Linearized Potential Flow Theory for ACVs in a Seaway 



The neglect of these potentials here is tantamount to invoking 

 the classic Froude - Kriloff hypothesis, namely that the waves affect 

 the ACV, but that the ACV does not affect the waves. Sufficient infor- 

 mation regarding the motion of the ACV can, however, be gathered 

 by studying the lowest order forces. 



The theory presented here is concerned solely with the hydro- 

 dynamic contribution to the motions of the ACV which is translating 

 in a straight line with a uniform speed V under the action of a cons- 

 tant thrust T. Other internal and external forces could also be taken 

 into account with a suitable modification of the results. A typical 

 quantity for inclusion will be the pneumatic effect of the wave -pumping 

 of the air cushion by the progressive waves. 



This theory must also be used with caution in dealing with the 

 actual motion of ACVs over water. In order to satisfy the assumptions 

 made in linearizing the problem, the results can be only applied when 

 the cushion pressure is low and the side hulls thin. Extrapolation of 

 these results with the object of predicting the motions in an irregular 

 seaway has also to be done with care since there is no positive expe- 

 rimental evidence to show that ACV motions are not non-linear. 



Although the expressions for the potentials and the forces and 

 moment derived here appear to be extremely complicated, their solu- 

 tion by numerical methods with the use of present-day high speed di- 

 gital computers need not present any serious problems. It is very 

 likely that the new technique provided by the Finite Element Method 

 (FEM) may prove to be a very useful and powerful tool in this respect 

 and particularly for the solution of the singular integral equations. 

 This is being investigated. 



II. GENERAL FORMULATION OF THE PROBLEM 



We start with the consideration of the general case of an ACV 

 moving on the surface of water at a mean speed V in its course, which 

 is defined as the vertical projection of the path of the centre of gravi- 

 ty of the craft on the undisturbed surface of water. We may also assu- 

 me that the ACV has a small angular velocity w about a vertical axis. 



II. 1 Co-ordinate Systems 



Three rectangular co-ordinate systems are employed. The 

 first is a fixed system, or inertial frame of reference (X, Y, Z), with 

 the X, Y- plane in the horizontal position of equilibrium of the undis- 



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