LIBRARY OF THE UNIVERSITY OF CALIFORNIA. I FT OF C/ass THE WINDMILL: ITS EFFICIENCY AND ECONOMIC USE A thesis presented to the Faculty of Cornell University for the Degree of Doctor of Philosophy, BY EDWARD CHARLES MURPHY, C.E. and M.S. Fellow in Civil Engineering. UNIVERSITY OF SiUFOR WASHINGTON, D. C. GOVERNMENT PRINTING OFFICE 1901 CONTENTS. Introduction Classification of windmills Regulating devices i Early experiments Experiments by writer Scope of tests Pumping mills Wells near Garden, Kansas Pumps Instruments and methods Mills tested Discussion of results of tests Relation between wind velocity and strokes of pump. Useful work Pressure-tank system Comparison of three pumping Aermotors Useful work of two pumping mills in a given time __. Proper load 2006S? ILLUSTRATIONS. Page. PLATE I. Dutch windmill at Lawrence, Kansas. 14 II. Elevation of apparatus used by Perry in wind- wheel tests 20 III. View of mill No. 2 (12-foot Woodmanse Mogul) and anemometer. 28 IV. View of mill No. 3 12-foot Aermotor 30 V. View of mills No. 4 (8-foot Ideal) and No. 5 (8-foot Aermotor) _ . . 32 VI. Working parts of mill No. 6 8- foot Gem 40 VII. View of mill No. 12 14-foot Ideal 42 VIII. View of mill No. 13 12-foot Aermotor 42 IX. View of mill No. 19 12-foot Gem. .. 44 X. A, View of mill No. 20 15|-foot Jumbo; B, View of Defender mill and "water elevator" : 46 XI. View of mill No. 21 12-foot Halliday 46 XII. View of mill No. 35 8-foot Dempster.. 52 XIII. View of mill No. 42 6-foot Ideal 58 XIV. View of mill No. 48 30-foot Halliday 60 FIG. 1. Section of common European post windmill mounted on central column 12 2. Early form of head of European tower windmill 13 3. View of Gause pump ... - 24 4. Working parts of Woodmanse Mogul 26 5. Sectional view of Woodmanse pump 27 6. Diagram showing results with mill No. 2 12-foot Woodmanse Mogul 28 7. Working parts of Aermotor 29 8. View of Stone pump _ 30 9. Details of Stone pump 31 10. Diagram showing results with mill No. 3 12-foot Aermotor 32 11. Diagram showing results with mill No. 4 8- foot Ideal . 32 12. Diagram showing results with mill No. 5 8-foot Aermotor 33 13. Diagram showing results with mill No. 9 16-foot Aermotor. 33 14. Working parts of mill No. 1 1 12-foot Ideal 38 15. Diagram showing results with mill No. 11 39 16. Working parts of Frizell cylinder _ 40 17. Diagram showing results with mill No. 12 14-foot Ideal. 41 18. Diagram showing results with mill No. 19 12-foot Gem 45 19. Diagram showing results with mill No. 20 15^- foot Jumbo. 46 20. Working parts of Halliday mill 47 21. Diagram showing results with mill No. 21 12-foot Halliday _ . 48 22. Diagram showing revolutions of wind wheel of mill No. 30 16- foot Irrigator ... 49 23. Diagram showing horsepower of mill No. 30 50 7 8 ILLUSTRATION?. Page. FIG. 24. Comparative diagram showing results with mills No. 35 (8-foot Dempster) and No. 36 (22i-foot Eclipse) 53 25. Pump, pressure- tank and hydraulic regulator of mill No. 37 12- foot Woodmanse Mogul _ ... 54 26. Diagram showing results with mill No. 37 55 27. Comparative diagram showing results with mills No. 38 (10-foot wooden Woodmanse) and No. 48 (30- foot wooden Halliday ) 56 28. View of mill No. 43 10-foot Perkins 58 29. Working parts of mill No. 51 8-foot Monitor .... 62 30. Diagram showing relation between horsepower and wind velocity for five 12-foot mills... .." 66 81. Diagram showing relation between horsepower and wind velocity for four 8-foot mills . . 67 THE mmill. ITS EFFICIENCY AND ECONOMIC USE. PART I. By EDWARD CHARLES MURPHY. INTRODUCTION. History does not record the name of the person who invented the windmill, nor give the date of the invention. The belief that wind- mills were used by the Romans is not well authenticated, and their use by the Bohemians in 718 is doubted. It is quite clear, however, that they were used in France and Italy in the twelfth century for grinding corn, and that they were used in Holland in the fifteenth century for pumping water over the dikes into the sea. Mr. John Burnham, of Connecticut, is said to be the inventor of the American windmill. Mr. L. H. Wheeler, an Indian missionary, patented the Eclipse mill in 1867. The first steel mill was the Aer- motor, invented by Mr. T. O. Perry in 1883. The common European windmill, shown in section in figs. 1 and 2, differs much in appearance from the American mill. The wind wheel of the European mill has usually four long wooden arms, to each of which is attached a sail, against which the wind presses. The sails consist of a framework, on which canvas is stretched, usually forming a warped surface, the angle with the plane of the arms (called the angle of weather) being about 7 at the outer end and 18 at the inner end. The length of sail was usually about five-sixths the length of the arm, the width of the outer end one-third the length, and the width of the inner end one-fifth the length. The sail area is seen to be small compared with the wind area or zone containing the sails. The arms were sometimes 60 feet long. The American wooden mill is much smaller and more compact than the European mill. It has six or eight arms, to which is attached a framework carrying many small sails. These sails are usually 3 or 4 feet long, 3 or 4 inches wide at the outer end, and 1 to 3 inches wide at the inner end, and are set at an angle of 30 to 40 to the plane of the wheel. For large wheels these sails are arranged in two or more concentric rings. The Ameri- 11 THE WINDMILL. can steel mill differs principally from the wooden mill in that it has larger and fewer sails for a given size of mill, its sails are curved instead of plane, and it offers less resistance to the passage of the air over the back of the sails. In the sails of the steel mill there is seen to be a partial return to those of the European mill. FIG. 1. Section of common European post windmill mounted on central column. CLASSIFICATION OF WINDMILLS. Windmills may be divided into two general classes paddle wheel and sail wheel. The Jumbo shown in PI. XVI, B (Part II), and Little Giant No. 56, described on pages 125 to 127, Part II, are good illus- trations of the first class. In both of these mills the sails move with the wind, and it is necessary to have a shield, or a method of feathering MURPHY.] CLASSIFICATION OF WINDMILLS. 13 the sails, in order to keep the wind from striking them when they are moving in a direction opposite to that of the wind. In the Jumbo the axis of the wheel is horizontal, in the Little Giant it is vertical; but the wind acts on the sails of both in substantially the same way. The air acts with full pressure on only one sail of the Jumbo at any one time, and on half the sails it has no action, or only negative action. In the sail- wheel mill (fig. 1, Part I, and PL XV, Part II) the wheel moves at right angles to the direction of the wind, instead of in the same direction, as in the paddle-wheel mill. The wind acts with a FIG. 2. Early form of head of European tower windmill. certain pressure 011 all of the sails all of the time. The circumference velocity of the sail wheel may be two or more times greater than the velocity of the wind that drives it, but the circumference velocity of the paddle wheel is always less than the velocity of the wind that drives it. The sails of the sail- wheel mill must be placed at an angle with the plane of the wheel, so that the wind will press on them; but the sails of the paddle-wheel mill may be IL the plane of the axis of the wheel. For greatest pressure on the sails of a sail-wheel mill the axis of the 14 THE WINDMILL. [NO. 41. wheel must be parallel to the direction of the wind. It is necessary, then, for the wheel to change its direction as the wind changes. In the German or post mill the whole building, as well as the wheel, can be turned around on a post by hand. In the tower or Dutch mill the upper part only of the mill turns with the wheel. This is accomplished by hand in the mill shown in fig. 1, and by an auxiliary windmill in the mill shown in fig. 2. In the American mills the upper part only turns on a turntable, which is usually on rollers or balls. This is accomplished, first, by the pressure of the wind on a long rudder vane extending out behind the mill, and in some mills by a side vane as well; or, second, by the pressure of the wind on the wheel itself, which is placed on the opposite side of the tower, as in fig. 46, Part II ; or, third, by side wheels, as in mill No. 52, fig. 50, Part II. REGULATING DEVICES. The wind is constantly changing in velocity as well as in direction, and if the load on the mill is constant the speed of the mill and of the machine which it operates will change with it. If the speed is to be kept 'nearly constant, some device is needed to reduce the wind pressure on the wheel when the wind velocity reaches a certain amount. In the European mill there are two methods of doing this, viz, by means of a brake or friction rings and by changing the sail area. The latter is accomplished by rolling or unrolling the canvas sails by hand or automatically. In the American mill the speed is regulated by changing the sail area in one of three ways : (a) By sec- tions of the wheel revolving about an axis which places each sail at an angle to the direction of the wind less than 90, as in fig. 36, Part II ; (b) by placing the axis of the wind wheel eccentric to the axis of the tower, so that the wind pressure on the wheel will cause it to revolve around the axis of the tower; and (c) by the wheel moving natu- rally around the axis of the tower in the direction in which it is revolving. This turning action around the axis of the tower is counter- acted by a spring or a weight, or, as we commonly say, "the wheel is held in the wind " by a spring or a weight. A weight is better than a spring, for by moving it out or in any desired pull can be placed on the wheel. A spring can not easily be adjusted and may lose some of its tension. The first method of regulation, called the centrifugal- governor method, is used in the Halliday mill (fig. 20) and in the Althouse-Wheeler mill (fig. 36, Part II). The second method is illus- trated in the Aermotor (fig. 33, Part II), which shows the axis of the wheel eccentric to the axis of the tower by 4.5 inches. It also shows the spring which holds it in the wind. This spring also resists the action of the load, which tends to turn the wind wheel out of the wind. The third method is illustrated by the Woodmanse mill. U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 41 PL. I DUTCH WINDMILL AT LAWRENCE, KANSAS. MURPHY.] EARLY EXPERIMENTS. 15 EARTHY EXPERIMENTS. Smeatori's experiments. The first experiments of which we have any record were made by John Smeaton, an English engineer, and published in 1755 to 1763. 1 These experiments were made on model windmills of the European type, for the purpose of determining the best shape of sail for a given sail area. The models each had four arms 21 inches long. For one set of tests the sails were 5.6 inches broad and 18 inches long, giving an area of 403 square inches. In another set of tests the sails were 18 inches long, 5.6 inches wide at the inner end and 8.4 inches wide at the outer end, with an area of 504 square inches. The sails were either plane or warped at various angles. These mills were worked by moving the windmill around in a circle of 5-j- feet radius, in still air, instead of placing them on a tower and allow- ing the natural wind to drive them. The wheel was moved around in this circle by means of a cord wound on a drum on a vertical shaft, the horizontal arm which held the wheel being fastened to this shaft. The work done by the wheel in a given time was measured by observing the length of string wound on the shaft of the wheel, a weight of known size being attached to the end of the string. The velocity of the wind, which was assumed to be the velocity of the end of the arm where the wheel was attached to it, varied from 4 to 8f "feet a second, or from 2.9 to 6 miles an hour. It will be noticed that these wheels are only 3.5 feet in diameter, that they were moved in a circle only 5.5 feet in diameter, and that wind velocities or wheel velocities were small and of only a limited range from about 3 to 6 miles an hour. Smeaton draws the follow- ing conclusions from his experiments : (1) The velocity of the windmill sails, whether unloaded, or loaded so as to pro- duce a maximum, is nearly as the velocity of the wind: their shape and position being the same. (2) The load at the maximum is nearly, but somewhat less than 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 less than as the cubes of the velocity of the wind. (4) The load of the same sails at the maximum is nearly as their 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 at a given velocity of the wind, and the velocity of the wind increases, the load remaining the same: first, the increase of effect, when the increase of the velocity of the wind is small, will be nearly as the squares of those velocities; secondly, when the velocity of the wind is doubled, the effects will be nearly as 10 to 27.5; but, thirdly, when the velocities compared are more than double of that where the given load produces a maximum, the effects increase nearly in a simple ratio of the velocity of the wind. (6) If sails are of similar figure and position, the number of turns in a given time will be reciproca'ly as the radius or length of the sail. Philos. Trans. Royal Soc. London, 1756-1763. 16 THE WINDMILL. [NO. 41. (7) The load afc a maximum that sails of a similar figure and position will over- come 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 extremity of Dutch sails, as well as of enlarged sails, in all their usual positions, when unloaded, or loaded to a maximum, is considerably quicker than the velocity of the wind. Regarding the ratio of the sail area to the wind area or zone contain- ing the sails, he found that where the ratio was greater than 7 to 8 the power of the mill was decreased instead of increased. Regarding the proper shape of sail, he found that the warped sail was more effective than the plane sail. He also found the following six angles of weather at equal distances from the shaft outward advantageous: 70, 71, 72, 74, 77.5, and 83. He states that a difference of two or three degrees in the angles of impact makes little difference in the power of the mill. Coulomb's experiments. C. A. Coulomb, a French engineer, made some tests of the work done by a Dutch windmill used for extracting oil from rape seed at Lille, in Flanders. His observations were pub- lished in 1821. 1 The mill was 70.2 feet in diameter. It had four warped canvas sails, each 28.7 feet long and 6.6 feet wide; the width of canvas was 5.5 feet. The angle which the plane of sail made to the plane of the wheel varied from 30 at the inner end to 12 at the outer end. The wind velocity was measured by the use of feathers carried along by the wind. Two men were stationed 150 feet apart, on slight elevations, to note the time required for each feather to pass over this distance. The velocity of the wind striking the wind wheel was assumed to be that found from these feathers. In a 14.9-mile wind, and with the load ordinarily used, he found that the wheel made 13 revolutions per minute with all the canvas spread. From these data he figured the useful work done by the mill per minute to be 232,388 foot-pounds and the useless work expended in shock of stamp- ers and friction to be 37,310 foot-pounds, or a total of 269,698 foot- pounds, equal to 8.17 horsepower. Coulomb did not consider this a complete or satisfactory test of this mill. He did not control the working of the mill, but simply observed what it did when handled by the miller who extracted the oil. He tried to induce the owner to permit him to use the mill for a time for experimental purposes, but did not succeed. It will be seen from what follows that even if we assume the wind velocity to be correctly measured, this test does not necessarily show the power of the mill, for we do not know that the load used was the proper load for the wind velocity. It shows what the mill was doing, not what it might do under a better loading. i Theorie de Machines Simple, by G. A. Coulomb. Paris, 1831. MURPHY.] EARLY EXPERIMENTS. 17 Griffiths' s experiments.^ In 1891-92 Mr. J. A. Griffiths made tests of six windmills used for raising water, with the following results: Results of windmill tests by J. A. Griffiths. ^ ^ 'S O 1 . s o o -0 03 '3 H -rH Og O * B 3 0) H P. P.-O No. Type of windmill tested. ;gs *1 ^ S^H ^ s^ 5^,S eu, d meter pump 4 *a o 5 fn P |! ^ 2*0 1*1 f o 1 fl^ S * ^'Soo eg , O ftto 'a; ^fl s5h o o x H O ^ s 00 ^ J ^ w ^ee^. Feet. Sqft / Tn. /W. Feet Ft.-lbs. Miles. Rev. 1 Toowoomba 22.3 8.3 39.20 18 47 5 6.75/ 25 120 4.3 5.0 0.018 100 480 7.0 6.8 0.098 v Stover 11.5 4.5 104. 43 3 4 { 29.2 29.2 5.8 13.0 0.011 \ 61.2 61.2 6.5 13.3 0. 025 B Perkins 16.0 6.0 201.0 36 3 10.75 39.0 105.0 6.0 7.5 0.024 4 Althouse -Wheeler . 14.2 4.5 157.0 30 3 clO 66.3 166.0 7.0 12.6 0.065 6 do 10.2 3.8 81.0 28 8 4f 38.7 51.0 8.5 20.5 0. 028 6 Carlyle 9 8 4.2 80.0 50 3 4 30.7 30.7 6.0 12.5 0.012 a These pump loads have been computed for comparison of these results with others. b At maximum efficiency. ^ c Pump is double acting; this is twice the length of stroke. No. 1 was a 22.5-foot wooden mill, with 20 warped sails each 87 by 36 by 9 inches, the weather angle at the outer end being 18 47' and at the inner end 40 20'. It worked a direct-acting single-stroke pump having a 5-inch cylinder and 6.75 inches stroke. Two lifts were used, one of 25 feet and the other of 100 feet. No. 2 was a 12-foot Stover wooden mill, having a wind wheel some- what like that of mill No. 38. It had 112 sails, each 43 by 3.75 by 1.5 inches, set at an angle of 43 to the plane of the wheel. It worked a direct-acting single-stroke pump having a 3-inch cylinder and 4 inches stroke. The lifts were 29.2 and 61.2 feet. No. 3 was a 16-foot Perkins solid wood wheel, the wind wheel hav- ing 160 sails, each 60 by 4 by 1.5 inches, set at an angle of 36 to the plane of the wheel. It worked a direct- acting double-stroke pump having a 3-inch cylinder and 5.375 inches stroke. The lift was 39 feet. No. 4 was a 14-foot Althouse- Wheeler wooden sectional mill, the wind wheel having 104 sails, each 48 by 4 by 1.5 inches, set at an angle of 30 to the plane of the wheel. It worked a direct-acting double- stroke pump having a 3-inch cylinder and 5 inches stroke. The lift was 66.3 feet. No. 5 was a 10-foot Althouse- Wheeler wooden sectional mill. The wind wheel had 84 sails, each 38 by 3.75 by 1.5 inches, set at an angle of 28 to the plane of the wheel. It worked a direct-acting single- stroke pump having a 3-inch cylinder and 4.625 inches stroke. The lift was 38.7 feet. No. 6 was a 10-foot Carlyle iron mill. It had 7 somewhat spoon- shaped sails, each having a spout-like extension through which the 1 Windmills for raising water, by J. A. Griffiths: Proc.Inst Civ. Eng., Vol. CXIX, p. 321, IRR 4101 2 18 THE WINDMILL. [NO. 41. air flowed. It worked a direct -acting single-stroke pump having a 3-inch cylinder and 4 inches stroke. The lift was 30.7 feet. The wind velocity was measured with the " f " wind gage, which was either on a tower near by or on an arm projecting as far as pos- sible to windward. It appears that it was necessary to be near the gagp in order to read the velocity, which would indicate a possible error in wind velocity and some interference with the wind striking the wind wheel. The range of wind velocities is not stated, and not more than two loads were used in any case. These results will be compared with others further on. King's experiments}- Prof. F. H. King conducted a series of experi- ments with a 16-foot geared Aermotor, covering a period of one year from March 6, 1897, to March 6, 1898. This mill was used to work one or more of four pumps: (1) A reciprocating piston pump with a 14-inch cylinder and 9 inches stroke; (2) a bucket pump having a normal capacity of 120 gallons per minute; (3) a No. 2 Gould centrif- ugal pump; and (4) the smallest size Menge pattern centrifugal pump. The bucket pump was used nearly all of the time. The reciprocating piston pump was used occasionally by itself and part of the time with the bucket pump, when the wind velocity was strong enough to carry both. The Menge was used occasionally with the piston pump and the bucket pump, when the wind velocity was strong enough to carry all. There was no automatic device for throwing into or out of use any of these pumps. It was necessary to do this by hand, so that a part of the time the load on the mill was not suited to the wind velocity. This can be seen from the record. For example, on February 10, from 1 to 7 p. m., the wind velocity varied from 9 to 12 miles an hour and 8.6 tankfuls of water were pumped, while on June 1, from 8 a. m. to 4 p. m., the wind velocity varied from 11 to 15 miles an hour, and not a tankful was pumped. The report gives the number of tankfuls of 141.2 cubic feet which were lifted 12.85 feet each hour during the year, and some interesting conclusions drawn from these records. Professor King has also made some tests of this mill with a Prony friction brake. The results of these tests, and the indicated horse- powers computed from them, are as follows : 1 Bull. No. 68, Wisconsin Agricultural Experiment Station. MURPHY.] EARLY EXPERIMENTS. Results of tests of 16-foot geared Aermotor. 19 Wind velocity per hour. Direction of wind. Indicated horse- power. Average wind velocity. Average horse- power. Barometer. Tempera- ture. Miles. 8.4 12.0 sw. 0.2715 0.5791 Miles. 8.4 } 0.2715 Inches. 29.40 ( 29. 36 Degrees. 0.0 0.5 12.4 0.7230 I 12.33 0. 5858 29. 36 0.5 12 6 0. 4553 ) 29.36 0.25 13.2 14.6 14.6 sw. sw. 0.6213 0. 7343 0.9449 13.2 1 14.68 0.6213 0. 8602 29.40 29.36 29.40 0.5 -0.5 0.5 14.8 18.6 18.8 21.2 21.6 21.6 21 8 sw. NW. sw. sw. w. N. NW 0.9016 2.054 1.692 2.593 3.715 3.227 2 597 J j 18.70 21.55 1.873 3.033 29.40 28.86 29.40 29.40 29.06 28.86 1.0 9.0 1.0 1.5 -2.0 7.0 22.0 22.0 22 2 W. w. NW 4.326 4.236 2 394 22.06 3. 652 {29.09 29.04 1.0 -2.0 23.0 23.0 24 W. w. 3.842 4.151 5 983 I 23. 00 3.996 29.07 1 29.05 / 28 75 -1.0 -1.0 6.8 24.6 25.2 27.3 27.0 39.0 40.0 w. w. N. W. N. 3.554 4.882 4.092 4.850 5. 953 5.971 j 24. 30 25.2 I 27.16 39.0 40.0 4.768 4.882 4.471 5.953 5.971 \ 29. 09 29.09 / 28. 66 1 29.10 " 28.69 28.69 1.5 1.5 6.3 1.5 6.5 6.3 This mill is similar to our 16-foot Aermotor No. 44, described in Part II. It will be seen later that the power found by Professor King is much greater than we have found it for high wind velocities. The probable reason for this difference will be discussed later. It may be stated here, however, that Professor King measured the wind velocity with an anemometer in a fixed position 40 feet due east of the windmill, and it will be seen that the wind was from the west, northwest, or south- west nearly all of the time when the brake tests were being made. (The wind came from the north around by the east to the south only three times while the brake tests were in progress. ) The revolving wheel must have interfered with the running of the anemometer and caused it to show a less wind velocity than really existed. Professor King also determined the work done by the mill in grind- ing corn. The power of the mill in a given wind velocity can not, however, be judged from these tests, since the grinder load was probably not suited to all wind velocities. 20 THE WINDMILL. Results of brake tests of 16-foot geared Aermotor. [NO. 41. Wind velocity per hour. Indicated horse- power. Wind velocity per hoxir. Indicated horse- power. 8 miles 0.25 26 miles . . . 4.82 10 miles 0.40 28 miles 5 14 12 miles 0.56 30 miles . . 5 40 14 miles . . 0.78 32 miles. 5.61 16 miles ._ 1.08 34 miles 5.76 18 mUes .. 1.62 36 miles ... ... 5.87 20 miles 2.39 38 miles 5.95 22 miles 3.31 40 miles 5.97 24 miles 4.31 Perry's experiments. From June, 1882, to September, 1883, Mr. T. O. Perry made experiments with 61 windmills, each 5 feet in diameter. The results were published in 1889. 