25'; ... 'r20u20'; ... 'r20u25'; ... 'r25u20'; ... 'r25u25'; ... ]; RunName=cellstr(RunNameArray); % Testing start and end times for 9/27/13 Start=[... 1380290853 ... r10u10 1380291207 ... r10u15 1380291710 ... r10u20 1380292375 ... r10u25 1380292775 ... r15u20 1380293286 ... r15u25 1380293580 ... r20u20 1380294012 ... r20u25 1380294394 ... r25u20 1380294862 ... r25u25 ]; End=[... 1380290962 ... r10u10 1380291347 ... r10u15 1380292040 ... r10u20 1380292528 ... r10u25 1380292916 ... r15u20 1380293429 ... r15u25 1380293765 ... r20u20

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1380294170 ... r20u25 1380294516 ... r25u20 1380295060 ... r25u25 ]; % Load Compass Data fname='C:\Users\John\Documents\School\Thesis\WAMV\T ESTS\092713\RawData\Compass.txt'; Compass=importdata(fname); clear fname % Load IMU Data fname='C:\Users\John\Documents\School\Thesis\WAMV\T ESTS\092713\RawData\imu.txt'; IMU=importdata(fname); clear fname % Load GPS Data fname='C:\Users\John\Documents\School\Thesis\WAMV\T ESTS\092713\RawData\gps.txt'; GPS=importdata(fname); clear fname % Load PortMotor Data fname='C:\Users\John\Documents\School\Thesis\WAMV\T ESTS\092713\RawData\PortMotor.txt'; MotorPort=importdata(fname); clear fname % Load StbdMotor Data fname='C:\Users\John\Documents\School\Thesis\WAMV\T ESTS\092713\RawData\StbdMotor.txt'; MotorStbd=importdata(fname); clear fname % Test Sort TestSorter(Compass,Start,End,RunName,'Comp') TestSorter(GPS,Start,End,RunName,'GPS') TestSorter(IMU,Start,End,RunName,'IMU') TestSorter(MotorPort,Start,End,RunName,'Port') TestSorter(MotorStbd,Start,End,RunName,'Stbd')

A.3 Force Transducer Data Splitter

This code was used to create data files that were limited to the extents of the test runs.

% FTSort % by John Grimes % 10/1/2013 %

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% Used to parse out the data from the various test runs from 9/27/2013 into % different mat files for loading into individual d ata processing programs %% Identify FT Files FTDir='C:\Users\John\Documents\School\Thesis\WAMV\T ESTS\092713\RawData\FTData\'; % File name components RunNameArray= [... 'r10u10'; ... 'r10u15'; ... 'r10u20'; ... 'r10u25'; ... 'r15u20'; ... 'r15u25'; ... 'r20u20'; ... 'r20u25'; ... 'r25u20'; ... 'r25u25'; ... ]; RunName=cellstr(RunNameArray); %% Identify start time of recording and start and end time of experiments %Start Time of recording in Unix Time RecStart=[... 1380290712.589 ... 10:05:12.589 1 1380291125.970 ... 10:12:05.970 2 1380291620.174 ... 10:20:20.174 3 1380292261.453 ... 10:31:01.453 4 1380292673.277 ... 10:37:53.277 5 1380293050.651 ... 10:44:10.651 6 1380293559.411 ... 10:52:39.411 7 1380293942.094 ... 10:59:02.094 8 1380294327.250 ... 11:05:27.250 9 1380294773.797 ... 11:12:53.797 10 ]; RecDt=.001; % Testing start and end times for 9/27/13 Start=[... 1380290853 ... r10u10 1380291207 ... r10u15 1380291710 ... r10u20 1380292375 ... r10u25 1380292775 ... r15u20 1380293286 ... r15u25 1380293580 ... r20u20 1380294012 ... r20u25 1380294394 ... r25u20 1380294862 ... r25u25

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]; End=[... 1380290961 ... r10u10 1380291347 ... r10u15 1380292040 ... r10u20 1380292528 ... r10u25 1380292921 ... r15u20 1380293429 ... r15u25 1380293765 ... r20u20 1380294170 ... r20u25 1380294516 ... r25u20 1380295060 ... r25u25 ]; %% Create loop to go through all of the ft files an d create data files for k1=1:length(RunName) k1 %load file fname=[FTDir, char(RunName(k1)), '.txt']; voltage=importdata(fname); clear fname; %create time vector tstart=RecStart(k1); t=zeros(length(voltage),1); t(1)=tstart; for k2=2:length(voltage) t(k2)=t(k2-1)+RecDt; end %create separate force vectors for each channel Volts(:,1)=floor(t); Volts(:,2)=voltage(:,1); Volts(:,3)=voltage(:,2); Volts(:,4)=voltage(:,3); Volts(:,5)=voltage(:,4); Volts(:,6)=voltage(:,5); Volts(:,7)=voltage(:,6); Vzero(1)=0; Vzero(2)=mean(voltage(1:100,1)); Vzero(3)=mean(voltage(1:100,2)); Vzero(4)=mean(voltage(1:100,3)); Vzero(5)=mean(voltage(1:100,4)); Vzero(6)=mean(voltage(1:100,5)); Vzero(7)=mean(voltage(1:100,6)); save([char(RunName(k1)),'_Vzero'],'Vzero'); %use test sorter to sort out from exp start to exp end TestSorter(Volts,Start(k1),End(k1),RunName(k1), 'Force') clear v* t* V*

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end

A.4 Data Splitting Code for Straight Line Tests

% % Sort of compass, IMU, and GPS data from 6/14 te sts into different vectors % % based on the individual runs % % % % Identify the start and end times for each run % File name components RunNameArray= [... 's1 '; ... 's2 '; ... 's3 '; ... 's4 '; ... 's5 '; ... 's6 '; ... 's7 '; ... 's8 '; ... 's9 '; ... 's10'; ... 's15'; ... 's20'; ... 's25'; ... ]; RunName=cellstr(RunNameArray); % Testing start and end times for 9/27/13 Start=[... 1380290755 ... 1 r10u10 1380291140 ... 2 r10u15 1380291642 ... 3 r10u20 1380292303 ... 4 r10u25 1380292698 ... 5 r15u20 1380293264 ... 6 r15u25 1380293572 ... 7 r20u20 1380293983 ... 8 r20u25 1380294343 ... 9 r25u20 1380294820 ... 10 r25u25 1380295207 ... s15 1380295440 ... s20 1380295645 ... s25 ]; End=[... 1380290845 ... 1 r10u10 1380291202 ... 2 r10u15 1380291703 ... 3 r10u20 1380292314 ... 4 r10u25 1380292745 ... 5 r15u20 1380293281 ... 6 r15u25

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1380293600 ... 7 r20u20 1380293990 ... 8 r20u25 1380294368 ... 9 r25u20 1380294839 ... 10 r25u25 1380295260 ... s15 1380295475 ... s20 1380295677 ... s25 ]; % Load Compass Data fname='C:\Users\John\Documents\School\Thesis\WAMV\T ESTS\092713\RawData\Compass.txt'; Compass=importdata(fname); clear fname % Load IMU Data fname='C:\Users\John\Documents\School\Thesis\WAMV\T ESTS\092713\RawData\imu.txt'; IMU=importdata(fname); clear fname % Load GPS Data fname='C:\Users\John\Documents\School\Thesis\WAMV\T ESTS\092713\RawData\gps.txt'; GPS=importdata(fname); clear fname % Load PortMotor Data fname='C:\Users\John\Documents\School\Thesis\WAMV\T ESTS\092713\RawData\PortMotor.txt'; MotorPort=importdata(fname); clear fname % Load StbdMotor Data fname='C:\Users\John\Documents\School\Thesis\WAMV\T ESTS\092713\RawData\StbdMotor.txt'; MotorStbd=importdata(fname); clear fname % Test Sort TestSorter(Compass,Start,End,RunName,'Comp') TestSorter(GPS,Start,End,RunName,'GPS') TestSorter(IMU,Start,End,RunName,'IMU') TestSorter(MotorPort,Start,End,RunName,'Port') TestSorter(MotorStbd,Start,End,RunName,'Stbd')

