Hitherto reference has only been made to the longitudinal or fore and-aft motions of a but as a yacht's righting power or statical stability is generally spoken of in connection with her heeling or rolling, it will be best to illustrate it in connection with these transverse motions.
Fig. 6 is a representation of a transverse section of a vessel supposed to be heeled to, say 20°. E is her centre of buoyancy in her upright position, and F her centre of gravity. Upon being heeled or inclined, the centre of buoyancy, owing to the irregular shape of the vessel, shifts to some point, M. As the centre of buoyancy has been shifted to E', the resultant of the water pressure no longer acts through E, but through E' ; and it must be remembered that this resultant always acts vertically, or at right angles to the water-level. The resultant of the force represented by the weight of the ship continues to act vertically downwards through her centre of gravity F, that being the point it would act through if the vessel had not been heeled; it is of course assumed that no part of the weight of the ship has been shifted, so as to cause her centre of gravity to shift.
Thus we have the weight of the ship acting downwards through the centre of gravity F, in a direction F H, and the weight of the water displaced acting upwards through the centre of buoyancy E', in the direction M ; and the point M, where M cuts what is the middle line of the upright position of the ship, is the meta-centre. The length of the righting couple is the horizontal distance between F H and E' M, represented in Fig. 6 by F K or x G.
The wedge-shaped piece of the hull A B 0 is called the wedge of immersion ; and the wedge-shape piece 0 C D the wedge of emersion. By naval architects they are usually referred to as the " in " and the " out " wedges. By the wedge of immersion, or the part that is put into the water, being largely in excess of the wedge of emersion, or the part that is taken out, the centre of buoyancy is made to shift very rapidly over to leeward as the vessel is inclined, and so the couple x G lengthens very fast. In all broad and shallow vessels the wedge of immersion, even at small inclination, is much in excess of that of emersion, and so they have con siderable stability at small angles of heel—which may be conveniently referred to as initial stability—which stability, however, rapidly vanishes as the deck becomes immersed.
as the weight of the vessel ; but if the volume of the wedge of immersion be in excess of the volume taken out, then the vessel shifts or rises bodily in the water, to an extent which is dependent upon the area of the new load water-plane and the excess in the volume of immersion.
The righting moment or power is computed by multiplying the weight of the ship, or displacement in tons, by the length of the righting couple x G (Fig. 6). That is, if the weight of the ship or her displacement be 40 tons, and the length of the righting couple at 20° inclination be 2ft., then her righting power or moment of stability at that inclination will be 40 x 2 = 80 foot-tons. If the righting moment of a yacht at 20° inclination be equal to 80 foot-tons, as described, then it will require a steady force equal to 80 foot-tons upon her canvas to maintain her at that inclination.
If a vessel with such a section as that portrayed in Fig. 7 were filled out in the garboards at 0 0 just above the keel, it is plain that the centre of buoyancy (B) would be lowered, and the point M would be brought nearer the centre of gravity (G) ; therefore the arm of the righting lever G Z would be shortened. But in the case of a yacht the added displace ment about 0 0 would be utilised for the stowage of additional ballast ; and by this means the centre of gravity (G) would be brought lower; so that it is quite possible that the original distance between G and Z would be maintained.
The effect of increasing the height of the centre of buoyancy relative to the surface of the water can be illustrated in this way. Assume that the displacement, or rather the hull, is cut away at the garboards as shown at P P, and added to the hull near the load water-line as at R R, then the centre of buoyancy would be higher, and upon inclination of the vessel would shift out farther to leeward than shown by B', so that the distance G Z would be increased, always supposing that G was kept in its original position by shifting the weights lower, such as could be done by putting additional weight on the keel. If the centre of gravity could be brought to K, and, with the centre of buoyancy at B, the length of the righting lever would be K L. As a matter of fact, however, we know of but few instances where the centre of gravity has been found below the centre of buoyancy.