1 Mr. Perry's methods were similar to those employed by Smeaton he used small wheels moved against still air in a circle of 14 feet radius. His experiments were made on a much larger scale than Smeaton's, however, and his apparatus was more perfect. Smeaton used wheels of European type; Mr. Perry used those of American type. PL II is an elevation of Mr. Perry's apparatus, showing the wheel as it revolved about the vertical shaft, driven by an 80-horsepower engine. The power was measured by means of a Prony friction brake placed on a brass cylinder on the wind- wheel shaft. In order to eliminate the effect due to differences in the condition of the air, and get results comparable with one another, Mr. Perry used one of his wheels as a standard with which to compare the others. After the best load for a wheel had been obtained, comparative tests were made with this one and with the standard wheel, by trying first one wheel and then the other until several measurements of each had been taken. The final result of each wheel was the average of eight or ten measurements. In comparing Smeaton's results with his own, Mr. Perry writes: We were not able to obtain the best results with weather angles as small as Smeaton's in any of our wheels. Nor did our sail speeds, as compared with wind velocity, nearly approach the speeds obtained by Smeaton. Even our unloaded wheels did not show the sail speed attained by the best of Smeaton's when loaded for maximum work. * * * Our loads at the maximum of work were sma'ler as compared with the greatest loads, and the speed of revolutions at maximum work as compared with the speeds of unloaded wheels, were smaller for our mills than for Smeaton's. He states, however, that the general conclusions drawn by Smeaton (see pages 15 to 16) were substantially confirmed by his experimonis. The difference between his results and Smeaton's lie attributes to the differences in the mills used. Water-Supply and Irrigation Paper U. S. Geol. Survey No. 20. MURPHY.] WRITER'S EXPERIMENTS. 21 Some of Mr. Perry's conclusions are as follows: (1) There is nothing gained by having the sail area more than seven- eighths of the wind area, and there is little gained by having it more than three-fourths of the latter area. (2) That the power varies as the cube of the wind velocity. (3) That the load for maximum power varies as the square of the wind velocity. (4) That the speed of the unloaded wheel increases somewhat faster than the wind velocity. (5) That the best speed for most of his wheels was about 0.55 per cent of the unloaded speed. (6) That the conical deflector at the center of the wheel does not increase the power. (7) That obstructions on the back of sails greatly reduce the power of the mill. (8) That the speed of wheel No. 48 was increased 48 per cent by removing the strip from the back of each sail. (9) That a deflector in front of the wheel increased the speed of a slow-moving wheel. (10) That a deflector in front of the wheel did not increase the speed of a rapidly moving wheel. (11) That a mast offers more obstruction in front of a wheel than behind it. EXPERIMENTS BY WRITER. The tests of wind wills described in the following pages were begun by the writer in the summer of 1895. They w r ere continued during the summer of 1896, Avith much better facilities than during the pre- vious season. The results obtained to that time were published in Water-Supply and Irrigation Paper No. 8, entitled Windmills for Irrigation. Since then the work has been continued as time could be spared mainly during a portion of three summer vacations. The work of the summer of 1896 was confined mainly to pump- ing mills. The tests show what each windmill and its pump were actually doing under certain conditions of load, lift, etc. They do not show what the mill might do under other conditions. It was evi- dent that the useful work of a mill varied with its load and the efficiency of the pump. The latter could not well be ascertained. It w T as, therefore, thought best to confine the tests principally to power mills, in which the unknown factor of pump efficiency is not present, and where the load on the mill can easily be varied. This has enlarged the scope of the work, making it cover windmills for power as well as those for irrigation. Many of our tests of pumping mills were made in the vicinity of Garden, Kansas. Perhaps nowhere in the United States is irrigation from wells by the use of windmills carried to the same extent as there, 22 THE WINDMILL. [NO. 41. where may be found hundreds of windmill pumping plants furnishing water to irrigate from 1 to 15 acres each and lifting from 3 to 14.5 quarts per stroke to a height of from 10 to 45 feet, as well as large steel mills running day and night, when the wind is strong enough, and working pumps of the best kind. SCOPE OF TESTS. There are many makers of American windmills, and with the great variety of mills in use no two are alike, though in some cases the difference is slight it was impossible to test a mill of each type. It was our purpose to test only the mills that were in good working order and subject to good wind exposure, and which would add new data to that already obtained or confirm in some particular that previously secured. In some cases two or more mills of the same size and make were tested to show as far as possible the effect of pump, well, etc. on the useful work. The parts of mill and pump on which the power depends were carefully measured. The temperature and barometric pressure were observed in each case and the mean given. The dis- charge of pump per stroke was measured when possible, and the diameter of cylinder and length of stroke are given, so that the dis- charge can be compared with the figured displacement. The lift was measured whenever the surface of the water in the well could be reached with a tapeline. The number of strokes of the pump per mile of wind was found for velocities from 6 or 8 miles to 20 or 30 miles an hour. In some cases the number of strokes is given when no water was being pumped. In fact, there was collected for each mill as much data as it was conveniently possible to obtain which would in any way affect the power of the mill or be of interest. PUMPING MILLS. The essential difference between pumping and power mills is that in the former there is a pump rod with an up and down motion, while in the latter there is a vertical rotating shaft. The former is usually geared back 2 or 3 to 1, while the latter is generally geared forward 6 or 8 to 1. The ordinary pumping mill, such as is used for stock purposes, is lighter than the power mill, but the irrigating mill is of nearly the same weight as the power mill. The larger power mills have a pumping attachment, so as to work a pump as well as a grinder or other machine. WELLS NEAR GARDEN, KANSAS. A brief description of the water supply and wells of this locality may be helpful in considering what follows. The water is found in sand and gravel at distances below the sur- face varying from 8 to 40 feet. This material is in layers of variable thickness and different degrees of coarseness, ranging from fine sand MURPHY.] WRITER'S EXPERIMENTS. 23 to large gravel. It is overlain by a layer of sandy clay, which in some places will for years stand vertical without any support; in other places there is very little clay in this layer. The wells are usually 3 to 4 feet square, and are cased with wood through the top sandy clay to the water-bearing sand; then a wood or galvanized-iron casing from 12 inches to 3 feet in diameter extends down from 8 to 20 feet into the sand to a layer of gravel. Where this latter casing is large, three or more galvanized-iron pipes 6 to 12 inches in diameter are put down in the bottom of it, and these sometimes have wire gauze over their tops to keep down the sand ; they also have perfora- tions about one-fourth of an inch in diameter for a distance of 2 feet or more from the bottom to admit the water. In many cases, instead of this small open well, the supply pipe is on a well point having the same diameter as the supply pipe, its length varying with the diame- ter. These well points have not given satisfaction and are being replaced b} 7 open wells. On examining well points that have been used for a time it was found that many of the little openings through which water is admitted to the pump had become filled with fine grains of sand, thus reducing the area. Although this water area was of the proper amount when the well was new, it becomes too small after the well has been used for a time or after it has stood without being used. If this area is too small to allow the free passage of water into the pump, an added load is put on the latter. PUMPS. Nearly all of the pumps in use in the vicinity of Garden are of the reciprocating-piston type. Fig. 8 shows the Stone pump, manufac- tured by R. G. Stone, of Garden. This pump is made in three sizes 6 inch, 8 inch, and 10 inch, these dimensions being the approximate diameter of the discharge pipe. The diameter of the cylinder is less than the diameter of the pipe by twice the thickness of the brass lin- ing. The valves (shown in fig. 9) are of the latest pattern. The plunger valve is of the single-fiap or clack variety and the check valvp is of the disc variety, made so that the water can pass up the center as well as around the sides. In an earlier form of this pump the plunger valve is of the double-flap or butterfly type and the chock valve of the lift type, but with no opening at the center. Probably nine-tenths of the pumps in use near Garden are of the Stone variety. Fig. 3 shows the Gause pump, one of the first pumps used there for irrigating purposes. It is more expensive than the Stone pump, and is not now so much used. Fig. 16 shows the cylinder of an 8-inch Frizell pump, a few of which are in use. Fig. 5 is a sectional view of the Woodmanse pump, which is used with mill No. 2. PI. X, B, shows a crude homemade pump called the ' ' water elevator. " One of these is in use in Garden. The efficiency of reciprocating pumps like those described varies 24 THE WINDMILL. [NO. 41. N directly with the lift, inversely with the number of strokes per minute, and with the design of the pump. For lifts of 10 or more feet and not more than 30 strokes per minute the efficiency in a good pump should be at least 70 per cent. Prof. O. P. Hood 1 has measured the efficiency of two Frizell pumps one 6 inch, with 14.1 inches stroke, like that shown in fig. 16, and one, ,4 inch, with 24 inches stroke, having a butterfly discharge valve. He found that for a 7.7-foot lift the efficiency of the 6-inch pump dropped from 75 per cent to 63 per cent as the number of strokes increased from 10 to 60 per minute; that for a 22.7-foot lift it decreased from 86 per cent to 82 per cent for the same range of speed; and that for a 37.8-foot lift it decreased from 84 per cent to 82 per cent, while the number of strokes increased from 10 to 50 per minute. The efficiency of the 4-inch pump dropped from 66 per cent to 60 per cent for a 12.8-foot lift, and from 83 per cent to 73 per cent for a 37.6-foot lift, as the number of strokes increased from 10 to 50 per minute. The valve area should be not less than 30 per cent of the cylinder area. The cylinder should be placed as near the water as possible; if it is more than 25 feet above the water, and the number of strokes is 30 or more, the cylinder will not fill properly, and pounding will result. INSTRUMENTS AND METHODS. The wind velocity was measured with a United States Weather Bureau cup anemometer, each mile of wind being recorded electrically b}^ one pen of a 2-pen register. By means of a little device fastened to the pump an electric circuit is closed at each stroke of the pump and a record made by a recorder. Another electric circuit, leading from the recorder to the other pen of the register, is closed at each hundred strokes of the pump and a record made on the register. Hence the graphic record of the register shows the number of miles of wind in any given time, also the number of hundred strokes of the pump in the same time. The anemometer was held on a pole at the height of the axis of the wheel of the wind- mill. The pole was made so that its length could be increased at will from 25 to 50 feet. The anemometer on the pole is shown in Pis. Ill and XI. S FIG. 3. Gause pump. JV, plunger; B, spout; F, dis- charge pipe; H, plunger; T, cylinder; Z, enlarged valve opening and check valve; S, suction pipe. 1 Water-Supply and Irrigation Paper U. S. Geol. Survey No. 14. MURPHY.] WRITER'S EXPERIMENTS. 25 The discharge of the pump per stroke was ascertained by catching the water for several strokes in a tub and measuring it with a quart measure. In a few cases it was found to vary with the number of strokes per minute. Where it varied the discharge given is for a nearly maximum speed of pump. The lift, or distance from the surface of the water in the well to the center of the -~ ater column as it leaves the discharge pipe, was measured when the pump was working quite rapidly. For pumps on well points it was estimated from the depth to water when the point was put down, making an allowance for the lowering of the water. Each mill tested is described and the results of the tests given in tabular form. Nearly all of the mills are illustrated. The number of strokes of the pumps per mile of wind and the horse- powers of the mills are in most cases explained by diagrams, which show at a glance the facts which otherwise can be comprehended only by a careful analysis of the tables. In these diagrams (figs. 6, 10, 11, 12, 13, 15, 17, 18, 19, and 21) the relation between the wind move- ment, in miles per hour, and the number of strokes made by the pump while the wind was moving over 1 mile is shown by the curved line. The space from left to right is proportional to the number of strokes of the pump. The data expressed by these diagrams were obtained directly from the record given by the anemometer register. In explanation we will assume that the pen connected with the anemometer makes three short marks (3 miles) in fifteen minutes, indicating a mile in five minutes, or at the rate of 12 miles an hour. At the same time the other pen connected with the pump, and regis- tering each 100 strokes, makes, saj 7 , two short marks, showing that the pump has made 200 strokes for this 3 miles of wind movement, or 67 strokes to the mile. This fact is entered on the diagram by a small circle placed at a distance from the right which corre- sponds to a wind velocity of 12 miles an hour, and at a distance from the bottom which corresponds to 67 strokes of the pump. In this way each observation is indicated. When the points have been plotted, the smooth curve is sketched so as to occupy an intermediate position among them. In order to obtain the number of strokes more accurately than by measurement on the register sheet, they were actually counted for a considerable number of observations in each test. The number of strokes per minute is obtained by dividing the number of strokes per mile of wind by the number of minutes required to make the mile. For example: If the number of strokes per mile in a 12-mile wind (which requires 60 -4- 12, or five minutes to make a mile) is 90, then 90 -r- 5 = 18, the number of strokes per minute. The number of gal- lons raised per minute is found by multiplying the number of gallons 26 THE WINDMILL. [NO. 41. per stroke by the number of strokes per minute. The horsepower of the mill in any wind velocity is found by multiplying the number of Ki<;. 4. Working parts of Woodmanse Mogul. per stroke by UK* number of strokes per minute, then by 8.3 pounds (the weight of one Ballon of water), then by the lift, in feet, MURPHY.] PUMPING MILLS TESTED. 27 and dividing the product by 33,000 (the number of foot-pounds in a horsepower), or by the following formula: Horsepower = nqgh -+- 33,000, where n number of strokes per minute, g = the weight of one gallon of water, q = the number of gallons per stroke of pump, h = the lift, in feet. The pump load is the weight of water lifted per stroke multiplied by the lift, or height to which it is raised. The number of revolutions of the wind wheel per minute is found by multiplying the number of strokes per min- ute by the number of revolu- tions per stroke. PUMPING MILLS TESTED. Mill No. 1. The tests of this mill were preliminary or experimental, being made for the purpose of perfecting the instruments employed, and were not completed for discussion. Mill No. '2. This is a 12-foot Woodmanse Mogul, manufactured by the Wood- manse-Hewitt Manufactur- ing Company, of Freeport, Illinois. PI. Ill shows the mill, tower, pump, and pond, and fig. 4 the working parts. The tower is of steel, 50 feet high to the axis of the wheel. The wind exposure on the north, is not good, the mill being 115 feet south of a large barn. The wheel has 30 curved sails, each 36 by 13 by 5.5 inches, 1 set at an angle of 30 (angle of weather) with the plane of the wheel. It is back- geared, 3 to 1, and held in the wind by a spring. FIG. "). Sectional view of Woodmanse pump. The pump 1 In this expression 36 is the length of the sail, 13 the width of sail at the outer end, and 5.5 the width of sail at the inner end. 28 THE WINDMILL. [NO. 41. also is of Woodmanse make, and is shown, in section, in fig. 5. The cylinder is 9.5 inches in diameter, the supply pipe 5.625 inches in diameter, the length of stroke 12 inches. The well is 3f feet by 3f feet to the water, a distance of 14 feet. At that point a 12-inch galvanized-iron pipe is put down 20 feet, forming a small open well. The lift at the time of test was 17f feet and the discharge per stroke 14| quarts. The mean barometric pressure was 26.98 inches, and the mean temperature 94 F. The cost of mill, tower, pump, and well was about $210. The results of the tests are as follows: Results of tests of mill No. 2 12-foot Woodmanse Mogul. [Load per stroke, 536.2 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. U hnrs 12 miles 15.6 5 2 18 8 16 miles 48.0 16.0 58 20 miles 60.9 20.3 73.6 25 miles 69.9 23.3 84.5 30 miles 75.9 25.3 91.7 Useful 0. 085 0.260 0. 322 0. 379 0. 41 1 The curve shown in fig. 6 is for a moderately loaded 12-foot mill (536.2 foot-pounds per stroke). It starts at a wind velocity of 11 10 VELOCITY OP WIND IN MILES PER HOUR, 15 20 25 70 FIG. ti. Diagram showing results with mill No. 2 12-foot Woodnuuiso Mogul. U. S. GEOLOGICAL SURVE1 WATER-SUPPLY PAPER NO. 41 PL. Ill VIEW OF MILL NO. 2 (12-FOOT WOODMANSE MOGUL) AND ANEMOMETER. MURPHY.] PUMPING MILLS TESTED. 29 miles an hour. It ascends very rapidly, reaching a maximum at 18 miles an hour, and giving 60 strokes to the mile. The rest of the curve to 30 miles has a gentle slope. The number of strokes per minute increases from about 5 at 12 miles to about 25 at 30 miles an hour, and will continue to increase to probably 28 a minute in a 40-mile wind. Mill No. 3. This is a 12-foot Aermotor manu- factured by the Aermotor Company, of Chicago, Illinois. PI. IV shows the mill with its tower, pump, and pond, and fig. 7 shows its working parts. This mill had been in use about one year at the time of test, and all of the parts were in good working order. The tower is of wood, the axis of the wheel being 30 feet above the ground. The exposure is very good. The wheel has 18 curved sails, each 44 by 18f by 7| inches, set at an angle of 31 to the plane of the wheel. It is back-geared, 3^ to 1, and is held in the wind by a spring. The pump is of the Stone type, shown in figs. 8 and 9; the check valve is of the single-flap variety, the plunger valve of the double-flap variety. The cylinder is 9 inches in diameter, the supply pipe 4 inches in diameter, and the discharge pipe 10 inches in outside diameter; the length of stroke is 12 inches and the discharge per stroke 14-J quarts. The well is 4 feet by 4 feet to a depth of 8 feet nearly down to water. From that point to a depth of 18 feet it is 3 feet in diameter; and from there three pipes, 12 inches in diameter, extend down 5 feet farther. The lift at the time of test was 13| feet, the barometric pressure 27.2 inches, and the temperature 85 F. The water is pumped into a pond FIG. 7. Working parts of Aermotor 30 THE WINDMILL. [NO. 41. 80 feet by 75 feet, and a depth of 22 inches can be drawn off. The cost of the plant, including mill, tower, pump, and pond, was $145. The greatest number of strokes per minute is probably 27 or 28 in a 40-mile wind. In general appearance this curve is seen to resemble that of mill No. 2, but it is about 4 miles farther to the left, due to lighter load. The results of the tests are as follows: Results of tests of mitt No. 3 12-foot Aermotor. [Load per stroke, 415.3 foot-pounds.] Wind velocity per hour. Revolu- tions of wind wheel per minute. Strokes of pump per minute. Gallons pompedper minute. Useful horse power. 8 miles 17.7 5.3 19.3 067 12 miles 16 miles 40.0 54.7 12.0 16.4 43.5 59 5 0. 151 207 20 miles 25 miles .. ... 30 miles . 66.0 77.0 83.3 19.8 23.1 25.0 71.8 83.6 90.6 0. 250 0.291 0.315 The curve shown in fig. 10 is for a rather lightly loaded mill (415.3 foot-pounds per stroke). It starts at a velocity of 6 to 7 miles an hour, ascends less rapidly than the one shown in fig. 6, attains a maximum at about 15 miles an hour, when the number of strokes per mile is 62, and then descends slowly, reaching 50 strokes at 30 miles. The number of strokes per minute increases from about 5 at 8 miles to 25 at 30 miles. Mill No. 4- This mill, shown in the foreground of PI. V, is an 8-foot Ideal windmill manufactured by the Stover .Manufacturing Company, of Free- port, Illinois. It had been in use about one year, and all of the parts were in good condition. The tower is of wood, the axis of the wheel being 48 feet above the ground. The wheel has 15 sails, each 16^ by 7 by 30 inches, set at an angle of 29 with the plane of the wheel. It is back-geared, 2| to 1, and is held in the wind by a spring. The pump is of the Stone make. The diameter of the discharge pipe is 5f inches, of the supply pipe 3 inches. The length of stroke is 8 inches. The plunger and check valves are of the single-flap variety. The \\ell is 2f feet by 2| feet down nearly to water a depth of 5 feet. The o-inch supply pipe extends down to a depth of 1 1 feet, and on the end of it is a 3-ineh well point 6 feet long. The lift may vary from s.l to 20 foot. It \vas probably about 12 feet at the time of tests. The discharge per stroke was 2 quarts. The mean barometric pressure was ^7.1!) inches, the mean tempera- FIG. 8. Stone pump. MURPHY.] PUMPING MILLS TESTED. 31 tare 83 F. The water is pumped into a pond 115 feet by 31 feet and 3 feet deep. The cost of the plant, including mill, pump, well, and pond, was $80. The results of the'tests are as follows: Results of tests of mill No. 4 8-foot Ideal. [Load per stroke, 50 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of Dump per minute. Gallons pumped per minute. Useful horse- power. 12 miles 25.5' 10.2 5.1 0.015 16 miles 48.2 19.3 9.6 0.029 20 ini!es - 63.2 25.3 12.6 0.038 25 miles 70.3 28.1 14.1 0.043 30 miles - - . . 62.5 25.0 12.5 0.038 FK;. '.). Details of Stone pump: a, Lower valve seat; 6, ring guide to lower valve; c, lower or check valve; d, hook for removing lower valve; e, plunger and valve; / is a, 6, and c com- bined. The curve shown in fig. 11, although for a rather lightly loaded mill 50 foot-pounds per stroke shows that the mill starts in a 10- mile to an 11-mile wind. The maximum is reached at 19 miles, with a speed of 78 strokes. The right side of the curve is quite steep, a characteristic of this make of mill. Mill No. 18 is the same size and make as this mill, and yet with a load of 89.2 foot-pounds it starts in a 7-mile to an 8-mile wind, reaching a maximum at about 13 miles, at 32 THE WINDMILL. [NO. 41. 10 VELOCITY OP WIND IN MILES PER HOUR. 70 fid 50 40 20 10 FIG. 10. Diagram showing results with mill No. 3 12-foot Aeruaotor. 10 VELOCITY OP WIND IN MILES PER HOUR. 15 20 o o H5 50 1 40 FIG. 11. Diagram showing results with mill No. 4 8-foot Ideal. MURPHY.] PUMPING MILLS TESTED. 33 a speed of 104 strokes per mile. A second test, when the spring that holds the wind wheel in the wind was tightened somewhat, gave the maximum at a velocity of about 15 miles, with a pump speed of about 114 strokes. The difference appeared to be due to the difference in pumps and wells. The rapid fall in the curve to the right of the high- est point is due to the easy governing of the mill. Mill No. 5. This mill, shown in the background of PI. V, is an 8-foot Aermotor manufactured by the Aerinotor Company, of Chicago, Illinois. The tower is of wood, and is 28. 