Linearized Potential Flow Theory for ACVs in a Seaway 



x ioio + x iooi 



m 



2\ 2_ icet 47ripg laet 



— cr x rt „ e + - e 



8 I e 001 k 



//exp[-kz' +i(kx+7)J-||T dx 

 1„ / m , \ 



'o 



x ono + x oioi 



r 



1\ 2_ iaet 



)a x^ rtl e - 27re 



|8 / e 001 



'dz' = 

 iaet 



i (kx + 7 ) 

 i<re t 



z ioio + z iooi " ' 



47ripg iaet 

 + ; — e 



o 



dxdy = 



rm. 



2\ 2 

 (*nm ■ X A W "IT/" 



001 



//exp [- kz' +i (kx +7 )J-^ 

 Si 



In 



+ 



5 / e 001 



dx'dz' = 



Z 0110 + z oioi 



iffet ,_ ° 



(x 001 +h G%0l) 



l\ 2 _ iaet 



dxdy -(— U z 0()1 e = 



ice t 



M ioio + M iooi = e 



m 



5 



^ h G ( % X 001 -^OOl) + 



+ Pg 



m 2\ 2 ^2 



77 gz B • % Va 



001 - pg z 



*¥*-*" jl«** l kz ' + i(kx +7 ) ][ z '^' " x '^ dx ' dz ' 



M 



+ M = 2 (x + h ) e 1(re // xp dxdy + 



)110 M 0001 M 001 G001 j -JJ P o 



+ 



Q) *c < * 



e 001 



001 } "W a e 6 001 



icret _ 

 e =0 



(8-5) 



The lowest order displacements in surge, heave and pitch are 

 given by «L e 1 ^ , «z e'« l and «» e'«t and it may ap- 

 pear from (8°-%) that there are six equations for these three unknown 

 quantities. However, these should be reduced to a set of three equa- 

 tions, by setting the total longitudinal force, vertical force and pitch- 

 ing moment equal to zero. This step is suggested by the fact that 



the masses supported by the air cushion 



ing moment equal to zero, 

 although [-J-] and ["g)» 



163 



