for the viscous drag R . Hence, in 

 this case forms of least total resis- 

 tance R. must be derived from addi- 

 tional considerations and may differ, 

 at least in principle, from the fa- 

 miliar streamlined forms. 



In the present report it 

 Figure 1 - Scheme of Submerged Body is intended to analyze the wave re- 

 sistance of a rather wide class of 

 elongated bodies of revolution, using an integral relation based on the work 

 of Havelock. 2 The first classical solutions for the circular cylinder 

 (Lamb) 17 and the sphere (Havelock) 18 have contributed much to the general 

 understanding of the subject, but these solutions must be applied v/ith great 

 caution to problems connected with elongated bodies. The reason herein is 

 the extreme simplicity of the cylinder and sphere; the resistance curves of 

 these bodies do not show the characteristic interference effects which are 

 peculiar for prolate bodies of revolution. Prom physical reasoning we infer 

 at once that in the latter case two similarity parameters are involved: the 

 common Proude number P = U/Pg~L referred to the length L and a parameter 

 characterising the depth of immersion f , say f/L or the depth Proude number 

 F- = U/Pgf, while the shape of the wave-resistance curves for the circular 

 cylinder and the sphere depend only upon F~, and the parameter f/L appears 

 as a scaling factor only. Thus, for instance, the peak of the resistance 

 curve is located at F- = 1 for the cylinder and just below P f = 1 for the 

 sphere. It can be easily shown that this unity value of the depth Froude 

 number has no special significance for the wave resistance of a very elon- 

 gated body of revolution. 



Solutions for the spheroid and general ellipsoid due to Havelock 3 ' 4 

 lead to results which admit of qualitative and even of quantitative esti- 

 mates of the resistance of "normal" bodies of revolution. The importance 

 of the spheroid for general research on the subject cannot be overemphasized. 



Using Havelock' s general expression valid for a plane source-sink 

 distribution, 3 formulas were obtained which represent the wave resistance 

 of a rather wide class of bodies of revolution. 5 By these formulas the 

 resistance of various forms has been investigated; 6 especially, some endea- 

 vors were made to find forms of least wave resistance. 5 These forms vary 

 obviously with the Proude number and to a lesser degree with the depth 

 parameter f/L. The rather striking results found in this way were checked 

 experimentally and good agreement between theory and measurements was es- 

 tablished as to the general trend. 6 



