f 

DEPARTMENT OF THE INTERIOR 

WATER-SUPPLY 

AND 

IRRIGA'l-,ION PAPERS 

OF THE 

UNITED STATES GEOLOGICAij SURVEY 

No. 42 

THE WINDMILL: ITS EFFICIENCY AND 

ECONOMIC USE, PART II.-MunPHY 

WASHINGTON 

GOVERNMEN1' PRINTING OFFICE 

1901 
IRRIGATION REPORTS. 

The following list contains titles and brief descriptions of the principal reports 

relating to water supply and irrigation, prepared by the United States Geological 

Survey since 1890: 

1890. 

First Annual Report of the United States Irrigation Survey, 1890; octavo, 123 pp. 

Printed as Part II, Irrigation, of the 'l'enth Annual Report of the United States Geolog- ical Survey, 1888-81l. Contains a statement of the origin of the Irrlgation Survey, a pre- liminary report on the organization and prosecution of the survey of the arid lands for 

purposes of irrigation, and report of work done during 1800. 

lS91. 

Second Annual Report of the United States Irrigation Survey, 1891; octavo, 395 pp. 

Published as Part II, Irrigation, of the Eleventh Annual Report of the Uniwd States 

Geological Survey, 1889-00. Contains a description of the hydrography of the arid region and of the engineering operations carried on by the Irrigation Survey during 1800; also 

the statement of the Director of the Survey to the House Committee on Irrigation. and 

other papers, including a bibliography of inigation literature. Illustrated by 29 plates and 4 figures. 

Third Annual Report of the United States Irrigation Survey, 1891; octavo, 576 pp. 

Printed as Part II of the Twelfth Annual Report of the United States Geological Survey, 1800-91. Contains" Report upon the location and survey of reservoir sites during the 

fiscal year ended June 30, 1891," by A. H. Thompson; "Hr.drograJ>hY of the arid regions." by F.H. Newell; "Irrigation in India," by He1•bert M. W1lsou. lllustrated by93platesand 100 figures. 

Bulletins of the Eleventh Census of the United States upon irrigation, prepared by F. H. Newell; quarto. 

No. 35, Irrigation in Arizona; No. 60, Irrigation in New Mexico; No. 85, 

Irrigation in Utah; No. 107, Irrigation in Wyoming; No. 153, Irrigation in 

Montana; No.157,Irrigation in Idaho; No. 163,Irri~ation in Nevada; No.178, 

Irrigation in Oregon; No. 193, Artesian wells for urigation; No. 198, Irriga- tion in Washington. 

189~. 

Irrigation of western United States, by F. H. Newell; extra census bulletin No. 

23, September 9, 1892; quarto, 22 pp. 

ConLu.ins tabulations showing the total number, average size, etc., of irrigated holdings, the total area and average size of irrigated farms in the subhumid regions, the percentage of number of farms irrigated, character of crops, value of irrigated lands, the average cost of irrigation, the investment and profits, together with a resume of the water sup-ply and a description of irrigation by artesian wells. Illustrated by colored maps showmg the 

location and relative extont of the Irrigated areas. 

1sua. 

Thirteenth Annual Report of the United States Geological Survey, 1891-92, Part 

III, Irrigation, 1893; octavo, 486 pp. 

Consists of three papors: "Water su-pply for irrigation," by F. H. Newell; "American 

irrigation en'?lneering" and "Engineermg results of the Irrigation Survey," by Herbert 

M. ·wilson; ' Construction of topographic maps and selection and survey of reservoir 

sites," by A. H. Thompson. Illustrated by 77 plates and 110 figures. 

A geological reconnaissance in central Washington, by Israel Cook Russell, 1893; 

octavo, 108 pp., 15 plates. Bulletin No. 108 of the United States Geological 

Survey; price, 15 cents. 

Contains a description of the examination of the geologic structure in and adjacent to the drainage basin of Yakima River and the great plains of the Columbia to the east of 

this area, with special reference to the occurrence of artesian waters. 

lS94.. 

Report on agriculture by irrigation in the western part of the United States at the 

Eleventh Census, 1890, by F. H. Newell, 18!!4; quarto, 283 pp. 

Consists of a general description of the condition of irrigation in the United States, tbe area irrigated, cost of works, their value and profits; also describes the water supply, the 

valuo of water, of artesian wells, reservoirs, and other details· then takes up each Stute 

and Territory in order, giving" general description of the condition of agriculture by irrigation, and disousses the physical condit-ions and local peculiarities in each county. 

Fourteenth Annual Report of the United States Geological Survey, 1892-93, in two 

parts; Part II, Accompanying papers, 1894; octavo, 597 pp. 

Contains papers on "Potablo wators of the eastern United States," by W J McGee; 

"Natural mineral waters of the United States," by A. C. Peale; "Results of stream mea.~urements," by F. H. Newell. Illustrated by maps and diagrams. 

IRR 42 (Continued on third page of cover.) 
DEPARTMENT OF THE INTERIOR 

W ATER~SUPPLY 

AND 

IRRIGATION PAPERS 

OF THE 

UNITED STATES GEOLOGICAL SURVEY 

No. 42 

' 

WASHINGTON 

GOVERNMENT PRINTING OFFICE 

1901 

UNITED STATES GEOLOGICAL SURVEY 

CHARLES D. WALCOTT, DIRECTOR 

THE ·WINDMILL: 

ITS EFFICIENCY AND ECONOMIC USE 

PART II 

BY EDWARD CHARLES :MURPHY 

WASHINGTON 

GOVERNMENT PRINTING OFFICE 

1901 

CONTENTS. 

Page. 

Letter of transmittal _____________ .. ____ . __________ . ______ . _. __ . _____ . _ . _ _ 81 

Experiments by writer-Continued __________ .. _____ . ______ . ----- __ __ _____ 83 

Power mills __ . _____ . __ .. ______ . _ . _____ .. ________ . _______________ . _ . . 83 

Method of testing _____ . __ . _ _ _ _ ___ . _______ . _________ . _____ . ______ . 84 

Mills tested .... _ . ___ ... ____ . _ _ ____ .. __ . ___ . ______ . ____ . ____ . _... 86 

Comparison of power mills. __ . _______ . _ _ ___ . ____ .... _ ... ____ . . . . 102 

Comparison of pumping mills with power mills ... ___ . . . . . . ___ , _. _ . . . 107 

Effect of tension of spring on speed and horsepower of milL _____ .... _.. 110 

Mathematical discussion of tests of two Aermotors .. _ ...... ___ .. _ _ . . . 110 

Action of air on the sail of an Aermotor . _ . ___ . _ _ . _ _ _ _ _ _ . __ ... __ . _ _ _ 117 

Useful work of two power mills in a given time. ____ ~ ___ . _ _ . _ _ _ _ _ _ _ _ _ 118 

Mathematical discussion of tests of Jumbo mill No. 55 . __ . __ .. ___ . _. _. 119 

Relation between wind velocity and circumference velocity of 

wheel ___ .. _ .. .. . _ _ _ ___ . . . _ ... __ . _ ... ___ ... _ _ _ .. __ . _ ... ___ . ___ . 122 

Mathematical discussion of tests of Little Giant mill No. 56 __ . _____ . _ _ 125 

Comparison of Little Giant and Jumbo mills .. _. ____ . _______ . ___ .. ____ 127 

Comparison of Little Giant and 8-foot Aerniotor ____________ .... ___ . _ _ _ _ 128 

Indicated and true velocities ______ .. ______ . ___ . ____ .. ______ ... _ _ _ _ _ _ _ _ 131 

Comparison of writer's experiments with those of others. __ . _. ___ . ___ . _ _ _ _ _ 135 

Economic considerations. __ . __ .. _______ . ____ .. ____ .. _______ .. __________ . _. 141 

Index to Papers 41 and 42 _________ .. _. _ . __________________ .. ___ .•.. __ , _. _ _ _ 145 

77 

ILLUSTRATIONS. 

Page. 

PLATE XV. View of mill No. 44-16-foot Aermotor _ . __ . ____ . _______ . _ _ _ _ _ 94 

XVI. A, View of mill No. 57-24-foot Little Giant; B, View of mill 

No. 55-7. 75-foot Jumbo .. __ ._ ....... ___ .. ________ . ____ .. _ _ _ _ 120 

FIG. 32. Working parts of mill No. 26-14-foot Perkins ...... -------- . ____ 85 

33. Working parts of mill No. 27-12-foot Aermotor. _____ . ______ . _. _. 87 

34. Foot gear of mill No. 27 _ .. _ _ _ _ _ __ . _ .... _______ ..... __ .. _ _ _ _ _ _ _ _ _ _ 88 

35. Diagram showing revolutions of wind wheel of mill No. 27 _______ . 88 

36. View of mill No. 28-16-foot wooden Althouse. __ . ___ .____________ 90 

37. Diagram showing revolutions of wind wheel of mill No. 28. _ _ _ _ _ _ 91 

38. Diagram showing horsepower of mill No. 28 .. _ _ _ _ . ___ ... _ . ___ .. _ 91 

39. Diagram showing revolutions of wind wheel of mill No. 29-16-foot 

Aermotor ________ . _ _ _ _ . . _ . ___________ . _____ . _ . _ . _ . __ . . _ _ . _ . _ _ _ 92 

40. Diagram showing revolutions of wind wheel of mill No. 34-14-foot 

Junior Ideal .. ___ .. _ _ . __ . _ _ _ ... ___ . ___________ . ____ .. _ . __ . _ . _ 93 

41. Diagram showing horsepower of mill No. 34 _ .. ______ .. ___ . ____ . _ . 94 

42. Diagram showing revolutions of wind wheel of mill No. 44-16-foot 

Aermotor ..... __ .. _ ... _ _ _ _ _ __ . __ ... _ . ____ . __ . __ . __ . _______ . _ _ 94 

43. Diagram showing horsepower of mill No. 44 . ______ . _________ . _ _ _ 95 

44. Diagram showing revolutions of wind wheel of mill No. 49-22-!-

foot Halliday .. _____ . __ _ ________ . ____ . _ .... _____________ , ___ . 96 

45. Diagram showing horsepower of mill No. 49 _______ . _ ... __ . ___ . __ . . 96 

46. View of mill No. 50-12-foot Monitor ______ . __ . __ .... ____ ---·.____ 97 

47. Swivel gearing of mill No. 50 ___ .. __ .. _. ______________ .. _ .. __ .. __ 97 

48. Diagram showing revolutions of wind wheel of mill No. 50. ___ .. _. 98 

49. Diagram showing horsepower of mill No. 50. _______ . ___ ------·____ 98 

50. View of mill No. 52-14-footChallenge_________________ 99 

51. Diagram showing revolutions of wind wheel of mill No. 52 ______ . 100 

52. Diagram showing horsepower of mill No. 52. _____ . ____ .. __ . __ . _ _ _ 100 

53. Diagram showing revolutions of wind wheel of mill No. 53-12-foot 

Ideal .. __ . __ . _ .. __ .. _ .. _ _ _ _ _ _ ___ ... __ ... _ .. _. _______ . _ ... ___ . _ . _ . 101 

54. Diagram showing horsepower of mill No. 53_. __ . _ .. ___ .. ____ . ___ . _ _ 101 

55. Comparative diagram of revolutions of wind wheels of mills Nos. 

50. 53, and 27 __ . . __ .. _____ .. _. .. _. _ _ _ _ _ _ _ ... _ .. _____ .. _____ . 105 

56. Comparative diagram of horsepower of mills Nos. 50, 53, and 27 _. _ 107 

57. Diagram showing effect of tension of spring of mill No. 44-16-foot 

Aermotor ____ ~ _ _ _ __ _ _____ . ___ .. ______ .. _____ .. ___ .... __ . _____ . 110 

58. Sail of H)-foot Aermotor .... ____________ ------------ ---· ___ ·------ 117 

59. Outer end of sail of 16-foot Aermotor ___________________ . ___ .. . . . . . 117 

60. Inner end of sail of 16-foot. Aermotor __ . _________ .. ___ . .. _ _ _ _ _ _ _ _ 118 

61. Diagram showing revolutions of wind wheel of mill No. 55-7.75-

foot Jumbo _____ . _______________ .... __ . __ . _ ... __ ... ____ - _ _ _ _ _ _ _ 12() 

79 
80 ILLUSTRATIONS. 

