Linearized Potential Flow Theory for ACVs in a Seaway 



knowledge that the pressure in the cushion at all points is uniform 

 and that the pressure on the water surface is also uniform and of the 

 same value. This kind of stepped cushion with an abrupt drop between 

 the pressure within the cushion and the ambient pressure outside will 

 have a hull in the form of a right cylinder with vertical sides and, in 

 our case will resemble a rectangular box. It is obvious that this type 

 of hull will be totally unsuitable for a fast planing type of displace- 

 ment vessel. It will appear during the course of this study that the 

 mathematical work is considerably simplified if it can be assumed 

 that the pressure is diffused continuously from a maximum value at 

 the centre in such a manner that it becomes zero at the boundary and, 

 preferably, with a zero gradient in the direction of motion. The pur- 

 pose will be equally served if the pressure is uniform in the main 

 part of the cushion and diffused over an annular region close to the 

 boundary. It is interesting to note that this type of diffusion of pres- 

 sure selected with the object of mathematical expediency in obtaining 

 an easier solution of the problem on hand gives a hull shape for the 

 air cushion with an aesthetic appeal and with a reasonable dead rise 

 and flare at the bow and at the stern which may be considered by the 

 naval architect as very acceptable for planing motions in the dis- 

 placement mode. 



The actual mechanism by which the above pressure distribu- 

 tion may be generated in the case of practical ACVs considered as 

 hardware is merely an engineering matter, although in the present 

 state of the art not much progress has been made in this direction, 

 presumably because no investigation as so far been made as to the 

 direction in which to proceed or, wether it is necessary to proceed 

 in any direction at all towards perfecting a "tailor made" cushion. 

 This could probably be achieved by suitable compartmentation of the 

 cushion and by introducing auxiliary flows in the (supposedly) quies- 

 cent air in the cushion. It is only a question of accentuating the en- 

 trainment of air and trapped vertices known to exist in the vicinity of 

 the boundary. Assuming that such a manipulation of the pressure 

 distribution is feasible (and there is no reason to doubt this), we are 

 indeed in a fortunate position with hovercraft for without altering the 

 deck space, it seems possible to give the ACV an arbitrary cushion 

 hull shape by a simple manipulation of cushion aerodynamics. 



The analytical methods used in this study are essentially those 

 first used in the classic work of Peters and Stoker v 2 ^ and later fol- 

 lowed by Newman Vvvv , Joosen ( 5 > and others. These works con- 

 stitute a rational approach to the unsteady motion of ships, but a solu- 

 tion has so far been obtained only for thin ships and slender ships. 



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