Chap. XT.
MECHANICS.
9J7
60° on the windward side of this right line, passing over the whole length of the piece sus-taining the sail, ami remaining always perpendicular to it, but uniformly increasing the anglewhich it forms with the turning axle b, in such a manner that at the extremity of the sailthe angle, which was 60° at the commencement, would become 78° if the axle b wereinclined 8° with the horizon, or 84° if the inclination were 15, and in proportion for inter-mediate inclinations. The position of the generating line serves to fix the direction of thecross pieces; together they form a frame which receives the sail-cloth: each sail mayalso be regarded as an irregular surface produced by the motion of a right line perpen-dicular to the piece sustaining the sail, and subject to touch in all its positions the rightline drawn through the corresponding extremities of the position which the generatingline should have at the two extremities of the sail, as previously stated.
The dimensions we have given are those mostly employed in Flanders, principallynear the town of Lille. Coulomb estimates the total effect of these mills workingthe whole year 8 hours per day, as raising a weight of 1000 lbs. 218 feet per minute.Supposing a man employing his strength in the most convenient manner can onlyelevate, when working 8 hours a day, a weight of CO lbs. 1 foot per second, whichgives 1,728,000lbs. elevated a foot for the daily effect; we shall have for 8 hours’ workper day a weight of 1000 lbs. elevated 3^ ff of a foot per minute : and as the mill working8 hours per day raises lOOOlbs. 218 feet in a minute, its effect is equivalent to the dailywork of 61 men.
Euler found the angle of 54° 44' the best for the sail to form with the axis inthe intermediate part, and one of 80° at its extremity, and that the velocity of theextremity of the sail should be to that of the wind = 2+ : 1. Mills with a horizontalaxis, the wheel of which we call a fly, carry four arms each 36 feet in length, perpen-dicular to the axle of motion, on which is spread a sail more or less inclined to theplane of motion of the wheel ; it is generally of a rectangular form, and instead ofbeing a single plane, it is constructed with an irregular surface perpendicular to thecorresponding arms. The arm itself is rectilinear, so that the surface of the sail applied tothe laths offers a concavity to the action of the wind ; the axle should always be parallel tothe direction of the wind, and as the wind blows in level countries at an angle of 18° withthe horizon, the axle is fixed at that angle.
The arms are thicker near the axle than at the extremities, and the laths which receivethe sails are fixed at right angles to these arms: as the axle must always be directedtowards the wind, a lever is made use of for that purpose which turns the frameworksupporting the mill round a fixed vertical axle; sometimes the mill carries a sail on theside opposed to the axle, which occasions the mill to set itself. The reason the windcauses the sails to turn, it must be remarked, is that the action is resolved into two others,one in the direction of the sail, and the other perpendicular to it; from the latter, thepressure is received by the sail, which is decomposed into two new actions, one of which,parallel to the axis, produces no effect, the other, situate on the plane of motion, turnsthe sail. If two opposite sails were inclined in the same direction with regard to the planeof motion, the pressure they would experience would turn the axle in two contrarydirections, in such a manner that the latter would not move; for this reason the inclinationsare made equal but contrary to the two opposite sails.
A Mill with a horizontal Axis —The sails being rectangular, the most advantageous form isthat called the Dutch , which offers to the wind a surface slightly concave, and whose elementsare disposed as follows:—the radius of the sail is divided into 6 + | parts ; the first isset out from the centre at a distance equal to § of the unity of the divisions, being designatedas No. 1., and that which answers to the extremity of the sail as No. 6. ; the breadth ofthe sails must not exceed ^ of the length, but generally it is £ or £. Experience hastaught that we ought rather to diminish the angle they make with the plane of motionthan increase it; according to Smeaton the sails which enlarge towards their extremitiesare more advantageous than those which are parallel throughout: the best form is thatof a trapezium ; at the extremity of the radius, a bar equal to a third of this radius isdivided at the point where it intersects, in the ratio of 3 to 2. "With sails so constructedwe have the best effect, and maintain the velocity of rotation in a constant ratio to that ofthe wind ; this velocity of rotation, measured at the extremity of the sail, should be, accord-ing to Smeaton =2*6 or 2*7 times that of the wind, which agrees with Coulomb’s experi-ments, from which he deduced the ratio 2*5 or 2*6. The sails being established accordingto the Dutch method, and their velocity being in the ratios of that assigned before 2'6, thew T ork transmitted increases as the surface of the sails, which is a little less rapidly than thecube of the velocity of the wind, and we shall have for the work transmitted in a secondaccording to Coulomb, P»2-60VP = 0-13 . a. V 3 kilogrammes; a formula in which P isthe effect in kilogrammes at the extremities of the sails, and in the direction of the motionof rotation of this extremity, V the velocity of the wind in metres, a the surface of a singlesail in square metres. Regard has not been paid in the experiments to the variation of thedensity of the air according to the temperature.