A.5 Force Transducer Data Splitting Code for Strait Line Tests

% FTSortStraight % by John Grimes % 10/23/2013

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% % Used to parse out the data from the various test runs from 9/27/2013 into % different mat files for loading into individual d ata processing programs %% Identify FT Files FTDir='C:\Users\John\Documents\School\Thesis\WAMV\T ESTS\092713\RawData\FTData\'; % File name components RunNameArray= [... 'r10u10'; ... 'r10u15'; ... 'r10u20'; ... 'r10u25'; ... 'r15u20'; ... 'r15u25'; ... 'r20u20'; ... 'r20u25'; ... 'r25u20'; ... 'r25u25'; ... 's15 '; ... 's20 '; ... 's25 '; ... ]; RunName=cellstr(RunNameArray); % File name components SaveNameArray= [... 's1 '; ... 's2 '; ... 's3 '; ... 's4 '; ... 's5 '; ... 's6 '; ... 's7 '; ... 's8 '; ... 's9 '; ... 's10'; ... 's15'; ... 's20'; ... 's25'; ... ]; SaveName=cellstr(SaveNameArray); %% Identify start time of recording and start and end time of experiments %Start Time of recording in Unix Time RecStart=[... 1380290712.589 ... 10:05:12.589 1 1380291125.970 ... 10:12:05.970 2 1380291620.174 ... 10:20:20.174 3 1380292261.453 ... 10:31:01.453 4

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1380292673.277 ... 10:37:53.277 5 1380293050.651 ... 10:44:10.651 6 1380293559.411 ... 10:52:39.411 7 1380293942.094 ... 10:59:02.094 8 1380294327.250 ... 11:05:27.250 9 1380294773.797 ... 11:12:53.797 10 1380295175.876 ... 11:19:35.876 11 1380295419.428 ... 11:23:39.428 12 1380295580.125 ... 11:26:20.125 13 ]; RecDt=.001; % Testing start and end times for 9/27/13 Start=[... 1380290755 ... r10u10 1380291140 ... r10u15 1380291642 ... r10u20 1380292303 ... r10u25 1380292698 ... r15u20 1380293264 ... r15u25 1380293560 ... r20u20 1380293983 ... r20u25 1380294343 ... r25u20 1380294820 ... r25u25 1380295207 ... s15 1380295440 ... s20 1380295645 ... s25 ]; End=[... 1380290845 ... r10u10 1380291202 ... r10u15 1380291703 ... r10u20 1380292314 ... r10u25 1380292745 ... r15u20 1380293281 ... r15u25 1380293580 ... r20u20 1380293990 ... r20u25 1380294368 ... r25u20 1380294839 ... r25u25 1380295260 ... s15 1380295475 ... s20 1380295677 ... s25 ]; %% Create loop to go through all of the ft files an d create data files for k1=1:length(RunName) k1 %load file fname=[FTDir, char(RunName(k1)), '.txt']; voltage=importdata(fname);

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clear fname; %create time vector tstart=RecStart(k1); t=zeros(length(voltage),1); t(1)=tstart; for k2=2:length(voltage) t(k2)=t(k2-1)+RecDt; end %create separate force vectors for each channel Volts(:,1)=floor(t); Volts(:,2)=voltage(:,1); Volts(:,3)=voltage(:,2); Volts(:,4)=voltage(:,3); Volts(:,5)=voltage(:,4); Volts(:,6)=voltage(:,5); Volts(:,7)=voltage(:,6); Vzero(1)=0; Vzero(2)=mean(voltage(1:100,1)); Vzero(3)=mean(voltage(1:100,2)); Vzero(4)=mean(voltage(1:100,3)); Vzero(5)=mean(voltage(1:100,4)); Vzero(6)=mean(voltage(1:100,5)); Vzero(7)=mean(voltage(1:100,6)); save([char(SaveName(k1)),'_Vzero'],'Vzero'); %use test sorter to sort out from exp start to exp end TestSorter(Volts,Start(k1),End(k1),SaveName(k1) ,'Force') clear v* t* V* end

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APPENDIX B - DATA PROCESSING CODE

The following code was used to generate the figures to analyze the data for the various test runs.

The CirR and CirU lines were modified to correspond with one of the test runs that were

performed.

% Data Processing of Run r25u25 from 9/27/2013 - Tu rning Circle % By John Grimes % Initalize Workspace clc; clear; close all; CirR=15; CirU=2.0; RunID=['r',num2str(CirR),'u',num2str(CirU*10)]; DateDir='C:\Users\John\Documents\School\Thesis\WAMV \TESTS\092713\'; dataDir='RunData'; CompFile=sprintf('%s%s\\%s%s.mat', DateDir, dataDir , RunID, '_Comp'); GPSFile =sprintf('%s%s\\%s%s.mat', DateDir, dataDir , RunID, '_Gps'); IMUFile =sprintf('%s%s\\%s%s.mat', DateDir, dataDir , RunID, '_IMU'); ForceFile = sprintf('%s%s\\%s%s.mat', DateDir, data Dir, RunID, '_Force'); VzeroFile= sprintf('%s%s\\%s%s.mat', DateDir, dataD ir, RunID, '_Vzero'); WaypointFile= sprintf('%s%s\\%s.txt', DateDir, 'Way points', RunID); %% Load IMU/GPS/Compass data files load(GPSFile); gpsdata = SensorInterpolate(DataAppend(values,10),1 0); clear values load(IMUFile); imudata = SensorInterpolate(DataAppend(values,10),1 0); clear values; load(ForceFile); Volts=values; load(VzeroFile) Waypoints= load(WaypointFile);

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%% Build Structures gps=[]; gps.raw=[]; imu=[]; imu.raw=[]; endtime=length(imudata); gps.raw.time=gpsdata(1:endtime,1); gps.raw.N=gpsdata(1:endtime,2); gps.raw.E=gpsdata(1:endtime,3); imu.raw.time=imudata(1:endtime,1); imu.raw.u=imudata(1:endtime,2); imu.raw.v=imudata(1:endtime,3); imu.raw.w=imudata(1:endtime,4); imu.raw.aX=imudata(1:endtime,5); imu.raw.aY=imudata(1:endtime,6); imu.raw.aZ=imudata(1:endtime,7); imu.raw.gX=imudata(1:endtime,8); imu.raw.gY=imudata(1:endtime,9); imu.raw.gZ=imudata(1:endtime,10); imu.raw.pitch=imudata(1:endtime,15); imu.raw.roll=imudata(1:endtime,14); imu.raw.yaw=imudata(1:endtime,16); figure; plot(gps.raw.E,gps.raw.N); % title({['Radius ',num2str(CirR), ' m, Speed ', nu m2str(CirU),' m/s'];... % 'GPS track'},'FontSize',14); xlabel('Meters E of Dock','FontSize',12); ylabel('Meters North of Dock','FontSize',12); axis equal; hold on; scatter(Waypoints(:,2),Waypoints(:,1)) hold off legend('Vehicle Path', 'Waypoints',... 'Location','SouthOutside',... 'Orientation','Horizontal'); %% Fix Time Vectors imu.raw.time=imu.raw.time-1.38029e9; gps.raw.time=gps.raw.time-1.38029e9; t_raw(1)=0; for k=2:length(imu.raw.time) t_raw(k)=t_raw(k-1)+.1; end %% Convert volts to lbs force Vlg(:,1)=Volts(:,1); Vlg(:,2)=Volts(:,2)-Vzero(2); Vlg(:,3)=Volts(:,3)-Vzero(3); Vlg(:,4)=Volts(:,4)-Vzero(4); Vlg(:,5)=Volts(:,5)-Vzero(5);

