seakeeping response of a surface effect ship in near-shore transforming

SEAKEEPING RESPONSE OF A SURFACE EFFECT SHIP IN NEAR-SHORE

TRANSFORMING SEAS

by

Michael Kindel

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

August 2012

iii

ACKNOWLEDGEMENTS

I would like to express here my gratitude to some of the individuals who have

helped me see this work to completion. First, I owe a debt of gratitude to my thesis

advisor Dr. Manhar Dhanak, who provided me with the opportunity to work on this

project and who's advice and encouragement enabled me to complete it, and my

committee members, Dr. Palaniswamy Ananthakrishnan and Dr. Karl D. von Ellenrieder,

for their advice and encouragmenent. I would also like to acknowledge the Office of

Naval Research and the T-CRAFT project for their support of this project. Additionally, I

am grateful to my family and friends for their encouragement. And finally, thank you

Kami for your understanding and encouragement over the past couple of years. I wouldn't

have done this without it!

iv

ABSTRACT

Author: Michael Kindel

Title: Seakeeping Response of a Surface Effect Ship in Near-Shore Transforming Seas Institution: Florida Atlantic University

Thesis Advisor: Dr. Manhar Dhanak

Degree: Master of Science

Year: 2012

Scale model tests are conducted of a Surface Effect Ship in a near-shore

developing sea. A beach is built and installed in a wave tank, and a wavemaker is built

and installed in the same wave tank. This arrangement is used to simulate developing sea

conditions and a 1:30 scale model SES is used for a series of experiments. Pitch and

heave measurements are used to investigate the seekeaping response of the vessel in

developing seas. The aircushion pressure and the vessel speed are varied, and the

seakeeping results are compared as functions of these two parameters. The experiment

results show a distinct correlation between the air-cushion pressure and the response

amplitude of both pitch and heave. The results of these experiments are compared

against results of a computer model of a Surface Effect Ship (SES).

DEDICATION

This thesis is dedicated to my childhood friend Thomas Tanner, with whom I conducted

my first wave tank experiments. Some pieces of tree bark, a mud puddle, and good

friends-the memory of those times always brings a smile.

v

SEAKEEPING RESPONSE OF A SURFACE EFFECT SHIP IN NEAR-SHORE

TRANSFORMING SEAS

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

LIST OF FIGURES ......................................................................................................... xiv

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

1.1. Objective ............................................................................................................. 1

1.2. Surface Effect Ships (SES) ................................................................................. 1

1.2.1. Drag............................................................................................................. 3

1.2.2. Bow Seal Wear ........................................................................................... 4

1.2.3. Aircushion Pressure .................................................................................... 6

1.3. Seakeeping .......................................................................................................... 7

1.4. Waves .................................................................................................................. 8

1.4.1. Linear Wave Theory ................................................................................. 10

1.4.2. Shallow Water Waves ............................................................................... 10

1.4.3. Nearshore Breaking Waves ....................................................................... 11

1.5. Scope of Thesis ................................................................................................. 12

2. COMPUTATIONAL FLUID DYNAMICS (CFD).................................................. 14

2.1. Description ........................................................................................................ 14

2.2. Uses, Advantages, and Limitations ................................................................... 15

2.3. Navier-Stokes Equations ................................................................................... 15

vi

2.3.1. Continuity Equation .................................................................................. 16

2.3.2. Balance of Momentum .............................................................................. 17

2.3.3. Energy Equation........................................................................................ 18

2.4. Numerical Techniques ...................................................................................... 20

2.5. Meshing............................................................................................................. 21

2.5.1. Structured Meshes:.................................................................................... 21

2.5.2. Unstructured meshes: ................................................................................ 23

2.5.3. Surface Mesh. ........................................................................................... 24

2.5.4. Grid Independent Study ............................................................................ 25

3. DEVELOPING THE COMPUTER MODEL .......................................................... 26

3.1. Description of Design Scenario Modeled ......................................................... 26

3.2. Geometry........................................................................................................... 27

3.3. Mesh .................................................................................................................. 30

3.3.1. Boundary Conditions ................................................................................ 30

3.4. Numerical Methods and Settings ...................................................................... 34

3.5. Convergence ..................................................................................................... 36

3.5.1. Grid Independence Study .......................................................................... 36

3.6. AIRCAT SES Simulation Results .................................................................... 39

3.7. Conclusions ....................................................................................................... 41

4. DEVELOPING THE PHYSICAL EXPERIMENT ................................................. 42

4.1. Overview of Experimental Setup ...................................................................... 42

4.2. Wave Scaling .................................................................................................... 42

vii

4.3. Wave Tank ........................................................................................................ 44

4.4. Wavemaker ....................................................................................................... 45

4.5. Beach................................................................................................................. 47

4.5.1. Background ............................................................................................... 47

4.5.2. Design ....................................................................................................... 48

4.6. AIRCAT ............................................................................................................ 51

4.7. Wave Gages. ..................................................................................................... 52

4.8. Aircushion pressure .......................................................................................... 54

4.9. Pitch and Heave ................................................................................................ 55

4.10. Bowskirt deflection ....................................................................................... 56

4.11. Vehicle Speed ............................................................................................... 58

4.12. Lamboley Swing Test and AIRCAT Radius of Gyration ............................. 59

4.13. X-direction Force transducer (For Stationary Tests) .................................... 60

5. RESULTS OF THE PHYSICAL EXPERIMENTS ................................................. 62

5.1. Description of Experiments .............................................................................. 62

5.2. Analysis Tools .................................................................................................. 65

5.2.1. Parameters Examined................................................................................ 65

5.2.2. Steady Stave Vs. Transient Responses ..................................................... 65

5.2.3. Time Domain Vs. Frequency Domain ...................................................... 65

5.3. Stationary Vessel .............................................................................................. 66

5.3.1. Wave data.................................................................................................. 66

5.3.2. Vehicle Data.............................................................................................. 68

viii

5.3.3. Pitch response ........................................................................................... 69

5.3.4. X-Direction Force Transducer .................................................................. 70

5.4. Vessel in Forward Motion ................................................................................ 70

5.5. Time Series ....................................................................................................... 71

5.6. Pitch Response ................................................................................................ 194

5.7. Heave Response .............................................................................................. 196

5.8. Discussion ....................................................................................................... 198

6. CONCLUSIONS AND DISCUSSION .................................................................. 200

6.1. Results ............................................................................................................. 200

6.1.1. Physical Experiments .............................................................................. 200

6.1.2. Computer Model ..................................................................................... 201

6.2. Future Work .................................................................................................... 201

6.2.1. Experiments ............................................................................................ 201

6.2.2. Computer Model ..................................................................................... 202

REFERENCES ............................................................................................................... 203

ix

LIST OF TABLES Table 3.1 Results from Physical Experiment .................................................................... 40

Table 5.1 Test 00 Vehicle and Wave Data ....................................................................... 71




Table 5.5 Test 04 Vehicle and Wave Data ...................................................................... 77





Table 5.10 Test 09 Vehicle and Wave Data ..................................................................... 85







Table 5.17 Table 16 Vehicle and Wave Data ................................................................... 95


x


Table 5.20 Test 19 Vehicle and Wave Data ................................................................... 100





















xi























xii





















Table 5.83 Pitch Response Vs. Encounter Frequency .................................................... 195

Table 5.84 Pitch RAO Vs. Encounter Frequency ........................................................... 196

xiii

Table 5.85 Heave Response Vs. Encounter Frequency .................................................. 197

Table 5.86 Heave RAO Vs. Encounter Frequency ........................................................ 198

xiv

LIST OF FIGURES Figure 1 Bottom View of SES (Kaplan et al 1981) ............................................................ 2

Figure 2 SES Bow Seal(Faltinsen 2005) ............................................................................ 4

Figure 3 Yamakita and Itoh's Simplified Bow Skirt Model(Faltinsen 2005) ..................... 5

Figure 4 A Random Sea Can be Expressed by a Wave Spectrum S(ω) ............................. 9

Figure 2.1 Fixed Infinitesimal Fluid Element with Fluid Moving Through It ................. 16

Figure 2.2 Simple Geometry ............................................................................................. 22

Figure 2.3 Simple Geometry with Structured Mesh ......................................................... 22

Figure 2.4 More Complex Geometry with Structured Mesh ............................................ 22

Figure 2.5 Types of Unstructured Volume Mesh Elements ............................................. 24

Figure 3.1 Air and Water Domains ................................................................................... 26

Figure 3.2 Surface Geometry with Finger Seals ............................................................... 27

Figure 3.3 Hull Geometry for AIRCAT with Simplified Bow Seal Geometry ................ 29

Figure 3.4 Isometric View of CFD Domain ..................................................................... 29

Figure 3.5 Boundary Conditions Applied to CFD Model................................................. 31

Figure 3.6 Surface Elevation Vs. Time for Four Grids..................................................... 36

Figure 3.7 Detail of Surface Elevation Vs. Time for Four Grids ..................................... 37

Figure 3.8 Coarse Grid ...................................................................................................... 37

Figure 3.9 Medium Coarse Grid ....................................................................................... 38

Figure 3.10 Medium Fine Grid ......................................................................................... 38

xv

Figure 3.11 Fine Grid ........................................................................................................ 38

Figure 3.12 Heave and Pitch Accelerations from CFD Simulation .................................. 39

Figure 3.13 Heave and Pitch Accelerations from CFD Simulation .................................. 40

Figure 4.1 Rendering of the Wave Tank ........................................................................... 44

Figure 4.2 Wave Tank....................................................................................................... 45

Figure 4.3 Wavemaker Paddle .......................................................................................... 45

Figure 4.4 Drive Mechanism for Wavemaker .................................................................. 46

Figure 4.5 Beach Sub-Frame Assembly ........................................................................... 49

Figure 4.6 Adjustable Leg for Beach Assembly ............................................................... 50

Figure 4.7 Beach in Place ................................................................................................. 50

Figure 4.8 AIRCAT SES 1:30 Scale Model ..................................................................... 52

Figure 4.9 Data from Wave Gage ..................................................................................... 53

Figure 4.10 Wave Gages ................................................................................................... 54

Figure 4.11 Pressure Sensor .............................................................................................. 55

Figure 4.12 IMU Sensor ................................................................................................... 56

Figure 4.13 Bowskirt Fingerseal ....................................................................................... 57

Figure 4.14 Flex Sensors to Measure Bowskirt Deflection .............................................. 57

Figure 4.15 Video Frames Used to Calculate Vessels Speed ........................................... 58

Figure 4.16 Example of a Lamboley Swing Test Rig ....................................................... 59

Figure 4.17 Load Cell Calibration Data ............................................................................ 61

Figure 5.1 Double-Sided FFT Graph of Wave Frequency ............................................... 66

Figure 5.2 Time Series of Water surface Elevation .......................................................... 68

xvi

Figure 5.3 Vehicle Data Time Series for Stationary Vehicle Experiment 5 ..................... 68

Figure 5.4 Pitch Power Spectrum for Stationary Vehicle Experiment 5 .......................... 69

Figure 5.5 Time Series of X-direction Force Transducer ................................................. 70

Figure 5.6 Test 00 Wave Elevation Data Time Series ...................................................... 72

Figure 5.7 Test 00 Vehicle Data Time Series ................................................................... 72

Figure 5.8 Test 01 Wave Elevation Data Time Series ...................................................... 73

Figure 5.9 Test 01 Vehicle Data Time Series ................................................................... 74

Figure 5.10 Test 02 Wave Elevation Data Time Series .................................................... 75

Figure 5.11 Test 02 Vehicle Data Time Series ................................................................. 75








Figure 5.19 Test 06 Vehicle Data Time Series ................................................................ 81






xvii

Figure 5.25 Test 09 Vehicle Data Time Series ................................................................ 86









Figure 5.34 Test 14 Wave Elevation Data Time Series ................................................... 93










Figure 5.44 Test 19 Wave Elevation Data Time Series ................................................. 100

Figure 5.45 Test 19 Vehicle Data Time Series ............................................................... 101

Figure 5.46 Test 20 Wave Elevation Data Time Series .................................................. 102

xviii























xix















Figure 5.83 Test 38 Vehicle Data Time Series .............................................................. 129








xx










Figure 5.100 Test 47 Wave Elevation Data Time Series ................................................ 142

Figure 5.101 Test 47 Vehicle Data Time Series ............................................................. 143









Figure 5.110 Test 52 Wave Elevation Data Time Series ............................................... 150



xxi























xxii























xxiii














1

1. INTRODUCTION

1.1.Objective

The goal of this thesis is to perform scale model tests of a Surface Effect Ship in

developing breaking waves, to compliment computer model studies in support of

determining the wave load and seakeeping responses of SES vehicles. The aim is to aid in

the development of a robust computational model that will allow designers to investigate

and validate designs that have never been built, without the expense of building and

testing physical prototypes. This will enable designers to push the envelop of current SES

technology.

1.2.Surface Effect Ships (SES)

Surface Effect Ships are a class of high-speed marine vehicles. They ride on a pressurized

cushion of air similar to a hovercraft, but they have rigid side hulls like catamarans. The

air cushion supports about 80 percent of the vehicle's weight, as a general rule (Faltinsen

2005). This reduces the draft of the craft significantly, and as a direct consequence the

hull drag of SES vehicles is much lower than the hull drag of crafts with a similar cargo

payload. Since SES vehicles have hulls that remain submerged in water, water-jets are a

viable method of propulsion, and in practice many SES craft utilize waterjet propulsion

rather than the air-props used by Air Cushioned Vehicles (ACVs). Water-jets are more

2

efficient than air propulsion up to speeds of around 120 knots, which is well within the

15-70 knot speeds typical of most modern SES vehicles (Butler 1985).

Figure 1 Bottom View of SES (Kaplan et al 1981)

SES vehicles are in use in commercial ferry operations throughout the world, since their

efficient high-speed and medium range attributes in small to medium sea-states make

them well suited for this type of application. SES craft are not particularly well-suited for

operation in high sea states because the water-jet inlets must remain submerged at all

times and the bow and stern seals need to be close to the waters surface to maintain the

pressurized air cushion, and the pitching and heaving associated with higher sea states

compromises the water-jet inlets and enlarges the gap between the bow and stern seals

and the water surface (Faltinsen 2005).

