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1.External force actions 1

1.1 Hydrodynamic forces on a moving body 2

1.2 Force actions and shed vorticity 7

1.3 External force fields and vorticity 9

1.4 Solution of linearized equation of motion 15

1.5 Vortex representation of solution 19

1.6 Singular force perpendicular to its velocity 23

1.7 Singular force in the direction of its velocity 28

1.8 Work done by external force field and moving body 30

1.9 Vorticity of a lifting surface，linearized theory 34

1.10 Bound vortex “ending” at a plate 39

1.11 Suction force at leading edge 44

2.The actuator surface 49

2.1 Linearized actuator surface theory 50

2.2 Actuator disk 53

2.3 Thrust deduction 60

2.4 Non linear actuator disk theory，1 62

2.5 Non linear actuator disk theory，2 70

2.6 Discussion of results and methods 77

3.The ship screw 79

3.1 The geometry of the ship screw 81

3.2 The screw blade with thickness and without load 85

3.3 The velocity field induced by rotating force 88

3.4 Screw blade of zero thickness，prescribed load，1 92

3.5 Screw blade of zero thickness，prescribed load，2 105

3.6 Some additional remarks 109

4.Unsteady propulsion 114

4.1 Some types of unsteady propulsion 115

4.2 Small amplitude propulsion，two dimensional 121

4.3 Solution of the Hilbert problem 125

4.4 Thrust and efficiency 130

4.5 Theoretical and experimental results 133

4.6 Elastically coupled profiles 135

4.7 The Voith-Schneider propeller 138

4.8 Large amplitude unsteady propulsion，rigid profile 140

4.9 Some additional remarks 146

5.Optimization theory 149

5.1 Lifting surface system 150

5.2 Energy extraction out of a disturbed fluid 152

5.3 The variational problem for lifting surface systems 158

5.4 Necessary condition for an optimum 160

5.5 Optimum wing in up- or downward flow 164

5.6 Classes of lifting surface systems，quality number 168

5.7 The ideal propeller 171

5.8 Comparison of the quality number of optimum propellers by inspection 175

5.9 Energy extraction，translating rigid wing 178

5.10 Optimum energy extraction by rigid wing 184

6.Applications of optimization theory 189

6.1 Optimum screw propeller with endplates 190

6.2 Properties of the potential 193

6.3 Circulation distribution，thrust 197

6.4 Efficiency and quality number 198

6.5 Numerical results 201

6.6 Optimization of the sails of a yacht 206

6.7 Numerical results 213

6.8 Optimum unsteady propulsion，large amplitude，two dimensional 216

6.9 Angles of incidence，large amplitude，two dimensional 220

6.10 Optimum large amplitude unsteady propulsion，finite span 222

6.11 On the optimum Voith-Schneider propeller 226

6.12 On the optimum large hub propeller 228

7.On the existence of optimum propellers 232

7.1 Small amplitude flexible profile 233

7.2 Nonexistence of optimum added motion 239

7.3 Large amplitude rigid profile 242

7.4 The wagging motion 244

7.5 Nonexistence of optimum base motion 249

7.6 Small amplitude heaving motion 252

7.7 The optimization problem 257

7.8 Existence of optimum added motion 259

7.9 Large amplitude propulsion flexible profile 263

Appendices 266

A.The Hilbert problem 266

A.1 The formulas of Plemelj 266

A.2 The Hilbert problem for an are 268

A.3 Singular integral equations 269

B.Curvilinear coordinates 271

B.1 Tensor representation of some operators 271

B.2 Two applications 274

References 277

Index 280