Linearized Potential Flow Theory for ACVs in a Seaway 



2 2 

 x + y > oo 



These conditions will be specifically stipulated in due course. 



Singularity of the Potential; 



It will be seen from (V. 3) and (V. 5) that the potentials 

 4> 100 _ and ^-joi relating to the steady motion and forced oscilla- 

 tion of the side hulls of an ACV in the full displacement mode (i. e. 

 without an air cushion) in calm water satisfy identical conditions 

 both on the EFS et IFS. However, they have to satisfy additional 

 boundary conditions on the hull surfaces given by (V. 7). On the other 

 hand, the potentials ^q^q and ^q-mq relating to the air cushion 

 of an amphibious ACV (without the side hulls) satisfy different condi- 

 tions on the EFS and on the IFS unless the basic pressure distribution 

 is truly uniform in the longitudinal direction such that 



p =0 and p =0 



o o 



x xx 



throughout the length of the cushion. However, this would imply a 

 discontinuity in the pressure at the boundary along the bow and the 

 stern where the pressure drops suddenly from the uniform cushion 

 pressure to the atmospheric. A discontinuity in the value of the 

 potential at the boundary is therefore to be expected. 



It is also to be noted that the cushion potentials $ 01Qn and 

 4> ni1 _ do not have to meet any specific conditions on the hull surfaces 

 and that the interference potential ^^nr, satisfies different boundary 

 conditions on the EFS and IFS and also a condition on the hull surface. 



The Green's Function. 



Let us now choose a Green's function G(x, y, z; £,»? ,f) such 

 that 



V 2 G = G +G +G = - 4tt 8 (x - £) g(y-rj) a(z-f) 

 xx yy zz 



where <5 is the Dirac delta -function. This ensures that G is a 

 harmonic function in z > with a singularity of the type — at 

 x = £ , y = rj , z= f. 



Let G also be such that 



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