If the table with the model is now turned through any angle, the distance the centre of gravity of the water has moved from the axis E of the table can easily be determined by shifting the weight H until the whole is balanced, then evidently from the principles of the lever, H × by its distance from fulcrum = weight of water in model × by the distance the centre of gravity of the water in the model is from fulcrum. Since the weight of H × its distance from fulcrum ÷ the weight of water in model is known, the distance that the centre of gravity of the water has shifted from centre line is easily ascertained and the righting lever determined.
From a lengthened series of experiments, conducted by Mr Heck—latterly in Messrs Denny’s Works where an apparatus from a special design by Mr Heck has been constructed for the firm’s use—the method gives promise of taking a firm place as an extremely simple and approximately accurate means of arriving at the stability of vessels.[18]
While a vessel’s qualities with respect to stability may be determined with great precision by the naval architect, his investigations are only directly applicable to the ship while empty or when in certain assumed conditions of loading which may or may not often occur in actual service. He cannot for obvious reasons estimate, far less control, the amounts and positions of centre of gravity of the various items of weight that may make up the loading.[19] This aspect of the subject has received attention at the hands of naval architects for a considerable time, but the forcible way in which it has been brought under view by recent experience has resulted in special efforts being made to practically meet the necessities of the case. In 1877 Mr William John read a paper before the Institution of Naval Architects, in which he dealt with the effect of stowage on the stability of vessels, and since that time such authorities as Martell, White, and Denny have given valuable papers or made suggestive comments bearing on this important matter. Much has also been done by several builders in the way of devising diagrams useful for regulating stowage and manipulating ballast with regard to initial stability. At the last meeting of the Institution, Professor Elgar read a paper on “The Use of Stability Calculations in Regulating the Loading of Steamers,” distinguished by its eminently practical character, and forming an important contribution to the solution of this problem. The author disapproved of curves of stability being supplied with vessels, as had been advised and was then becoming the practice. General notes, giving in a simple form easily applied in daily practice, particulars respecting the character of a ship’s stability in different conditions, are what the author recommended and had found through actual experience to meet the case most effectually. In the discussion which followed it was intimated by Mr William Denny that his firm had already resolved to furnish every new steamer produced by them with a volume containing general and special notes and diagrams dealing not only with stability but with several other important technical properties (see [footnote, page 59]). After consultation with Professor Elgar, however, he had abandoned his intention of supplying stability curves.
An arrangement designed to readily find the position of the centre of gravity experimentally by inclining, and to indicate at once the stability of loaded vessels as represented by metacentric height, has been devised and introduced on board several ships by Mr Alexander Taylor, of Newcastle—already referred to in connection with the triple expansion principle in marine engines. The instrument and apparatus, which he appropriately names the “Stability Indicator,” was described in a paper read by him before the Institution of Naval Architects at its last meeting. When once an inclining operation has been made, the degree of inclination is read from a glass gauge and the position of centre of gravity and corresponding metacentric height from a previously prepared scale set up alongside the gauge, or from tabulated figures.
The advance made within recent years in connection with steam propulsion comprises many matters necessarily left unconsidered in the chapter on speed and power of modern steamships. Scientific methods have undoubtedly contributed in no small degree to the realization of the remarkable results therein outlined. The achievement of one triumph after another as demonstrated in the actual performances of new vessels, and especially the confidence with which pledges of certain results are given and received long before actual trials are entered upon—and that sometimes with regard to ships embodying very novel features—are evidences of the truth of this.
The oldest method of approximating to the horse-power required to propel a proposed vessel at a given speed is to compare the new ship with ships already built by the use of formulæ known as “co-efficients of performance” deduced from the results of their speed trials. Two such co-efficients have been deduced from Admiralty practice, the one involving displacement, the other area of mid-section, with speed as the variable in both cases. Another method which has been largely used, consists in first determining the ratio of the indicated horse-power to the amount of “wetted surface,” or immersed portion of the vessel’s skin, in the exemplar ship, and then estimating from this ratio the probable value of the corresponding ratio for the proposed ship at her assigned speed. Inasmuch as these methods of procedure do not take account of the forms of the hulls, and consequently of that factor in the total resistance due to wave-making, they cannot be used with any degree of confidence, or without large corrections, except in connection with vessels whose speeds are moderate in proportion to their dimensions: those in fact in which the resistance varies nearly as the square of the speed. A further method, somewhat resembling the one based upon the relation between indicated horse-power and the “wetted surface,” was proposed by the late Prof. Rankine, but has never been extensively employed. Apart from the unreliable nature of the results which an application of it gives—except for certain speeds—it is open to several serious objections in practice.
A method of analysis and prediction, meeting with considerable acceptance from shipbuilders on the Clyde and elsewhere, has been introduced within recent years by Mr A. C. Kirk, of Messrs R. Napier & Sons.[20] The method consists in reducing all vessels to a definite and simple form, such as readily admits of comparison being made between their immersed surface, length of entrance and angle of entrance and their indicated horse-power, and from this judging of the form and proportions best suited to a given speed or power in proposed vessels. The form in question consists of a block model, having a rectangular midship section, parallel middle body, and wedge-shaped ends; its length being proportioned to that of the ship, its depth to the mean draught of water, its girth of mid-section to the girth of immersed mid-section of the ship, and the surface of its sides, bottom and ends, to the immersed surface of the ship. By finding from one or more exemplar ships—the selection of which is obviously governed by the conditions of analysis—the rate of indicated horse-power required per unit of wetted surface at the speed assigned for the proposed vessel, the appropriate rate for the latter may easily be determined.
The data afforded by the modern system of progressive speed trials, especially when taken in conjunction with that of experiment with models as systematised by Mr Froude, supplies in a reliable way much of what is most lacking in the older methods of comparison and prediction. Progressive speed trials on the measured mile were first systematically instituted by Mr William Denny about nine years ago, since which it has been the practice of his firm to make such trials with all their vessels. The practice has been followed by other firms on the Clyde and elsewhere, and there is every probability it will be still more widely adopted in the future. The system consists in trying the vessel at various speeds, ranging from the highest to about the lowest of which she is capable. The several speeds are the mean of two runs—one run with the tide and one against, the object being to eliminate the tide’s influence from the results.[21]
Essentially noteworthy in connection with the system is the manner in which the data obtained from the trials is recorded for future use. This consists of a series of curves, representing the chief properties of ship, engines, and propeller—e.g., “speed and power,” “revolutions” and “slip”—which show to the eye, more easily and clearly than bare figures, the whole course and value of a steamer’s performances. For that of speed and power the various speeds made at the trials are set off to convenient scale as horizontal distances, and the indicated horse-power corresponding to those speeds are set off to scale as vertical distances. The intersection of the offsets so made, give spots for the curve. The other curves alluded to are similarly constructed, the requisite data being the direct or deduced results of the measured mile trials.