3

1.2.1. Drag

Calm water resistance on watercraft is generally broken into viscous drag, wave drag,

spray drag, and air drag.

The hull drag of an SES is much lower than the hull drag of a similarly sized

catamaran vessel. This is due to the fact that the aircushion supports around 80% of the

vehicle weight, on average (Faltinsen 2005).

The presence of the aircushion adds to the wave resistance, since the aircushion

causes a depressed free-surface elevation under the vessel, so that when the vessel is in

forward motion this depressed water surface creates surface waves. Newman (1977)

showed how to analytically solve for the wave resistance of a vessel in deep water, by

relating the complex wave amplitude function A(θ) to wave resistance Rw.

∫−

=2/

2/

322 cos)(21 π

π

θθθπρ dAURw (1.1)

Then Faltinsen (2005) gives the following expression for the wave amplitude function

( )θπ

θ 8

22

82

42

cos4)( QP

UgA +

= (1.2)

where

( )dydxeyxp

giQP

yxU

gi

Ab

θθθ

ρ

sincoscos22),(

21 +

∫∫=+ (1.3)

Where Ab is the horizontal cross-section area of the air cushion at the mean free surface

and p(x,y) is the excess pressure in the cushion. Simplifying with constant pressure and

rectangular cushion area (length L and width b), we get a non-dimensional wave

resistance of:

4

( )θ

θθ

θθθ

πρρ

π

dFn

LbFngpU

RW

= ∫ cos

tan)/(5.0sincos5.0sin

sincos16

/ 22

2/

02

222

02

(1.4)

One trend to note is that the non-dimensional wave resistance increases with increasing

b/L (beam to length) ratio.

1.2.2. Bow Seal Wear

Bow seals have a hard life, and experience very high rates of wear. The wear rate of an

SES bow seal is proportional to the speed of the vessel raised to the fourth power, U4

(Faltinsen 2005). Consequently, much interest has been placed in trying to understand

how the bow seals wear and how to minimize it. To this end, Yamakitah and Itoh (1998)

used the Meguro-2 SES vessel as a test platform to investigate the effect of different bow

seal materials and of different angles α between the bow seal and mean free surface.

Figure 2 SES Bow Seal(Faltinsen 2005)

The angle of α that gave the most favorable wear characteristics was found to be around

40º. Yamakita and Itoh also proposed a simplified mathematical model of the bow seal's

5

finger vibrations. They assumed the bow seal finger was two rigid plates, hinged about

point A, with the lower plate in contact with the water free surface.

Figure 3 Yamakita and Itoh's Simplified Bow Skirt Model(Faltinsen 2005)

Faltinsen (2005) and Kouvaras (2010) expounded on this model, giving a qualitative

analysis by assuming steady two-dimensional hydrodynamic flow past the rigid flat plate.

Summing the moments about point A, we get the following expression for the pitch

moment F5 (per unit length) about A:

θπρ 225 8

lUF = (1.5)

Dividing θ into a static part and a time dependent part (a time-dependent pitch angle η5),

the above is re-written as:

08

)( 522

25

2

5555 =⋅⋅⋅⋅++ ηπρη lUdt

dAI (1.6)

)1977(256

9:4

555555 NewmantoAccordinglAandAINoting ⋅⋅⋅=<<

ρπ

0329 52

5

..2 =⋅⋅+⋅⋅ ηη Ul (1.7)

6

This equation adheres to the mass-spring paradigm, with no damping term. Thus, the

differential equation can be solved using the exponential form of a solution, with the

spring equivalent 232 Ukeq ⋅= and the mass equivalent 29 lmeq ⋅= . The natural

frequency is then shown to be:

lU

lU

mk

neq

eqn ⋅

⋅⋅=⇒

⋅⋅

==3

249

322

2

ωω (1.8)

This was the result obtained by Faltinsen, but he recognized that this method failed to

provide a rigorous quantitative prediction of the accelerations of the flapping bow seal.

Faltinsen suggested the addition of a negative damping term to account for instabilities,

which he said were the probable cause of the finger vibrations. He also suggested

introducing non-linear free-surface effects for 2-D planing.

1.2.3. Aircushion Pressure

The aircushion is the defining feature of an SES. Without it, the craft would simply be a

twin-hulled vessel. The aircushion is generated by large fans, which have the ability to

provide an excess pressure p0 of about 5% of atmospheric pressure (Faltinsen 2005).

Atmospheric pressure is ~101 kPa, so that means the upper limit for the aircushion excess

pressure is around 5 kPa, or about 0.508 meters of water column. In other words, the

water inside the aircushion cavity of an SES when on full cushion is about 0.5 meters

lower than the water level surrounding the SES. The pressure in a column of water is

given by

7

zgpp a ⋅⋅−= ρ (1.9)

Here pa is atmospheric pressure. The pressure on the surface of the water inside the air

cushion volume is given by

(1.10)

Or,

gph⋅

=ρ

0 (1.11)

Here, h is the difference in the free surface levels between the water inside the cushion

and outside it.

1.3.Seakeeping

Seakeeping is the term given to a watercraft's performance when in operation. Four broad

areas have been defined as comprising a vessel's seakeeping characteristics, these being

mission, environment, ship responses, and seakeeping performance criteria (Lewis 1989).

For this thesis, only the environment and ship responses will be considered. The

environment is defined as a near-shore transforming sea, where waves are shoaling and

breaking. The environment is simulated in a wave tank with a wave maker and a beach,

and in a computational model by applying appropriate boundary conditions to a geometry

that includes the presence of a beach. For the physical experiments, the ship responses are

measured directly with an Inertial Measurement Unit (IMU). This senses and records

hgppp aa ⋅⋅+=+ ρ0

8

pitch, yaw, roll, surge, sway, and heave, the six accelerations associated with rigid

body motion. This thesis is only concerned with the pitch, heave, and surge accelerations.

1.4.Waves

The effect of any kind of disturbance on a water's surface results in the creation of waves.

When these disturbances are large enough and sustained for long enough, a set of waves

is created which propagates along the water's surface until the energy of the absorbed

disturbance is dissipated, possibly by a beach or by the effects of surface tension and

gravity. On the ocean and in large bodies of water, the waves traveling along a given

expanse of water can be characterized as a 'sea', and a sea is categorized according to the

amplitudes and wavelengths of the waves it contains, and this is called a sea-state. When

ships are designed, it is necessary to define what sea-states it is to be operational in and

for how long, and what its desired performance is to be in a given sea-state. To predict a

proposed design's response in a given sea-state, the model is subjected-either numerically

or with a scaled model test-to a set of regular waves of known amplitude and frequency,

and its response is recorded for each frequency/amplitude combination. These results are

then superposed to determine the model's response in a sea-state characterized by the set

of frequency/amplitude combinations to which the model was exposed.

9

Figure 4 A Random Sea Can be Expressed by a Wave Spectrum S(ω)

As the figure above shows, a random sea-state can be approximated by taking regular

waves components from a frequency domain wave spectrum and superposing them. The

sea-state that results is dependent on how the frequency-domain wave spectrum is shaped

(defined), and different spectrums have been proposed. The Joint North Sea Wave Project

(JONSWAP) for limited fetch was recommended by the 17th International Towing Tank

Conference (ITTC) as:

)()3.3)(944exp(155)( 244

154

1

23/1 sm

TTHS Y

ωωω −

= (1.12)

where

−

−=2

2/11

21191.0exp

σωTY (1.13)

And

1

1

/24.509.0/24.507.0TforTfor

>=≤=

ωσωσ

10

1.4.1. Linear Wave Theory

A theoretical model for regular, sinusoidal, propagating waves has been developed,

known as either Airy Wave Theory or Linear Wave Theory. This theory is developed in

great detail by Dean and Dalrymple (1984), and an equation for the free-surface elevation

as a function of time is given as:

)cos(2

tkxH ση −= (1.14)

When generated in a wave tank with a simple harmonic wavemaker, the wave profile can

be expressed as:

−=

Lx

TtH ππη 22cos

2 (1.15)

Where H, T, L, x, and t are the wave height, wave period, wave length, and distance and

time coordinates, respectively (Dean and Dalrymple 1984).

1.4.2. Shallow Water Waves

As regular waves approach a beach, the decrease in water depth causes the waves to shoal

and break. The full equations of linear wave theory can be simplified for shallow water

cases where 0⇒⋅ hk or, alternatively, where 20

0λ<h , and the simplified form of the

linear wave equations is given by:

)(21)(

00 xhk

AxA⋅

⋅= (1.16)

11

)()( 00 xhkx ⋅⋅= λλ (1.17)

Clearly, the amplitude increases and the wavelength decreases as the water depth h

decreases. This causes the wave profile to become unstable and collapse or break. The

vertical and horizontal velocities can also be expressed, and these prove useful in

defining the waves in the computer model.

)sinh()sin()cosh(

khtkxkzau ωω −

= (1.18)

)sinh()cos()sinh(

khtkxkzaw ωω −−

= (1.19)

The wave amplitude is here given as a. It is noted from the above equations that the

velocity is a function of the depth, h, so that as h increases the velocity decreases, in other

words the velocity due to the wave motion decreases the further down into the water one

goes.

1.4.3. Nearshore Breaking Waves

No theoretical model exists that fully describes breaking waves, although criteria have

been established that predict when a wave can be expected to break. The two methods

available to study breaking waves are to create them physically, in a wave tank for

instance, or to study them numerically, for instance with a Reynold's Averaged Navier

Stokes (RANS) solver. This thesis used both methods, using a wave tank and a RANS

solver (ANSYS CFX). Waves are predicted to break in deep water when the amplitude to

wavelength ratio, A/λ, exceeds 1/14. This criteria does not have to be met for a wave to

12

break in shallow water, since other factors play a role in wave breaking such as the beach

slope and relative water depth h/ λ. In shallow water, the amplitude to water depth ratio,

A/h, is used, and breaking is expected for A/h values between 0.4-0.6.

1.5.Scope of Thesis

This thesis begins by outlining the objectives for the work undertaken, and provides the

necessary background information to allow the reader to make sense of the discussion on

SES vehicles, waves, wave tank experimentation, and CFD. Each of these topics are

discussed further, as the paper details how the physical experiments were set up and

conducted, and how the computer model was set up and validated. The results from the

physical experiments and computational model are then given and discussed.

Recommendations for further work are then outlined. The thesis follows this breakdown:

• Chapter 1 describes the objective of the thesis and outlines relevant background

information.

• Chapter 2 gives an overview of the field of computational fluid dynamics, the

governing equations, and some of the applications of CFD with its strengths and

weaknesses.

• Chapter 3 explains how the computational model was created and set up, and

details what solver (ANSYS CFX) was selected and what equations it utilizes.

13

The chapter then explains how the boundary conditions were selected and

describes the expressions that were used to simulate the waves. It reviews

preliminary results from the computer model. Plots of the pitch and heave time

series are given. The results are compared against the physical experiments for

validation

• Chapter 4 describes the set-up of the physical experiments, including a

description of the wave tank, the beach, the wave-maker, the SES scale model,

and the instrumentation.

• Chapter 5 reviews the results of the wave tank experiments, looking at both the

time series and frequency domain results. Plots of time series that were typical of

the experiments are shown, as well as some plots of the frequency domain results

of the inputs (waves) and outputs (vehicle response). The results of all the

experiments are then given in tables, with the statistical data derived from

conducting multiple runs with the same input conditions.

• Chapter 6 concludes the thesis, discussing the results from the computer model

and physical experiments. Recommendations are made for further improvements

to the computer model, and how the results of the physical experiments can be

used for validating a future computer model.

14

2. COMPUTATIONAL FLUID DYNAMICS (CFD)

2.1.Description

Computational fluid dynamics (CFD) is a powerful synthesis between the world of

theoretical fluid dynamics and the world of experimental fluid dynamics (Anderson

1995). The seventeenth century saw much of the groundwork laid for the field of

experimental fluid dynamics, and the eighteenth and nineteenth centuries gave rise to the

discipline of theoretical fluid dynamics. The twentieth century, however, gave rise to the

field of computational fluid dynamics, which took the theory of fluid dynamics and

coupled it with the new fields of numerical analysis and digital computing. By

developing numerical solutions of the complex, and often unsolvable, Navier-Stokes

equations governing dynamic fluid behavior, it was possible to bridge the gap between

the two worlds of theory and experiment (Anderson 1995). Since about the 1950s, many

people and groups have developed and refined numerical methods to solve the three

dimensional Navier-Stokes equations that describe fluid flow, and there are now many

commercial CFD codes available.

15

2.2.Uses, Advantages, and Limitations

CFD is used for widely ranging applications, for everything from the flow of air in a

building to the behavior of the shock wave across a supersonic aircraft to the erosion of

shorelines in coastal areas. Its main advantage is that it allows the investigation of

scenarios without the expense of physical experiments. This also means it is often much

faster to get results with CFD than it is by conducting experiments. However, it is not

always possible to resolve all the scales and it becomes necessary to model flows at these

scales and seek verification of the computational results with results from experiments.

The simulations can take long periods of computational time, and they must be set up

with care.

2.3.Navier-Stokes Equations

The equations governing fluid flow are known as the Navier-Stokes equations. Three

basic laws are called upon to set up the governing equations, and these are the

conservation of mass, Newton's second law (F=m*a), and the conservation of energy.

This overview follows the layout of John Anderson's excellent synopsis (Anderson

1995). First, let us set up a graphical representation of the control volume.

16

Figure 2.1 Fixed Infinitesimal Fluid Element with Fluid Moving Through It

This control volume represents an infinitesimal fluid element, fixed in space, with a fluid

moving through it. Note the word 'infinitesimal'. It should immediately pull up memories

of differential calculus. That is exactly where we are going next, for we are going to

develop the equations for the mass flow into and out of this small element. We will begin

with the continuity equation, then develop the equations for the balance of momentum

and conservation of energy.

2.3.1. Continuity Equation

The net flow (Volume Outflow-Volume Inflow = Rate Change in Volume) in the x

direction is given by:

dzdydxxudzdyudzdydx

xuu

∂∂

=−

∂∂

+)()()( ρρρρ (2.1)

This is similar for the flow in the y and z directions. The total net mass flow is given by:

dzdydxzw

yv

xuFlowMassNet

∂

∂+

∂∂

+∂

∂=

)()()( ρρρ (2.2)

17

2.3.2. Balance of Momentum

The momentum equation arises from Isaac Newton's powerful second law,

F=m*a (2.3)

In words, this equation states that the force on an object is equal to the mass of the object

times the acceleration of the object.

