Ship Waves and Wave Resistance 



I share Dr. Yim's cautions regarding a study of the asymptotic influence of 

 the speed parameter. The potential is certainly more intricately dependent on 

 the Froude number than is apparent from explicit factors. But I shall try to ex- 

 tend my investigations in this direction. 



Fortunately, I can meet Dr. Yim's request for some numerical results; 

 these are selected for a parabolic ship with a draft/length ratio equal to 1/20 

 and 7o = 10' Additional resistance due to the free-surface singularity <'(X,Y) is 

 K^2^' = -0.04(B'T.)R< 2>, additional resistance due to second-order singularities to 

 represent the ship is R^^^^ = 0, 15(B/L)R( 2) with 10% accuracy, where R^ ^^ is the 

 resistance from linear theory. Unfortunately, only the free-wave part of the 

 first-order flow on the hull was accounted for when calculating ^\^\ though the 

 local component is of equal magnitude. The local component gave contributions 

 obviously inconsistent and too large. Very probably the Fourier series repre- 

 sentation in Y is not appropriate at the center plane for the local part of the 

 potential due to the discontinuity in the Y derivative. We shall try either to 

 evaluate the integrals on the actual ship surface or to split off the singular part 

 and integrate it in some closed form. 



The effect of i//^ ^ ^ ^ "^ *" "^ on the free wave spectrum is a uniform phase shift 

 of all wave components toward the bow. 



REPLY TO THE DISCUSSION BY WARD 



I thank Prof. Ward for his well meaning comments, which need no additional 

 clarification. Prof. Ward is certainly right in pointing out that my result on the 

 X-Y method is incomplete; thus I welcome his elucidating remarks. 



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