WIN
VJwd-MM, a kind of Mill which receives its Motion frcm the Impulfe of the Wind. SeeMin,.
The Windmill, tho' a Machine common enough, has yet fomewhat in it more ingenious than is ufually imagined.— Add, that it is ufually granted to have a degree of Per- fection which few of the popular Engines have attained
to, and which the Makers are but little aware of Tho*
the new Geometry, &c. has furnithed ample Matter for its Improvement.
Structure of the VJmn-MiU.
The internal Structure of the Windmill™ much the fame
with that of Water-Miils The difference between
'em lies chiefly in an external Apparatus for the Applica- tion of the Power.
This Apparatus confifts of an Axis LF (Tab. Pneuma- tics, Fig- 15.) thro' which pafs two Rods or Yards, A B and C D, interjecting each other at right Angles in E,whofe length is ufually about 32 Feet : On thefe Rodsare form'd a kind of Sails, Vanes, or Flights, in the Figure of Trape- ziums, with parallel Bales, the greater whereof II I is about fix Feet, and the lefs F G determined by Radii drawn from the Centre E, to C and H.
Thefe Sails are to be capable of being always turn'd to the Wind, that they may receive its Impreflion : In order to which, there are two different Contrivances, which confti- tute the two different kinds of Wind-Mills in ufe.
In the one, the whole Machine is fuitain'd upon a mo- vable Arbor or Axis perpendicular to the Horizon, on a Stand or Foot ; and turn'd occafionally this way or that, by means of a Lever.
In the other, only the Cover, or Roof of the Machine,
with the Axis and Sails turn round In order to which,
The Cover is built Turret-wife, and the Turret encom- pafs'd with a Wooden-Ring, wherein is a Groove, at the bottom whereof are placed at certain alliances, a number of Bra fa Truckles, and within the Groove is another Ring upon which the whole Turret {lands. To the moveable Ring are connected Beams a b and/c ; and to the Beam a b, in b is faften'd a Rope, which at the other extreme thereof is fitted to a Windlafsor Axis in Feritrochio : This Rope being drawn through the Iron Hook G, and the Wind- lafe turn'd, the Sails will be moved round, and put in the direction requir'd.
'Theory of the Motion of a WiND-yW///, ivith the Pofition of the Saih or Vanes thereof.
The Angle the Sails are to make with their common Axis, fo as the Wih& may have the greateit Eff-ct, is a Matter of nice Enquiry, and has employ *d the Thoughts of the Mathematicians.
To conceive why a Wind-Mill moves at all, the Theory
of compound Motions muit be fuppofed A Body moving
perpendicularly againit any Surface, (hikes it with alt its
force. If it move parallel to the Surface, it does not
llrike it at all : And if it move obliquely, its Motion being compounded of the perpendicular and parallel Motion, only acts on the Surface confidcr'd as it is perpendicular, and only drives it in the direction of the Perpendicular. So that every oblique Direction of a Motion is the Diagonal of a Parallelogram, whofe perpendicular and parallel Directions are the two Sides. Add, That if a Surface, which being {truck obliquely has only received the perpendicular Di- rection, be faflen'd to fome other Body, fo as that it cannot purfue'its perpendicular Direction, but mult change it for fome other; in that Cafe, the Perpendicular itfelf becomes the Diagonal of a new Parallelogram, one of whofe Sides is the Direction the Surface may follow, and the other, that it cannot, ' ^ . .^ „
Thus, a Rudder faften'd obliquely to the Keel of a Veflel, being llruck by the Current of Water parallel _ to the Keel, and of conference obliquely with regard to itfelf; it will appear, by drawing the Line of perpendicular Impulfe, that it tends to tear the Rudder from the Keel, and to carry it away : And that this Direction perpendicular to the
Rudder, is oblique to the Keel. The Rudder, then,
would be carried off in an oblique Direction : But, as, in effect, it is fofecur'd, that it cannot be torn or carried off; we are only to confider, in this compound Motion, that of the two Directions wherewith it can move without being torn from the Keel ; and leave the other which would tear it off, as ufelefs.
Now, the Direaionin which it can move without parting from the Keel, is that which carries it circularly about its Ex- tremity as a Centre. So that the effect of the oblique Im- pulfe of the Water on the Rudder, is reduced, fir ft to a per- pendicular Impreflion, which is again reduced to the mere turning the Rudder round; or, if the Rudder be im- moveable, to the turning of the Vcffel.
