Murthy 



to the free oscillation in waves etc. The evaluation of these quantities 

 and the derivation of the higher order potentials such as those due to 

 the interference between the air cushion and the side hulls, the diffrac- 

 tion of the incident wave by the side hulls and the disturbance of the 

 incident wave by the air cushion are not carried out here, but the 

 simpler results such as the steady trim taken up by the craft during 

 uniform translation in calm water and the expression for the wave 

 resistance which combines the well-known results of Michell and 

 Havelock and also introduces an additional term representing the ef- 

 fects of interference between the air cushion and the side hulls show 

 that our method of approach to the solution of the problem is a prac- 

 tical one. The expression for the side force on a drifting amphibious 

 ACV and the response functions for the amphibious and non-amphi- 

 bious ACV (for which expressions have been derived although not 

 explicitly solved here) will also have practical applications. The 

 ride comfort in waves can also be estimated by combining the levels 

 of acceleration in surge, pitch and heave in an appropriate manner 

 depending on the location in the ACV. It would, however, be prema- 

 ture to suggest that these response functions can be used for the pre- 

 diction of the performance of the ACV in an irregular seaway by the 

 application of the theory of linear superposition in the absence of 

 experimental results confirming the linearity of the motions in waves 

 of small amplitude. 



The method of solution presented here can also be used 

 in the case of the water contact of the flexible extensions and even 

 in the case of immersion in water if the flexible extensions are assu- 

 med to be of a fixed shape. A later extension could cover the case of 

 flexible extensions compliant to the water pressure. 



It cannot be stressed too highly that the theory presented here 

 must be used with a certain amount of caution when applied to the 

 actual operation of an ACV over water. The underlying assumptions 

 for the linearized theory are that the cushion pressure is small, that 

 the hull is "thin" and that the speed of translation is moderate or lar- 

 ge. The slope of the induced wave may then be considered to be small. 

 Also, the oscillatory displacements and the slope of the incident wave 

 should also be small quantities. 



It is needless to add that the theoretical results derived here 

 should be confirmed (or corrected) by experimental work such as 

 that with a mechanical oscillator of the PMM type and also by full 

 scale trials so that the scale effect can also be established. Apart 

 from the configuration of the side hulls, which can no doubt be per- 



166 



