TABLE OP CONTENTS 



Page 



ABSTRACT 1 



1 . INTRODUCTION 1 



2. THE REPRESENTATION OP SINGULARITY DISTRIBUTIONS 



AND SECTIONAL-AREA CURVES BY POLYNOMIALS ' . 4 



2.1 . Connection between Body Form and Generating 



Hydrodynamic Singularities 4 



2.2. Representation by Polynomials 6 



2.2.1 . General Remarks 6 



2.2.2. The TMB (Landweber) Class of Bodies 



and Some Generalizations 7 



2.3. Connection between Strength of Singularities 



and Body Shape 13 



3. EVALUATION OP HAVELOCK'S INTEGRAL 14 



3.1 . General Considerations 14 



3.2. Tabulation of Resistance Integrals for a 



Five -Parameter Class of Bodies 1 6 



4. REPRESENTATION OP^ RESISTANCE CURVES 18 



4.1 . The Dimension Factor C and Dimensionless 



Representations 18 



4.2. Resistance Curves of Simple Symmetrical Bodies 20 



4.3. Resistance Curves of Asymmetrical Bodies 26 



4.4. Limiting Depth of Immersion 37 



5. BODIES OF REVOLUTION OF LEAST WAVE RESISTANCE . 38 



5-1 . Two-Parameter Forms 38 



5.2. Isoperimetric Problems, One -Parameter Forms 40 



6. RESISTANCE CURVES OF THE FAMILY (2 , 4, 6; ; t ) 44 



SUMMARY 45 



APPENDIX I - APPROXIMATE CALCULATION OF THE SURFACE S OF 



A CLASS OF ELONGATED BODIES OF REVOLUTION 51 



APPENDIX II - EVALUATION OP THE AUXILIARIES INTEGRALS* 53 



APPENDIX III - AUXILIARY INTEGRALS FOR VARIOUS FROUDE NUMBERS. ... 55 



REFERENCES 58 



*By J. Blum, National Bureau of Standards 



