Wave resistance : some cases of unsymmetrical forms

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 theore­tical 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 vis­cosity 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 inter­ference 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.