Upload
others
View
3
Download
0
Embed Size (px)
Citation preview
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 5.2 Test 01 Vehicle and Wave Data ....................................................................... 73
Table 5.3 Test 02 Vehicle and Wave Data ....................................................................... 74
Table 5.4 Test 03 Vehicle and Wave Data ....................................................................... 76
Table 5.5 Test 04 Vehicle and Wave Data ...................................................................... 77
Table 5.6 Test 05 Vehicle and Wave Data ....................................................................... 79
Table 5.7 Test 06 Vehicle and Wave Data ....................................................................... 80
Table 5.8 Test 07 Vehicle and Wave Data ....................................................................... 82
Table 5.9 Test 08 Vehicle and Wave Data ....................................................................... 83
Table 5.10 Test 09 Vehicle and Wave Data ..................................................................... 85
Table 5.11 Test 10 Vehicle and Wave Data ..................................................................... 86
Table 5.12 Test 11 Vehicle and Wave Data ..................................................................... 88
Table 5.13 Test 12 Vehicle and Wave Data ..................................................................... 89
Table 5.14 Test 13 Vehicle and Wave Data ..................................................................... 91
Table 5.15 Test 14 Vehicle and Wave Data ..................................................................... 92
Table 5.16 Test 15 Vehicle and Wave Data ..................................................................... 94
Table 5.17 Table 16 Vehicle and Wave Data ................................................................... 95
Table 5.18 Test 17 Vehicle and Wave Data ..................................................................... 97
x
Table 5.19 Test 18 Vehicle and Wave Data ..................................................................... 98
Table 5.20 Test 19 Vehicle and Wave Data ................................................................... 100
Table 5.21 Test 20 Vehicle and Wave Data ................................................................... 101
Table 5.22 Test 21 Vehicle and Wave Data ................................................................... 103
Table 5.23 Test 22 Vehicle and Wave Data ................................................................... 104
Table 5.24 Test 23 Vehicle and Wave Data ................................................................... 106
Table 5.25 Test 24 Vehicle and Wave Data ................................................................... 107
Table 5.26 Test 25 Vehicle and Wave Data ................................................................... 109
Table 5.27 Test 26 Vehicle and Wave Data ................................................................... 110
Table 5.28 Test 27 Vehicle and Wave Data ................................................................... 112
Table 5.29 Test 28 Vehicle and Wave Data ................................................................... 113
Table 5.30 Test 29 Vehicle and Wave Data ................................................................... 115
Table 5.31 Test 30 Vehicle and Wave Data ................................................................... 116
Table 5.32 Test 31 Vehicle and Wave Data ................................................................... 118
Table 5.33 Test 32 Vehicle and Wave Data ................................................................... 119
Table 5.34 Test 33 Vehicle and Wave Data ................................................................... 121
Table 5.35 Test 34 Vehicle and Wave Data ................................................................... 122
Table 5.36 Test 35 Vehicle and Wave Data ................................................................... 124
Table 5.37 Test 36 Vehicle and Wave Data ................................................................... 125
Table 5.38 Test 37 Vehicle and Wave Data ................................................................... 127
Table 5.39 Test 38 Vehicle and Wave Data ................................................................... 128
Table 5.40 Test 39 Vehicle and Wave Data ................................................................... 130
xi
Table 5.41 Test 40 Vehicle and Wave Data ................................................................... 131
Table 5.42 Test 41 Vehicle and Wave Data ................................................................... 133
Table 5.43 Test 42 Vehicle and Wave Data ................................................................... 134
Table 5.44 Test 43 Vehicle and Wave Data ................................................................... 136
Table 5.45 Test 44 Vehicle and Wave Data ................................................................... 137
Table 5.46 Test 45 Vehicle and Wave Data ................................................................... 139
Table 5.47 Test 46 Vehicle and Wave Data ................................................................... 140
Table 5.48 Test 47 Vehicle and Wave Data ................................................................... 142
Table 5.49 Test 48 Vehicle and Wave Data ................................................................... 143
Table 5.50 Test 49 Vehicle and Wave Data ................................................................... 145
Table 5.51 Test 50 Vehicle and Wave Data ................................................................... 146
Table 5.52 Test 51 Vehicle and Wave Data ................................................................... 148
Table 5.53 Test 52 Vehicle and Wave Data ................................................................... 149
