ON THE DIMENSIONS AND DIFFERENT FORMS OF SHIPS.
One of the first and most important considerations which a naval constructer has to attend to, is the rela tion which the co-ordinate dimensions of a ship bear to each other;—how the length should be related to the breadth, and how both these elements are connected with the depth. Duhamel, in his Architecture Xavale, has made it the subject of a particular examination, but we shall prefer following Chapman in his important re marks on this subject.
This able writer enters on the investigation, by sup posing two bodies of different forms, one being that of a rhomboid, of which the uppermost surface is taken for the load water line, as Fig. 5, Plate CCCCXCII. and the other that of a body formed by the junction of two wedges A BGE, CGED, as Fig. 6, and whose upper surface, the rectangle A BCD, is, in like manner, taken for the load water section.
Suppose these bodies to be impelled through the wa ter by a quantity of sail proportional to their stability; and let their half lengths moreover be represented by L, their half baeadths by B, and their draught of water by D. The moment of stability for the first of these bodies will be B3 x, and the plane of resistance 4 B3 x A body of such a figure, however, could not ± acquire a great velocity by means of sails, and would sail badly close to the wind.
The moment of stability of the second body will be B L, and the plane of resistance + Dz . And since the moment of stability increases in a triplicate ratio of the breadth, whilst the plane of resistance increases only in the simple proportion of the same dimension, this form is the best adapted for sailing close to the wind. This body also being impelled through the water, the square of its velocity will be in the direct ratio of the area of the sails, and in the inverse ratio of the plane of resistance. But the moment of stability is as that of the sails ; and the moment of the sails, as the area of the sails multiplied by the height of a certain point, and which altitude is also proportional to the height of the sails ; consequently, the area of the sails is, as the mo ment of stability, raised to the power of 4, that is to say, as The area of the sails, therefore, divided by (B3 L)x the plane of resistance = x + = B Cs I. 7 + IT ; and hence the velocity will be as A 1 LT 1 + - . But since is very small when corn (DI 4 pared with we may neglect the last term of the expression, and regard the velocity as proportional to 4.
x 3 I)' From this expression for the velocity, Chapman draws some useful practical inferences. In the first place, that when the area of the load water surface is given, a ship to sail well by the wind should have great length ac cording to its breadth, and the draught of water the smallest possible. If, however, the area of the load wa
ter section be not given, but only the length of the ves sel, it will be necessary to give very great breadth, be cause the velocity increases as the square root of that dimension. But if the breadth be given, the length should he considerable, because this dimension is raised to the lrd power, when the draught of water is given. If, on the other hand, from a certain determined length or breadth, we have the choice of augmenting one of these dimensions, it is most advantageous, if the object be to increase the velocity, to augment the length rather than the breadth. And from all these considerations, Chapman infers that there cannot be any constant pro portion assigned between the length, the breadth, and the draught of water.
From these circumstances also we may derive some information why a small ship, built on what is techni cally called the model of a large ship, known to possess very desirable qualities, should be found to have no pro perties analogous to the vessel from which she was de duced. This will be apparent, by attending for a mo ment to the elements of the expression for the velocity, all of which by the supposition are variable, but as they are constituted in the formula, vary by different laws. Suppose velocity to be the standard of comparison, and that its value in some determinate case be denoted by 10; that is, the question is, what ought to be the other dimensions of a vessel, whose length is previously fixed at /, to pos sess an equal degree of velocity with that which is given? To this interesting and important question, no satisfac tory answer, we fear, can be afforded in the present state of our knowledge. There is no doubt some relation ex isting between these primary dimensions in ships of dif ferent classes; so that having the length, the breadth, and draught of water of a ship of one class given, with a certain numerical velocity, the same velocity might be obtained, with dimensions suited to a ship of another class. Such a relation, and even we fear the feeblest beginnings towards it, can hardly be made the subject of calculation; but it.is, however, a condition, to the at tainment of which all our efforts will, we hope, continu ally tend. Had Euler, for example, been as well ac quainted with the Philosophy of Naval Architecture, as with those beautiful systems of analysis, which it was ever the object of his sublime and original genius to create and improve, some approximations towards these relations would, no doubt, have been attained. Let us hope that the future cultivators of Naval Architecture will unceasingly endeavour to attain these things.* The qualities of similar ships varies, Mr. Chapman imagines, in a different proportion from what a consider ation of their size would give.