Yim 



BOW WAVES AND STERN WAVES 



We consider a source distribution m(xj,Zj) on a ship centerplane D in the 

 plane y = 0. If we use the principle of superposition, the regular ship wave can 

 be represented as 



C = — I m(Xi,Zj) exp(-koZi sec^ 6) 



4k, 



- I I m(Xi,Zj) 



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X sec^ e cos (kow sec^fii) dedxjdzj , (10) 



where L and H are the ship length and the ship draft respectively. This regular 

 wave is important because this is the only wave which contributes to the wave 

 resistance no matter what method we use to calculate the wave resistance. For 

 example, Havelock's (4,5) formula is from the regular waves far behind the 

 ship, while Lagally's method is from the regular waves on the singularity plane 

 (3). If we change the order of integration in Eq. (10), we obtain 



^ = -T^ dd \ U(koH,Xj,e) cos (kpo; sec'^e)dy.^ 



•'^-(7T/2)+S J 



4ko r"^' c"^ 



+ -^ de \ U(koH,Xi,5) cos (kpoj sec^^) dxj , 



(11) 



where 



r 



U(koH,Xi,5) = m(Xj,Zj) expC-kgZj sec^ ^) sec^ 6 dz j , (12) 







§1 = tan" * (y/x) , 



and 



§2 = tan"* (y/x-L) . 



When we consider the wave height on the x axis (y = 0), 



4k 



4 = -T^ r dd { U(koH,Xi,6') cos [ko(x-Xj) sec 6] dy.^ (13) 



for < X < L and 



4k -^/^ -'' 



i = — de U(koH,Xj,5) cos [k(,(x-Xi) sec 9] dxj 



(14) 



■77/ 2 



for x > L. 



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