Table 5.54 Test 53 Vehicle and Wave Data ................................................................... 151
Table 5.55 Test 54 Vehicle and Wave Data ................................................................... 152
Table 5.56 Test 55 Vehicle and Wave Data ................................................................... 154
Table 5.57 Test 56 Vehicle and Wave Data ................................................................... 155
Table 5.58 Test 57 Vehicle and Wave Data ................................................................... 157
Table 5.59 Test 58 Vehicle and Wave Data ................................................................... 158
Table 5.60 Test 59 Vehicle and Wave Data ................................................................... 160
Table 5.61 Test 60 Vehicle and Wave Data ................................................................... 162
Table 5.62 Test 61 Vehicle and Wave Data ................................................................... 163
xii
Table 5.63 Test 62 Vehicle and Wave Data ................................................................... 164
Table 5.64 Test 63 Vehicle and Wave Data ................................................................... 166
Table 5.65 Test 64 Vehicle and Wave Data ................................................................... 167
Table 5.66 Test 65 Vehicle and Wave Data ................................................................... 169
Table 5.67 Test 66 Vehicle and Wave Data ................................................................... 170
Table 5.68 Test 67 Vehicle and Wave Data ................................................................... 172
Table 5.69 Test 68 Vehicle and Wave Data ................................................................... 174
Table 5.70 Test 69 Vehicle and Wave Data ................................................................... 175
Table 5.71 Test 70 Vehicle and Wave Data ................................................................... 177
Table 5.72 Test 71 Vehicle and Wave Data ................................................................... 178
Table 5.73 Test 72 Vehicle and Wave Data ................................................................... 179
Table 5.74 Test 73 Vehicle and Wave Data ................................................................... 181
Table 5.75 Test 74 Vehicle and Wave Data ................................................................... 182
Table 5.76 Test 75 Vehicle and Wave Data ................................................................... 184
Table 5.77 Test 76 Vehicle and Wave Data ................................................................... 185
Table 5.78 Test 77 Vehicle and Wave Data ................................................................... 187
Table 5.79 Test 78 Vehicle and Wave Data ................................................................... 188
Table 5.80 Test 79 Vehicle and Wave Data ................................................................... 190
Table 5.81 Test 80 Vehicle and Wave Data ................................................................... 191
Table 5.82 Test 81 Vehicle and Wave Data ................................................................... 193
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 5.12 Test 03 Wave Elevation Data Time Series .................................................... 76
Figure 5.13 Test 03 Vehicle Data Time Series ................................................................. 77
Figure 5.14 Test 04 Wave Elevation Data Time Series .................................................... 78
Figure 5.15 Test 04 Vehicle Data Time Series ................................................................. 78
Figure 5.16 Test 05 Wave Elevation Data Time Series .................................................... 79
Figure 5.17 Test 05 Vehicle Data Time Series ................................................................. 80
Figure 5.18 Test 06 Wave Elevation Data Time Series .................................................... 81
Figure 5.19 Test 06 Vehicle Data Time Series ................................................................ 81
Figure 5.20 Test 07 Wave Elevation Data Time Series .................................................... 82
Figure 5.21 Test 07 Vehicle Data Time Series ................................................................. 83
Figure 5.22 Test 08 Wave Elevation Data Time Series .................................................... 84
Figure 5.23 Test 08 Vehicle Data Time Series ................................................................. 84
Figure 5.24 Test 09 Wave Elevation Data Time Series .................................................... 85
xvii
Figure 5.25 Test 09 Vehicle Data Time Series ................................................................ 86
Figure 5.26 Test 10 Wave Elevation Data Time Series .................................................... 87
Figure 5.27 Test 10 Vehicle Data Time Series ................................................................. 87
Figure 5.28 Test 11 Wave Elevation Data Time Series .................................................... 88
Figure 5.29 Test 11 Vehicle Data Time Series ................................................................. 89
Figure 5.30 Test 12 Wave Elevation Data Time Series .................................................... 90
Figure 5.31 Test 12 Vehicle Data Time Series ................................................................. 90
Figure 5.32 Test 13 Wave Elevation Data Time Series .................................................... 91
Figure 5.33 Test 13 Vehicle Data Time Series ................................................................. 92
Figure 5.34 Test 14 Wave Elevation Data Time Series ................................................... 93
Figure 5.35 Test 14 Vehicle Data Time Series ................................................................. 93