5 feet high to the axis of wheel. The exposure is good, and all of the parts were in good working order at the time of tests, the plant having been in use about one year. The wheel has 18 curved sails, each 30 by 12-j- by o^ inches, making an angle of 29-j- with the plane of the wheel. It is back-geared, 3 to 1. The pump is of the Stone make. The discharge pipe is 6 inches in diameter, the supply pipe 3 inches in diameter. The valves (check and plunger) are of the single-flap variety. The length of stroke is 8 inches. The well is 4 feet by 4 feet to water, a depth of 10. 5 feet. A 12-inch wooden curb extends 12 feet farther into the sand and gravel. The discharge per stroke was 3^ quarts, and the lift 13 feet. The cost of plant, including pond, was $80. VELOCITY OP WIND IN MILES PER HOUR. 10 15 20 35 ICO 70 a i 40 FIG. 12. Diagram showing results with mill No. 5 8-foot Aermotor. IRR 41 01 8 34 THE WINDMILL. The results of the tests of mill No. 5 are as follows: Results of tests of mill No. 5 8-foot Aermotor. [Load per stroke, 94.9 foot-pounds.] [NO. 41. "Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 12 miles 62.0 18.6 16 3 053 16 miles 83.7 25.1 22.0 072 20 miles 99.3 29.8 26.1 0.086 25 Tnilfis 115.3 34.6 30 3 099 30 miles 128.3 38.5 33.7 111 This 8-foot mill, with a load of 95 foot-pounds, is seen to start in an 8-mile to a 9-mile wind (fig. 12), reaching a maximum at 13 to 15 miles, with 95 strokes per mile. At 30 miles an hour it is making 77 strokes per mile, or 39 strokes per minute. This curve indicates a rather heavily loaded mill. Mill No. 6. This mill, shown in the background of PI. IV, is an 8-foot Gem, manufactured by the United States Wind Engine and Pump Company, of Kansas City, Missouri. The working parts of the mill are shown in PI. VI. The exposure was good and all of the parts were in good working order, the mill having been in use only about one year at the time of tests. The wheel has 24 curved sails, each 30| by 10 by 4 inches, set at an angle of 35 with the plane of the wheel. It is back-geared, 3 to 1. The wheel is held in the wind by means of a weight. The pump is of the Stone make. The discharge pipe is 6 inches in diameter, the supply pipe 4 inches in diameter. The length of stroke is 8 inches. The well is open to the water a depth of 6-J feet. The supply pipe is on a well point, the end of which is Ifi feet below the surface of the ground. The lift was 9 T ^ feet and the dis- charge per stroke 3.9 quarts. The tower is of wood, and is 24 feet high to the axis of the wheel. The mean barometric pressure was 27.02 inches, the mean temperature 85 F. The plunger valve is of the double-flap variety, and the check valve of the single-flap variety. The results of the tests are as follows: Results of tests of mill No. c, 8-foot Gem. [Load per stroke, 77.6 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. 12 miles 37.2 12.4 16 miles .:',. 7 17.9 20 miles 86.0 22.0 25 miles 76.2 25.4 30 miles 85. 5 28. 5 Gallons pumped per minute. Useful horse- power. 12. 1 0. 029 17.5 0.0-12 21.5 0.051 24. 7 0. 059 27.8 0.065 MURPHY.] PUMPING MILLS TESTED. 35 Comparing the number of strokes per minute of mills Nos. 4, 5, and 6, it is seen that although No. 5 is carrying a much heavier load than either of the other mills, it makes more strokes and does much more work at all velocities. Mill No. 7. This is a 12-foot Aermotor similar to mill No. 3. The tower is of steel, having a height of 31 feet to the axis of the wheel. The exposure was good and all of the parts were in good working order, the plant having been in use less than one year when tests were made. The pump is of the Stone make and is like that of mill No. 3, except that the check valve is of the solid-lift variety. The lift was 15-J- feet and the discharge 14.3 quarts per stroke. The water is pumped into a pond 135 feet by 50 feet by 2| feet. Comparing the results of the tests of this mill with those of mill No. 3, it is seen that the latter is somewhat more heavily loaded than the former and makes a few less strokes per minute, but that its horsepower is a little greater. The effect of the larger load is shown. The results of the tests of mill No. 7 are as follows: Results of tests of mill No. 7 12-foot Aermgtoj\ [Load per stroke, 461.9 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of puinp per minute. Gallons pumped per minute. Useful horse- power. 12 miles 38.0 11.4 40.7 0.160 16 miles 52.7 15.8 56.5 0.221 20 miles 63.3 19.0 67.9 0.266 25 miles . 73.7 22.1 79.0 0.309 30 miles 78.3 23.5 84.0 0.329 Mill No. 8. This is a 10- foot Star wooden mill, manufactured by Bradley, Wheeler & Company, of Kansas City, Missouri. The tower is of wood, and the axis of the wheel 35| feet above the ground. The water is pumped into an elevated tank 20 feet above the surface of the ground and is used for irrigation. The wheel has 60 plane sails, each 37 by 5 by 2f inches, set at an angle of 33 to the plane of the wheel. It is held in the wind by means of a weight. It is not back- geared, a stroke of the pump being made to each revolution of the wheel. The supply pipe is 2 inches in diameter and terminates in a well point, the end of which is 18 feet below the surface of the ground. The discharge pipe is 1 inches in diameter. The cylinder is 3 inches in diameter, the length of stroke 5 inches. The lift may vary between 28-J- and 37 feet. It was estimated to be about 30 feet at the time of measurement. The discharge per stroke was 0.24 quart. The cylin- der leaked some at the time of tests. After a new cylinder was put in the discharge per stroke was increased to 0.40 quart. The mean 36 THE WINDMILL. [NO. 41. barometric pressure was 27.04 inches, the mean temperature 78 F. The results of the tests are as follows: Results of tests of mill No. 8 10-foot Star icooden mill. [Load per stroke, 15 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 28.0 28.0 1.7 0.013 12 miles ... 30.0 30.0 1.8 0.014 These results show the effect of the very light load and the readi- ness with which the wind wheel turns out of the wind. It makes 28 strokes per minute in an 8-mile wind and less than that in a 16-mile or higher wind. Mill No. 9. This is a 16-foot Aermotor. The tower is of steel, and the axis of the wheel is 30 feet above the ground. The wheel has 18 10 VELOCITY OF WIND IN MILES PER HOUR. 15 30 25 80 till . 40 Fio. 13. Diagram showing results with mill No. 9 Itt-foot Aermotor. curved sails, each 59 by 25| by 10J inches, set at an angle of 30 with the plane of the wheel. It is back-geared, 3 to 1. The discharge pipe is 12 inches in diameter, the supply pipe 6 inches in diameter, the cylinder 8 inches in diameter. The stroke is 1 6 inches. The well is 4 feet by 6 feet to a depth of 23 feet, 2 feet by 2 feet for the next 8 feet, and 1 8 inches in diameter for the next 14 feet. The water was 39 feet below the surface of the ground. . The lift was 44J feet and the MURPHY.] PUMPING MILLS TESTED. 37 discharge per stroke 11 quarts. The check valve is of the single-flap variety and the plunger valve of the double-flap variety. The mean barometric pressure was 27.04 inches, and the mean temperature 93 F. This plant had been in use about three years. The results of the tests are as follows: Results of tests of mitt No. 9 16-foot Aermotor. [Load per stroke, 1,013 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 12 miles 31.8 10.6 29.1 0.325 16 miles 42.3 14.1 38.8 0.433 20 miles 51.6 17.2 47.3 0.548 25 miles 58.8 19.6 53.9 0.601 30 miles 63.0 21.0 57.7 0.644 The curve shown in fig. 13 starts at a wind velocity of 8 to 9 miles, and reaches a maximum at 13 miles, with a speed of 53 strokes per mile. From that point to a velocity of about 19 miles the curve is nearly horizontal; after 19 miles it descends slowly to 32 miles, with 38 strokes per mile. The speed increases from 11 strokes per minute at 12 miles to 21 strokes per minute at 30 miles an hour. Mill No. 10. This is an 8-foot Ideal. The tower is of wood, the axis of the wheel being 30 feet above the ground. The wheel has 15 curved sails, each 31 by 19 by 7 inches, set at an angle of 29-J- with the plane of the wheel. It is back-geared, 2-j- to 1. The supply pipe- is 1-j- inches in diameter, the cylinder 2-J- inches in diameter. The pump is a common hand pump, with lift valve of the flap form and plunger of the lift variety. The valves leak some, as the discharge is greater when the pump is working rapidly than when it is working slowly. The supply pipe is on a well point 2 feet long and 1-J inches in diameter, the lower end of which .is 50 feet below the surface of the ground. The lift was 33 feet and the discharge per stroke one-third of a quart when pumping quite rapidly. The mean barometric pres- sure was 26. 94 inches, the mean temperature 97 F. The results of the tests are as follows: Results of tests of mitt No. 10 8-foot Ideal. [Load per stroke, 22. 8 foot-pounds. ] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 35 2 14 1 1 2 010 12 miles 62 5 25 2 1 0017 16 miles 83 2 33 3 2 8 03 20 miles 032 38 THE WINDMILL. [NO. 41. Mill No. 11. This is a 12-foot Ideal, the working parts of which are shown in fig. 14. The tower is of steel, the axis of the wheel being 30 feet above the ground. The exposure was good, and all of the FIG. 14. Working parts of mill No. 11 13-foot Ideal. parts were in good working order when mill was tested. The wheel has 21 curved sails, each 31 by 19 by 7 inches, set at an angle of 29| to the piano of t.h<> wheel. II is b;i<-k-ivaivd, 24 to 1, and the wheel MURPHY.] PUMPING MILLS TESTED. 39 is held in the wind by a spring. The discharge pipe is 8 inches in diameter, and the length of stroke is 12 inches. The supply pipe consists of two 3-inch pipes 14 feet long, each terminating in a 3-inch well point 3 feet long. The valves (check and plunger) are of the single-flap variety. The water was 39 feet below the surface of the ground. The lift, as nearly as could be ascertained at the time of measurement, was 45 feet, the discharge per stroke 9 quarts. The water is pumped into a pond 60 feet by 40 feet by 6 feet. This plant had been in use about three years. The mean barometric pressure was 26.91 inches, the mean temperature 91 F. The results of the tests are as follows : Results of tests of mill No. 11 12-foot Ideal. [Load per stroke, 843.7 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 12 miles 12.0 4.8 10.8 0.123 16 miles 31.7 12.7 28.6 0.325 20 miles . - 47.0 18.8 42.3 0.481 25 miles . 58.2 23.3 52.5 0.600 30 miles 62.5 25.0 56.2 0.639 Mills Nos. 9 and 11 pump water into the same pond from the same depth. It will be seen from these results that for wind velocities of 10 VELOCITY OF WIND IN MILES PER HOUR. 15 30 25 40 30 10 FIG. 15. Diagram showing results with mill No. 11 13-foot Ideal. 40 THE WINDMILL. [NO. 41. 20 miles or more the 12-foot mill is pumping nearly as much water as the 16-foot mill; for velocities of 12 miles or less the 16-foot mill is pumping much more water than the 12-foot mill. This curve (fig. 15) is for a heavily loaded (843.7 foot- pounds per stroke) 12-foot mill. It starts with a velocity of about 10 miles an hour, and reaches a maximum at about 23 miles, with a speed of 57 strokes per mile. At 30 miles it is making 51 strokes per mile. The maxi- mum point of this curve is much farther to the right than that of any other curve. The number of strokes increases from 5 per minute at 12 miles to 25 per minute at 30 miles. Mitt No. 12. This is a 14-foot Ideal, shown in PL VII. The tower is of steel and is 30 feet high to the axis of the wheel. The wheel has 24 curved sails, each 48f by 17-J- by 8 inches, set at an angle of 30 with the plane of the wheel. It is back-geared, 2-J- to 1. The pump is of the Frizell make (shown in fig. 16). The discharge pipe is 10 inches in diameter, the cylinder 9| inches in diameter, the supply pipe 6 inches in diameter, ter- minating in a well point 10 feet long and 6 inches in diameter, the lower end of which is 32 feet below the surface of the ground. The lift, as nearly as could be estimated, was 11 fed, the dis- charge per stroke 11. (J quarts. The mean barometric pressure was 27.04 indies, the mean tern- FK,ir,-Workin g parts of Prize., cyHnder. I"'' >< '"'<' *1" *' The Water U pumped into a reservoir KM) feet by 100 feet by 3 feet deep. The pump had been in use about one year. The results of the tests are as follows: U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 41 PL. VI WORKING PARTS OF MILL NO. 6 8-FOOT GEM. MURPHY.] PUMPING MILLS TESTED. 41 Results of tests of mill No. 12 14-foot Ideal. [Load per stroke, 363.5 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 7.7 3.1 8.9 0.025 12 miles 27.2 10.9 30.1 0.087 16 miles 39.3 15.7 45.1 0.125 20 miles 48.0 19.2 55.2 0.153 25 miles . ..... 53.7 21.5 61.8 0.173 This curve (fig. 17) is for a very lightly loaded (263.5 foot-pounds) 14-foot mill. This load is only 31 per cent of that of the 12-foot mill, No. 11. The curve starts in a 7-mile to an 8-mile wind, and reaches a maximum at 15 miles, with a speed of 58 strokes per mile of wind. At 30 miles the speed is 47 strokes. Although this is a very lightly 10 VELOCITY OF WIND IN MILES PER HOUR. 15 30 60 1C FIG. 1?. Diagram showing results with mill No. 13 14-foot Ideal. loaded mill it does not make many strokes per minute. In fact, although it is not as heavily loaded as the 12-foot mill, No. 3, it does not make as many strokes per minute as the latter mill, and it is pro- ducing much less power than mill No. 3. Mitt No. 13. This is a 12-foot Aermotor (shown in PL VIII). The tower is of wood, with the axis of the wheel 25 feet above the ground. The exposure was good and the plant in excellent condition, having 42 THE WINDMILL. [NO. 41. been in use about one year at the time of tests. The wheel is the same as that of No. 3. The pump is of the Stone make. The discharge pipe is 10 inches in diameter, the supply pipe 5 inches in diameter, on a well point 10 feet long, the lower end of which is 17 feet below the surface of the ground. The length of stroke is 12 inches. The plunger valve is of the double-flap type, and the check valve of the single-flap type. The discharge per stroke at the time of test was 14.4 quarts and the lift about 11 feet. The mean barometric pres- sure was 27.09 inches, the mean temperature 91 F. The results of the tests are as follows: Results of tests of mill No. 13 12-foot Aermotor. [Load per stroke, 330 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 12 miles . 36.7 11.0 39.6 0.110 16 miles 57.0 17.1 61.6 0.171 20 miles . . 70.0 21.0 75.6 0.210 25 miles 82.0 24.6 88.6 0.247 30 miles 91.7 27.5 99.0 0.275 The important difference between this plant and No. 3 is that the latter has a 4-inch supply pipe and an open well, while the former has a 5-inch supply pipe on a well point. The useful load per stroke of mill No. 13 is 20 per cent less than that of mill No. 3, and the num- ber of strokes per minute of No. 13 is slightly greater than that of No. 3. It appears that the well point offers some resistance, but how much can not be said from this data. Mitt No. 14- This is a 12-foot Gem, like the one shown in PI. IX, on a 60-foot steel tower. The pump is of the Gause make. The cylinder is 8 inches in diameter, the length of stroke 9 inches. The supply is from a 12-inch pipe in an open well. The discharge per stroke was 9f quarts and the lift 15-J- feet. The wind velocity was not measured. Mill No. 15. This is a 10-foot Gem similar to that shown in PL IX. The tower is of wood, the axis of the wheel being 34 feet above the ground. The mill was in good working order, but the exposure was not good, on account of trees. The wheel has 24 sails, each 36 by 11 by 4f inches, set at an angle of 35 with the plane of the wheel. It is back-geared, 3 to 1. The pump is of the Stone make. The dis- charge pipe is 8 inches in diameter. The supply pipe is on a 3-inch well point 8 feet long, the lower end of which is 21^ feet below the sur- face of the ground. The plunger valve is of the single-flap form. Depth to water is 10 feet. The discharge per stroke was 7 quarts, the lift about 15 feet. The mean barometric pressure was 27.05 inches, the mean temperature 84 F. lit MTIRPHY.I PUMPING MILLS TESTED. The results of the tests are as follows: Results of tests of mill No. lf> 10-foot Gem. [Load per stroke, 219 foot-pounds.] 43 Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 12 miles 23.4 7.8 13.6 0.053 16 miles 35.7 11.9 21.0 0.082 20 miles 44.1 14.7 25.7 0.101 25 miles 43.8 14.6 25.5 0.099 This mill revolves very slowly, indicating a heavy load. Its useful horsepower, however, is little greater than that of mill No. 5. Mill No. 16. This is a 10-foot Halliday, pumping water into the same pond as No. 15. It is similar to the mill shown in fig. 20. The tower is of wood, the axis of the wheel being 28 feet above the ground. The wheel has 78 sails, each 36 \ by 4 by 2^ inches, set at an angle of 35.5 to the plane of the wheel. It is not back-geared. The pump is of the Gause make, with a discharge pipe 6 inches in diame- ter and a supply pipe 4 inches in diameter. There is a 6-inch galvan- ized-iron pipe, forming an open well, extending 15 feet into the water. The depth to water was 11 feet, the lift 16 feet, and the discharge per stroke 3 quarts. The mean barometeric pressure was 27.02 inches, the mean temperature 94 F. The results of tests are as follows : Results of tests of mill No. 16 10-foot wooden Halliday. [Load per stroke, 100 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 4.0 4.0 3.0 0.012 12 miles . 22.6 22.6 16.9 0.067 16 miles 33.9 33.9 25.4 0.103 20 miles... 42.7 42.7 32.0 0.130 25 miles 52.5 52.5 39.3 0.159 This 10-foot wooden mill is seen to be doing more useful work than the 10-foot steel Gem, No. 15. Usually, however, the direct-stroke wooden mills do less work than the back-geared steel mills of the same size. Mill No. 17. This is a 12-foot improved Gem on a 30-foot steel tower. The wheel has 32 curved sails, each 42 by 11-J- by 4f inches, set at an angle of 37 with the plane of the wheel. It is back-geared, 2 to 1. The pump is of the Gause type, with an 8-inch discharge pipe, a 4-inch supply pipe, 12 inches stroke, and an open well formed of a 12- inch wooden casing. The depth to water was 17^ feet, and the 44 THE WINDMILL. [NO. 41. discharge per stroke 8f quarts. The mean barometric pressure was 27.05 inches, the mean temperature 93 F. The results of the tests are as follows : Results of tests of mill No. 17 12- foot improved Gem. [Load per stroke, 385 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 12 miles 12 6 12 7 070 16 miles 25 6 12 8 27 2 149 20 miles 34.6 17.3 36 8 202 This mill, although nearly new, does not work well. It is out of plumb. Only a few measurements of the number of strokes per mile of wind were made. Mill No. 18. This is an 8-foot Ideal on a 36-foot wooden tower. The exposure was good and the parts in good working order. The wheel is like that of mill No. 4. The pump is of the Stone make, with a 6-inch discharge pipe. There is no supply pipe, the cylinder being under water, with 3 inches opening to it from below. The check valve is of the lift variety, the plunger valve of the single-flap variety. The well is dug to a depth of 8 feet. It is 4 feet in diameter. In the bottom a 10-inch galvanized-iron pipe extends down several feet. It was 11 feet to water. The lift was 14 J feet and the discharge per stroke 2.92 quarts. The mean barometric pressure was 27.01 inches, the mean temperature 83 F. The cost of the plant, including pond, was $125. The results of the tests are as follows: Results of tests of mill No. 18 8-foot Ideal. [Load per stroke, 89.2 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 20.0 8.0 5 8 022 12 miles 50.5 20.2 14.6 0.054 16 miles 65.2 26.1 18.9 0.070 20 miles . . 70.0 28.0 20.3 0.076 25 miles 68.7 27.5 19.9 0.074 After the spring which holds the wind wheel of this mill in the wind was tightened, the number of strokes per mile of wind was increased from 98 to 114 in a 16-mile wind, from 84 to 102 in a 20-mile wind, and from 66 to 79 in a 25-mile wind. Mill No. 19. This is a 12-foot Gem (shown in PL IX) on a 30-foot wooden tower. The exposure was good and the mill in good work- ing order. The wheel is like that of mill No. 17. The pump is of the Stone make, with ;i 10-inch discharge pipe and a 4-inch supply VIEW OF MILL NO. 19 12-FOOT GEM. MURPHY.] PUMPING MILLS TESTED. 45 pipe. The length of the stroke is 10 inches. The supply pipe is on a 4-inch well point 9 feet long, the end of which is 23 feet below the surface of the ground. The check valve is of the lift type and the plunger valve of the single-flap type. The lift was about 18 feet and the discharge per stroke 12 quarts. The mean barometric pressure was 27.13 inches, the mean temperature 70 F. The water is pumped into a reservoir 120 feet by 60 feet. The results of the tests are as follows : Results of tests of mill No. 19 12-foot Gem. [Load per stroke, 450 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Stroke of pump per minute. Gallons pumped per minute. Useful horse- power. 12 miles 12.4 6.2 18.6 0.085 16 miles 23.8 11.9 35.7 0.162 20 miles 29.4 14.7 44.1 0.201 25 miles 32.0 16.0 48.0 0.219 This curve (fig. 18) shows that a 9-mile wind is necessary to start this mill, and that the greatest number of strokes per mile of wind 10 VELOCITY OF WIND IN MILES PER HOUR. 15 20 40 30 FIG. 18. Diagram showing results with mill No. 19 12-foot Gem. is 45 about 25 per cent less than most 12-foot steel back-geared mills, being at the rate of 6 strokes at 12 miles and 16 strokes at 25 miles an hour. The load of this mill is somewhat greater than that of No. 3, and its power should be equal or greater, but it is seen to be much less. U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 41 PL. XI VIEW OF MILL NO. 21 12-FOOT HALLIDAY. MURPHY.] PUMPING MILLS TESTED. 47 Mitt No. %!. This is a 12-foot Halliday (shown in PI. XI) on a 31- foot wooden tower. It was made by the United States Wind Engine and Pump Company, of Batavia, Illinois. The working parts are FIG. 20.-Working parts of Halliday mill: A, bed plate; A', fan arm; , turntable; B', regu- lating rod; C, front plate; C", assisting weight; A sliding head ; E, tie rod; F, forked lever; F', fans or sails; G, truss frame; H, truss rod; L, pitman; I/, fan lever; If, crank plate; 31' If', masts; P, weight lever; R, shut-off rod ; R' , shut-off rod lever; S, main shaft; -S", sleeve; F, vane; F', vane arm; TT, weight; W, counterweight; JT, swivel box; F, spider; Z, sliding box. shown in fig. 20. The wheel has 64 sails, each 42| by 5 by 2f inches, set at an angle of 35 with the plane of the wheel. It is not back- geared, and regulates itself on the centrifugal principle the sails 48 THE WINDMILL. [NO. 41. taking the direction of the wind. The pump is of the Stone make, with 7|-inch discharge pipe, 4-inch supply pipe, and 7 inches stroke. The check valve is of the lift variety, the plunger valve of the double-flap variety. The well, which is open, is formed by a wooden curb, 12 inches in diameter, sunk in the bottom of a dug well 9 feet deep. The depth to water was 11 feet and the lift 11 feet. The dis- charge per stroke was 4-J quarts when pumping quite rapidly (30 strokes per minute). The valves were not in very good repair and the pump lost its priming after a time. The results of the tests are as follows: Results of tests of mill No. 21 12-foot wooden Halliday. [Load per stroke, 141.5 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 12 miles.. _. . . 14.0 14.0 15 9 060 16 miles 28 5 28 5 32 1 121 20 miles . 37.3 37 3 42 159 25 miles 44.6 44.6 50 2 184 This curve (shown in fig. 21), which is for a lightly loaded (141.5 foot-pounds) direct-stroke 12-foot mill, will be seen to start at a wind 10 VELOCITY OF WIND IN MILES PER HOUR. 15 30 130 100 80 FIG. 21. Diagram showing results with mill No. 31 12-foot Halliday. velocity of 9 to 10 miles and to reach a maximum at 19 miles, with a speed of 112 strokes per mile. At 30 miles the number of strokes is MURPHY.] PUMPING MILLS TESTED. 49 about 98 per mile. The number of strokes per minute varies from 14 at 12 miles to 45 at 25 miles. The power of this mill is only about half that of the 12-foot Aermotor, No. 3. Mill No. 25. This is an 8-foot steel mill on a 32-foot steel tower, made by Fairbanks, Morse & Company. The wheel has 18 curved sails, each 29 by llf by 5 inches, set at an angle of 29 with the plane of the wheel. It is back-geared, 2^ to 1. The pump is of the com- mon hand variety, with a 2^-inch cylinder, 1^-inch supply and dis- charge pipes, and 4 inches stroke. The well is open, 6J feet to water. The discharge per stroke was 0. 