While the vertical distance between the centre of gravity and the metacentre—commonly termed the “metacentric height”—forms a measure of the “initial stability,” or the stability at very small angles of inclination, it is imperfect by itself, and may be very misleading as regards the stability at larger angles. This was conclusively demonstrated by Atwood in his papers read before the Royal Society in 1796 and 1798, while other grounds for discrediting the standard of stability furnished by mere metacentric height were discovered subsequently, and have been signally emphasised, with additional reasons, by recent occurrences. Atwood, in the papers referred to, laid down a general theorem for determining the righting moments at any required angles of inclination possessed by a ship having a given draught of water and a fixed height of centre of gravity, the principle of which involved the use of the moments of the volumes of the “Wedges,” i.e., those parts of a vessel (see W O W1, L1 O L, fig. 15), which become immersed and emerged as she is inclined. Several methods of simplifying Atwood’s calculations had been devised previous to 1861,[13] but in that year Mr F. K. Barnes, in a paper read before the Institution of Naval Architects, described a method of accomplishing this which until within recent years has been the one ordinarily adopted in computing the stability of a vessel at various angles of inclination.[14]
Owing to questions having arisen at the Admiralty in 1867 respecting the stability of some low freeboard monitors at very large angles of inclination, Sir E. J. Reed, then Chief Constructor, directed the matter to be investigated. The work was placed in the hands of Mr William John, who embodied for the first time the results of the calculations in the form of a curve of stability, which exhibited the variations of righting moments with angles of inclination up to the particular angle at which stability vanished. The entire range of a vessel’s stability was thus made evident, and in such a form as enabled the general problem to be far more comprehensively and accurately treated than before. The results of Mr John’s labours were described in a paper read by Sir E. J. Reed before the Institution of Naval Architects in 1868, and a further paper, containing an improved method of applying Atwood’s theorem to the calculation of stability upon this extended scale, was read before the same Institution by Messrs John and W. H. White in 1871. The loss of H.M.S. Captain, in 1870, as already pointed out near the beginning of this chapter, occasioned an immediate and serious regard for the stability of war vessels. This disaster, with other losses at sea from instability, also forcibly directed the attention of mercantile naval architects to the subject, and investigations on the same complete scale as those undertaken in the Admiralty have for some years been adopted in a few leading mercantile shipyards.
In this way the peculiar dangers attaching to low freeboard, especially when associated with a high centre of gravity, have been pretty fully made known, but the character of the stability which is often to be found associated with very light draught appears to have escaped the attention it demands. Light draught is often as unfavourable to stability as low freeboard, and in some cases more so.
These truths were forced into prominence at the inquiry held by Sir E. J. Reed on behalf of the Government into the disaster which befell the Daphne, a screw-steamer of 460 tons gross register, which capsized in the middle of the Clyde immediately on being launched from the yard of the builders, Messrs Alexander Stephen & Sons, Linthouse, on July 3rd, 1883. Sir E. J. Reed, in his exhaustive report, published in August, 1883, emphasised the lessons adduced at the inquiry as to the peculiar dangers attaching to light-draught stability; and Mr Francis Elgar, (now Professor of Naval Architecture in Glasgow University), who was employed to make investigations respecting the stability possessed by the Daphne at the time of the disaster, did much to guide consideration of the subject into this channel. In a letter to the Times on 1st September, 1883, Mr Elgar, by way of explaining portions of his evidence at the inquiry, called attention to the relation which exists between the righting moments at deep and light draughts in certain elementary forms of floating bodies, his communication throwing further light on the subject of light-draught stability. It appears that the fundamental proposition which underlies the variations in the stability of a floating body with draught of water had never before been demonstrated or enunciated.
It will be readily understood that a curve of stability for a given draught of water and position of centre of gravity ceases to be applicable if changes are made in the weight and consequent draught of water of a ship or the position of the centre of gravity, or in both. Now in mercantile steamers, from the extremely light condition in which they are launched to the uncertain loaded condition of their daily service as cargo-carriers, the variation of draught is very considerable, and imports into the subject considerations which do not obtain to any great extent in war ships.
