Muvthy 



area which determines the wave making at any particular speed. A 

 large planform area is therefore desirable (for a given weight) and 

 as the popular value for beam/length ratio of present-day hovercraft 

 is about 2/3, it appears that the geometrical dimensions are to be 

 unrestricted for hovercraft in order so that the theory may be success- 

 fully applied. 



In the case of a rigid sidewall ACV, the total weight of the 

 craft is usually supported mainly by the air cushion with a smaller 

 contribution of the order of 10% from the buoyancy of the immersed 

 side hulls. We shall select 6 as the small parameter representing 

 the thin width of the side hulls and /? to denote the smallness of the 

 cushion pressure. We shall not make any a priori assumptions as to 

 the fractional weights supported by the air cushion and by the hulls so 

 that we shall not stipulate the relative orders of magnitude of 8 and 

 /3 .As stated above, the smallness of /3 is ensured by having a 

 large length and a large beam for the cushion and as the latter implies 

 a wide separation for the hulls the effects of mutual interference bet- 

 ween the two hulls may be considered negligible. The solution of the 

 problem therefore becomes easier. At a later stage we may have to 

 stipulate that the draught of the hulls should also be small (thus, in 

 effect, treating them as slender hulls) so that an integral representa- 

 tion for the cushion potential may be derived from the integral equa- 

 tion. This stipulation makes the buoyancy contribution from the side 

 hulls to the support of the ACV of a smaller order than the "cushion 

 lift" and is probably in keeping with present-day practice. 



The other two parameters selected are those indicating the 

 smallness of the oscillations of the ACV and the small slope of the 

 incident wave. Having selected these perturbation parameters, the 

 procedure would be to expand all the physical variables relating to 

 the motion of the fluid, the boundary conditions and the motion of 

 the ACV in terms of these parameters. Perturbation expansions are 

 thus obtained in the form of a series comprising powers of the pertur- 

 bation parameters and when terms of the same order are collected 

 together, the result is a sequence of linear boundary-value problems 

 which are, in the general case, more readily solved because the 

 boundary conditions can then be imposed on fixed domains. Thus, for 

 example, the free surface boundary conditions can be satisfied on the 

 known plane z = instead of the unknown surface z = f - . 



On the basis of the equations of motion developed in Appendix 

 III of Reference 1, expressions for the forces and moments are deri- 

 ved in Section 5 in the form of surface integrals over the steady posi- 



106 