FIG. 62. Diagram showing revolutions of wind wheel of mill No. 55 _____ . __ 

63. Diagram showing horsepower of mill N C!· 55 .. _ .. ___ .. . _ _ _ _ _ _ _ _ 

64. Diagram showing revolutions of wind wheel of mill No. 56-4.67-

footLittleGiant.--------··-----·--- __________ -------------

65. Diagram showing horsepower of mill No. 56 _______ . ____ . ________ _ 

66. Diagram showing action of wind on sails of mill No. 56_ .. _ _ _ _ _ _ __ 

67. Two views of anemometer and cups _________ . ____ . _____________ _ 

68. Diagrammatic section of anemometer cups _ _ _ ..... _ _ _ _ _ ___ . _____ _ 

69. Diagram showing horsepowflr of mill No. 27-12-foot Aermotor ___ . 

70. Diagram showing horsepower of two 16-foot Aermotors_. ___ . ____ _ 

Page. 

121 

122 

126 

129 

130 

131 

132 

134 

139 
LETTER OF TRANSMITTAL. 

DEPARTMENT OF THE INTERIOR, 

UNITED STATES GEOLOGICAL SURVEY, 

DIVISION OF HYDROGRAPHJ, 

Washington, January 14, 1901. 

SIR: I have the honor to transmit herewith a manuscript entitled 

The Windmill: Its Efficiency and Economic Use, Part II, by Edward 

Charles Murphy, formerly professor of civil engineering in the University of Kansas, and to request that it be published in the series of 

Water-Supply and Irrigation Papers. 

This manuscript is a continuation of the material published as Paper 

No. 41, it being necessary to divide the manuscript on account of the 

limitation imposed by law of 100 printed pages for each pamphlet. 

Very respectfully, 

Hon. CHARLES D. WALCOTT, 

F. H. NEWELL, 

Hydrographer in Charge. 

Director United States Geological Survey. 

81 

• 
• 
THE WINDMILL: ITS EFFICIENCY AND ECONOMIC USE. 

PART II. 

By EDWARD CHARLES MURPHY. 

EXPERIMENTS BY WRITER-CONTINUED. 

In Part I of this paper, published as Water-Supply and Irrigation 

Paper No. 41, will be found a classification of windmills, a discussion 

of regulating devices, a synopsis of early experiments with windmills, 

and a discussion of the writer's experiments with pumping mills. 

This part (II) of the paper contains the results of the writer's experi.: 

ments with power mills, a comparison of pumping mills with power 

mills, and discussions of various facts developed by the tests, together 

with a comparison of the writer's experiments with those of other 

experimenters, and the economic considerations of the subject. 

POWER MILLS. 

The power mill differs essentially from the pumping mill in that the 

latter gives a reciproc>ating motion to a pump piston, while the former gives a rotary motion to a vertical shaft, and this, in turn, to a 

horizontal shaft, which drives the grinder or other machine. The 

mechanism by which this is accomplished in the Aermotor is shown 

in figs. 33 and 34. The small plane cogwheel makes three revolutions to one revolution of the wind wheel, and the small beveled cogwheel makes two revolutions to one revolution of the small plane 

wheel; so that the vertical shaft makes six revolutions to one revolution of the wind wheel; or, as we say, the shaft is geared forward 6 

to 1. The two beveled cogwheels of the foot gear (fig. 34) change the 

motion around a vertical axis to a motion around a horizontal axis 

without changing the rate of speed. In fig. 7, Part I, which shows 

the pumping ~ilJ, it will be seen that the large cogwheel which gives 

the up-and-down motion to the piston makes one revolution to each 3.3 

revolutions of the wind wheel, or that, the pump is geared back 3. 3 to 1; 

s.o that the vertical shaft of a power mill makes tw:enty revolutions to 

one stroke of a pump worked by a pumping mill the wind wheel of 

·which is running at the same rate as that of the power mill. The 

83 
84 THE WINDMILL. [N0.42. 

term "geared mill" is sometimes applied to power mills, but inappropriately, since the pumping mill also is geared. The latter is geared 

back, the former is geared forward. 

Power mills are heavier than pumping mills. They ordinarily do 

more work and carry heavier loads than the latter. The load on the 

pumping mill is constant for all wind velocities, but it may be varied 

in the power mill. The grinder is made so that as the speed increases 

the quantity of corn which enters increases, and thus the load and 

work done are increased. The mill is expected to do three or four 

kinds of work-for example, pump water, shell and grind corn, and 

turn a grindstone. In a light wind the pump only can be worked, 

but as the wind increases one after another of the three other machines 

can be set at work, and thus the load be suited to the velocity of the 

wind and the mill be made to do the maximum amount of work. Power 

mills are not made smaller than 12 feet in diameter, for the reason 

that a small size will not give power enough to be of account except 

for pumping. The ordinary steel power mills are 12 feet, 14 feet, and 

16 feet in diameter. 

The power t;hat a windmill is capable of developing can be determined better from a power mill than from a pumping mill, because 

the efficiency of the pump--which may be anywhere from 20 to 85 per 

cent-is eliminated, and because the load on the mill can be varied at 

will, and thus the effect of the load on the power of the mill be determined for different wind velocities. 

METHOD OF TESTING. 

The power was measured by the use of a Prony friction brake placed 

on an iron pulley on the foot gear or horizontal shaft. The brake 

was of wood, and had an arm 3 or 4 feet long. Near the· end of this 

arm was fastened a spring balance reading to quarters of a pound. 

By turning the nuts on the brake the spring balance could be made 

to read any desired amount. As the brake on the pulley was tightened, the reading of the spring balance was increased and the number of revolutions of the shaft decreased. The brake is shown in Pl. 

XV. The speed of the shaft was found in one of three ways-whichever was most convenient. A small electric device was used whenever it could conveniently be attached to the wind wheel. The clicks 

of this instrument could easily be counted, and gave the number of 

revoh1tions of the wind wheel for each half mile of wind movement. 

A speed counter was used, but did not prove satisfactory. Whenever 

the electric device could not conveniently be employed, the number 

of revolutions of the wind wheel was found by coup.ting the revolutions of a mark on the wind wheel as reflected in a mirror conveniently placed. 

To illustrate: If u is the number of revolutions per minute of the 

brake pulley as found from the revolutions of the wind wheel per 
MURPHY.] WRITER'S EXPERHIENTS. 85 

half mile of wind, L the load in pounds as read from the spring balance, and R the length of the arm, then the useful work, in footpounds per minute, is-W = 2 n: R 1.t L, and the horsepower is-H. P. 

= 2 n: R u L ...;-. 33 000. 

The number of revolutions per minute of wind wheel was found for 

each mill for from two to six different brake loads, for wind velocities 

as small as would keep the mill working for the particular load used 

FIG. 32.- Working parts of mill No. 26- 14-foot Perkins. 

up to about 25 miles an hour. That is, the reading of the sprmg balance was kept as nearly constant as possible until we had obtained 

points and a curve like that shown in fig. 10. Then the load was 

changed and the. tests continued in the same way, getting another 

curve. From these curves the number of revolutions of wind wheel 

per minute for different loads and wind velocities was easily found, 

as before indicated. These are given in the table of results for each 

mill tested, and in mauy cases are also shown by diagram. The horse-
86 THE WINDMILL. [No.42. 

power of any mill for different loads and velocities is easily found by 

the foregoing formula. '.rhese are given in the tables of results of 

tests, and are also shown by 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 o 

with the plane of the wheel. rrhe shaft is geared forward 0 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. 

F i Number of revolutions of wind Uoeful horsepower at given wind I 

I Load wheel per minute at given wind velocities (per hour). 

per velocities (per hour). 

revoluI tion of . a:i 00 a:i 00 00 <1i wind ff5 Q) OJ OJ OJ ~ • • • I Q) Q) Q) 

I wheel. :;:: ] ] ,] ] ~ '§ ] ] ] 

I ~ ~ ~ ~ ~ 00 ~ ·-----_--------- -------

I Pound~ 645 ------ ------ 16 31 48 -~ J:Pt.-lbs. 

;'l ., 11 I 

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 1). 

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. 'fhe 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. 

I I Number of revolutione of 

wind wheel per minute Ueeful horeepower at given wind ve-l 

Load at given wind velocities locities (per hour). 

per (per hour). 

Load on revolubrake. tion of 

I I 

wind al a:i <1i 00 00 00 00 00 <1i 00 Q) Q) Q) ~ Q) Q) ~ Q) wheel. ~ ] ] ] Q) ] ] ] "§ I "§ i ] "§ 

~ ~ 0 ~ ~ "' ~ ~ 00 ~ I 00 ,...; .-I ~ 

-- ---~--·- ---- -

I -----------

Pounds. Ft.-lbs. I 

LJ 0 30 49 63 75 "I··· .. --o:285- ··o:38i'>" ··o:458-

--nrl 

222 

:::~~:1---~- 57 70 444 48 65 ~~ --~~o~:- (}.303 0. 653 0.890 666 12 50 72 --- --- ~--- . -- - . --- --- . 1.03 
MURPHY.] POWER MILLS TESTED. 87 

The revolutions of wind wheel per minute fol' 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 standing 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-foot 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. 'fhe work done in overcoming this resistance is 

1.25X2nx6=47.1 foot-pounds per revolution. The work done per 
88 THE WINDMILL. (N0.42. 

revolution of wind wheel per pound on the brake arm is-27t X 35.25 X 

6-;- 12=111 foot-pounds. The ratio of these is 47.1-;-111 = 0.425 pound. 

Hence a brake load of 0.425 pound is equivalent to the friction load. 

FIG. 34.-Foot gear of mill No. 27- 12-foot 

Aermotor. a indicates point where brake 

pulley was attached. 

The effect of each additional 2 

pounds lqad on the brake in reducing the speed of the wheel at 

different wind velocities is clearly 

shown here. It is seen that an 

added load makes a greater proportionate reduction in the speed 

when the velocity is low than when 

·it is high. Thus, in an S-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 

VELOCITY OF WIND IN MILES PER HOUR. 