To complete the representation of stability as it should be known for merchant ships, it is now recognised that curves showing the stability at every possible draught of water and for different positions of centre of gravity should be constructed. By means of “cross-curves” of stability, or curves representing the variation of righting moment, with draught of water at fixed angles of inclination, this comprehensive want can be met with something like the necessary expedition. From such curves it is a simple operation, involving no calculation save measurement, to construct curves of the ordinary description, showing the righting moment at all angles for any fixed draught of water and position of centre of gravity. Professor Elgar was the first to publicly direct attention to this valuable development of stability investigation of merchant ships, doing so in an able paper “On the Variation of Stability with Draught of Water in Ships,” read before the Royal Society on March 13th of the present year. Simultaneously with Prof. Elgar’s employment of such curves in actual practice their use had been independently instituted by Mr William Denny in his firm’s drawing office, and the mode in which they were worked out in this case was communicated in a paper read by Mr Denny in April of the present year before the Institution of Naval Architects.[15] Several important improvements with respect to simplifying and shortening calculation distinguish the method employed by Mr Denny, and that gentleman, in the paper referred to, accords individual credit to members of the scientific staff in his firm’s employ, who, on being entrusted with the work of calculation, brought considerable originality to bear upon their labours. The cross-curves described by Prof. Elgar were constructed from a series of curves of stability calculated in the ordinary way. This, however (as pointed out in an after-note to that gentleman’s Royal Society paper), is less simple and very much less expeditious than the method carried out under Mr Denny, which consists in calculating the cross-curves directly by applying Amsler’s mechanical integrator[16] to the under-water portion of the ship instead of to the wedges of immersion and emersion, thus determining at once the positions of the vertical lines through the centres of buoyancy at the required angles of inclination. As thus carried out a complete set of cross-curves can be produced with about one-third the labour involved in employing the older method. The ease and rapidity with which ordinary curves for separate draughts can be taken from cross-curves has already been commented upon.
Many other investigators besides those already mentioned have recently been working at the subject of stability, and a considerable number have read papers, dealing with the extension and simplification of stability calculations, before one or other of the scientific societies concerned with naval architecture, most of the methods put forward being well worthy of study.[17] To very many shipbuilders, however, and to others besides them responsible for the stability of ships, processes of arithmetical calculation—even allowing for all the simplification which mathematical skill has recently effected—appear still to be too intricate, or to absorb too much time for their being entirely followed. As a simple means of readily, although approximately, arriving at the results attained more elaborately and reliably by calculation, attention has recently been directed to an experimental process by which a complete curve of stability may be constructed almost without the use of a single figure! The method was first brought forward in 1873 by Capt. H. A. Blom, chief constructor of the Norwegian Navy, formerly a student of the South Kensington School of Naval Architecture, who described it to the United Service Institution. The method has been employed by shipbuilding firms on the Tyne and Clyde when a curve of stability had to be produced in a very limited time, and when extreme accuracy was not a desideratum. As practised by the firms in question, the modus operandi differs in some slight respects from that described by Captain Blom, but the changes in no way affect the principles as first laid down by him. The modern mode of procedure may be briefly described:—
From the body plan of the ship, i.e., that portion of the draught plan representing the vessel’s form by a series of equidistant transverse sections—any convenient number of sections lip to the load water-line are pricked upon and then cut out of a sheet of drawing paper of uniform thickness. These sections are then gummed together in their correct relative positions, care being taken to spread the gum thinly and evenly. This paper model—greatly foreshortened, of course—represents the immersed portion of the ship (in other words, the displacement) when she is floating upright. By suspending this model from two different points, and taking the intersection of two vertical lines through the points of suspension—or better still, by balancing it horizontally on a pin and fixing the point when the model is in equilibrium—the centre of gravity of the model, or in other words, the actual centre of buoyancy is obtained.
Water lines at various angles of inclination are then drawn on the body plan, all intersecting the water line for the upright condition at the centre line of ship. The displacement represented by the inclined water lines thus drawn, generally not being equal to that for the upright position, a correcting layer has to be added or subtracted for each inclination, in order to obtain this end. By employing the planimeter the necessary thickness of this layer can be most readily ascertained. Where a planimeter is not available the actual floating line may be obtained, after the model has been made, by cutting off layers, allowance having been made for this purpose. The same number of sections as before are then cut out to each of the inclined corrected water-lines, the paper model prepared and the centre of buoyancy obtained as already described.
Through this new centre of buoyancy a line is drawn perpendicular to the inclined water line, and the distance between this line and the centre of gravity of the ship, already obtained, is the righting arm. If this process is repeated for each angle of inclination, it is thus seen a complete curve of stability may be approximately obtained.