31 quart and the lift 8-J feet. The water raised is used for watering stock. The results of the tests are as follows: Results of tests of mill No. 25 8-foot Fairbanks-Morse steel mill. [Load per stroke, 5.5 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 30.7 12 3 1 002 12 miles 73.0 29 2 2 3 005 16 miles 93.2 37.3 2 9 007 20 miles . 95.0 38 3 008 25 miles. 83.2 33.3 2 6 005 VELOCITY OF WIND IN MILES PER HOUR. 10 15 20 25 o co 20 This is a very lightly loaded mill only 5.5 foot-pounds per stroke of pump. The number of strokes per minute in light winds is large; the number of strokes per minute in a 25-mile wind is only 33.3, compared with 38 in a 20-mile wind. A comparison of this mill with No. 5 will show the difference between a small pumping outfit for stock pur- poses and one for irrigation. Mill No. 30. This is a 16-foot Irrigator manufactured by M. Schow, of Kinsley, Kansas. It is a power mill, but not geared for- ward, and works a pump called a ' ' water elevator. " The tower is of wood, 22 feet to axis of wheel. The wind wheel has 10 plane wooden sails, each 70 by 16 by 13 inches, set at an angle of 39 to the direction of the wind. The vertical shafting is geared back 30 to 13, and the horizontal shaft is geared forward 13 to 30. The water is lifted from a well 8 feet IRR 4101 4 o 10 9 FIG. 22. Diagram showing revolutions of wind wheel of mill No. 30 16-foot Irrigator. AB is for a load of 32 foot-pounds per revolution of wind wheel; CD is for a load of 251 foot-pounds; ED is for a useful pump load of 337 foot-pounds. 50 THE WINDMILL. [NO. 41. by 10 feet (7 feet depth to water), cased with wood. The buckets of the elevator are made of galvanized iron and are 14 by 7-J- by 5-j- inches, set 18 inches center to center, and hold 3 gallons each. Each bucket has a valve in its bottom. The lift is about 11 feet, and there are 20 buckets on the elevator chains. There is a box in fche bottom of the well into which the buckets dip to get their supply of water. This box has a screen in its bottom to keep out the sand. The mill does not govern well, on account of side draft. The mean barometric pressure was 27.7 inches, the mean temperature 72 F. The results of the tests are as follows : Results of tests of mill No. 30 16-foot Irrigator. Load on brake. Load per rev- olution of wind wheel. Number of revolutions of wind wheel per minute at given wind velocities (per hour). Useful horsepower at given wind velocities (per hour). 8 miles. 12 miles. 15 miles. 30 miles. 25 miles. 8 miles. 13 miles. 15 miles. 20 miles. 25 miles. Pounds. 2 16 Pump. Ft.-lbs. 32 251 837 12 26 19 14 33 39 36 41 39 38 44 4/W 43 0.013 0.025 0.140 0.140 0.032 0.220 0.250 0.040 0.300 0.400 0.043 0.320 0.440 .2 Fig. 22 shows the number of revolutions per minute of the wind wheel for three loads. Fig. 23 shows the horsepower for these loads. VELOCITY OF WIND IN MILES PER HOUR. Comparing the useful pump 10 15 20 25 horsepower of this mill with that of the 16-foot mill No. 9, it will be seen that this mill is not so powerful as No. 9. The power of the Aermotor for low velocities is much greater than that of the Irrigator. Mill No. 31. This is a 14-foot Elgin wooden power mill, manu- factured at Elgin, Illinois. It works a rotary (Wonder) pump. The wind wheel is on a 48-foot wooden tower. It has 88 plane wooden sails, each 52 by G by 34 inches, set at an angle of 37 to the plane of the wheel. It is a sectional vaneless wheel; in place of the vane there is a heavy counterpoise. The wheel is geared forward about 7.19 to 1. The rotary pump is a 3 inch. It is on a well point G inches in diameter and 8 feet long; the point penetrates the water to a deptli of 8 feet. The lift was about 18 feet. The suction and discharge pipes FIG. 23. Diagram showing horsepower of mill No. 30. Curve AB shows the horsepower for a 33 foot-pound load; CD, the power for a 251 foot- pound load ; EF, the power for a 3137 foot-pound load ; dotted curve shows maximum horsepower for best load. MUKPHY.] PUMPING MILLS TESTED. 51 are each 3 inches in diameter. The discharge was 2 quarts per revo- lution of pump. The pump is manufactured by the National Pump Company, of Kansas City, Missouri. In a 15-mile to a 20-mile wind the windmill worked the pump before priming, but would not start it in that wind after priming. After several attempts of the mill to start the pump the pulley turned on the shaft so that it could not be used. It was very evident that the pump was too great a load for the mill. The owner stated that the mill would only run during a strong wind. Mill No. 32. This mill is like the 12-foot Aermotor, the working parts of which are shown in fig. 7. It is on a 40-foot steel tower. The wheel has 18 curved sails, each 44 by 18f by 7f inches, set at an angle of 31 to the plane of the wheel. The pump is of the Wood- manse t} 7 pe, a sectional view of which is shown in fig. 5, and has an 8-inch cylinder and 12 inches stroke. It is in an open well. The depth to water was 14 feet, the lift 20 feet, and the discharge per stroke 7 quarts. It is back-geared, 3 to 1. The water is pumped into a pond and used for irrigation. The mean barometric pressure was 27.9 inches, the mean temperature 82 F. The results of the tests are as follows : Results of tests of mill No. 32 12-foot Aermotor. [Load per stroke, 313 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. Smiles 17.7 5.3 9.3 0.047 12 miles 49.3 14 8 25.9 131 15 miles 60.0 18.5 32.4 0.164 20 miles 73.0 22.0 38.5 0.195 Mill No. 33 This is a 10-foot Woodmanse pumping mill on a 40-foot steel tower. The working parts are like those shown in fig. 4. The wheel has 24 curved sails, each 30^ by 12| by 5^ inches, set at an angle of 29 to the plane of the wheel. It is back-geared, 2-j- to 1. The pump is of the Woodmanse make (like that shown in fig. 5), with a 6-inch cylinder and 10 inches stroke. The depth to water was 14 feet. The pump is on a well point 3 inches in diameter, 4 feet long, and 67 feet below the surface of the ground. The suction pipe is 3 inches in diameter, the discharge pipe 6 inches in diameter. The lift was about 22 feet, the discharge per stroke 3f quarts. The water is pumped into a pond and used for irrigation. The mean barome- tric pressure was 27.9 inches, the mean temperature 88 F. 52 THE WINDMILL. The results of the tests are as follows: Results of tests of mill No* 33 10-foot Woodmanse. [Load per stroke, 173 foot-pounds.] [NO. 41. Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 8.7 3.5 3.3 0.020 12 miles 36.0 14.4 13.5 0.075 15 miles 51.2 20.5 19.2 0.110 Mill No. 35. This is an 8-foot steel Dempster pumping mill, manu- factured by the Dempster Manufacturing Company, of Beatrice, Nebraska, and is shown in PI. XII. The tower is of steel, 80 feet to axis of wheel. The wind wheel has 18 curved sails, each 30 by 14-j- by 7 inches, set at an angle of 27 to the plane of the wheel. It is back- geared, 3 to 1. The well is an open dug well. The distance from the surface of the ground to the water was 39 feet. The water is pumped into a tank 22 feet above ground, and is used for irrigation. The pump has an 8-inch stroke, a 3^-inch cylinder, and 2-inch suction and discharge pipes. The lift was 58 feet, the discharge per stroke 1.1 quarts. The mean temperature was 51 F. , the mean barometric pres- sure 28.9 inches. The results of the tests are as follows: Results of tests of mill No. 35 8-foot steel Dempster. [Load per stroke, 133.5 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 12 miles 57.6 19.2 5.3 0.077 16 miles 86.4 28.8 7.9 0.116 20 miles 99.9 33.3 9.2 0.134 In a 15-mile wind the pump made 26 to 27 strokes per minute, and when the pump rod was uncoupled from the pump it made 34 strokes per minute in the same wind. Fig. 24 shows the number of strokes per minute for different wind velocities. This mill is heavily loaded 133 foot-pounds per stroke of pump. It starts at a wind velocity of about 9 miles an hour, and as the wind increases the number of strokes increases rapidly at first, then more slowly. At 25 miles an hour the number of strokes is 37 per minute. This mill is back-geared, 3 to 1, so that in a 25-mile wind the wind wheel makes 111 revolutions per minute and has a circumference velocity of 46.5 feet per second. Mill No. 36. This is a 22|-foot Eclipse wooden pumping mill, lift- U. S. GEOLOGICAL SURVE VIEW OF MILL NO. 35 8-FOOT DEMPSTER. MURPHY.] PUMPING MILLS TESTED. 53 40 30 ing water into a tank for railroad purposes. The tower is of wood, 52 feet to the axis of the wheel. The wind wheel has 136 plane sails, each 105 by 6 by 2 inches, set at an angle of 39 to the plane of the Wheel. It works by direct VELOCITY OF WIND IN MILES PER HOUR. stroke. The well, which is in 15 20 25 open, is 20 feet in diameter; the depth to water was 19 feet from the surface of the ground. The pump is double-acting, and has a 44-inch cylinder, 7 inches stroke, and 2-inch suction and discharge pipes. The lift was 39 feet. The tank is 90 feet from the well. The discharge could not be measured, but as the pack- ing of the pump was new it was approximately equal to twice the volume of the 10 FIG. 24. Comparative diagram showing results with mills No. 35 (8-foot Dempster) and No. 36 (22Hoot Eclipse). cylinder, or 0.76 gallon per double stroke. The mean temperature was 58 F., the mean barometric pressure 29.43 inches. The results of the tests are as follows : Results o/ tests o/ mill No. 36 22%-foot wooden Eclipse. [Load per stroke, 248 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 4.8 4.8 3.8 0.036 12 miles 12.0 12.0 9.4 0.090 16 miles. 16.5 16.5 12.8 0.124 20 miles.. . 20.0 20.0 15.6 0.150 25 miles 24.2 24.2 18.8 0.182 Fig. 24 shows the strokes per minute at different wind velocities. The diagram is seen to be quite different from that of mill No. 35. The mill starts at a wind velocity of 6 or 7 miles an hour, and increases gradually to 24 strokes in a 25-mile wind. The circumfer- ence velocity of the latter is 46.5 feet per second, that of the former 29 feet. The wind wheel of this mill is making 24 revolutions per minute; that of No. 35 is making 111 revolutions per minute in a 25-mile wind. Mitt No. 37. This is a 12-foot steel Woodrnanse Mogul like that shown in fig. 4. It pumps water into a pressure tank 9-J- feet by 2 feet in a cellar and about 170 feet from the well. The pump and pressure 54 THE WINDMILL. [NO 41. tauk are shown in fig. 25. The tower is of steel, and is 40 feet to the axis of the wheel. The wind wheel has 30 curved sails, each 37 by 13 by 5.5 inches, set at an angle of 29 to the plane of the wheel. The well is 50 feet deep and 8 inches in diameter; the depth to water was 42 feet. The pump has a 3-inch cylinder and 9 inches stroke. The discharge pipe is 1 inch in diameter, the suction pipe 1 inches in FIG. 25. Pump, pressure tank, and hydraulic regulator of mill No. 37 -12 foot Woodnmnse Mogul. diameter. The discharge per stroke was 1.05 quarts. The load on the pump was equal to 43 feet head of water (the friction in about 200 feet of 1-inch pipe) and a compressed-air pressure the amount of which was recorded on a gage. The mean temperature was 00 F., the mean barometric pressure 29.1 inches. The results of the tests are as follows : MURPHY.] PUMPING MILLS TESTED. Results of tests of mill No. 37 12-foot steel Woodmanse Mogul. 55 6 1 Number of strokes of pump per min- ute at given wind velocities (per hour). Useful horsepower at given wind velocities (per hour). 8 miles. 12 miles. 16 miles. 20 miles. 1 i 8 30 miles. 8 miles. 12 miles. 16 miles. 1 i 8 1 i & 1 1 8 Ft.-lbs. 94 254 350 473 7.7 18.4 12.2 24.5 19.0 29.3 23.3 18.0 10.7 34.2 26.7 21.0 38.0 29.0 21.5 0.022 0.053 0.094 0.071 0.146 0.083 0.180 0.191 0.153 0.097 0.205 0.223 0.108 0.223 0.228 Fig. 26 shows the number of strokes per minute for different wind velocities for four useful pump loads, viz, 43 feet, 43 feet plus 32 pounds, 43 feet plus 50 pounds, and 43 feet plus 75 pounds, or, reducing the pounds pressure to head in feet, the four useful loads are: 43 feet for the curve aa', 116 feet for VELOCITY OF WIND IN MILES PER HOUR. 10 15 20 25 the curve bb', 160 feet for the curve cc', and 216 feet for the curve dd'. The effect of in- creased load on the number of strokes is well shown here. The effect of the hydraulic regulator may be seen in the curve cc', but it is shown to a greater extent in the curve dd'. Mill No. 38. This is a 10-foot Woodmanse wooden mill on a 30-foot wooden tower, and is used to pump water for stock. The wind wheel has 96 plane sails, each 34 by 3| by 1 inches, set at an angle of 38 to the plane of the wheel. The well is driven and is 107 feet deep; the depth to water was about 44 feet. The pump works direct and has a 2^-inch cylinder and 4 inches stroke. The lift was about 50 feet, and the discharge per stroke of pump -fa gallon. PIG. 26. Diagram showing results with mill No. 37 12- foot Woodmanse Mogul. The curve aa' is for a useful pump load of 43 feet head; bb' is for a useful pump load of 116 feet head; cc' is for a useful pump load of 160 feet head; dd' is for a use- ful pump load of 216 feet head. The effect of the hydraulic regulator is shown in the curves cc' and dd'. 56 THE WINDMILL. The results of the tests are as follows : Results of tests of mill No. 38 10-foot wooden Woodmanse. [Load per stroke, 21 foot-pounds.] [NO. 41. Wind velocity per hour. Revolutions of wind wheel per minute, Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 18 18 9 012 12 miles . . . 29 29 1.5 0.019 16 miles 36 36 1.8 0.023 20 miles 41 41 2 1 026 25 miles 46 46 2.3 0.029 Fig. 27 shows the number of strokes per minute for different wind velocities. This is a lightly loaded mill, working direct stroke. It VELOCITY OF WIND IN MILES PER HOUR. 10 15 20 25 50 10 FIG. 27. Comparative diagram showing results with mills No. 38 (10-foot wooden Woodmanse) and No. 48 (30-foot wooden Halliday). starts in a 5-mile wind ; the number of strokes increases very rapidly at first, and more slowly for high velocities. In a 30-mile wind the number of strokes per minute is 50. The circumference velocity of this wheel in a 25-mile wind is 24 feet per second. Mill No. 39. This is a 10-foot Woodmanse direct-stroke iron pump- ing mill, used to pump water for stock. The tower is of iron, 35 feet to the axis of the wheel. The wind wheel has 18 curved sails, each 30 by 12 by 7f inches, set at an angle of 40 to the plane of the wheel. The pump is on a well point 24 feet below the surface of the ground. It has a stroke of 6 inches, a 3^-inch cylinder, and 1^-inch suction and discharge pipes. The lift was about 27 feet, the discharge per stroke 1 quart. The results of the tests are as follows : MURPHY.] PUMPING MILLS TESTED. 57 Results of tests of mill No. 39 10-foot iron Woodmanse. [Load per stroke, 36 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 15 15 3.7 0.017 12 miles 30 30 7.5 0.034 16 miles 40 40 10.0 0.044 20 miles . ... 47 47 11.7 0.052 Mill No. 40. This is an 8-foot steel pumping mill manufactured by Fairbanks, Morse & Company. It is used to pump water for stock. It is on a 30-foot steel tower. The wind wheel has 18 curved sails, each 29 by 10^ by 5 inches, set at an angle of 29 to the plane of the wheel. It is back-geared, 2^- to 1. The pump is on a well point 20 feet below the surface of the ground. It has a stroke of 6 inches, a 3^-inch cylinder, and 1^-inch suction and discharge pipes. The lift was about 22 feet, and the discharge per stroke -^ gallon. The results of the tests are as follows : Results of tests of mill No. 40 8-foot Fairbanks-Morse steel mill. [Load per stroke, 13 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 32.5 13.0 0.8 0.005 12 miles. . ... 55.0 22.0 1.5 0.009 16 miles 72.0 29.0 1.9 012 20 miles 85.0 34.0 2.3 0.014 Mill No. Jt-1. This is a 12-foot Woodmanse direct-stroke iron pump- ing mill, used for pumping water for stock. The tower is of iron, 30 feet to the axis of the wheel. The pump has a 3-inch cylinder and 6 inches stroke. The wind wheel has 24 curved sails, each 36 by 14-J by 7f inches, set at an angle of 39 to the plane of the wheel. The lift was 28 feet, and the discharge per stroke ^ gallon. The results of the tests are as follows : Results of tests of mill No. 41 12-foot iron Woodmanse. [Load per stroke, 29 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 14 14 1 7 012 12 miles 25 25 3 1 022 16 miles. .. 33 33 4.1 029 20 miles . 40 40 5 036 58 THE WINDMILL. [NO. 41. Mill No. 4%- This is a 6-foot Ideal pumping mill on a 22-foot steel tower, and is used for pumping water for stock. It is shown in PI. XIII. The wheel has 12 curved sails, each 26 by 14 by 5 inches, set at an angle of 39 to the plane of the wheel. It is back-geared, 4 to 1. The well is a dug well; depth to water, 15 feet. The pump has a 3-inch cylinder and 6 inches stroke. The lift was 16 feet, the discharge per stroke 1 quart. The results of the tests are as follows: Results of tests of mill No. 42 6-foot Ideal. [Load per stroke, 35 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 16 4 1.0 004 12 miles 52 13 3.2 014 16 miles .._ 76 19 4.7 0.020 20 miles - 92 23 5.7 0.024 FKJ. as. View of mill No. 43 10-foot Perkins. This is the smallest mill yet tested. It is rather heavily loaded for its size; in fact, it is more heavily loaded than the 12-foot mill No. 41. It is doing very good work for a mill of its size. MURPHY.] PUMPING MILLS TESTED. 59 Mill No. 43. This is a 10-foot Perkins direct-stroke pumping mill on a 32-foot steel tower, and is used to pump water for stock. The working parts are shown in fig. 28. The wind wheel has 30 curved sails, each 30 by 10J- by 5 inches, set at an angle of 29 to the plane of the wheel. The pump is on a well point 34 feet below the surface of the ground. It has a 3-inch cylinder and 4 inches stroke. The lift was about 36 feet, the discharge per stroke | quart. The exposure was not good. The results of the tests are as follows: Results of tests of mill No. 43 10-foot Perkins. [Load per stroke, 37 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 20 20 2.5 0.022 12 miles 32 32 4.0 0.035 16 miles 41 41 5.1 0.045 20 miles 45 45 5.6 0.050 Mill No. 4$- This is a 10-foot Eclipse direct-stroke pumping mill used to pump water for stock. The tower is of wood, 40 feet to the axis of the wheel. The wind wheel has 84 plane sails, each 36 by 4 by 1 inches, set at an angle of 35 to the plane of the wheel. The well is a (Jug well; depth to water, 12 feet. The pump has a stroke of 6 inches, a 3-inch cylinder, and 1/J-inch suction and discharge pipes. The lift was 14 feet, and the discharge per stroke 0.62 quart. The results of the tests are as follows : Results of tests of mill No. 45 10-foot wooden Eclipse. [Load per stroke, 18 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles _. 18 18 2.8 0.010 12 miles . 28 28 4.3 0.014 16 miles 32 32 5.0 0.016 20 miles 35 35 5.4 0.018 25 miles 38 38 5.9 0.019 Mill No. 46- This is a 10-foot Cornell direct-stroke wooden mill manufactured at Louisville, Kentucky, and is used to pump water for stock. The tower is of wood, 30 feet to the axis of the wheel. The wind wheel has 90 plane sails, each 36 by 4 by 1-J inches, set at an angle of 47 to the plane of the wheel. The well is a dug well; the water is only about 3 feet below the surface of the ground. The pump has a 3^-inch cylinder and 4 inches stroke. The discharge 60 THE WINDMILL. (NO. 41 . per stroke was 1 pint when pumping rapidly. The lift was 5f feet. The results of the tests are as follows: Results of tests of mill No. 46 10-foot wooden Cornell. [Load per stroke, 6 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 16 16 2.0 0.003 12 miles 25 25 3 1 0.004 16 miles 36 36 4.5 0.006 20 miles . . 42 42 5.2 0.007 25 miles - 48 48 6.0 0.007 30 miles 52 52 6.5 0.008 Mill No. 47- This is a 10-foot Dempster steel mill, like that shown in PL XII, on a 40-foot steel tower. The wind wheel has 24 curved sails, each 30-J- by 13 by 6 inches, set at an angle of 29 to the plane of the wheel. The pump is back-geared, 2J- to 1, and has a 3-inch cylinder and 7 inches stroke. The well is open, 20f feet to water, and situated under the porch of a house. The mill is located 76 feet from the well. The cylinder is directly under the mill, in a chamber 4 feet by 4 feet, and 6 feet deep. The lower end of the cylinder was about 12 feet vertically above the surface of the water in the well. The discharge per stroke was 1 quart when pumping rapidly. The lift was about 18 feet. The wind wheel of this mill is not well balanced, and the spring which holds it in the wind is not stiff enough. The results of the tests are as follows : Results of tests of mill No. 47 10-foot steel Dempster. [Load per stroke, 37 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 37 13 3.2 0.014 12 miles 66 23 5.7 0.026 16 miles . . 89 31 7.8 0.035 20 miles 95 33 8.3 0.037 25 miles 0.000 A diagram which was platted for this mill shows that the curve drops at about 19 miles an hour, and reaches the axis line at 24 miles. Above 24 miles an hour the wheel is entirely out of the wind and does no work. On this diagram was also platted the number of strokes per minute of the 8-foot Dempster (No. 35), to show the effect of the different loads upon the number of strokes per minute. The 8-foot mill was found to be carrying more than three times the load that the 10-foot mill was carrying. U. S. GEOLOGICAL SURVEY 'ATER-SUPPLY PAPER NO. 41 PL. XIV VIEW OF MILL NO. 48-30-FOOT HALLIDAY. MUKPHY.] PUMPING MILLS TESTED. 61 Mill No. 48. This is a 30-foot Halliday wooden pumping mill on a 70-foot wooden tower. It is owned by the city of Valley Falls, Kansas, and is used to pump water for the city supply. The mill and tower are shown in PL XIV. The sail area; is arranged in two concentric rings. In the outer ring there are 192 sails, in the inner ring 144 sails, each 43 by 4-J by 3^ inches, set at an angle of 25 to the plane of the wheel. There are two wells; one (11 feet in diameter) directly under the mill, and another (10 feet in diameter) near the bank of the river 375 feet from the mill. A 3-inch suction pipe connects the wells, and a 3-inch supply pipe leads from the lower well to the river. The pump is double-acting, and has a 4-inch cylinder and 11 inches stroke. The water is pumped directly into the distribution pipes, also into an elevated tank. The tank is of wood, 20 feet by 30 feet, and is 5,570 feet distant from the mill. Of the connecting pipe, 50 feet is 3 inches in diameter, 1,200 feet is 4 inches in diameter, and 4,300 feet is 6 inches in diameter. The bottom of the tank is 111 feet above the well platform. The lift or head at any time is, then, the distance from the well to the well platform and 111 feet plus the amount registered on the gage on the tank. The mean lift when the test was made was 135 feet. The cylinder capacity is 2.4 quarts, the measured discharge per double stroke 4.5 quarts. The mean temperature was 90 F., the mean barometric pressure 28.9 inches. The results of the tests are as follows: Results of tests of mill No. 48 30-foot wooden Halliday. [Load per stroke, 1,265 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles 6 6 6 7 0.23 12 miles 15 15 16 9 58 16 miles 20 20 22.5 0.77 20 miles 24 24 27 92 25 miles . . 28 28 31. 5 1.07 This windmill and pump had been in use about ten years. It fur- nishes enough water during nine months in the year, but during the months of July and August and part of June and September a steam engine is at times employed to work the pump. The cost of repairs to the mill and pump has been from $50 to $60 a year. The number of strokes per minute for different wind velocities is shown in fig. 27. This is the largest windmill pumping outfit that we have tested. It is interesting to compare its power with that of the smaller wooden mills and with that of the steel mills. Mill No. 51. This is an 8-foot Monitor steel pumping mill on a 30- foot steel tower (see fig. 29). The wind wheel has 18 curved sails, each 31| by 13 by 5 inches, set at an angle of 35 with the plane of 62 THE WINDMILL the wheel. The well is a dug well; depth to water, 18| feet. The water is used for stock. The pump has a 3-inch cylinder, 6 inches stroke, and 1^-inch suction and discharge pipes. The cylinder is 1 foot above -the lower end of the suction pipe, and is always under water. A peculiarity of this mill is that the downstroke of the pump FIG. 39. Working parts of mill No. 51 8-foot Monitor. is made in less time than the upstroke. The mill is back-geared, 35 to 13, 13 of the cogs being passed over on the downstroke and 22 on the upstroke. This arrangement makes the mill run easily and prolongs its usefulness. The wind wheel is held in the wind by the weight of the tail ; there is no spring. The li f t was 25 feet, the discharge per stroke 0.7 quart. The mean temperature was 84 F., the mean MURPHY.] RESULTS OF TESTS OF PUMPI barometric pressure 27.8 inches. The results lows: Results of tests of mill No.' 51- -8-foot steel Monitor [Load per stroke, 36.5 foot-pounds.] Wind velocity per hour. Revolutions of wind wheel per minute. Strokes of pump per minute. Gallons pumped per minute. Useful horse- power. 