double the depth. A lattice-work in which the area of the openings was 55% of the whole area experienced a pressure of 80% of that upon a plate of the same area. The pressure upon cylinders and cones was proved to be equal to half that upon the diametral planes, and that upon an octagonal prism to be 20% greater than upon the circumscribing cylinder. A sphere was subject to a pressure of .36 of that upon a thin circular plate of equal diameter. A hemispherical cup gave the same result as the sphere; when its concavity was turned to the wind the pressure was 1.15 of that on a flat plate of equal diameter. When a plane surface parallel to the direction of the wind was brought nearly into contact with a cylinder or sphere, the pressure on the latter bodies was augmented by about 20%, owing to the lateral escape of the air being checked. Thus it is possible for the security of a tower or chimney to be impaired by the erection of a building nearly touching it on one side. Pressures of Wind Registered in Storms.-Mr. Frizell has examined the published records of Greenwich Observatory from 1849 to 1869, and reports that the highest pressure of wind he finds recorded is 41 lbs. per sq. ft., and there are numerous instances in which it was between 30 and 40 lbs. per sq. ft. Prof. Henry says that on Mount Washington, N. H., a velocity of 150 miles per hour has been observed, and at New York City 60 miles an hour, and that the highest winds observed in 1870 were of 72 and 63 miles per hour, respectively.

Lieut. Dunwoody, U. S. A., says, in substance, that the New England coast is exposed to storms which produce a pressure of 50 lbs. per sq. ft. Engineering News, Aug. 20, 1880.

WINDMILLS.

Power and Efficiency of Windmills.-Rankine, S. E., p. 215, gives the following: Let Q = volume of air which acts on the sail, or part of a sail, in cubic feet per second, v = velocity of the wind in feet per second, s = sectional area of the cylinder, or annular cylinder of wind, through which the sail, or part of the sail, sweeps in one revolution, c = a coefficient to be found by experience; then Q cvs. Rankine, from experimental data given by Smeaton, and taking c to include an allowance for friction, gives for a wheel with four sails, proportioned in the best manner, c=0.75. Let A weather angle of the sail at any distance from the axis, i.e., the angle the portion of the sail considered makes with its plane of revolution. This angle gradually diminishes from the inner end of the sail to the tip; u = the velocity of the same portion of the sail, and E the effi ciency. The efficiency is the ratio of the useful work performed to whole energy of the stream of wind acting on the surface s of the wheel, which Dsvs energy is D being the weight of a cubic foot of air. Rankine's formula for efficiency is

2g

in which c = 0.75 and ƒ is a coefficient of friction found from Smeaton's data 0.016. Rankine gives the following from Smeaton's data:

Rankine gives the following as the best values for the angle of weather at different distances from the axis:

66

But Wolff (p. 125) shows that Smeaton did not term these the best angles, but simply says they "answer as well as any," possibly any that were in existence in his time. Wolff says that they cannot in the nature of things be the most desirable angles." Mathematical considerations, he says, conclusively show that the angle of impulse depends on the relative velocity of each point of the sail and the wind, the angle growing larger as the ratio becomes greater, Smeaton's angles do not fulfil this condition. Wolff devel

ops a theoretical formula for the best angle of weather, and from it calculates a table for different relative velocities of the blades (at a distance of one seventh of the total length from the centre of the shaft) and the wind, from which the following is condensed:

Distance from the axis of the wheel in sevenths of radius.

The effective power of a windmill, as Smeaton ascertained by experiment, varies as s, the sectional area of the acting stream of wind; that is, for similar wheels, as the squares of the radii.

The value 0.75, assigned to the multiplier c in the formula Q = cvs, is founded on the fact, ascertained by Smeaton, that the effective power of a windmill with sails of the best form, and about 15 ft. radius, with a breeze of 13 ft. per second, is about 1 horse-power. In the computations founded on that fact, the mean angle of weather is made 13°. The efficiency of this wheel, according to the formula and table given, is 0.29, at its best speed, when the tips of the sails move at a velocity of 2.6 times that of the wind.