FIG. 35.-,-Diagram showing revolutions of wind wheel of mill No. 27- 12-foot Aermotor. Curve 

mar ked o is for no brake load; curve marked 2 is for a brake load of2 pounds; cm·ve war ked 4is 

for a brake load of4 pounds; curve marked 6 is for a brake load o(G 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 velocity necessary to start 

the mill increases more rapidly than the increment of loading. That 

is, the 0-pounclload 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 difference 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 fo:r: 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 t.o 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 ~ith 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. 

Mill No. 28.-This is a 16-foot Althouse wooden power mill manufactured 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. rrwo half sails are missing 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 necessary 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 

fly wheel was put on the shaft, which steadied the motion of the mill 

somewhat. The 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 

IRR 42-Ql--2 

• 
90 THE WINDMILL. [N0. '12. 

give better results. It is with the aid of better results obtained from 

tests of other mills of similar make that we a rc able to give tlto results 

in the following table and iu the diagrams. 

FIG. 36.-View of mill No. 28-H>·foot wooden Althouse. 

Results of tPsts of mill No. 28-16-foot wooden Althouse. 

Number of revolutions of wind 

wheel per minutfl at given Horsepower of mill at given wind I 

velocities c..-er hour). Load wind velocities (per !lour). 

Load on ~T~ti~~· !--,--- br ake. ofwind 

wheel. 00 00 00 ..!l ..!l ..!l 

"§ "§ "§ 

~ "' 00 rl 

Pounds. Ft.-lbs. 

0 0132330 

1t 427 ------ 20 27 

G. ---------- ------ 5 13 

5t 914 ------ ------ 19 

8t 1, 462 ------ -- ---- 8 

00 

..!l 

"§ 

., 

0 

36 

31 

20 

23 

13 

<II 

" :;::1 

s 

C-'l 

00 00 00 00 00 

..!l " " " " ] :;::1 ] ] "§ s 00 ~ '"' a '" rl ., 

40 ·--· ---- · ·-- ·-- - ---- ··-· ·--- ·--- -- ·- ---·--

;:: :::::::: n-' "- ... ':"' .... ":~ ..... ~.-~ 27 ·--- --- -------· 0. 52 0. 64 0. 75 

15 -------- ---- ·--- 0.35 0. 60 0. 67 

Fig. 37 shows the number of revolutions per minute of the wind 

wheel of this mill for t.he brake loads 0, L75, 5.75, and 8.75 pounds, 
MURPHY.] POWER MILLS TESTED. 91 

and for grinder load. The curve for the grinder load is a nearly 

st,raight line. This is due to the fact that the grinder is construeted 

so that as its speed increases the 

amount of corn it receives increases; thus the load increases 

automatically as the wind. velocVEI,OCITY OF WIND IN MILES PER HOUR. 

ity increases. By comparing ~ 

these speed curves, as they may ~ 30 

be called, with those of·fig. 35, A 

z for the Aermotor, it will be seen ; 

10 1.5 20 25 

that the speed of the latter is ~ 20t-----Y-~--f---:---,.;L----,i~----l 

much greater than that of mill 

No. 28. 

Fig. 38 shows the horsepower of 

this mill for three brake loads1. 7 5 pounds, 5. 7 5 pounds, and 

8. 7 5 pounds. The latter load is 

too great for the mill. By comparing the results for this mill 

with those for the 12-foot Aermotor (fig. 35) it will be seen 

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. 

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 Pl. XV. 

VELOCITY OF WIND IN MILES PER HOUR • 

It is manufactured by the Aermotor Company, of Uhicago, 

..----1r

0 

___ 1

1

1l ___ .,_ __ ...,

25 Illinois. The tower is of wood, 

~ 

l'il 

~ .t~---+---+-~~~----; ~ 

l'il 

00 

~ 

0 

= 

FJG. 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, respectively; dotted curve HK shows maximum 

power. 

42 feet to the axis of the wheel. 

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 forward 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 distance of about40 feet. It has a 

cylinder 1. 5 inches in diameter 

and a stroke of 8 inches. '"rhe 

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-
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. 

D Number of .revolutions of wind Horsepower of mill at given wind 

wheelperminuteatgiven wind velocities (per hour). Load velocities (per hour). 

Load on ~Y~B~~- ~----~---,---,---1----.---.,---------;----;-----l 

brake. of wind a5 ~ ai ~ rJ:, I ~ ~ I rJ:, ,;, 

wheel. ~ ] ~ ] ~ ~ ] ] ] ] 

-----~~ ~ ~~~~~~--00-1~~-~-~ 

Pounds 1i Ft.-lbs. 212 20 351 ________ --------I -------- 0.13 I 0.23 I -------- --------I -------- P+lt 487 11 30 41 -------- ------- 0.17 0.44 0.636 -------- ---- __ ·- P+2i 629 25 35 -------- ---------------- 0.48 0.714 ----------------

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, VELOCITY OF WIND IN MILES PER On aCCOUnt Of the failure Of the Shaft- HOUR. 

lfl 1 i ~?l ing, they are complete up to a wind 

Or----...----.-----. velocity of 15 mile'S an hour, and when 

E 

studied in connection with the complete test of ~ 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. 

ri.l 

z 

Mill No. 30.-This is a 1·6-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 

~ 2()~~+-7rT---r---~ 

p 

...:l 

0 

> r;.'l 

IXl 

A C 

arm 2. 5 feet long. Curves showing the 

number of revolutions of the wind wheel 

per 1ninute for t,hese loads and the useful elevator load are reproduced in fig. 

22, Part I; . the horsepowers for these 

FIG.39.-Diagramshowingrevolutions loads are shown in fig. 23, Part I. 

of wind wheel of mill No. 29-16-foot 

Aermotor. CurveABis for a load of Mill No. 31.-This is a 14-foot Elgin 

212 foot-pounds; OE is for a load of wooden power mill used to lift water 

487 foot-pounds; DF is for a load of with a rotary (\Vonder) pump. It is 

629 foot-pounds. 

described on pages 50 to 51, Part I. 

Mill.1Vo. 34.-This is a 14-foot Junior Ideal steel power mill manufactured by the Stover Manufacturing Company, of Freeport, Illinois. 

The tower is of wood, 41 feet to the axis of the wheel. The wheel has 
MURPHY.] POWER MILLS TESTED. 93 

24 curved sails in eight sections, 

ciple. Each sail is 49 by 18 

regulated on the centrifugal prinby 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 a counterpoise. It is geared 

forward 8 t,o 1. The mill is 

used for shelling and grinding corn and elevating. The 

brake pulley is on a line shaft 

1'5 or 20 feet long. In a 12-

mile win~ the mill ground 12 

pounds quite fine for a mile of 

wind, or at the rate of 144 

pounds an hour. In an ISmile 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 Company, of Evansville, Wisconsin. The wind was unsteady, 

the temperature high-100° 

in the shade at noon. Theresults of the tests are as follows : 

VELOCITY 0 F WIND IN MILES PER HOUR. 

10 1.') 20 

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, l, and 3.5 pounds, respectively, 

and for grinder load. 

Results of tests of mill No. 34-llrfoot steel Junior Ideal. 

D Number of revolutions of wind H f .11 · . d I wheelperminuteatgiven wiud orsepower .o. mi at given wm Load per velocities (per hour). veloCltieA (per hour). r~volubrake. t~rnd.f oo ui oo' oo ,;, oo oo ui oo oo 

wheel ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ·a a a a a a a a a a 00 ~ ~ ~ ~ 00 ~ ~ ~ ~ ----_--------------------;-

JPounds. Ft.-lbs. 

lJ 0 20 34 44 53 58 w------- -------- -------.. -------- -------- 180 13 29 40 49 55 0.07 0.16 0.22 0.27 0.33 

G. 4 19 32 39 47 ------0- ------0- -------- -------- 631 0 0 24 32 40 0.46 0.61 0.76 

Fig. 40 shows the number of revolutions of the wind wheel per minute for brake loads of 0, 1, and 3. 5 pounds, and for the grinder load. 

F'ig. 41 shows the horsepower for brake loads of 1 and 3. 5 pounds. 

Mill No. 44.-This is a 16-foot Aermotor 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 [N0.42. 

The results of the tests are as follows: 

Results of tests of mill No. 44-16-foot Aermotor. 

Number wheel per of minute revolutions at given of wind wind Horsepower of mill at given 3 wind 

Load per velocities (per hour). velocities (per hour). 

Load on r~volu1 brake. t~~t ~ ~ ~ ~ 00 00 ~ ~ ' ~ ~ 

wheel. ] ] ] '§ ~ ~ ] ] ] ] 

00 ~ ~ ~ ~ 00 ~ ~ ~ ~ -----------------------------

Pounds. Ft.-lbs. 

1,936 

23 38 

28 

13 

48.0 

41.0 

33.5 

16.0 

56 64.5 -------- 50 58.5 44 53.5 

36 47.0 ---.. --- ~ 

25 39.5 --------

~-- -.. ~"-- -------- -------- -------- 0.45 0.66 0.80 0.94 

0.35 0.89 1.16 1.43 

----·---- 0.68 1.53 2.01 Ul -------- -------- 1. 47 2.31 

o •• i 

----~-~-~-~~-~--~--~-~~-~--~-~ 

VELOCITY 0~' WIND IN MILES PER HOUR. 

10 15 20 25 

FIG. 41.-Diagram showing horsepower of mill 

No. 34-14-foot Junior Ideal. Curves marked 3i 

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 

revolutions per minute of the 

wind wheel for these brake 

loads. The n urn ber 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 

Am·motor. Fig. 43 shows the 

horsepower of this mill for loads 

of 3, 5, 8, and 11 pounds, respectively. The curves for this mill 

closely resemble those of the 

12-foot Aermotor. The curves 

of the latter were platted, but the diagr<tm is not reproduced because 

Of lack Of Space. Jt Will be VELOCITY OF WIND IN MILES PER HOUR. 

shown further on that these 10 15 20 25 

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 parabola, that the load for it 

increases nearly as the first 

power of the wind velocity, 

and that the speed of the 

wheel increases also as the 

first power of the wind velocity. 

Mill No. 49.-This is a 

FIG. 42.-Diagram showing revolutions of wind wheel 

of mill No. 44-l6·foot Aermotor. Curves marked 0, 

3, 5, 8, and 11 are for brake loads of 0, 3 pounds, 5 

pounds, 8 pounds, and 11 pounds, respectively; curve PQ is speed of wheel for maximum load; RS is load curve for maximum power. 
U. S. GEOLOGICAL SURVEY WATER- SUPPLY PAPFR NO. 42 PL. XV 

VI EW OF MILL NO. 44-16-FOOT AERMOTOR. 
MURPHY.] POWER MILLS TESTED. 

22.5-foot Halliday wooden power mill on a 43-foot wooden tower. 

The sail area is in two concentric rings, the outer ring 

having 144 sails, the inner 

ring 100 sails, each 43 by 4.5 

by 3.5 inches, set at an 

angle of 25° t,o the plane 

of the wheel. The upper 

gearing has a ratio of 50 to 

14, the lower gearing a ratio 

of 53 to 26, so t,hat the 

. horizon tal- shaft is geared 

forward 7. 28 t,o 1. The 

brake pulley is 8 inches in 

diameter, the brake arm 4. 7 5 

feet long. The mean temperature was 82° F., the 

mean barometric pressure 

28.7 inches. The mill is 

used for shelling and 

grinding corn. Four brake 

loads (0, 1.5, 5, and 9 

pounds, respectively) were 

used, also the grinder load. 

