As a rule no calculation is made in fitting a vessel with a tiller, farther than making it bear some proportion to the length of vessel ; if the rudder cannot be readily used with the tiller, extra tackles are fitted to it, or the tiller is discarded and a larger one used in its place. However, a very simple calculation will approximately show the force that would be required at the tiller head for any given area and angle of rudder, length of tiller and speed. At a speed of 6 knots the resistance of a plane moved at right angles to its surface is 112113. per square foot, and the resistance increases as the square of the speed ; also, the resistance to a plane moved obliquely in water, varies nearly as the sine of the angle of inclination. Then, say that the rudder is 12ft. deep and 5ft. broad, equal to 60 square feet, and put over to an angle of 30° ; then 112 x 60 x sine of angle) = 33601b. That is, the pressure on the rudder put over 30° whilst the vessel is moving at a continuous speed of 6 knots, will be 33601b. This force of 33601b. is exerted on a lever, the length of which is the distance the centre of pressure on the rudder is from the stern post. We have shown that the centre pressure on planes moved obliquely in fluids is not at the geometrical centres, and ex periments have shown that the resultant of pressure on a rudder, when inclined to 30°, is at or near one-third the breadth from the anterior edge, or edge next the stern post. This has been well proved by "balanced" rudders pivoted at or near one-third their breadth from their front edge; no power is required to put the rudder, so pivoted, over beyond that necessary to "move" the water, to overcome the friction of pintles, rudder post, and the effort that would be required to move the rudder if the vessel were not in the water.
If the rudder were a rectangular parallelogram, the resultant of pressure on it would thus be 1.666ft. from its edge next the stern post, and the length of lever on which the pressure on the rudder acted, would therefore be 1.666ft.; and the product of 33601b. x 1.666ft. is 5597/, which is the moment in foot pounds that would have to be overcome by a force at the tiller head. The magnitude of this required force can be calculated by a very simple equation : thus, say the tiller is 10ft. long, then the force required at its head to balance the moment of the rudder, when put over to 30°, will be thus found : That is to say, a steady pressure of 5601b. would be required at the tiller head to keep the rudder over at 30° if the vessel were moving at a con tinuous speed of 6 knots.
All other things being equal, the diameters of the circles vessels will make in turning are in direct ratio to their dimensions. Thus, take two yachts, one of 25 tons and the other 200 tons : their length would be 50ft• and 100ft., and the yacht of 50ft. should in turning describe a circle of just half the diameter of the one 100ft. long. The latter will describe a circle in turning of about twice her own length, or 200ft. in diameter (assuming her to be under uniform steam power, with her helm over to 35°), at a speed of eight knots in about two minutes, as the direct speed would be retarded nearly two thirds. Under sail, however, and in getting from one tack to the other, a yacht does not describe a circle, but only one fourth, or the arc of a quadrant, if she lies four points from the wind; and presuming a yacht in tacking traversed the whole arc of a quadrant from the force of a direct speed of eight knots an hour, she would be a little under half a minute in getting from one tack to the other. But we know that a yacht of 100ft.
long cannot get from one tack to the other in half a minute, nor does she describe exactly the arc of a quadrant. However, for the purpose of illustration, we can assume that a yacht maintains uniform speed whilst turning. In Fig. 15 (p. 36) A N D form a quadrant, and let E be a yacht proceeding in a direction parallel to B A D, with the wind blowing as shown by the arrow, four compass points or 45° from her course. The yacht when in the position F would be head to wind, and when at H would be on the other (port) tack, on a course at right angles to that at E. But the speed of the yacht would diminish from the time her helm was put down, and when she arrived at F, head to wind, her propelling power would be gone entirely. She would proceed a little farther on the arc of the quadrant under the influence of her rudder, but would eventually pay off, under the action of her head sails, and come fairly on the other tack (proceeding in a direction parallel to A N), somewhat in the direction K.
As a matter of fact, the portion of the circle which a yacht describes in tacking is always of greater radius than her own length, or the circle in diameter is greater than twice that length. The helm cannot (and frequently it would be inadvisable so to do) be put over to 35° suddenly in large yachts, and generally the yacht will be head to wind before the helm is so over to 35°. Thus in a large yacht, say of 100 tons, the helm cannot very well be put down too quickly, or indeed even quickly enough. On the other hand, in small vessels, the helm may be put over too suddenly, and, by forcing the yacht to describe a segment of a circle of very small radius, her way becomes deadened ; so that, when she gets on the other tack, she rests motionless in irons, instead of springing off almost with way unchecked. This is a very important matter, es successful tacking does not depend upon merely getting from one tack to the other, but in getting off on the other tack without losing way. The helmsman of a large craft cannot easily make a blunder, as generally the speed with which he can walk a tiller down to leeward is that most suitable for preserving continuous way in tacking. This is not the case in small vessels, as the tiller can be put over with one hand suddenly, and the vessel brought head to wind (when, of course, all her propelling power is gone) in from five to ten seconds. Now it is obvious that some turning power is required after a vessel is head to wind, as at that point she is only half-way towards getting on the other tack, and no help can be obtained from the rudder if there be no way on the vessel. Thus, if a vessel's way be stopped before she be fairly on the other tack, the head sails will have to be kept a-weather; but in smooth water at least, and in a whole-sail breeze, a skilful helmsman will never require such aid, but will tack his vessel fairly by the influence of the rudder, the head sheets being lightened up of course ; but not before the luff of the sails begin to lift, and as a rule the jib sheet should be the first to be eased, as it will be the first to lift when the yacht is about half way towards the head to wind point. The sail will no longer be of use as a propelling force, and what little wind it holds will now only tend to check the vessel coining into the wind.