Linearized Potential Flow Theory for ACVs in a Seaway 



a h i a h i 



which vanishes as p , ->- — - and 



are even functions of y' 



The k-component also vanishes and both components similarly vanish 

 on the inner hull surfaces for the same reason. 



M. 



We are therefore left only with the pitching moment 



„->#*(••£-•#) 



+ p (z 1 — — r - x 



d: 



dx'dz 1 



and using the expression for p + and p — given in (ill. 3) we derive 

 finally the following result for the pitching moment where the inte- 

 gration is reduced as before to S. incorporating the correction 

 terms where necessary. 



M. 



, ■ I 



28 Pg x' h(x', z') 



"L 



o 

 2 8 2 p 



{ V *1000 x ,( Z '^. - X 'i^ ) + g W 'h(x',z')j 



-2 5/3p/ V 



! 



. h . h 



*0100 , {z ^T x "5^' 



x 1 



+ 4> 



0100 



--— - x '-&)] + ^oio z,h ( x '- z '»|- 



h 

 cSx' 



iat 



25a e ^g^ 00 i z ' h ( x '' z ') 



or 2 io-t 

 - 25 a e P 



v < x oo> + z, + Vooi)* 10 oo , , 



\ x'x' 



+ ( *ooi - x '%oi )$ iooo 



+ V4> - iad> 



1010 . M010 



-*A -x'-^L) 



3x' 



dz' 



203 



