CHAPTER II.

CENTRE OF LATERAL RESISTANCE.

LATERAL resistance is the resistance the water offers to a vessel being moved sideways or laterally; this sideway or broadside motion when a vessel is underway is at right angles, or nearly at right angles, to her forward or direct motion, and is usually termed leeway; thus the resistance to leeway is properly described as "lateral resistance." The centre of lateral resistance is usually understood to mean the centre of the vertical longitudinal section of the immersed portion of the vessel, including the rudder. In other words, this immersed longitudinal section is assumed to be a plane; and if this plane be moved through the water in a direction at right angles to its own (the plane's) surface, then the resultant of the resistance it will meet with will act through its centre. For instance, let Fig. 8 be the immersed longitudinal section of a vessel with its centre at . If a towing line were attached to the point æ, the vessel or plane would be towed laterally or "broadside on" through the water, without exhibiting any tendency to turn one way or the other; in fact, the plane representing the longitudinal section of the vessel would keep

FIG. 8.

normal, or at right angles to the towing line.

But if the towing line stern would come round

be attached farther aft, then on being towed the towards the line; or if attached farther forward, the bow would turn round towards the line.*

* A simple experiment conducted as indicated with any model and piece of string will determine the centre of lateral resistance, disregarding its actual position, due to forward motion, and which motion would not be given to the model during the broadside towing. The centre can also be found by taking a piece of board shaped to represent the longitudinal

In calculating the centre of lateral resistance of a ship or yacht, it is always assumed that a plane has to be dealt with, and the immersed longitudinal section is taken as that plane. As a matter of fact, the centre of this plane would not be the centre through which the resultant pressure on the side of the ship would act. Owing to the varying form of a ship or yacht, it is almost impossible to determine by calculation the point through which the resultant of the horizontal pressure of the water actually acts; and, moreover, if the exact point could be readily determined, the knowledge of it would be of small practical value, for the reason that, owing to the forward motion of the vessel in a line with her keel, there is an excess of pressure on the bow and a constantly decreasing pressure towards the stern; the bow is continually entering "solid" water, whilst towards the stern the water becomes more and more disturbed; and beyond this there will be an accumulation of water rising on the lee bow which has the effect of altering the form of the immersed portion of the vessel, and this of itself carries the centre farther forward. And further, even supposing the centre of pressure could be accurately calculated for the upright position, it would be useless for any other position of the vessel, as a different portion of her hull would be immersed, or its position relative to the horizon altered, each time the vessel rolled or was heeled.

The use of knowing approximately the position of the centre of lateral resistance is that the "handiness" of a vessel can be regulated thereby; and for this use the centre of the plane described by the immersed longitudinal section of a vessel is, fortunately, a sufficiently determinate point, as will hereafter be shown.

It need scarcely be pointed out that a flat surface is more effective in resisting lee way than a convex one; hence a vessel with a large area of dead wood aft, a very sharp flat entrance, and a deep keel will make less lee way than one that has a less flat surface immersed, all other things being equal. It must always be remembered, however, that the upper part of the dead wood aft, owing to the disturbed water it passes through, meets with less pressure than does the dead wood forward, as the bow is always entering new or undisturbed water. Hence "drag," or a much greater draught aft than forward, has been found of great use in keeping the centre of lateral resistance in a required distance aft, as the lower parts of what may be termed a raking keel are continually being moved into solid or undisturbed water. This matter can be illustrated in this way :immersed section of the vessel, and suspending it with a plumb line attached to the point of suspension. Mark where the plumb line cuts the board, then suspend the board from another point, and mark where the plumb line intersects the other plumb line mark; the intersection will be the centre. The centre of buoyancy can be determined by a similar experiment; the model for such purpose must be made of clean stuff, and cut down exactly to the water's edge.

In the diagram (Fig. 9) let A be an immersed plane moving in the direction of the arrow s; and let it be assumed that the plane has also a sideway or lateral motion, as indicated by t. Next, k and a are points or spots on the plane, and æ and a1 are particles of water. As the plane moves forward and glides past x and a1, the spots k and a will push them severally on one side, it being always remembered that the plane has sideway motion, and it is resistance to this sideway motion which we are considering. When any other indefinitely near spots on the plane, as bh, arrive abreast of a and a1, they find the latter receding, in consequence of the push they received from k and a; the result is that b and h meet with less resistance to sideway or lateral motion than did k and a; and so on for g and c, &c. It is thus evident that what is required for an effective surface of lateral resistance is not a number of spots in the horizontal direction, a b c and kh g, but a number in the vertical direction, k a. It

