Rolling of Ships

The problem has also been attacked from an entirely different angle and a theory was propounded by W. Froude in which the action of each elementary portion of the blade surface is sepa rately estimated from the forces on planes moved through water at various speeds and at different angles of obliquity (see Trans. I.N.A. 1878). The investigation is of importarice though it does not completely represent the actual conditions; for the deduc tions from a small element moving through undisturbed water are applied to the whole blade ; the disturbance of the water when a blade reaches it and the consequent effects of each element on adjoining elements and of one blade on another are not taken into account. The momentum theory of R. E. Froude has been strikingly confirmed by some exhaustive experiments in a wind channel; and it is found that when the velocity deduced from this theory combined with certain interference factors is applied to the blade element theory of W. Froude in the light of modern experiment data, good agreement is obtained with actual practi cal results in the case of narrow bladed screws such as air pro pellers.

In recent years the general application of the circulation theory to hydrodynamical problems has resulted in the conception of the vortex theory of the screw propeller. This theory when more fully developed promises not only to clarify the physical nature of propeller action but to assist the quantitative estimating of propeller performance. The large wide blades used in marine propellers and the confused nature of the water flow at the stern of a ship make the application of theory to all marine screw pro peller problems extremely complicated.

Experiment Results.

The complicated nature of screw pro peller problems was recognized early and recourse was made to model experiments for information on thrust and torque of pro pellers of various proportions at different speeds and revolutions. These experiments have necessarily been made on a small scale; but some which have been made on larger propellers have sug gested that the scale effect if any is not large ; and it is generally assumed that the results of model experiments on propellers can be applied to ship propellers in accordance with the law of com parison, no correction being made for skin friction. The most important sets of experiments published covering the proportions of screw propeller met with in practice have been made by Froude, Taylor, Durand and Schaffran. A paper by Taylor in Transactions of the American Society of Naval Architects and Marine Engineers 1924 shows that these experiments made on different sizes of models in different parts of the world practically corroborate each other. The experiments of R. E. Froude cover

a very complete range and the results can be used for most prac tical problems. (See Trans. I.N.A. 1908.) The thrust horse power is given by Froude in the following formula :— where H is the thrust horsepower, V speed of advance in knots and D the diameter in feet ; p is the effective pitch ratio calcu lated from the revolutions for zero thrust. For full sized screws Froude considers this is 1.02 times the face pitch ratio ; for mod ern screws it is probable that the ratio should exceed 1.02. The "blade factor" B depends only on the type and number of blades; its value for various "disc area ratios," i.e., ratio of total blade area (assuming the blade to extend to the centre of shaft) to the area of a circle of diameter D is given in the following table :— Reference should be made to the paper for curves of efficiency obtained.

Interaction Between Ship and Screw.

In the foregoing theoretical and experimental consideration it has been assumed that the propeller is advanced into undisturbed water, which is very different from the conditions existing behind the ship. The vessel is followed by a body of water in complex motion called the "wake." It is assumed that this water has a uniform forward velocity V' over the propeller disc, V being the speed of the ship; the speed of advance of the propeller is then and ' the V' =w is termed the wake value. The pro peller acts generally as a screw advancing into undisturbed water at speed V — V' and the real slip is v— (V — V') =v— w is in general a positive fraction so that the real slip is greater than the apparent slip v —V ; and real slip must be taken into account in the design of propeller dimensions.

The influence of the screw also extends sufficiently far forward to cause a diminution of pressure on the after part of the ship, thereby causing an increase in resistance. The thrust T, exerted by the screw working behind the ship must be sufficient to bal ance the tow rope resistance R. This increase of resistance as well as this diminution of pressure is conveniently expressed as a fraction t of the thrust exerted by the screw, whence it follows that TO —1)=R. The power exerted by the propeller or the thrust horsepower is proportional to T X (V—V'); the effective horsepower is R x V and the ratio of these two, is termed the hull efficiency. The hull efficiency value does not differ greatly from unity with different positions of the screw. An account of an interesting series of experiments to determine the values of w and t is given by W. J. Luke, Trans. I.N.A. 1910.