For the left side of the equation, we can break the forces into two categories, body forces

and surface forces.

)( dzdydxfdirectionxinforcesBody xρ= (2.4)

And then, for the surface forces,

dzdydxzyxx

pdirectionxinforcessurfaceNet zxyxxx

∂∂

+∂

∂+

∂∂

+∂∂

−=τττ (2.5)

Then, for the right hand side of the equation, we can express the mass as

dzdydxm ρ= (2.6)

The acceleration is expressed as the substantial derivative,

DtDuax =

Combining all the equations, and expressing them in the conservation form, we get:

xzxyxxx fzyxx

putu ρτττρρ

+∂∂

+∂

∂+

∂∂

+∂∂

−=•∇+∂

∂ )()( V (2.7a)

yzyyyxy fzyxy

pvtv ρ

τττρρ

+∂

∂+

∂

∂+

∂

∂+

∂∂

−=•∇+∂

∂ )()( V (2.7b)

zzzyzxz fzyxx

pwtz ρτττρρ

+∂∂

+∂

∂+

∂∂

+∂∂

−=•∇+∂

∂ )()( V (2.7c)

18

2.3.3. Energy Equation

The energy equation depends upon the principle that energy is conserved. Put another

way, the rate of the change of energy inside a fluid element is equal to the net flux of heat

into the element plus the rate of work done on the element due to body and surface

forces. Expressing this in conservation form, we get:

Vf •+∂

∂+

∂

∂+

∂∂

+

∂

∂+

∂

∂+

∂

∂+

∂∂

+∂

∂+

∂∂

+

∂∂

−∂

∂−

∂∂

−

∂∂

∂∂

+

∂∂

∂∂

+

∂∂

∂∂

+=

+•∇+

+

∂∂ •

ρ

τττ

τττ

τττ

ρρρ

zw

yw

xw

zv

yv

xv

zu

yu

xu

zwp

yvp

xup

zTk

zyTk

yxTk

xqVeVe

t

zzyzxz

zyyyxy

zxyxxx

)()()(

)()()(

)()()(

)()()(

22

22

(2.8)

Finally, we can express all of the equations (mass, momentum, energy) in conservation

form:

JzH

yG

xF

tU

=∂∂

+∂∂

+∂∂

+∂∂ (2.10)

Where:

19

+

=

2

2Ve

wvu

U

ρ

ρρρρ

−−−∂∂

−+

+

−

−−+

=

xzxyxx

xz

xy

xx

wvuxTkpuuVe

wuvu

puu

F

τττρ

τρ

τρτρ

ρ

2

2

2

−−−∂∂

−+

+

−

−+

−

=

yzyyyx

yz

yy

yx

wvuyTkpvvVe

wvpv

uvv

G

τττρ

τρ

τρ

τρρ

2

2

2

−−−∂∂

−+

+

−+

−−

=

zzzyzx

zy

zy

zx

wvuzTkpwwVe

pw

vwuww

H

τττρ

τρ

τρτρ

ρ

2

2

2

( )

+++

=

•

qwfvfuf

fff

J

zyx

z

y

x

ρρ

ρ

ρρ0

These equations together with appropriate boundary and initial conditions accurately and

thoroughly describe the physics behind fluid flow. The problem with these equations is

that they are unsolvable for all but the most basic flow scenarios. To overcome this,

numerical techniques have been developed to approximate these equations.

20

2.4.Numerical Techniques

The power of CFD lies in the application of numerical techniques to solve the governing

equations. The equations we developed in the last section provide a very thorough

description of fluid behavior, the only problem being that there are not very many

applications that allow exact solutions of these equations (Couette flow is a notable

exception). It was discovered that by applying numerical techniques to solve these

equations, the problem of their insolvability could be largely overcome.

To begin our explanation of numerical techniques we will introduce the finite difference

method. Let us say we want to solve the equation )cos()( xxf π= numerically. If we

know the value at a point, say at x=i, we can solve for a value at another point by doing a

Taylor expansion of the equation as:

⋅⋅⋅+∆

∂∂

+∆

∂∂

+∆

∂∂

+=+ 62

3

,3

32

,2

2

,,,1

xx

fxx

fxxfff

jijijijiji (2.11)

Referring to our example, let's say we want know the value of our function at the point

2.0, and want to know the value at the point 2.02.

valueexactxfxAtvalueexactxfxAt

xxf

998026.0)(:02.20.1)(:0.2

)cos()(

====

= π

Now, to approximate the value of our function at x=2.02, we take the value at x=i, which

in our case is 2.0, and evaluate f, which yields 1.0. We then add the next two terms in our

equation, which yields:

21

998026.00.0019740.00.1

2

2

,2

2

,,,1

=−−≈

∆

∂∂

+∆

∂∂

+≈+x

xfx

xfff

jijijiji

Thus, after only three terms, we have agreement to six decimal places. There are different

variations of the finite difference method, including the forward difference method,

backward difference method, and central difference method. Different schemes are better

suited for different mesh types.

2.5.Meshing

Before any computational analysis can commence, the geometry of the case of interest

must be created and this geometry must then be broken into tiny, discrete elements that

can be solved numerically. This process is referred to as meshing. Meshes can be roughly

categorized as either structured or unstructured.

2.5.1. Structured Meshes:

Structured meshes feature regular connectivity. The most important result of this feature

is that the elements can be described by an array - a 2D array for two-dimensional

geometry, and a 3D array for three-dimensional geometry. For two-dimensional

geometry, the elements must be of a quadrilateral shape. For three-dimensional geometry,

the elements are of a hexahedral shape.

22

Figure 2.2 Simple Geometry

Figure 2.3 Simple Geometry with Structured Mesh

Fig 2.3 shows how a two-dimensional geometry has been meshed with a structured mesh,

characterized by very regular connectivity. All the elements are very uniform and

regularly spaced. A structured mesh does not have to have uniformly shaped elements.

For instance, they can conform to the geometry of interest, such as an airfoil or car body

(Fig 2.4), but they maintain an underlying uniformity that is lacking in an unstructured

mesh.

Figure 2.4 More Complex Geometry with Structured Mesh

23

2.5.2. Unstructured meshes:

Unstructured meshes have irregular connectivity between the elements, with two primary

results. The first result is that the mesh can accommodate very irregular geometry, and

typically with significantly less work by the user. The second result is that the mesh takes

much more memory to store, because the connectivity must also be defined and stored as

well as the elements.

With unstructured meshes, more shapes are available from which to make elements. For

two-dimensional grids, the most common shapes are quadrilaterals (four sided shapes)

and triangles (three sided shapes). Three-dimensional grids are commonly composed of

hexahedra, tetrahedra, square pyramids, and extruded triangles. Fig. 2.5 shows examples

of these different shapes. Many meshing programs combine elements of more than one

type, for instance a mesh could contain tetrahedral elements with some hexahedral

elements along boundaries, forming a 'prism layer' to capture near-surface effects, and

some square pyramids and extruded triangles in a few areas with tight corners or some

irregular geometrical features.

24

Figure 2.5 Types of Unstructured Volume Mesh Elements

2.5.3. Surface Mesh.

In addition to the structured and unstructured classifications, meshes can also be

classified as two-dimensional or three-dimensional. There is actually a third group,

sometimes called 2.5D for "two-and-a-half dimensional". This refers to a surface mesh,

which can be the outside elements of a volume (3D) mesh that are 'exposed'. The reason a

surface mesh is sometimes considered a 2.5D mesh rather than a 2D mesh is that it may

not lie strictly in one plane. Think of the surface of an airfoil. The curved surface is not

two-dimensional, but it is also not three-dimensional if we are speaking strictly of the

surface - no volume, no third dimension! Surface meshes are very important in CFD,

because much of what is of interest is happening on a surface, whether the lift on an

airfoil, the heat transfer on a copper pipe, or the drag force on a ship's hull. All these

quantities are calculated at a surface.

25

2.5.4. Grid Independent Study

To determine whether or not a simulation's results are being affected by the refinement of

the mesh being used, a grid independent study is performed. This simply means that

several grids are used, with varying degrees of refinement. The simulation is carried out

using the different meshes and the results compared. If there is good agreement between

results, it can be reasonably inferred that the results are not varying because of the mesh

refinement and the simulation can be claimed to be 'independent' of the grid being used.

One of the motivating factors behind a grid independent study, besides validating an

arbitrary grid, is validating a grid that is as coarse as possible without a loss of validity.

This is because the more elements the software has to solve for, the longer it takes to

compute. The finer the mesh, the more elements it has. This is termed 'expensive'

computing, because it takes more computing resources (RAM, processor time) to run a

simulation on a fine mesh than it does to run the same simulation on a coarse mesh.

In concluding this chapter, it can be said that the power of CFD surpasses it's limitations

for a great variety of cases, and many industries are making use of CFD simulations to

help make engineering decisions. In naval architecture, the field of CFD is becoming

more commonplace and CFD results are beginning to earn more acceptance among the

naval community. The main criticism from the naval community is the time required to

run simulations, and that is being reduced continually by more powerful computers and

more efficient software.

26

3. DEVELOPING THE COMPUTER MODEL

3.1.Description of Design Scenario Modeled

When creating a model of a system, whether it is a physical model or a computer model,

it is important to identify what are the specific items that one is interested in

investigating. Models, by their nature, are simplifications of what they represent and only

capture a few of the more important details. For this thesis, several options were

considered and a few different scenarios were actually modeled. With the information

learned from those preliminary models, a final simulation was developed of a stationary

SES vessel in the near-shore region with waves approaching and breaking upon its bow

skirt. This model was then used to measure the forces upon the skirt and the vessel pitch

response and heave response. The waves were defined at the inlet, which was the side of

the domain opposite the beach. The waves were defined as linear waves, and propagated

towards the shore.

Figure 3.1 Air and Water Domains

The AIRCAT SES vessel was placed near the shoreline facing away from the beach so

that the waves would break onto the bow skirt.

27

3.2.Geometry

The geometry was created using SolidWorks. A surface model of the AIRCAT SES had

been created previously and supplied to the author. This surface model was used to create

a solid model of the AIRCAT SES. This was necessary because ANSYS ICEM uses solid

geometry to generate a volume mesh. The surface geometry and the solid geometry are

pictured.

The solid model utilized a simplified skirt design. This arose from meshing concerns.

When a finger-seal design was used, as on the surface geometry, the mesh had difficulties

capturing the shape. In order to accurately capture the shape, the mesh had to be highly

refined and this led to a mesh that was too large to be usable. As a result, it was decided

to use a simplified shape for the bow-seal.

Figure 3.2 Surface Geometry with Finger Seals

It should be noted that the bow and stern seals do not go all the way to the bottom of the

hull. This is because the hull is designed to remain submerged even when on cushion.

Remember from chapter 1 that this is the primary difference between the SES and ACV.

Because of this, the seals terminate above the hull. The location of the seals was

28

determined from conversation with Trigva Halvorson, an engineer with Umoe-Mandal

who had first-hand experience with SES vessels. The 35-40[m] class of SES craft he

worked with were typically designed to have approximately 1[m] of the hull submerged

at the stern and 0.2[m] of the hull submerged at the bow, when the seals were new. As the

seals wear, the bow will sink to 0.3[m] or 0.35[m]. As would be expected, this drives up

the wave resistance of the vehicle and adds to the operating costs. However, the

replacement cost of the seals is also high, and so a tension exists between replacing seals

and running a vessel with worn seals. Usually, seals are run until the sinkage of the bow

approaches 0.3-0.4[m] before being replaced. Typical SESs are designed to have around

1.0 [deg] of trim when on cushion, so the author designed the AIRCAT SES in this

simulation to have 1.0 [deg] of trim when on cushion as well. There was no

superstructure included in the model. Since this thesis was not investigating the effects of

wind on the vessel, the superstructure was not considered important to the study. What

was important was the shape of the hull, particularly near and below the water line, and

the location of the center of buoyancy and the center of mass. The shape of the hull in the

solid model accurately captured the shape of the AIRCAT SES. The center of buoyancy

was determined from the geometry of the submerged hull, which was accurately

modeled. And the location of the center of mass was input by the user as an x-y-z

coordinate, and was input according to guidelines set forth by Trigva Halvorson to reflect

the center of mass of a typical SES of the AIRCAT's size.

29

Figure 3.3 Hull Geometry for AIRCAT with Simplified Bow Seal Geometry

The whole domain, including the water, beach, air, and AIRCAT SES hull, was modeled

as a single part. There was a zero thickness split between the top and bottom parts of the

domain which helped during the meshing process by giving greater control of the mesh

refinement in certain areas like the water free-surface elevation and the shoreline.

Figure 3.4 Isometric View of CFD Domain

30

3.3.Mesh

The mesh was created using ANSYS ICEM. The geometry was imported as a .STEP file,

and the surfaces renamed. Element sizes were then defined for different surfaces, with

smaller elements around the hull and around the water mean free-surface height. A tetra-

dominated mesh was used, meaning the meshing algorithm favored a tetrahedral element

when possible, although it would allow other element types when necessary. The

meshing algorithm used was the Octree method, and the mesh was smoothed iteratively

after it was created. ANSYS 13 had problems running the mesh without having it

collapse, but ANSYS 12 would run it without crashing, so ANSYS 12 was used for this

study.

3.3.1. Boundary Conditions

Once the mesh was created, it was imported into ANSYS CFX, and boundary conditions

were defined. The picture shows some of the boundary conditions used and their

locations. The domain was a long trapezoidal box, with the boat hull close to one end.

Using a volume of fluid (VoF) method, part of the domain was filled with water and the

other part with air. A user defined function was applied at the inlet to create a regular

wave train propagating towards the boat hull. CFX allows the use of the following

boundary conditions.

• Fluid Boundaries

o Inlet- Fluid flows into the domain.

o Outlet- Fluid flows out of the domain.

31

o Opening- Fluid may flow into or out of a domain.

• Solid Boundaries

o Wall-Impenetrable boundary to fluid flow.

o Symmetry Plane- A plane of both geometric and flow symmetry.