VELOCITY OF WIND IN MILES PER HOUR. 

10 15 20 25 

FIG. 43.-Diagram showing horsepower of mill No. 44-

16-foot Aermotor. Curves marked 3, 5, 8, and 11 show 

power for brake loads of 3, 5, 8, and 11 pounds, respectively; dotted curve DK shows maximum power. 

The results of the tests are as follows: 

Results of tests of mill No. 49-22.5-foot wooden Halliday. 

Horsepower at given wind velocities 0 (per hour). 

Number of revolutions of wind 

wheel per minute at given Load per wind velocities (per hour). 

Load revolu· on tio_n of 1----,,-----. -;---.--.~-. ---,-1

--. -1---,-----,-~-;------;~--: 

brake. wmd 00 gj gj i£ g'5 wheel. _$ :;::: :;::: :;::: :;::: 

..... s s s s ~ ~ ;=; ~ ~ 

Pounds. li't.-lbs. 0 0 11 20 

16 

11 

30 

26 

22 

a5 00 rD rD rD 

<D .$ .$ ~ ] ·a s s i ~l ;=; c 00 ..... ~ ~ 

32 ·------- -------- ·--- ·--- ---- ·--- ------ ·--- 30 0. 059 0.163 0. 217 0. 257 0. 296 26 --··-·--- 0.342 0.593 0.724 0.856 I 

~ 

ts 1 __ ._~:~. ====~= 1,956 ·-----8 

2 

25 

22 

18 

16 

10 22 ----·--- ---···--- ---· ·--- -------· ---- ·--- 15 19 ---- ---· 0.118 9.593 0.890 1.126 

In a 13.5-mile wind the mill ground 20 pounds of chop quite fine in 

4.5 minutes. Fig. 44 shows the number of revolutions per minute of 

the wind wheel for the five loads. This mill requires a 5.5-mile wind 

to start it without any load, and it makes only 32 revolutions in a 25-

mile wind. This is about half as many as are made under the same 

conditions by the 16-foot mill No. 44. Since the circumference of the 

22.5-footmill is 1.4 times greater than that of the 16-foot mill, the circumference velocity of the 16-foot mil~ is 44 per· cent greater than that 

of the 22. 5-foot mill. The dotted curve, showing the speed of the wheel 

for the grinder load, will be seen to be a nearly straight line, showing a 
96 THE WINDMILL. (N0.42. 

constantly increasing load with increase of wind velocity. Fig. 45 shows 

the horsepower for three loails, also the maximum horsepower. It will 

be seen that the power is small for so large a mill. The shafting of 

this mill is very heavy, and the grinder is run by a belt from the main 

shaft. The mill, although on a 43-foot tower, should be at least 20 

feet higher. It will be seen to be a very poor mill. 

.j 

"l 

VELOCITY OF WIND IN MILES PER HOUR. 

10 15 20 25 

4.rn-----~------~----~-------

~30•~-----+------4-----~~----~ "" 

A 

z 

.~ 

.~ 2011------+--.,£-~4--~~~----l 

(/J 

z 

0 

8 

p 

... 1(11----,f.--7'-l---7f-y.-...f?<::..._--4----1 

~ !iiil 

~ 

FIG. 44.-Diagram showing revolutions of 

wind wheel of mill No. 49-22.5-foot wooden 

Halliday. Curves marked 0, 1.5, 5, and 9 

are for brake loads of 0, 1.5, 5, and 9 pounds, 

respectively; the dotted curve shows the 

speed of wheel for grinder load. 

Mill No. 50.-This is a 12-foot 

VELOCITY OF WIND IN MILES PER HOUR. 

10 15 20 25 

l. ::----T-------~---

Monitor wooden power mill on a Fro. 45.-lJlagram showing hor,epower of mill 

36-foot wooden tower. (See fig. No. 49-22.5-foot Halliday. Curves marked 9, 5, and 1.5 pounds show horsepower for brake 

46.) It is a sect,ional mill and has loads of 9, 5, and 1.5 pounds, respectively; the 

96 sails, each 44 by 4.25 by 1. 75 dotted line DKshows maximum horsepower. 

inches, set at an angle of 34 o t,o the plane of the wheel. . The shaft 

is geared forward 3.66 to 1. The swivel gearing, which enables the 

fi1ill to turn easily and keep full in the wind, is shown in fig. 47. 

The mill is used for shelling and grinding corn and pumping water. 

It is in very good condition, and the wind exposure is very good. 

ThB mill had been in use about three years. The mean temperature 

during the time of test was 83° F., the mean barometric pressure 28.6 

inches. 
)fUHPHY.] }>OWER ~HLLS TESTED. 97 

FIG. 46.-Mill No. 511- 12-foot wooden Monitor. 

]'l G. 47.-Swivel gearing of mill No. 00-12-foot wooden Monitor. 
98 THE WINDMILL. (No.42. 

The results of the tests are as follows: 

Results of tests of mill No. 50-12-foot wooden Monitor. 

Number of revolutions of wind ~ . wheel per minute at given Horsepower of mill at gi.ven w_ind 

Load per wind velocities (per hour). velocities (per hour). 

Load revolu-

~ ~~ I brake. wind 00 ~ ~ ~ ~ 00 ~ ~ ~ ~ wheel. ~ :;::1 ~ ~ r;::: ~ :;:::: ~ ~ :;:::: I ..... s s s s ..... s s s s I 

-------·-- I ~ -----------.-------------1 ~ ~ ~ ~ ~ ~ ~ ~ ~I 

I 

~ 

"f:; I F<A!~90;~, ---~~- ---~- ~140; I ~ 3~0~ ::::::~~ ~~~:~~~ --s:~r --08:_§35-~·7 --I~r~ ---·-- ·-·--- """ -------- ·---·--- 0.150 0.445 

The revolutions of the wind wheel for three brake loads (0, 1.5, and 

2.875 pounds) are shown in fig. 48. This figure also shows the numVELOCITY 01!' WIND IN MILES PER HOUR. 

10 15 20 25 

60 

~ f"1 

f"1 :45 

~ 

z 

~ 

~ 

zoo 

w. 

z 

0 

~ 

E-1 

p 8 15 

> f"1 

~ 

FIG. 48.-Diagram showing revolutions of wind 

wheel of mill No. 50--12-foot wooden Monitor. 

Curves mar ked 0, 1.5, Zf, 4.5 are for brake loads 

of 0, 1.5, 2f, and 4.5 pounds, respectively. 

ber of revolutions for a 4.5-pound 

load, found by interpolation from 

the other results. This mill will 

be seen to. require about a 6-mile 

VELOCITY OF WIND IN MILES PER HOUR. 

10 15 20 25 

.5 

.4 

~ f"1 

~ 0 

~ .3 w. 

~ 

0 

~ 

~ 

f"1 

~ .2 

0 

s 

~ 

.1 

D 

FIG. 49.-Diagram showing horsepower of mill 

No. 51)...::.12-foot wooden Monitor. Curves 

marked 4.5, 2~, and 1.5 are for brake loads of 

4.5, Zl, and 1.5 pounds, respectively; dotted 

curve DK shows maximum power. 

wind to start it, without any load and to make only 64 reYolutions 

per minute in a 25-mile wind. The 12-foot Aermotor will start in a 

4.5-mile wind and make 87 revolutions per minute in a 25-mile wind 

with no load. Fig. 49 shows the horsepower of this mill for the four 

loads; also the maximum horsepower. 

Jlfill No. 52.-This is a 14-foot Challenge wooden power mill on a 

45-foot wooden tower, manufactured by the Challenge Windmill 

Company, of Batavia, Illinois. (See fig. 50.) It is a sectional mill, and 

has two side wheels for keeping the main wheel in the wind. The 
MURPHY.] POWER MIU .. S 'l'ES'I.'ED. 99 

wind wheel has 102 sails, each 51.5 by 5 by 1. 75 inches, set at an angle 

of 39° to the plane of the wheel. The mill works a sheller, a grinder, 

and a pump. There are two 

horizontal shafts, one of 

which works the grinder and 

sheller, the other the pump. 

The shaft that works the 

pump is 12 feet long and 1.5 

inches in diameter; it is 

geared forward 1.5 to 1. The 

shaft that works the grinder 

is 6 feet long and 1. 5 inches 

in diameter; it is geared forward 15.25 to 1. The well is 

a drilled well, 192 feet deep. 

The lift was 180 feet, the discharge 0.25 quart per stroke. 

The water is pumped into a 

large box, and passes to 

watering troughs when 

needed. The pump has a 

counterweight which raises 

on the downstroke and assists 

in lifting the water on the 

upstroke. The mean temFIG. 50.- Mitl No. 52-14-foot wooden Challenge. 

perature was 92° F., the mean barometric pressure 28.6 inches. 

results of the tests are as follows: 

T'he ' 

Results of tests of rnill No. 52-llrfoot wooden Challenge. 

D Number wheel per 

of evommute ~utions at of given ~nd Horsepo~< . o< 

. . .run •< •••• ,. will' I 

Load per wind velocities (per hour). veloCities (pel hour). 

revoluon tion of l--;---1 ,-----------,--1 ----..-1 I I --,--- 1 1 

brake. ,:~~~ f ~ ~ ~ ~ ~ ~ ~ ~ ~ 

----- Lbs. Ft.-lbs. ~~~ --~-_l_~-=- ~ o_ ___ __ o 1 1s 25 ao ________________________ _____________ __ § _______ _ Pump _______ __ ------ 14 22 27 _______ -------- 0.059 0.093 0.115 --- -----

L_____ ~32 ------ ------~ 17 22~- -----· -------- -------- 0.2'22 1 0.287 -------- 2____ __ 864 ------------ 8 16 ---- --- ----- ---- --- ----- 0.210 0.~ --------

The revolutions of wind wheel per minute for loads of 0, 1, and 

2 pounds are shown in fig. 51. For 0 load the pump shaft was running with the pump detached; the grinder shaft was not working. 

When pumping the grinder was not working. \Vhen the brake loads 

of 1 and 2 pounds were being used the pump shaft was not working. A curve was 9btained giving the speed of the wind wheel for 

no brake load with the grinder shaft working and with the pump 

shaft not working. This cm·ve nearly coincided with that for the 
100 THE WINDMILL. [No. 42. 

pump load, showing that the friction of the grinder shaft was abo ut 

equal to the pump load. With the pump shaft working, but not 

the pump, the mill will be seen to require a 7-mile wind to start it, 

and it mak3s only 30 revolutions in a 20-mile wind. Fig. 52 shows 

the horsepower of this mill. 

This is a hard-running mm; there is too much friction. The side , 

wheelR do not respond to changes in the direction of the wind as quickly 

J 

w 

r.l 

Ill 

I'; 

A 

z 

~ 

0 "' 

w 

z 

::: 

E< 

1:> 

"' 0 

;;. 

~ 

~ 

VELOCITY OF 'VIND IN MILES PER 

noun. 

