Linearized Potential Flow Theory for ACVs in a Seaway 



and for the pressure moment. 



M p = M + M 



= - /7p (? x n) dS - //p (? x n) dS 



S^ (5-2) 



The surface integrals are taken over the displaced position 

 of the effective hull, S, of the air cushion, i. e. the instantaneous 

 position of the IFS and the instantaneous wetted surfaces S and 

 S of the side hulls. 



r 1 is the position vector of an element of area dS with o' 

 as origin and the unit normal n is taken out of the water and into 

 the cushion hull and the side hulls. Also, p s is the surface distri- 

 bution of pressure acting on the cushion hull (z = f ) and p the 

 pressure of water at an interior point (z >f ) of the immersed sur- 

 face of the side hulls. 



The rigid body force and moment are 



and 



M R 



= Jjfy r' x (tf - gk) dm (5-4) 



where r 1 is the position vector of an element of mass dm of the 

 ACV with absolute velocity U , and the triple integral is taken 

 throughout the volume of the ACV contained by matter. 



These are the forces and moments acting at and about the 

 C. G. of the ACV due to its inertia and the pressure of the water on 

 the effective hull of the air cushion and on the side hulls. 



The above expressions are written partly in the moving 

 (x, y, z) system and partly in the fixed (x 1 ,y' , z 1 ) system, but it is 

 obviously to be preferred that we should study the motion of the 

 craft in the steady (x, y, z) system particularly in view of the fact 

 that the pressure distribution on the water surface and the motion 

 of the water are given in this system. 



The detailed derivation of the forces and moments are carried 

 out in Appendix, II, III, and IV where the forces and moments on the 

 cushion hull, those on the side hulls and the rigid body forces and 



131 