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Vlg(:,6)=Volts(:,6)-Vzero(6); Vlg(:,7)=Volts(:,7)-Vzero(7); gain=[... 2000; ... Fx 2000; ... Fy 4000; ... Fz 1000; ... Mx 1000; ... My 1000; ... Mz ]; sens= [... 1.5818; ... Fx 1.5848; ... Fy 0.3912; ... Fz 2.3309; ... Mx 2.3375; ... My 1.5793; ... Mz ]; Ve= [... 10; ... Fx 10; ... Fy 10; ... Fz 2.5; ... Mx 2.5; ... My 2.5; ... Mz ]; lbs2N=4.44822162825; Convfac=1e-6*Ve.*sens.*gain/lbs2N; FT=[]; FT.raw=[]; FT.raw.Ftime_lg=Vlg(:,1)-1.38029e9; FT.raw.Fz_lg=Vlg(:,4)/Convfac(3); % Downsample Thrust Data FT.raw.Fz=zeros(length(t_raw),1); for k=1:length(t_raw) FT.raw.Fz(k,1)=mean(FT.raw.Fz_lg(((k-1)*100+1) :(k*100))); end %% Perform FFT of raw thrust N=length(FT.raw.Fz_lg); Fs=1000; % Calculate the DFT using the scaled FFT algorithm and shift the spectrum df = Fs/N; fvec = ((1-(N/2)):(N/2))*df; Fzf = fftshift(fft(FT.raw.Fz_lg)/N); figure;plot(fvec,real(Fzf),'b',fvec,imag(Fzf),'r');

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legend('Real Component','Imaginary Component'); xlabel('Frequency (Hz)');ylabel('Force Spectrum of Rays(N)'); %% Perform FFT analysis of thrust N=length(FT.raw.Fz); Fs=10; % Calculate the DFT using the scaled FFT algorithm and shift the spectrum df = Fs/N; fvec = ((1-(N/2)):(N/2))*df; Fzf = fftshift(fft(FT.raw.Fz)/N); figure;plot(fvec,real(Fzf),'-b',fvec,imag(Fzf),'--r '); legend('Real Component','Imaginary Componenty'); xlabel('Frequency (Hz)');ylabel('Force spectrum of rays (N)'); % Split Force into different frequency spectrums % Filter out very high and low frequency signal s to look at mid frequency % information FT.raw.midfreq=Fzf; FcutLow=1; FcutHigh=2.5; Cut=(abs(fvec) <= FcutLow)|(abs(fvec) >= FcutHi gh); FT.raw.midfreq(Cut)=0; FT.raw.mid = real(ifft(fftshift(FT.raw.midfreq* N))); figure; plot(t_raw,FT.raw.Fz,'o',t_raw,FT.raw.m id); xlabel('Time (s)'); ylabel('Force (N)'); legend('Unfiltered Force','Force with Middle Fr equency Only') % Low frequency only FT.raw.lowfreq=Fzf; FcutLow=1; Cut=(abs(fvec) >= FcutLow); FT.raw.lowfreq(Cut)=0; FT.raw.low = real(ifft(fftshift(FT.raw.lowfreq* N))); plot(t_raw,FT.raw.Fz,'.b',t_raw,FT.raw.low,'-r' ,'LineWidth',2); xlabel('Time (s)'); ylabel('Force (N)'); legend('Unfiltered Force','Force with Low Frequ ency Only') figure; plot(t_raw,FT.raw.low,t_raw,FT.raw.mid) ; xlabel('Time (s)','FontSize',12); ylabel('Force (N)','FontSize',12); legend('Primary Frequency Thrust Component',... 'Secondary Frequency Thrust Component'); %% Remove outliers % Identify Threshold for acceptance of data thresh=[]; thresh.u=[]; thresh.a=[]; thresh.g=[]; thresh.pitch=[]; thresh.roll=[]; thresh.yaw=[];

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thresh.u.u=6; thresh.u.l=-6; %twice max vehicle speed thresh.a.u=9.8*4; thresh.a.l=-9.8*4; %Max Se nsor reading thresh.g.u=1; thresh.g.l=-1; % thresh.pitch.u=90; thresh.pitch.l=-90; %Max Se nsor reading thresh.roll.u=180; thresh.roll.l=-180; %Max Se nsor reading thresh.yaw.u=180; thresh.yaw.l=-180; %Max Se nsor reading % Use thresholds to identify inlying data points inliers=find(... (imu.raw.u <= thresh.u.u)&(imu.raw.u >= thresh. u.l)... &(imu.raw.v <= thresh.u.u)&(imu.raw.v >= thresh .u.l)... &(imu.raw.w <= thresh.u.u)&(imu.raw.w >= thresh .u.l)... &(imu.raw.aX <= thresh.a.u)&(imu.raw.aX >= thre sh.a.l)... &(imu.raw.aY <= thresh.a.u)&(imu.raw.aY >= thre sh.a.l)... &(imu.raw.aZ <= thresh.a.u)&(imu.raw.aZ >= thre sh.a.l)... &(imu.raw.gX <= thresh.g.u)&(imu.raw.gX >= thre sh.g.l)... &(imu.raw.gY <= thresh.g.u)&(imu.raw.gY >= thre sh.g.l)... &(imu.raw.gZ <= thresh.g.u)&(imu.raw.gZ >= thre sh.g.l)... &(imu.raw.pitch <= thresh.pitch.u)&(imu.raw.pit ch >= thresh.pitch.l)... &(imu.raw.roll <= thresh.roll.u)&(imu.raw.roll >= thresh.roll.l)... &(imu.raw.yaw <= thresh.yaw.u)&(imu.raw.yaw >= thresh.yaw.l)); % Remove Outliers from all datasets t=t_raw(inliers); %GPS gps.time =gps.raw.time(inliers); gps.N=gps.raw.N(inliers); gps.E=gps.raw.E(inliers); %IMU imu.time=imu.raw.time(inliers); imu.u=imu.raw.u(inliers); imu.v=imu.raw.v(inliers); imu.w=imu.raw.w(inliers); imu.aX=imu.raw.aX(inliers); imu.aY=imu.raw.aY(inliers); imu.aZ=imu.raw.aZ(inliers); imu.gX=imu.raw.gX(inliers); imu.gY=imu.raw.gY(inliers); imu.gZ=imu.raw.gZ(inliers); imu.pitch=imu.raw.pitch(inliers); imu.roll=imu.raw.roll(inliers); imu.yaw=imu.raw.yaw(inliers); %Force FT.Fz=FT.raw.Fz(inliers); FT.low=FT.raw.low(inliers); FT.mid=FT.raw.mid(inliers); % Roll is upside down so Fix Roll

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for kr=1:length(imu.roll) if imu.roll(kr)>90 imu.roll(kr)=imu.roll(kr)-180; elseif imu.roll(kr)<-90 imu.roll(kr)=imu.roll(kr)+180; end end %% Compose Velocity, Accelerations and Gryo into st ate space matrices % Create Direction Cosine matrix dcm=angle2dcm(... (zeros(length(imu.roll),1))*pi/180, ... yaw (imu.pitch)*pi/180, ... Pitch (imu.roll)*pi/180); % Roll A=zeros(length(imu.time),3); G=A; U=A; for k=1:length(imu.pitch) A(k,:)=(dcm(:,:,k)*[imu.aX(k); imu.aY(k); imu.a Z(k)]); G(k,:)=(dcm(:,:,k)*[imu.gX(k); imu.gY(k); imu.g Z(k)]); U(k,:)=(dcm(:,:,k)*[imu.u(k); imu.v(k); imu.w(k )]); end % figure; % plot(t,imu.u,t,imu.v,t,imu.w,t,U(:,1),t,U(:,2),t, U(:,3)); % xlabel('time (s)','FontSize',12); ylabel('Velocit y (m/s)','FontSize',12); % title({['Radius ',num2str(CirR), ' m, Speed ', nu m2str(CirU),' m/s'];... % 'Correction for Pitch/Roll of vehicle and Ang ular Missalignment of sensor'},'FontSize',14); % legend('IMU Surge', 'IMU Sway', 'IMU Heave', ... % 'Corrected Surge', 'Corrected Sway', 'Correct ed Heave',... % 'Location','Best'); %% Identify important locations and distance vector s Ximu=.0254.*[25; ... 0.5; ... -25]; Xcg=.0254.* [10; ... 0; ... -7.6]; Xwj=.0254.* [-30;... -34;... 0]; Rimu=Ximu-Xcg;

