On the Smith effect 1 2

Abstract

The motion of a ship in a seaway was considered by A.N. Kriloff in his two well known papers [1] and [2] in 1896–98. In [1] A.N. Kriloff concluded that the difference between the hydrostatic distribution of buoyancy and the distribution following Gerstner’s theory of waves, the so-called Smith Effect, has no important influence on the motion of a ship, so that it can be neglected. This opinion has prevailed up the present. So, for instance, on the basis of that conclusion, G.P. Weinblum and M. St. Denis, have neglected the Smith Effect, when discussing in the paper [3] the motions of a ship in a seaway.

In the present paper the author considers the motion of a ship in a seaway on the same assumption as A.N. Kriloff, except that he:

a. takes into consideration approximately the influence of added mass;

b. accepts the cosinusoidal wave profile, and

c. substitutes the real hull surface by approximative analytical expressions corresponding to the coefficients and the main dimensions of a ship.

For the case were the length of the waves λ is equal to the length of the ship L, the author shows that Smith Effect can not be neglected, and that the decreases of amplitudes caused by it can be over 50% for heaving, and over 30% for pitching.

The author gives the diagrams by means of which it is possible to estimate approximatively Smith Effect, and to determine the heaving and the pitching of a ship in every particular case, when the waterplane coefficient α, the block coefficient δ and the main dimensions of a ship: the breadth B, the length L and the draft T are given.