Merivale (Notes and Formulæ for Mining Students), using Smeaton's coefficient of efficiency, 0.29, gives the following:

U

W

units of work in foot-lbs. per sec.;

weight, in pounds, of the cylinder of wind passing the sails each second, the diameter of the cylinder being equal to the diameter of the sails;

velocity of wind in feet per second;

effective horse-power;

WV

0.29 WV

-; H.P. =

64

64 X 550

A. R. Wolff, in an article in the American Engineer, gives the following (see also his treatise on Windmills):

Let c = velocity of wind in feet per second;

n = number of revolutions of the windmill per minute;

bo, b1, by, by be the breadth of the sail or blade at distances lo, la, la, la, and 1, respectively, from the axis of the shaft;

distance from axis of shaft to beginning of sail or blade proper; 1= distance from axis of shaft to extremity of sail proper; Vo, V1, V2, V3, V = the velocity of the sail in feet per second at distances lo, 11, 12, 1, respectively, from the axis of the shaft; аo, α1, ag, ag, a the angles of impulse for maximum effect at distances lo, 11, 12, 13, 1 respectively from the axis of the shaft; a = the angle of impulse when the sails or blocks are plane surfaces, so that there is but one angle to be considered;

N= number of sails or blades of windmill;

K = .93.

d

density of wind (weight of a cubic foot of air at average tempera. ture and barometric pressure where mill is erected);

W weight of wind-wheel in pounds;

coefficient of friction of shaft and bearings;

D= diameter of bearing of windmill in feet.

The effective horse-power of a windmill with plane sails will equal

The effective horse-power of a windmill of shape of sail for maximum effect equals

The mean value of quantities in brackets is to be found according to Simpson's rule. Dividing into 7 parts, finding the angles and breadths corresponding to these divisions by substituting them in quantities within brackets will be found satisfactory. Comparison of these formulæ with the only fairly reliable experiments in windmills (Coulomb's) showed a close agreement of results.

Approximate formulæ of simpler form for windmills of present construction can be based upon the above, substituting actual average values for a, c, d, and e, but since improvement in the present angles is possible, it is better to give the formulæ in their general and accurate form.

Wolff gives the following table based on the practice of an American manufacturer. Since its preparation, he says, over 1500 windmills have been sold on its guaranty (1885), and in all cases the results obtained did not vary sufficiently from those presented to cause any complaint. The actual results obtained are in close agreement with those obtained analysis of the impulse of wind upon windmill blades.

by

theoretical

70 to 75 60 to 65 55 to 60 50 to 55 45 to 50 40 to 45

19.179
33.941
45.139
64.600

97.682

20

66

16

31.654 19.542 16.150 9.771 8.075 0.41 52.165 32.513 24.421 17.485 12.211 0.61 35 to 40 124.950 63.750 40.800 31.248 19.284 15.938 0.78 30 to 35 212.381 106.964 71.604 49.725 37.349 26.741

1.34

These windmills are made in regular sizes, as high as sixty feet diameter of wheel; but the experience with the larger class of mills is too limited to enable the presentation of precise data as to their performance. If the wind can be relied upon in exceptional localities to average a higher velocity for eight hours a day than that stated in the above table, the performance or horse-power of the mill will be increased, and can be obtained by multiplying the figures in the table by the ratio of the cube of the higher average velocity of wind to the cube of the velocity above recorded

He also gives the following table showing the economy of the windmill. All the items of expense, including both interest and repairs, are reduced to the hour by dividing the costs per annum by 365 X 8 2920; the interest,

etc., for the twenty-four hours being charged to the eight hours of actual work. By multiplying the figures in the 5th column by 584, the first cost of the windmill, in dollars, is obtained.

Lieut. I. N. Lewis (Eng'g Mag., Dec. 1894) gives a table of results of ex• periments with wooden wheels, from which the following is taken:

The wheels were tested by driving a differentially wound dynamo. The 19 useful horse-power was measured by a voltmeter and ammeter, allowing 500 watts per horse-power. Details of the experiments, including the means used for obtaining the velocity of the wind, are not given. The results are so far in excess of the capacity claimed by responsible manufacturers that they should not be given credence until established by further experiments.

A recent article on windmills in the Iron Age contains the following: According to observations of the United States Signal Service, the average velocity of the wind within the range of its record is 9 miles per hour for the year along the North Atlantic border and Northwestern States, 10 miles on the plains of the West, and 6 miles in the Gulf States.

The horse-powers of windmills of the best construction are proportional to the squares of their diameters and inversely as their velocities; for example, a 10-ft. mill in a 16-mile breeze will develop 0.15 horse-power at 65 revolutions per minute; and with the same breeze

A 20-ft. mill, 40 revolutions, 1 horse-power.
A 25-ft. mill, 35 revolutions, 134 horse-power.
A 30-ft. mill, 28 revolutions, 3% horse-power.
A 40-ft. mill, 22 revolutions, 7% horse-power.
A 50-ft. mill, 18 revolutions, 12 horse-power.