67

Rwj=Xwj-Xcg; %% Perform coordinate transformation from sensor su rge/sway to vechicle % surge/sway for k=1:length(imu.time) U_g(k,:)=U(k,:)-cross(G(k,:),Rimu); end for k=1:length(imu.time) U_wj(k,:)=U_g(k,:)+cross(G(k,:),Rwj); end %% Filter Results of Coordinate Transformation U_g_fil(:,1)=smooth(U_g(:,1),'moving'); U_g_fil(:,2)=smooth(U_g(:,2),'moving'); U_g_fil(:,3)=smooth(U_g(:,3),'moving'); U_wj_fil(:,1)=smooth(U_wj(:,1),'moving'); U_wj_fil(:,2)=smooth(U_wj(:,2),'moving'); U_wj_fil(:,3)=smooth(U_wj(:,3),'moving'); figure; plot(t,U_g_fil,t,U_wj_fil); xlabel('time (s)','FontSize',12); ylabel('Velcity (m/s)','FontSize',12); legend('Vehicle Surge','Vehicle Sway', 'Vehicle Hea ve', ... 'Waterjet Surge', 'Waterjet Sway', 'Waterjet He ave',... 'Location', 'Best'); A_fil(:,1)=smooth(A(:,1),'moving'); A_fil(:,2)=smooth(A(:,2),'moving'); A_fil(:,3)=smooth(A(:,3),'moving'); FTs.Fz=[]; FTs.Fz.normal=smooth(FT.Fz,11,'moving'); FTs.Fz.low=smooth(FT.low,11,'moving'); FTs.Fz.mid=smooth(FT.mid,11,'moving'); % figure; % plot(t,FT.Fz,'.b',t,FTs.Fz.low,'-r','LineWidth',2 ); % xlabel('Time (s)','FontSize',12); ylabel('Force ( N)','FontSize',12); % legend('Thrust', 'Low Frequency Thrust with Movin g Average',... % 'Location','Best');

68

%% Perform comparison of vehicle sway velocity to i ntegrated y acceleration % % VfromA(1)=U_g_fil(1,2); % for k=2:length(t) % VfromA(k)=A_fil(k,2)*1/400+VfromA(k-1); % end % figure; % plot(t,VfromA,'-b',t,U_g_fil(:,2),':g') % xlabel('Time (s)'); ylabel('Velocity (m/s)'); % legend('Integrated Y Acceleration','Vehicle Sway Velocity') %% Non-Dimensionalize Data meanU=mean(U_g_fil(:,1)); rho=1024; nozzleR=.037 / 2; nozzleA=pi*((nozzleR)^2); NonD=[]; NonD.v=U_wj_fil(:,2)/meanU; NonD.thrust=[]; TloadingDen=0.5 * rho * nozzleA * meanU^2; NonD.thrust.low=FTs.Fz.low/TloadingDen; NonD.thrust.mid=FTs.Fz.mid/TloadingDen; %% Calculate Slip Angle CGslipA=atand(U_g_fil(:,2)./U_g_fil(:,1)); figure; plot(t,CGslipA); xlabel('Time (s)','FontSize',12) ylabel('Slip Angle (degrees)','FontSize',12) %% Analysis Plots % Plot Nondimensionalized Low Freq Thrust and Sway Compared to Yaw Rate figure; subplot(5,1,[1 3]) NonD_axis = plotyy(t,NonD.thrust.low,t,NonD.v); legend('Primary Frequency Thrust Loading Coeff','Sw ay Velocity Ratio',... 'Location','Best'); set(get(NonD_axis(1),'Ylabel'),'String','Thrust/ 0. 5{\rho}A_NU_o^2'); set(get(NonD_axis(2),'ylabel'),'String','V_w_j / U_ 0') grid on; subplot(5,1,[4 5]) plot(t,G(:,3))

69

xlabel('time(s)','FontSize',12) ylabel('Yaw Rate (rad/sec)','FontSize',12) grid on; % Plot Nondimensionalized Mid freq Thrust and Sway Compared to Yaw Rate figure; subplot(5,1,[1 3]) NonD_axis = plotyy(t,NonD.thrust.mid,t,NonD.v); legend('Secondary Frequency Thrust Loading Coeff',' Sway Velocity Ratio',... 'Location','Best'); set(get(NonD_axis(1),'Ylabel'),'String','Thrust/ 0. 5{\rho}A_NU_o^2'); set(get(NonD_axis(2),'ylabel'),'String','V_w_j / U_ 0') grid on; subplot(5,1,[4 5]) plot(t,G(:,3)) xlabel('time(s)','FontSize',12) ylabel('Yaw Rate (rad/sec)','FontSize',12) grid on; % %% Propegation of Error % accPR=0.5; % Degrees % accG=0.172*pi/180; % Gyro accuracy % accR=0.02; %accuracy of position estimates % accU=0.1; %Accuracy of velocity measurement (m/s ) % % error=[]; % error.uimu=accU*ones(length(t),1); % error.gz=accG*ones(length(t),1); % RimuMag=sqrt(Rimu(1).^2+Rimu(2).^2+Rimu(3).^2); % RwjMag=sqrt(Rwj(1).^2+Rwj(2).^2+Rwj(3).^2); % % % error.ucg=error.uimu+(RimuMag)*error.gz+G(:,3)*ac cR; % error.uwj=error.ucg+(RwjMag)*error.gz+G(:,3)*accR ; % % figure; % plot(t,(U_wj_fil(:,2)+error.uwj),t,(U_wj_fil(:,2) -error.uwj),t,U_wj_fil(:,2)); % xlabel('Time(s)') % ylabel('Sway Velocity (m/s)') % legend('Waterjet Sway + error','Waterjet Sway-err or','WaterjetSway Velocity') %% Cross Covariance between sway and Low Frequency thrust [cov_VFz,covVFz_Lags]=xcov(U_wj_fil(:,2),FTs.Fz.low ,'biased'); covcoef_VFZ=cov_VFz/(std(U_wj_fil(:,2))*std(FTs.Fz. low)); figure; subplot(2,1,1)

70

plot(covVFz_Lags,covcoef_VFZ); % title('Cross-Correlation Coefficients of Force an d Waterjet Sway Velocity','FontSize',14) xlabel('Lag in number of Samples','FontSize',12); ylabel({'Normalized Cross-'; 'Correlation Coefficients'},'FontSize',12); legend('Primary Frequency Thrust','Location','Best' ); %% Cross Covariance between sway and Middle Frequen cy thrust [cov_VFz,covVFz_Lags]=xcov(U_wj_fil(:,2),FTs.Fz.mid ,'biased'); covcoef_VFZ=cov_VFz/(std(U_wj_fil(:,2))*std(FTs.Fz. mid)); subplot(2,1,2) plot(covVFz_Lags,covcoef_VFZ); % title('Cross-Correlation Coefficients of Force an d Waterjet Sway Velocity','FontSize',14) xlabel('Lag in number of Samples','FontSize',12); ylabel({'Normalized Cross-'; 'Correlation Coefficients'},'FontSize',12); legend('Secondary Frequency Thrust','Location','Bes t') %% Looking at Accleration N=length(t); Fs=10; % Calculate the DFT using the scaled FFT algorithm and shift the spectrum df = Fs/N; fvec = ((1-(N/2)):(N/2))*df; AXf = fftsh ift(fft(A(:,1))/N); figure;plot(fvec,real(AXf),'b',fvec,imag(AXf),'r'); grid on; legend('Re(AXf)','Im(AXf)'); xlabel('Frequency (Hz)');ylabel('Acceleration spect rum of rays (m/s^2)'); % title('Discrete Fourier Transform'); % Filter out very high and low frequency signals FcutLow=0.5; FcutHigh=5; Cut=find((abs(fvec) <= FcutLow)|(abs(fvec) >= FcutH igh)); AXf(Cut)=0; % Calculate the IDFT of X(f) and overlay with trans mitted signal Ax_ifft = real(ifft(fftshift(AXf*N))); % Smooth the Filtered Acceleration Axfil=smooth(Ax_ifft,5,'moving'); % NonDimensionalize Acceleration Lnot=3.66; %vehicle length in meters NonD.axMid=Axfil.*Lnot/meanU;