8 miles . 27 10 1.7 0.011 12 miles 56 21 3.7 023 16 miles 81 30 5.2 0.034 20 miles 91 34 6.0 0.037 When the mill was running uncoupled from the pump, the pump rod made 24 strokes per minute in a 12-mile wind, i. e., the pump load of 36. 5 foot-pounds per stroke reduced the number of the strokes of the pump rod from 24 to 21. For the purpose of ready comparison the principal results of these tests of pumping mills have been tabulated. (See table on p. 64.) DISCUSSION OF RESULTS OF TESTS. In this discussion of the results of the tests of these pumping mills we wish to call attention to the principal facts shown by them. The explanation of some of the points is not easy. The useful work which a windmill will do at a given wind velocity depends on several factors, and it is difficult to measure or even estimate the value of each. If the mills could be tested under conditions easily controlled by the experimenter, the problem would be greatly simplified ; but each mill is tested under its own conditions of pump, well, wind exposure, and atmosphere. A comparison of the results of the tests of pumping mills with the results of the tests of power mills throws much light on some of the facts (see Part II, pages 107 to 109, inclusive). A fact very evident from the following table is that the useful work done by windmills in pumping water is small. Only one mill, the largest (No. 48), is doing 1 horsepower of useful work in a 25-mile wind. The best 12-foot mill is doing less than 0.64 horsepower and the best 8-foot mill less than 0.12 horsepower in a 25-mile wind. 64 THE WINDMILL. [NO. 41. r-i lO SO r- 1 MS (35 ' 3J iffi iM5 " ' rH i-H CO rH CO $} ' ^ CO i- ' ' **COOrHOCO 'O !0 *5 J J dddddd Id d oil dddddd >d ddddd dddddd Iddd O^OOOO'HCD i GO ^ I CO O 4 O C3 ^O r- I O OS OO MS OTWOOOcS '^O^J <OOOOt-OOOOU5Cy diagrams. MILLS TESTED. Mill No. 26. This is a 14-foot Perkins steel power mill on a 40-foot steel tower, made by the Perkins Windmill Company, of Mishawaka, Indiana. The working parts are shown in fig. 32. The wind wheel has 32 curved sails, each 41 by 14.25 by 7.75 inches, set at an angle of 31 with the plane of the wheel. The shaft is geared forward 6 to 1. The radius of the brake pulley was 5 inches, the length of brake arm 33.5 inches. This mill was tested twice. Between the dates of testing some repairs were made to the shafting, causing the cogwheels to bind less tightly. The following figures are those obtained from the second test. The mill had been in use only about one year, and showed very poor workmanship. The results of the test are as follows : Results of test of mill No. 26 14-foot steel Perkins. Load on brake. Load per revolu- tion of wind wheel. Number of revolutions of wind wheel per minute at given wind velocities (per hour). Useful horsepower at given wind velocities (per hour). 1 1 oo 12 miles. 16 miles. 20 miles. 25 miles. GO 12 miles. 16 miles. 20 miles. 25 miles. Pounds. 6 Ft.-lbs. 645 16 31 48 0.313 0.609 0.937 Mill No. 27. This is a 12-foot Aermotor on a 30-foot steel tower. The wind wheel is like that of mill No. 3 (see pp. 29 to 30, Part I). The horizontal shaft is geared forward 6 to 1. Fig. 33 shows the working parts, and fig. 34 the foot gear. The brake pully was 9.5 inches in diameter and was fastened to the foot gear at a in fig. 34. The brake arm was 35.25 inches in length. The mean temperature during the test was 46 F., and the mean barometric pressure 28.9 inches. The results of the tests are as follows: Results of tests of mill No. 27 12 foot Aermotor. Load on brake. Load per revolu- tion of wind wheel. Number of revolutions of wind wheel per minute at given wind velocities (per hour). Useful horsepower at given wind ve- locities (per hour). I fj co 12 miles. 16 miles. 20 miles. 25 miles. 8 miles. 12 miles. li) miles. 1 1 1 & Pounds. 2 4 6 Ft.-lbs. 222 444 886 30 1C, 49 43 23 88 57 4S 12 75 70 86 60 87 81 77 72 0. 089 0.285 (i.: 1 ,!).! O.UW5 0.653 6.458 (l.-Sltl) 1.03 0. 523 1.02 1.45 MURPHY.] POWER MILLS TESTED. 87 The revolutions of wind wheel per minute for the four brake loads 0, 2, 4, and 6 pounds, respectively, are shown in fig. 35. The pull necessary to overcome the frictional resistance was found by stand- ing on the platform of the mill and slowly turning the wind wheel around with a spring balance. This was checked by winding a FIG. 33. Working parts of mill No. 27 12-1'oot Aermotor. cord around the circumference of the wind wheel, and, standing on the ground, moving the wheel when there was no wind by pulling on the spring balance attached to the cord. A pull of 1.25 pounds applied at the circumference was sufficient to overcome this resistance at a low velocity. The work done in overcoming this resistance is 1. 25 x27rx 0=47.1 foot-pounds per revolution. The work done per 88 THE WINDMILL. [NO. 42. revolution of wind wheel per pound on the brake arm is 27rx35.25x (j-r- 12=111 foot-pounds. The ratio of these is 47. 1-r- 111 =0.425 pound. Hence a brake load of 0.425 pound is equivalent to the friction load. The effect of each additional 2 pounds load on the brake in re- ducing the speed of the wheel at different wind velocities is clearly shown here. It is seen that an added load makes a greater pro- portionate reduction in the speed when the velocity is low than when it is high. Thus, in an 8-mile wind the addition of 2 pounds to the load reduces the speed 50 per cent, while in a 25-mile wind the same load reduces the speed only about 7 per cent. It will be seen that for wind velocities above a certain amount, with the load not too great, each additional pound of load reduces the speed of the wheel by about the same amount. For example, in a 25-mile wind the addition of 2 pounds changes the speed from 87 revolutions to 81 revolutions. The addition of 2 pounds more changes PIG. 34. -Foot gear of mill No. 27-12-foot Aermotor. a indicates point where brake pulley was attached. VELOCITY OF WIND IN MILES PER HOUR. 10 15 20 so FIG. 35. Diagram showing revolutions of wind wheel of mill No. 27 12-foot Aermotor. Curve marked o is for no brake load; curve marked 2 is for a brake load of 2 pounds; curve marked 4 is for a brake load of 4 pounds; curve marked 6 is for a brake load of 6 pounds; curve PQ is speed curve for maximum power. the speed from 81 revolutions to 77 revolutions. It will be seen that as the load increases the increment of wind velocitj^ necessary to start the mill increases more rapidly than the increment of loading. That is, the 0-pound load curve starts in about a 4.5-mile wind, the 2-pound MURPHY.] POWER MILLS TESTED. 89 curve in about a 7-mile wind, the 4-pound curve in about a 10,5-mile wind, and the 6-pound curve in about a 15. 5-mile wind. The dif- ference between these starting velocities is constantly increasing. A diagram was platted showing the horsepower of this mill for the 2-pound, 4-pound, and 6-pound brake loads. The curves showed that for any brake load the power of the mill increased rapidly as the wind velocity increased, and that it reached a maximum for some velocity greater than 30 miles an hour. As the load increased the velocity required to start the mill increased rapidly and the curve became steeper. For a given wind velocity the power increased rapidly as the load increased. For a velocity of 25 miles an hour the power was nearly proportional to the load for loads of less than 6 pounds. It showed that when the velocity was less than 12 miles an hour a 4-pound load was too great, and when it was less than 19 miles an hour a 6-pound load was too great. It showed also that the efficiency decreased as the wind velocity for a given load increased, and that it increased as the load increased. The efficiency for a load of 2 pounds and a wind velocity of 9 miles an hour was 40 per cent. At 14 miles an hour and with a 4-pound load it was 36 per cent. If the load at that velocity was reduced to 2 pounds, the efficiency was reduced to 24 per cent. Finding the efficiency by using the wind area (area of circle 12 feet in diameter) instead of the sail area, as is sometimes done, the foregoing efficiency of 40 per cent with a 2-pound load in a 9-mile wind became 26 per cent. The results for this mill will be discussed from a mathematical point of view further on. Mitt No. 28. This is a 16-foot Althouse wooden power mill manu- factured by Althouse, Wheeler & Company, of Waupun, Wisconsin. It is shown in fig. 36. The axis of the wind wheel is 32 feet above the ground and 15 feet above the roof of a near-by blacksmith's shop. The wind wheel has 130 sails, each 48 by 4 by 1.5 inches, set at an angle of 32 to the plane of the wheel. Two half sails are miss- ing and two others are slightly injured, making a loss of about one and a half sails. The horizontal shaft, which works a sheller, grinder, emery wheel, and wood saw, is geared forward 8.377 to 1. A pull of from 7 to 13 pounds at a distance of 6 feet from the center was neces- saiy to start the mill, showing it to be a hard-running one. The brake pulley was 8 inches in diameter, the brake arm 3.5 feet long. A second visit to this mill was necessary in order to get results for high velocities. During the interval between the tests a 510-pound ny wheel was put on the shaft, which steadied the motion of the mill somewhat. Tlie owner is well pleased with the action of this balance wheel. Single measurements of the power of this mill for the same load and wind velocity differ considerably. It is very evident that this mill is not high enough; if it were 30 or 40 feet higher it would IKK 4^01 2 90 THE WINDMILL. [NO. 42. give better results. It is with the aid of better results obtained from tests of other mills of similar make that we are able to give tho results in the following table and in the diagrams. , ft FIG. 36. View of mill No. 28 16-foot wooden Althouse. Results of tests of mill No. 2S Ki-foot wooden AltJtonxe. - Load Number of revolutions of wind wheel per minute at given wind velocities (per hour). Horsepower of mill at given wind velocities (^er hour). Load oil brake. per rev- olution of wind . A 03 B wheel. i r2 | I I i 1 s I 1 a i a a 1 a a a g 00 M s 8 K CO 23 1 8 Pounds. Ft.-lbs. 13 23 30 36 40 U 437 20 27 31 36 0.26 35 40 0. 40 G. 5 13 20 88 5J 914 19 23 27 0.52 0. 64 (. 75 4 1,462 8 13 15 0.35 0.00 0.67 Fig. 37 shows the number of revolutions prr minute of the wind wheel of this mill for the brake loads 0, 1.75, 5.75, and S.75 pounds, MURPHY.] POWER MILLS TESTED. 91 -VELOCITY OP WIND IN MILKS PEK HOUR. 10 15 20 40 Id FIG. 37. Diagram showing revolutions of wind wheel of mill No. 28 16-foot wooden Althouse. Curves marked 0, 1. 75, 5.75, 8.75, and grinder are for brake loads of 0, 1.75, 5.75, and 8.75 pounds, respectively, and for grinder load. and for grinder load. The curve for the grinder load is a nearly straight line. This is due to the fact that the grinder is constructed so that as its speed increases the amount of corn it receives in- creases ; thus the load increases automatically as the wind veloc- ity increases. By comparing these speed curves, as they may be called, with those of fig. 35, for the Aermotor, it will be seen that the speed of the latter is much greater than that of mill No. 28. Fig. 38 shows the horsepower of this mill for three brake loads 1.75 pounds, 5.75 pounds, and 8. 75 pounds. The latter load is too great for the mill. By com- paring the results for this mill with those for the 12-foot Aer- motor (fig. 35) it will be seen that the latter mill is superior to the 16-foot wooden mill. Mill No. 29. This is a 16-foot Aermotor like that shown in PI. XV. It is manufactured by the Aer- OF WIND IN MILES PER HOUR. motor Company, of Chicago, 25 Illinois. The tower is of wood, 42 feet to the axis of the Avheel. The wind wheel has 18 curved sails, each 59 by 25.75 by 10.5 inches, set at an angle of 30 to the plane of the wheel. It is used for shelling and grinding corn and for working a small pump. The shafting is 20 feet above the ground, near the roof of a granary. It is geared for- ward 6 to 1, and arranged so that the pump makes 1.011 strokes to each revolution of the wind wheel. The pump lifts 0.022 gallon per stroke a dis- tance of about 40 feet. It has a cylinder 1.5 inches in diameter and a stroke of 8 inches. The supply pipe is on a well point. The brake pulley is 12 inches in diameter, the brake arm 3.75 feet long. The test was continued until the shafting failed. The mean baro- FIG. 38. Diagram showing horsepower of mill No. 28 16-foot wooden Althouse. Curves marked 1.75, 5.75, and 8.75 show horsepower for brake loads of 1.75, 5.75, and 8.75 pounds, respec- tively; dotted curve HK shows maximum power. 92 THE WINDMILL. [NO. 42. metric pressure was 27.8 inches, the mean temperature 70 F. This mill had been in nearly constant use about five years. It replaced a 22.5-foot Halliday. The owner claims that the 16-foot steel mill does more work than the 22.5-foot Halliday wooden mill did. The results of the tests are as follows : Results of tests of mill No. 29 16-foot Aermotor. Load on brake. Load per rev- olution of wind wheel. Nun: wh vel 1 1 oo iber of revolutions of wind eel per minute at given wind ocities (per hour). Horsepower of mill at given wind velocities (per hour). 12 miles. 16 miles. 20 miles. 1 a & 8 miles. 12 miles. 1 1 s 20 miles. 25 miles. Pounds P+li P+24 Ft.-lbs. 212 487 629 20 11 35 30 25 0.13 0.17 0.23 0.44 0.48 4i 35 0.636 0.714 VELOCITY OF WIND IN MILES PER HOUR. o 2 30 Fig. 39 shows the number of revolutions of the wind wheel for three loads 212 foot-pounds, 487 foot-pounds, and 629 foot-pounds. Although these results are incomplete, on account of the failure of the shaft- ing, they are complete up to a wind velocity of 15 miles an hour, and when studied in connection with the com- plete test of a mill of the same size and make (No. 44) it will be seen that this mill has about the same power for the same loads at any given wind velocity. Mill No. 30. This is a 16-foot wooden power mill known as an Irrigator, used for lifting water. (For description see pp. 49-50, Part I.) Two brake loads (2 pounds and 16 pounds) were used on an arm 2.5 feet long. Curves showing the number of revolutions of the wind \vhcol per minute for these loads and the use- ful elevator load are reproduced in fig. 22, Part I; the horsepowers for these loads are shown in fig. 23, Part I. Mill No. 31. This is a 14-foot Elgin wooden power mill used to lift water with a rotary (Wonder) pump. It is described on pages 50 to 51, Part I. Mill No. 34. This is a 14- foot Junior Ideal steel power mill manu- factured by the Stover Manufacturing ( 1 onipany, of Freeport, Illinois. The tower is of wood, 41 feet to the axis of the wheel. The wheel has A C PKJ. W. -Diagram showing revolutions of wind wheel of mill No. 29 16-foot Aermotor. Curve AB is for a load of 212 foot-pounds; CE is for a load of 47 foot-pounds; DF is for a load of 629 foot-pounds. MURPHY.] POWER MILLS TESTED. 93 VKLOCITY OF WIND IN MILES PER HOUR. 10 15 20 25 41; 24 curved sails in eight sections, regulated on the centrifugal prin ciple. Each sail is 49 by 18 by 8 inches, set at an angle of 29 to the plane of the wheel. This is a sectional vaneless mill. In place of a vane there is M counterpoise. It is geared forward 8 to 1. The mill is used for shelling and grind- ing corn and elevating. The brake pulley is on a line shaft 15 or 20 feet long. In a 12- mile wind the mill ground 12 pounds quite fine for a mile of wind, or at the rate of 144 pounds an hour. In an 18- mile wind it ground 26 pounds for a mile of wind, or at the rate of 468 pounds an hour. The grinder was made by the Baker Manufacturing Com- pany, of Evansville, Wiscon- sin. The wind was unsteady, the temperature high 100 in the shade at noon. The re- sults of the tests are as follows : 10 FIG. 40. Diagram showing revolutions of wind wheel of mill No. 34 14-foot Junior Ideal. Curves marked 0, 1, 3, and grinder are for brake loads of 0, 1 , and 3.5 pounds, respectively, and for grinder load. Results of tests of mill No. 34 14-foot steel Junior Ideal. Load on brake. Load per revolu- tion of wind wheel. Number of revolutions of wind wheel per minute at given wind velocities (per hour). Horsepower of mill at given wind velocities (per hour). 3 a CO 12 miles. 16 miles. 20 miles. 93 * 1 g 1 a 00 12 miles. 16 miles. 1 1 25 miles. Pounds. 1 G. Ft.-lbs. 180 G. 631 20 13 4 34 29 19 44 40 32 24 53 49 39 32 58 55 47 40 0.07 0.16 0.22 0.27 0.33 0.46 0.61 0.76 Fig. 40 shows the number of revolutions of the wind wheel per min- ute for brake loads of 0, 1, and 3.5 pounds, and for the grinder load. Fig. 41 shows the horsepower for brake loads of 1 and 3.5 pounds. Mill No. 44. This is a 16-foot Aer motor on a 40-foot steel tower. (See PL XV.) The working parts of the mill are like those shown in fig. 33 ; the foot gear is like that shown in fig. 34. The sail area is the same as that of mill No. 29, page 91. The power was measured with a wooden brake having an arm 4.67 feet long, on a 10-inch iron pulley on the foot gear. Five brake loads were used 0, 3, 5, 8, and 11 pounds, respectively. The shafting is geared forward 6 to 1. 94 THE WINDMILL [NO. 42. The results of the tests are as follows : Results of tests of mill No. 44 16-foot Aermotor. Load on brake. Load per revolu- tion of wind wheel. Number of revolutions of wind wheel per minute at given wind velocities (per hour). Horsepower of mill at given wind velocities (per hour). 8 miles. 12 miles. 16 miles. 1 8 25 miles. 1 oo 12 miles. 16 miles. 20 miles. 25 miles. Pounds. 3 5 8 11 Ft.-lbs. 528 880 1,408 1,936 23 38 28 13 48.0 41.0 33.5 16.0 56 50 44 36 25 64.5 58.5 53.5 47.0 39.5 0.45 0.35 0.66 0.89 0.68 0.80 1.16 1.53 1.47 0.94 1.43 2.01 2.31 VELOCITY OF WIND IN MILES PEK HOUR, 10 15 20 FIG. 41. Diagram showing horsepower of mill No. 34-14- f oot Junior Ideal. Curves marked 3J and 1 show power for brake loads of 3.5 pounds and 1 pound, respectively; dotted curve IK shows maximum power. Fig. 42 shows the number of 25 revolutions per minute of the wind wheel for these brake loads. The number on each curve indicates the brake load for that curve. These curves are seen to closely resemble the corresponding curves for the 12- foot Aermotor (fig. 35). The 16-foot mill will be seen to start, with no load, in about a 4. 5-mile wind the same as the 12-foot Aermotor. Fig. 43 shows the horsepower of this mill for loads of 3, 5, 8, and 11 pounds, respec- tively. The curves for this mill closely resemble those of the 12-foot Aermotor. The curves VELOCITY OF WIND IN MILES PER HOUR. ]() 15 20 25 of the latter were platted, but the diagram is not reproduced because of lack of space. It will be shown further on that these load curves are parabolas, and hence that the power increases as the square root of the wind velocity. It will be shown also that the curve of maximum power is a para- bola, that the load for it increases nearly as the first power of the wind velocity, and that the speed of Ihr wheel increases also as the , PIG. 42. Diagram showing revolutions of wind wheel first power Of the Wind Ve- of mill No. 44 16-foot Aermotor. Curves marked 0, , .. 3, 5, 8, and 11 are for brake loads of 0,3 pounds, 5 lOClty. pounds, 8 pounds, and 11 pounds, respectively; curve n/T'n \r in r ni ''V i s *P<'f 25 48 1.88 30 56 1.32 0.06 0.16 2.67 0.34 0.48 1.41 0.62 0.93 1.50 0.88 1.55 1.76 16- foot Aermotor Ratio of circumference velocities ( ! 6 Y .. Comparison of 12-foot Aermotor (No. 27) with 22.5-foot Halliday wooden mitt (No. 4^). Comparing the power of these mills, Ave have the following: Comparison of results for 13-foot Aermotor and 22.5-foot Halliday. Mill. Number of revolutions of wind wheel per minute at given wind velocities (per hour). Maximum horsepower at given wind velocities (per hour). 8 miles. 12 miles. 16 miles. 20 miles. 8 miles. 12 miles. 16 miles. 20 miles. 12- foot Aermotor ... 30 11 1.46 49 20 1.31 n 25 1.34 75 30 1.32 0.09 0.06 1.50 0.33 0.32 1.1)3 0.66 0.63 1.05 1.05 0. !4 1.12 22 5-foot Halliday Ratio of circumference velocities Q~) It will be seen that this 22.5-foot wooden mill does not furnish as much power as a good 12-foot steel mill. MURPHY.] COMPARISON OF POWER MILLS. 105 Comparison of wooden power mills. Of the mills in the following table the 12-foot has the least friction; the tower being in front of the windmill obstructs the wheel and' reduces the power. The 14-foot mill probably has more friction than the others. The 16-foot Irri- gator has too few sails ; with more sails the power could probably be increased 75 per cent or more. Comparison of results of tests of wooden power mills. Number of revolutions of wind wheel per minute Horsepower at given wind at given wind velocities velocities (per hour). (per hour). Mill CO V. t t 1 . $ t g J g 1 1 1 1 1 1 1 1 CO a s 8 oo M s s 12-foot Monitor (No. 50) 16 7 13 12 33 18 23 25 44 25 30 32 54 30 36 41 64 0.02 0.01 0.06 0.02 0.10 0.10 0.29 0.16 0.23 0.25 0.52 0.30 0.38 0.42 0.84 0.44 14-foot Challenge (No. 52).... 16-foot Althouse (No. 28) 16-foot Irrigator (No. 30) 40 44 22.5- foot Halliday (No. 49) ... 11 20 25 30 0.06 0.32 0.63 0.94 VELOCITY OP WIND IN MTLKS PER HOUR. 5 10 15 2') 35 It will be seen that the 16-foot mill (No. 28) is furnishing from -2. 2 to 2.9 times more useful power than the 12-foot mill (No. 50). It will also be seen that the power of this 16-foot mill compared with that of 90 the 12-foot mill increases faster than as the squares of the diameters, while 75 the power of the 22. 5-foot mill compared with that of the 12-foot mill does | 6<> not increase as fast as the Q squares of the diameters, and the power of the 22. 5- 45 foot mill compared with g that of the 16-foot mill g does not increase as fast g 30 as the first power of the H diameters. Comparison of 12-foot 15 Monitor wooden mill (No. 50} with 1%-footAer- moto-r (No. 27) and with 12-foot Ideal (No. 53).- Fig. 55 shows the speed, in revolutions, of the wind wheels of these mills for no useful load. The friction is small in each case. The Monitor has a swivel gearing, and the Ideal has a ball IKR 4201 3 FIG. 55. Comparative diagram of revolutions of wind wheels of mills Nos. 50, 53, and 27. Curve aa' is for 12-foot Aermotor; bb' is for 12-foot Ideal; , and 20 2 =u+1.556. Solving these, we have a =28, 6=240, and the equation of the curve is # 2 =28+240?/. (12) The values of y for four values of x are #=8, t/=l5; #=12, ?/=0.48; #=16, |/ = 0.f)5; and #=20, y=l.55. It will be seen that these values agree closely with the measured horsepower for these velocities. By making #=0 in equation 12 we have y 0.125. The vertex of this maximum power curve is at a distance 0.125 below the axis of x. If the origin of coordinates be changed to this point, equation 12 will 116 THE WINDMILL. [NO. 42. take the form x 2 =Ky', K being a constant and y' the horsepower referred to the new origin. Hence we see that the maximum horse- power varies as the square of the wind velocity. To find the variation of the speed and load for this curve DK, we notice that the 3-pound curve is tangent at #=10.5, the 5-pound curve at #=14, the 8-pound curve at #=19, and the 11-pound curve at #=24. The horsepower is known at these points, so that the speed can be found from equation 7. The wind velocity, load, horsepower, and speed for each of these points are as follows : Data regarding points of tangency of power curves with c,urves of maximum power of Aermotor No. 27. Wind velocity per hour. Load. Horsepower. Revolutions per minute. 5 miles .. Pounds. 