10 15 20 ;)() 

20 

10 

F1c. vL- Diagram showing revolutions of wind wheel of mill No. 52-

14-foot wooden Challenge. Curve 

marked 0 is for no brake load; curve 

P is for pump load; curves 1 and 2 

are for brake loads of 1 and 2 

pounds, respectively. 

' as does the vane or rudder 

in other mills. The wind 

exposure was very good and 

the mill was nearly new. 

VELOCITY OF ' VIND 1" :'1 l\TTLP.S "l'l•: rt ITOU it, 

10 20 25 

. 5 

i 4 

"' r.l 

I'; 

0 

0. .3 [>< 

w 

c:: 

0 

Ill 

A 

r.l 

E< .2 < 0 

s 

~ 

. 1 

I 

;V 

1/f 

I / 

]:--

;r vn ..-""J 

FIG. 52.- Diagram showiug horsepower of mill N o. 

5Z--14-foot wooden Challenge. Curves marked 

1 and 2 are for brake loads of 1 and 2 pounds, 

respectively; curve Pis for pump load; dotted 

curve DK shows maximum power. 

Mill No. 53.-This is a 12-foot Ideal power mili on a R3-foot wooden 

tower. The wind wheel has 21 curved sails, each 43.25 by 16.5 by 

8. 25 inches, set at an angle of 32° to the plane of the wheel. The 

horizontal shaft is geared forward 6.07 to 1. The mill had been in 

u se about four years . .for shelling and grinding corn. Three brake 

loads were used in the test-0, 1.5, and 2.5 pounds. The mean temperature during the tests was 92° F., the mean barometric pressure 

28.7 inches. 'fhe results of the tests are as follows: 

DLoadper r~volu

brake. t~ln~f 

wheel. 

Pouru.ls. Ft.-lbs. 

0 0 

1. 5 272 2.5 455 

Results of tests of mill No. 58- 12-joot I deal. 

Number of revolutions of wind 

wheel per minute at given wind velocities (per hour). 

00 00 

"' " ] :;::1 

s .. "" .... 

25 40 

29 

00 

" ] 

"" rl 

51 

41 

32 

00 

.$ 

'§ 

~ 

60 

51 

44 

00 

.$ 

'§ 

~ 

Horsepower of mill at given wind v e- locities (per bour). 

00 00 00 00 00 

~ " ] " ~ :;::1 

a a ~ ~ ~ ~ , "" "" 
MURPHY.} POWER MILL~ TESTED. 101 

Fig. 53 shows the number of revolutions per minute of the wind 

wheel for the three brake loads. rrhe mill will be seen to start in 

about a 5-mile wind and to make 69 revolutions a minute in a 25-mile 

wind with no load. Fig. 54 shows the horsepower for the several loads. 

Mill No. 54.-This is a 12-foot Aermotor like No. 27, on a 47-foot 

tower. The 12-foot Aermotor No. 27 was found to be so much greater 

in power and speed than other 12-foot mills tested that we thought 

VELOCITY OF WIND IN MILES PER HOUR. VELOCITY OF WI~D IN MILES PER HOUR. 

10 Hi 20 25 10 lfl 20 23 

75 1.0 

60 

j 0.8 f;l;l 

f;l;l 

III ~ 

~ f;l;l 

~ 

~45 0 

~ ~ 0.6 rtJ 

r.. Q:; 

0 0 III rtJ I Z30 ~ 

0 f;l;l 

~ ~ 0.4 

p 0 

..:l s 0 

> ~ ~ 15 

0.2 

n/ 

FIG. 53.-Diagram showing revolutions of wind 

wheel of mill No. 53-12-foot Ideal. Curves 

marked 0, 1.5, 2.5, and3.5arefor brake loads of 

0, 1.5, 2.5, and 3.5 pounds, respectively. 

it wise to test another of the same 

FIG. 54.-Diagram showing horsepower of mill 

No. 53-12-foot Ideal. Curves marked 3.5. 2.5. 

and 1.5 are for brake loads of 3.5, 2.5, and 1.5. 

pounds, respectively; dotted curveDKshows 

maximum power. 

make and size under somewhat different conditions. No. 54 had been 

in use about two years. Two brake loads were used-0 and 297 footpounds per revolution of wind wheel. The mean temperature during 

the test was 92° F., the mean barometric pressure 29.2 inches. The 

results of the tests are as follows: 

Results of tests of mill No. 5/p-12-foot Aernwtor. 

D wheel per minute at given Horsepower at given wind velocities Number of revolutions of wind =:l 

Load per wind velocities (per hour). (per hour). 

Load on r~villu- l----~--~--~----~-----1-----~--------------------l brake. t~~~f 

wheel. 00 00 00 rt5 rt5 rt5 rt5 rt5 rt5 rt5 

~ c;) Q;) $ Q;) Q;) Q;) Q;) ~ ] ] $ ] a "§ "§ ] ] ~ a ()'! eo 00 ,...; ,...; ~ ~ 00 ~ ~ ~ ~ 

~~·5~-;--;~----;===:~=::~:::1 

It will be seen that the results of the tests of_ this mill apparently 

ag-ree closely with those of No. 27, page 86. The agreement, however, 
102 THE WINDMILL. [No.42. 

is not so close as it appears, since t.he temperature for No. 54 is much 

higher. It is, however, about the same as the temperature for other 

mills, so that we can still use the results found for mill No. 27 in comparing its power and speed with those of other mills. 

COMPARISON OF POWER MILLS. 

Comparison of 12-foot Ideal (No. 53) with 14-foot Ideal (No. 34).-It 

must be remembered that in this and in all other comparisons no correction is made for difference in tempera~ure and barometric pressure. 

The speeds for no load and the maximum horsepowers for these mills 

are as follows: 

Comparison of results for 1f!-foot Ideal and 14-foot Ideal. 

I 

Number of revolutions of 

wind wheelperminuteat given wind velocities 

(per hour). 

Maximum horsepower at I 

given wind velocities I 

(per hour). 

Mill. 

ril 00 00 00 00 00 00 00 00 Q) ] Q) Q) 00 ~ ~ Q) Q) ~ ] ] ] Q) "§ :;.:: "§ ] ] s s ~ <:0 ~ ~ ~ <:0 00 ...... 00 ...... ~ ~ ~----------1·-- ------------------

12-foot Ideal .... ------ ____ ____ 25 40 51 60 68 0.06 0.23 0.44 0.70 ---·-- 14-foot Ideal ____ -------------- 20 34 44 53 58 0.06 0.22 0.46 0. 74 ·------ Ratio of circumference 

velocities (if) ________ ; 1.07 1. 00 0. 99 0. 97 1. 00 

It will be seen that the useful power of the 14-foot mill is very little 

more than that of the 12-foot mill, and that the circumference velocities are nearly the same for no load, where no horizontal shaft is being 

t.urned. In the case of the 12-foot mill the brake was on the foot 

gear and there was no horizontal shaft to turn, but in the case of the 

14-foot mill the brake pulley was on a shaft 15 or 20 feet long. We 

believe that if the brake pulley had been on the foot gear and the 

line shaft thrown out of gear, so as to eliminate shaft friction, the 

mill would have shown at least 10 per cent more power. The tower 

obstructs the wheel somewhat and reduces the power. 

Comparison of 12-foot Aermotor (No. 27) with 14-foot Ideal (No. 

34).-The speeds for no load and the maximum horsepowers for these 

mills are as follows: 

Comparison of results for 12-foot Aer1notor and 14-foot Ideal. 

I Number of revolutions of Maximum horsepower at wind wheel per minute at given wind veloc1 ties given wind velocities (per hour). (per hour). 

Mill. 

00 00 ril 00 00 00 00 00 00 Q) Q) ~ ~ Q) Q) ~ ~ ] ] "§ "§ ~ ] ] "§ ·a ~ ~ 0 tt:l 

"§ 00 IN IN 00 ~ ~ ~ -- ----------

~Aermotor .............. 30 49 63 75 87 0.09 0.33 0.66 

.A:~·-1 Ideal--------·--· ...... 20 34 44 53 58 0.06 0.22 0.46 

Ratio of circumference 

velocities (U)----- ·--- 1.29 1.23 1. 22 1.21 1.28 -------- -------- -·-----
MlTRPHY.) COMPARISON OF POWER MILLS. 103 

It will be seen that the number of revolutions per minut,e of the 

12-foot mill is 50 per cent greater than for the 14-foot mill. This is 

true for the lower as well as for the higher velocities, where the governing of the mill does not enter to reduce the speed. It will be seen 

also that the 12-foot mill is producing from 42 to 50 per cent more 

horsepower than the 14-foot mill. The temperature was 49° higher 

and the pressure 0.6 inch lower when the 14-f.;:>ot mill was tested 

than when the 12-foot mill was tested. The effect is to lessen the 

difference between the power and speeds of the mills. 

Comparison of 12-foot Aermotor (No. 27) with 16-foot Aermotor 

(No. 44).-Attention has already been drawn to the similarity between 

the speed curves of these mills (figs. 35 and 42) and between the power 

curves. (The power curves for mill No. 44 are shown in fig. 43; those . 

for mill No. 27 were platted, but are not published because of lack of 

space.) If we compare the number of revolutions per minute for no 

load, we shall see that they are to each other nearly inversely as the 

diameter, or that the circumference velocities of the two mills are the 

same in all wind velocities. We may compare the brake horsepower 

and the speed as follows: 

Comparison of results for 12-foot Aermotor and 16-foot Aermotor . 

. 

Number of revolutions of wind Maximum horsewheel per minute at given wind power at given wind velocities velocities (per hour). (per hour). 

Mill. 

ui I 

ui ui I ui ui ui I ui ui 

~ ~ ~ ~ Q;) Q;) 

~ Q;) r.:: ] ] '§ '§ '§ s s ~ 00 ~ lO 00 ,.... tN s ~ ~ --------------

12-foot Aermotor _ .... ___ .... 30 :il 63 75 87.0 0.21 

·~I 1.05 

16-foot Aermotor .•.......... 23 48 56 64.5 0.29 0.82 1.55 

Ratio of circumfer- ence velocities CU) .. l.O'Z 1.03 1.02 0.99 0.99 1.381 1.41 1. 48 

From this it will be seen that the power of the 16-foot Aermot'or is 

about 1.22 times that of the 12-foot. The ratio of the squares of the 

diameters is 1. 78; the ratio of the diameters 1. 33. It will be seen t,hat 

th~ power does not increase as the squares of the diameters, as is often 

stated; it increases faster than as the diameters, but more nearly as 

the diameters than as the squares of the diameters. 

Comparison of 16-foot Althouse wooden mill (No. 28) with 16-foot 

Aermotor (No. 44).-From the following table it will be se~n that the 

wind wheel of No. 44 is revolving from 56 to 77 per cent faster than 

the wind wheel of No. 28. The latter, however, has to overcome the 

friction of 10 or 12 feet of line shafting. It will be seen that No. 44 

is yielding from 70 to 167 per cent more power than No. 28. .The 

superiority of the steel mill over the wooden mill is very evident in 

this case. 
104 THE WINDMILL. [No.42. 

Cmnparison of results for 16-foot Althmuw and 16-foot Aernwtor. 

I • I Number of revolutions of 

I 

wind wheel per minute Maximum horsepower at given wind veloei ties at given wind velocities (per hour). (per hour). 

