# 1911 Encyclopædia Britannica/Windmill

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​WINDMILL, a term used, in the widest sense, for a machine by which the energy of the wind is applied to useful purposes. Fig. 1.—Windmill near Delft. Windmills were certainly used as early as the 12th century and are still largely employed in Holland in draining the polders and grinding trass. They are somewhat extensively used in America for pumping and driving agricultural machinery. In spite of the competition of more powerful and tractable motors, they are serviceable, especially in new countries, where fuel is scarce and where work can be done intermittently. An inquiry was made in India in 1879 as to the possibility of using windmills for irrigation (Professional Papers on Indian Engineering, July 1879), with the result that it was concluded their usefulness would be very limited.
A windmill is not in any case a very powerful or efficient motor, and its work is variable and intermittent. In favourable positions, it will run on an average for eight hours out of the twenty-four. For pumping on a small scale, the intermittent action is least an objection, because there is generally a tank or storage reservoir regulating the delivery of the water. For driving dynamos windmills are least suitable, on account of the variation of speed, though some attempts to generate electricity by wind power have been made, special arrangements being adopted for automatically regulating the speed.
European Windmills.—In all the older windmills a shaft, called the wind shaft, carried four to six arms or whips on which long rectangular narrow sails were spread. The wind shaft was placed at an inclination of 10° or 15° with the horizontal, to enable the sails to clear the lower part of the mill. The whip carrying the sail was often 30 to 40 ft. in length, so that the tips of the sails described a circle 60 to 80 ft. in diameter. The sails were rectangular, 5 to 6 ft. wide, and occupying five-sixths of the length of the whip. A triangular leading sail was sometimes added. Sometimes the sails consisted of a sail-cloth spread on a framework; at other times narrow boards were used. The oldest mill was no doubt the post mill, the whole structure being carried on a post; to bring the sails to face the wind, the structure was turned round by a long lever. The post mill was succeeded by the lower, smock or frock mill, in which the mill itself consisted of a stationary tower, and the wind shaft and sails were carried in a revolving cap rotating on the top of the tower. Andrew Meikle introduced in 1750 an auxiliary rotating fan at right angles to the principal sails, which came into action whenever the wind was oblique to the axis of the sails, automatically veering the sails or placing them normal to the wind. For safety, the sails must be reefed in high winds. In 1807, Sir W. Cubitt introduced automatic reefing arrangements. The sails were made of thin boards held up to the wind by weights. If the force of the wind exceeded a certain value the boards were pressed back and exposed little surface.
American Windmills.—These generally have the sails, 18 or more in number, arranged in an annulus or disk. The sails consist of narrow boards or slats arranged radially, each board having a constant or variable inclination to the wind's direction. An American mill presents a larger surface for a given length of sail than the older type, and consequently the construction is lighter. To turn the mill face to the wind a rudder is sometimes used projecting backward in a plane at right angles to the plane of rotation of the sails. Various arrangements are adopted for reefing the sails automatically. (a) In some an action equivalent to reefing is obtained by turning the sail disk oblique to the wind. The pressure on a side vane in the plane of rotation, controlled by a weight, turns the sail disk edgeways to the wind if the pressure exceeds a safe amount. (b) In centrifugal governor mills the slats forming the sails are connected in sets of six or eight, each set being fixed to a bar at the middle of its length. By rotating this bar the slats are brought end on to the wind, the action being analogous to shutting an umbrella. The slats are held up to the wind by a weight. A centrifugal governor lifts the weight if the speed becomes excessive and the sails are partially or completely furled. Many of the veering and reefing arrangements are very ingenious and too complicated to be described without detailed drawings. A description of some of these arrangements will be found in a paper by J. A. Griffiths (Proc. Inst. Civ. Eng., 119, p. 321) and in a “Report on Trials of Wind Pumping Engines at Park Royal in 1903” (Journ. Roy. Agric, Soc., 64, p. 174).
Warner's Annular Sail Windmill.—Messrs Warner of London make a windmill somewhat similar to American mills. The shutters or vanes consist of a frame covered with canvas, and these are pivoted between two angle-iron rings so as to form an annular sail. The vanes are connected with spiral springs, which keep them up to the best angle of weather for light winds. If the strength of the wind increases, the vanes give to the wind, forcing back the springs, and thus the area on which the wind acts diminishes. In addition, there are a striking lever and tackle for setting the vanes edgeways to the wind when the mill is stopped or a storm is expected. The ​wheel is kept face to the wind by a rudder in small mills; in large mills a subsidiary fan and gear are used. Fig. 2 shows a large mill of this kind, erected in a similar manner to a tower mill. The tower is a framework of iron, and carries a revolving cap, on which the wind shaft is fixed. Behind is the subsidiary fan with its gearing Fig. 2.—Warner's Annular Sail Windmill. acting on a toothed wheel fixed to the cap.