10 5 miles 3 0.33 21 14 miles 5 0.70 26 19 miles 8 1.40 33 24 miles 11 2.17 37 The speeds here found are platted in fig. 42, giving the curve PQ, which gives the speed of the wheel for the maximum load. This curve is seen to be a nearly straight line for velocities above 9 or 10 miles an hour. Hence we may say that the speed increases as the first power of the wind velocity for maximum power. The load for any wind velocity can now be found from the formula 176 Lu H. P. = , the speed being taken from the speed curve PQ. 33,000 Or the loads can be measured from the load curve RS, fig. 42. This load curve (RS) for maximum power is seen to be a straight line, show- ing that for wind velocities above 9 or 10 miles an hour the load for maximum power varies nearly as the first power of the wind velocity. The following table contains some interesting facts in regard to the working of this mill : Data in regard to speed of mill No. 44 16-foot Aermotor. No load. Maximum load. Ratio of speed at Wind velocity per hour. Revolu- tions per minute. Circum- ference velocity in miles. Ratio of circum- ference velocity to wind Revolu- tions per minute. Circum- ference velocity in miles. Ratio of circum ference velocity to wind maxi- mum load to speed at no load. velocity. velocity. Smiles 23 13.2 1.67 15 8.6 1.08 0.65 12 miles 38 21.7 1.81 23 13.2 1.10 0.61 16 miles 48 27.4 1.71 29 16.6 1.04 0.60 20 miles 56 32.0 1.60 34 19.4 0.97 0.60 25 miles 64 36.6 1.46 38 21.6 0.86 0.60 MURPHY.] ACTION OF AIR ON SAIL OF AERMOTOR. 117 It will be seen that the ratio of the circumference velocity of the wheel to the wind velocity increases to 12 miles an hour and then decreases. In a 12-mile wind the circumference of the wheel is mov- ing 1.81 times faster than the wind tliat drives it. It will be seen also that the circumference \ \ velocitjr of the wheel when carrying the max- \ \ imum load is about equal to that of the wind \ that drives it, and that the speed of the wheel when carrying a maximum load is about 39 per cent less than its speed when carrying no use- ful load. ACTION OF AIR ON THE SAIL OF AN AER- MOTOR. It is not our purpose to discuss this action from a theoretical point of view, but to explain it from the observed and computed results of the 16-foot Aermotor. Fig. 58 shows the con- cave surface of one sail of a 16-foot Aermotor in a nearly horizontal position as it moves down- ward ; w represents the velocity of the wind, and v the circumference velocity of the sail. The curve JAE, fig. 59, shows the outer end of the sail, and to, in fig. 60, shows the inner end. The cords of these arcs, or the plane of the sail, makes an angle (JOP) of 30 with the plane of the wheel. The point E, fig. 59, repre- sents a particle of air as it comes in FIG. 58,-san^of w-foot Aer- contact with the sail when the wheel is carrying its best load; EF represents the velocity of the wind, EH the velocity of this point of the sail ; then EG, the other side of the paral- lelogram constructed on EH and EF, is the velocity of this particle of air over the sail; EG is not tangent to the sail. The point A represents a particle of air as it comes in contact with the moving sail, when the mill is carrying no load; AC represents the relative velocity of the particle of air. It will be seen that the air does not enter the sail tangent to it, but more nearly tangent for best load than for no load. FIG. 59. Outer end of sail of 10-foot Aermotor. 118 THE WINDMILL. [NO. 42. Iii fig. 60 t represents a particle of air as it strikes the inner .end of the sail when the mill is carrying no load, and a represents a particle of air as it strikes the inner end of the sail when the mill is carrying its maximum load. It will be seen that the air does not strike the sail tangent to it at any place for any load, but that it is most nearly tan- gent at the outer end of the sail at maximum load. In order for the air to enter the sail tangent to it at maximum load, the angle POJ should be a little greater than 30 at the outer end, and considerably greater than 30 at the inner end. As the load is decreased the angle POJ should be decreased. USEFUL WORK OF TWO POWER MILLS IN A GIVEN TIME. We can find the useful work of the 12- foot and the 16-foot Aermotors in a year, as we have for two pumping mills (pp. 69- 71). For this purpose we will use the mean wind movement at Dodge, Kansas, from 1889 to 1893, as given by Mr. Willis L. Moore, Chief of Weather Bureau. 1 The mean number of hours per month that the wind velocity was to 5, 6 to 10, etc. miles an hour at this place is given in the following table, also the mean horsepower of these two mills for each month. The num- ber of horsepower hours for each mill each month is given at the bottom of the table. The horsepower hours for any month are found by multiplying the number of hours by the horsepower and adding the products. Table showing useful work of 12-foot and 16-foot Aermotors in a year. r FIG. 60. Inner end of sail of 16-foot Aermotor. Month. Mean wind movement at Dodge, Kansas, 1889-1893. Total hours. Horsepower hours. Oto5 miles. 6 to 10 miles. 11 to 15 miles. 16 to 20 miles. 21 to 25 miles. 26 to 30 miles. 31 + miles 12-foot mill. 16-foot mill. January Hrs. 200.9 176.0 126.5 115.2 119.0 122.4 141.4 178.6 165.6 208.3 194.4 186.0 Hrs. 253.0 230.1 208.3 172.8 193.5 187.2 215.8 230.6 180.0 230.6 266.4 267.9 Hrs. 156.2 128.6 178.6 158.4 171.1 136.8 178.6 156.3 151.2 141.4 129.6 141.4 Hrs. 74.4 74.4 119.0 115.2 119.0 108.0 119.0 96.7 93.6 74.4 64.8 81.8 Hrs. 37.2 40.6 59.5 72.0 74.4 86.4 59.5 eo.s 72.0 52.1 36.0 44.6 Hrs. 14.9 20.3 29.8 43.2 37.2 50.4 22.3 14.9 36.0 22.3 14.4 14.9 Hrs. 7.4 6.8 22.3 43.2 29.8 28.8 7.4 7.4 21.6 14.9 14.4 7.4 744 677 744 720 744 720 744 744 720 744 720 744 250.5 251.6 386.6 461.2 433. 9 452.0 339.8 297.5 379.6 294.0 244.9 262.2 358.0 361.5 558.9 671.3 629.4 658.2 489.3 427.6 550. 5 423.5 350.9 374.6 March. April May June July August September October November December Mean 337.8 487.8 Horsepower 16- foot mill 0.13 0.10 0.56 0.41 1.25 0.85 2.00 1.36 ;}. 15 2.12 Horsepower 12- foot mill 1 Some Climatic Features of the Arid Region, by Willis L. Moore. Washington, 1H1H5. MURPHY.] MATHEMATICAL DISCUSSION. 119 The work done by these mills is greatest at this place in April (401 horsepower hours for the 12-foot and 671 horsepower hours for the 16-foot) and least in November (245 horsepower hours for the 12-foot and oo 1 horsepower hours for the 16-foot). The mean monthly power is 338 for the 12-foot mill and 488 for the 16-foot mill. Stating these results in another way, we may say that the 12-foot mill at this place will furnish on an average 1.3 horsepower 10 hours a day for 26 days a month, and the 16-foot mill will furnish 1.9 horsepower 10 hours a day for 26 days a month. It must be remembered that the wind velocity on the Great Plains is considerably greater than in the east- ern part of the United States, and that consequently the horsepower hours of these mills when used in New York State, for example, will be considerably less than those given in the foregoing table. MATHEMATICAL DISCUSSION OF TESTS OF JUMBO MILL NO. 55. On page 46 we have given the results of tests of a 15.5-foot Jumbo mill working two 6-inch pumps. In order more fully to deter- mine the power of this mill and its variation with the number and size of the sails, we have had constructed mill No. 55, shown in PI. XVI, B. It is made of wood, the parts being fastened together with bolts. The diameter is 7.75 feet; length of sails, 11-J- feet. There are 8 sails, each made of two boards 11^ feet long and 8 inches wide. There is no governor or other method of regulating the speed of the mill at high wind velocities, as in other mills, but there is a large door or shield on each side. By opening these the mill may be stopped. The mill is not fastened to the ground, but may be moved around by hand so that the wind strikes the sails at right angles. The shaft is 4 by 4 inches and 14 feet long, carefully turned down in a lathe to a diameter of 3 inches near each end. The friction brake is of wood, has an arm about 3^ feet long, and is made so as to fit on the end of the shaft. Oil was freely used on the brake. It was not found practi- cable to use loads greater than about 6 pounds on a 35-inch arm, as the friction burned the shaft; but the results for the four loads used showed that up to the maximum load the speed of the wheel, or the number of revolutions per minute, varies directly as the load, so that we can easily compute the load and speed for maximum power in any wind velocity. The weight of the wheel with its 8 sails was about 450 pounds. The coefficient of axle friction for well-oiled yellow pine is probably about 0.10, so that the axle friction was about 45 pounds. This weight (45 pounds), acting with a 1^-inch arm, is equivalent to about 2 pounds applied on the brake with a 35-inch arm. The friction on starting is probably 50 to 100 per cent greater than the friction of motion. The brake load then really corresponds to a brake load of 2 or more pounds. Four sets of tests were made of this mill, numbered 1, 2, 3, and 4. In the first set the full sail area of 8 sails, each 11^ feet by 16 inches, 120 THE WINDMILL. [NO. 42. was used. The number of revolutions of the wheel for the four brake loads of 0, 1.75, 2.5, and 4.5 pounds was determined for velocities from 7 to 22 miles an hour. In the second set of tests there were 8 sails, each having an area of 11| feet by 8 inches; that is, each sail was only half as wide as those used in the first set of tests. In the third set of tests the sail area consisted of 4 sails, each 11| feet by 16 inches; that is, every other full sail was removed. The fourth set of tests was made to determine the effect of concentrating the air on the sails and reducing the resistance due to air striking the shield and glancing upward by the use of an inclined surface of approach to wheel. This inclined VELOCITY OF WIND IN MILES PER HOUR. 10 >5 '?5 Q 0* O W FIG. 61. Diagram showing revolutions of wind wheel of mill No. 55 7. 75- foot Jumbo. Curve marked is for no brake load; curve marked 4 is for a brake load of 4.5 pounds. surface had a length of 7 feet and formed an angle of 11 with the horizontal. Test No. ./.In PL XVI, B, the mill is shown with 8 sails, each 11-j- feet by 16 inches. Fig. 61 shows the num- ber of revolutions of the wheel per half mile of wind for two loads and 4.5 pounds on a 35-inch arm, for the wind velocities shown. These curves for a mill without any means of governing in high velocities are given for comparison with curves of mills having a governor. It will be seen that these curves are nearly horizontal straight lines beyond the point of maximum revolutions per half mile. Thus, for no brake load the revolutions at 12 miles are about 62, and at 25 miles about 59. In a mill with a governor, as, for instance, that shown in fig. 36, the curve is more inclined, or the drop in the number of revolutions is greater. Fig. 62 shows the number of revolutions per minute for several loads, fig. 63 shows the horsepower. The results of these tests are as follows : Results of tests of Jumbo mill No. 55 with 8 sails 11\ feet by 10 inches. Load on brake. Load per rev- olution of wind wheel. Revolutions of wind wheel per minute at given wind veloci- ties (per hour). Horsepower at given wind velocities (per hour). I i co 12 miles. 16 miles. 20 miles. 25 miles. 8 miles. | a M It) miles. 20 miles. 25 miles. Lbs. 1.75 2.5 4.5 Ft.-lbs. 32.0 45.8 KJ. 5 11 24 22 20 17 ,33 30 88 tt 41 38 36 88 49 45 43 40 0.022 0.028 0.043 0. 030 O.IK!) 0.063 ().{ (1.050 0.082 0.043 0.060 0.100 U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 42 PL. XVI A. VIEW OF MILL NO. 57 24-FOOT LITTLE GIANT. B. VIEW OF MILL NO. 55 7J-FOOT JUMBO. MURPHY.] MATHEMATICAL DISCUSSION. 121 10 15 20 From these results it is seen that the reduction in the number of revolutions per minute is proportional to the load. For example, in a 20-mile wind a 4^-pound load reduces the number of revolutions from 41 to 34, or 1. 75 revolutions per brake pound. The power = In RnL -r- 33,000, where n = the number of revolutions of the wheel per minute, L = the load on brake, in pounds, R = the arm of brake (35 inches), n = 3.1416, and 33,000 = the number of foot-pounds per minute in a horsepower. We may write the power thus: P = KnL, and compute its value as follows, K being a constant equal to 2?rR -> 33,000: P = K X 41 (revolutions) X (L) = P, = K X 33 (revolutions) X 4.5 (L) = U8.5K. P 2 = #X26 (revolutions) X 8.5 (L) = 221.0K. P 3 = K X 22.5 (revolutions) X 10.5 (L) = 236.3#. P 4 = K X 20.75 (revolutions) X 11.4 (L) = 238.6 tf. P 5 = K X 19 (revolutions) X 12.5 (L) = 237.5K. P 4 is seen to be larger than any of the other values of P, and gives an approximate value of the VELOCITY OF WIND IN MILES PER HOUR. power of the mill for that wind velocity (20 miles). We may find a more accurate value in an easier way. Let x be the load for maximum horse- power in any given wind veloc- ity. We have seen that 1 pound of load reduces the speed by 1.75 revolutions. Then we can write P=K (41-1.75aj) (x). For a maximum value of P we must differentiate P with re- spect to x, place the first differ- ential coefficient 0, and solve for x. This value of x, accord- ing to calculus, makes the power a maximum. Differentiating, we have P 4- dx = 412 (1.75oj) = 0. Solving for x we have J5 = 11.7 pounds. The corre- sponding value of the revolu- tions of the wheel per minute is 41 1.75 x 11.7 = 20.5 revolutions. For a 25-mile wind we have x = 49 -^- 3.5 = 14 pounds, and -n 16.5. In a similar way we get the load and revolutions for maximum power IBB 4201 o 20 10 FIG. 62. Diagram showing revolutions of wind wheel of mill No. 55 7.75-foot Jumbo. Curves marked 0, If, 4, and 4 are for brake loads of 0, 1.75, 2.5, and 4.5 pounds, respectively; AB is for best load. 122 THE WINDMILL. [NO. 12. for other wind velocities. These and the corresponding horse powers are as follows: Values for the curve DK (maximum power) fig. 63. Wind Revolu- velocity Load in tions of Horse- (miles pei- hour). pounds. wind wheel per minute. power. 8 3.1 6.0 0.010 12 7.0 12.0 0.046 16 9.4 16.5 0.086 20 11.7 20.5 0. 133 25 14.0 ^4.5 0.190 The curve DK is nearly a parabola. The revolutions per minute for the best load are seen to be very nearly equal to the wind velocity VELOCITY OF WIND IN MILES PEB HOUR. 10 15 20 25 .20 .M .04 PIG. 63. Diagram showing horsepower of mill No. 55 7.75-foot Jumbo. The curves show the horsepower for brake loads of 1.75, 2.5, and 4.5 pounds, respectively; dotted curve DK shows maximum power. in miles. These are platted in fig. 62, giving the line AB, which is nearly straight. RELATION BETWEEN WIND VELOCITY AND CIRCUMFERENCE VELOCITY OF WHEEL. If we multiply the number of revolutions of the wind wheel for any wind velocity by 24.4 feet (the circumference of the wheel) and divide by the wind velocity, in feet per second, we have the followii g results for no brake load and for best load : MURPHY.) MATHEMATICAL DISCUSSION. 123 Table showing ratio between wind velocity and circumference velocity of wheel. Load. Wind velocity per hour. 8 miles. 12 miles. 16 miles. 20 miles. 25 miles. No load 0.38 0.21 0.55 0.27 0.57 0.28 0.57 0.28 0.55 0.27 Best load From this we see that the velocity of the circumference of the wheel is not more than 57 per cent of the velocity of the wind. For veloci- ties above a certain amount it remains nearly constant for any load. It will be seen too that the speed of the wheel for best load is almost exactly half that for no brake load. Test No. 2. Sail area, 11-j- feet by 8 inches each inner half sail removed. The results of this set of tests are as follows : Results of tests of Jumbo mill No. 55, with 8 sails 11% feet by 8 inches. Load. Revolutions of wind wheel per minute at given wind veloci- ties (per hour). Horsepower at given wind velocities (per hour). 8 miles. 12 miles. 16 miles. 8 25 miles. 8 miles. 12 miles. s a 8 25 miles. Pounds. 3.25 Ft.-lbs. 59.6 9 22 17 30 26 39 32 47 40 0.031 0.047 0.058 0.072 By comparing these results with those of test No. 1 it will be seen that the number of revolutions per minute for no load is from two to three times less when the half sails are used. The 3^-pound load with half sails gives about the same speed as the 4^-pound load with whole sails. The weight of the wheel is reduced about 40 per cent, which makes the reduction in speed less than it would be if the weight of the wheel remained constant. It will be seen, then, that for this size of wheel very little power is gained by the use of the inner 8-inch board of each sail. It is quite likely that sails 12 inches wide would give fully as much power as sails 16 inches wide. Test No. 3. The sail area was 4 sails, each 11-j- feet *by 16 inches every other full sail removed. The results of this set of tests were almost the same as those of test No. 1. There was no measura- ble reduction in the speed of the wheel when every other full sail was removed. The weight of the wheel was reduced about 40 per cent, and consequently the friction. The gain in pressure on the extra sail area is counterbalanced by the additional friction. Test No. 4- The sail area was 8 sails, each 11-j- feet by 16 inches the same as for test No. 1. There was an inclined surface (shown in PL XVI, B} for concentrating air 011 sails and in a measure prevent- 124 THE WINDMILL. [NO. 42. ing an upward current from the front shield. The results of this set of tests are the same as those of No. 1. There was no measurable increase in the number of revolutions when the mill was loaded or unloaded, or when the incline was used or not used. For this size of mill 4 sails each 12 inches wide give the maximum power. From our tests of other mills we should say that the sail width should increase directly as the diameter increases. For diam- eters of 12 feet or more it is likely that the addition of one or two more sails, say 5 for a 12-foot mill and 6 for a 16-foot mill, may increase the power over that for 4 sails. In 1895 we made some measurements of the pressure of air on small curved surfaces, 1 from which we infer that if galvanized-iron sails curved to a radius about twice the width and with the concave sur- face to the wind were used the power of the mill would be increased about 15 per cent over that with the plane fans. Putting the results of these tests of Jumbo mills in the most prac- tical form, we have the following as the proper sail area and the probable horsepower of wooden Jumbo mills in a 16-mile wind when properly loaded, assuming the power to increase as the square of the diameter: Table showing proper sail area and probable horsepoiver of Jumbo wooden mills in a 16-mile ivind. Diameter of wheel. Number of sails. Width of sails. Length of sails. Horsepower. 8 feet 4 Inches. 12 Feet. 12 09 12 feet 5 18 12 0.20 16 feet 6 24 12 0.36 20 feet . . . 6 30 12 0.56 The formula used for computing the pressure on a series of plane surfaces moving in the direction of the velocity of the wind is In this F is the area, in square feet, of the vane, r the heaviness of air at the observed temperature and barometric pressure, c the velocity of wind, and v the velocity of wind wheel, each in feet per second. The heaviness of the air is found from the formula B To In this To is the absolute temperature in centigrade degrees. 1 Kansas University Quarterly, Vol. IV, July, 1895. MURPHY.] MATHEMATICAL DISCUSSION. 125 29 273 From equation b we have r =0.08X30X30^=0. 07 pound per square foot. From the table on page 123 it will be seen that for maximum power in a 16-mile wind v=0.2Sc. Substituting in equation a we have, for the pressure on one sail P=11.5X^X0.07 (1-0.27) 2 c 2 =4.1 pounds. The arm of this pressure about the axis of the wheel is about 3.06 feet. Hence the moment of this force is 4.1x3.6=14.76 foot-pounds. This moment is equal to the moment of the brake load, and we have 14.76=35^, and #=4.24 pounds. The load actually carried on the brake, including friction, is about 8 pounds; hence nearly half of the working pressure comes from wind pressure on the approaching and receding sails, or only a little more than half the* pressure comes from the sail which is at the highest position possible. MATHEMATICAL DISCUSSION OF TESTS OF LITTLE GIANT MILL NO. 56. This is a 4.67-foot mill made by Mr. C. Hunt, of Wichita, Kansas. These mills are made in sizes from 4 to 24 feet in diameter, to rest on a low tower or on a building. The largest one yet built is shown in PI. XVI, A. It is used for grinding wheat. The Little Giant mill will be seen to resemble the Jumbo in that the wind wheel moves in the direction of the wind and not across it. It differs from the Jumbo, how- ever, in having a vertical axis and many curved iron sails, instead of a horizontal axis and few plane wooden sails. The wind is prevented from striking the sails as they come around toward the wind by a shield which, when closed, covers about one-third of the circumfer- ence. The shield can move freely about the axis of the mill and has hinged to it a wing which can be held at right angles to the circum- ference. There is also a vane fastened to the shield, to aid in the government of the mill. When the wing of the shield is closed, the vane takes the direction of the wind and places the shield directly in front of the wind wheel, shutting off the wind from the wheel. When the wing is open, the pressure of the wind against it carries the shield around, admitting the wind to one-half of the wheel. By properly placing the vane and using the proper weight on the wing, the wind is admitted to a small or a large portion of the wheel, and thus the speed of the wheel is regulated. The mill receives the wind from all directions and regulates automatically. Mill No. 56 has 24 curved iron sails, each 3 feet 10 inches long and 6 inches wide, set at an angle of 27 to the radius. The radius of curvature of the sails is 7-j- inches. The vertical shaft of the wind wheel has a beveled cogwheel, which gears into another beveled cog- wheel on a short horizontal shaft. The latter has a pitman for work- ing a pump. The horizontal shaft on which the brake was placed 126 THE WINDMILL. [xo.42. was geared back 43-f-13. The 6rake arm was 2 feet 1O inches long. The number of revolutions per minute of the brake shaft was found for the four loads 0, 2, 4, and 6 pounds, respectively. The corre- sponding speed of the wind wheel is found by multiplying by 3. The results of the tests were as follows: Results of tests of Little Giant mill No. 56. Load. Revolutions of brake shaft per minute at given wind veloci- ties (per hour). Horsepower at given wind velocities (per hour). I 1 oo 12 miles. 16 miles. I 1 8 25 miles. 8 miles. 12 miles. 16 miles. ! 25 miles. Pounds. 2 4 6 Ft.-lbs. 35.7 71.4 107.1 10 6 19 16 11 6 " 25 21 18 14 31 27 23 19 38 34 30 26 0.007 0.017 0.024 0.019 0.023 0.039 0.045 0.030 0.050 0.062 0.040 - 0.065 0.084 VELOCITY OF WIND IN MILES PER HOUR. 10 15 20 25 40 Referring to fig. 64, the mill will be seen to start for no load in a light wind about 5 miles an hour. More than half of each speed curve is a nearly straight line. This is due to failure to govern, the mill being held wide open all of the time. It will be seen that each pound of load reduces the speed about two revolutions per minute for about 0.67 of each curve. Fig. 65 shows the brake horsepower for three loads 2, 4, and 6 pounds, respectively. The curve DK, to which these load curves are tan- gent, shows the maximum power of the mill. This curve passes through the points y (horse- power) =0 when x (wind veloc- FIG. 64. Diagram showing revolutions of wind wheel of mill No. 56 4.67- foot Little Giant. The curves marked 0, 2, 4, and 6 are for brake loads of 0, 2, 4, and 6 pounds, respectively. ity)=5, and 7/=0.024 when x=l2. Hence, if we assume this curve DKto be a parabola, we have for its equation The horsepower from this equation and from fig. 65 is as follows, y' being taken from fig. 65 : MURPHY.] COMPARISON OF LITTLE GIANT AND JUMBO MILLS. Horsepower of mill No. 56 at given wind velocities. 127 X y y' 5 0.000 0.000 8 0.008 0.007 12 0.024 0.024 16 0.046 0. 