Figure 3.5 Boundary Conditions Applied to CFD Model

Figure 3.5 shows the various boundaries of the CFD simulation, and the boundary type

associated with each of them. These boundaries are discussed in detail next.

Back

The back of the domain, comprising the faces WALL1, WALL2, WALL3, and WALL4,

was defined as a symmetry plane which means the flow field is symmetric with respect to

32

the back plane. This was justified because the disturbed flow field generated from the

AIRCAT SES hull did not extend into the back plane.

Bottom

The faces comprising the bottom of the domain representing the ocean floor, BEACH1

and BEACH2, were defined as a no slip smooth wall.

Bowskirt

The bowskirt required three boundary conditions, since the bowskirt was divided into

lower (BOWSKIRT_LOWER), middle (BOWSKIRT_MID), and upper

(BOWSKIRT_UPPER) regions. The bowskirt boundary conditions were all defined as no

slip smooth walls. Mesh motion was activated, tied to the rigid body solution of the

AIRCAT rigid body solution.

Fan Input

Two boundary conditions were required for the aircushion fans. The fans were applied to

faces FAN1 and FAN2. These faces had opening boundary conditions applied with static

pressure conditions. The static pressure would be defined differently for different levels

of blower output, and a wall condition was used for the case of zero blower output.

Mesh motion was activated, tied to the rigid body solution of the AIRCAT rigid body

solution.

33

Front

The front of the domain, faces SYM1-SYM4 and HULLSYM, was also defined as a

symmetry plane, because the AIRCAT SES geometry is symmetric about its center plane

and the flow field was applied at a 0 degree heading, or parallel with the AIRCAT's

symmetry plane. No mesh motion was applied.

Hull

The faces comprising the hull geometry, HULL, STERNSEAL_LOWER,

STERNSEAL_UPPER, and Primitive 2D, were given no slip smooth wall boundary

conditions. Mesh motion was activated, tied to the rigid body solution of the AIRCAT

rigid body solution.

Inflow

The inflow, or inlet, of the domain was the surfaces at which the waves were defined,

INLET1 and INLET2. The waves were defined the horizontal and vertical components of

the water velocity. The equations used were based upon linear wave theory.

Outflow

The outflow of the domain, the face opposite the inflow, was defined as an opening, with

entrainment and a relative pressure defined as the hydrostatic pressure due to the water

depth.

34

Top

The top of the domain, surfaces TOP1 and TOP2, was defined as an opening with

entrainment and a relative pressure of zero pascals. The fluid values were defined by

volume fractions, and air had a value of 1 while water had a value of 0.

3.4.Numerical Methods and Settings

CFX solved the unsteady Navier-Stokes equations in their conservation form (ANSYS

2010). CFX solved the conservation equations using a single system of linear equations,

and all the equations were fully coupled (Westphalen 2008). The equations were

discretized in an unstaggered, collocated way and solved by a multigrid solver.

Every simulation in CFX required a region of fluid flow and/or heat transfer, called a

domain. There could be more than one domain per model, though only one was

necessary. A domain required three things to be defined:

• A region composed of one or more 3D primitives.

• The physical nature of the flow, including specifics such as heat transfer or

buoyancy.

• The properties of the materials comprising the region.

In this model, a single domain was used, comprised of a 3D volume mesh generated with

ICEM. The following settings were defined for this domain.

• Two homogenous fluids were defined, water and air at 25 [C]. The volume of fluid

(VoF) approach was used to fill the domain with air and water at the appropriate

locations. The VoF approach defines a fluid to be present at a location when its

35

volume fraction value at that location is 1, and the fluid is absent at that location

when its volume fraction at the location has a value of 0. In this way, two fluids can

be used to 'fill' a domain by defining their volume fractions as the inverse of each

other, so that when one of the fluids has a value of 1 the other has a value of 0, and

vice versa.

• A buoyancy model was used, with a buoyancy reference density of 1.185 [kg m^-3],

the buoyancy of air at standard atmospheric conditions. Since buoyancy is activated,

the pressure in the momentum equation excludes the hydrostatic gradiant due to the

reference density, in this case the air density.

• Gravity was defined along the z-axis, with a value of -9.81 [m s^-2].

• Mesh deformation was allowed, applied to the regions of motion specified. In this

case, the regions of motion were specified as all the faces comprising the AIRCAT

geometry.

• The mesh stiffness was defined as 1.0 [m^3 s^-1] /(Water.Wall Distance).

• Reference pressure was 1 atmosphere.

• The turbulence model used was the k-ε model, with automatic wall functions. This is

a very prominent and widespread turbulence model. It has been proven to be

numerically robust and stable (ANSYS 2010).

36

3.5.Convergence

3.5.1. Grid Independence Study

To determine the level of mesh refinement necessary to achieve good results, a grid

independence study was conducted. To perform the grid independence study, a

rectangular domain was created with a length 10[m] long by 3[m] tall by 1.5[m] wide.

Applying symmetry conditions to this domain, a 3[m] width is obtained. This domain

was meshed with four different levels of refinement for the grid independent study, and

each mesh was used for a 15[sec] simulation of a regular wave with an amplitude of

0.597[m] and a wavelength of 3.75[m]. The time domain results of the four simulations is

given in figures 3.6 and 3.7 below.

Figure 3.6 Surface Elevation Vs. Time for Four Grids

37

Figure 3.7 Detail of Surface Elevation Vs. Time for Four Grids

There is good agreement between the results of the medium fine mesh and the fine mesh,

so a mesh with a resolution as fine as the medium mesh was used for the AIRCAT SES

simulation studies.

Figure 3.8 Coarse Grid

38

Figure 3.9 Medium Coarse Grid

Figure 3.10 Medium Fine Grid

Figure 3.11 Fine Grid

39

3.6.AIRCAT SES Simulation Results

A simulation of the scale model AIRCAT SES in a transforming sea was set up and run

with ANSYS CFX. Figures 3.12 and 3.13 show the heave and pitch accelerations for the

vessel. This computer model can be run for longer simulation periods, with simulation

times of up to 30-60 seconds being reasonable, and these results could then be used to

predict ship response and wave loadings on an SES vehicle. For this trial simulation only

about 15 seconds of steady state vessel response time was simulated.

Figure 3.12 Heave and Pitch Accelerations from CFD Simulation

40

Figure 3.13 Heave and Pitch Accelerations from CFD Simulation

Below are the tabulated results from one of the physical experiments in which the blower

level was 0%, which is the same as the blower level in the CFD simulation.

Test

12

A ω µ σ

[m/s2,rad/s2,Pa,mm] [rad/s] [m/s2,rad/s2,Pa,mm

]

[m/s2,rad/s2,Pa,mm

]

az 0.124 9.183 -9.781 0.066

gy 0.074 9.666 0.001 0.050

Table 3.1 Results from Physical Experiment

41

3.7.Conclusions

The results from the grid independence study and the trial AIRCAT SES scale model

CFD simulation have reinforced the viability of using commercial CFD code to predict

wave loadings and seakeeping responses of a prototype SES vessel. The results should

closely predict the actual loadings and responses of a physical prototype, without the

expense of building such a prototype until later in the design process.

42

4. DEVELOPING THE PHYSICAL EXPERIMENT

4.1.Overview of Experimental Setup

The scenario that was modeled was a 40[m] SES encountering breaking waves with a

4[m] amplitude. To model this scenario in a wave tank a 1:30 scale model of an SES, the

AIRCAT, was selected. The full sized AIRCAT SES is a German vessel, built to provide

service as a high speed ferry. A 1.2[m] wide by 1.5[m] tall and 19.5[m] long wave tank

was used. The wave tank had a paddle type wavemaker to generate regular waves. The

wavetank also had a 7.3[m]x3.3[deg] beach with a 2.44[m]x6.6[deg] continental shelf.

4.2.Wave Scaling

Since the AIRCAT model was 1:30 scale, the waves needed to be scaled as well. To scale

the waves, the geometry was scaled at the same scale as the model geometry, in this case

1:30 which meant that a 4[m] wave amplitude was represented in the wavetank as a

4[m]/30 or a 13.3[cm] wave amplitude. The geometry scaled directly, but the frequency

required some more manipulations to solve. To begin with, the dispersion relation was

given as:

)(3

2 kdTanhskgk

+=

ρω (4.1)

Where

43

≡

sradinfrequencyangularω

tconsonacceleratilgravitionag tan≡

Lnumberwavek π2

=≡

wavelengthL ≡

tcoefficientensionsurfaces ≡

fluidofdensity≡ρ

depthwaterd ≡

By investigating the order-of-magnitude of the terms on the right hand side of the

dispersion relation, it could be shown that the effects of surface tension was insignificant

for the wave amplitudes of interest in this project, and the dispersion relation thus

simplified:

[ ] )(2 kdTanhgk=ω (4.2)

Using the definition for the wavenumber k, the ratio of the full-scale wave frequency to

the model wave frequency could be expressed as:

)tanh()tanh(

)tanh(2

)tanh(2

)tanh()tanh(

221

112

222

2

111

1

2222

11112

2

21

dkLdkL

dkL

g

dkL

g

dkkgdkkg

===π

π

ωω (4.3)

Note that g1=g2. Also, noting that k1d1= k2d2

2

112 L

Lωω = (4.4)

44

For the case of a 1:30 ratio, our scaled frequency is equal to the full-scale frequency

multiplied by 5.48.

4.3.Wave Tank

The wave tank at SeaTech was 1.2[m] wide by 1.5[m] tall and 19.5[m] long. It was filled

with chlorinated fresh water and had the capability of generating a steady water current

with a volumetric flowrate of 0.74 [m3/s], which is equivalent to approximately

11,740[gal/min]. The wave tank also had a towing carriage with the capacity to travel at

speeds up to 0.6[m/s].

Figure 4.1 Rendering of the Wave Tank

45

Figure 4.2 Wave Tank

4.4.Wavemaker

The wavemaker was a flap style, hinged at the bottom so that the displacement of the flap

is a v-shape.

Figure 4.3 Wavemaker Paddle

46

Figure 4.4 Drive Mechanism for Wavemaker

Dean and Dalrymple provide an excellent overview on the theory of wavemakers in their

book "Water Wave Mechanics". The following discussion follows their outline closely.

Galvin reasoned that the water displaced by a wavemaker paddle should be

approximately equal to the volume of water in the crest of the wave propagated by the

wavemaker. The volume of water in the crest of the wave is given by the equation:

∫ =

2/

0)sin(

2L

kHdxkxH (4.5)

The volume of water displaced by the wavemaker paddle is given by Sh/2. S is the

wavemaker stroke, H is the wave height, and h is the water depth. Setting the two

equations equal to each other and simplifying,

47

ππ 222HL

L

HkHSh

=== (4.6)

2kh

SH

= (4.7)

This simple relation is accurate for values of kh up to about 2~2.5. Above this, and the

ratio tends to overestimate the H/S ratio. A more robust equation for the H/S ratio of a

flap type wavemaker is given as

hkhkhkhkhk

hkhk

SH

pp

ppp

p

p

2)2sinh(1)cosh()sinh(sinh

4+

+−

= (4.8)

Where kp is the wavenumber associated with a progressive wave.

For this project, the water depth in the wavetank was 0.8[m] and the wavenumber was

1.2[rad/m], so kh=0.96. Since this value of kh is less than 2, the ratio of H/S is very close

to kh/2 or 0.96/2, about 0.5. This means that for a wave height of 12.7[cm] the

wavemaker paddle must travel 25.6[cm]. Note that this distance of travel is at the mean

water surface elevation.

4.5.Beach

4.5.1. Background

To create breaking waves for the experimental validation study, it was necessary to

design a beach for the existing wavetank. The wavetank at FAU SeaTech was 1.2[m]

wide by 1.5[m] tall and 19.5[m] long. The goal was to build a beach that would allow a

48

wave to break on the bow of the AIRCAT model. The model would be placed in the

wavetank, a wave train generated, and the response of the AIRCAT and the forces

exerted on its bow skirt would be recorded and analyzed. To accomplish this, the wave

needed to break far enough from the shoreline so that the AIRCAT could float without

touching the beach. The water depth must become shallow enough to cause the wave to

break, but still leave enough depth for the model to float. A 7.3[m] beach section with a

slope of 3.4 [deg] was used, with a 2.44[m] x 6.6[deg] 'continental shelf' portion.

4.5.2. Design

The beach was designed from materials that are stable in water and very resistant to

corrosion. The design needed to be modular to make it easy to install and remove the

beach assembly from the wave tank. It needed to store compactly. It was designed to be

sturdy enough to handle waves with 6" amplitudes, but with no support structure above

the beach surface. By keeping all the supporting members below the beach surface, any

interaction between the waves and support structure was eliminated. This allowed for

waves with more two-dimensional behavior. The main structure of the beach was a sub-

frame constructed of type E fiberglass channel. The pieces were attached with L-brackets

made from UHMW plastic using stainless steel screws. Two 4'x8' sub-frames and two

4'x12' sub-frames were constructed. Over this sub-frame was placed UHMW sheet. At

the very end of the beach pultruded fiberglass grating was used to cover the sub-frame.

This helped to eliminate wave reflection. The leg system was designed to allow the beach

angle to be adjusted. The leg system also needed to resist vertical forces in both the

upward and downward directions, since there was no support structure above the beach to

49

handle upward forces. These objectives were realized by using telescoping fiberglass

tubes with quick-release clamps in the middle and suction cups on the bottom end. The

quick-release clamp allowed the telescoping tubes to be slid into or out of each other as

necessary to accommodate changes in height induced by changes in the angle of the

beach. The suction cups prevented upward forces in addition to downward forces. The

legs were spaced approximately every 4 feet.

Figure 4.5 Beach Sub-Frame Assembly

50

Figure 4.6 Adjustable Leg for Beach Assembly

Figure 4.7 Beach in Place

51

4.6.AIRCAT

A scale model SES was developed into an experimental platform by Nikolas Kouvaras, a

graduate student at FAU. The original model was built at the

National Technical University of Athens as a thesis subject. The model parameters are

given in the table.

