Ship Hydrostatics and Stability (eBook)

Cover 1
Contents 8
Preface 14
Acknowledgements 18
1. Definitions, principal dimensions 20
Introduction 20
Marine terminology 21
The principal dimensions of a ship 22
The definition of the hull surface 28
Coordinate systems 28
Graphic description 30
Fairing 32
Table of offsets 34
Coefficients of form 34
Summary 38
Example 39
Exercises 40
2. Basic ship hydrostatics 42
Introduction 42
Archimedes’ principle 43
A body with simple geometrical form 43
The general case 48
The conditions of equilibrium of a floating body 51
Forces 52
Moments 53
A definition of stability 55
Initial stability 56
Metacentric height 58
A lemma on moving volumes or masses 59
Small angles of inclination 60
A theorem on the axis of inclination 60
Metacentric radius 63
The curve of centres of buoyancy 64
The metacentric evolute 66
Metacentres for various axes of inclination 66
Summary 67
Examples 69
Exercises 86
Appendix –Water densities 89
3. Numerical integration in naval architecture 90
Introduction 90
The trapezoidal rule 91
Error of integration by the trapezoidal rule 94
Simpson’s rule 96
Error of integration by Simpson’s rule 98
Calculating points on the integral curve 99
Intermediate ordinates 102
Reduced ordinates 103
Other procedures of numerical integration 104
Summary 105
Examples 106
Exercises 109
4. Hydrostatic curves 110
Introduction 110
The calculation of hydrostatic data 111
Waterline properties 111
Volume properties 114
Derived data 115
Wetted surface area 117
Hydrostatic curves 118
Bonjean curves and their use 120
Some properties of hydrostatic curves 123
Hydrostatic properties of affine hulls 126
Summary 127
Example 128
Exercises 128
5. Statical stability at large angles of heel 130
Introduction 130
The righting arm 130
The curve of statical stability 133
The influence of trim and waves 135
Summary 136
Example 138
Exercises 138
6. Simple models of stability 140
Introduction 140
Angles of statical equilibrium 143
The wind heeling arm 143
Heeling arm in turning 145
Other heeling arms 146
Dynamical stability 147
Stability conditions – a more rigorous derivation 150
Roll period 152
Loads that adversely affect stability 154
Loads displaced transversely 154
Hanging loads 155
Free surfaces of liquids 156
Shifting loads 160
Moving loads as a case of positive feedback 161
The stability of grounded or docked ships 163
Grounding on the whole length of the keel 163
Grounding on one point of the keel 164
Negative metacentric height 165
The limitations of simple models 169
Other modes of capsizing 170
Summary 171
Examples 173
Exercises 174
7. Weight and trim calculations 178
Introduction 178
Weight calculations 179
Weight groups 179
Weight calculations 180
Trim 183
Finding the trim and the draughts at perpendiculars 183
Equilibrium at large angles of trim 184
The inclining experiment 185
Summary 190
Examples 191
Exercises 193
8. Intact stability regulations I 196
Introduction 196
The IMO code on intact stability 197
Passenger and cargo ships 197
Cargo ships carrying timber deck cargoes 201
Fishing vessels 201
Mobile offshore drilling units 202
Dynamically supported craft 202
Container ships greater than 100m 204
Icing 204
Inclining and rolling tests 204
The regulations of the US Navy 204
The regulations of the UK Navy 209
A criterion for sail vessels 211
A code of practice for small workboats and pilot boats 213
Regulations for internal-water vessels 215
EC regulations 215
Swiss regulations 215
Summary 216
Examples 217
Exercises 220
9. Parametric resonance 222
Introduction 222
The influence of waves on ship stability 223
The Mathieu effect – parametric resonance 226
The Mathieu equation – stability 226
The Mathieu equation – simulations 230
Frequency of encounter 234
Summary 235
Examples 236
Exercise 238
10. Intact stability regulations II 240
Introduction 240
The regulations of the German Navy 240
Categories of service 241
Loading conditions 241
Trochoidal waves 242
Righting arms 246
Free liquid surfaces 246
Wind heeling arm 247
The wind criterion 248
Stability in turning 249
Other heeling arms 250
Summary 250
Examples 251
Exercises 255
11. Flooding and damage condition 258
Introduction 258
A few definitions 260
Two methods for finding the ship condition after flooding 262
Lost buoyancy 265
Added weight 267
The comparison 269
Details of the flooding process 270
Damage stability regulations 271
SOLAS 271
Probabilistic regulations 273
The US Navy 275
The UK Navy 276
The German Navy 277
A code for large commercial sailing or motor vessels 278
A code for small workboats and pilot boats 278
EC regulations for internal-water vessels 279
Swiss regulations for internal-water vessels 279
The curve of floodable lengths 280
Summary 282
Examples 284
Exercise 287
12. Linear ship response in waves 288
Introduction 288
Linear wave theory 289
Modelling real seas 292
Wave induced forces and motions 296
A note on natural periods 300
Roll stabilizers 302
Summary 305
Examples 306
Exercises 309
Appendix – The relationship between curl and rotation 309
13. Computer methods 312
Introduction 312
Geometric introduction 313
Parametric curves 313
Curvature 314
Splines 315
B´ezier curves 317
B-splines 321
Parametric surfaces 322
Ruled surfaces 324
Surface curvatures 324
Hull modelling 327
Mathematical ship lines 327
Fairing 327
Modelling with MultiSurf and SurfaceWorks 327
Calculations without and with the computer 335
Hydrostatic calculations 336
Simulations 338
A simple example of roll simulation 341
Summary 343
Examples 345
Exercises 345
Bibliography 346
Index 356