would be found inconvenient to so increase the depth at the fore end to obtain an effective surface, but fortunately it is found to be an advantage to have an increase in depth at the aft end. Assume a triangular piece v to be cut off the fore-end of the plane A, and to be placed underneath aft as shown by v in the diagram B; the area of the surface remains exactly the same, but a double number of spots as n m o and p are obtained that will enter solid water to meet particles of water as a x, &c., as the plane advances. It is quite patent that, although of equal surface, the plane B would more greatly resist lateral motion, if attended by a simultaneous forward motion, than would the plane B; and if the ends of the plane had been reversed so that the deep end came forward, similar results would accrue, but as there would then be such an accumulation of pressure about the anterior edge, it would be almost impossible to give a vessel with such

a form a satisfactory sail spread. With the sloping edge turned forward, a quantity of what may be termed perfect pressure, is graduated aft; this feature, coupled with the fact that the centre of gravity of the figure is relatively aft, instead of relatively forward, as it would be with the ends reversed, admits of a convenient and satisfactory arrangement of sail.

There is yet another strong argument in favour of a raking keel, which involves a question of speed. If the triangle v were taken away from A, the surface would be reduced one-fourth; and, consequently, the resistance to forward motion, dependent on surface friction, would be proportionately reduced. It might not be prudent to make this

reduction of surface if the effectiveness of the lateral resistance were going to be thereby reduced; but the fact is that the effectiveness of the lateral resistance would be almost unimpaired; a comparatively useless piece of wood would be removed, and a positive gain would ensue in the matter of frictional resistance.

The necessity of keeping the centre of lateral resistance, relatively to the length of the vessel, far aft, and the fashion of much raking the sternpost, led builders to by degrees advantageously increase the rake of keel, and there have been some extraordinary examples of disproportionate. draught of water fore and aft ;* but at the present time, with perhaps a more intimate knowledge of the theory of lateral resistance, most designers prefer the "rockered" keel to the keel that simply rakes upward in a straight line from the sternpost, as with the "rocker" other important advantages can be secured. By having the greatest draught, or what might be termed the termination of the effective surface for lateral resistance, amidships, the after part or heel of the keel can be very much rounded up somewhat in the fashion of the fore foot; and, as this is done the necessity for a great rake to the sternpost is removed, and the sternpost is fixed in a position nearly in accordance with the vertical. The effect is, that for the same tonnage-it is assumed that the sternpost on deck is kept at the same distance from the stem piece-a longer body can be obtained, and presumably a more capable, a larger, and faster vessel.+ Beyond this, a deeper middle body is practicable, which is found to be of the utmost advantage, as it admits of the weights being stowed lower without being much distributed in a fore-and-aft direction.

* The Jullanar has a draught of 14ft. aft, and only 1ft. 2in. forward. (See her lines given further on; see also the lines of Fiona in "Yacht Designing.")

As the Yacht Racing Association has recently altered length on deck for tonnage to length on load water-line, the reason for keeping the sternpost vertical to obtain the greatest length of body for any given tonnage no longer exists.

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The effectiveness of triangular centre-boards is well known, and it is astonishing how small a piece of board will check lee way, providing the board is deep and not long. Nevertheless, one supposed disadvantageespecially in small boats-of a keel very much rockered, or of a triangular centre-plate instead of a keel, is that in very disturbed water a vessel's head, in beating to windward, gets "knocked off the wind; " but it is overlooked that if the bow is readily knocked off the wind the same facility exists for "coming-to" the wind during favourable puffs.

A vessel with a much rockered keel will probably steer wildly off the wind, and will require watching, and on any point of sailing she is likely to run off her helm. To meet these drawbacks, some eastern boats (such as those of Bombay) have cambered keels, i.e., the reverse of rockered, as the back of the arch is turned upwards; and a few boats in America and in this country have been fitted with double boards. However, we think that the balance of advantages for close-hauled sailing are overwhelmingly in favour of the rockered keel for yachts or the centreplate for small boats. If, as before said, the vessel is quick in falling off, she will be equally sensitive in coming to; and a careful helmsman will take his "rocker" farther up to windward than any similarly careful helmsman could a "straight keel," all other things being equal; and further, the helmsman will find the vessel with a rockered keel, when sailing by the wind, a much pleasanter one to steer; she will readily answer her weather helm for a foul puff, or spring to quickly under a little lee helm for a free one. It is undeniable, however, that in sailing very much off the wind the craft with "drag," or a large area of dead wood aft, will require much less helm than one whose heel is rounded up-that is, she will have less tendency to yaw.