Name AIRCAT

Type Surface Effect Ship

Scale 1:30

LOA 1.210 [m] Length Overall

LBP 1.030 [m] Length Between Perpendiculars

B 0.400 [m] Breadth

D 0.135 [m] Draft

Δ 8.4[kg] Displacement

52

Figure 4.8 AIRCAT SES 1:30 Scale Model

This model was instrumented with an IMU (Inertial Measurement Unit) to measure the

pitch, heave, and roll; pressure sensors to measure the pressure in the air cushion; and

flex sensors to measure the displacement of the bow skirt. The vehicle can communicate

via a serial connection or wirelessly through a transceiver.

4.7.Wave Gages.

The water elevation was measured with four Wave Staff III sensors provided by Ocean

Sensor Systems. These sensors measured the water depth in the wave tank, and this

directly corresponded to the free surface height of the water. The water surface elevation

was recorded in the time domain, and this information is used to determine the wave

amplitude, frequency, and wavelength. Figure 4.9 below shows 10[s] of wave data from

53

one of the wave gage sensors. From close visual inspection, it can be seen that the water

surface goes through 5 cycles in 5[s], so the wave period is 1[s] and the frequency is

1[Hz] or 6.3[rad/s]. A more accurate method for determining the wave frequency is using

a Fast Fourier Tranformation (FFT). One of the benefits of using an FFT is that it will

often find underlying frequencies that a visual inspection would miss.

Figure 4.9 Data from Wave Gage

The FFT is given by:

1,...,2,1,0,21

0−=⋅=

⋅⋅−−

=∑ NkexX N

ikjN

iik

π

(4.8)

This was applied to the wave elevation data yielding the wave elevation frequency

spectrum from which the dominant wave frequency could be easily determined.

The wave gages were each 500[mm] in length, which was discretized into 212 sections for

a total resolution of 500/(212-1)[mm], which was about 0.12[mm]. The wave amplitudes

54

in this study ranged from 50-130[mm], so the discretization error was on the order of 0.1-

0.25 percent of the wave amplitude.

Figure 4.10 Wave Gages

4.8.Aircushion pressure

The pressure in the aircushion was monitored by a differential pressure sensor; one input

measured atmospheric pressure and the other input measured the pressure inside the

cushion. By subtracting the atmospheric pressure from the aircushion pressure, the

aircushion gage pressure was determined. Gage pressure is the total pressure minus the

atmospheric pressure, GageAtmTotal PPP =− . This was important because atmospheric

pressure is constantly varying and the gage pressure removed the effects of this variance.

The pressure in the cushion was in the range of 200-400 [Pa], so the effect of atmospheric

variations would completely overpower the pressure readings. The pressure sensor used

55

was an SDP2000-L from Sensirion, which had a range of 0-3500[Pa] with a resolution of

1[Pa].

Figure 4.11 Pressure Sensor

4.9.Pitch and Heave

The seakeeping motions of pitch and heave were recorded by using an Attitude and

Heading Reference System [AHRS] from VectorNav, the VM-100. The VM-100 was an

Attitude and Heading Reference System [AHRS], which was similar to an IMU but

instead of providing only raw acceleration data an AHRS not only measured these

accelerations but used this information to solve for the attitude and heading of the unit.

These are commonly used in aircraft to replace mechanical gyroscope systems.

56

Figure 4.12 IMU Sensor

4.10. Bowskirt deflection

The deflection of the bow skirt was measured using flex sensors. These sensors changed

resistance in proportion to how much they were deflected. Since the bow skirt was

deflected when waves impacted upon it, these flex sensors could be used to indirectly

measure the wave loading on the bow skirt. The flex sensors used on the AIRCAT model

were manufactured by Spectra Symbol, and were connected to the microcontroller

through an Analog to Digital Converter (ADC) circuit.

57

Figure 4.13 Bowskirt Fingerseal

Figure 4.14 Flex Sensors to Measure Bowskirt Deflection

58

4.11. Vehicle Speed

To calculate the speed of the vehicle, video footage of the tests was analyzed to calculate

the time required for the vehicle to traverse a known distance. The vertical supports of the

wavetank were 4[ft] apart, center to center. This distance divided by the time required for

the vehicle to traverse the distance yielded the velocity.

][sTimeElapsedT = (4.9)

The velocity of the vehicle can be calculated from the time taken to cross this known

distance of 4[ft] (1.2192[m]) according to the equation:

TmVelocity ][2192.1

= (4.10)

Figure 4.15 Video Frames Used to Calculate Vessels Speed

Figure 4.15 shows two frames from a video of an experiment, with the vehicle 1.2192

[m] apart (notice the bow location in each frame). The pictures are 1.16[s] apart. Thus,

the speed of the vehicle in this experiment was about 1.1[m/s].

59

4.12. Lamboley Swing Test and AIRCAT Radius of Gyration

When conducting the model tests, it was necessary to scale the model geometrically and

ballast it so that the waterline of the model reflected the waterline of the full scale

prototype. Additionally, when conducting tests in waves, it was necessary to ballast the

model in such a way that its radius of gyration-or gyradius-reflected the gyradius of the

full scale prototype. To calculate the gyradius of the scale model AIRCAT SES, a

Lamboley swing test was performed.

Figure 4.16 Example of a Lamboley Swing Test Rig

The Lamboley test was developed by Gilbert Lamboley as a method for determining the

gyradius of a vessel by measuring its period of oscillation when pivoted about two axes a

known distance apart. Measuring the two periods allowed one to solve for the two

unknowns, d (vertical distance from pivot to model center of gravity) and k5 (pitch

gyradius).

( )dgkdT

25

2

1 2 += π (4.11)

( )( )xdg

kxdT−+−

=2

52

2 2π (4.12)

60

Where

T1= swing period [s]

T2= swing period [s]

d= vertical distance from pivot to model center of gravity [m]

x= vertical distance between pivots [m]

k5= pitch gyradius [m]

Solving for an intermediate quantity, c, allowed us to easily express the equations for d

and k5.

xgc 24π

= (4.13)

( )( ) 2

12

12

2

22

+−+

=TTc

cTxd (4.14)

( ) 2215 ddxcTk −= (4.15)

For the AIRCAT SES, the results for the Lamboley test gave a longitudinal radius of

gyration of 0.289 [m]. The traditionally expected gyradius value for ships was about 25%

of the length between perpendiculars, Lpp. The Lpp of the AIRCAT model is 1.03[m], and

25% of 1.03[m] is 0.2575 [m]. The calculated value of 0.289[m] was 35.6% of the Lpp, or

within 29% of the expected value for the gyradius of the AIRCAT model.

4.13. X-direction Force transducer (For Stationary Tests)

For the stationary tests where the vehicle was stationary facing into the breaking waves,

the AIRCAT model was held in place with a wire running from the bow of the vessel to a

bracket approximately 3[m] away. This wire was connected to a force transducer to

61

record the force required to keep the AIRCAT from being pushed back by the waves

crashing against its bow. The force transducer was an Omega 0-100[lbf] uni-axial unit.

The unit was calibrated by the author and could be accurately and repeatably read with

0.1[lbf] accuracy, so the charts and force readings from this unit are given with accuracy

of 0.1[lbf]. The response of the unit was very close to linear, with the following table and

chart showing the voltage measured plotted against the force applied. The slope of the

voltage response to the load force was 0.0926 [V/lbf], with a standard deviation for the

slope of 0.0018. The inverse of the slope is 10.8042 [lbf/V].

Figure 4.17 Load Cell Calibration Data

The force measured by this transducer was a direct measurement of the horizontal forces

imparted to the craft by the waves, and related directly to the surge acceleration that

would have been experienced by the model if it had not been constrained by the wire

connected to its bow.

62

5. RESULTS OF THE PHYSICAL EXPERIMENTS

5.1.Description of Experiments

To test the AIRCAT SES vehicle's seakeeping response to wave loading, it was necessary

to determine which variables would be fixed and which would be varied. It was decided

to use three different wave conditions, characterized by the amplitude and frequency of

the waves. For each set of wave conditions, two parameters were varied: blower level

(aircushion pressure) and vessel speed. Three blower levels were used, 00% blower, 31%

blower, and 100% blower. Three vessel speeds were also used, slow, medium, and high

speeds. With three speeds at each of three blower levels, a total of 9 cases needed to be

examined for each of the three wave conditions. It was decided to run three experiments

at each of these 9 cases, for statistical reasons, so a total of 27 experiments was conducted

for each of the three wave conditions for a grand total of 81 experiments. Fifteen

parameters were recorded during each experiment.

• 3-Axis linear accelerations (Surge, Sway, Heave)

• 3-Axis magnetic field measurements

• 3-axis angular accelerations (Roll, Pitch, Yaw)

• Aircushion pressure

• Lower bowskirt deflection

• Upper bowskirt deflection

63

• Surface elevation at three locations

Amp: 2.0 [cm] CASE 1

ω: 9.42 [rad/s]

SLW SPEED Run 1 Run 2 Run 3

BL 00 1 2 3

BL 31 4 5 6

BL 100 7 8 9

MED SPEED Run 1 Run 2 Run 3

BL 00 10 11 12

BL 31 13 14 15

BL 100 16 17 18

HGH SPEED Run 1 Run 2 Run 3

BL 00 19 20 21

BL 31 22 23 24

BL 100 25 26 27

Amp: 3.5 [cm] CASE 2 ω: 7.85 [rad/s]

SLW SPEED Run 1 Run 2 Run 3

BL 00 28 29 30

BL 31 31 32 33

BL 100 34 35 36


64

BL 00 37 38 39

BL 31 40 41 42

BL 100 43 44 45

HGH SPEED Run 1 Run 2 Run 3

BL 00 46 47 48

BL 31 49 50 51

BL 100 52 53 54

Amp: 4.0 [cm] CASE 3 ω: 6.28 [rad/s]

SLOW

SPEED

Run 1 Run 2 Run 3

BL 00 55 56 57

BL 31 58 59 60

BL 100 61 62 63


BL 00 64 65 66

BL 31 67 68 69

BL 100 70 71 72

HIGH SPEED Run 1 Run 2 Run 3

BL 00 73 74 75

BL 31 76 77 78

BL 100 79 80 81

65

5.2.Analysis Tools

As part of his master's thesis, Nikolas Kouvaras developed MATLAB code to be used in

analyzing the AIRCAT SES's seakeeping responses as recorded by the data logging

system he developed for the AIRCAT platform (Kouvaras 2010). This code was modified

for use with the data recorded from these 81 experiments.

5.2.1. Parameters Examined

The parameters that this study examined were the pitch, heave, and surface elevation.

From examination of the surface elevation, the input to the AIRCAT SES vessel could be

determined, namely the amplitude and frequency of the waves to which the vessel was

subjected.

5.2.2. Steady Stave Vs. Transient Responses

A steady state case is one in which things are in a state which would continue

indefinitely, whereas a transient state is a changing state. Since this study primarily

focused on the vessel response to wave loadings in a developing sea, the results would be

considered transient, because as the vessel traverses a transforming sea it would

encounter waves of differing amplitude and wavelength, thus the inputs to the system (in

this case the AIRCAT SES vessel) are not steady with time but are changing with time.

5.2.3. Time Domain Vs. Frequency Domain

For some of the analysis, the frequency domain was used to analyze the responses. The

benefits of using the frequency domain is that it enabled the comparison of the frequency

66

of the responses, and this could be compared to the frequency of excitation or the 'forcing

function', in this case the waves.

5.3.Stationary Vessel

Some tests were run with the vessel fixed in place by a cable to prevent its backward

motion. In total, nine runs were conducted. The vessel's forward motion was resisted by

the aircushion of the vehicle and the action of the waves breaking on its bow. These

stationary tests were run to maintain the vessel in an area of breaking waves. During the

non-stationary tests, the vehicle advanced through the surf zone and quickly left the

region of breaking waves.

5.3.1. Wave data

The wave data was analyzed using MATLAB. The following chart shows one of the

frequency spectrum graphs of the wave frequency spectrum. The dominant frequency of

test 5 was 6.54[rad/s], which is 1.04[Hz]. This value corresponded closely to the

wavemaker's target frequency of 1.00[Hz], so it is the value that would be expected.

Figure 5.1 Double-Sided FFT Graph of Wave Frequency

67

The dominant frequencies for the experiments are given in the following table.

Test Rad/sec Hz T [sec]

1 7.2387 1.152075 0.867999

2 6.6976 1.065956 0.938125

3 6.6496 1.058317 0.944897

4 6.2741 0.998554 1.001448

5 6.5378 1.040523 0.961055

6 6.5111 1.036274 0.964996

7 6.6622 1.060322 0.94311

8 6.7617 1.076158 0.929232

9 6.4985 1.034268 0.966867

The amplitude, deep water wave number, and deep water wavelength was determined for

each case, with the results given in the following table.

k [rad/m] λ [m] A [m] T(timesteps)

5.3414 1.1763 0.0571 26

4.5727 1.3741 0.0614 28

4.5073 1.394 0.0586 28

4.0127 1.5658 0.0557 30

4.3571 1.4421 0.0563 29

4.3215 1.4539 0.0701 29

4.5244 1.3887 0.0574 28

4.6607 1.3481 0.0655 28

4.3049 1.4596 0.0737 29

68

Figure 5.2 Time Series of Water surface Elevation

5.3.2. Vehicle Data

Figure 5.3 Vehicle Data Time Series for Stationary Vehicle Experiment 5

The figure above shows the time series data from the IMU onboard the AIRCAT. Row

one shows the surge acceleration (ax). Row 2, the heave acceleration (az). Row 3, the

69

pitch acceleration (gy). Row 4, the roll acceleration (gx). Row 5, the gage pressure inside

the aircushion (Pcushion). And rows 6 and 7 show the deflection of flex sensor 1 and 2,

respectively. Inspection of the figure above reveals that flex sensor 2 does not appear to

have been working for this run. The pressure sensor data also appears to have a high level

of noise. All the data channels seemed to be affected when the blower motor was

running, with the signals appearing to have more noise added to them when the blower

was running. This noise could have been induced from the current running to the blower

motor or by the vibrations caused by the blower, or both.

5.3.3. Pitch response

Conducting a power spectral density analysis on the pitch data (gy), the dominant

response frequency is determined to be 6.43[rad/s]. This is quite close to the wave

frequency of 6.54[rad/s], so the vehicle response mirrors the wave input at a frequency

1% lower than that of the wave frequency.

