Doctors 



its full value down to a zero value in a staircase fashion rather than 

 in a smooth way. We found, in the same way as in Dr Doctors' case, 

 a certain effect at lower Froude numbers and very little effect at 

 higher Froude numbers. Again, it appeared that it is only in the case 

 of using a very large smoothing area that it had any real effect. I 

 wonder if Dr Doctors could comment on what the alpha and beta really 

 mean in physical terms ? 



REPLY TO DISCUSSION 



Lawrence J. Doctors 



University of New South Wales 

 Sydney 3 Australia 



I thank Dr. Strom-Tejsen for his questions. In answer to the 

 first question regarding the shape of the planform, I have not made 

 numerical studies of this parameter myself. Other workers, mention- 

 ed in the paper, have studied shapes which include elliptical and 

 triangular ones. At high Froude numbers (i. e. in the region of the 

 hump speed, and above), smoothing of the planform shape has a simi- 

 lar effect to decreasing the rate of pressure fall -off at the edges. 

 That is, the wave resistance is reduced a little. These two types of 

 smoothing have, however, different effects at low Froude numbers. 



For example, the sharp-edged rectangular distribution has a 

 wave resistance coefficient which oscillates between and 2 at 

 asymptotically low speeds, while the smooth rectangular distribution 

 has a resistance which approaches zero (see Fig. 3). On the other 

 hand, the wave resistance coefficient of a sharp-edged circular area 

 appears to have a behaviour somewhat intermediate to these two 

 (see Barratt (1965)). 



With regard to the second question, the limitation to the ap- 

 plication of the linear theory is basically the slope of the waves ge- 

 nerated by the pressure distribution. Thus, for typical ACV's, only 

 the main or secondary hump have been realised in practice. On the 

 other hand, by using models with a smaller nominal pressure (more 

 precisely : p /pga), more low speed humps and hollows may be 

 measured. My thesis supervisor at the University of Michigan, 

 Dr. S. D. Sharma, initially suggested the method of smoothing in the 

 manner described. We found that smoothing in the transverse direc- 



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