71

%Plot high frequency accelerations and compare to S way Velocity Ratio figure; NonD_axis = plotyy(t,NonD.axMid,t,NonD.v); xlabel('time(s)','FontSize',12) legend('Middle Frequency NonDimensional Accerlation ','Sway Velocity Ratio',... 'Location','Best'); set(get(NonD_axis(1),'Ylabel'),'String','Ax L /U_o^ 2'); set(get(NonD_axis(2),'ylabel'),'String','V_w_j / U_ 0') grid on; %% Cross Covariance between sway and accelerationX [cov_VA,covVA_Lags]=xcov(U_wj_fil(:,2),A_fil(:,1),' biased'); covcoef_VA=cov_VA/(std(U_wj_fil(:,2))*std(A(:,1))); figure; subplot(2,1,1) plot(covVA_Lags,covcoef_VA); ylabel({'Normalized Cross-'; 'Cocorrelation Coefficient'},'FontSize',12); legend('Total Surge Acceleration') %% Cross Covariance between sway and Filtered accel erationX [cov_VAf,covVAf_Lags]=xcov(U_wj_fil(:,2),Axfil,'bia sed'); covcoef_VAf=cov_VAf/(std(U_wj_fil(:,2))*std(Axfil)) ; subplot(2,1,2) plot(covVAf_Lags,covcoef_VAf); % title('Cross-Correlation Coefficients of X Accele ration and Waterjet Sway Velocity','FontSize',14) xlabel('Lag in number of Samples','FontSize',12); ylabel({'Normalized Cross-'; 'Cocorrelation Coefficient'},'FontSize',12); title('High Pass Filtered Surge Acceleration');

72

APPENDIX C - MOTOR CONTROLLER CODE

top: speed = getvalue(_BS, 1) volts = getvalue(_V,2) amps = getvalue(_A,1) motpower = getvalue(_M, 1) print("$",volts,",",amps,",",speed,",",motpower,"*" ,"\r\n") wait(200) goto top

73

APPENDIX D - FIGURES

Run 1

Target Radius: 10 m

Target Speed: 1.0 m/s

Run 1 - GPS Path

185 190 195 200 205 210 215 220 225

-15

-10

-5

0

5

10

Meters E of Dock

Met

ers

Nor

th o

f Doc

k

Vehicle Path Waypoints

74

Run 1 - Primary and Secondary Components of Thrust

Run 1 - Vehicle and Local Waterjet Velocities

0 20 40 60 80 100 120-20

-10

0

10

20

30

40

50

60

70

Time (s)

For

ce (N

)

Primary Frequency Thrust Component

Secondary Frequency Thrust Component

0 20 40 60 80 100 120-0.5

0

0.5

1

1.5

2

2.5

time (s)

Vel

ocity

(m/s

)

Vehicle Surge

Vehicle Sway

Vehicle HeaveWaterjet Surge

Waterjet Sway

Waterjet Heave

75

Run 1 - Slip Angle

Run 1 - Thrust Loading Coefficient (Main Frequency), Sway Velocity, and Yaw Rate

0 20 40 60 80 100 120-6

-4

-2

0

2

4

6

8

10

12

14

Time (s)

Slip

Ang

le (d

egre

es)

0 20 40 60 80 100 1200

20

40

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120-0.2

0

0.2

Vw

j / U

0

Primary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 1200.05

0.1

0.15

0.2

0.25

time(s)

Yaw

Rat

e (r

ad/s

ec)

76

Run 1 - Thrust Loading Coefficient (Secondary Frequency), Sway Velocity, and Yaw

Rate

0 20 40 60 80 100 120-2

0

2

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120-0.2

0

0.2

Vw

j / U

0

Secondary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 1200.05

0.1

0.15

0.2

0.25

time(s)

Yaw

Rat

e (r

ad/s

ec)

-1500 -1000 -500 0 500 1000 1500-0.4

-0.2

0

0.2

0.4

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Primary Frequency Thrust

-1500 -1000 -500 0 500 1000 1500-0.02

-0.01

0

0.01

0.02

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Secondary Frequency Thrust

77

Run 1 - Normalized Cross-Correlation Coefficients Between Thrust and Sway Velocity

Run 2

Target Radius: 10 m

Target Speed: 1.5 m/s

Run 2 - GPS Path

185 190 195 200 205 210 215

-10

-5

0

5

10

Meters E of Dock

Met

ers

Nor

th o

f Doc

k

Vehicle Path Waypoints

78

Run 2 - Primary and Secondary Components of Thrust

Run 2 - Vehicle and Local Waterjet Velocities

0 20 40 60 80 100 120 140-20

-10

0

10

20

30

40

50

Time (s)

For

ce (N

)

Primary Frequency Thrust Component

Secondary Frequency Thrust Component

0 20 40 60 80 100 120 140-0.5

0

0.5

1

1.5

2

2.5

time (s)

Vel

ocity

(m/s

)

Vehicle Surge

Vehicle Sway

Vehicle HeaveWaterjet Surge

Waterjet Sway

Waterjet Heave

79

Run 2 - Slip Angle

Run 2 - Thrust Loading Coefficient (Main Frequency), Sway Velocity, and Yaw Rate

0 20 40 60 80 100 120 140-6

-4

-2

0

2

4

6

8

10

12

14

Time (s)

Slip

Ang

le (d

egre

es)

0 20 40 60 80 100 120 140-10

0

10

20

30

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120 140-0.2

-0.1

0

0.1

0.2

Vw

j / U

0

Primary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 120 140-0.2

0

0.2

0.4

0.6

time(s)

Yaw

Rat

e (r

ad/s

ec)

80

Run 2 - Thrust Loading Coefficient (Secondary Frequency), Sway Velocity, and Yaw Rate

Run 2 - Normalized Cross-Correlation Coefficients Between Thrust and Sway Velocity

0 20 40 60 80 100 120 140-2

-1

0

1

2

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120 140-0.2

-0.1

0

0.1

0.2

Vw

j / U

0

Secondary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 120 140-0.2

0

0.2

0.4

0.6

time(s)

Yaw

Rat

e (r

ad/s

ec)

-1500 -1000 -500 0 500 1000 1500-0.4

-0.2

0

0.2

0.4

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Primary Frequency Thrust

-1500 -1000 -500 0 500 1000 1500-0.02

-0.01

0

0.01

0.02

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Secondary Frequency Thrust

81

Test Run 3

Target Radius: 10 m

Target Speed: 2.0 m/s

Run 3 - GPS Path

180 185 190 195 200 205 210 215 220 225

-20

-15

-10

-5

0

5

10

15

Meters E of Dock

Met

ers

Nor

th o

f Doc

k

Vehicle Path Waypoints

82

Run 3 - Primary and Secondary Components of Thrust

Run 3 - Vehicle and Local Waterjet Velocities

0 50 100 150 200 250 300 350-30

-20

-10

0

10

20

30

40

50

Time (s)

For

ce (N

)

Primary Frequency Thrust Component

Secondary Frequency Thrust Component

0 50 100 150 200 250 300 350-0.5

0

0.5

1

1.5

2

2.5

3

time (s)

Vel

ocity

(m/s

)

Vehicle Surge

Vehicle Sway

Vehicle HeaveWaterjet Surge

Waterjet Sway

Waterjet Heave

83

Run 3 - Slip Angle

Run 3 - Thrust Loading Coefficient (Main Frequency), Sway Velocity, and Yaw Rate

0 50 100 150 200 250 300 350-10

0

10

20

30

40

50

Time (s)

Slip

Ang

le (d

egre

es)

0 50 100 150 200 250 300 350-20

0

20

40

Thr

ust/

0.5

ρANU

o2

0 50 100 150 200 250 300 350-0.5

0

0.5

1

Vw

j / U

0

Primary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 50 100 150 200 250 300 350-0.2

