Linearized Potential Flow Theory for ACVs in a Seaway 



A .11 



k 



and the wave number 

 2 



k =-£- 



g 

 The frequency of encounter 



a - <y + kV 

 e 



and 7 is the phase angle of the wave. 



As we have denoted the amplitude/length ratio of the incident 

 waves by the small perturbation parameter t , we may write 



$= € — !Li_ exp -kz + i(kx + a t + 7 ) 

 crk L e J 



so that in our notation 



*0001=4lf eXp |>z + i(kx + 7)] (8-1) 



VIII. 2 Lowest Order Exciting Forces 



We are now in a position to compute the lowest order exciting 

 force in the longitudinal direction from (5-6) 



aeX iooi + * x oioi = ""^jflKW V *oooi x ,>f!. dx ' dz ' 

 ■•• + 7^ i * et ff (i %*oooi 1 °- v *oooi ' Po «* 



and substituting for the derivatives of 3> nn , from (8-1) we get 

 s y j. R y _ s, 4 7ripg io-e t 



6eX iooi +/3eX oioi - 6e -X- e 



f/exp - kz' + i(kx +7 ) \-r— - dx'dz' - 



- 2tt /3 ee laet //exp ["i(kx+7)J p Q dxdy (8-2) 



The vertical force and pitching moment due to wave excitation arise 

 mainly from the side hulls as the air cushion provides no contribu- 

 tion and we have 



161 



