Читать книгу Experimental Mechanics - Robert S. Ball - Страница 15

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30. The action of the wind upon the sails of a vessel affords a very instructive and useful example of the decomposition of forces. By the parallelogram of forces we are able to explain how it is that a vessel is able even to sail against the wind. A force is that which tends to produce motion, and motion generally takes place in the line of the force. In the case of the action of wind on a vessel through the medium of the sails, we have motion produced which is not necessarily in the direction of the wind, and which may be to a certain extent opposed to it. This apparent paradox requires some elucidation.

Fig. 13.

31. Let us first suppose the wind to be blowing in a direction shown by the arrows of Fig. 13, perpendicular to the line ab in which the ship’s course lies.

In what direction must the sail be set? It is clear that the sail must not be placed along the line ab, for then the only effect of the wind would be to blow the vessel sideways; nor could the sail be placed with its edge to the wind, that is, along the line o w, for then the wind would merely glide along the sail without producing a propelling force. Let, then, the sail be placed between the two positions, as in the direction p q. The line o w represents the magnitude of the force of the wind pressing on the sail.

We shall suppose for simplicity that the sail extends on both sides of o. Through o draw o r perpendicular to p q, and from w let fall the perpendicular w x on p q, and w r on o r. By the principle of the parallelogram of forces, the force o w may be decomposed into the two forces o x and o r, since these are the sides of the parallelogram of which o w, the force of the wind, is the diagonal. We may then leave o w out of consideration, and imagine the force of the wind to be replaced by the pair of forces o x and o r; but the force o x cannot produce an effect, it merely represents a force which glides along the surface of the sail, not one which pushes against it; so far as this component goes, the sail has its edge towards it, and therefore the force produces no effect. On the other hand, the sail is perpendicular to the force o r, and this is therefore the efficient component.

The force of the wind is thus measured by o r, both in magnitude and direction: this force represents the actual pressure on the mast produced by the sail, and from the mast communicated to the ship. Still o r is not in the direction in which the ship is sailing: we must again decompose the force in order to find its useful effect. This is done by drawing through r the lines r l and r m parallel to o a and o w, thus forming the parallelogram o m r l. Hence, by the parallelogram of forces, the force o r is equivalent to the two forces o l and o m.

The effect of o l upon the vessel is to propel it in a direction perpendicular to that in which it is sailing. We must, therefore, endeavour to counteract this force as far as possible. This is accomplished by the keel, and the form of the ship is so designed as to present the greatest possible resistance to being pushed sideways through the water: the deeper the keel the more completely is the effect of o l annulled. Still o l would in all cases produce some leeway were it not for the rudder, which, by turning the head of the vessel a little towards the wind, makes her sail in a direction sufficiently to windward to counteract the small effect of o l in driving her to leeward.

Thus o l is disposed of, and the only force remaining is o m, which acts directly to push the vessel in the required direction. Here, then, we see how the wind, aided by the resistance of the water, is able to make the vessel move in a direction perpendicular to that in which the wind blows. We have seen that the sail must be set somewhere between the direction of the wind and that of the ship’s motion. It can be proved that when the direction of the sail supposed to be flat and vertical, is such as to bisect the angle w o b, the magnitude of the force o m is greater than when the sail has any other position.

32. The same principles show how a vessel is able to sail against the wind: she cannot, of course, sail straight against it, but she can sail within half a right angle of it, or perhaps even less. This can be seen from Fig. 14.

The small arrows represent the wind, as before. Let o w be the line parallel to them, which measures the force of the wind, and let the sail be placed along the line p q; o w is decomposed into o x and o y, o x merely glides along the sail, and o y is the effective force. This is decomposed into o l and o m; o l is counteracted, as already explained, and o m is the force that propels the vessel onwards. Hence we see that there is a force acting to push the vessel onwards, even though the movement be partly against the wind.

Fig. 14.

It will be noticed in this case that the force o l acting to leewards exceeds o m pushing onwards. Hence it is that vessels with a very deep keel, and therefore opposing very great resistance to moving leewards, can sail more closely to the wind than others not so constructed; a vessel should be formed so that she shall move as freely as possible in the direction of her length, for which reason she is sharpened at the bow, and otherwise shaped for gliding through the water easily; this is in order that o m may have to overcome as little resistance as possible. If the sail were flat and vertical it should bisect the angle a ow for the wind to act in the most efficient manner. Since, then, a vessel can sail towards the wind, it follows that, by taking a zigzag course, she can proceed from one port to another, even though the wind be blowing from the place to which she would go towards the place from which she comes. This well known manœuvre is called “tacking.” You will understand that in a sailing-vessel the rudder has a more important part to play than in a steamer: in the latter it is only useful for changing the direction of the vessel’s motion, while in the former it is not only necessary for changing the direction, but must also be used to keep the vessel to her course by counteracting the effect of leeway.