[Reprinted from the PROCEEDINGS OF THE Roya Society, A, Vol. 110.] 
Wave Resistance: Some Cases of Unsymmetrical Forms. 
By T. H. Have ocr, F.R.8. 
(Received November 14, 1925.) 
1. One of the chief features of interest in curves showing the variation of wave 
resistance with velocity is the occurrence of oscillations about a mean curve, 
which may be regarded as due to interference between the waves produced by 
the front and rear portions of the model. In various comparisons made between 
theoretical curves and such suitable experimental results as are available, the 
greatest divergence is perhaps in the magnitude of these oscillations, the theore- 
tical curves showing effects many times greater than similar experimental results. 
There are, no doubt, many approximations in the hydro-dynamical theory 
which preclude too close a comparison between theoretical and experimental 
results in any particular case, but it seems fairly certain that the divergence 
in question must be largely due to neglecting the effects of fluid friction. For 
several reasons it is useless to attempt at present a direct introduction of vis- 
cosity into the mathematical problem, but a consideration of its general effect 
suggests one or two calculations which may be of interest The direct effect 
of viscosity upon waves already formed may be assumed to be relatively small ; 
the important influence is one which makes the rear portion of the model 
less effective in generating waves than the front portion. We may imagine 
this as due to the skin friction decreasing the general relative velocity of model 
and surrounding water as we pass from the fore end to the aft end ; or we may 
picture the so-called friction belt surrounding the model, and may consider 
the general effect as equivalent to a smoothing out of the curve of the rear portion 
of the model. Without pursuing these speculations further, they suggest 
calculations which can be made for models in frictionless liquid when the form 
of the model is unsymmetrical in this manner ; and the particular point to be 
examined is the effect of such modification upon the magnitude of the inter- 
ference phenomena. 
The first sections compare, in this respect, two bodies entirely submerged in the 
liquid. The form in each case is a surface of revolution ; one is symmetrical 
fore and aft and has sharp pointed ends, while in the other the rear portion is 
cut away so as to come to a fine point. By inspection of the expressions for the 
wave resistance it is seen that the oscillating terms are of a lower order of 
magnitude in the latter than in the former case. 
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