A ship floating upright and at rest in still water must fulfil two conditions—1st, as stated above, she must displace, a weight of water equal to her own weight; 2nd, her centre of gravity must lie in the same vertical line with the centre of gravity of the volume of displacement or “centre of buoyancy.”
The whole weight of the ship may be supposed to be concentrated at her centre of gravity, and to act vertically downwards, and the resultant vertical pressure of the surrounding water in the same way to act upwards through the centre of buoyancy.
When the ship has been inclined from the upright position, by any force, the downward and the upward forces—weight and buoyancy respectively—act through two separate but parallel vertical lines, and form what is technically known as a “couple.” The perpendicular distance between the vertical lines usually varies with the inclination, and is called the “arm” of the couple. This arm measures the leverage with which the weight and buoyancy of the ship tend either to force her back into the upright position, or to incline her still further, and, it may be, to capsize her. The former effect would be the result of what is known as a “righting couple,” the latter the result of an “upsetting couple.”
FIG. 14. FIG. 15.
This may be made clearer by illustration. On Figs. 14 and 15, which show in outline a vessel’s midship section, the vessel being inclined to a small angle, G represents the centre of gravity of vessel, and B the centre of buoyancy. The water line W.L. corresponding to the upright position, in the inclined position becomes W1.L1., and the centre of buoyancy B shifts out on the immersed side of the vessel to B1. Assuming in the case of Fig. 14 that some external force not involving any shifting of the centre of gravity has produced the inclination, then the weight of the vessel acts downwards through G, and the buoyancy of her displacement acts upwards through B1, as indicated by the arrows passing through these points. The combined effect of these forces, in this case, is to rotate the vessel towards the upright, i.e., it forms a “righting couple.” Fig. 15 illustrates a case of the opposite kind. The angle of inclination may be supposed to be greater than in Fig. 14, and the centre of gravity G is much higher in the vessel. The vertical through B1 is to the left instead of to the right of the vertical through G. The effect of the forces in this case is to rotate the vessel in the direction of inclining her still further, and to capsize her—i.e., it forms an “upsetting couple.” A line at G, therefore (Fig. 14), taken at right angles to the new vertical line, gives the distance which corresponds to the righting arm (G Z). A similar line at G (Fig. 15) represents the upsetting arm. The lengths of these arms when multiplied into the displacement, gives the “moments” at the respective degrees of inclination. The “curve of stability” for a vessel is simply a graphic representation of these arms or moments. When calculated for the various degrees of inclination, they are set off as ordinates along a base line—the righting arms or moments above, and the upsetting arms or moments below, the line—at distances corresponding to the number of degrees in the respective inclinations. A curve drawn through the extremities of these ordinates is the curve of stability.
The two points above named whose relative positions are vitally concerned with this subject—i.e., centre of buoyancy and centre of gravity—are determined by shipbuilders for many of their vessels, although the stability may not be calculated to its full extent. The position of the centre of buoyancy is easily ascertained from, and in fact usually forms part of, the displacement calculation. While the position of centre of gravity may be found by means of calculation alone, i.e.—by the process of estimating the position of the centre of gravity of each of the component parts, and from this deducing the common centre of gravity of the whole ship—the work is so laborious, complex, and so liable to error, that it is scarcely ever adopted at the present day by mercantile shipbuilders. The position can be ascertained with comparative ease and greater accuracy by means of “inclining” experiments with the finished vessel, or closely estimated before-hand by means of data obtained in the manner alluded to from previous vessels of similar type.[6]
Another point concerned with stability is that termed the “metacentre,” which is found by calculation from the lines of the vessel. Referring to Fig. 14, a vertical line drawn through the centre of buoyancy B1 cuts the original vertical line at M. The intersection M, when the vessel is inclined to an indefinitely small angle, is the “metacentre.” It is approximately the same in all ordinary vessels for inclinations less than say 10°, but varies with greater inclinations. The corresponding intersections of the consecutive vertical lines for all degrees of inclination are embraced in the term “metacentrique.” These features in stability investigations were originated by Bouguer, to whom reference has already been made. The manner in which they are concerned with stability will be indicated further on. (See also [footnote on preceding page].)
RESISTANCE POWER AND SPEED.
A ship, in moving through the water, experiences resistance due to a combination of causes, which combination, according to modern accepted theory, is made up of three principal elements.