Figure 5.36 Test 15 Wave Elevation Data Time Series .................................................... 94
Figure 5.37 Test 15 Vehicle Data Time Series ................................................................. 95
Figure 5.38 Test 16 Wave Elevation Data Time Series .................................................... 96
Figure 5.39 Test 16 Vehicle Data Time Series ................................................................. 96
Figure 5.40 Test 17 Wave Elevation Data Time Series .................................................... 97
Figure 5.41 Test 17 Vehicle Data Time Series ................................................................. 98
Figure 5.42 Test 18 Wave Elevation Data Time Series .................................................... 99
Figure 5.43 Test 18 Vehicle Data Time Series ................................................................. 99
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
Figure 5.47 Test 20 Vehicle Data Time Series ............................................................... 102
Figure 5.48 Test 21 Wave Elevation Data Time Series ................................................. 103
Figure 5.49 Test 21 Vehicle Data Time Series ............................................................... 104
Figure 5.50 Test 22 Wave Elevation Data Time Series ................................................. 105
Figure 5.51 Test 22 Vehicle Data Time Series ............................................................... 105
Figure 5.52 Test 23 Wave Elevation Data Time Series ................................................. 106
Figure 5.53 Test 23 Vehicle Data Time Series ............................................................... 107
Figure 5.54 Test 24 Wave Elevation Data Time Series .................................................. 108
Figure 5.55 Test 24 Vehicle Data Time Series ............................................................... 108
Figure 5.56 Test 25 Wave Elevation Data Time Series .................................................. 109
Figure 5.57 Test 25 Vehicle Data Time Series ............................................................... 110
Figure 5.58 Test 26 Wave Elevation Data Time Series ................................................. 111
Figure 5.59 Test 26 Vehicle Data Time Series ............................................................... 111
Figure 5.60 Test 27 Wave Elevation Data Time Series .................................................. 112
Figure 5.61 Test 27 Vehicle Data Time Series ............................................................... 113
Figure 5.62 Test 28 Wave Elevation Data Time Series ................................................. 114
Figure 5.63 Test 28 Vehicle Data Time Series ............................................................... 114
Figure 5.64 Test 29 Wave Elevation Data Time Series .................................................. 115
Figure 5.65 Test 29 Vehicle Data Time Series ............................................................... 116
Figure 5.66 Test 30 Wave Elevation Data Time Series .................................................. 117
Figure 5.67 Test 30 Vehicle Data Time Series ............................................................... 117
Figure 5.68 Test 31 Wave Elevation Data Time Series .................................................. 118
xix
Figure 5.69 Test 31 Vehicle Data Time Series ............................................................... 119
Figure 5.70 Test 32 Wave Elevation Data Time Series ................................................. 120
Figure 5.71 Test 32 Vehicle Data Time Series ............................................................... 120
Figure 5.72 Test 33 Wave Elevation Data Time Series .................................................. 121
Figure 5.73 Test 33 Vehicle Data Time Series ............................................................... 122
Figure 5.74 Test 34 Wave Elevation Data Time Series .................................................. 123
Figure 5.75 Test 34 Vehicle Data Time Series ............................................................... 123
Figure 5.76 Test 35 Wave Elevation Data Time Series ................................................. 124
Figure 5.77 Test 35 Vehicle Data Time Series ............................................................... 125
Figure 5.78 Test 36 Wave Elevation Data Time Series ................................................. 126
Figure 5.79 Test 36 Vehicle Data Time Series ............................................................... 126
Figure 5.80 Test 37 Wave Elevation Data Time Series .................................................. 127
Figure 5.81 Test 37 Vehicle Data Time Series ............................................................... 128
Figure 5.82 Test 38 Wave Elevation Data Time Series ................................................. 129
Figure 5.83 Test 38 Vehicle Data Time Series .............................................................. 129
Figure 5.84 Test 39 Wave Elevation Data Time Series .................................................. 130
Figure 5.85 Test 39 Vehicle Data Time Series ............................................................... 131
Figure 5.86 Test 40 Wave Elevation Data Time Series .................................................. 132
Figure 5.87 Test 40 Vehicle Data Time Series ............................................................... 132
Figure 5.88 Test 41 Wave Elevation Data Time Series ................................................. 133
Figure 5.89 Test 41 Vehicle Data Time Series ............................................................... 134
Figure 5.90 Test 42 Wave Elevation Data Time Series ................................................. 135
xx
Figure 5.91 Test 42 Vehicle Data Time Series ............................................................... 135
Figure 5.92 Test 43 Wave Elevation Data Time Series ................................................. 136