Figure 5.4 Pitch Power Spectrum for Stationary Vehicle Experiment 5

70

5.3.4. X-Direction Force Transducer

The X-direction force transducer measured the force required to keep the AIRCAT SES

model from being pushed backwards by the force of the waves breaking against it. The

time series of the force measured against time are given for experiment 5. Close

inspection of the data revealed that the force required to keep the AIRCAT SES from

moving backwards was less when the blower was at 31% than when the blower was at

0%. This is what would be expected, since the vehicle's draft is reduced when it is on

cushion.

Figure 5.5 Time Series of X-direction Force Transducer

5.4.Vessel in Forward Motion

When the vessel was in forward motion, it was encountering a developing sea due to the

presence of the beach. As discussed in Chapter 1, when a wave advances into water of

decreasing depth, its wavelength decreases and amplitude increases until it reaches a

point at which the wave crest is unstable and collapses, at which point the wave is said to

71

break. This study focused on the seakeeping responses of an SES vessel in developing

seas, so these experiments with the AIRCAT SES advancing into a developing sea were

of the most interest.

5.5.Time Series

The time series data for the vehicle sensors and the wave gages are given in the following

sections. The following figures show the time series data for the vehicle sensors; the

surge, heave, pitch, pressure, deflection 1, and deflection 2. The time series of the surface

elevation at two points are also given in the following figures, the first point upstream of

the vessel and the second point was near the point where the waves were breaking.

Test

00

A ω µ σ

[m/s2,rad/s2,Pa,mm] [rad/s] [m/s2,rad/s2,Pa,mm] [m/s2,rad/s2,Pa,mm]