045 20 0.075 0.065 It will be seen that the horsepower of this mill does not increase as fast as the square of the wind velocity. From fig. 65 it will be seen that the 2-pound curve is tangent at 8 miles, the 4-pound curve at 12 miles, and the 6-pound curve at 16 miles an hour. Hence the load for maximum power increases about as the first power of the wind velocity. The speed of the brake shaft for these loads is 6, 11, and 14 revolutions per minute, respectively. Hence the speed of the wind wheel does not increase as fast as the first power of the wind velocity. The ratios of circumference velocity of wind wheel to wind velocity for no load and for maximum load for five wind veloc- ities are as follows: Table showing relation of circumference velocity of wind wheel to wind velocity. Wind velocity per hour. No load. Maximum load. Ratio of revolu- tions at maxi- mum load to revolu- tions at no load. Revolu- tions of brake shaft per minute. Circum- ference velocity in miles per hour. Ratio of circum- ference velocity to wind velocity. Revolu- tions of brake shaft per minute. Circum- ference velocity in miles per hour Ratio of circum- ference velocity to wind velocity. 8 miles 10 19 25 31 38 5.2 9.9 13.0 16.1 19.8 0.65 0.74 0.81 0.80 0.79 6 11 14 16 3.1 5.7 7.3 8.3 0.39 0.47 0.46 0.42 0.60 0.58 0.56 0.52 12 miles .... 16 miles 20 miles 25 miles From this we see that for no load the greatest circumference veloc- ity is only 81 per cent of the wind velocity. For best load the ratio is 47 per cent. Here is the great disadvantage of these wheels, which move in the direction of the wind instead of across it they move too slowly. The ratio of circumference velocity to wind velocity in an Aermotor is 1.75. This is 2.16 times the greatest corresponding circumference velocity of the Little Giant mill. COMPARISON OF LITTLE GIANT AND JUMBO MILLS. From the following table it will be seen that the circumference velocity of the Jumbo is only from 0.55 to 0.70 of that of the Little Giant for best load. The horsepower of the Jumbo is about 1.9 times that of the Little Giant; the ratio of the Jumbo diameters is 1.67; 128 THE WINDMILL. [NO. 42. hence the ratio of the power is a little greater than that of the diam- eters. It must be remembered, however, that the Jumbo is about three times the length of the Little Giant. For the same sail lengths the latter does 1.57 more work than the Jumbo. Comparative data of Little Giant and Jumbo mills. Mill. Maximum horsepower at given wind velocities (per hour). Circumference velocity for maximum load at given wind velocities (per hour). 8 miles. 13 miles. 16 miles. 30 miles. 1 1 g 8 miles. 13 miles. 1 1 ?D 30 miles. 25 miles. 7f-foot Jumbo 0. 010 0.007 0.046 0.024 0.086 0.045 0.133 0.066 0.190 0.100 1.7 3.1 3.40 5.70 4.70 7.30 5.80 8.30 4|-fbot Little Giant Ratio 1.4 1.9 1.9 2.0 1.9 0.55 0.60 0.64 0.70 Taking into account the difference in the diameters of the wind wheels of these mills, we may say that the Little Giant will furnish about 2.5 more power than the Jumbo for the same diameter and length of sail. The Jumbo requires a 7-mile wind to start it with no load; the Little Giant will start with no load in less than a 5-mile wind. The Jumbo has no means of governing; the Little Giant gov- erns easily and completely. The Jumbo gets the full pressure of the wind when it comes from two directions only; the Little Giant works equally well with the wind from any direction. The Little Giant is less likely to be injured in a windstorm than the Jumbo. The first cost of the Jumbo is somewhat less than that of the Little Giant. A 5-foot Little Giant with stub tower can be bought for about $15. COMPARISON OF LITTLE GIANT WITH 8-FOOT AERMOTOR. The efficiency of the pump and well of Aermotor No. 5 (for descrip- tion and results of tests, see pages 33 and 34, Part I) is probably about 60 per cent. For the speeds and horsepowers of these mills we have the following : Comparative data of Little Giant and 8-foot Aermotor. Revolutions of wind Load per wheel per minute at given wind ve- locities (per hour). Horsepower at given wind velocities (per hour). Mill. revolu- tion of Sail area. wind t | I i t wheel. a gj a a i a a a a a s 50 8 3 a CD 8 8 Ft.-lbs. Sq.ft. 8-foot Aermotor (No. 5) ... 45 34 62 84 99 115 0.084 0.115 0.138 0.158 4|-foot Little Giant (No. 56) 24 54 34 66 71 QO 0.024 0.039 0.050 0.065 Ratio 2.76 1.96 0.63 1.82 1.53 1.40 1.25 3.50 3.00 2.43 MURPHY.] COMPARISON OF LITTLE GIANT AND AERMOTOR. 129 VELOCITY OF WIND IN MILES PER HOUR. 10 15 20 25 .08 It will be seen that the sail area of the Aermotor is only 0.63 that of the Little Giant, that the wind wheel of the former makes from 1.25 to 1.82 more revolutions per minute than the latter, and that the power of the former is from 3.5 to 2.4 times greater than the power of the latter. While the sail area of the Aermotor is only 0.63 that of the Little Giant, the wind area of the former is much greater than that of the latter. The wind can not enter the wheel of the Little Giant over an area greater than the radius multiplied by the length of the sail, or 9.1 square feet. In the Aermotor the wind enters the wheel over an area equal to the difference between the areas of the two circles, one having a diameter of 8 feet, the other having a diameter of 3 feet. This wind area is 43.2 square feet. Hence the wind area of the Aermotor is 43.2-:- 9.1 = 4.75 times that of the Little Giant. Here is the great advan- tage that the Aermotor has over the Little Giant it has only 0. 63 of the sail area, and hence cost less for sails, and 4.75 times more air strikes its sails than strikes those of the Little Giant. It will be shown later that in the Little Giant the air acts on its sails while passing out of the wind wheel as well as while pass- ing into the wheel, and thus the power for the same wind area is greater in that mill than in the Aermotor. Fig. 66 is a diagram showing the action of the wind on the sails of the Little Giant mill. AH, BK, etc., are the curved sails. The cord AH makes an angle of 27 with the radius AP. CD is the shield, with the wing DE open. Let Aa represent the direction and magnitude of the wind with respect to the earth. We have seen that for maximum load the ratio of the circumference velocity of the wheel to the wind velocity is 0.47; hence drawing Ac tangent to the circumference Aa and equal to 0.47 of Aa, and completing the parallelogram on them, we have Ab representing the direction of the wind with respect to the moving sail. If we assume this to be the velocity of the air over the sail (it is somewhat less than this, since Ab is not quite tangent to the sail at entrance), we can construct the path of a particle of air with respect to the earth. The points 1, 2, and 3 are on this path, and L3 gives the approximate direction of the particle of air through the wheel. At L we combine this velocity with the inner circumference velocity .04 .08 FIG. 65. Diagram showing horsepower of mill No. 56 4.67-foot Little Giant. The curves marked 2, 4, and 6 show horsepower for brake loads of 2, 4, and 6 pounds, respectively; dotted curve DK shows maximum power. 130 THE WINDMILL. [NO. 42 of the sail, giving the velocity Lp with respect to the moving sail. This is seen to make a large angle with the tangent at entrance, reducing its magnitude somewhat. L/4 is approximately the absolute path of the particle over the sail, and 4-5 is the direction of the parti- cle at exit. B6 represents the absolute path of a particle of air as it moves over the sail BK. This particle of air passes through the FIG. 66. Diagram showing action of wind on sails of mill No. 56 4.67-foot Little Giant. wheel in the direction 6-7. The path 6-7 of this particle crosses the path of the particle from 3; hence there is interference inside the wheel, which prevents our tracing with accuracy the path of a parti- cle out of the wheel. It is evident, however, that after passing into the wheel the air strikes the concave side of the sails on the opposite side, and aids in pushing the wheel around, so all the work is not done by the sails on the side where the air enters. MURPHY.] INDICATED AND TRUE VELOCITIES. 131 INDICATED AND TRUE VELOCITIES. Thus far all of our results for speed and power of windmills are given in terms of indicated velocities, that is, velocities as read from the Robinson cup anemometer. It is necessary, or at least desirable, to examine these to see whether they agree with true velocities or dis- tances actually passed over by the wind per hour. Fig. 67 shows the Robinson cup anemome- ter as used by the United States Weather Bureau. This instrument was in- vented in 1846 by Dr. T. R.Robinson, of Armagh, Ireland, and is now used by several meteorolog- ical bureaus for the meas- urementof wind velocity. It gives a continuous rec- ord of wind movement and requires no device, such as a vane, to give it the proper direction with respect to the wind. It is made so that each 50 revolutions of the cups can be read on the dial, and there is an electrical device for recording each 250 or each 500 rev- olutions of the cups. Referring to fig. 68, let A the upper and B = the lower cup of a Robin- son anemometer rotat- ing about the axis, let c equal the velocity of the wind, and v the velocity of the cup center, each in feet per second ; x = the ratio of the velocity of the wind to that of the cup center, P l = the pressure on the concave FIG. 67. Anemometer and cups, c, spindle which forms the axis of revolution of the cups; m, 50-tooth wheel which engages an endless screw on the end of the spindle; /, small toothed wheel which engages an endless screw on the axis of the wheel m ; e, pair of dial wheels which are moved by the wheel 7; p, one of ten contact pins to aid in closing the electric circuit at the end of each mile of wind; p', two of these pins connected, forming the tenth mill pin; ?r, contact spring; q, a contact point at the end of contact spring; t, small insulated tube connecting q with the insulated binding post u and with the second binding post v. surface, and P 2 = the pressure on the convex surface of the cup. Dr. Robinson found from sixteen experiments with stationary cups exposed to wind of several velocities that for all velocities the pressure when the concave surface of 132 THE WINDMILL. [NO. 42. the cup is toward the wind is about four times that when the convex sur- face is presented to the wind. The pressure on the moving cup A is P l =K l Fr(c v) 2 -t-2gS and the pressure on the cupB\sP 2 =K 2 Fr(c+ v) 2 -- 2g; F being the area of the cup, K^ and K z being constants the ratio of which, as found by Robinson, is 4, r the heaviness of air, and c+v and c v the relative velocities of the cups. Neglecting friction in the anemometer, inertia of cups and arms, and the influence of two of the cups until they are near the position shown in fig. 68, we see that for uniform velocity P l must equal P 2 ; if P 1 is greater than P 2 , v will increase ; if P 1 is less than P 2 , v will decrease. We have, therefore, for uniform velocity K^ FT (cv) 2 -:-2g=K 2 FT (v+c) 2 -r-2g or 4 (c v) 2 = (c+v) 2 . This equation can be put in the form 4(^1 ) 2 =(x+ I) 2 . Solv- ing we have o?=3; that is, the velocity of the wind is three times that of the cup centers. For an anemometer having arms 6.72 inches long, the distance passed over by a cup center in 500 revolutions is 2x22 6 72 d=y X -jg- X 3 x 500=5,280 feet, or 1 mile. Dr. Robinson believed that this ratio of wind velocity to that of cup center was true for all velocities, and con- sequently the makers of the instrument have marked the dial in miles. We shall see, however, from the rat- ing of the one that we have used in these wind- mill tests that this ratio is not a constant. It will be seen that 'for wind of uniform veloc- ity this ratio is a vari- able which has the value 3 for 9 miles an hour, is greater than 3 for less velocities, and is less than 3 for greater veloc- ities than 9 miles an hour; in other words, to get true velocities we must add a correction below 9 miles an hour and subtract a correction above that velocity. Friction and inertia were neglected in deriving the foregoing value of this ratio. The former has little influence in an instrument kept in good condition, but in a poorly kept instrument it may have a large influence for low velocities. This ratio has been found to be 8 to 10 with much friction. The inertia of the arms and cups has a marked influence on this ratio, especially for ordinary gusty wind. As the c Fio. 68. Diagrammatic section of anemometer cups. Church's Mechanics of Engineering, j>. 815. MURPHY.] INDICATED AND TRUE VELOCITIES. 133 gustiness of the wind increases the correction to be subtracted to get the true velocity increases also. The relation between the indicated and true velocity of an anemom- eter is found by moving the anemometer in still air at different velocities, and noting the distance passed over, also the readings of the instrument. It is seldom that the air out of doors is still for any considerable length of time, so that this comparison is usually made within an inclosure, the anemometer being carried around in a circle. The radius of the whirler should be as long as possible, and made so as to affect the circulation of air as little as possible, and to reduce the effect of the centrifugal force. The whirling machine that we have used for rating the anemometer is the property of the United States Weather Bureau. It consists essentially of an arm 28 feet long and 8 feet above the ground, on the end of which the anemometer is carried at an elevation of 2 feet above the arm. This arm is counterweighted and is stiffened by the rods. It is clamped to a vertical shaft, which carries a cogwheel near its lower end. A cogwheel on a horizontal shaft engages the large cog- wheel and gives rotation to the arm. For low velocities the power was applied through a crank on the horizontal shaft, and for higher velocities by a crank on a second shaft, the latter working the first shaft by means of two sprocket wheels and a chain. The machine was set up out of doors, in a sheltered place away from any building, and was used on several nights when there was scarcely any wind. It was made to rotate about half the time in the positive direction and the other half in the negative direction. A new Robinson anemometer was used with which to compare results obtained for the one used in our windmill tests. The results for these instruments agree quite closely. The results obtained on December 29, when there was no perceptible wind, are as follows: Table showing relation between indicated and true velocity of anemometer. Indicated velocity, in miles per hour. Revolu- tions of long arm in i mile of wind. True veloc- ity, in miles per hour. Correction, in miles. Correction, in miles, for gusty wind. 6 15.5 6.20 + 0.20 8 15.1 8.05 +0.05 -0.2 11 14.7 10.78 -0.22 -0.6 15 14.2 14.20 -0.80 -1.2 20 13.8 18.40 -1.60 -2.2 25 13.53 22.55 -2.45 -3.2 30 13.3 26.60 -3.40 -4.3 It will be seen that the indicated velocity is less than the true velocity for velocities less than miles an hour; above 9 miles the true velocity is less than the indicated velocity. In other words, the correction is added below 9 miles an hour and subtracted above that velocity. It will be seen that up to 11 miles an hour these 134 THE WINDMILL. [MX 42. anemometer readings differ very little from the true readings, but for higher velocities the correction becomes quite large. The last column of the foregoing table gives the corrections to be applied to the indicated velocities of the Weather Bureau Robinson anemometer for gusty wind. 1 The motion of ordinary moving air, when studied with a very light anemometer recording each revolution, is found to vary suddenly by large amounts. The rate of motion changes 20 or 30 miles an hour in a few seconds. 2 The record of the standard Rob- inson anemometer, recording miles or half miles, does not show these sudden changes, but gives an average velocity for the wind. Its VELOCITY OF WIND IN MILES 9 11 13 15 PER HOUR. 17 19 l.r, 1.4 L8 1.1 II.Q 2 0.9 t! B ' 0.7 M | 0.6 0.6 0.4 Oit o. ] 7 4 FIG. 69. Diagram showing horsepower of mill No. 27 12-foot Aermotor. Curve AB shows power for indicated velocity, assuming wind to be not gusty; AD shows power for true velocity; AE shows power in average gusty wind; A F shows power from H. P. = weight and consequent inertia cause it to continue its rotation for a time after the impulse is passed, and when the next impulse strikes the cups their weight will not allow them to take the velocity of the impulse. The less the weight the more nearly will the velocity of the cups be that of each gust. The effect is that the cups revolve faster in a gusty wind of, say, 20 miles an hour, than in wind of the same velocity but not gusty. Two difficulties arise in dealing with gusty wind: (1) The gustiness of any wind varies from time to time, and the anemometer gives no indication of it; (2) we have no means of producing artificial gusty wind in which to rate anemom- eters. If the anemometer is rated in natural wind, then a correction 1 Anemometry, by C. F. Marvin. Washington, 1893. 3 The Internal Work of the Wind, by S. P. Langley. Washington, 1893. MURPHY.] COMPARISON OF EXPERIMENTS. 135 must be applied, but its amount is uncertain. The velocity of gusty wind can not, therefore, be measured with certainty. This, however, does not lessen the value of the Robinson anemometer as an instru- ment for measuring wind velocity, nor introduce an error in our results. For a given velocity and gustiness the anemometer will always give the same reading, and the same gusty wind which strikes the anemometer strikes the windmill directly behind it. The diffi- culty arises when we try to compare results in which the Robinson anemometer was used in measuring velocity with those in which some other form of anemometer was used. The corrections given in the last column of the table were found by Prof. C. F. Marvin, of the United States Weather Bureau, and are for ordinary gusty wind. The Robinson anemometer is now so generally used to measure wind velocity that it is better to express the speeds and powers of wind- mills in terms of these than of any other. If results are desired in terms of true velocities, they can be found approximately by means of the table of corrections given on page 133. Fig. 69 shows the power of mill No. 27 expressed in terms of three kinds of velocity: AB shows the power assuming the wind to be not gusty; AD shows the power for true velocity, that is, after applying the corrections in the fourth column of the table; AE shows the power in average gusty wiud, that is, after applying the corrections in the last column of the table; AF would give its power if the power increased as the cube of the indicated velocity. COMPARISON OF WRITER'S EXPERIMENTS WITH THOSE OF OTHERS. Comparison with Smeaton' s experiments. In this comparison we use indicated velocities and results for best mills. Smeaton's results are given on pages 15 and 16, Part I. It will be remembered that his wheels were 3.5 feet in diameter, moved against still air in a circle of 5.5 feet radius, and that his wind velocities varied from 3 to 6 miles an hour. Smeaton found (maxim 1, page 15, Part I) that the velocity of a wind- mill sail, whether loaded, so as to produce maximum power, or un- loaded, is nearly as the velocity of the wind. We have found that the velocity of wind wheel when loaded increases nearly as the wind velocity, but when it is unloaded it increases as the square root of the wind velocity. Smeaton found (maxim 3) that the maximum power increases some- what less rapidly than as the cube of the wind velocity. We have found that the maximum power increases as the square of the wind velocity for true velocities somewhat faster than as the square of the wind velocity. Smeaton found (last part of maxim 5) that the power for a constant load increases as the first power of the wind velocity. Our experi- ments show that for a constant load the power increases as the square root of the wind velocity. 136 THE WINDMILL. [NO. 42. Smeaton found (maxim 6) that the circumference velocities of sim- ilarly made mills of different diameters vary inversely as the diameters. We have found this to be true. Smeaton found (maxim 8) that the maximum power for similarly made mills increases as the squares of the diameters. We have found that it increases about as the 1 . 25 power of the diameters. Smeaton found (maxim 9) that the circumference velocity of the Dutch sail, whether loaded or unloaded, is considerably greater than the wind velocity. We find that it is nearly equal to the wind veloc- ity for loaded sail, and about 1.75 times the wind velocity for the unloaded sail. Comparison with Coulomb's experiments. In this comparison indi- cated velocities are used. Coulomb's observations (see page 16, Part I) were made on a Dutch mill (fig. 1, Part I) having a wind wheel 70 feet in diameter. He found that at a wind velocity of about 15 miles an hour the wind wheel was making 13 revolutions per min- ute and yielding about 7 horsepower of useful work. Comparing this with the results for the 16-foot Aermotor for maximum load, we have the following: Comparison of results of tests of Coulomb's 70-foot mill with writer's 16-foot Aermotor. Mill. Revolutions of wind wheel per minute. Circumfer- ence velocity in feet per minute. Horsepower. 70-foot mill 13 2,860 7.0 16- foot Aermotor 28 1,408 0.8 The circumference velocity of the large mill is more than twice that of the smaller one. The ratio of the powers is 7 -i- 0.8 = 8.8. The ratio of the diameters is 704-16 = 4.4. The ratio of the powers is about twice that of the diameters. The ratio of the squares of the diameters is 19. 14. It is very likely that the wind velocity as found by Coulomb is too small; the very large circumference velocity of his wheel indicates this. It is probable that the wind velocity during his observations was about 20 miles an hour instead of 15. In a 20-mile wind the horse- power of the 16-foot mill is about twice that in a 15-mile wind, and the speed 34 revolutions per minute against 28. The ratio of the horsepowers would then be about as the diameters of the wind wheels. Comparison with Griffith's experiment. The performance of a pumping windmill depends on so many factors, most of which may affect the result to a large degree, that it is doubtful whether it is worth while to make a comparison where the conditions differ much. There is the pump efficiency alone, other conditions being the same, MURPHY.] COMPAKISON OF EXPERIMENTS. 137 which may make the horsepower of one four or more times that of the other. For example : Both mills have a brake power of 1 horsepower ; one mill works a pump which has an efficiency, under present condi- tions, of 20 per cent, its useful horsepower being 0.2; the other mill operates a pump which has an efficiency of 80 per cent, its horsepower being 0.8, or four times that of the other. We have seen that for wind velocities above a certain amount the power increases nearly as the load, so that by doubling the load for the higher velocities the power is doubled. The gearing and means of governing affect the power in a somewhat less degree. The way in which the wind velocity is measured may affect the recorded power and speed. If the wind wheel, or tower, or any other obstacle obstructs the free flow of the air to the anemometer, the recorded velocity will not be as great as it should be. If the anemometer is placed on the platform, it will give a less velocity than if held some distance in front of the wheel and at the height of the axis. The temperature and barometric pressure affect the power. In Mr. Griffiths's data (see pages 17 and 18, Part I) the load factor is known, but the wind velocities he gives are small, and for small velocities it is difficult to compute the effect on the power of differ- ences in load. In fact, most of his velocities are less than are required to start irrigating mills. Only four of his mills, viz, Nos, 1, 2, 5, and 6, are comparable with mills that we have tested. The mills with which we have compared them are Nos. 36, 38, and 47 very lightly loaded mills with low pump efficiency. Comparison of results of Griffiths's tests with those of writer's tests. Mill. Outer di- ameter of sail. Load per stroke of pump. Wind ve- locity. Strokes of pump per minute. Horse- power. Feet. Ft.-lbs. Miles. Griffiths's No. 1 ... 22.3 480.0 7.0 6.8 0.098 Writer's No. 36 .. 22.5 248.0 7.0 5.0 0.038 Griffiths's No. 2 . 11.5 29.2 5.8 13.0 0.011 Writers No. 38 .. 10.0 21.0 5.8 9.0 0.006 Griffiths's No. 5 . . 10.2 51.0 8.5 20.5 0.028 Writer's No. 38 . . 10.0 21.0 8.5 21.0 0.014 Griffiths's No. 6... 9.8 30.7 6.0 12.5 0.012 Writer's No. 47 . . . 