Ship Waves and Wave Resistance 



DISCUSSION 



John V. Wehausen 



University of California, Berkeley 



Berkeley, California 



I am not convinced by, and probably do not understand correctly, Dr. Egg- 

 ers' reason for not using his approach (b) to determine the wave resistance 

 (second subsection of his analysis section). His discarding it seems especially 

 puzzling in view of the fruitful use that he has made in other contexts of the as- 

 sociated formula 



~''' L 



R = y Pg I ^ (Xg,y) dy + 2 



•T 



\p \ dy r 



J-T J-H 



^("e'V) r 



<Px (''e-y-^)"^ ^y + ^; 



dz . 



If one is^ granted the assumption of irrotational flow of an inviscid fluid, and Dr. 

 Eggers makes this assumption, the above formula is exact; i.e., no further ap- 

 proximations are required to derive it. This being so, an approximation to rp 

 and i of any particular sort should at the same time also yield an approximation 

 to R of an appropriate sort. If we suppose then, following Dr. Eggers, that 



cp = ecp( '^ + e^ cp(^' + ... , 

 = e^(pl^\x,y,0) 



2 1 C (2) 1 



^ g " 2g 



. ,,„ = 



( 1 ) ( 1 ) ^ ( 1 ) 



c ( 1 ) (1)1 



+ CD cp >■+ ... 



2 ^x ^xz I 



(see e.g., Eq. (14) of Ref. 1 or Eq. (27.6) of Ref. 2), substitution into the formula 

 for R and some easy manipulations yield 



R = e- 



2g 



1 f -^ 



(Xp,y,0) dy + 2" P I dy 



{^ I V^'\x^,y,0) cp^'\x^,y,0) dy 

 + p dy 



J-T J-H 



-cp^^Ve^y.^-^^^^^l^'' 



dz 



'.l"Ve.y.o)-^.<"%i;' 



dy 



(l)x v(2) (1)(2) (1)(2) 



-f^x (''e-y-O^x + ^y ^y + ^z ^'z 



673 



