Linearized Potential Flow Theory for ACVs in a Seaway 



to be satisfied for z = ? . This condition applies both to the external 

 free surface (EFS) and the internal free surface (IFS) defined and 

 discussed in the Introduction. 



The dynamic conditions on the free surface z = f are obtained 

 from (2-8) by setting p = for the EFS and p = p (x, y), the surface 

 pressure applied by the air cushion on the IFS, respectively. 



The kinematic condition (1-9) is also applicable to the instant- 

 aneous position of the moving (and oscillating) side hulls of the ACV 

 and to the lower edges of the flexible extensions immersed below the 

 surface of water. 



II. 5 The General Non-Linear Problem 



The strict formulation of a very general type of ACV problem 

 would be on the following lines. A rigid body in the form of an ACV is 

 supported above the water surface partly by the air cushion (contain- 

 ing air at a pressure higher than atmospheric) and partly by the 

 buoyancy of the immersed part of the side hulls. In the position of 

 "static hovering", i. e. at zero speed ahead, the steady pressure ap- 

 plied by the air cushion to the IFS may be assumed to have a distribu- 

 tion of the form 



P c = P rt (x, y) 

 s o 



over a region S of the water surface which is the vertical projection 

 of the cushion opening on the water surface. This region is therefore 

 bounded by the inner sides of the side hulls and the curves representing 

 the vertical projection of the hemline of the skirts at the bow and at 

 the stern. The "cushion hull form" is thus determined by the plan 

 form of S and the pressure distribution thereon. It may be assumed 

 as an approximation that the latter is unaltered during steady forward 

 motion in the horizontal plane. However, the water surface will now 

 be disturbed due to the generation of surface waves by the air cushion 

 and by immersed side hulls (with perhaps a complicated kind of cou- 

 pling between the two as will be shown later). The steady disturbance 

 will travel with the same speed as the ACV but will cause a steady 

 variation of the shape of the IFS i. e. of the cushion hull form. If the 

 ACV now performs oscillations during steady translation, which may 

 be forced oscillations in calm water or wave excited oscillations in a 

 seaway, the pressure distribution on the water surface will no longer 

 be steady or of the basic form. This is because the region S over 

 which the pressure is apllied is now a fluctuating domain, as it is the 

 instantaneous position of the vertical projection of the cushion opening 



113 



