Linearized Potential Flow Theory for ACVs in a Seaway 



order will be sufficient. In a similar manner the surface pressure 

 during oscillations will also be restricted to the same order. 



We may now write down the expansions we shall actually be 

 using in the subsequent work. 



»(*, 7 , .ft*;**;.) = ** 100 + **0100 +i/3 *1100 + 



+ Re e iat [5«<l> 1()10 +^* ()110 + e<J> 0001 



+ 6 ^iooi + ^*oioi] +0(52 ^ 6a '^ €2 ) 



x(t;5;0;a.) = 8 x 10Q + x + Re . a e 10 



+ 5/3x no + (5 2 ,/3 2 , Woe, a 2 ) 



x ooi +5x ioi +/3x oii 



iUilfiia) = 8 z 1Q0 + ^z Qlo + Re .« e^^ + Sz^ + /Jz Q1 J 



+ ^z no + (5 2 ,/3 2 ,5^a 2 ) 



e (*«;*«) = «e 10 o + /Je oio + Re - aei<rt [ e ooi + ae ioi +/,e oii] 



+ 5/30 llo + (5 2 ,/8 2 ,5^a, a 2 ) 



(2-3) 



The linearization of our problem is achieved by substituting 

 the above expansions in Laplace's equation and in the boundary con- 

 ditions and collecting terms of the same order. The result is a se- 

 quence of linear boundary value problems for the potentials $ 

 Having derived the potentials, the pressure of the water particles 

 on the side hulls and the shape of the cushion hull can be calculated. 

 The forces and moments on the ACV considered as a rigid body can 

 thus be evaluated. 



IV. DEVELOPMENT OF BOUNDARY CONDITIONS 



In the case of a conventional displacement vessel there are 

 two types of boundary conditions for the velocity potential 



123 



