Murthy 



on the water surface and its shape and location in space will be there- 

 fore dependent on the oscillations of the craft in all modes expect, 

 perhaps, in heave. The actual pressure distribution during oscilla- 

 tions will also be different from the basic distribution on account of 

 the cushion and peripheral jet (or plenum chamber) characteristics 

 peculiar to hovercraft which dictate the pressure in the cushion in 

 terms of the local clearance between any point of the periphery and 

 the elevation of the water surface directly below it. In our case, the 

 pressure variations will be initiated in annular regions adjacent to 

 the bow and stern skirts, but the perturbation pressures will no 

 doubt be transmitted to the interior due to induced flows and entrain- 

 ment of external air with the result that the distribution over the enti- 

 re region may be substantially altered. 



The basic problem is essentially that of determining the velo- 

 city potential <I> (x, y, z;t) as a harmonic function satisfying Laplace's 

 equation in the domain z> f(x, y;t) for all time t > when the ini- 

 tial position and velocity of the ACV and of the water particles are 

 prescribed at time t = . A singularity has to be accepted for the 

 solution of <{> at the boundary of the region S if the applied pressure 

 is discontinuous there, i. e. if the pressure is different from atmos- 

 pheric. The velocity potential can be used to calculate the elevation 

 and slope of the IFS on which the pressure is applied by the air cushion. 

 The forces and moments on the ACV considered as a rigid body are 

 in part due to the action of the applied pressure on the IFS which is 

 the cushion hull and can therefore be determined in terms of the ap- 

 plied pressure and the slope of the disturbed water surface. It is 

 appreciated that in common with other surface wave problems the 

 elevation and slope at individual points of the region S cannot be de- 

 termined accurately from the potential due to interference effects 

 although the evaluation will be corrected at some distance away from 

 the pressure field. However, we only require the total integral effect 

 of the applied pressure and for this purpose the potential can be used 

 to obtain practical results. 



The other contribution to the forces and moments on the ACV 

 arises from the action of the pressure of the water particles acting 

 on the instantaneous position of the immersed portion of the side 

 hulls. The boundary conditions dictate that the relative velocity of the 

 water particles at each point in a direction normal to the instantane- 

 ous position of the oscillating side hulls is zero. The pressure on the 

 free surface is also prescribed as zero. But both the immersed hulls 

 and the free surface of water are moving boundaries of the domain in 

 which the velocity potential is to be determined. A coupling between the 

 motion of the side hulls and that of the water therefore exists. As 



114 