The increase in power from increase in velocity of the wind is equal to the square of its proportional velocity; as for example, the 25-ft. mill rated

above for a 16-mile wind will, with a 32-mile wind, have its horse-power in creased to 4 × 1347 horse-power, a 40-ft. mill in a 32-mile wind will run up to 30 horse-power, and a 50-ft. mill to 48 horse-power, with a small de duction for increased friction of air on the wheel and the machinery.

The modern mill of medium and large size will run and produce work in a 4-mile breeze, becoming very efficient in an 8 to 16-mile breeze, and increase its power with safety to the running-gear up to a gale of 45 miles per hour. Prof. Thurston, in an article on modern uses of the windmill, Engineering Magazine, Feb. 1893, says: The best mills cost from about $600 for the 10-ft. wheel of horse-power to $1200 for the 25-ft. wheel of 11⁄2 horse-power or less. In the estimates a working-day of 8 hours is assumed; but the machine, when used for pumping, its most common application, may actually do its work 24 hours a day for days, weeks, and even months together, whenever the wind is "stiff" enough to turn it. It costs, for work done in situations in which its irregularity of action is no objection, only one half or one third as much as steam, hot-air, and gas engines of similar power. At Faversham, it is said, a 15-horse-power mill raises 2,000,000 gallons a month from a depth of 100 ft., saving 10 tons of coal a month, which would otherwise be expended in doing the work by steam.

Electric storage and lighting from the power of a windmill has been tested on a large scale for several years by Charles F. Brush, at Cleveland, Ohio. In 1887 he erected on the grounds of his dwelling a windmill 56 ft. in diameter, that operates with ordinary wind a dynamo at 500 revolutions per minute, with an output of 12,000 watts-16 electric horse-power-charging a storage system that gives a constant lighting capacity of 100 16 to 20 candle-power lamps. The current from the dynamo is automatically regulated to commence charging at 330 revolutions and 70 volts, and cutting the circuit at 75 volts. Thus, by its 24 hours' work, the storage system of 408 cells in 12 parallel series, each cell having a capacity of 100 ampère hours, is kept in constant readiness for all the requirements of the establishment, it being fitted up with 350 incandescent lamps, about 100 being in use each evening. The plant runs at a mere nominal expense for oil, repairs, and attention. (For a fuller description of this plant, and of a more recent one at Marblehead Neck, Mass., see Lieut. Lewis's paper in Engineering Magazine, Dec. 1894, p. 475.)

COMPRESSED AIR.

Heating of Air by Compression.-Kimball, in his treatise on Physical Properties of Gases, says: When air is compressed, all the work which is done in the compression is converted into heat, and shows itself in the rise in temperature of the compressed gas. In practice many devices are employed to carry off the heat as fast as it is developed, and keep the temperature down. But it is not possible in any way to totally remove this difficulty. But, it may be objected, if all the work done in compression is converted into heat, and if this heat is got rid of as soon as possible, then the work may be virtually thrown away, and the compressed air can have no more energy than it had before compression. It is true that the compressed gas has no more energy than the gas had before compression, if its temperature is no higher, but the advantage of the compression lies in bringing its energy into more avail.

able form.

The total energy of the compressed and uncompressed gas is the same at the same temperature, but the available energy is much greater in the former. When the compressed air is used in driving a rock-drill, or any other piece of machinery, it gives up energy equal in amount to the work it does, and its temperature is accordingly greatly reduced.

Causes of Loss of Energy in Use of Compressed Air. (Zahner, on Transmission of Power by Compressed Air.)-1. The compression of air always develops heat, and as the compressed air always cools down to the temperature of the surrounding atmosphere before it is used, the mechanical equivalent of this dissipated heat is work lost.

2. The heat of compression increases the volume of the air, and hence it is necessary to carry the air to a higher pressure in the compressor in order that we may finally have a given volume of air at a given pressure, and at the temperature of the surrounding atmosphere. The work spent in effect ing this excess of pressure is work lost.

3. Friction of the air in the pipes, leakage, dead spaces, the resistance offered by the valves, insufficiency of valve-area, inferior workmanship, and slovenly attendance, are all more or less serious causes of loss of power.