It is important that a wind-mill should control itself so that it works efficiently in moderately strong winds and at the same time runs in very light winds, which are much more prevalent. It should also, by reefing or otherwise, secure safety in storms.
Table I. gives the mean velocity of the wind in miles per hour for an inland station, Kew, and a very exposed station, Scilly, for each month during the period 1890-1899.
The pressure of the wind on a plane normal to its direction, composed partly of an excess front pressure and negative back pressure, is given by the relation
p = 0.003 v$^2$,
where p is in pounds per square foot and v the velocity of the wind in miles per hour. It varies a little with the form and size of the surface, but for the present purpose this variation may be disregarded. (See experiments by Dr Stanton at the National Physical Laboratory, Proc. Inst. Civ. Eng. 156, p. 78.). For velocities of 5, 10 and 20 m. per hour the pressures on a plane normal to the wind would be about 0.075, 0.3 and 1.2 ℔ per sq. ft. respectively, and these may be taken to be ordinary working velocities for windmills. In storms the pressures are much greater, and must be reckoned with in considering the stability of the mill. A favourable wind velocity for windmills is 15 m. per hour.
Table I. :
| Kew Scilly | Jan. | Feb. | March. | April. | May. | June. |
| Kew Scilly | 8.0 20.6 | 8.5 19.5 | 8.5 18.4 | 7.5 16.1 | 7.5 14.1 | 7.0 12.9 |
| Kew Scilly | July. | Aug. | Sept. | Oct. | Nov. | Dec. |
| Kew Scilly | 7.0 12.4 | 7.0 13.9 | 6.0 14.6 | 6.5 17.2 | 7.0 19.3 | 8.0 22.0 |
Pressure on Surfaces oblique to the Wind.—Let fig. 3 represent a plane at rest on which a wind current impinges in the direction YY, making an angle θ with the normal Oa to the plane. Then the pressure n normal to the plane is given very approximately by Duchemin's rule
n = p2 cos θ/1 + cos$^2$ θ ℔ per sq. ft.
where p is the pressure in pounds per square foot on a plane struck normally by the same wind.
In fig. 3 let AB be part of a windmill sail or vane at rest, XX being the plane of rotation and YY the direction of the wind. The Fig. 3. angle θ is termed the weather of the sail. This is generally a constant angle for the sail, but in some cases varies from a small angle at the outer end to a larger angle near the axis of rotation. In mills of the European type, θ − 12° to 18°, and the speed of the tips of the sails is 21/2 to 3 times the velocity of the wind. In mills of the American type, θ = 28° to 40°, and the speed of the tips of the vanes is 3/4 to 1 time that of the wind. Then if Oa = n be the normal pressure on the sail or vane per square foot, ba = t is the effective component of pressure in the direction of rotation and
t = n sin θ = p2 sin θ cos θ/1 + cos$^2$ θ
When the sail is rotating in a plane at right angles to the wind direction the conditions are more complicated. In fig. 4 let XX be the plane of rotation of the vane and YY the direction of the wind. Let Oa be the normal to the vane, θ being the weather of the vane. Let Ov = v be the velocity of the wind, Ou = u the velocity of the vane. Completing the parallelogram, Ov$_r$=v$_r$ is the velocity and direction of the wind relatively to the vane.
v$_r$ = √ (v$^2$+u$^2$) = v sec φ,
tan φ = u/v,
and the angle between the relative direction of wind and normal to the vane is θ+φ. It is clear that θ+φ cannot be greater than 90°, or the vane would press on the wind instead of the wind on the vane. Substituting these values in the equations already given, the normal pressure on the oblique moving vane is
n = .003 v$^2$ sec$^2$ φ2 cos(θ+φ)/1+cos$^2$(θ+φ)
The component of this pressure in the direction of motion of the vane is
t = .003 v$^2$ sec$^2$ φ2 sin(θ+φ) cos(θ+φ)/1+cos$^2$(θ+φ)
and the work done in driving the vane is
tu = tv tan φ
= .003 v$^3$ sec$^2$ φ tan φ2 sin(θ+φ) cos(θ+φ)/1+cos$^2$(θ+φ)
foot ℔ per sq. ft. of vane per sec., where v is taken in miles per hour. Fig. 4. For such angles and velocities as are usual in windmills this would give for a square foot of vane, near the tip about 0.003 v$^2$ ft. ℔ per sec. But parts of the vane or sail nearer the axis of rotation are less effective, and there are mechanical friction and other causes of inefficiency. An old rule based on experiments by Coulomb on mills of the European type gave for the average effective work in foot ℔ per sec. per sq. ft. of sail
W = 0.0011 v$^3$
Table II.—In 150 Working Hours. :
| | I. | II. | III. | IV. | V. | VI. |
| Revolutions of wheel | 208,000 | 308,000 | 264,000 | 322,000 | 222,000 | 202,000 |
| Double strokes of pump | 40,000 | 122,000 | 264,000 | 160,000 | 78,000 | 202,000 |
| Gallons lifted | 78,000 | 40,000 | 46,000 | 40,000 | 36,000 | 48,000 |
| Average effective horse-power | 0.53 | 0.27 | 0.31 | 0.27 | 0.24 | 0.32 |
I. Goold Shapley and Muir, Ontario; wheel 16 ft. diameter, 18 vanes, 131 sq. ft. area (first prize). II. Thomas & Son (second prize). III. J. W. Titt. IV. R. Warner. V. J. W. Titt. VI. H. Sykes. :
​Some data given by Wolff on mills of the American type gave for the same quantity
W = 0.00045v$^3$.