Figure 5.93 Test 43 Vehicle Data Time Series ............................................................... 137
Figure 5.94 Test 44 Wave Elevation Data Time Series .................................................. 138
Figure 5.95 Test 44 Vehicle Data Time Series ............................................................... 138
Figure 5.96 Test 45 Wave Elevation Data Time Series ................................................. 139
Figure 5.97 Test 45 Vehicle Data Time Series ............................................................... 140
Figure 5.98 Test 46 Wave Elevation Data Time Series .................................................. 141
Figure 5.99 Test 46 Vehicle Data Time Series ............................................................... 141
Figure 5.100 Test 47 Wave Elevation Data Time Series ................................................ 142
Figure 5.101 Test 47 Vehicle Data Time Series ............................................................. 143
Figure 5.102 Test 48 Wave Elevation Data Time Series ................................................ 144
Figure 5.103 Test 48 Vehicle Data Time Series ............................................................. 144
Figure 5.104 Test 49 Wave Elevation Data Time Series ................................................ 145
Figure 5.105 Test 49 Vehicle Data Time Series ............................................................. 146
Figure 5.106 Test 50 Wave Elevation Data Time Series ................................................ 147
Figure 5.107 Test 50 Vehicle Data Time Series ............................................................. 147
Figure 5.108 Test 51 Wave Elevation Data Time Series ................................................ 148
Figure 5.109 Test 51 Vehicle Data Time Series ............................................................. 149
Figure 5.110 Test 52 Wave Elevation Data Time Series ............................................... 150
Figure 5.111 Test 52 Vehicle Data Time Series ............................................................. 150
Figure 5.112 Test 53 Wave Elevation Data Time Series ............................................... 151
xxi
Figure 5.113 Test 53 Vehicle Data Time Series ............................................................. 152
Figure 5.114 Test 54 Wave Elevation Data Time Series ............................................... 153
Figure 5.115 Test 54 Vehicle Data Time Series ............................................................. 153
Figure 5.116 Test 55 Wave Elevation Data Time Series ............................................... 154
Figure 5.117 Test 55 Vehicle Data Time Series ............................................................. 155
Figure 5.118 Test 56 Wave Elevation Data Time Series ............................................... 156
Figure 5.119 Test 56 Vehicle Data Time Series ............................................................. 156
Figure 5.120 Test 57 Wave Elevation Data Time Series ............................................... 157
Figure 5.121 Test 57 Vehicle Data Time Series ............................................................. 158
Figure 5.122 Test 58 Wave Elevation Data Time Series ................................................ 159
Figure 5.123 Test 58 Vehicle Data Time Series ............................................................. 159
Figure 5.124 Test 59 Wave Elevation Data Time Series ................................................ 160
Figure 5.125 Test 59 Vehicle Data Time Series ............................................................. 161
Figure 5.126 Test 60 Wave Elevation Data Time Series ............................................... 162
Figure 5.127 Test 60 Vehicle Data Time Series ............................................................. 162
Figure 5.128 Test 61 Wave Elevation Data Time Series ................................................ 163
Figure 5.129 Test 61 Vehicle Data Time Series ............................................................. 164
Figure 5.130 Test 62 Wave Elevation Data Time Series ................................................ 165
Figure 5.131 Test 62 Vehicle Data Time Series ............................................................. 165
Figure 5.132 Test 63 Wave Elevation Data Time Series ................................................ 166
Figure 5.133 Test 63 Vehicle Data Time Series ............................................................. 167
Figure 5.134 Test 64 Wave Elevation Data Time Series ............................................... 168
xxii
Figure 5.135 Test 64 Vehicle Data Time Series ............................................................. 168
Figure 5.136 Test 65 Wave Elevation Data Time Series ............................................... 169
Figure 5.137 Test 65 Vehicle Data Time Series ............................................................. 170
Figure 5.138 Test 66 Wave Elevation Data Time Series ............................................... 171
Figure 5.139 Test 66 Vehicle Data Time Series ............................................................. 171
Figure 5.140 Test 67 Wave Elevation Data Time Series ................................................ 172
Figure 5.141 Test 67 Vehicle Data Time Series ............................................................. 173
Figure 5.142 Test 68 Wave Elevation Data Time Series ................................................ 174
Figure 5.143 Test 68 Vehicle Data Time Series ............................................................. 174
Figure 5.144 Test 69 Wave Elevation Data Time Series ................................................ 175
Figure 5.145 Test 69 Vehicle Data Time Series ............................................................. 176
Figure 5.146 Test 70 Wave Elevation Data Time Series ................................................ 177
Figure 5.147 Test 70 Vehicle Data Time Series ............................................................. 177