Mill. 

ui ui ui .,;, ui ui rJi ui 00 

~ Q) Q) ..9Z Q) ~ ~ $: $: 

s ] ] ·a ] s s '§ "§ CL) :::1 ~ ~ ~ CL) :::1 ~· 0 

~! 

--------------------

16-foot Althouse _________ ----· 13 23 30 36 40.0 0.06 0.29 0.52 

I 16-foot Aermotor ......... ____ 2H 38 48 56 64.5 0.16 0.48 

Ratio of o.m ·Ti;i; I circumference 

L 1 "t" (steel) 1. 77 1.65 1.60 1.55 1. 61 2.671 1.65 1. 78 ------ ve oc1 1es wood _______ 

Compwrison of 22.5-foot Halliday wooden mill (No. 49) with 16-foot 

Aermotor (No. 4-4-).-From the following table it will be seen that the 

steel mill makes about two revolutions to one revolution of the wooden 

mill, and that its power is from 41 to 167 per cent greater. 

Comparison of results for 22.5-foot Halliday and 16-foot Aermotor. 

Number of revolutions of Maximum horsepower at wind wheel per minute given wind velocities at given wind velocities (per hour). (per hour). 

Mill. 

w 00 ui I w w ui w w ..9Z $: Cl.> Q) £ Q) $: ] $: ] ] "§ '§ "§ s "§ 

CL) :::1 ~ ~ CL) ::3 ~ ~ ---------------------

22.5-foot Halliday.------------ 11 20 25 30 0.06 0.34 0.62 0.88 

16-foot Aermotor. -~-- ....... 23 38 48 56 0.16 0.48 0.93 1.55 

Ratio of circumference I 

velocities (~~ ) ......... 1.48 1.35 1.36 1.32 2.67 1.41 1.50 1. 76 

Comparison of 12-foot Ae1·moto'r (No. 27) with 22.5-foot Halliday 

wooden rnill (No. 49).-Comparing the power of these mills, we have 

the following: 

Comparison of results for 12-foot Aermotor and 22.5-foot Halliday. 

Number of revolutions of Maximum horsepower at wind wheel per minute given wind velocities at given wind velocities (per hour). (per hour). 

Mill. 

w ui rf, w w w w w Ill ..9Z ~ ..9Z ..9Z $: $: $: 

I ] ·a '§ '§ ·a '§ "§ '§ ~ 

~ 0 ~ <C 0 CL) M ~ CL) M M ~ 

---------------------

12-foot Aermotor. ------------ 30 49 63 75 0.09 0.33 0.66 1.05 

22.5-foot 

· Ratio Halliday of circumference ............. 11 20 25 30 0.06 0.32 o.B 

velocities ~~ )------ _ 1. 46 1.31 1.34 1.32 1.50 1.03 1.05 1.12 

It will be seen that this 22.5-foot wooden mill do·es not furnish as 

much power as a good 12-foot steel mill. 
MURPHY.) COMPARISON OF POWER MILLS. 105 

Cornparison of wooden pmoe'r rnills.-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 Irrigator 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. 

I 

-----

Number of revolutions of 

wind wheel per minute Horsef,ower at given wind at given wind velocities ve ocities (per hour). 

(per hour). 

MilL --------~---------- ---

rti ri ri. rti rti rti rti rti 00 Q) $ ] $ Q) a; Q) 

] ] Q) 

·a ·s ] ] ] ] ~ "' 0 ~ ::-1 00 ..... IN 00 .... ~ ~ --------------

12-foot Monitor (No. 50) ______ 16 33 44 54 64 0.02 0.10 0.23 0.38 

14-foot Challenge (No. 52) ____ 7 18 25 30 

·::~:1 0.01 0.10 0.25 0.42 

16-foot Althouse (No. 28) _____ 13 23 30 36 0.06 0.29 0.52 0.84 

16-foot Irrigator (No. 30) _____ 12 25 32 41 0.02 0.16 0.30 0.44 2"~.5-foot Halliday (No. 49) ____ 11 20 25 30 0.06 0.32 0.63 0.94 

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 

the 12-foot mill increases 

faster than as the sq nares 

of the diameters, while. 

the power of the 22.5-foot 

mill compared with that 

of t,he 12-foot mill does 

not increase as fast as the 

squares of the diamet,ers, 

and the power of the 22.5-

foot mill compared with 

that of the 16-foot mill 

does not increase as fast 

as the first power of the 

diameters. 

Comparison of 12-foot 

Monitor wooden mill 

• (No. 50) with 12-footAermotor (No. 27) and with 

,j 

~ 

~ 

VELOCITY OF WIND IN MILES PER HOUR. 

5 10 15 20 25 

~~r------T------~----~------~------, 

: 00~-----+------+-----~~---~-~~ 

12-foot Ideal (No. 53}.- FIG. 55.-Comparative diagram of revolutions of wind 

F · h l wheels of mills Nos. 50, 53, and 27. Curve aa' is for 12-foot 

Ig. 55 S OWS t le speed, Aermotor; bb1 isfor12-footldeal; cc'isfor12-footMonitor. 

in revolutions, of the 

wind wheels of these mills for no useful load. The friction 1s small in 

each case. The Monitor has a swivel gearing, and the Ideal has a ball 

IRR 42-01--3 
106 THE WINDMILL. [No.42. 

gearing to carry the weight of the shaft, both of _which reduce the 

friction. It is fair to say that t,he friction load of the Aermotor is at 

]east as great as that of the other mills. It will be seen that the speed , 

of the Ideal is noticeably greater than that of the Monitor; and that 

the speed of the Aermotor is much greater than that of the Ideal, 

especially for high wind velocities. This is the reason the Am·motor 

is so much more powerful than other mills. It revolves much faster, 

and the power is directly proportional to the speed. But why is its 

speed greater for the same load? 

Comparison of r:sults for 12-foot Monitor, 12-foot Ideal, and 12-foot Aertnotor. 

Number of revolutions of 

wind wheel per minute 

1 

Horsepower at given wind 

=1 

velt>cLoad at given wind velocities _ ities (per hour). 

(per hour). 

~i~B~~~----~--~--~--~--~----~--~~~----------1 of wind · · · · · oo • I oo whflel. 00 gj ~ l ~ I ~ 1J ~ ~ ~ ~ ] ·a ·s ·s ] ·s ·s ·s ·a 1 oo ~ ~ ~ ~ oo ~ ~ ~~~ I - -----------------~~-

Ft.-lbs. 

Mill. 

64 -------------- ------- ------- --------

{ 

o 16 sa 

12-footMonitor AiJ, ------ ---~-

44 

35 

27 

51 

41 

32 

63 

57 

48 

12 

54 

43 

34 

60 

51 

44 

75 

70 

65 

50 

52 

40 

68 

60 

54 

87 

81 

77 

72 

-------0.091 0.127 0.156 0.189 ------- ·------ 0.230 0.324 0.381 

12-foot IdeaL .. { m ---~- ---~-

12-=t"':or'"o-{ ~ 1::~: _j_ 

------- 0.239 0.338 0. 420 0.500 -------------- 0.440 0.606 0.745 -------------- -~----- ______ 

ill! _______ j_ 0. 089 0. 285 0. 386 0. 458 0. 523 ------- 0.303 0.6.rJ3 0.890 1.020 ------- ------- 0.234 1.028 1.451 

The dimensions of the principal parts of the wind wheels of these 

mills and the mean temperature and pressure when the tests were 

made are as follows: 

Dimensions of principal parts of mills Nos. 50, 53, and 2'1. 

1- Num- Angle Mill. ber Dimensions 

of of sails. of 

sails. sails. 

I 1---

------------~--, 

Mean ] Mean baroGearing. temper metric ature. pres-

__ _:~-~ Inches. 0 

12-foot Monitor (No. 50) _____ 96 « x 4-txlt 34 12-foot Ideal (No. 53) ____ .----~ 21 43tx16tx8t 32 

12-foot Aermotor (No. 27) .. _ 18 44. x18tx7t 31 

o F. Inches. I 3. 66 : 1 83 28. 6 6. 07 : 1 92 28. 7 6. oo: 1 46 28.9 1 

I ! 

The temperature when the 12-foot Aermotor was tested was much 

lower than when the other two mills were tested, but, as already • 

stated, the temperature when Aermotor No. 54 was tested was 92° F., 

and it showed a speed and power about the same as Aermotor No. 27; 

so we may leave this difference in temperature out, of account. 

It will be seen that the l\lonitor is not geared forward as much as 

the other two, but this does not affect the speed for no load. The 

sail angle is about the same for all, also the length of sail; but the 
MURPHY.] PUMPING MILLS AND POWER MILLS COMPARED. 107 

number of sails and the width are quite different. The Aermotor has 

few sails, but of large size; the Ideal has more and sgmewhat smaller 

sails; the Monitor has many small sails, and its tower is located in 

front of the wind wheel. Its sails are plane, instead of curved, all of 

which tends to decrease its power. 

Fig. 56 shows the curves of maximum horsepower. It will be seen 

that the difference between the horsepower of the Am·motor and that 

of the Ideal is about the same as the difference in their speeds for the 

same wind velocity, but 

the difference between 

the power of the Monitor and that of the Ideal 

is much greater than the 

correspondi:gg difference 

in their speeds. The 

wooden mill, therefore, 

not only 1\as a less speed 

at a given wind velocity 

than the steel mill, but 

it c.arries a proportionately less load. For example, in a 20-mile wind 

a load of 120 foot-pounds 

per revolution reduces 

the speed of the :Monitor 

from 54 to 43 (or 11) 

revolutions per minute, 

while in the case of the 

Aermotor a load of 220 

VELOCITY 0~' WIND IN l'tHLES PER HOUR. 

10 15 20 

foot-pounds (about 80 FIG. 56.-Comparative diagram of horsepower of mills NOS. 

t ) d 50, 53, and 27. Curve aa' is for 12-foot Aermotor; bb' is for 

per cen greater re uces 12-foot Ideal; cc' is for 12-foot wooden Monitor. 

the speed from 7 5 to 70 

(only 5) revolutions per minute. In the case of the Ideal a load of 

272 foot-pounds per revolution (2.3 times the load of the Monitor) 

reduces the speed from 60 to 51 (or 9) revolutions per minute. 

COMPARISON OF PUMPING MILLS WITH POWER MILLS. 

Compar,1:son of 12-foot pumping min (No.3) with 12-foot powe'r mill 

(lVo. 27).-The load per stroke of No.3 (see page 30, Part I) is 415.3 

foot-pounds. The wind wheel makes 3.3 revolutions to 1 stroke of 

the pump, so that the load per revolution of wind wheel is 124.5 footpounds. This is less than the smallest load used in testing No. 27, viz, 

222 foot-pounds per revolution. A diagram was platted showing the 

useful work, in horsepower, of these mills for these loads. The curve 

for the pumping mill was seen to start with a Uttle less wind velocity 

than that of the power mill, indicating a somewhat less total load. 
108 THE WINDMILL. (N0.42. 

