CHAPTER IV. THE ACTION OF THE RUDDER AND STEERING EFFICIENCY. THE ACTION OF THE RUDDER. A VESSEL 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 æ, 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 a 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 a q. Next join q y, and y k is drawn at right angles to qy, cutting a 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 generally 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, a. 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 * When a yacht carries weather helm the rudder is turned to leeward, but the turning power of the rudder is balanced by the ardency of the pressure on the lee bow; hence the whole effect of the rudder is to check the forward speed and to press the vessel bodily to windward; and the latter influence may considerably lessen the leeway. 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. Now the moment of the water pressure on the rudder varies as the length of the couple a o and the area of the rudder; and the radius of gyration is dependent upon the length of the ship and the stowage of her weights, and thus a long vessel would have her already slow turning further diminished by the stowage of weights in her ends.* If the arm of the couple on which acts the pressure on the rudder be shortened, the steering efficiency will be diminished; and it has been contended that a raking sternpost so shortens the arm of the couple. But, so far as we can judge, this is a mistaken contention, as generally the centre of lateral resistance is carried farther forward by the raking sternpost than is the centre of effort of the rudder. Beyond this, there is usually a much greater length of sternpost when it rakes, and generally the area of the rudder is thereby increased, inasmuch as the breadth only of the rudder appears to be regarded as a matter of importance, and not its depth, so far as yachts are concerned. Some yachts with raking sternposts have enormous rudders, and, although there may be some danger in using them in the case of sternway and in scending, there is no doubt that they are efficient. But a rudder hung on a raking sternpost is not wholly effective, inasmuch as a component of the pressure on it is exerted in a vertical direction, and tends to drag the vessel's stern under. This can only be regarded as a disadvantage, and a further disadvantage is that the rudder is difficult to put over, as it has to be lifted every time; but the latter difficulty is overcome by making the tiller longer than would be required for a similar rudder hung on an upright sternpost. With regard to resistance to rotation, this mainly depends upon the area of the immersed longitudinal section, and particularly upon the amount of dead wood fore and aft. By reducing the dead wood fore and aft the resistance is proportionately decreased, and, moreover, the radius of gyration would be somewhat shortened by the reduction of the fore and aft weight; but almost equal effects would be produced by taking away from the dead wood forward and aft, and concentrating it in the middle * The bad effect of weights in the "ends" of small boats is very noticeable, and we have known cases where a boat has been cured of a tendency to miss-stays by simply concentrating her weights or ballast amidships. On the other hand, a very old practice to insure a boat staying is for someone to get into the bow as the helm is put down; but the bow should be relieved of the weight directly the boat is head to wind, or the boat may fail to "fill" or fall off. of the vessel under the keel. The effective surface for lateral resistance would be maintained, and the radius of gyration would be still shortened.* To sum up, the quickness of a vessel in answering her helm and the smallness of the circle in which she will turn depend: 1. Upon the smallness of the weight of the vessel and her radius of gyration. 2. Upon the area of the rudder, and the length of the couple upon which it acts, and upon the time it takes to put the rudder over. 3. Upon the area and form of the immersed longitudinal-vertical section of the vessel. The double-boarded boat as depicted in Fig. 14, affords peculiar advantages for lengthening the arm of the turning couple, as by lifting the board (h) the centre of lateral resistance is thrown very much forward, and the area of dead wood at the after end (which might be necessary in a sailing vessel to check leeway or to balance sails) is considerably reduced. In tacking, if the vessel's "way" were stopped as she came head to wind, and the rudder thereby became useless, the fore board a could be raised and the after board lowered, and thus the head of the vessel, by aid of the fore sails, would readily fall off the wind. All kinds of fanciful forms have been given to rudders, and a practice came in a few years ago of putting the greatest breadth near the surface of the water. We believe this practice was owing to a vessel once having * Large centre-board yachts are frequently said to be more sluggish in stays than keel yachts, and no doubt there is some truth in this, although, looking to their immersed form alone, they ought undoubtedly to turn quicker than keel yachts. In the races between the Cambria and the centreboard yachts in America in 1870, it was repeatedly shown that she was quicker in stays than any of her competitors, but we are inclined to think that the superiority in this respect was due to her raking sternpost, to her handier rig, and, in strong breezes, perhaps, to her greater weight, so that she carried her way until well round on the other tack. If two vessels are to be impelled by an equal force at equal speeds, and one vessel is heavier than the other, then it will take a greater time to get the heavier vessel up to the required speed than it would the lighter vessel; so also when the force is withdrawn it will take a greater time to exhaust the momentum due to the speed of the heavier vessel than it would the momentum of the lighter vessel. Thus heavy vessels (although they may be turning in a circle of greater radius) are said to "shoot" far in stays, and fill on the other tack without losing way. However, the assumed advantages which a heavy vessel has in this respect will be only apparent in strong winds when the momentum, due to high speeds, is very great; and the advantages do not exist for a vessel that has continuous propulsion whilst turning, as a steamship has, the lower half of her rudder accidentally carried away, and the subsequent report that she steered better with the part than with the whole. We are inclined to think that in this case the inefficiency of the entire rudder depended on its being too big for the crew to use; at any rate, an experiment made by Mr. Froude with a model of H.M.S. Encounter clearly proved that the lower half of a rudder is more effective than the upper half. The rudder was in two parts, i.e., squares of equal dimensions, and it was found that the upper half required to be put over to 20° to balance the lower half at 10°, in order that the vessel might follow a straight line. In the case of a very raking sternpost there may be a small advantage in having the broadest part of the rudder in the top half, as its centre of effort would thereby be carried farther aft; but generally there can be no doubt that the deeper the main area of the rudder is immersed, clear of the fulness of the after body, the more effective it is. As a clean run aft is a great assistance to the effectiveness of the rudder, it is quite possible, if an experiment similar to that tried on the Encounter were tried with a yacht, that a less difference in the effectiveness of the two halves might be found. The advantage of keeping the rudder well immersed-both in smooth and disturbed water-is so well understood by small boat sailers that we find many small and shallow craft with their rudders dropping considerably below the keel. The only disadvantage of this arrangement is that, if the boat carried much weather helm, and if the centre of effort of the rudder were much below the centre of lateral resistance, the pressure on the rudder would tend to increase the boat's heel, although not to a considerable extent. (These rudders are so hung that in shallow water they lift without unshipping.) There appears to be no definite rule for determining the breadth of rudders in sailing yachts, but generally we find the breadth to be onetwentieth of the length on the load line, and about one-thirtieth of that length in steam yachts. With regard to the efficiency of broad and narrow rudders, it would appear, from experiments made for the Admiralty some years ago, that a rudder of, say, 3ft. in breadth, put over to an angle of 30°, would have double the efficiency or turning power of one 6ft. in breadth put over to half the angle, or 15°; and the force required to move the rudder would be the same in either case. Thus there can be no increase in the efficiency of a rudder by the mere addition of breadth without an increase in the power to use it, and a very large rudder, if used so as to obtain its greatest efficiency—which is found to be when put over to an angle of about 35°-means a great retardation of speed; or, the smaller the circle a vessel is made to turn in, the more speed will be retarded. So far as small steam yachts are concerned, no rudder offers greater advantage for facility D |