Figure 5.148 Test 71 Wave Elevation Data Time Series ............................................... 178
Figure 5.149 Test 71 Vehicle Data Time Series ............................................................. 179
Figure 5.150 Test 72 Wave Elevation Data Time Series ................................................ 180
Figure 5.151 Test 72 Vehicle Data Time Series ............................................................. 180
Figure 5.152 Test 73 Wave Elevation Data Time Series ............................................... 181
Figure 5.153 Test 73 Vehicle Data Time Series ............................................................. 182
Figure 5.154 Test 74 Wave Elevation Data Time Series ................................................ 183
Figure 5.155 Test 74 Vehicle Data Time Series ............................................................. 183
Figure 5.156 Test 75 Wave Elevation Data Time Series ................................................ 184
xxiii
Figure 5.157 Test 75 Vehicle Data Time Series ............................................................. 185
Figure 5.158 Test 76 Wave Elevation Data Time Series ............................................... 186
Figure 5.159 Test 76 Vehicle Data Time Series ............................................................. 186
Figure 5.160 Test 77 Wave Elevation Data Time Series ............................................... 187
Figure 5.161 Test 77 Vehicle Data Time Series ............................................................. 188
Figure 5.162 Test 78 Wave Elevation Data Time Series ............................................... 189
Figure 5.163 Test 78 Vehicle Data Time Series ............................................................. 189
Figure 5.164 Test 79 Wave Elevation Data Time Series ................................................ 190
Figure 5.165 Test 79 Vehicle Data Time Series ............................................................. 191
Figure 5.166 Test 80 Wave Elevation Data Time Series ............................................... 192
Figure 5.167 Test 80 Vehicle Data Time Series ............................................................. 192
Figure 5.168 Test 81 Wave Elevation Data Time Series ................................................ 193
Figure 5.169 Test 81 Vehicle Data Time Series ............................................................. 194
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
MED SPEED Run 1 Run 2 Run 3
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
MED SPEED Run 1 Run 2 Run 3
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
[m/s2,rad/s2,Pa,mm] [rad/s] [m/s2,rad/s2,Pa,mm] [m/s2,rad/s2,Pa,mm]
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
Table 5.2 Test 01 Vehicle and Wave Data
Figure 5.8 Test 01 Wave Elevation Data Time Series
74
Figure 5.9 Test 01 Vehicle Data Time Series
Test
02
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 0.338 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
Table 5.3 Test 02 Vehicle and Wave Data
75
Figure 5.10 Test 02 Wave Elevation Data Time Series
Figure 5.11 Test 02 Vehicle Data Time Series
76
Test
03
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 0.317 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
Table 5.4 Test 03 Vehicle and Wave Data
Figure 5.12 Test 03 Wave Elevation Data Time Series
77
Figure 5.13 Test 03 Vehicle Data Time Series
Test
04
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 0.296 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
Table 5.5 Test 04 Vehicle and Wave Data
78
Figure 5.14 Test 04 Wave Elevation Data Time Series
Figure 5.15 Test 04 Vehicle Data Time Series
79
Test
05
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 0.308 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
Table 5.6 Test 05 Vehicle and Wave Data
Figure 5.16 Test 05 Wave Elevation Data Time Series
80
Figure 5.17 Test 05 Vehicle Data Time Series
Test
06
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 0.273 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
Table 5.7 Test 06 Vehicle and Wave Data
81
Figure 5.18 Test 06 Wave Elevation Data Time Series
Figure 5.19 Test 06 Vehicle Data Time Series
82
Test
07
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 0.486 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
Table 5.8 Test 07 Vehicle and Wave Data
Figure 5.20 Test 07 Wave Elevation Data Time Series
83
Figure 5.21 Test 07 Vehicle Data Time Series
Test
08
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 0.506 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
Table 5.9 Test 08 Vehicle and Wave Data
84
Figure 5.22 Test 08 Wave Elevation Data Time Series
Figure 5.23 Test 08 Vehicle Data Time Series
85
Test
09
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 0.487 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
Table 5.10 Test 09 Vehicle and Wave Data
Figure 5.24 Test 09 Wave Elevation Data Time Series
86
Figure 5.25 Test 09 Vehicle Data Time Series
Test
10
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 0.362 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
Table 5.11 Test 10 Vehicle and Wave Data
87
Figure 5.26 Test 10 Wave Elevation Data Time Series
Figure 5.27 Test 10 Vehicle Data Time Series
88
Test
11
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 0.303 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
Table 5.12 Test 11 Vehicle and Wave Data
Figure 5.28 Test 11 Wave Elevation Data Time Series
89
Figure 5.29 Test 11 Vehicle Data Time Series
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]
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
Table 5.13 Test 12 Vehicle and Wave Data
90
Figure 5.30 Test 12 Wave Elevation Data Time Series
Figure 5.31 Test 12 Vehicle Data Time Series
91
Test
13
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 0.412 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
Table 5.14 Test 13 Vehicle and Wave Data
Figure 5.32 Test 13 Wave Elevation Data Time Series
92
