As with surface vessels, theoretical forms of least wave resis- 

 tance are symmetrical with respect to the midship section. Any departure 

 from symmetry causes an increase in wave resistance, and this increase can 

 become appreciable in some ranges of Proude numbers when the asymmetry is 

 pronounced. The degree of asymmetry can be described in the usual way, 

 though roughly, by the location of the center of buoyancy x , or the dif- 

 ference of the prismatic coefficients <£ p , <f>, of the fore and afterbody. 

 For instance, a difference <j>„ - 0„ = 0.2 means a large deviation from sym- 

 metry. Again, the resistance results are qualitatively supported by experi- 

 ments, 6 



An extensive hydrodynamic study of bodies of revolution is under- 

 way at the Taylor Model Basin. It is based on a systematic variation of 

 analytically defined forms. 2 ' 11 As an extension of this work it was decided 

 to make a more comprehensive theoretical investigation on the wave resistance 

 of bodies of revolution. This is the subject of the present report. 



In Section 1 of this report polynomials are discussed which are 

 suitable for the representation of hydrodynamic singularity distributions 

 (doublets, sources and sinks); to the first approximation the equation of 

 the doublet distribution coincides with the equation of the sectional-area 

 curve except for a scale factor. 7 ' 8 A class of curves is selected which in- 

 cludes the TMB Series 2 generalized by one additional arbitrary parameter. 

 For this family a set of auxiliary integrals covering a large range of 

 Froude numbers has been tabulated. The values of these integrals furnish 

 immediately the variable part of the wave resistance of the simplest forms 

 (parabolas of the type 1 - | n ) . In the general case the wave resistance is 

 given by a quadratic form of the parameters of the body in which the tabu- 

 lated values appear as coefficients. Thus the computation of the wave re- 

 sistance involves only some multiplications and an algebraic addition. 



The auxiliary integrals mentioned have been computed by the Bureau 

 of Standards. A short description of the work involved, contributed by Mr. 

 Blum of that Bureau, and tables of functions are found in Appendices II and 

 III. 



As mentioned before, the resistance formula for a line distribution 

 of singularities used throughout this report follows immediately from a more 

 general expression due to Havelock 3 ' 5 and therefore will be called Havelock's 

 integral. 



Using the tables annexed, resistance curves are plotted for vari- 

 ous basic forms of sectional-area curves (doublet distributions); they cover 

 three depths of immersion ratios f/L except for the spheroid where a fourth 



