Approximation to the Value of the Tons-per-inch Immersion.—If L is the length between perpendiculars, and B is the breadth of the hull Then (1) for ships with fine L.W.P. as cruisers— (2) for ships of fuller form as battle-ships— These approximations will be found useful in the absence of the correct figure for a particular ship. The correct tons per inch is usually given in the Ship's Book. The length between perpendiculars and breadth of hull are used above instead of the length and breadth on L.W.L., as the latter are not usually known without reference to the drawings. The following show how far the approximation holds in different ships :actual 18.7, approximation 18-25 Third class cruiser Curve of Tons-per-inch Immersion.-The above figures refer to the tons per inch at the L.W.L. In order to determine the tons per inch at any other line at which a ship happens to float we construct a tons-per-inch curve. We calculate the tons per inch at the several level lines parallel to the L.W.L., and set these out at the corresponding draughts on a convenient scale. Thus, for a battle-ship, the tons per inch at level lines 4 ft. 3 in. apart, commencing at 31 ft. draught, were found to be respectively-575, 57-2, 56·5, 537, 510, 46 3, 390, 240. The curve drawn through the spots thus obtained, as in Fig. 157, is the curve of tons-per-inch immersion. If the vessel floats at a draught of 19 ft. 6 in. forward and 20 ft. 10 in. aft, i.e. 20 ft. 2 in. mean, this draught is set up and the ordinate of the curve, 548, is the tons per inch required. In ordinary ships the value of the tons per inch varies very little for considerable changes of draught in the neighbourhood of the L.W.L. Coefficient of Fineness.-This is the ratio which the actual volume of displacement bears to the volume of a rectangular block having the same length as that of the ship between perpendiculars, the same breadth and the depth equal to the mean draught of the ship (the draught should be excluding any keel projection, if any, as in a sheathed ship). The value of this coefficient gives us a good idea of the degree of fineness of a ship, as the following examples show: "Formidable.”-400 ft. x 75 ft. x 263 ft. x 15,000 tons; 15,000 I.H.P., 18 knots. B 120,000 "Duncan.”—405 ft. × 75 ft. × 261 ft. x 14,000 tons; 18,000 I.H.P., 19 "Drake."-500 ft. x 71 ft. x 26 ft. x 14,100 tons; 30,000 I.H.P., 23 3000 × 35 knots. Coefficient of fineness = 14,100 × 35 500 x 71 x 26 = 0.53. The following are average values of this coefficient of fineness, viz. Battle-ships 06 to 0·65 As illustrating the importance of the fineness of a ship in connection with the attainment of speed, reference may be made to the Formidable and Duncan. In the former ship a coefficient of fineness of 0.65 was adopted, 15,000 I.H.P. being intended to realize 18 knots. In the latter ship, in order to attain 19 knots without an excessive expenditure of I.H.P., a finer form had to be adopted with a coefficient of fineness of 06. Difference of Draught of Water when Floating in Salt Water and River Water.-(Salt water 64 lbs., river water 63 lbs. to the cubic foot.) The weight of the ship going from the one to the other remains the same = W tons = W x 2240 lbs. If T be the tons per inch in salt water and t the difference of draught in inches, the weight of the layer = Txt x 2240 lbs., Txt x 2240 64 and the volume of the layer = cubic ft. We have thus found the volume of the layer in two ways, and we can then equate, viz.— Thus for a battle-ship 57-2 tons per inch, 15,000 tons displace ment, the difference of draught = 15,000 63 × 57.2 = 4 in. If for W and T we put approximate values, we have We can therefore say, roughly speaking, that the difference of draught in inches is one-seventh the draught in feet. In the general case of a ship passing from water of density d' to water of density d (d' being greater than d), the difference of W d'-d draught is T d Reserve of Buoyancy and Freeboard.-We have seen that buoyancy is the upward support given by the water to the ship, and this upward force exactly equals the weight of the ship. Freeboard is the height of the upper deck at side (to top of deck plank if fitted) from the water surface. Reserve of buoyancy is the volume of the ship above the waterplane which can be made watertight. In many ships this will be to the upper deck, but in some ships there are erections, as poop and forecastle, which can be made watertight. The sum of the buoyancy and the N reserve of buoyancy is the total floating power of the vessel. Reserve of buoyancy is expressed as a percentage of the buoyancy, and this varies considerably in different types of ship, e.g. in the Devastation, a low freeboard ship, this percentage was about 50 per cent. For modern battle-ships with good freeboard it amounts to about 90 per cent., and for cruisers and destroyers higher values than this are usual. In merchant vessels sufficient reserve of buoyancy is obtained by specifying the minimum freeboard, this being obtained from tables drawn up by the Board of Trade. All British war-ships have freeboard and reserve of buoyancy considerably in excess of what the Board of Trade would require for merchant vessels of corresponding dimensions. Ships like the torpedo gunboats appear to disadvantage in comparison with merchant vessels of similar size, because of the absence of bulwarks which extend several feet above the upper deck of the latter ships. The presence of the bulwarks, although affording protection from the sea, does not, of course, increase the reserve of buoyancy. Indeed, bulwarks are likely to become a source of danger, if provision is not made for a sufficient number of large clearing ports for the purpose of speedily clearing the deck of water. The reserve of buoyancy possessed by a ship is important, because this has to be drawn upon if a ship is damaged, and a ship with small reserve could only stand a small amount of damage before being entirely submerged. Freeboard and reserve of buoyancy are also important, however, because of the necessity of providing sufficient stability at large angles of inclination. This will be dealt with in a later chapter. Sinkage caused by a Central Compartment being open to the Sea. The principles involved will be well illustrated if we take a box-shaped vessel. Such a vessel 100 ft. long, 20 ft. broad, 20 ft. deep floats at a draught of 10 ft. What will be the draught if a central compartment, 20 ft. long, is laid open to the sea (Fig. 159). The weight of the vessel is the same before and after the bilging, but the buoyancy has been diminished, and the vessel is in a similar condition to one having the watertight side and bottom between the bulkheads replaced by a lattice-work. In consequence of the loss of buoyancy the vessel must draw on the reserve of buoyancy by sinking down to the waterline W'L' to the draught d feet, say |