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



and the hollows occur approximately when 



F = 1 /\2irn for n = 1, 2, 3, ... (3) 



In the limit of infinite beam (a two-dimensional pressure band), the 

 humps and hollows are given precisely by Eqs (2) and (3). This re- 

 sult was found by Lamb (1932). 



In water of finite depth, the main, or "last", hump (n = l) 

 is shifted to a lower Froude number, and for sufficiently shallow 

 water, occurs at a depth Froude number, F,j , equal to unity 

 (that is, at the depth critical speed). Similar calculations were given 

 by Barratt (1965). 



Newman and Poole also considered the effect of a restricted 

 waterway, such as a canal. In such a case, the wave pattern is cons- 

 tituted from wavelets of discrete frequencies only, which can exist 

 in the tank, whereas in laterally unrestricted water a continuous 

 distribution of frequencies exists. As the speed is increased past 

 the critical speed, the transverse wave component can no longer 

 occur, and as a result there is a discontinuity in the wave resistance 

 curve. This sudden drop in resistance is given by 



3W 2 ... 



AR = (4) 



2pgBd 



where W is the weight of the ACV, B is the width of the tank and 

 d is the water depth. 



Havelock (1922) also presented some results for a very 

 smooth pressure distribution moving over water of finite depth. These 

 too, showed the shift of the main hump and the increase in its magni- 

 tude in shallower water. Havelock' s curves displayed only the main 

 hump. The secondary (n = 2) and other humps did not occur because 

 of his choice of pressure distribution. 



In recent years, a number of experiments have been carried 

 out in order to check the above-mentioned theoretical results. These 

 have been performed in particular by Everest (1966a, 1966b, 1966c 

 and 1967) and Hogben (1966). The fundamental question pointed out in 

 these papers is the resolution of the total drag on the ACV into its 

 components. Apart from the wave resistance, the forces acting on 

 the craft are aerodynamic drag and wetting drag. 



37 



