Linearized Potential Flow Theory for ACVs in a Seaway 



All these curves are to be traversed in the clockwise direction in 

 order to keep the positive side of S Q (which is below the free surfa- 

 ce) to the left. 



We may now write (V. 12) in the form 



1 



S 1 + S 2 



+_ 4^g // (V *** " 2iaY *C a *" Z*P G d S dl 



V 



4-rrg 



2i<r 



(*G^ - G*£ +— — *G) d v + 



V 



Lt 



47 rg L 4 -^L H l 



(*G^ - G^^ + ^—^G) d v 



Now, the function of >£ and its derivatives in the integrand of the 

 surface integral over S is given exactly by the free surface condi- 

 tion (V. 6) on the IFS applicable to potentials of 0( 8, j3, 8a, /3a) , 

 namely, 



-4- (v P ^ - i*p s ) 



Substituting this value and combining the line integrals, we may write 



BG 



¥(x ( .y,..z) =• 



fc/»* 



an 



) dS + 



V s ; 



// (Vp - iap ) G d^dr, + 



pg JJ s £ 



v 



4ir 



g L 



2i cr 

 *G t - G^. +— — - ^G 

 k ? V 



d7? 

 (V. 13) 



225 