0

0.2

0.4

0.6

time(s)

Yaw

Rat

e (r

ad/s

ec)

84

Run 3 - Thrust Loading Coefficient (Secondary Frequency), Sway Velocity, and Yaw Rate

Run 3 - Normalized Cross-Correlation Coefficients Between Thrust and Sway Velocity

0 50 100 150 200 250 300 350-5

-4

-3

-2

-1

0

1

2

3

4

5

Thr

ust/

0.5

ρANU

o2

0 50 100 150 200 250 300 350-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Vw

j / U

0

Secondary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 50 100 150 200 250 300 350-0.2

0

0.2

0.4

0.6

time(s)

Yaw

Rat

e (r

ad/s

ec)

-4000 -3000 -2000 -1000 0 1000 2000 3000 4000-0.4

-0.2

0

0.2

0.4

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Primary Frequency Thrust

-4000 -3000 -2000 -1000 0 1000 2000 3000 4000-0.1

-0.05

0

0.05

0.1

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Secondary Frequency Thrust

85

Test Run 4

Target Radius 10 m

Target Speed: 2.5 m/s

Run 4: GPS Path

180 185 190 195 200 205 210 215 220

-20

-15

-10

-5

0

5

10

Meters E of Dock

Met

ers

Nor

th o

f Doc

k

Vehicle Path Waypoints

86

Run 4 - Primary and Secondary Components of Thrust

Run 4 - Vehicle and Local Waterjet Velocities

0 20 40 60 80 100 120 140 160-30

-20

-10

0

10

20

30

40

50

Time (s)

For

ce (N

)

Primary Frequency Thrust Component

Secondary Frequency Thrust Component

0 20 40 60 80 100 120 140 160-0.5

0

0.5

1

1.5

2

2.5

time (s)

Vel

ocity

(m/s

)

Vehicle Surge

Vehicle Sway

Vehicle HeaveWaterjet Surge

Waterjet Sway

Waterjet Heave

87

Run 4 - Slip Angle

Run 4 - Thrust Loading Coefficient (Main Frequency), Sway Velocity, and Yaw Rate

0 20 40 60 80 100 120 140 160-10

-5

0

5

10

15

Time (s)

Slip

Ang

le (d

egre

es)

0 20 40 60 80 100 120 140 16010

15

20

25

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120 140 160-0.4

-0.2

0

0.2

Vw

j / U

0Primary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 120 140 1600.1

0.15

0.2

0.25

time(s)

Yaw

Rat

e (r

ad/s

ec)

88

Run 4 - Thrust Loading Coefficient (Secondary Frequency), Sway Velocity, and Yaw Rate

Run 4 - Normalized Cross-Correlation Coefficients Between Thrust and Sway Velocity

0 20 40 60 80 100 120 140 160-2

0

2

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120 140 160-0.5

0

0.5

Vw

j / U

0

Secondary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 120 140 1600.1

0.15

0.2

0.25

time(s)

Yaw

Rat

e (r

ad/s

ec)

-2000 -1500 -1000 -500 0 500 1000 1500 2000-0.5

0

0.5

1

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Primary Frequency Thrust

-2000 -1500 -1000 -500 0 500 1000 1500 2000-0.04

-0.02

0

0.02

0.04

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Secondary Frequency Thrust

89

Run 5

Target Radius: 15 m

Target Speed: 2.0 m/s

Run 5 - GPS Path

180 190 200 210 220 230

-25

-20

-15

-10

-5

0

5

10

15

Meters E of Dock

Met

ers

Nor

th o

f Doc

k

Vehicle Path Waypoints

90

Run 5 - Primary and Secondary Components of Thrust

Run 5 - Vehicle and Local Waterjet Velocities

0 20 40 60 80 100 120 140-20

-10

0

10

20

30

40

50

Time (s)

For

ce (N

)

Primary Frequency Thrust Component

Secondary Frequency Thrust Component

0 20 40 60 80 100 120 140-0.5

0

0.5

1

1.5

2

2.5

time (s)

Vel

ocity

(m/s

)

Vehicle Surge

Vehicle Sway

Vehicle HeaveWaterjet Surge

Waterjet Sway

Waterjet Heave

91

Run 5 - Slip Angle

Run 5 - Thrust Loading Coefficient (Main Frequency), Sway Velocity, and Yaw Rate

0 20 40 60 80 100 120 1400

2

4

6

8

10

12

14

16

18

20

Time (s)

Slip

Ang

le (d

egre

es)

0 20 40 60 80 100 120 140-20

0

20

40

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120 140-0.2

0

0.2

0.4

Vw

j / U

0

Primary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 120 140-0.2

0

0.2

0.4

0.6

time(s)

Yaw

Rat

e (r

ad/s

ec)

92

Run 5 - Thrust Loading Coefficient (Secondary Frequency), Sway Velocity, and Yaw Rate

Run 5 - Normalized Cross-Correlation Coefficients Between Thrust and Sway Velocity-

0 20 40 60 80 100 120 140-1.5

-1

-0.5

0

0.5

1

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120 140-0.2

-0.1

0

0.1

0.2

0.3

Vw

j / U

0

Secondary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 120 140-0.2

0

0.2

0.4

0.6

time(s)

Yaw

Rat

e (r

ad/s

ec)

-1500 -1000 -500 0 500 1000 1500-0.4

-0.2

0

0.2

0.4

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Primary Frequency Thrust

-1500 -1000 -500 0 500 1000 1500-0.04

-0.02

0

0.02

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Secondary Frequency Thrust

93

Run 6

Target Radius: 15 m

Target Speed: 2.5 m/s

Run 6 - GPS Path

180 185 190 195 200 205 210 215 220

-15

-10

-5

0

5

10

15

Meters E of Dock

Met

ers

Nor

th o

f Doc

k

Vehicle Path Waypoints

94

Run 6 - Primary and Secondary Components of Thrust

Run 6 - Vehicle and Local Waterjet Velocities

0 50 100 150-40

-20

0

20

40

60

80

Time (s)

For

ce (N

)

Primary Frequency Thrust Component

Secondary Frequency Thrust Component

0 50 100 150-0.5

0

0.5

1

1.5

2

2.5

time (s)

Vel

ocity

(m/s

)

Vehicle Surge

Vehicle Sway

Vehicle HeaveWaterjet Surge

Waterjet Sway

Waterjet Heave

95

Run 6 - Slip Angle

Run 6 - Thrust Loading Coefficient (Main Frequency), Sway Velocity, and Yaw Rate

0 50 100 150-2

0

2

4

6

8

10

12

14

Time (s)

Slip

Ang

le (d

egre

es)

0 50 100 1500

20

40

Thr

ust/

0.5

ρANU

o2

0 50 100 150-0.2

0

0.2

Vw

j / U

0

Primary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 50 100 150-0.1

0

0.1

0.2

0.3

time(s)

Yaw

Rat

e (r

ad/s

ec)

96

Run 6 - Thrust Loading Coefficient (Secondary Frequency), Sway Velocity, and Yaw Rate

Run 6 - Normalized Cross-Correlation Coefficients Between Thrust and Sway Velocity

0 50 100 150-3

-2

-1

0

1

2

3

Thr

ust/

0.5

ρANU

o2

0 50 100 150-0.2

-0.1

0

0.1

0.2

Vw

j / U

0

Secondary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 50 100 150-0.1

0

0.1

0.2

0.3

time(s)

Yaw

Rat

e (r

ad/s

ec)

-1500 -1000 -500 0 500 1000 1500-0.5

0

0.5

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Primary Frequency Thrust

-1500 -1000 -500 0 500 1000 1500-0.1

-0.05

0

0.05

0.1

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Secondary Frequency Thrust

97

Run 7

Target Radius: 20 m

Target Speed: 2.0 m/s

Run 7 - GPS Path

180 190 200 210 220-20

-15

-10

-5

0

5

10

15

20

Meters E of Dock

Met

ers

Nor

th o

f Doc

k

Vehicle Path Waypoints

98

Run 7 - Primary and Secondary Components of Thrust

Run 7 - Vehicle and Local Waterjet Velocities

0 20 40 60 80 100 120 140 160 180 200-20

-10

0

10

20

30

40

50

60

Time (s)