Comparing the ordinates of these curves for different wind velocities, 

the following ratios were obtained, which give, approximately, the 

pump efficiency, no allowance being made for difference in temperature 

and pres~ure: 

8 12 16 20 25 30 

0.60 0.53 0.54 0.54 0.58 0.58 

Tbe mean of these ratios is 0.56. If the useful load of t,he pumping 

mill had been somewhat greater, so that the mills would have started 

at the. same wind velocity, the ratio, or pump efficiency, would be 

about 60 per cent, which is about what might be expected of this pump 

under this lift. The ratio of the useful)oads is 125-:-222=0.57. This 

ratio would probably be about 0.60 if the loads were such that the 

mills would start at the same wind velocity. 

Comparison of 16-foot pumping Aermoto1· (No. 9) with 113-foot power 

Aermoto·r (No. +4).-The useful load of No. 9 (see pages 36 to 37, 

Part I) is 1,013 foot-pounds per stroke of pump, or 304 foot-pounds per 

revolution of wind wheel. The smallest useful load of No. 44 is 528 

foot-pounds per revolution of wind wheel. A diagram was platted 

showing the useful horsepower of these mil1s for these loads. For this 

particular load (1,013 foot-pounds) the pumping inill was seen to start 

at a somewhat less wind velocity than the power mill, indicating that the 

total load of the pumping mill was somewhat less than that of the power 

mill. ,.~rhe ratio of any two of the ordinates gave, approximately, the 

pump efficiency for that wind velocity, the difference in temperature 

and p1·essure being neglected. 

These ratios for four velocities are as follows: 

12 16 20 25 

0.72 0.67 0.69 0.63 

If the pump load had been somewhat great.er-such that the mills 

would start at the same wind velocity-the mean ratio would be about 

70 per· cent. This, again, is about what is expected for the efficiency of 

this pump, which is somewhat better than mill No. 3 and has a higher 

lift. The ratio of the useful loads of these mills is 304 + 528 = 0.57. 

This ratio would probably be about 60 per cent if the mills started at 

the same wind velocity. 
MURPHY.) PUMPING MILLS AND POWER MILLS COMPARED. 109 

It is interesting to compare the performance of these mills still 

further. ~rhe speeds of the wheels and the horse powers are as follows: 

Cornparison of results for 16-foot purnping Aerrnotor and 16-foot power Aerrnotor. 

I· 

Number of revol u- tions of wind wheel 

per minute at given wind velocities 

Mill. (per hour). 

00 00 00 00 

] ~ Q) .$ 

s ] "§ '!'! ~ ...... ...... ~ ~ 

Horsepower at given wind velocities (per hour). 

00 u.i 00 u.i 

~ .$ Q) Q) 

s "§ ] ] ~ ~ ~ ~ 

-:l per 

revolution of 

wind 

wheel. 

------------

I 

16-foot pumping mill (No. 9) _ 31 42 52 511 0.325 0.433 0. !l48 0.601 

16-foot power mill (No. 44) ___ 28 41 50 58 0.45 0.65 0.80 0.95 

Ratio of pump power to mill· 

I power _____ --------------- ___ ------ ------ ------ ............ 0.72 0.67 0.69 0.63 

It will be seen that the wind wheel of the pumping mill is making 

from one to two more revolutions per minute than that of the power 

mill. 

Comparison of 22.5-foot pumping mill (1Vo. 36) with 22.5-foot po~wer 

mill (No. 49).-In this comparison we will use the curve of 5 pounds, 

or 1,087 foot-pounds, per revolution of wind wheel as the speed for 

this load, corresponding mo1'e nearly with that for the pump load 

than any other. 'J.:'he speeds of the mills and the horse powers are as 

follows: 

Comparison of results for 22.5-foot purnping rnill and 22.5-foot power rnill. 

I Number of revolu- -:l tions of wind wheel Horsepower at given 

per minute at ¢ven wind velocities (per wind v e I o cit i e s hour). 

(per hour). pet 

Mill. revolution of u.i u.i 00 00 u.i u.i ai u.i wind 

.$ Q) Q) Q) 

~ Q) ~ Q) wheel. 

"§ ] ] ] s ] s ~ ~ ~ ~ lO <:<! <:<! ...... ~ ~ ~ ---------------

Ft.-lbs. 

22. 5-foot pumoing mili (No. 36) __ 12 17 20 24 0.090 0.124 0.150 0.182 0.248 

22.5-foot power mill (No. 49). ·--- 11 18 22 26 0.342 0.593 0.724 0.856 1.087 

Ratio of. pump power to mill 

power _______ -------------------- ------ ............. ............ ............ 0.26 0.20 0.20 0.22 0.23 

The efficiency of the pump is, therefore, not more than 22 per cent. 

~rhe ratio of useful loads is 22 per cent. (For description of pumping 

mill No. 36, see pages 52 to 53, Part I.) 
110 THE WINDMILL. [N0.42. 

EFFECT OF TENSION OF SPRING ON SPEED AND HORSEPOWER 

OF MILL. 

The effect of tightening the spring which holds the wind wheel of 

mill No. 11:-) in the wind has been shown on page 44, Part I. The effect 

of a reduction in the tension of the spring of the 16-foot power mill 

VELOCITY OF WIND IN MILES PER HOUR. 

10 15 20 

(No. 44) is shown in fig. 57. The 

curve aa' is for no load and the 

25 

n~----~------~-----,------~ spring new and stiff. The curve 

aa" is for the same load (none) 

<P' and spring aft.er the mill had 

been out of use about eight 

months. It will be seen that 

these curves coincide up to a 

velocity of about 10 miles an 

hour, after which they separate 

rapidly. In a 25-mile wind the 

number of revolutions of the 

wind wheel per minute has been 

FIG. 57.-Diagram shuwing effect of tension of 

spring of mill No. 44-Hi-foot Aermotor. Curve 

aa' is for no load, spring new and stiff; aa" is 

for no load, spring relaxed, mill having been out 

of use eight months; bb' iA for 3-pound brake 

load with relaxed spring. 

red need from 64. 5 to 54 by the 

decrease in the tension of the 

spring. The curve bb' is for a 

3-pound brake load with relaxed 

spring. It will be seen to be 

nearly parallel to the curve aa", .• 

showing that the effect of the 

load when t,he spring is relaxed 

is similar to that when it is taut. 

We see how important a factor 

tension of spring is on the power of a mill. It also shows that if a 

spring is to be used in place of a weight there should be some easy 

way to change its tension. 

MATHEMATICAL DISCUSSION OF TESTS OF TWO AERMOTORS. 

In this discussion the wind velocities are those found by the use of 

the Robinson cup anemometer. A comparison of these velocities with 

true wind velocities will be given later. The Aermotors are selected 

for this discussion because their power is great,er than that of any other 

form of mill that we have tested, and because their speed and power 

curves are derived from a greater number of observations than those 

of any other mill. 

Discussion of te:-;ts of 12-foot Aermotor ( 1Vo. 27) .-The curves showing 

the number of revolutions of wind wheel (<'ailed speed curves) of this 

mill for four brake loads are given on page 88-fig. 35. Each of these 

curves is seen to resemble a parabola theaxis of which is the x coordinate axis on which the wind velocit.ies are marked. Each of these 

has the form y 2 = a + bx, in which x is the wind velocity in miles per 
MURPHY.) MATHEMATICAL DISCUSSION. 111 

hour, y the speed of wind wheel in revolutions per minute, and a and 

b constants. For the curve of no load (0) we have y =50 when x = 12, 

andy= 75 when x = 20. Hence we have 

50:l = a + 12b, and 

752 =a.+ 20b. 

·Solving these, for a. and b we have a=- 2,187 and b = 391; and the 

equation of the curve is 

y2 = - 2,187 + 391x. (1) 

For t.he speed curve of 2 pounds we see that y = 43 when x = 12, and 

that y = 70 when x = 20. Hence we have 

432 = a + 12b, and 

702 =a+ 20b. 

Solving these, we have a= - 2, 728 and b = 381; and we have the 

eq nation of this 2-pound curve 

y2 = - 2, 728 + 381x. (2) 

Proceeding in a similar way, we have for the equation of the 4-pound 

curve 

y2 = - 4, 384 + 424x. (3) 

For t,he equation of the 6-pound curve we have 

y2 = - 9,400 + 595x. (4) 

The speed as determined by measurement and as found from these 

,3quations for several wind velocities is shown the following table. 

The starting velocities are found by making y = 0 and solving for x 

in equations 1 to 4. 

7'able showing revolutions per minute of 12-foot Aermotor (No. 27) under differo:-tt6 

loads and at different wind velocities. 

;I Wind vel~ity per hour. 

No load. j2-pound load. 

Meas· Com- I Meas· Com- I ured. puted. ured. puted. 

R3o·l ~e6. --

Rev. Re1•. 8 miles . __ . _ .. _ . __ 30 18 i 12 miles . _ .. ____ . _ . 49 50 I 43 43 

16 miles --·- ·----~ 63 64 57 58 

20 miles --- - .. ---- 75 75 70 70 

! 25 miles ... - - . ---- 87 87 I 81 82 

Starting velocity _ . 4.5 5. 6 7.0 7.1 

I 

4-pound load. l I ~-=d ,_, 

Me as- ured. 

--

Rev. 

23 

48 

65 

77 

10.2 

puted. Com-~ 

--

Rev. 

27 

49 

64 

78 

10.31 

Meas- Comured. pu ted. 

Rev. Rev. 

12 10 

50 iJ50 72 74 

15.3 15.8 

If the origin of coordinates for eq nation 1 be moved to the point 

where the curve crosses the axis of x, the equation will then be of the 
112 THE WINDMILL. (N0.42. 

form y2 =391x', from which we have y= v3H1x'; that is, the speed 

for a constant load increases as the square root of the wind velocity. 

The close agreement between the measured and computed. speeds, 

especially for the curve of no load, is noticeable. 'rhe measured and 

computed st,arting velocities differ somewhat. This was expected, 

since it is difficult to get the starting velocities from observation. 

Hereafter in this discussion the computed instead of the observed. 

speeds and starting velocities will be used. It must be remembered, 

however, that these are not what may be called theoretical results. 

They are obtained from measurements, not from theory, and are the 

adjusted values of the observed quantities. 

~.rhe power curves for this mill for three brake loads were platted, but 

are not published because of lack of space. The curves are parabolas with their axes horizontal. This follows at once from the fact 

that the corresponding speed curves are parabolas. The power is 

proportional to the product of the load and speed. When the load is 

constant, as it is for one of these speed curves, the power varies as the 

speed, and hence the load curves are parabolas. 

The equation of any one of the curves-as, for example, the 2-pound 

curve-may be found as follows:, The formula for horsepower is 

H. P. = 2 7£ RuL-:- 33,000, R = 35.5 + 12 and L = 2. Hence H. P. = 

2 X 22-:- 7 X 6 X 35.5 X 2 X 'lt-7- 12 X 33,000 = 0.0067u = Ku where K 

= 0.0067. 

In the speed equations u is what we have called y, and y = - 2, 728 

+ 381x. HenceH. P. = Ky = K"'- 2,728 + 3S1x, and 

(H. P.) 2 = K 2 (- 2,728 + 381x) =- 0.1225 + 0.017x. (5) 

In the diagram of power curves, platted but not reproduced here, 

the curve of maximum power was found to resemble a parabola the 

axis of which was vertical with its vertex on they coordinate axis below 

the origin. The form of its equation is x2 =a+ by, x being the wind 

velocity, in miles per hour, y the horsepower, and a and b constants. 

