Linearized Potential Flow Theory for ACVs in a Seaway 



The third parameter need not be specifically defined at this 

 stage, but one criterion is that this parameter should be sufficiently 

 small so that the water contact of the flexible extensions does not 

 take place at the bow and at the stern. It will be shown later that this 

 parameter is of the same order as that of the incident wave. 



The fourth small parameter (like the first two) ensures that 

 the orbital velocities of the water particles in the incident wave are 

 sufficiently small so that the squares of the perturbation velocities 

 may be neglected in the linearized theory. 



All the four parameters are assumed to be sufficiently small 

 to ensure the convergence of the perturbation series which follow. 



Assuming that the motion is periodic of frequency <r , we may 

 write the following perturbation expansions for the motion of the wa- 

 ter and of the ACV considered as a rigid body. It will be assumed 

 that the unsteady flow of water is produced by the periodic forced 

 oscillation of the craft. Since we shall only consider the linearized 

 problem, the motion for arbitrary periodic oscillations may be dedu- 

 ced by the method of Fourier transforms. 



Basic "Hull Form" of the air cushion p (x, y) = # p (x, y) 



Hull surface of the side hulls 



S Starboard side of starboard hull y 1 - b = 8 h (x' , z' ) 



S Port side y' - b = - 8 h (x 1 , z') 



S Starboard side of port hull y 1 + b = 8 h (x 1 , z" ) 



S Port side y' + b = - 5 h (x' , z' ) 



Surface pressure distribution due to the air cushion 



/ <- n \ t* V i°"t- k,„l m n , x 



p (x, y;t;<5 ;/?;«; e ) = Re Z_, e 8 j8 a t p, , (x, y) 

 s klmn 



k, 1, m, n 

 Velocity potential 



4> (x, y, z;t;5,0 ,a,e) = Re Le 1 8 jS<a m e n $ (x, y, z) 



klmn 

 k, 1, m, n 



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