Studies in wave resistance: the effect of parallel middle body

Abstract

1. If a ship is altered by inserting different lengths of parallel middle body between the same bow and stern, the main features of the variation in the wave resistance may be inferred from the principle of wave interference, and may be expressed in terms of a certain length, sometimes called the wave­-making length of the ship. The problem proposed for examination is the alteration in this length with varying length of parallel middle body at the same speed, and, further, its variation for a given ship at different speeds. Recent discussions have attracted renewed attention to this problem. It may be said that there are two approximations based on experimental results of various kinds obtained from ship models. On the one hand the wave-making length is supposed to be approximately independent of speed for a given ship, and to increase directly with the increase of parallel middle body; on the other hand, an empirical formula which agrees with experimental results over a certain range makes the length increase with velocity, the increase being one-quarter of the increase in the wave-length of regular transverse waves. The following contribution to the solution of this problem is mathematical, and necessarily deals with a simplified form of ship. It is true that one cannot compare absolute values of the wave resistance with those of actual ship models; but it has been shown in former studies of the dependence of wave resistance on ship form that one obtains a rather remarkable agreement, at least in the character of the results and in the positions at which changes occur. Leaving detailed discussion of the present extension till later, it may be stated that as regards the two approximate formulæ mentioned above the results are intermediate; after an initial decrease the wave-making length increases until velocity, but not so rapidly as in the quarter wave-length formula.