Murthy 



for then the integral will be of a higher order. The expression for 

 the interference potential, namely, the potential representing the 

 interference between the air cushion and the side hulls have not been 

 derived here, as it is only required in the higher order theory, but 

 a brief sketch of the method of its solution is indicated in Appendix V. 



The restoring forces and moment acting on ACV which is forced 

 to oscillate in calm water are discussed in Section 7. In the lowest 

 order they contain inertial and hydrostatic terms only as the dynamic 

 pressure of the water represented by the steady and unsteady poten- 

 tials enter only in the higher order. The expression for the higher 

 order forces and moment could be used for the calculation of the 

 mean increased wave resistance due to the oscillations and the added 

 mass and damping of water by the appropriate combination of the real 

 and imaginary parts of the oscillatory potentials with those of the 

 oscillatory displacements. 



The free oscillation of an ACV moving with uniform speed in- 

 to a regular train of sinusoidal waves is discussed in Section 8. The 

 lowest order exciting forces and moment are again of a hydrostatic 

 nature. The pitch and heave response functions can be obtained from 

 the expressions presented in this section so that a statistical predic- 

 tion of the performance of the craft in an irregular seaway can be ma- 

 de if it can be assumed that the behaviour of the craft is linear in 

 small waves. There appears to be no positive experimental evidence 

 in this respect at the moment. 



The accelerations in surge, heave and pitch which can be cal- 

 culated from the expressions derived in Section 8 will combine toge- 

 ther in different forms at various locations in the craft and dictate 

 the level of passenger comfort at that point during a ride in a seaway. 

 The optimization of the shape of the side hulls could be carried out 

 by well established methods, but it would be interesting to ascertain 

 the effect of different shapes for the cushion hull on the motions and 

 accelerations. 



The potentials representing the disturbance of the incident 

 waves by the side hulls (the diffracted wave) and the corresponding 

 potential representing disturbance by the air cushion have not been 

 derived here. These potentials enter only in the higher order forces 

 and moment, but they will have to be derived if the added mass and 

 damping of water, the mean increased resistance in waves and other 

 similar quantities are to be calculated. 



108 