Figure 5.33 Test 13 Vehicle Data Time Series
Test
14
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 0.324 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
Table 5.15 Test 14 Vehicle and Wave Data
93
Figure 5.34 Test 14 Wave Elevation Data Time Series
Figure 5.35 Test 14 Vehicle Data Time Series
94
Test
15
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 0.348 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
Table 5.16 Test 15 Vehicle and Wave Data
Figure 5.36 Test 15 Wave Elevation Data Time Series
95
Figure 5.37 Test 15 Vehicle Data Time Series
Test
16
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 0.252 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
Figure 5.38 Test 16 Wave Elevation Data Time Series
Figure 5.39 Test 16 Vehicle Data Time Series
97
Test
17
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 0.417 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
Table 5.18 Test 17 Vehicle and Wave Data
Figure 5.40 Test 17 Wave Elevation Data Time Series
98
Figure 5.41 Test 17 Vehicle Data Time Series
Test
18
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 0.861 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
Table 5.19 Test 18 Vehicle and Wave Data
99
Figure 5.42 Test 18 Wave Elevation Data Time Series
Figure 5.43 Test 18 Vehicle Data Time Series
100
Test
19
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 0.290 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
Table 5.20 Test 19 Vehicle and Wave Data
Figure 5.44 Test 19 Wave Elevation Data Time Series
101
Figure 5.45 Test 19 Vehicle Data Time Series
Test
20
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 0.327 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
Table 5.21 Test 20 Vehicle and Wave Data
102
Figure 5.46 Test 20 Wave Elevation Data Time Series
Figure 5.47 Test 20 Vehicle Data Time Series
103
Test
21
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 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
Table 5.22 Test 21 Vehicle and Wave Data
Figure 5.48 Test 21 Wave Elevation Data Time Series
104
Figure 5.49 Test 21 Vehicle Data Time Series
Test
22
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 0.649 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
Table 5.23 Test 22 Vehicle and Wave Data
105
Figure 5.50 Test 22 Wave Elevation Data Time Series
Figure 5.51 Test 22 Vehicle Data Time Series
106
Test
23
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 0.353 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
Table 5.24 Test 23 Vehicle and Wave Data
Figure 5.52 Test 23 Wave Elevation Data Time Series
107
Figure 5.53 Test 23 Vehicle Data Time Series
Test
24
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 0.364 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
Table 5.25 Test 24 Vehicle and Wave Data
108
Figure 5.54 Test 24 Wave Elevation Data Time Series
Figure 5.55 Test 24 Vehicle Data Time Series
109
Test
25
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 0.823 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
Table 5.26 Test 25 Vehicle and Wave Data
Figure 5.56 Test 25 Wave Elevation Data Time Series
110
Figure 5.57 Test 25 Vehicle Data Time Series
Test
26
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 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
Table 5.27 Test 26 Vehicle and Wave Data
111
Figure 5.58 Test 26 Wave Elevation Data Time Series
Figure 5.59 Test 26 Vehicle Data Time Series
112
Test
27
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 0.325 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
Table 5.28 Test 27 Vehicle and Wave Data
Figure 5.60 Test 27 Wave Elevation Data Time Series
113
Figure 5.61 Test 27 Vehicle Data Time Series
Test
28
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 0.440 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
Table 5.29 Test 28 Vehicle and Wave Data
114
Figure 5.62 Test 28 Wave Elevation Data Time Series
Figure 5.63 Test 28 Vehicle Data Time Series
115
Test
29
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 0.440 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
Table 5.30 Test 29 Vehicle and Wave Data
Figure 5.64 Test 29 Wave Elevation Data Time Series
116
Figure 5.65 Test 29 Vehicle Data Time Series
Test
30
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 0.808 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
Table 5.31 Test 30 Vehicle and Wave Data
117
Figure 5.66 Test 30 Wave Elevation Data Time Series
Figure 5.67 Test 30 Vehicle Data Time Series
118
Test
31
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 0.504 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
Table 5.32 Test 31 Vehicle and Wave Data
Figure 5.68 Test 31 Wave Elevation Data Time Series
119
Figure 5.69 Test 31 Vehicle Data Time Series
Test
32
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 0.623 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
Table 5.33 Test 32 Vehicle and Wave Data
120
Figure 5.70 Test 32 Wave Elevation Data Time Series
Figure 5.71 Test 32 Vehicle Data Time Series
121
Test
33
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 0.648 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
Table 5.34 Test 33 Vehicle and Wave Data
Figure 5.72 Test 33 Wave Elevation Data Time Series
122
Figure 5.73 Test 33 Vehicle Data Time Series
Test
34
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 0.209 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
Table 5.35 Test 34 Vehicle and Wave Data
123
Figure 5.74 Test 34 Wave Elevation Data Time Series
Figure 5.75 Test 34 Vehicle Data Time Series
124
Test
35
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 0.483 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
Table 5.36 Test 35 Vehicle and Wave Data
Figure 5.76 Test 35 Wave Elevation Data Time Series
125
Figure 5.77 Test 35 Vehicle Data Time Series
Test
36
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 0.681 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
Table 5.37 Test 36 Vehicle and Wave Data
126
