Yim 



He further considered (1934b) the energy carried away by regular waves 

 far aft of a ship in connection with the wave resistance, and he derived the wave 

 resistance formula related to the regular waves (8). From (9) and (10), (8) can 

 be rearranged as 



77/ 2 



^s "" [a^(i9) sin (kjX sec 61) + A2((9) COS (kjX sec 61)] COS (kjY sin 61 sec^ei) d^ 



(17) 



where 

 AjC^) = 8[l- exp (-k^ sec^^)] [SjCO) - SjCl) cos (k^ sec 0) - S^d) sin (k^ sec 0)] (18) 



AjC^) = 8[l - exp (-k^sec^^)] [SjCO) + S/1) sin(kj sec 6^) - SjC 1) cos (k^ sec 0)]. (19) 



Then Havelock's wave resistance formula is 



R = y [ [Ai'(^) + A^(9)] cos 30 



d0 (20) 



where R is related to the wave resistance R^ by 



R = — 



Since the integrand of (20) is positive definite, R is zero if and only if 



AjC^') = A^(0) = , for < < tt/2 . (21) 



The wave resistance (20) can be written as 



R = Rr + R + Rr, (22) 



Rg = bow wave resistance 



y| [s/cO) + S^'CO)] ^2 



(0) + S, (0) K2 cos^^^ d0 



(23) 



R = stern wave resistance 



:2 cos^^y dd (24) 



Ij [s^D + s^cd] 



(1) + S, Cl) K^ cos-^^y dd 



1072 



