The Effect of Shallow Water on Wave Resistance

1. The general character of experimental results dealing with the effect of shallow water on ship resistance may be stated briefly as follows:—At low velocitie the resistance in shallow water is greater than in deep water, the speed at which the excess is first appreciable varying with the type of vessel. As the speed increases, the excess resistance increases up to a maximum at a certain critical velocity, and then diminishes. With still further increase of speed, the resistance in shallow water ultimately becomes, and remains, less than that in deep water at the same speed. The maximum effect is the more pronounced the shallower the water. For further details and references one may refer to standard treatises, but one quotation may be made in regard to the critical velocity: "This maximum appears to be at about a speed such that a trochoidal wave travelling at this speed in water of the same depth is about times as long as the vessel... It was at one time supposed that the speed for maximum increase in resistance was that of the wave of translation. This, however, holds only for water whose depth is less than 0.2 times the length of the vessel. For greater depths the speed of the wave of translation rapidly becomes greater than the speed of maximum increase of resistance." In a recent analysis of the data, H. M. Weitbrecht expresses a similar conclusion by stating that for each depth of water there is a critical velocity, but that the critical velocity does not vary as the square root of the corresponding depth. It should be noted that experimental results are for the total resistance. If we assume that this can be separated into three terms, which are simply additive, namely, eddy, frictional, and wave-making resistance, it must be admitted that probably all are affected by limited depth of water. However, the main differences are due to the altered wave-making, and the general explanation is to be found in the fact that there is a limiting velocity, √( gh ), for simple straight-crested waves on water of depth h .