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



c W p 

 o 



Fig. 3a shows the wave resistance of a distribution with a 

 beam to length ratio of 1/2. The variable used for the abscissa is 

 A = l/2 F . This has the effect of expanding the horizontal scale 

 at low Froude numbers. Curve 1, with a a = 0a = °° , displays the 

 unrealistic low-speed oscillations which are characteristic of the 

 sharp-edged distribution and were referred to previously. It is seen, 

 that with increasing degrees of smoothing (smaller values of a a and 

 /3a), the low-speed humps and hollows may be eliminated. The case 

 with a a = /3a = 5 results in only about three humps, more in keep- 

 ing with experiments. Fig. 3b presents results for finite depth water 

 for three different distributions. The chief difference now is that the 

 main hump is shifted to the right and occurs near the critical depth 

 Froude number. It is seen that Curve 2 has smoothing applied only 

 at the bow and stern -equivalent to a sidewall ACV. The result is 

 similar to the case for smoothing all around, showing that the wave 

 pattern is essentially produced by the fore and aft portions of the 

 cushion and not the sides. The resistance in the region of the main 

 hump is hardly affected by the smoothing. 



The result of varying the depth of water is displayed in Fig. 

 4. The peak resistance increases in magnitude as the depth decrea- 

 ses, and occurs in each case at a depth Froude number slightly less 

 than unity. The location of the other humps is also affected, but to 

 a lesser degree. 



Beam to length ratio is varied in Fig. 5. The general effect 

 of increasing the beam is to increase the maxima and to decrease the 

 minima in the wave resistance curve. This is due to the transverse 

 waves assuming greater importance as the two-dimensional case is 

 approached. A secondary effect is a shift in the locations of the oscil- 

 lations to the right, so that in the limit of infinite beam, they occur 

 at Froude numbers given precisely by Eqs (2) and (3). 



We now turn to the effect of constant levels of acceleration 

 of the craft from rest. Fig. 6a applies to a smooth (aa = 5) two- 

 dimensional pressure band moving over deep water. A general dis- 

 placement of the oscillations to higher Froude numbers occurs. This 

 shift is greater for the higher acceleration. In addition, most of the 

 low-speed oscillations apparent in steady-state motion do not occur 

 in accelerated motion. The resistance of a smooth band over finite 

 depth water is shown in Fig. 6b. Here the reduction of the peaks is 



47 



