Linearized Potential Flow Theory for ACVs in a Seaway 



0(Wv2 *noo " g *iioo =2V(v4> iooo- v *oioo +v *oioo-^iooo } 



g 



010C 

 x xx 



+ — — 4> — — (Vd> - e* ) 



1000 £z K ^0100 6 0100 ' 



1 ' 1 xr* 



g x P ^010 0100 



A(v 2 ) + 



3* 1000 xx-8 10 00 



z 



V V 



~p~e" P 010 ^1000 + _ P~ P 010 

 6 x xz x 



P '*1000 P 010 



x x 



+ *iooo p oio } (v ' 5) 



y y 



The first four of the above equations may be written in the form 



2 2 1- 



- 2i<r V^ - o * - g* z =— - (V p - iff p ) (V. 6) 



V * 



where p is the time -independent part of p 



(iv) On the side hulls the condition (4. 10) is 





= 8 



dh. 



1_ C os 6 — sin^ + (z' + h)0+Vcos0> -rr— ; 



x z G I dx' 



!— — sinl 

 x 



I ah i ■« 



+ cosfl - x 1 6 + V sin0>^^— 



z I oz 1 



2 ah ! 2 2 * h l 2 



1 + 5 ^) +6 (^-) 2 



-1/2 



217 



