Forces on an A.C.V. Executing an Unsteady Motion 



does fall-off at a finite rate, corresponding approximately to a a = /? a 

 = 40. Nevertheless, it was found that only by selecting »a = & a = 5, 

 could the humps in the resistance curve above the third be essentially 

 eliminated. Thus clearly, viscosity and non-linearity are important 

 at low speeds. Some of these calculations are reviewed in this paper. 



Another problem of practical interest is the wave resistance 

 during accelerated motion, as one is frequently concerned with the 

 ability of a heavily-laden craft to overcome the hump resistance in 

 order to reach the cruising speed. 



The problem of accelerated motion for a ship has been treat- 

 ed by Sretensky (1939), Lunde (1951b, 1953a and 1953b) and Shebalov 

 (1966). Wehausen (1964) made numerical calculations for a particu- 

 lar motion of a ship model starting from rest. His results consisted 

 of asymptotic expressions valid for large values of the time after a 

 steady speed was obtained. 



Djachenko (1966) derived an expression for the resistance 

 of an arbitrary pressure distribution moving with a general accele- 

 ration pattern in deep water. He also presented some results for a 

 two-dimensional distribution. 



Doctors and Sharma found that the main effect of accelerat- 

 ed motion on an ACV is to shift the main hump to a higher Froude 

 number, and in finite depth to reduce the magnitude of the hump quite 

 significantly. These results are partially presented in this paper. 



1.2. Present Work 



The basic theory for the wave resistance of a time varying 

 pressure distribution will first be given. Then the results will be 

 applied to the case of an ACV executing rectilinear motion in a hori- 

 zontally unrestricted region. 



The work will then be extended to the case of an ACV moving 

 along the centerline of a rectangular channel. From these calcula- 

 tions it is possible to determine the effect of the tank walls on the 

 wave resistance. 



Finally, the case of a yawing ACV will be examined. In 

 particular, the induced side force acting on the craft will be deter- 

 mined, so that its importance during a manoeuver may be assessed. 



39 



