putting further 



x = 27rtjf = 27rp2L 

 g 



-/ 



h = h e 

 m 



Tf* 



and prescribing h/h , for instance assuming h/h < 0.01 , one obtains 



f >~0.75^ 

 or 



f o /L > 1 . 5ttF 2 



This estimate is superficial for many reasons: 



a. The resistance depends rather on the square of the generated wave 

 amplitudes, 



b. The actual problem is three dimensional, and 



c. The body shape is neglected. 



However, it shows at least that in principle the limiting depth cannot be 

 expressed as a fraction of the dimensions of the body alone, since it depends 

 upon the length of the free wave A or the Proude number P. 



From practical considerations matters are somewhat different. As 

 mentioned before, at very high Proude numbers the ratio of wave resistance 

 to frictional drag is normally very small. Thus the problem of fjnding an 

 accurate value of the limiting depth becomes rather unimportant since even 

 grave errors in computing it do not lead to appreciable errors in the total 

 resistance. 



5- BODIES OP REVOLUTION OP LEAST WAVE RESISTANCE 

 5.1. TWO-PARAMETER FORMS 



In an earlier paper 5 endeavors were made to determine distributions 

 of least resistance for given Proude numbers. The results varied with Proude 

 numbers and depths of immersion, which is quite natural in the light of such 

 resistance graphs as represented by Figures 6, 7 and 8. - 



An important feature is the peculiar "swan neck" form obtained for 

 higher Froude numbers— equal to and above F = 0.35- Because of the limited 

 accuracy of these former calculations the problem has been reconsidered here. 

 The present investigation supports the earlier statements. 



The formalism needed is very simple. Some controversy arose as to 

 how far the application of exact methods of the calculus of variation is 

 consistent When dealing with surface ships; 5 the results obtained did not 