For

ce (N

)

Primary Frequency Thrust Component

Secondary Frequency Thrust Component

0 20 40 60 80 100 120 140 160 180 200-0.5

0

0.5

1

1.5

2

2.5

time (s)

Vel

ocity

(m/s

)

Vehicle Surge

Vehicle Sway

Vehicle HeaveWaterjet Surge

Waterjet Sway

Waterjet Heave

99

Run 7 - Slip Angle

Run 7 - Thrust Loading Coefficient (Main Frequency), Sway Velocity, and Yaw Rate

0 20 40 60 80 100 120 140 160 180 200-4

-2

0

2

4

6

8

10

Time (s)

Slip

Ang

le (d

egre

es)

0 20 40 60 80 100 120 140 160 180 200-20

0

20

40

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120 140 160 180 200-0.2

0

0.2

0.4

Vw

j / U

0

Primary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 120 140 160 180 200-0.2

0

0.2

0.4

0.6

time(s)

Yaw

Rat

e (r

ad/s

ec)

100

Run 7 - Thrust Loading Coefficient (Secondary Frequency), Sway Velocity, and Yaw Rate

Run 7 - Normalized Cross-Correlation Coefficients Between Thrust and Sway Velocity

0 20 40 60 80 100 120 140 160 180 200

0

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120 140 160 180 200-0.5

0

0.5

Vw

j / U

0

Secondary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 120 140 160 180 200-0.2

-0.1

0

0.1

0.2

0.3

time(s)

Yaw

Rat

e (r

ad/s

ec)

-2000 -1500 -1000 -500 0 500 1000 1500 2000-1

-0.5

0

0.5

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Primary Frequency Thrust

-2000 -1500 -1000 -500 0 500 1000 1500 2000-0.1

-0.05

0

0.05

0.1

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Secondary Frequency Thrust

101

Run 8

Target Radius: 20 m

Target Speed: 2.5 m/s

Run 8 - GPS Path

180 190 200 210 220

-20

-15

-10

-5

0

5

10

15

20

Meters E of Dock

Met

ers

Nor

th o

f Doc

k

Vehicle Path Waypoints

102

Run 8 - Primary and Secondary Components of Thrust

Run 8 - Vehicle and Local Waterjet Velocities

0 20 40 60 80 100 120 140 160-20

-10

0

10

20

30

40

50

Time (s)

For

ce (N

)

Primary Frequency Thrust Component

Secondary Frequency Thrust Component

0 20 40 60 80 100 120 140 160-0.5

0

0.5

1

1.5

2

2.5

time (s)

Vel

ocity

(m/s

)

Vehicle Surge

Vehicle Sway

Vehicle HeaveWaterjet Surge

Waterjet Sway

Waterjet Heave

103

Run 8 - Slip Angle

Run 8 - Thrust Loading Coefficient (Main Frequency), Sway Velocity, and Yaw Rate

0 20 40 60 80 100 120 140 160-4

-2

0

2

4

6

8

10

Time (s)

Slip

Ang

le (d

egre

es)

0 20 40 60 80 100 120 140 1600

10

20

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120 140 160-0.2

0

0.2

Vw

j / U

0Primary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 120 140 160-0.1

0

0.1

0.2

0.3

time(s)

Yaw

Rat

e (r

ad/s

ec)

104

Run 8 - Thrust Loading Coefficient (Secondary Frequency), Sway Velocity, and Yaw Rate

Run 8 - Normalized Cross-Correlation Coefficients Between Thrust and Sway Velocity

0 20 40 60 80 100 120 140 160-1

-0.5

0

0.5

1

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120 140 160-0.2

-0.1

0

0.1

0.2

Vw

j / U

0

Secondary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 120 140 160-0.1

0

0.1

0.2

0.3

time(s)

Yaw

Rat

e (r

ad/s

ec)

-2000 -1500 -1000 -500 0 500 1000 1500 2000-0.5

0

0.5

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Primary Frequency Thrust

-2000 -1500 -1000 -500 0 500 1000 1500 2000-0.02

-0.01

0

0.01

0.02

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Secondary Frequency Thrust

105

Run 9

Target Radius: 25 m

Target Speed: 2.0 m/s

Run 9 - GPS Path

170 180 190 200 210 220 230

-20

-15

-10

-5

0

5

10

15

20

25

Meters E of Dock

Met

ers

Nor

th o

f Doc

k

Vehicle Path Waypoints

106

Run 9 - Primary and Secondary Components of Thrust

Run 9 - Vehicle and Local Waterjet Velocities

0 20 40 60 80 100 120 140-20

-10

0

10

20

30

40

50

60

Time (s)

For

ce (N

)

Primary Frequency Thrust Component

Secondary Frequency Thrust Component

0 20 40 60 80 100 120 140-0.5

0

0.5

1

1.5

2

2.5

time (s)

Vel

ocity

(m/s

)

Vehicle Surge

Vehicle Sway

Vehicle HeaveWaterjet Surge

Waterjet Sway

Waterjet Heave

107

Run 9 - Slip Angle

Run 9 - Thrust Loading Coefficient (Main Frequency), Sway Velocity, and Yaw Rate

0 20 40 60 80 100 120 140-6

-4

-2

0

2

4

6

8

Time (s)

Slip

Ang

le (d

egre

es)

0 20 40 60 80 100 120 140-20

0

20

40

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120 140-0.1

0

0.1

0.2

Vw

j / U

0

Primary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 120 140-0.2

-0.1

0

0.1

0.2

time(s)

Yaw

Rat

e (r

ad/s

ec)

108

Run 9 - Thrust Loading Coefficient (Secondary Frequency), Sway Velocity, and Yaw Rate

Run 9 - Normalized Cross-Correlation Coefficients Between Thrust and Sway Velocity

0 20 40 60 80 100 120 140-2

0

2

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120 140-0.2

0

0.2

Vw

j / U

0

Secondary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 120 140-0.2

-0.1

0

0.1

0.2

time(s)

Yaw

Rat

e (r

ad/s

ec)

-1500 -1000 -500 0 500 1000 1500-0.5

0

0.5

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Primary Frequency Thrust

-1500 -1000 -500 0 500 1000 1500-0.04

-0.02

0

0.02

0.04

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Secondary Frequency Thrust

109

Run 10

Target Radius: 25 m

Target Speed: 2.5 m/s

Run 10 - GPS Path

170 180 190 200 210 220 230-25

-20

-15

-10

-5

0

5

10

15

20

25

Meters E of Dock

Met

ers

Nor

th o

f Doc

k

Vehicle Path Waypoints

110

Run 10 -Primary and Secondary Frequency Thrust Components

Run 10 - Vehicle and Local Waterjet Velocities

0 20 40 60 80 100 120 140 160 180 200-10

0

10

20

30

40

50

Time (s)

For

ce (N

)

Primary Frequency Thrust Component

Secondary Frequency Thrust Component

0 20 40 60 80 100 120 140 160 180 200-0.5

0

0.5

1

1.5

2

2.5

time (s)

Vel

ocity

(m/s

)

Vehicle Surge

Vehicle Sway

Vehicle HeaveWaterjet Surge

Waterjet Sway

Waterjet Heave

111

Run 10 - Slip Angle

Run 10 - Thrust Loading Coefficient (Main Frequency), Sway Velocity, and Yaw Rate

0 20 40 60 80 100 120 140 160 180 200-4

-2

0

2

4

6

8

Time (s)

Slip

Ang

le (d

egre

es)

0 20 40 60 80 100 120 140 160 180 2005

10

15

20

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120 140 160 180 200-0.2

-0.1

0

0.1

Vw

j / U

0Primary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 120 140 160 180 200-0.1

0

0.1

0.2

0.3

time(s)

Yaw

Rat

e (r

ad/s

ec)

