Linearized Potential Flow Theory for ACVs in a Seaway 



8 ' V * + 1000 (X ' Y ' Z) = 5pV4> 1000 ,(x',b + ,z') 

 X x' 



+ 880V (r 4> + r' * ) + 

 Pp v 010 1000 . .010 1000 . / 



x'x' 



i<rt 



+ 5ae nV (r $ + r 1 $ 



p v 001 1000 , , 001 1000 



X'X' 



when 0( 5 2 ) is neglected. 



The expansion on the inner side i. e. on S- will be 



identical but the argument of the potential will now be (x',b-, z'). 



Similar expansions can be written down for the other terms 

 in (III. 2) giving finally 



p<*, y. .it) = «pV» +*V» 010() 



X 1 X 1 



P< V [r 4> +r'4> \ 



I V 0101010 x.x. 01 ° l01 Vz'j 



2 0100 0100 



+ 83p /Vi r $ + r 1 * 



'000 , , 010 1000 , 



x'x' x'z 



( r $ 



\ 010 H 



.) 



+ r <|> + r' * +4> 



100*0100 , , 100*0100 , , 1100 



x'x' x'z' x" 



■ v *iooo • v *oiooj 



P \ \ 001 l n ' 



000 , , 001 1000 , , 

 x'x' x'z' 



>1010 x.)- ^1010 J 



0ae P< V (r^* 



} V001 0100 , , 

 V v x'x' 



+ r 1 4> 



001 0100 . . 

 x'z 1 



189 



