THE ACTION OF THE RUDDER.
A man moving through water is steered or turned by the action of a couple, the arm of which is the centre of lateral resistance and the centre of effort of the rudder (see k z, Fig. 11, page 22). The streams of water that meet the oblique surface of the rudder when it is put over represent a pressure which can be decomposed into a force acting at right angles to its surface; and it is evident that the application of this force would cause a vessel pivoted on a vertical axis through her centre of gravity to rotate about that axis, and the speed of the rotation would be dependent upon the magnitude of the force applied, the extent of area of the rudder, and the length of the arm of the couple before referred to. But a vessel is not so pivoted, and turns as it were in a ring and, at first, about an instantaneous axis, which does not pass through the centre of gravity of the ship. The following conditions dependent upon the putting over a rudder to turn a vessel are gleaned from a paper read by Dr. Woolley before the British Association.
Assume that Fig. 13, on the next page, is a yacht proceeding in the direction of the arrow A. B is the rudder put over to starboard to an angle of 35° by the tiller being pushed to port, and the arrow D represents the magnitude of a force acting upon the rudder in a direction at right angles to its surface ; a will be regarded as the point of application of that force ; but the force D can also be taken as an equal force acting in a parallel direction through the centre of gravity of the yacht x, and shifting the vessel sideways in the direction of the arrow E, combined with the couple of the force whose arm is represented by the distance the centre of effort of the rudder, a, and the distance the centre of the lateral resistance, o, are apart.
The effect is that the direct forward motion of the vessel becomes altered to one of rotation in the direction shown by the curved arrow t about an instantaneous axis k, thus determined : draw x q at right angles to D a through the centre of gravity ; and draw x y (equal to the radius of gyration of the vessel) at right angles to x q. Next join q y, and y k is drawn at
right angles to q y, cutting x q in k produced ; and k is the instantaneous axis. By " instantaneous axis " is meant the point upon which the vessel turns upon feeling the first influences of the rudder, and this point gene rally lies considerably before the centre of gravity ; hence it always appears that the stern of a vessel moves much faster than her head in turning; and this is really so at first, but when the vessel is kept turning the axis of rotation shifts aft until it rests in the centre of gravity of the vessel.
Components of the force in the direction E or D are employed partly in checking the vessel's way, and partly in driving her sideways nearly at right angles to her keel.* These components ultimately balance each other, and the vessel then continues to turn under the influence of the couple formed by a o round a vertical axis passing through the centre of gravity, x. Dr. Woolley, in reference to handiness in turning, says : " Sensibility to the helm, i.e., quickness and readiness in a ship to go about, is a most important quality. At the first moment the angular acceleration, which is the measure of this sensibility, varies directly as the moment of the water-pressure on the rudder, and inversely as the product of the weight of the ship and the square of the radius of gyration about a vertical axis through the centre of gravity." The angular acceleration or turning motion is at first very small, and its initial magnitude mainly depends upon the rapidity with which the rudder is moved so as to bring pressure on it, and upon the radius of gyration of the vessel. As the angular velocity is accelerated, so does the resistance to rotation increase until the moment of resistance balances the moment of the couple formed by the pressure on the rudder. The angular velocity, or turning motion, then becomes uniform.