112

Run 10 - Thrust Loading Coefficient (Secondary Frequency), Sway Velocity, and Yaw

Rate

Run 10 - Normalized Cross-Correlation Coefficients Between Thrust and Sway Velocity

0 20 40 60 80 100 120 140 160 180 200-1.5

-1

-0.5

0

0.5

1

1.5

Thr

ust/

0.5

ρANU

o2

0 20 40 60 80 100 120 140 160 180 200-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

Vw

j / U

0

Secondary Frequency Thrust Loading Coeff

Sway Velocity Ratio

0 20 40 60 80 100 120 140 160 180 200-0.1

0

0.1

0.2

0.3

time(s)

Yaw

Rat

e (r

ad/s

ec)

-2000 -1500 -1000 -500 0 500 1000 1500 2000-0.5

0

0.5

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Primary Frequency Thrust

-2000 -1500 -1000 -500 0 500 1000 1500 2000-0.05

0

0.05

Lag in number of Samples

Nor

mal

ized

Cro

ss-

Cor

rela

tion

Coe

ffici

ents

Secondary Frequency Thrust

113

APPENDIX E - DESCRIPTION OF MOMENTUM FLUX METHOD

Figure E-1: Section Lines and Control Volume [5]

Figure E-1 above describes of the control volume designated by the ITTC for

use in momentum flux calculations and also defines several stations of interest. The

control volume is defined by the stream tube between station 1A and station 6. The

boundaries of the control volume consist primarily of the ducting of the jet, but also

includes the face of the nozzle (station 6), the capture area (Designated as A1 located at

station 1A), and the dividing stream line forward of the inlet opening which no mass

flow crosses (designated A2). The nozzle was used instead of the vena contracta

because the ITTC assumes that “in the vast majority of cases, the diameter of the vena

contracta is approximately the same as the nozzle diameter.” Additionally, the nozzle

diameter can be measured accurately while the vena contract is difficult to measure.

As stated in Newton's Second Law, the change in momentum flux over a control

volume equals the net forces acting on that control volume. In the case where the

114

nozzle is either completely immersed or completely ventilated this can be expressed as:

Equation 1

��� = ���� Using the given definitions for the boundaries of the control volume allows us to

define the change in momentum flux using stations 1A and 6.

Equation 2

Δ��� = ���� −����

The Momentum flux at station 6 can be obtained from a flow rate measurement

that has been calibrated to the thrust measured during a bollard pull experiment, which

is designated as the jet thrust.

Equation 3

���� = ���

The momentum flux ingested by the waterjet can be defined as the using the

velocity profile at the capture area A1.

Equation 4

���� =������

!�

This can also be determined by the flow rate and the ship velocity V0 using the

given relationship.

Equation 5

���� = �"�#$�%

115

Where #$� is defined as the momentum velocity coefficient at station 1 which

by definition is:

#$� = 1&'1 − �(�)"�%

* ���!��

And where �( is the local pressure coefficient.

�( = + − +0.5�%�

This is then enough information to calculate the net thrust of the waterjet

system. There are other thrust deduction coefficients involved which allow you to

compare this to the hull resistance and a series of efficiencies can be derived which

allow for the comparison between of models and prototypes.

116

APPENDIX F - WIRING DIAGRAMS

Cooling

Pump

60V 10A

Crydom

Solid State Relay3+ 4-

1+2-

Battery12V 1.2Ah

NiCad

+ -

KILL +

KILL -

Manual

Switch

+

-

Figure F-1 - Cooling System Wiring Diagram

117

From Electronics Box

Figure F-2 - Motor Circuit Wiring Diagram

118

APPENDIX G - CENTER OF GRAVITY CALCULATIONS AND

VERIFICATION

Preliminary estimates of the location of the center of gravity of the vehicle were

performed by recording the masses and centers for individual components and

identifying their location relative to a common reference point. For purposes of the

following calculations, the origin of the coordinate system is located at the intersection

of the centerline of the vehicle, the plane of the bottom of the pontoons, and the back

plane of the pontoons where the motor pods connect.

119

Vehicle Calculations

Vehicle

Weight

(lbs) LCG (in) VCG (in)

Bare Hull 90 36 13.21

Engine Pods 106 -18 4

Vehicle Total 196 6.80 8.23

Cargo Area Calculations

Cargo Area Components

Weight

(lbs) LCG (in) VCG (in)

Strobe Light

Light 1.5 -4.5 27

Mounting Bracket 3.9 0 25

Batteries 0 0 25

Strobe Light Total 5.4 -1.25 25.56

Control Box 30 26 26

Data Logging Box

Data Logging Box (empty) 8.25 39 31.5

Laptop 3 39 31

Force Transducer Amplifier 4.5 39 31

battery 1.6875 39 31

cDAQ 1.8125 39 31

Data Box Total 19.25 39 31.21

Cargo Area Total 54.65 27.89 27.80

Total Vehicle

Total

Weight

(lbs) LCG (in) VCG (in)

Vehicle Total 196 6.80 8.23

Cargo 54.65 27.89 27.80

TOTAL 250.65 11.40 12.50

Table G-1: Center of Gravity Estimation

After the estimation was performed, the location of the center of gravity was

confirmed by loading the vehicle with all equipment that would be mounted on the

vehicle for the actual experiments. The only exception to this was that the force

120

transducer was replaced with a blank of equal mass to prevent damage to the transducer.

During normal operation, the pods are held in an horizontal orientation by their

buoyancy and an elastic strap. To maintain the same orientation as during testing, a

rope loop was placed in place of the elastic strap.

The vehicle was then connected to the cable of a davit. Two different lifting

points were used and the angle that the vehicle made with respect to the cable. Using

the geometric relation between these two points, the center of gravity could then be

determined relative to the lifting points.

Figure G-1: Geometric Relation Between Two Lifting Points

and the Center of Gravity

Lifting Point 1

Lifting Point 2

121

The reference point for the hang test estimates for the center of gravity were

then compared to the reference point for the initial estimates. It was determined that the

initial estimates correlation well with the measured center of gravity of the vehicle.

122

REFERENCES

[1] ITTC, "Report of Specialist Committee on Validation of Waterjet Test

Procedures," 1999.

[2] J. Allison, "Marine Waterjet Propulsion," SNAME Transactions, pp. 275-335,

1993.

[3] O. M. Faltinsen, Hydrodynamics of High Speed Marine Vehicles, New York:

Cambridge University Press, 2005.

[4] ITTC Procedures, "Waterjets, Propulsive Performance Prediction (7.5-02-05-

03.1)," Recommended Procedures and Guidelines, 2005.

[5] ITTC, "Report of Specialist Committee on Validation of Waterjet Test

Procedures," in ITTC Proc of 24th ITTC, 2005.

[6] W.-G. Park, J. H. Jang, H. H. Chun and M. C. Kim, "Numerical flow and

performance analysis of waterjet propulsion system," Ocean Engineering, pp.

1740-1761, 2005.

[7] K. D. von Ellenrieder, "Free Running Tests of a Waterjet Propelled Unmanned

Surface Vehicle," Journal of Marine Engineering Technology, vol. 12, no. 1,

January 2013.

[8] K. von Ellenrieder, "Design and Instrumentation for Direct Thrust Measurements

123

from a Waterjet Propelled Unmanned Suface Vehicle," T-Craft Tools Review

Meeting, 2011.

[9] E. O. D. C. M. Albert S. Huang, "LCM: Lightweight Communications and

Marshalling," in Proc. Int. Conf. on Inteligent Robots and System (IROS), Taipei,

Taiwan, 2010.

[10] ITTC, "Report of Specialist Committee on Validation of Waterjet Test

Procedures," in ITTC Proc of 23rd ITTC, 2002.

[11] K. von Ellenrieder, "Experimental Testing of a Waterjet Propulsion System,"

TCraft Tools Review Meeting (Presenetation), 2012.

[12] T. I. Fossen, Guidance and Control of Ocean Vehicles, West Sussex, England:

John Wiley and Sons, Ltd, 1999.