Wavemaking Resistanoe of Ships with Transom Stern 



ship section. 



The slender ship approxinnation is useful for the ship with a 

 transom stern because this may give better chances to represent the 

 ship shape near the transom than Michell approximation. 

 Yet for the case of low Froude numbers it is well known that the usual 

 slender ship theory is also very poor. Tq improve this situation, the 

 slender ship theory can be modified further from that developed by 

 Maruo [ 1 1] • 



In the equations of wave resistance Eqs. (19) through (22), by 

 consecutive applications of integration by part to Eq, (22) 



P + iQ = \ 0- exp j kb(zb + ix) + i2TTy — } dS 



- \ (r(- 1 ,y ,z) exp ] kb(zb - i) + i2Try — [ dc 

 Jc(.|) ' w ) 



- r dx e''*'''' ^ r (T exp (kzb^ + i2Try ^) dc i 

 = TiTJr "! \ o-(0,y,z) exp (kzb +i2Try^) dc 



- \ or(-i ,y ,z) exp j kb(zb - i) + i2iTy — C *^"^ ( 

 + —5-5 \-T-\ 0^ exp (kzb + i2iry — ) dc ?• e 



- \ dx e — 2 \ ^ ®^P (kzt) + i27ry — ) d 

 ^-1 dx Jc{x) ^ 



x=0 

 x=-l 



(36) 



where 



dS = dx dc 



(37) 



The last integral can be approximated by 



581 