Now, in an oblique and compound Motion, where only one of theDireaions is of fervice; the greater Ratio the
( m )
WIN
other has thereto, the lefs effect will the Motion have ; and
vice verfa. In examining the compound Motions of the
Rudder, we find that the more oblique it is to the Keel, the Ratio of the Direftion that ferves to turn it to the other, is the greater. But, on the other hand, the more oblique it is to the Keel, and of confequence to the Courfe of the Water which is fuppofed parallel thereto, the more weakly it ftrikes. The obliquity of the Rudder, therefore, has at the fame time both an Advantage and a Difad vantage ; but as thofe are not equal, and as each of 'em are ftiU varying with every different Pofition of the Rudder, they become complicated varioufly, fo that fometimes the one prevails, and lometimes the other.
It has been a Point of Enquiry to find the Pofition of the Rudder wherein the Advantage thould be the greateft. M. Rcnait, in his famous Theory of the Working of Ships, has found that the belt fituation of the Rudder is when it makes an Angle of 55 Degees with the Keel. See Sail- ing, Steering, £«7c.
it, now,a Wind-Mill expofed directly to the Wind, /hould have its tour Sails perpendicular to the common Axis wherein they are fitted, they would receive the Wind per- pendicularly ; and it is vifible that Impulfe would only tend to over-turn 'em —There is a neceflity, therefore,
to have 'em oblique to the common Axis, that they may receive the Wind obliquely.
For the greater eafe 5 let us only confider one Vertical
Sail— The oblique Impulfe of the Wind on this Sail
is reducible to a perpendicular Impulfe : And that Di- reflion, as the Sail cannot abfolutely keep to it, is com- pounded of two ; one whereof tends to make it turn on its Axis, and the other to fall backwards. But it is only thefirft of thefe Directions can be obey'd. Of confequence the whole Impulfe of the Wind on the Sail has no oiher effect but to make it turn from right to left, or from left to right, as its acute Angle turns this way or that. And the Structure of the Machine is fo happy, that the three other Sails are determined, from the fame reafons, to move the fame way.
The Obliquity of the Sails with regard to their Axis, has precifely the fame Advantage, and Difadvamage, with the
Obliquity of the Rudder to the Keel. And M. 'Parent,
feeking, by the new Analyfis, the moft advantageous Situa- tion of the Sails on the Axis, finds it pr<:cifely the fame Angle of 55 Degrees. Yet, in practice this Rule is very little obferved ; as, indeed, being little known. They are ufually about 60 Degrees, which is very much out of the way.
Elliptical Vltxv-Mlt.
M. 'Parent confiders further, what Figure the Sails of a Wind-Mill mall have, to receive the greateft Impulfe from the Wind ; and he determines it to be a S^or of an Ellipfis whofe Centre is that of the Axis or Arbor of the Mill 5 and the little Semi-Axis, the height of thirty-two Feet. As for the greater, it follows neceffarily from the Rule that directs the Sail to be inclined to the Axis 55 Degrees.
On this foot, he affumes four fuch Sails, each whereof is one-fourth of an Ellipfis ; which, he {hew?, will receive all
the Wind, and lofe none, as the common ones do. Thefe
four Surfaces multiply'd by the Lever with which the Wind acts on one of 'em, exprefs the whole force the Wind has to move the Machine, or the whole force the Machine has when in Motion.
The fame manner of Reafoning apply'd to a common Wind-Mitt whofe Sails are Rectangular, and their Height about five times their Breadth ; thews that the Elliptic Wind-Mill has above feven times the force of the common one. A prodigious Advantage ! And worthy, fure, to have the common Practice fet afide for, could fo common a Practice beeafily changed.
A Wind-Mill with fix Elliptic Sails, he thews, would ftill have more force than one with four-- -It would only have the fame Surface with the four; fince the four contain the whole Spa:e of the Eliipfis as well as the fix. But the force of the fix would be greater than that of the four in the Ratio of 245 to 23T. If it were defir'd to have only two Sails, each being a Semi-Ellipfis, the Surface would be {till the fame, but the force would be diminifhed by near one- third of that with fix Sails ; by reafon the greatnefsof the Sectors would much fhorten the Lever with which the Wind ads.
The bejl Form and Proportion of RetfangzdaryJiN-D-MiUs.
But, as Elliptical Sails would be fomething Co new, that there is little room to expect they will come into common Ufe ; the fame Author has confider'd which Form, among the reaangular ones, will be the moft advantageous, i. e. which, the" Product of whofe Surface by the Lever of the Wind will be the greateft. And by the Method de Max-
inns
