Rolling of Ships

From these experiments certain deductions were made as to the dependence of the speed of a ship ( V knots) on its length (L feet) and the slightly different length (D) between component bow and stern waves ; these deductions are to a great extent con firmed by experience with ships of all classes, and may be stated thus:—for economic propulsion at a speed V the length L of the ship should be generally equal to or slightly less than cor responding to the "favourable" value of I•2 of the ratio Vessels of extremely high speed such as torpedo-boat destroyers ' are an exception, the value of being then frequently as great as 4, which approximately coincides with the highest "favour able" value of • These early experiments by Froude were es pecially valuable in directing attention to the important influence of length of ship on resistance; and his conclusions have been verified and amplified by Taylor, Baker and other experimenters in more recent times.

Law

of Comparison.—The complex nature of wave resistance renders any simple estimate such as that for frictional resistance, impossible of general application. There is no simple law con necting wave resistance with size, form and speed. The effect of size alone can be eliminated by means of the "principle of simili tude" enunciated by Newton, and the law of comparison is the application of this principle to the resistance of ships. To W. Froude is due the credit of making the application, which he did in the following terms : "If the linear dimensions of a ship be n times those of its model, and the resistances of the latter be R,, • • • at speeds V3, • • • , then the resistances of the ship at the cor responding speeds, VI Voin • • • will be Rol', , • • • and, therefore the effective horsepowers at correspond ing speeds are increased in the ratio : I." This law is applicable to the residuary resistance but not to frictional resistance, the laws governing which so far as is known do not satisfy the conditions underlying the principle of similitude stated above. Consequently in applying the law of comparison to ships and models where the linear ratio is considerable, the resid uary resistance alone should be compared by that means, the frictional resistance being independently calculated for ship and model. When the ships compared do not differ considerably in linear dimensions, the law may be extended to total resistance without appreciable error. Before the law of comparison could be accepted as applicable to ships it was necessary to test it prac tically and the first tests of this kind were made by W. Froude on H.M.S. "Greyhound" for the Admiralty, the results being recorded in Trans. I.N.A.

"Greyhound" was towed at a number of speeds, draughts and trims and the resistance, speed and other data carefully measured. Experiments were also made on the model under corresponding conditions. Similar, but much less exhaustive experiments were made by Yarrow on a torpedo boat (see Trans. I.N.A. 1883). In each case the measured resistance of the ship was greater than that deduced from the model experiments, particularly in "Grey hound"; but having regard to the deteriorated condition of the surface of the hull it was considered that the agreement was close enough to justify the method adopted for powering This method or its equivalent with modifications in detail has been used ever since, and is practically justified by the results obtained by ships on speed trials. There are, however, certain unexplained inconsistencies in converting the results deduced from models to the ship scale which are allowed for by empirical factors based on experience. These require further experimental elucidation. The adoption in quite recent years of means of ascertaining the thrust exerted by the propellers of ships on trials may help in clearing this up. Other experiments have been made, notably some by Kempf at Hamburg on long cylinders, as a result of which in 1923 an alternative basis for assessing the skin friction of ships was proposed. Further experiments are in progress by Kempf, and the results of these and other efforts should afford valuable data for assessing the true skin friction of ships.

Model Experiments.—As a result of the "Greyhound" trials the accepted method of estimating the horse-power required for a new ship is by running a scale model under corresponding con ditions in an experiment tank fitted and equipped for the purpose. The law of comparison is applied to the residuary resistance, or, if used for the total resistance, a "frictional correction" is made. In 1871, W. Froude constructed a tank and suitable apparatus at Torquay for the British Admiralty. In 1886 a new tank was in augurated at Haslar from the designs and under the supervision of R. E. Froude, such improvements being introduced as experi ence at Torquay had shown to be desirable. Similar establish ments have been instituted by several foreign governments and by some private firms. One of the more recent and up-to-date tanks is that at Teddington forming part of the National Physical Laboratory. This tank was opened in 1911: it is used for general research and is available for undertaking private work required by shipbuilding firms. A brief account of some of the earlier experiment tanks with their equipment is given by Dr. Glazebrook in a paper in Trans. I.N.A. 1909.