Figure 5.78 Test 36 Wave Elevation Data Time Series
Figure 5.79 Test 36 Vehicle Data Time Series
127
Test
37
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 0.330 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
Table 5.38 Test 37 Vehicle and Wave Data
Figure 5.80 Test 37 Wave Elevation Data Time Series
128
Figure 5.81 Test 37 Vehicle Data Time Series
Test
38
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 0.727 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
Table 5.39 Test 38 Vehicle and Wave Data
129
Figure 5.82 Test 38 Wave Elevation Data Time Series
Figure 5.83 Test 38 Vehicle Data Time Series
130
Test
39
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 0.813 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
Table 5.40 Test 39 Vehicle and Wave Data
Figure 5.84 Test 39 Wave Elevation Data Time Series
131
Figure 5.85 Test 39 Vehicle Data Time Series
Test
40
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 0.649 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
Table 5.41 Test 40 Vehicle and Wave Data
132
Figure 5.86 Test 40 Wave Elevation Data Time Series
Figure 5.87 Test 40 Vehicle Data Time Series
133
Test
41
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 0.649 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
Table 5.42 Test 41 Vehicle and Wave Data
Figure 5.88 Test 41 Wave Elevation Data Time Series
134
Figure 5.89 Test 41 Vehicle Data Time Series
Test
42
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 0.649 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
Table 5.43 Test 42 Vehicle and Wave Data
135
Figure 5.90 Test 42 Wave Elevation Data Time Series
Figure 5.91 Test 42 Vehicle Data Time Series
136
Test
43
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 0.992 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
Table 5.44 Test 43 Vehicle and Wave Data
Figure 5.92 Test 43 Wave Elevation Data Time Series
137
Figure 5.93 Test 43 Vehicle Data Time Series
Test
44
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 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
Table 5.45 Test 44 Vehicle and Wave Data
138
Figure 5.94 Test 44 Wave Elevation Data Time Series
Figure 5.95 Test 44 Vehicle Data Time Series
139
Test
45
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 0.813 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
Table 5.46 Test 45 Vehicle and Wave Data
Figure 5.96 Test 45 Wave Elevation Data Time Series
140
Figure 5.97 Test 45 Vehicle Data Time Series
Test
46
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 0.813 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
Table 5.47 Test 46 Vehicle and Wave Data
141
Figure 5.98 Test 46 Wave Elevation Data Time Series
Figure 5.99 Test 46 Vehicle Data Time Series
142
Test
47
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 0.992 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
Table 5.48 Test 47 Vehicle and Wave Data
Figure 5.100 Test 47 Wave Elevation Data Time Series
143
Figure 5.101 Test 47 Vehicle Data Time Series
Test
48
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 0.499 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
Table 5.49 Test 48 Vehicle and Wave Data
144
Figure 5.102 Test 48 Wave Elevation Data Time Series
Figure 5.103 Test 48 Vehicle Data Time Series
145
Test
49
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 0.597 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
Table 5.50 Test 49 Vehicle and Wave Data
Figure 5.104 Test 49 Wave Elevation Data Time Series
146
Figure 5.105 Test 49 Vehicle Data Time Series
Test
50
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 0.693 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
Table 5.51 Test 50 Vehicle and Wave Data
147
Figure 5.106 Test 50 Wave Elevation Data Time Series
Figure 5.107 Test 50 Vehicle Data Time Series
148
Test
51
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 0.703 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
Table 5.52 Test 51 Vehicle and Wave Data
Figure 5.108 Test 51 Wave Elevation Data Time Series
149
Figure 5.109 Test 51 Vehicle Data Time Series
Test
52
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 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
Table 5.53 Test 52 Vehicle and Wave Data
150
Figure 5.110 Test 52 Wave Elevation Data Time Series
Figure 5.111 Test 52 Vehicle Data Time Series
151
Test
53
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 0.850 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
Table 5.54 Test 53 Vehicle and Wave Data
Figure 5.112 Test 53 Wave Elevation Data Time Series
152
Figure 5.113 Test 53 Vehicle Data Time Series
Test
54
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 0.813 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
Table 5.55 Test 54 Vehicle and Wave Data
153
Figure 5.114 Test 54 Wave Elevation Data Time Series
Figure 5.115 Test 54 Vehicle Data Time Series
154
Test
55
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 0.699 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
Table 5.56 Test 55 Vehicle and Wave Data
Figure 5.116 Test 55 Wave Elevation Data Time Series
155
Figure 5.117 Test 55 Vehicle Data Time Series
Test
56
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 0.817 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
Table 5.57 Test 56 Vehicle and Wave Data
156
Figure 5.118 Test 56 Wave Elevation Data Time Series
Figure 5.119 Test 56 Vehicle Data Time Series
157
Test
57
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 0.924 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
Table 5.58 Test 57 Vehicle and Wave Data
Figure 5.120 Test 57 Wave Elevation Data Time Series
158
Figure 5.121 Test 57 Vehicle Data Time Series
Test
58
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 0.844 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
Table 5.59 Test 58 Vehicle and Wave Data
159
Figure 5.122 Test 58 Wave Elevation Data Time Series
Figure 5.123 Test 58 Vehicle Data Time Series
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
