Wavemaking Resistance of Ships with Transom Stern 



zero at both ends of a ship such as we considered In Eq, (11), although 

 this is not a basic necessity for evaluating physical quantities, namely, 



a(0,y,z) = cr(-l ,y,z) = 



By making use of this assumiption we Integrate the wave- height Eq. (39) 

 by parts 



^(X|.y|) = -^ (x,»y, .0) 



1 f° -iTTXCosS^ d r . T, r fsec'^ee""' ' dt dB 



= Tt \ e dx-r- \ cr dc Re \ \ — 



ttU J_, dx J g(j^^ J_Tr Jo ^ 



J \ " 



*^ir *^0 t 



,oO o r» ^.TT ^00 tCiw, +2) 



:'^0 e 



- k sec 9 - i|jL sec 9 



Re r r i(x,,y;t,9) ^^ ^Q (^2) 



ttU J_ J« ^ \^sec 9 - ifjLsec9 



where 



<jOj = X| cos 9 + (yi - y) sin 9 (43) 



I(x|,y, ;t,9) = - \ e dx -^ \ a sec 9e dc (44) 



^c(x) 

 Integrating I by parts with respect to x, we obtain 



1 r d r ^ t{iW| + z) 



I(x,,y,;t,9) = -i^[-^J o-(0,y,z) sec^9 e dc 



_ ^\ o-(-l ,y,z)sec^9 exp jti(xrTI cos 9 +y, -y sin9)+tzjdc 



P -ifXCOSSd^r* , ^ 3„ f(iuJl+z)l , /^r\ 



-\ dxe — gV o-(x,y,z)sec^9e^^'"'' ^Mdc (45) 



•J-1 dxJc(x) -^ 



For simplicity o-^(9,y,z) and o-^(-l,y,z) are assumed to be uni- 

 formly distributed, respectively, along the stern on the free surface 

 and along the bow stern vertically. For investigation of the flow 

 field near the transom stern, the contribution of (r^(9,y,z) to the 

 wave height may be approximated by two-dimens ional values; the 

 contribution of o-j(-l ,y,z) may be approximated by the stationary 

 phase; and the contribution from the last integral of I(x,y;t,9) may 

 be approximated by a slender body theory, and will be investigated 

 first, here. 



583 