10.0 37.0 6.0 7.0 0.008 It will be seen from this table that the horsepowers of the mills tested by Mr. Griffiths are greater than the horsepowers of the mills we have tested. The speeds of the wheels are also greater, except in Nos. 5 and 38. We are of the opinion that a part of the difference in results is due to difference in the method of measuring the wind velocity. The wind velocity found by Mr. Griffiths is less than we have found it. Comparison with King's experiments. Professor King's measure- ments of the brake horsepower of a 16-foot Aermotor are given on IRR 138 THE WINDMILL. page 20, Part I. These results are plotted in fig. 70, giving the curve AB*". f > The curve of maximum power for the 16-foot Aermotor No. 44 is redrawn in this figure as curve CD. It will be seen that these curves are nearly parallel to 16 or 17 miles an hour, and then diverge rapidly. Believing that much of this difference is due to the wind wheel of Professor King's mill interfering with the anemometer, we have experi- mented with two anemometers, one located 29 feet directly south of the wind wheel of mill No. 44, the other located 27 feet directly north of it, and each recording, side by side, the wind velocity on an elec- tric register. The hourly wind velocity for fourteen consecutive hours, during the first ten of which the mill was working and during the last four of which it was out of the wind, is given in the follow- ing table: Table showing wind velocities during writer's experiments with anemometers on mill No. 44. Hour. Direction of wind. Wind velocities. Ratio. Front ane- mometer. Rear ane- mometer. First SE Miles. 15.0 18.0 18.0 19.5 18.0 16.3 15.2 12.7 10.5 7.7 7.2 8.6 10.5 10.3 Miles. 10.2 13.4 13.5 12.8 13.5 12.6 10.0 9.6 7.5 5.5 7.2 8.6 10.6 10.4 Per cent. 0.68 0.74 0.75 0.65 0.74 0.77 0.65 0.76 0.71 0.72 1.00 1.00 1.00 1.00 Second _. ..do.. Third do Fourth . do Fifth SW . _ do _ . Sixth . ... Seventh S .. Eighth SE Ninth do Tenth ..do . Eleventh .-do.. Twelfth do Thirteenth . do . Fourteenth . . ...do The direction of the wind is the mean for each hour, as shown by an anemoscope. When the wind was from the southeast it occasion- ally came for a short time almost directly from the east; and, again, when from the southwest it occasionally came for a time from the west. It will be seen that the hourly velocity, 27 feet, behind the running wheel was only 65 to 77 per cent of that in front of the wheel. As soon as the wheel was turned out of the wind the two anemometers recorded nearly the same velocity. Referring now to the direction of the wind when Professor King's windmill tests were made, and remembering that his anemometer was 40 feet directly east of the moving wheel, it will be seen that nearly all of the tests were made when the wind came from the northwest or MURPHY.] COMPARISON OF EXPERIMENTS. 139 VELOCITY OF WIND IN MILES PER HOUR. 10 15 20 25 the southwest, and that consequently the moving wheel must have interfered with the proper working of the anemometer, causing it to record a less velocity than actually existed, and making the horse- power greater than if the anemometer had been in front of the wheel. In fig. 70 it will be seen that an increase of from 5 to 25 per cent in Professor King's wind velocities would move his curve over to the right of our curve. These curves are found in very different ways Professor King's from 26 single observations, ours from more than 150 observations. Instead of finding points on this curve when the proper load is unknown, we have found speed and power curves for constant loads, and from these drawn the curve of maximum power. None of the mills that we have tested have given a power curve like AB in fig. 70. It will be noticed too that the curve CD is quite like the corresponding one for the 12-foot Aermotor. This we should expect, since the mills are similar in construction. Comparison with Perry's ex- periments. Indicated velocities are used in this comparison. Some of Mr. Perry's results are given on pages 20 and 21, Part I. His tests were made on wheels 5 feet in diameter, carried against still air in a circle 14 feet in diameter, and his wind velocities were not greater than about 11 miles an hour. Mr. Perry states that his results agree with those of Smeaton. A comparison of our results with Smeaton's has been given on pages 135 and 136. We will compare in detail the working of two of Mr. Perry's wheels, viz, Nos. 44 and 48, with that of our 12-foot Aermotor No. 27. Mr. Perry's wheel No. 44 is somewhat like the wind wheel of our 12-foot Aermotor No. 27. It has 12 curved wooden sails, each 18 by 12.3 by 5.8 inches, having a weather angle at the inner end of sail of 30 and an angle of 25 at the outer end. The air is more obstructed in its passage through this wheel than through the wheel of No. 27. The following are some of the results for these mills in an 8.5-mile wind, the only velocity which Mr. Perry gives for his mill. HORSEPOWER. W * Cr B 1 1 GATED ts 1 / / / g i // <~>* x" FIG. 70. Diagram showing horsepower of two 16-foot Aermotors. Curve AB shows brake horsepower of Professor King's 16-foot Aer- motor; CD shows maximum power of writer's 16-foot Aermotor No. 44. 140 THE WINDMILL. [NO. 42. Comparison of results of tests of Perry's 5-foot mill No. 44 with -writer's tests of 12-foot Aermotor No. 27. Mill. Area of sail. Wind veloc- ity. Load per revolu- tion. Maximum load. Horse- power. No load. Revolu- tions per minute. Circum- ference velocity. Revolu- tions per minute. Circum- ference velocity. Perry's mill No. 44. . 12-foot Aermotor No. 37 *WS 73.0 Miles. 8.5 8.5 Ft.-lbs. 11.3 22.2 44.4 19.0 8.6 11.9 0.016 0.13 84.3 32.5 22.1 20.4 Ratios 5.3 19.6 1.38 I 8.12 0.92 It will be seen that the load, ID foot-pounds, per revolution of wind wheel is 19.6 times greater and the circumference velocity for maxi- mum load is 1. 38 times greater for No. 27 than for the 5-foot wheel, but that the circumference velocity for no load is a little less for No. 27 than for the other mill. The power of the 12-foot Aermotor is more than 8 times that of the 5-foot mill, and its sail area is 5.3 times greater. ' We will next compare the 12-foot Aermotor No. 27 with Mr. Perry's 5-foot mill No. 48, which gave the greatest power of the 61 wheels tested by him. It had six curved pasteboard sails, each 19 by 23.7 by 10.9 inches, set at a weather angle of 35 at the inner end of the sail, and at an angle of 25 at the outer end. All obstructions to the free flow of air over the back of the sails were removed. The following are some of the results for these mills at a wind velocity of 11 miles an hour : Comparison of results of tests of Perry's 5-foot mill No. 12-foot Aermotor No. 27. ivitli writers tests of Mill. Area of sail. Wind veloc- ity. Load per revo- lution. Maximum load. Horse- power. No load. Revolu- tions per minute. Circum- ference velocity. Revolu- tions per minute. Circum- ference velocity. Perry's mill No. 48 . 12-foot Aermotor No. 27 \& 73.0 5.2 Miles. 11 11 Ft.-lbs. 23.3 333 66.8 28.5 17.4 17.9 0.047 0.288 Itt 45 37. 2 28.3 0.76 Ratios 14.3 1.03 5.96 It will be seen that the circumference velocities of these wheels for maximum power are nearly equal, but for no load the circumference velocity of the 5-foot mill is about 25 per cent greater than that of the 12-foot Aermotor. The power of the latter mill is nearly six times that of the 5-foot mill. There are more air obstructions in the wheel of the 12-foot mill than in that of the 5-foot mill, so that the difference in the power would be greater for equal air obstructions. For a cor- MURPHY.] ECONOMIC CONSIDEBATIONS. 141 responding amount of obstruction the ratio of power would probably be 6.5 to 7. This ratio is greater even than 12-7-5 2 =5.76, the ratio of the squares of the diameters. From this comparison of the results of our tests with those of Smeaton and Perry it will be seen that the power of a natural moving air of a given measured velocity is greater than the resistance of the air to a wheel carried around in a circle. Some of the laws (see page 114) which have been found to govern wheels moved against still air notably that the power increases as the cube of the wind velocity are not applicable to windmills in moving air. ECONOMIC CONSIDERATIONS. The power of windmills has been computed from tests on model windmills, in artificial air of low velocity, assuming, first, that the power increases as the cube of the wind velocity, and, second, that the power increases as the square of the diameter. Our tests of wind- mills recorded in the preceding pages show that the power does not increase much faster than as the square of the wind velocity, and about as 1.25 times the power of the diameter of the wind wheel. We believe that to these two false assumptions is due the exaggerated power of windmills claimed by windmill makers and others interested. A good 12-foot steel mill should furnish 1 horsepower in a 20-mile wind (indicated) and 1.4 horsepower in a 25-mile wind. This is the smallest amount of power that will do any considerable amount of useful work. A 16-foot mill will furnish 1.5 horsepower in a 20-mile wind (indicated) and 2.3 horsepower in a 25-mile wind. A 12-foot steel mill and a 50-foot steel tower as commonly made weigh about 2, 000 pounds. A 16-foot steel mill and a 50-foot steel tower weigh about 4,250 pounds. The 16-foot outfit weighs more than twice that of the 12 foot, and its power is only 1.5 that of the latter. In addition, the 12-foot mill will govern more easily and is less likely to be injured in a storm than the 16-foot mill. In most cases, therefore, it is better to use two 12-foot mills than one 16-foot mill. The economic value of a windmill depends on its first cost, on the cost of repairs, and on its power. Most of the effort put forth at the present time to improve windmills is directed toward reducing the first cost. Competition is so strong that the cost must be kept low, and this is often accomplished at the sacrifice of the other two factors cost of repairs and power. The pumping mills and their towers are, as a rule, too light and lacking in stiffness. It is said that in some parts of the West wooden mills are coming into use again, on account of the lightness and poor quality of the steel mills. This, however, is a fault of the making, not of the material. The wooden tower is stiffer and more rigid than the steel tower. Power is the most important factor, and next to that should come strength, stiffness, and durability. 142 THE WINDMILL. [NO. 42. It has been shown that the steel mills, with their few large sails, have much more power than the wooden mills with their many small sails. (See page 106.) A mill should have as few moving parts as possible, in order that the loss of power by friction shall be small, also the liability to get out of working order be reduced to a minimum. The power of a mill is at best so small that if there is much friction there is little power left to do useful work. The grinder should be on the foot gear and not worked by a belt, and the shafting and cog- wheels should not be too heavy. In the large wooden mills the shaft- ing is much too heavy; apparently it is designed on the assumption that the mill will furnish several times more power than it really can. The mill should be carefully erected, the vertical shafting exactly vertical and the horizontal shafting truly horizontal, so that there will be no binding of the parts. Poor workmanship is an important cause of the small power of some mills. Only a skilled workman who understands the business should be employed to erect a windmill. The mills should be placed at a proper height above surrounding obstructions at least 30 feet above the highest trees and buildings. This calls for a tower from 50 to 70 feet high. It is better to use a small wheel on a high tower than a large wheel on a low tower. An 8-foot wheel on a, 70-foot tower will probably do more work in a given time than a 12-foot wheel on a 30-foot tower with trees and buildings around it. The tower should be firm and rigid, no shaking under a heavy wheel load. Steel towers are in constant vibration under heavy loads. A mill should govern readily at the proper wind velocity, but this velocity need not be less that 30 miles an hour. A weight appears to be better than a spring for holding the wind wheel in the wind. The tension of a spring can not readily be changed when desired but may gradually lose its tension. (See pages 60 and 110. ) There is very great need of an automatic device for changing the load on a pumping mill as the wind velocity changes. The mill should start in a light wind, say 4 to 5 miles an hour, or it will be idle many hours when it should be at work; but in order to do this it must be lightly loaded. In the higher wind velocities, with a light load the mill will do only a small fraction of the work it would do with a much heavier load. The increase in the load should be nearly proportional to the increase in the wind velocity. (See page 113.) Until such a device is invented the load should depend on the wind velocity of the place where the mill is to be used and on the amount of storage. The pumping mill is ordinarily constructed so that all of the useful work is done on the upstroke of the pump, producing a jerky motion and excessive strain on the working parts. This defect is partly remedied by the use of a large plunger rod, which will force up some of the water on the downstroke. A second remedy is the use of a MURPHY.] ECONOMIC CONSIDERATIONS. 143 lever with a heavy weight at one end, the other end being attached to the plunger rod. As the plunger moves down the weight on the end of the lever is raised on the upstroke. The descent of the weight assists the mill in lifting the water. Neither device is satisfactory. A pumping mill working direct stroke makes too many strokes per minute at wind velocities above about 15 miles an hour. The valves ordinarily used for small pumps will not work well if the number of strokes is greater than 30 per minute. The mill should be geared back about 2 to 1 for large mills and about 3 or 4 to 1 for small mills. INDEX TO PAPERS 41 AND 42. Page. Aermotor, air action on sail of 117-118 annual useful work of 118-119 comparisons with other mills 50, 103-104, 128-130, 136 descriptions of 29-30, 33-34, 35, 36-37, 41-42, 51, 86-89, 91-92, 93-94, 101-102 effect of air on sails of, diagrams show- ing 117,118 effect of tension of spring of, diagram showing 110 foot gear of, view showing 88 forms of, comparisons of different 69, 103, 107-109 horsepower of, diagrams showing. 95, 134, 139 invention of 11 King's experiments with 18-20 manufacturers of 29 revolutions of wind wheels of, diagrams showing 88, 92, 94 sail of, view showing 117 tests of discussed mathematically 110-117 tests of, results of 29-30, 33-34, 35, 36-37, 41-42, 51, 64, 86-89, 91-92, 93-94, 101-102 views of 30. 32, 42, 94, 117 working parts of, views showing 29, 87 Althouse windmill, Aermotor compared with 103-104 description of 89-91 horsepower of, diagram showing 91 manufacturers of 89 method of governing 14 revolutions of wind wheel of, diagram showing 91 tests of, results of ; 17, 89-91 view of 90 American Avindmill, European windmill compared with 11-12.14 invention of 11 tests of, results of 17-135 Anemometer, description of 131-135 cups of, diagrammatic section of 132 inventor of 131 measurement of wind velocity by 24-27 v i e w s of 28, 46, 131 Back-geared steel windmills, comparison of direct-stroke wooden windmills with 43 Burnham.J., invention of American wind- mill by 11 Carlyle windmill, test of, results of 17 Centrifugal-govern or method of regulation, explanation of 14 IRK 4:2 01 Page. Challenge windmill, description of 98-100 horsepower of, diagram showing 100 manufacturers of 98 revolutions of wind wheel of, diagram showing 100 tests of, results of 98-100 view of 98 Cornell windmill, description of 59-60 manufacturers of 59 tests of, results of -59-60, 64 Cost of windmill plants 28, 30,^81, 33, 44 Coulomb, C. A., windmill experiments by. . 16 windmill experiments by, compared with Murphy's experiments 136 Defender windmill, view of " water eleva- tor" and 46 Dempster windmill, descriptions of 52, 60 manufacturers of 52 tests of, results of 52, 60, 64 view of 62 Direct-stroke wooden windmills, compari- son of back-geared steel windmills with 43 Dodge, Kans., wind movement at 70, 1 18 Dutch windmill, features of 14 test of, at Lille, Flanders 16 view of, at Lawrence, Kans 14 Eclipse windmill, descriptions of 52-53, 59 invention of 11 tests of, results of 52-53, 59, 64 Elgin windmill, descriptions of 50-51, 92 tests of, results of 50-51, 64, 92 where manufactured 50 European windmill, compared with Amer- ican windmill 11-12, 14 early experiments with 15-16 European post windmill, section of 12 European tower windmill, diagram show- ing head of 13 Fairbanks-Morse windmill, descriptions of 49,57 manufacturers of 49 tests of, results of . . .* 49, 57, 64 Flanders, test of Dutch windmill at 16 France, early use of windmills in 11 Frizell pump, efficiency of 24 working parts of, view of 40 Garden, Kans., irrigation by windmills at. . 21-22 pumps near 23-24 wells near 22-23 windmill experiments at 21-22 Gause pump, view of 2-1 145 146 INDEX. Gem windmill, descrip Pag*. ot 34-35, 42-43, 43-44, 44-45 manufacturers of 34 tests of, results of. . 34-35, 42-43, 43-44, 44-45, 64 view of 44 working parts of, view of 40 German windmill, features of 14 Griffiths, J. A., windmill experiments by.. 17-18 windmill experiments by, compared with Murphy's experiments 136-137 Halliday windmill, comparisons of other mills with 104, 109 description of 43, 47, 49, 61, 94-96 horsepower of, diagram showing 96 manufacturers of 47 method of governing 14 tests of, results of 43, 47-49, 61, 64, 94-% revolution of wind wheels of, diagram showing 96 view of 46, 60 working parts of, view of 47 Holland, early use of windmills in 11 Hood, O. P., tests of Frizell pumps by 24 Horsepower, relation between wind veloc- ity and, diagrams showing 66, 67, 91, 94, 95, 96, 98, 100, 101, 107, 122, 129, 134, 139 Horsepower and speed, effect of tension of spring on 110 Ideal windmill, comparisons with other mills 102-103, 105-107 description of 30-33, 37-41, 44, 58, 100-101 horsepower of, diagram showing 101 manufacturers of 30 revolutions of wind wheel of, diagram showing 101 tests of, results of . 30-33, 37-41, 44, 58, 64, 100-101 viewsof 32, 42, 58 working parts of, view of 38 Indicated and true velocities of windmills, discussion of 131-135 Irrigator, comparison of Aermotor with 50 descriptions of 49-50, 92 manufacturers of 49 tests of, results of 49-50, 64, 92 Italy, early use of windmills in 11 Jumbo windmill, comparisons of other mills with 12-14, 127-128 description of 46 horse power of, diagram showing 122 mathematical discussion of results of tests of 119-125 revolutions of wind wheel of, diagram showing 120,121 tests of, results of 46, 64 views of 46, 120 Junior Ideal windmill, description of 92-93 horsepower of, diagram showing 94 revolutions of wind wheel of, diagram showing 93 tests of, results of 92-93 Kansas windmills and pumps for use in 71-72 King, F. H., windmill experiments by is 20 windmill experiments by, compared with Murphy's experiments 137-139 Lanvc'.ey. s. 1'.. cited 1:51 Lawrence, Kans., Dutch windmill at, view of... 14 Little Giant windmill, air action on sails of 129-130 action of wind on sails of, diagram show- ing 130 comparisons of other mills with 12-14, 127-128, 128-130 description of 125-1-26 horsepower of, diagram showing 129 manufacturers of 125 revolutions of wind wheel of, diagram showing 129 tests of, results of 125-127 view of 120 Marvin, C. F., cited 134 Mathematical discussion of tests of wind- mills 110-117, 119-127, 129-130 Monitor windmill, comparison of other mills with 105-107 description of 61-63, 96-98 horsepower of, diagram showing 98 revolutions of wind wheel of, diagram showing 98 swivel gearing of, view of 97 tests of, results of 61-63, 64, 96-98 view of 97 working parts of, view of 62 Moore, W. L., cited 118 Newell, F. H., letters of transmittal by 9, 81 Nebraska, windmills and pumps for use in. 71-72 Paddle-wheel windmills, comparison of sail-wheel windmills and 12-14 Perkins's windmill, descriptions of 59, 8(5 manufacturers of 86 tests of, results of 17, 59, 64, 86 view of 58 working parts of, view of 85 Perry, T. O., comparison of Murphy's experi- ments with windmill, experiments by 20, 139-141 elevation of wind-wheel apparatus used by 30 invention of Aermotor, by 11 windmill experiments by 20-21 Power windmills, comparisons of . 102-107, 127-128 comparison of pumping mills and. . . 107-109, 128-130 description of 83-84 difference between pumping mills and . 22 economic considerations of 141-14:5 horsepower of, comparative diagram showing 107 method of testing 84-S6 relation between wind velocity and horsepower of, diagrams showing . 91, 94, 95, 96, 98, 100, 101, 107, 122, 129, 134, 139 relation between wind velocity and revolutions of wind wheels of, dia- grams showing 88, 91 , 92, 93, 94, 96, 98, 100, 101, 105, 120, 121 , 12(i revolutionsof wind wheels of, compara- tive diagram showing 1C"> tests of, results of 15-1C>, 19, s;-l(>2 useful work 01... 118-119 INDEX. 14' Page. Power windmills, views of 90, 94, 97, 99, 120 Pressure-tank system, description of 68-69 Pumping windmills, backgeared and direct- stroke, comparison of 65-08 comparison of power mills and 107-109, 128-130 difference between power mills and 22 economic considerations of 141-143 instruments and methods used in test- ing _ -1-27 pressure-tank system of 68-69 proper load for 71-72 relation between wind velocity and horsepower of, diagrams showing. 50, 66,67 relation between wind velocity and revolutions of wind wheels of, dia- gram showing 49 relation between wind velocity and strokes of pumps of, diagrams show- ing ... 28, 32, 33, 36, 39, 41 , 45, 46, 48, 53, 55, 56 relation between wind velocity and strokes of pump of 65 tests of, results of 27-72 useful work of 65-68, 69-71 views of 26, 28, 30, 32, 40, 42, 44, 46, 52, 58, 60 Pump strokes and wind velocity, relations between, diagrams showing 28, 32, 33, 36, 39, 41, 45, 46, 48, 53, 55, 56 discussion of 65 Pumps near Garden, Kans., description of.. 2r!-24 Reciprocating piston pumps, efficiency of . . 23-24 Revolutions of wind wheel and wind ve- locity, relations between, diagrams showing 49, 88, 91, 92, 93, 94, 96, 98, 100, 101, 105, 120, 121, 126 Regulating devices of windmills, descrip- tion of 14 Robinson, T. R., anemometer experiments by 131, 135 invention of anemometer by 131 Sail-wheel windmills, comparison of paddle- wheel windmills and 12-14 Semiarid regions, mills and pumps for use in 71-72 Smeaton, .T., windmill experiments by 15-16, 20, 135-136 Speed and horsepower, effect of tension of spring on 110 Page. Star windmill, description of 35-36 manufacturers of 35 tests of, results of 35-36, 64 Stone, R. G., pumps manufactured by 23 Stone pump, details of 23, 31 view of 30 Stover windmill, test of, results of 17 Tension cf spring, effect of, on speed and horsepower no Toowoomba windmill, test of, results of 17 Valley Falls, Kans., test of windmill plant at 61 "Water elevator," description of 50 view of 46 Wells near Garden, Kans., description of .. 22-23 Wheeler, L. H., invention of Eclipse wind- mill by n Wind movement at Dodge, Kans., details regarding 413 relation between circumference veloc- ity of wind wheel and 122-125 Wind velocity, relation between horse- power and, diagrams showing 50, 66, 67, 91, 94, 95, 96, 98, 100, 101, 107, 122, 129, 134, 139 relation between revolutions of wind wheels and, diagrams showing 49, 88, 91,92,93,94,96,98,100, 101, 105, 120, 121, 126 relation between strokes of pump and . . 65 relation between strokes of pumps and, diagrams showing 28, 32, 33, 36, 39, 41, 45, 46, 48, 53, 55, 56 Wind-wheel tests, elevation of apparatus used by Perry in ( . . 20 Wonder pump, description of 50-51 manufacturers of * 51 Woodmanse pump, sectional view of 27 Woodmanse windmill, descriptions of 51-52, 55-57 methods of governing 14 tests of, results of 51-52, 55-57, <>4 Woodmanse Mogul windmill, descriptions of 27-29, 51-52, 53-55, 55-57 manufacturers of 27 tests of, results of 27-29, 53-55, 64 views of _> pump, etc., of, view of 54 working parts of, view of 26 o OF THE UNIVERSITY OF THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW TO T "NT IP f! 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