ax 0.003 0.471 0.001 0.002

az 0.010 11.624 -9.788 0.005

gy 0.003 1.571 0.000 0.002

P0 8.624 9.739 0.238 4.629

d1 0.885 62.832 0.056 0.431

d2 1.563 32.830 0.116 0.787

η1 0.06 27.33 N/A N/A

η2 0.07 42.73 N/A N/A

Table 5.1 Test 00 Vehicle and Wave Data

72

Figure 5.6 Test 00 Wave Elevation Data Time Series

Figure 5.7 Test 00 Vehicle Data Time Series

Test

01

A ω µ σ


73

ax 10.340 11.310 -0.085 0.212

az 0.256 11.310 -9.780 0.158

gy 0.115 11.310 -0.005 0.084

P0 8.191 12.881 0.064 4.911

d1 1.362 40.841 -46.631 0.962

d2 2.067 11.310 -57.663 1.284

η1 16.23 9.42 N/A N/A

η2 4.84 9.42 N/A N/A



74


Test

02

A ω µ σ


ax 0.338 11.624 -0.078 0.210

az 0.307 11.624 -9.813 0.183

gy 0.119 11.624 -0.003 0.086

P0 7.774 27.018 0.339 5.246

d1 1.258 24.190 -46.871 0.862

d2 9.399 0.314 -57.855 1.823

η1 16.85 9.42 N/A N/A

η2 7.67 9.42 N/A N/A


75



76

Test

03

A ω µ σ


ax 0.317 10.681 -0.084 0.203

az 0.256 10.681 -9.790 0.154

gy 0.109 10.681 -0.002 0.077

P0 7.219 28.274 0.300 4.759

d1 1.227 57.177 -46.669 0.870

d2 2.086 10.996 -58.226 1.266

η1 16.72 9.42 N/A N/A

η2 5.67 9.42 N/A N/A



77


Test

04

A ω µ σ


ax 0.296 10.681 0.244 0.158

az 1.885 10.681 -9.831 1.064

gy 0.328 10.681 -0.003 0.227

P0 8.928 5.655 -0.746 4.814

d1 0.975 54.664 -46.463 0.627

d2 1.584 17.593 -60.009 0.961

η1 0.03 0.31 N/A N/A

η2 0.09 0.31 N/A N/A


78



79

Test

05

A ω µ σ


ax 0.308 11.938 0.265 0.173

az 1.774 11.938 -9.830 0.983

gy 0.356 11.938 -0.002 0.248

P0 7.121 24.504 -0.177 4.782

d1 0.857 37.385 -46.490 0.630

d2 1.367 61.575 -60.927 0.919

η1 17.79 9.42 N/A N/A

η2 8.24 9.42 N/A N/A



80


Test

06

A ω µ σ


ax 0.273 11.624 0.266 0.156

az 1.733 11.624 -9.846 0.955

gy 0.320 11.624 -0.002 0.225

P0 6.958 34.558 -0.014 4.603

d1 1.742 2.513 -46.539 0.599

d2 1.742 2.513 -60.725 1.068

η1 17.52 9.42 N/A N/A

η2 10.76 9.42 N/A N/A


81



82

Test

07

A ω µ σ


ax 0.486 11.938 0.486 0.282

az 2.756 11.938 -9.653 1.644

gy 0.426 11.938 -0.001 0.307

P0 17.639 0.314 2.299 7.903

d1 0.875 62.832 -44.211 0.603

d2 4.537 0.628 -56.951 1.186

η1 17.06 9.42 N/A N/A

η2 17.73 9.42 N/A N/A



83


Test

08

A ω µ σ


ax 0.506 13.509 0.469 0.300

az 3.420 13.195 -9.611 2.110

gy 0.432 13.195 0.002 0.314

P0 11.339 13.509 1.476 7.099

d1 1.090 8.168 -44.138 0.521

d2 1.366 13.195 -57.193 0.849

η1 18.72 9.42 N/A N/A

η2 16.97 9.42 N/A N/A


84



85

Test

09

A ω µ σ


ax 0.487 11.624 0.475 0.285

az 2.928 11.624 -9.632 1.744

gy 0.413 11.624 0.001 0.285

P0 16.986 0.314 1.593 6.682

d1 0.761 45.553 -44.079 0.556

d2 8.967 0.314 -56.716 2.427

η1 20.37 9.42 N/A N/A

η2 10.72 9.42 N/A N/A



86


Test

10

A ω µ σ


ax 0.362 13.509 -0.095 0.262

az 0.336 13.509 -9.781 0.200

gy 0.135 13.509 0.001 0.096

P0 7.154 62.832 -0.112 4.811

d1 1.403 13.823 -46.942 0.788

d2 7.886 0.314 -56.516 1.579

η1 16.60 9.42 N/A N/A

η2 8.34 9.42 N/A N/A


87



88

Test

11

A ω µ σ


ax 0.303 12.881 -0.116 0.191

az 0.316 12.881 -9.800 0.181

gy 0.127 12.881 0.001 0.089

P0 7.578 62.832 -0.262 4.739

d1 1.553 12.881 -47.012 0.845

d2 9.831 0.314 -56.591 1.851

η1 17.39 9.42 N/A N/A

η2 8.11 9.42 N/A N/A



89


Test

12

A ω µ σ


ax 0.200 9.666 -0.055 0.135

az 0.124 9.183 -9.781 0.066

gy 0.074 9.666 0.001 0.050

P0 7.287 55.582 -0.309 4.505

d1 1.213 56.549 -46.854 0.820

d2 2.875 9.666 -59.705 1.489

η1 17.48 9.42 N/A N/A

η2 9.13 9.42 N/A N/A


90



91

Test

13

A ω µ σ


ax 0.412 12.566 0.178 0.302

az 2.371 12.566 -9.787 1.286

gy 0.374 12.566 0.000 0.264

P0 6.566 55.606 -0.393 4.225

d1 1.458 10.681 -46.394 0.755

d2 12.748 0.314 -60.949 2.141

η1 16.45 9.42 N/A N/A

η2 14.44 9.42 N/A N/A



92


Test

14

A ω µ σ


ax 0.324 9.425 -0.217 0.216

az 0.202 9.425 -9.800 0.119

gy 0.110 9.425 0.000 0.075

P0 8.026 10.053 -0.053 4.382

d1 1.023 19.478 -46.465 0.690

d2 2.128 9.425 -59.778 1.119

η1 16.68 9.42 N/A N/A

η2 7.16 9.42 N/A N/A


93



94

Test

15

A ω µ σ


ax 0.348 13.509 0.362 0.252

az 2.482 13.509 -9.762 1.373

gy 0.325 13.509 0.000 0.229

P0 6.892 58.748 -0.948 4.642

d1 0.933 31.416 -46.219 0.610

d2 4.429 0.628 -60.818 1.037

η1 0.94 6.28 N/A N/A

η2 0.92 0.31 N/A N/A



95


Test

16

A ω µ σ


ax 0.252 9.874 -0.031 0.174

az 0.245 9.874 -9.680 0.151

gy 0.102 9.874 0.001 0.071

P0 15.026 2.693 -3.534 6.504

d1 0.899 26.030 -44.244 0.613

d2 3.673 0.898 -51.257 1.657

η1 19.51 9.42 N/A N/A

η2 20.39 9.42 N/A N/A

Table 5.17 Table 16 Vehicle and Wave Data

96



97

Test

17

A ω µ σ


ax 0.417 17.593 0.641 0.272

az 4.127 17.593 -9.684 2.442

gy 0.204 17.593 0.000 0.138

P0 14.300 17.593 0.091 8.187

d1 0.747 52.150 -44.221 0.533

d2 1.921 17.593 -55.826 1.497

η1 20.61 9.42 N/A N/A

η2 12.72 9.42 N/A N/A



98


Test

18

A ω µ σ


ax 0.861 51.522 0.527 0.982

az 4.142 17.593 -9.775 2.398

gy 0.243 17.593 0.003 0.199

P0 11.498 35.186 0.731 7.778

d1 1.429 3.142 -44.236 0.516

d2 4.321 0.628 -56.195 1.537

η1 19.37 9.42 N/A N/A

η2 10.18 9.42 N/A N/A


99



100

Test

19

A ω µ σ


ax 0.290 9.425 -0.029 0.190

az 0.122 9.425 -9.773 0.066

gy 0.117 9.425 0.001 0.081

P0 7.480 53.721 0.319 4.946

d1 1.245 13.823 -46.795 0.737

d2 2.690 9.425 -59.564 1.372

η1 18.65 9.42 N/A N/A

η2 10.38 9.42 N/A N/A



101


Test

20

A ω µ σ


ax 0.327 14.362 -0.027 0.213

az 0.335 14.362 -9.774 0.195

gy 0.119 13.913 0.001 0.082

P0 9.408 6.732 -0.025 4.988

d1 4.701 0.449 -47.453 0.948

d2 6.914 0.449 -56.068 1.513

η1 18.62 9.42 N/A N/A

η2 10.06 9.42 N/A N/A


102



103

Test

21

A ω µ σ


ax 1.011 17.593 0.316 1.485

az 0.919 18.850 -9.725 0.790

gy 0.153 18.850 -0.009 0.112

P0 20.971 18.850 3.514 14.636

d1 5.255 0.628 -46.501 2.460

d2 6.914 0.628 -45.357 1.978

η1 18.31 9.42 N/A N/A

η2 16.73 9.42 N/A N/A



104


Test

22

A ω µ σ


ax 0.649 2.094 0.984 0.295

az 1.962 18.850 -9.656 1.168

gy 0.159 23.038 -0.014 0.114

P0 15.135 20.944 18.479 10.273

d1 1.072 20.944 -40.404 0.724

d2 8.211 1.047 -47.162 2.683

η1 18.68 9.42 N/A N/A

η2 15.43 9.42 N/A N/A


105



106

Test

23

A ω µ σ


ax 0.353 18.064 0.889 0.272

az 2.562 18.064 -9.683 1.517

gy 0.151 18.064 -0.009 0.104

P0 12.331 36.914 0.878 7.600

d1 1.106 21.206 -40.257 0.752

d2 6.914 0.785 -49.075 2.947

η1 19.68 9.42 N/A N/A

η2 13.82 9.42 N/A N/A



107


Test

24

A ω µ σ


ax 0.364 19.635 0.923 0.291

az 2.215 19.635 -9.625 1.279

gy 0.155 14.137 -0.008 0.112

P0 12.168 32.987 1.253 7.601

d1 1.452 20.420 -40.484 1.060

d2 9.075 0.785 -47.963 3.602

η1 19.57 9.42 N/A N/A

η2 13.83 9.42 N/A N/A


108



109

Test

25

A ω µ σ


ax 0.823 3.142 0.910 0.387

az 3.118 16.493 -9.549 1.906

gy 0.322 13.352 -0.003 0.211

P0 12.319 17.279 0.960 7.795

d1 0.998 17.279 -44.198 0.668

d2 10.587 0.785 -52.530 3.637

η1 22.24 8.17 N/A N/A

η2 16.49 8.48 N/A N/A



110


Test

26

A ω µ σ


ax 3.099 1.257 0.520 0.709

az 2.543 30.159 -9.594 1.557

gy 0.274 12.566 0.013 0.211

P0 12.485 17.593 -1.712 10.013

d1 1.936 5.027 -44.356 0.639

d2 6.050 1.257 -51.412 2.646

η1 11.21 7.85 N/A N/A

η2 11.11 5.97 N/A N/A


111



112

Test

27

A ω µ σ


ax 0.325 12.566 0.405 0.187

az 1.798 27.826 -9.750 1.173

gy 0.257 8.976 0.003 0.156

P0 16.463 7.181 2.849 7.913

d1 0.603 22.440 -44.134 0.431

d2 3.025 0.898 -54.816 0.916

η1 21.52 9.74 N/A N/A

η2 14.18 9.74 N/A N/A



113


Test

28

A ω µ σ


ax 0.440 7.121 -0.060 0.284

az 0.301 7.121 -9.813 0.146

gy 0.203 6.702 0.001 0.137

P0 47.038 0.419 7.608 16.090

d1 0.576 23.876 -44.177 0.389

d2 1.325 46.496 -54.135 0.866

η1 1.32 47.12 N/A N/A

η2 1.94 47.12 N/A N/A


114



115

Test

29

A ω µ σ


ax 0.440 7.121 -0.060 0.284

az 0.301 7.121 -9.813 0.146

gy 0.203 6.702 0.001 0.137

P0 47.038 0.419 7.608 16.090

d1 0.576 23.876 -44.177 0.389

d2 1.325 46.496 -54.135 0.866

η1 1.32 47.12 N/A N/A

η2 1.94 47.12 N/A N/A



116


Test

30

A ω µ σ


ax 0.808 9.802 -0.068 0.450

az 1.138 9.802 -9.737 0.586

gy 0.272 9.802 -0.001 0.186

P0 71.260 9.802 6.472 37.519

d1 3.468 9.802 -46.701 2.334

d2 5.244 9.802 -44.986 3.781

η1 35.62 7.85 N/A N/A

η2 29.54 7.85 N/A N/A


117



118

Test

31

A ω µ σ


ax 0.504 9.739 0.310 0.314

az 2.293 9.425 -9.595 1.077

gy 0.379 9.425 0.002 0.236

P0 45.698 19.164 79.911 38.877

d1 3.042 0.314 -44.961 0.800

d2 10.479 0.314 -50.768 5.149

η1 32.80 7.85 N/A N/A

η2 32.56 7.85 N/A N/A



119


Test

32

A ω µ σ


ax 0.623 9.739 0.303 0.395

az 2.546 9.739 -9.616 1.150

gy 0.520 9.739 0.001 0.321

P0 84.276 0.314 20.852 35.014

d1 1.817 9.739 -45.404 1.100

d2 9.538 9.739 -41.619 6.589

η1 33.47 7.85 N/A N/A

η2 34.34 7.85 N/A N/A


120



121

Test

33

A ω µ σ


ax 0.648 9.739 0.310 0.397

az 1.914 19.478 -9.651 1.108

gy 0.500 9.739 -0.002 0.311

P0 86.235 0.314 58.940 36.843

d1 1.666 9.739 -45.321 0.968

d2 8.365 9.739 -42.443 5.901

η1 33.47 7.85 N/A N/A

η2 30.46 7.85 N/A N/A



122


Test

34

A ω µ σ


ax 0.209 6.283 -0.073 0.182

az 0.138 5.969 -9.715 0.093

gy 0.000 0.000 -0.001 0.142

P0 6.860 51.836 -0.190 4.353

d1 0.923 40.527 -43.532 0.622

d2 4.537 0.314 -50.840 1.285

η1 27.35 7.85 N/A N/A

η2 31.69 7.85 N/A N/A


123



124

Test

35

A ω µ σ


ax 0.483 9.425 0.306 0.304

az 3.084 9.425 -9.683 1.612

gy 0.471 8.901 -0.005 0.318

P0 24.172 1.571 6.436 10.614

d1 2.074 0.524 -43.747 0.581

d2 5.834 0.524 -53.214 1.551

η1 1.67 1.57 N/A N/A

η2 1.57 26.39 N/A N/A



125


Test

36

A ω µ σ


ax 0.681 9.425 0.239 0.376

az 3.684 18.535 -9.626 2.377

gy 0.636 9.425 0.002 0.411

P0 38.545 0.314 5.768 14.810

d1 1.936 0.314 -43.818 0.521

d2 6.698 0.314 -53.297 2.568

η1 33.12 7.85 N/A N/A

η2 34.59 7.85 N/A N/A


126



127

Test

37

A ω µ σ


ax 0.330 11.729 -0.063 0.451

az 1.798 23.876 -9.720 0.492

gy 0.274 11.729 0.000 0.173

P0 93.349 11.729 -0.571 50.533

d1 3.234 11.729 -48.009 2.216

d2 8.643 0.419 -44.241 3.728

η1 33.34 7.85 N/A N/A

η2 32.32 7.85 N/A N/A



128


Test

38

A ω µ σ


ax 0.727 12.566 -0.033 0.435

az 0.908 24.609 -9.744 0.596

gy 0.270 12.566 0.001 0.167

P0 106.406 12.566 -2.459 61.377

d1 3.275 12.566 -48.515 2.205

d2 10.803 0.524 -41.644 3.962

η1 27.35 7.85 N/A N/A

η2 28.38 7.85 N/A N/A


129



130

Test

39

A ω µ σ


ax 0.813 12.566 -0.035 0.469

az 1.253 12.566 -9.728 0.710

gy 0.282 12.566 -0.007 0.181

P0 103.322 12.566 -9.134 65.299

d1 3.085 12.566 -48.835 2.131

d2 7.828 12.566 -34.880 5.640

η1 35.05 7.85 N/A N/A

η2 28.16 7.85 N/A N/A



131


Test

40

A ω µ σ


ax 0.649 13.138 0.476 0.415

az 2.672 13.138 -9.664 1.448

gy 0.142 0.000 -0.001 0.142

P0 32.229 13.138 18.305 18.473

d1 2.010 13.138 -44.989 1.394

d2 5.085 13.138 -46.024 3.343

η1 38.13 8.09 N/A N/A

η2 33.79 8.09 N/A N/A


132



133

Test

41

A ω µ σ


ax 0.649 13.138 0.476 0.415

az 2.672 13.138 -9.664 1.448

gy 0.528 13.138 0.003 0.338

P0 32.229 0.000 18.305 18.473

d1 2.010 13.138 -44.989 1.394

d2 5.085 13.138 -46.024 3.343

η1 33.07 7.85 N/A N/A

η2 30.02 7.85 N/A N/A



134


Test

42

A ω µ σ


ax 0.649 13.138 0.476 0.415

az 2.672 13.138 -9.664 1.448

gy 0.528 13.138 0.003 0.338

P0 32.229 13.138 18.305 18.473

d1 2.010 13.138 -44.989 1.394

d2 5.085 13.138 -46.024 3.343

η1 34.00 7.85 N/A N/A

η2 32.93 7.85 N/A N/A


135



136

Test

43

A ω µ σ


ax 0.992 12.566 0.579 0.540

az 5.368 12.566 -9.704 3.056

gy 0.784 12.566 -0.022 0.481

P0 33.670 12.566 7.930 19.208

d1 0.975 23.876 -44.074 0.662

d2 3.042 12.566 -51.496 1.751

η1 31.54 7.85 N/A N/A

η2 36.63 7.85 N/A N/A



137


Test

44

A ω µ σ


ax 1.002 12.566 0.466 0.182

az 5.203 12.566 -9.654 0.093

gy 0.701 12.566 -0.008 0.142

P0 22.947 12.566 9.627 4.353

d1 0.801 31.416 -44.100 0.622

d2 2.957 12.566 -51.575 1.285

η1 32.96 7.85 N/A N/A

η2 33.86 7.85 N/A N/A


138



139

Test

45

A ω µ σ


ax 0.813 14.661 0.123 0.496

az 1.870 14.661 -9.814 1.079

gy 0.273 14.661 -0.007 0.186

P0 140.532 14.661 -6.564 80.316

d1 2.689 14.661 -50.056 1.852

d2 3.889 14.661 -39.276 2.628

η1 29.93 7.85 N/A N/A

η2 32.42 7.85 N/A N/A



140


Test

46

A ω µ σ


ax 0.813 14.661 0.123 0.496

az 1.870 14.661 -9.814 1.079

gy 0.273 14.661 -0.007 0.186

P0 140.532 14.661 -6.564 80.316

d1 2.689 14.661 -50.056 1.852

d2 3.889 14.661 -39.276 2.628

η1 34.38 7.85 N/A N/A

η2 30.26 7.85 N/A N/A


141



142

Test

47

A ω µ σ


ax 0.992 14.451 0.017 0.886

az 1.423 11.938 -9.758 0.779

gy 0.277 14.451 -0.003 0.185

P0 134.667 14.451 2.900 82.984

d1 2.784 14.451 -49.400 2.199

d2 4.422 14.451 -39.232 3.533

η1 36.96 7.85 N/A N/A

η2 28.68 7.85 N/A N/A



143


Test

48

A ω µ σ


ax 0.499 6.283 -0.069 0.375

az 0.416 8.796 -9.650 0.205

gy 0.124 8.796 0.001 0.077

P0 23.228 8.796 -1.255 14.039

d1 1.936 0.628 -44.486 0.757

d2 5.402 0.628 -48.890 2.126

η1 32.96 7.85 N/A N/A

η2 33.40 7.85 N/A N/A


144



145

Test

49

A ω µ σ


ax 0.597 14.661 0.712 0.394

az 3.094 14.661 -9.710 1.621

gy 0.438 14.661 -0.010 0.281

P0 20.035 14.661 6.110 12.350

d1 2.873 14.661 -45.905 2.137

d2 6.242 14.661 -43.781 4.783

η1 33.58 7.85 N/A N/A

η2 31.93 7.85 N/A N/A



146


Test

50

A ω µ σ


ax 0.693 14.137 0.693 0.462

az 3.159 14.137 -9.779 1.692

gy 0.529 14.137 0.008 0.342

P0 12.413 7.275 -0.206 7.230

d1 2.351 14.137 -45.520 1.716

d2 5.276 14.137 -44.557 3.506

η1 34.42 7.85 N/A N/A

η2 32.22 7.85 N/A N/A


147



148

Test

51

A ω µ σ


ax 0.703 14.362 0.690 0.445

az 3.285 14.362 -9.696 1.718

gy 0.498 14.362 -0.002 0.320

P0 17.900 14.362 4.585 10.066

d1 2.531 14.362 -45.651 1.764

d2 5.315 14.362 -45.112 3.344

η1 35.33 7.85 N/A N/A

η2 35.81 7.85 N/A N/A



149


Test

52

A ω µ σ


ax 1.012 13.823 0.782 0.590

az 5.417 13.823 -9.652 3.006

gy 0.793 13.823 -0.016 0.498

P0 41.531 13.823 13.326 24.377

d1 1.096 13.823 -44.204 0.760

d2 3.874 13.823 -50.327 2.713

η1 32.62 7.85 N/A N/A

η2 27.80 7.85 N/A N/A


150



151

Test

53

A ω µ σ


ax 0.850 18.850 0.727 0.577

az 4.690 15.259 -9.663 2.684

gy 0.506 15.259 -0.013 0.346

P0 19.243 15.259 5.239 12.636

d1 2.351 15.259 -44.957 1.706

d2 6.541 15.259 -46.812 4.794

η1 33.40 7.85 N/A N/A

η2 29.35 7.85 N/A N/A



152


Test

54

A ω µ σ


ax 0.813 15.259 0.813 0.517

az 5.310 14.362 -9.650 2.838

gy 0.774 14.362 -0.023 0.473

P0 29.398 14.362 5.649 17.219

d1 1.867 14.362 -44.572 1.218

d2 5.315 14.362 -47.288 3.536

η1 31.27 7.85 N/A N/A

η2 33.23 7.85 N/A N/A


153



154

Test

55

A ω µ σ


ax 0.699 6.393 -0.101 0.420

az 0.864 6.393 -9.771 0.510

gy 0.596 6.393 -0.013 0.407

P0 12.262 0.000 -0.206 7.230

d1 4.840 1.102 -44.102 1.324

d2 3.193 6.393 -47.237 2.346

η1 5.76 4.71 N/A N/A

η2 0.67 3.14 N/A N/A



155


Test

56

A ω µ σ


ax 0.817 7.854 -0.007 0.510

az 0.968 7.854 -9.745 0.621

gy 0.634 7.854 0.002 0.435

P0 13.066 7.854 -0.327 6.763

d1 2.843 7.854 -45.370 1.787

d2 3.687 7.854 -45.139 2.128

η1 39.58 6.28 N/A N/A

η2 37.29 6.28 N/A N/A


156



157

Test

57

A ω µ σ


ax 0.924 7.540 0.025 0.509

az 1.145 7.540 -9.762 0.681

gy 0.600 7.540 -0.004 0.419

P0 16.332 7.540 0.607 8.395

d1 3.215 7.540 -45.637 2.227

d2 6.185 7.540 -44.406 3.252

η1 36.45 6.28 N/A N/A

η2 34.37 6.28 N/A N/A



158


Test

58

A ω µ σ


ax 0.844 7.540 0.432 0.487

az 2.130 15.080 -9.758 1.301

gy 0.829 0.000 0.002 0.550

P0 99.697 15.080 55.686 60.432

d1 1.019 14.765 -39.816 0.623

d2 3.862 7.540 -50.707 2.086

η1 31.27 7.85 N/A N/A

η2 36.11 6.28 N/A N/A


159



Test A ω µ σ

160

59 [m/s2,rad/s2,Pa,mm] [rad/s] [m/s2,rad/s2,Pa,mm] [m/s2,rad/s2,Pa,mm]

