TABLE OF CONTENTS 



Page 



LIST OF FIGURES iii 



ABSTRACT 1 



ADMINISTRATIVE INFORMATION 1 



INTRODUCTION 1 



RAY EQUATIONS 2 



RAYS OF SHIP WAVES AND LINEAR THEORY 3 



RAYS OF SHIP WAVES AND SHIP BOUNDARIES 5 



RAY REFLECTION 7 



NUMERICAL EXPERIMENTS OF RAY PATHS AND FREE 



SURFACE SHOCK WAVES 7 



WAVE AMPLITUDE AND PHASE 9 



WAVE RESISTANCE 10 



DISCUSSION 13 



ACKNOWLEDGMENTS 13 



APPENDIX A 13 



REFERENCES i5 



LIST OF FIGURES 



1 - Ray Paths for a Wigley Hull (b = 0.1, h = 0.625) ' 4 



2 - Ray Paths for a Wigley Hull (b = 0.2, h = 0.0625) 6 



3 - Ray Paths for a Wigley Hull (b = 0.2, h = 0. 03) 6 



4 - Ray Paths for a Wigley Hull (b = 0.5, h = 0.0625) 6 



5 - Angles of Waves Reflecting on the Ship Hull 



6 - Width of the Second Caustic, a/x , for Wigley Hulls 8 



7 - Rays of the Wigley Ship (b = 0.2, h = 0.0625) with Bulb 



(radius, r b = 0.0214h, depth, 2.^ = 0.5h) 



iii 



