WINDMILL

In Mechanics, a mill which receives its motion from the impulse of the wind. The general appearance of the windmill is familiar to every one. The building containing the machinery is usually circular. To the extremity of the principal axis, 6r wind-shaft, are attached rectangular frames (generally five), on which cloth is usually stretched to form the sails. The surfaces of the sails are not perpendicular to the axis, but inclined to it at a certain angle, about 72° at the extremities nearest the axle, and 83° at the farther extremities; so that their form is in some degree twisted, and different from a plane surface. Suppose the axis to be placed in the direction of the wind; the wind will then strike the sails obliquely, and the force may therefore be resolved into two parts, one of which, acting in the direction perpendicular to the axis, gives a motion of rotation to the sails, and consequently to the wind-shaft, from which it is communicated to the machinery. The wind-shaft is inclined to the horizon in an angle of from 8° to 15°, principally with a view to allow room for the action of the wind at the lower part, where it would be weakened if the sails came too nearly in contact with the building. As the direction of the wind is constantly changing, some apparatus is required for bringing the axle and sails into their proper position. This is sometimes effected by supporting the machinery on a strong vertical axis, the pivot of which moves in a socket firmly fixed in the ground; so that the whole structure may be turned round by a lever. But it is now usual to construct the building with a moveable roof, which revolves upon friction rollers; and the shaft being fixed in the roof is brought round along with it. The roof is brought into the required position by means of a small vane wheel furnished with wind sails, which turns round when the wind strikes on either side of it, and drives a pinion which works into the; teeth of a large crown wheel connected with and surrounding the moveable roof. Of the Form and Position of the Sails. — From the investigations of Parent and Belidor, it appears that the maximum effect of the wind on the sails is produced when their inclination to the axis of rotation is about 54| degrees; or when the angle of weather, that is to say, the angle formed by the plane of the sail and the plane of its revolution, is 35i degrees. But this result, being obtained from considering the effect of the wind on the sails when at rest, does not agree with that which is found by experiment. In fact, as the velocity of the sail tends to withdraw it from the action of the wind, it is nece ary to counteract the diminution of force by diminishing the angle of weather, or to bring the sail into such a position that the wind strikes its surface more directly; and since the velocity of the different parts, of the sail is in proportion to their distance from the axis, it follows that in order to produce the greatest effect every elementary portion of it ought to have a different angle of weather, diminishing from the centre to the extremity of 1320 WINDMILL. the sail. Euler has given a theorem which determines the law of variation. Let a be the velocity of the wind, and b the velocity of any given part of the sail; then the action of the wind upon that part of the sail will be a maximum when the tangent of its inclination to the axis, or the cotangent of the angle of weather, = N/ ^ + { 9~ ) ■*■ 9~ • Suppose that at a given part of the sail the velocity of the sail is equal to the velocity of the wind, we have then a = bj and the formula becomes -^^2+1 + I = 3-561 = tangent of 74° 19', which gives 15° 41' for the angle of weather. This subject was investigated experimentally by Smoaton (Philosophical Trans, vol. li.), who found that the common practice of inclining the sails from 72° to 75° to the axis is much more efficacious than the angle a igned by Parent, the effect being as 45 to 31. When the sails were weathered in the Dutch manner, or with their surface concave to the wind, and the angle of inclination greater towards the extremities, the effect was greater than when weathered either in the common way or according to Euler's theorem. But the effect was greatest of all when they were enlarged at their extremities, and had the form c df e, represented in the annexed figure; so that c d was one third of the radius A B, and c B to B d as 5 to 3. If the sails be farther enlarged, the effect is not increased in proportion to the surface; and besides, when the quantity of cloth is great the machine is much exposed to injury from sudden squalls. In Smeaton's experiments the angle of weather varied with the distance from the axis; and it appeared from several trials that the most efficacious angles at the different parts of the sail were those in the following table: — Parts of A B, which is divided into Six equal Parts. Angle with the Axis. Angle of Weather. 1 2 3 4 5 6 72° 71 72 1? 180 19 18 16 If the radius A B of the sail be 30 feet, then the sail will commence at l-6th of A B,or 5 feet from the axis, where the angle of inclination will be 72°. At 10 feet from the axis, the angle will be 71°; and so on, as in the table. Of the Effect of Windmill Sails — The following maxims relative to the effect of the sails were deduced by Smeaton from his experiments: — 1. The velocity of windmill sails, whether loaded or unloaded, so as to produce a maximum effect, is nearly as the velocity of the wind, their shape and position being the same. 2. "Kie load at the maximum is nearly, but somewhat le , as the square of the velocity of the wind, the shape and position of the sails being the same. 3. The effects of the same sails at a maximum are nearly, but somewhat le , as the cubes of the velocity of the wind. 4. The load of the same sails at the maximum is nearly as the squares, and their effects as the cubes of their number of turns in a given time. 5. When the sails are loaded so as to produce a maximum effect at a given velocity, and the velocity of the wind increases, the load continuing the same, then the increase of effect, when the increase of the velocity of the wind is small, will be nearly as the square of those velocities; when the velocity of the wind is doubled, the effect is nearly as 10 to 27^. When the velocities compared are more than double of that where the given load produces a maximum, the effects compared increase nearly in the simple ratio of the velocity of the wind. 6. In sails where the positions and figures are similar and the velocity of the wind the same, the number of turns in a given time will be reciprocally as the radius or length of the sail. 7. The load at a maximum that sails of a similar figure and position will overcome at a given distance from the centre of motion will be as the cube of the radius. 8. The effects of sails of similar figure and position are as the square of the radius. 9. The velocity of the extremities of Dutch sails, as well as of the enlarged sails in all their usual positions, when unloaded, or even loaded to a maximum, is considerably quicker than the velocity of the wind. Horizontal Windmills. — Windmills are sometimes constructed in such a manner that the planes of the sails intersect each other in the wind-shaft, in which case they are called horizontal windmills; because the wind-shaft being usually vertical, the sails have a horizontal motion. Tlie wind-shaft, however, might be placed with equal advan4Q [s. 1342]