Linearized Potential Flow Theory for ACVs in a Seaway 



where the Green's function G(x, y, z, £ , V , » ) is a harmonic function 

 in the lower half- space z > , f > , except near the point 

 (x = £ , y = V , z=T) where it behaves like a unit source with a 

 singularity of the type l/r , 



2 / 1 v 



i. e. V (G ) = 



v r 



with 



[■ 



(x - n z + (y - v ) 2 + (z - r ) 2 



The surface integral and normal derivatives are taken with 

 respect to the dummy variables ( S, q , f ) which have the same 

 disposition as (x, y, z) . The integration is performed over an arbi- 

 trary closed surface Vj which completely surrounds the point 

 (x, y, z) at which the potential is to be determined and the derivatives 

 are evaluated in the direction of the normal out of 22 • 



The potential <5> is assumed to be composed of potentials 

 of various orders (see (2.3)) : 



*(x,y, z;t) = 5 4> 1000 (x, y, z) + P<*> Q1Q0 (x, y, z) + 5 ^* noo (x,y, z) + 



. i<r t _ / x a i<rt , , v 



+ dae 4> 101Q (x, y, z) +^ae *oilO^ X ' y ' Z ^ + 



+ c ^^ *oooi (x ' y ' z) + 5eel0et *iooi (x,y ' z) + 



+ /3ee 1<7 e t <t>oioi ( x , y, z) (V. 2) 



where 



4> „^„ is the potential due to the motion of the side hulls 

 1000 . , ^ 



in calm water, 



$ is the potential due to the motion of the air cushion 



over calm water, 



<j> is the potential due to the interference between the 



side hulls and the air cushion in calm water, 



213 