Table 5.60 Test 59 Vehicle and Wave Data
Figure 5.124 Test 59 Wave Elevation Data Time Series
161
Figure 5.125 Test 59 Vehicle Data Time Series
Test
60
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 0.835 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
Table 5.61 Test 60 Vehicle and Wave Data
Figure 5.126 Test 60 Wave Elevation Data Time Series
Figure 5.127 Test 60 Vehicle Data Time Series
163
Test
61
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 0.689 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
Table 5.62 Test 61 Vehicle and Wave Data
Figure 5.128 Test 61 Wave Elevation Data Time Series
164
Figure 5.129 Test 61 Vehicle Data Time Series
Test
62
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 0.838 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
Table 5.63 Test 62 Vehicle and Wave Data
165
Figure 5.130 Test 62 Wave Elevation Data Time Series
Figure 5.131 Test 62 Vehicle Data Time Series
166
Test
63
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 0.602 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
Table 5.64 Test 63 Vehicle and Wave Data
Figure 5.132 Test 63 Wave Elevation Data Time Series
167
Figure 5.133 Test 63 Vehicle Data Time Series
Test
64
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 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
Table 5.65 Test 64 Vehicle and Wave Data
168
Figure 5.134 Test 64 Wave Elevation Data Time Series
Figure 5.135 Test 64 Vehicle Data Time Series
169
Test
65
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 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
Table 5.66 Test 65 Vehicle and Wave Data
Figure 5.136 Test 65 Wave Elevation Data Time Series
170
Figure 5.137 Test 65 Vehicle Data Time Series
Test
66
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 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
Table 5.67 Test 66 Vehicle and Wave Data
171
Figure 5.138 Test 66 Wave Elevation Data Time Series
Figure 5.139 Test 66 Vehicle Data Time Series
172
Test
67
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 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
Table 5.68 Test 67 Vehicle and Wave Data
Figure 5.140 Test 67 Wave Elevation Data Time Series
173
Figure 5.141 Test 67 Vehicle Data Time Series
Test
68
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 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
Table 5.69 Test 68 Vehicle and Wave Data
Figure 5.142 Test 68 Wave Elevation Data Time Series
Figure 5.143 Test 68 Vehicle Data Time Series
175
Test
69
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 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
Table 5.70 Test 69 Vehicle and Wave Data
Figure 5.144 Test 69 Wave Elevation Data Time Series
176
Figure 5.145 Test 69 Vehicle Data Time Series
Test
70
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 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
Table 5.71 Test 70 Vehicle and Wave Data
Figure 5.146 Test 70 Wave Elevation Data Time Series
Figure 5.147 Test 70 Vehicle Data Time Series
178
Test
71
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 0.000 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
Table 5.72 Test 71 Vehicle and Wave Data
Figure 5.148 Test 71 Wave Elevation Data Time Series
179
Figure 5.149 Test 71 Vehicle Data Time Series
Test
72
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 0.953 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
Table 5.73 Test 72 Vehicle and Wave Data
180
Figure 5.150 Test 72 Wave Elevation Data Time Series
Figure 5.151 Test 72 Vehicle Data Time Series
181
Test
73
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 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
Table 5.74 Test 73 Vehicle and Wave Data
Figure 5.152 Test 73 Wave Elevation Data Time Series
182
Figure 5.153 Test 73 Vehicle Data Time Series
Test
74
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 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
Table 5.75 Test 74 Vehicle and Wave Data
183
Figure 5.154 Test 74 Wave Elevation Data Time Series
Figure 5.155 Test 74 Vehicle Data Time Series
184
Test
75
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 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
Table 5.76 Test 75 Vehicle and Wave Data
Figure 5.156 Test 75 Wave Elevation Data Time Series
185
Figure 5.157 Test 75 Vehicle Data Time Series
Test
76
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 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
Table 5.77 Test 76 Vehicle and Wave Data
186
Figure 5.158 Test 76 Wave Elevation Data Time Series
Figure 5.159 Test 76 Vehicle Data Time Series
187
Test
77
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 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
Table 5.78 Test 77 Vehicle and Wave Data
Figure 5.160 Test 77 Wave Elevation Data Time Series
188
Figure 5.161 Test 77 Vehicle Data Time Series
Test
78
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 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
Table 5.79 Test 78 Vehicle and Wave Data
189
Figure 5.162 Test 78 Wave Elevation Data Time Series
Figure 5.163 Test 78 Vehicle Data Time Series
190
Test
79
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 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
Table 5.80 Test 79 Vehicle and Wave Data
Figure 5.164 Test 79 Wave Elevation Data Time Series
191
Figure 5.165 Test 79 Vehicle Data Time Series
Test
80
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 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
Table 5.81 Test 80 Vehicle and Wave Data
192
Figure 5.166 Test 80 Wave Elevation Data Time Series
Figure 5.167 Test 80 Vehicle Data Time Series
193
Test
81
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 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
Table 5.82 Test 81 Vehicle and Wave Data
Figure 5.168 Test 81 Wave Elevation Data Time Series
194
Figure 5.169 Test 81 Vehicle Data Time Series
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.