Linearized Potential Flow Theory for ACVs in a Seaway 



e< 



f 



p sin 



[p(x- £) cos Q] cos |_(y- 77) sin d\ 



dp 



p - k sec 

 o 



Substituting in (6-31) and noting that the second term on the RHS 

 makes no contribution to the double surface integrals, we have 



:z R w 



cushion irpV'J, 

 72 



§ 



*dP o (x,y) /ydp Q (| v ) 

 T7" " dxd W/ Jf~ 



f r 1 T 2 1 3 



/cos k (x- £ ) sec 5 cos k (y- v) sec 6 sin0 sec d# 



It is easy to reduce this as before to the form 



71"/ 2 



~T R w 



j3 cushion r pV 



= ^—r- / [p 2 (6) + Q 2 (0)] sec 3 e d0 



(6-32) 



where now 



P(0) 



Q(d) 



*dp Q (x, y) (cos) 



3 j Ik (xcos0 + ysin0) sec dxdy 



I sin I L 



(6-33) 



These expressions may be compared with (6-2 8) and (6-2 9) for the 

 hull wave resitance. 



It is clear from (6-33) that we may write by the use of 

 Stokes' theorem, 



P(») 



Q(e) 



p o (x, y) 



sin 



k (xcos0 + ysin0) sec q dy - 



- k sec 

 o 



ff [~ S * n ) r 



9 //p (x, y) J ( k (xcos ^ + ysin^sec 



JJ I cos| L 



dxdy 



The line integral vanishes and we have 



2 V2 



~2 R W 



/3 cushion 7rp^ 



k C 



=—^2" / [p 2 (0) + Qf (0) ] sec 5 dd (6-34) 



7TpV J 



where 



155 