ax 1.010 8.168 0.484 0.637

az 2.120 16.336 -9.725 1.179

gy 1.051 8.168 -0.004 0.703

P0 44.345 16.336 25.844 29.847

d1 2.123 8.168 -40.591 1.260

d2 5.630 8.168 -46.084 3.768

η1 39.25 6.28 N/A N/A

η2 34.39 6.28 N/A N/A



161


Test

60

A ω µ σ


ax 0.835 7.540 0.418 0.489

az 2.232 14.765 -9.770 1.276

gy 0.841 7.540 0.011 0.561

P0 84.755 14.765 23.028 49.157

d1 1.191 12.881 -39.886 0.652

d2 6.532 8.976 -50.519 2.078

η1 39.76 6.28 N/A N/A

η2 36.40 6.28 N/A N/A

162




163

Test

61

A ω µ σ


ax 0.689 7.226 0.341 0.410

az 3.082 22.934 -9.730 1.969

gy 0.685 7.540 0.011 0.418

P0 40.605 6.597 28.588 22.297

d1 0.993 13.195 -43.669 0.551

d2 5.078 0.628 -51.176 1.309

η1 36.47 6.28 N/A N/A

η2 36.57 6.28 N/A N/A



164


Test

62

A ω µ σ


ax 0.838 7.854 0.291 0.511

az 3.202 15.708 -9.662 1.901

gy 0.983 7.854 -0.005 0.657

P0 33.155 7.854 17.253 18.907

d1 0.976 16.650 -43.678 0.596

d2 2.809 7.854 -54.265 1.568

η1 34.33 6.28 N/A N/A

η2 33.33 6.28 N/A N/A


165



166

Test

63

A ω µ σ


ax 0.602 6.283 0.320 0.313

az 2.656 23.876 -9.749 1.606

gy 0.693 6.283 0.004 0.378

P0 20.906 6.283 9.433 11.595

d1 0.695 41.469 -43.799 0.480

d2 2.427 6.283 -53.627 1.175

η1 38.50 6.28 N/A N/A

η2 39.11 6.28 N/A N/A



167


Test

64

A ω µ σ


ax 1.020 9.183 0.029 0.568

az 1.483 9.183 -9.740 0.899

gy 0.663 9.183 -0.007 0.460

P0 120.316 9.183 8.626 63.785

d1 3.999 9.183 -47.658 2.956

d2 8.643 0.483 -42.807 4.609

η1 35.53 6.28 N/A N/A

η2 32.89 6.28 N/A N/A


168



169

Test

65

A ω µ σ


ax 1.186 8.976 -0.031 0.667

az 1.796 8.976 -9.707 1.011

gy 0.733 0.000 -0.005 0.497

P0 132.670 8.976 5.519 66.179

d1 4.308 8.976 -47.920 3.091

d2 0.000 0.000 -44.625 3.735

η1 37.63 6.28 N/A N/A

η2 36.10 6.28 N/A N/A



170


Test

66

A ω µ σ


ax 1.099 8.796 -0.068 0.654

az 1.913 8.796 -9.787 0.999

gy 0.772 8.796 -0.001 0.517

P0 141.984 8.796 17.455 72.641

d1 4.210 8.796 -47.951 3.022

d2 6.626 8.796 -44.286 3.751

η1 35.47 6.28 N/A N/A

η2 32.33 6.28 N/A N/A


171



172

Test

67

A ω µ σ


ax 1.238 10.053 0.643 0.783

az 2.785 10.053 -9.666 1.510

gy 0.994 10.053 0.006 0.689

P0 25.936 20.735 -0.667 21.055

d1 3.708 10.681 -45.693 2.624

d2 4.602 10.053 -44.175 2.397

η1 42.44 7.54 N/A N/A

η2 28.00 7.54 N/A N/A



173


Test

68

A ω µ σ


ax 1.127 9.425 0.552 0.654

az 3.734 9.425 -9.687 1.727

gy 1.067 9.425 -0.003 0.733

P0 105.780 18.850 99.477 67.827

d1 2.408 9.425 -40.706 1.377

d2 4.411 9.425 -45.621 2.353

η1 35.53 6.28 N/A N/A

η2 36.09 6.28 N/A N/A

174




175

Test

69

A ω µ σ


ax 1.236 9.425 0.584 0.716

az 2.959 9.425 -9.592 1.638

gy 1.147 9.425 -0.007 0.782

P0 162.671 9.425 107.637 83.742

d1 2.821 9.425 -41.068 1.787

d2 4.948 9.425 -45.113 2.605

η1 39.32 6.28 N/A N/A

η2 38.79 6.28 N/A N/A



176


Test

70

A ω µ σ


ax 1.553 8.796 0.482 0.766

az 4.565 8.796 -9.701 2.260

gy 1.201 8.796 0.016 0.792

P0 94.946 8.796 46.462 51.553

d1 0.947 59.690 -43.990 0.625

d2 7.562 0.628 -52.172 1.878

η1 41.30 5.97 N/A N/A

η2 34.33 5.97 N/A N/A

177




178

Test

71

A ω µ σ


ax 0.000 52.970 0.001 0.031

az 0.000 32.684 -0.027 0.566

gy 0.000 52.689 -0.003 0.058

P0 0.000 42.264 -0.020 0.414

d1 0.000 42.264 -0.097 2.056

d2 0.000 28.176 -0.111 2.339

η1 37.24 5.97 N/A N/A

η2 33.07 6.28 N/A N/A



179


Test

72

A ω µ σ


ax 0.953 8.378 0.463 0.548

az 3.217 24.714 -9.818 2.010

gy 1.104 8.796 -0.008 0.758

P0 41.251 8.796 18.418 24.057

d1 1.620 5.027 -44.070 0.630

d2 3.488 8.796 -53.346 2.167

η1 32.87 6.28 N/A N/A

η2 34.57 6.28 N/A N/A


180



181

Test

73

A ω µ σ


ax 1.112 10.053 0.049 0.761

az 1.670 10.053 -9.744 0.969

gy 0.678 10.053 -0.013 0.455

P0 67.028 10.053 11.745 58.126

d1 3.581 10.053 -47.654 2.892

d2 11.668 0.628 -39.908 5.330

η1 36.09 5.97 N/A N/A

η2 32.14 6.28 N/A N/A



182


Test

74

A ω µ σ


ax 1.494 10.681 0.283 0.963

az 2.650 10.681 -9.651 1.388

gy 0.797 10.681 0.008 0.520

P0 134.461 10.681 13.444 81.962

d1 3.809 10.681 -46.899 2.825

d2 6.914 10.681 -41.403 4.447

η1 37.40 6.28 N/A N/A

η2 33.75 6.28 N/A N/A


183



184

Test

75

A ω µ σ


ax 1.243 10.053 0.171 0.753

az 2.068 10.053 -9.679 1.160

gy 0.770 10.053 -0.010 0.524

P0 139.675 10.053 18.631 78.028

d1 4.273 10.053 -47.369 2.873

d2 7.930 10.053 -39.467 4.774

η1 37.15 6.28 N/A N/A

η2 33.84 6.28 N/A N/A



185


Test

76

A ω µ σ


ax 1.160 8.378 0.682 0.802

az 2.338 8.378 -9.626 1.400

gy 0.816 8.378 -0.029 0.567

P0 39.416 18.850 6.894 27.100

d1 2.696 8.378 -45.608 2.060

d2 7.886 8.378 -46.161 3.697

η1 19.41 5.97 N/A N/A

η2 7.76 4.08 N/A N/A


186



187

Test

77

A ω µ σ


ax 1.185 10.210 0.824 0.763

az 3.595 10.210 -9.737 1.837

gy 1.101 10.210 0.006 0.763

P0 81.907 21.206 53.877 51.028

d1 3.785 10.210 -46.203 2.516

d2 4.888 10.210 -47.663 2.614

η1 39.83 6.28 N/A N/A

η2 39.96 6.28 N/A N/A



188


Test

78

A ω µ σ


ax 1.216 10.996 0.539 1.827

az 3.332 10.996 -9.703 1.854

gy 0.905 10.996 -0.009 0.618

P0 78.541 10.996 31.616 57.025

d1 3.933 10.996 -46.075 2.923

d2 7.178 10.996 -42.742 4.152

η1 37.40 6.28 N/A N/A

η2 18.20 7.23 N/A N/A


189



190

Test

79

A ω µ σ


ax 1.577 10.210 0.864 0.847

az 3.370 29.845 -9.660 2.095

gy 1.376 10.210 -0.005 0.931

P0 36.748 9.425 13.176 20.444

d1 3.180 1.571 -44.101 0.807

d2 2.458 19.635 -50.323 1.877

η1 34.47 6.28 N/A N/A

η2 34.86 6.28 N/A N/A



191


Test

80

A ω µ σ


ax 1.531 9.425 0.898 0.822

az 4.738 9.425 -9.688 2.398

gy 1.348 9.425 -0.033 0.932

P0 34.788 9.425 15.169 20.890

d1 1.321 10.996 -44.198 0.807

d2 5.834 0.785 -51.341 1.868

η1 39.35 6.28 N/A N/A

η2 37.56 6.28 N/A N/A


192



193

Test

81

A ω µ σ


ax 1.435 10.210 0.957 0.799

az 4.905 10.210 -9.712 2.519

gy 1.430 10.210 -0.008 1.011

P0 20.089 10.210 6.104 10.662

d1 1.590 10.210 -44.348 0.842

d2 4.834 10.210 -49.669 2.559

η1 37.85 6.28 N/A N/A

η2 36.63 6.28 N/A N/A



194


5.6.Pitch Response

To calculate the pitch response, the power spectral density (PSD) function was computed

from the time series data for each experiment. The dominant response frequency, f0, was

determined from the PSD, and the power of the response at this frequency was computed

by integrating the PSD from (f0-f0/2) to (f0+f0/2). The result of this operation was in units

of power squared, so to obtain the amplitude of the pitch response the relationship

Power=Amplitude2/2 was used by manipulating it to Amplitude=sqrt(2*Power). The

following figures show graphs of the vessel's pitch response as it advances into the

transforming sea. A general trend can be noticed from examination of the figures. The

amplitude of the pitch response appears to reach a maximum as the encounter frequency

195

approaches 1.5[Hz]. The pitch amplitude appears to increase with increasing blower level

at all encounter frequencies, but the effect seems to be diminished at high encounter

frequencies and most pronounced at 1.5[Hz].

Table 5.83 Pitch Response Vs. Encounter Frequency

The pitch response can also be plotted as a function of the encounter frequency. This is

how naval architects typically represent the response amplitude function, or RAO, of a

vessel. The response amplitude is typically normalized with respect to the wave

amplitude, which is what was done for the RAO in table 5.84.

196

Table 5.84 Pitch RAO Vs. Encounter Frequency

5.7.Heave Response

The AIRCAT SES vehicle's heave response as a function of vessel speed was calculated

in a manner similar to the pitch response. As in the pitch response, the power spectral

density (PSD) function was computed from the time series data for each experiment. The

dominant response frequency was determined from the PSD, and the power of the

response at this frequency was computed by integrating the PSD from (f0-f0/2) to

(f0+f0/2). The amplitude was found using the method outlined for the pitch response. A

trend can be noticed with the heave response. The amplitude of the heave response

increases as the speed increases and also as the blower increases.

197

Table 5.85 Heave Response Vs. Encounter Frequency

As the blower increases, less of the vessel is submerged reducing the mass of the system

which could result in an increased system output, in this case the heave motion of the

vessel. The vessel forward speed also affects the trim of the vessel and through the

planing effect it reduces the draft of the craft as well, having similar effects on the heave

response as an increase in the blower pressure.

198

Table 5.86 Heave RAO Vs. Encounter Frequency

The heave response amplitude can be plotted against the encounter frequency, as with the

pitch response amplitude. The result is typically referred to in naval architecture as the

response amplitude operator, or RAO, and is normalized against the wave amplitude. It is

seen in table 5.86 above that the heave response increased steadily with increasing

encounter frequency.

5.8.Discussion

Inspection of the pitch and heave responses indicates that the amplitude of both responses

decreases as the blower and/or speed increases. The one parameter that might increase

199

negatively with either blower or speed input would be the high frequency cobblestone

oscillations, but unfortunately that phenomenon does not scale to allow it to be studied

with this scale model vessel. To study the cobblestone oscillations, one would have to use

either a larger scale model-preferably full-scale-or do numerical simulations. To conduct

numerical simulations, a computer model using CFD code holds much potential. The

experimental results from this thesis could be used to validate such a computational

model.

200

6. CONCLUSIONS AND DISCUSSION

6.1.Results

In review, the primary aim of this thesis was to conduct experiments with a scale model

SES vehicle in a wave tank which could be used to characterize the wave loading and

seakeeping response of an SES vessel in transforming seas. The wave tank had a beach

installed to allow for the formation of a transforming sea state, with waves shoaling and

breaking. A secondary aim of this thesis was to determine if commercially available CFD

codes could be used to simulate these experiments in the future, removing the need for

physical facilities to investigate the seakeeping characteristics of SES vessels. The results

of these objectives follow.

6.1.1. Physical Experiments

A beach was created and installed in the wave tank at FAU's SeaTech facility. A

wavemaker was built and installed on the wavetank as well, allowing for the simulation

of a transforming sea state. A 1:30 scale model of an SES vessel, the AIRCAT, was used

to conduct experiments of 27 separate scenarios. Three experiments were run at each

scenario, for a total of 81 experiments. The results of these experiments show that the

amplitude of both the pitching and heaving motion of the SES vessel increased as the

aircushion pressure increased, and reached a maximum for encounter frequencies around

201

1.5[Hz]. This is in line with what would be expected, since the aircushion reduces the

draft of the vessel and it is a well-known principle of naval architecture that shallow draft

craft are more effected by waves than craft with larger draft. The forward motion creates

a planing effect which also reduces the draft of the vessel.

6.1.2. Computer Model

The results from the computer model simulations demonstrated that commercially

available CFD codes can, indeed, be successfully used to create simulations of SES

vessels in transforming seas. Using a 2.66 GHz desktop machine, a 30 second simulation

could be run in about one and a half days. This is probably too much time to make CFD a

useful tool for preliminary design iterations, but once a few designs are selected CFD

would be an efficient way of testing them compared to building a physical model and

testing it in a wave tank.

6.2.Future Work

6.2.1. Experiments

The best place to begin any future work on these results would be to conduct more

experiments at each of the 27 scenarios this study investigated. Increasing the number of

experiments from three to five or even seven would greatly increase the statistical

strength of the results.

202

Another area that could be improved would be to replace the bowskirt with a more supple

material which would flex and deform in a manner that is closer to the flexing and

deforming of a full-scale bowskirt.

An interesting experiment would be to adjust the ballast of the scale model SES to

achieve the same trim and sinkage levels with zero blower that the model currently

experiences when on an aircushion with a blower level of 31% and 100%. The

experiments conducted in this thesis could then be replicated, into what role the

aircushion contributes to the seakeeping characteristics, to determine if an SES vessel

behaves similarly to a vessel with the same hull geometry but with a reduced mass.

6.2.2. Computer Model

The computer model that was developed could be used to run experiments in different

wave conditions, building a table of results for different wave amplitude/frequency

combinations. The most important refinement that could be made to the computer model

that was developed for this thesis would be adding scripts that would allow the vessel to

move forward through the domain. This can be done in ANSYS CFX, and it would add to

the usefulness of the computer model.

203

REFERENCES Faltinsen, Odd M. 2005. Hydrodynamics of High-Speed Marine Vehicles. Cambridge:

Cambride University Press.

Dean, Robert G. 1991. Water Wave Mechanics for Engineers and Scientists. Singapore:

World Scientific Publishing Company.

Faltinsen, Odd M. 1990. Sea Loads on Ships and Offshore Structures. Cambridge:

Cambridge University Press.

Anderson, John D. 1995. Computational Fluid Dynamics. New York: McGraw-Hill, Inc.

Kaplan, Paul, Bentson, James, and Davis, Sydney 1981. Dynamics and Hydrodynamics

of Surface Effect Ships. SNAME Transactions, Vol. 89, 1981, 211-247.

Westphalen, Jan, Greaves, Deborah, and Williams, Chris. 2007 Comparison of Free

Surface Wave Simulations using STAR CCM+ and CFX.

Lewis, Edward V. 1989 Principles of Naval Architecture, Volume III, SNAME.

seakeeping response of a surface effect ship in near-shore transforming

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