Linearized Potential Flow Theory for ACVs in a Seaway 



+ z 



d*f 2 (x',y») 



+ (0 2 ,z 2 ) 



+ (x + h_0)" 



where h is the height of the C. G. above the undisturbed water sur- 

 face and f and f are the pitch and heave stiffness functions of the 

 air cushion. 



It will be seen from (2-2) that the basic hull form is assumed 

 to be of 0(j3). The pitch and heave stiffness functions are therefore 

 also of 0(/3) and we may write 



0P O ( x » y) for p Q (x, y) 



0£ x (x« ,y> ) forfj (x' ,y« ) 



and 



0f 2 (x> ,y< ) for f 2 (x 1 ,y' ) 

 we may also substitute from (2-3) 



i<rt ,_ 



x =5x ioo +/3x oio + ^ x no + Re ' ae (x ooi + * X 101 + < 3X 011 ) + 



+ ( 8 Z Z ,8(3a,a 2 ) 

 with similar expansions for z and 6 and derive finally 



P s (x,y)^p o (x,y) + /3 2 F 01() p o + 80r lQQ ^ + 0ae 1<Tt r^^ + 



XX X 



+ 6/3ae 10t (r^s^ + r^s^ + r^^ + ^7^^ )+ 



2 lot,- - _ _ _ 



+/3ae (r oio s ooi + r ooi s oio +r on p o +r oio r ooi p o )+ 



X XX 



+ ^ 2{7 ioo s oio +Y oio s ioo +7 no p o +7 ioo 7 oio p o ) + 



+ 5 2 )S(7 s +— r 2 p ) + 

 v 100 100 2 100 P o y 

 xx 



171 



