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access to the ship through hatchways, etc., and the movement down by the head was greatly accelerated. Fig. 182 has been drawn for a box-shaped vessel 175 ft. long, 30 ft. broad, 15 ft. deep, 8 ft. draught, before damage. If an empty compartment between bulkheads 25 ft. and 55 ft. from the bow is laid open to the sea the vessel will float at a draught of 13 ft. 5 in. forward and 6 ft 8 in. aft. It is seen that the stem head is quite close to the water, and although the loss of buoyancy is not very considerable, yet this, with the change of trim, causes a dangerous condition. It is thus seen to be most important to carry watertight transverse bulkheads well above water. Figs. 52 and 54, which show the watertight subdivision of a large and small cruiser respectively, show that most of these bulkheads are carried to the upper deck.
STABILITY AT LARGE ANGLES OE INCLINATION.
We have seen that the stability of a ship at any angle is the effort she makes to return to the upright when put over to that angle. For small angles of inclination, up to 10 to 15°, this depends directly on the metacentric height. Thus at 10° the Royal Sovereign, with 3\ ft. GM and 14,150 tons displacement, will have a righting moment of
14,150 x 3-5 X sin 10° = 8,600 foot tons.
It is possible, however, for a vessel to have sufficient metacentric height but insufficient stability at large angles. This was specially brought out in the investigations which followed the loss of H.M.S. Captain. Metacentric height alone, apart from other
considerations, principally freeboard, will not ensure a vessel having sufficient stability, and special calculations are necessary to determine the righting moment at large angles of inclination.
Curve of Stability.—Take a vessel inclined to a large angle 0, as Fig. 183. The upward force of the buoyancy acts through B', the new centre of buoyancy, and the couple tending to right the ship is W x GZ, GZ being the righting lever. The length of this righting lever will depend on how far the centre of buoyancy shifts out, and this length will vary for different angles. Thus for H.M.S. Captain the following values of GZ were calculated, viz. 7°, 41 in.; 14°, 8 J in.; 21°, 10| in.; 28°, 10 in.; 35°, 7| in.; 42°,
5 j in.; 54J°, zero. A convenient way of representing these results is to draw a base line to represent angles of inclination and set up as ordinates the lengths of GZ as found. A curve drawn through the spots thus obtained is a curve of statical stability. The curve for the Captain is in Fig. 184.
Fig. 185 shows a curve of stability constructed as above. The angle at which GZ obtains its maximum value is termed the angle of maximum stability (in this case 47°). The angle at which the
curve crosses the base line (in this case 77°) is termed the angle of vanishing stability, or the range of stability. Up to this angle the vessel possesses a righting lever which will take her back to the upright. At 77° the ship is in equilibrium, the C.G. and C.B. being in the same vertical, but this equilibrium is unstable, and a small inclination either side of 77° will take her away from that angle; if to 75°, say, she will go back to the upright; if to 79°, say, she will capsize.
In striking contrast to the curve for the Captain is that for the Monarch (Fig. 184). In this case the angle of maximum stability is not reached until 40° as against 21° in the Captain, and the value of the maximum GZ is about twice as great. The stability does not vanish until the large angle of 70° is reached. The reason for the difference between the two ships is seen by comparing the sections. The Monarch had high freeboard, which pulls out the centre of buoyancy as the ship heels over. The Captain had a low freeboard, giving a curve of stability which was dangerously small for a ship carrying a large amount of sail.
In considering a curve of stability certain assumptions have to
be made, which are necessary, in order to make the calculations at all feasible.
1. The sides and deck are assumed to be watertight for the range over which the curve is drawn. Thus all sidelights and gun-ports are supposed to be closed below the upper deck. If the effect of the forecastle or poop is included, any openings in these superstructures are supposed to be closed.
2. The C.G. of the ship is taken in the same position in the ship throughout the inclination, i.e. it is supposed that no shift of weights takes place.
The important features of a curve of stability are:—
1. Inclination which the curve has to the base line at the start. This inclination depends directly on the metacentric height.
2. The angle at which the maximum value of the righting arm occurs and its value at that angle.
3. The range or the angle at which the curve crosses the base line, and the vessel becomes unstable.
Effect on a Curve of Stability by variation of Beam, Freeboard, and Position of C.G.—In order to illustrate these points a box-shaped vessel is taken having a breadth of 50^ ft., draught of 21 ft., freeboard of 6£ ft., and metacentric height of 2-6 feet.
The curve of stability of this vessel is shown by A in Fig. 186, in which the range is seen to be 39°.
1. If now the beam of the vessel be increased by 7 ft., we should expect the GM to increase also, and this is seen by the curve of stability D starting from the origin at a steeper angle. This curve shows that, although the GM has increased from 2'6 ft. to 5-0 ft., owing to the increase of beam, yet the range of stability has only increased from 39° to 48°.
2. If instead of the beam we increase the freeboard by 7 ft., we obtain a strikingly different curve of stability, B. The increased freeboard is assumed not to affect the position of the C.G., and the