From some of the data of experiments by Griffiths on mills of the American type used in pumping, the effective work in pumping when the mill was working in the best conditions amounted to from 0.0005v$^3$ to 0.0003v$^3$ ft. ℔ per sec. per sq. ft.
In 1903 trials of wind-pumping engines were carried out at Park Royal by the Royal Agricultural Society (Journ. Roy. Agric. Soc. lxiv. 174). The mills were run for two months altogether, pumping against a head of 200 ft. The final results on six of the best mills are given in Table II.
A valuable paper by J. A. Griffiths (Proc. Inst. Civ. Eng. cxix. 321) contains details of a number of windmills of American type used for pumping and the results of a series of trials. Table III. contains an abstract of the results of his observations on six types of windmills used for pumping:—
TABLE III.
| | I. | II. | III. | IV. | V. | VI. |
| Diameter of wheel, feet | 22.3 | 11.5 | 16.0 | 14.2 | 10.2 | 9.8 |
| Sail area, square feet | 392.0 | 104.0 | 201.0 | 157.0 | 81.0 | 80.0 |
| Weather angle, outer ends | 18° 47′ | 43° | 36° | 30° | 28° | 50° |
| Weather” angle,” inner ends | 38° 20′ | 43° | 36° | 30° | 28° | 14° |
| Pitch of vanes, outer ends, feet | 23.8 | 33.7 | 36.5 | 25.7 | 17.0 | 22.4 |
| Pitch of” vanes,” inner ends, feet | 20.6 | 13.1 | 13.7 | 8.2 | 6.4 | 7.2 |
| Height of lift, feet | 25.000  100.000 | 29.200   61.2 | 39.0 | 66.3 | 38.7 | 30.7 |
| Velocity of wind at maximum efficiency, | | | | | | |
| miles per hour | 4.300  00 7.0 | 5.800  00 6.5 | 6.0 | 7.0 | 8.5 | 6.0 |
| Ratio of velocity of tips of vanes to velocity of wind | 00 .93  000 .77 | 00 .92  000 .82 | .65 | .91 | .87 | .73 |
| Revolutions of mill, per minute | 5.000  00 6.8 | 13.000   13.3 | 7.5 | 12.6 | 20.5 | 12.5 |
| Actual horse-power | 00 0.018 00 0.098 | 00 0.011 00 0.025 | 0.024 | 0.065 | 0.028 | 0.012 |
| In 100 average hours in a calm locality— | | | | | | |
| Quantity of water lifted, gallons per hour | 495.000  306.000 | 153.000  135.000 | 259.0 | 267.0 | 115.0 | 145.0 |
| In 100 average hours in a windy locality— | | | | | | |
| Quantity of water lifted, gallons per hour | 816.000  629.000 | 287.000  271.000 | 525.0 | 540.0 | 237.0 | 270.0 |
I. Toowoomba; conical sail wheel with reefing vane. II. Stover; solid sail wheel with rudder; hand control. III. Perkins; solid wheel, automatic rudder. IV. and V. Althouse; folding sail wheel, rudderless. VI. Carlyle; special type, automatic rudder.
Table IV. gives the horse-power which may be expected, according to Wolff, for an average of 8 hours per day for wheels of the American type.
| Diameter of Wheel in Feet. | Velocity of Wind in Miles per Hour. | Horse-power of Mill. | Revolutions of Wheel per Minute. |
| 8½ 8½ | 16 | 0.04 | 70-75 |
| 10 | 16 | 0.12 | 60-65 |
| 12 | 16 | 0.21 | 55-60 |
| 14 | 16 | 0.28 | 50-55 |
| 16 | 16 | 0.41 | 45-50 |
| 18 | 16 | 0.61 | 40-45 |
| 20 | 16 | 0.78 | 35-40 |
| 25 | 16 | 1.34 | 30-35 |
Further information will be found in Rankine, The Steam Engine and other Prime Movers; Weisbach, The Mechanics of Engineering; and Wolff, The Windmill as a Prime Mover. (W. C. U.)