For x = 5, y =:= 0, and for x = 20, y = 1.05. Substituting these values 

in the above equation we have: 25 =a, and 400 =a+ 1.05b. From 

these we have: a= 25, b = 357, and the equation of the maximum 

power curve isx 2 = 25 + 357y. (6) 

For x = 5, 10, 15, 20, and 25, y has the values 0, 0.21, 0.56, 1.05, and 

1. 6H, which agree closely with those taken from the curve. 

For the mill to yield the greatest amount of power possible the load 

should increase as the wind velocity increases. In an 8.5-mile wind 

a 2-pound load gives the maximum power; in a 14-mile wind a 4-pound 

load gives the maximum power, and in a 21-mile wind a 6-pound load 

gives thb maximum power. 

We wish to determine how the load and speed of the mill vary with 
MURPHY.) MATHEMATICAL DI~CUSSION. 113 

the wind velocity for the curve of maximum power. The load curves 

were found to be tangent to the curve of maximum power for loads 

and velocities about as follows: The 0 curve is tangent at x = 5, the 

2-pound curve at x = 8.5, the 4-pound curve at x = 21. For a constant increment of 2 pounds in the load the increment of wind velocity 

changed from 3. 5 miles to 7 miles. Hence the velocity increases 

faster than the loading. For each of these four points on the curve 

the load and horsepower are known. ·Hence we can find the number 

of revolutions from the equationH. P. = ~ X 1t X R X li X -± X L + 33,000. (7) 

The wind velocities, loads, powers, and speeds for these four points 

of tangency are as follows: 

Data regarding points of tangency of power curves with curves of maximum power 

of Aermotor No. 27. 

I Wtnd velocity per hour. Load. Horsepower. Revolutions 

per minute. 

I 

Pounds. 

1~ I 

5 miles_ .... _______ · __ . 0 0 8.5 miles .. ___________ 2 0. 13 14 miles . _ _ _ _ _ _ _ _ _ _ _ . 4 0.50 lJ 21 miles _____________ . 6 1.15 7 

The speeds, in revolutions, as here given are platted in fig. 35, giving the curve PQ, which is the speed curve for maximum power. The 

proper load for maximum power can now be found for any wind velocity from equation 7, the speed being taken from this speed curve. 

The ratio of the speed at· maximum load to the speed at 0 load, for 

the wind velocities 10, 15, and 20 miles an hour, is 0.63, 0. 70, and 0. 74, 

respectively, showing quite an increase. The following table gives 

additional information in regard to speed and load for the curve of 

maximum power: 

Data regarding speed and load for curve of maximum po'wer of Aermotor No. 27. 

,---

Load per Wind Revolu- velocity revolution tionsper L-L'. S-S'. LS. LS- !:;.2. per hour. of wind L'S'. 

wheel. minute. 

Pounds. 5 miles ____ 0 0 ... ------- -------- ----.. -... . ... J 10 miles. ____ 2.1 25 2.1 25 52.5 52.5 

15 i:niles . ___ 4.0 41 1.9 16 160.4 107.9 55.4 

20 miles. ___ 5.9 55 1.9 14 324.5 164.1 56.2 

The fourth column gives the differences betwe.en the successive 

loads, or t.he increments of loading. These are seen to decrease somewhat, showing that the load does not increase quite as fast as the 

wind velocity. The fifth column gives the differences between the 

successive speeds, and shows that the speed does not increase quite 
114 THE WINDMILL. [No.42. 

as fast as the wind velocity. The sixth column gives the products of 

the loads and speeds, which is proportional to the horsepower. The 

seventh column gives the increments of horsepower, the eighth column t.he difference between the figures in the seventh column. These, 

being nearly constant, show that the curve of maximum power is of 

the second degree. 

The following table contains additional interesting. information in 

regard to the speed of this mill : 

Data in regard to speed of mill No. 27-12-foot Aermotor. 

Revolu- Circumfer- Ratio of cir- Revolu- Ratio of 

Wind velocity per tions per ence velocity, cumference tions per speed at 

hour. minute, in miles, velocity to minute at maximum 

no load. no load. wind velocity, maximum load to speed no load. load. at no load. 

8 miles . ___ . _ 30 12.9 1. 61 17 0.57 

i 

12 miles ______ 49 21.0 1. 75 32 0.65 

16 miles ______ 63 27.0 1. 70 44 0.70 

I 

20 miles. _____ 75 32.1 1. 60 54 0.72 

25 miles ___ .. __ 87 37.3 1. 50 ---- - -- --... -- .. -- ----

The results obtained from this 12-foot mill may be stated a~ follows, 

in terms of cup anemometer velocities: 

(1) The speed of the wheel for a constant. load varies as the square 

root of the wind velocity. 

(2) The speed of the wheel for maximum load increases slightly 

faster than the first power of the wind velocity. 

(3) The power of the 1nill for a constant load varies as the square 

root of the wind velocity. 

(4) The maximum power of the mill varies as the square of the 

wind velocity. 

( 5) The load for maximum power does not increase quite as fast as 

the wind velocity. 

(6) The ratio of speed for maximum load to the speed for no load 

increases somewhat with the wind velocity. 

Discussion of tests of 16-foot Aermotor _No. 44.-The speed curves 

for this mill are shown in fig. 42. They are seen to resemble t.he 

parabolas with horizontal axis. The equation of each has the form 

y2=a+bx, y being the speed in revolutions per minute, x the wind 

velocity in miles per hour, and a and b being constants for any curve. 

We see that for x=12, y=38, and that for x=20, y=56. Hence we 

have 

382=a+ 12b, and 

562=a+20b. 

Solving these equations, we have a=-1,094, b=211.5, and the equation of the no-load speed curve is 

y=-1,094+211.5x. (8) 
MURPHY.] MATHEMATICAL DISCUSSION. 115 

Proceeding in a similar way, we have for the equation of the 3-pound 

load speed curve 

y 2=-1,790+214.5x. (9) 

For the 5-pound load we have 

y2=-2, 304+ 212x. (10) 

For the 8-pound load we have 

yz=-2,715+197x. (11) 

The speed and starting velocities as computed from these equations 

and as found by measurement are as follows: 

Speed and starting velocities for 16-foot Aermotor No. 44. 

Wind velocity per hour. 

No load. -13·pound load. 

Meas- Com- Meas- Comured. puted. ured. puted. 

1--------1------

8 miles. _________ _ 12 miles ______ . __ .. 

1 

16 miles _____ -_____ _ 

I 20 miles ___ . __ ... _ 

L ~~a':~";- V610citY: -_ 

23.0 

38.0 

48.0 

56.0 

64.5 

4.5 

24.0 

38.0 

48.0 

56.0 

65.0 

5.1 

28.0 28.0 

41.0 40.0 

50.0 50.0 

59.-0 60.0 

8.0 8.3 

5-pound load. 

Meas- Comured. puted. 

----

------ ---· .... 1~ 15.0 

33 33.0 

44 44.0 

54 54.0 

11 10.9 

8-pound load. I 

Meas- Comured. puted. 

------ ---- ---- -- ---- - . -- ----

16.0 20.0 

36.0 35.0 

47.0 47.0 

14.5 13.8 

I 

The computed values are seen to agree closely with the measured 

values, so that these speed curves are parabolas of the form y= va +bx. 

The power curves sho~n in fig. 43 are parabolas of this form for the 

reason given for the corresponding case of the 12-foot Aermotor. The 

curve of maximum power to which these power curves are tangent is 

a parabola with its axis vertical. Its equation has the form x2=a+ by. 

We may obtain the data for finding the value of a and b by observing 

that when x=10, y=0.30; and that when x=20, y=1.55. 

We have 

l02=a+0.30b, and 

202=a+1.55b. 

Solving these, we have a=28, b=240, and the equation of the curve is 

(12) 

The values of y for four values of x are x=S, y=l5; x=12, y=0.48; 

;.t=16, y=0.95; and x=20, y=1.55. It will be seen that these values 

agree closely with the measured horsepower for these velocities. By 

making x=O 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. (N0.42. 

take the form x 2=K y', ]{ being a constant and y' the horsepower 

referred to the new origin. Hence we see that the maximum horsepower varies as the square of the wind velocity. 

To find the variation of the speed and load for this curve D K, we 

notice that the 3-pound curve is tangent at x=10.5, the 5-pound curve 

at x=14, the 8-pound curve at x=19, and the 11-pound curve at x=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 curve.s of maximum power 

of Aermotor No. 27. c Wind velocity per hour. Load. Horsepower. Revolutions 

per minute. 

I 

Pounds. 5 miles __________________________ _ 0 0 0 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 

'.rhe 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 firAt 

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. = 33,

000 , the speed being taken fro'lli_the speed curve PQ. 

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, showing 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. 

I I 

No load. Maximum load. 

Ratio of 

Ratio of speed at 

Wind Ratio of maxi- velocity Circum- circum- Revolu- Circum- circum- mum per hour. Revolu- ference ference ference ference load to tionsper velocity velocity tionsper velocity velocity speed at minute. in miles. to wind minute. in miles. to wind no load. 

velocity. velocity. 

8 miles._. ___ 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 EJ 20 miles. __ ... 56 32.0 1. 60 34 19.4 0.97 0 25 miles ______ 64 36.6 1. 46 38 21.6 0.86 0 

---- -------
MURPHY.] ACTION OF AIR ON SAIL OF AERMOTOR. 117 

It will be seen that the ratio of the circumference velocity of the 

wheel tp the wind velocity increases to 12 miles an hour and then 

decreases. In a 12-mile wind the circumference of the wheel is moving 1.81 times faster than the wind that drives 

it. It will be seen also that the circumference 

velocity of t,he wheel when carrying the maximum 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 useful load. 

ACTfON OF AIR ON THE SAIL OF AN AERMOTOR. 

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 concave surface of one sail of a 16-foot Aermotor in 

a nearly horizontal position as it moves downward; w represents the velocity of the wind, and 

v the circumference velocity of the sail. The 

curve J AE, fig. 59, shows the outer end of the 

sail, and to, in fig. 60, Rhows the inner end. The 

p 

I 

I 

cords of these arcs, 

J or the plane of the 

/ sail,makesanangle 

/ (JOP) of 30° with I 

,' the plane of the 

/ wheel. The point 

,' E, fig. 59, repre-

,' sents a particle of 

air as it comes in 

contact with the 

FIG. 58.-Sail of 16-foot Aermotor 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I I 

L_Jo I I ''J 

: / H 

I I 

I I 

~I 

0 

D 

FIG. 59.-0uter end of sail of 16-foot 

Aermotor. 

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 parallelogram constructed on EH and EF, is 

the velocity of this particle of air over the 

sail; EGis not tangent to the sail. Th~ 

point .A represents a particle of air as it 

comes in contact with the moving sail, 

when the mill is carrying no load; .A 0 

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. 
118 THE WINDMILL. (N0.42. 

In 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 tangent at the 9uterend 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 

I 

I 

I 

I 

I 

I 

I 

·I 

I I r.~~ I ~~ 

I I fl 

il 

be a little greater than 30° at the outer 

o 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 

FIG. 60.-Inner end of sail of 16-foot The mean number of hours per month 

Aermotor. 

that the wind velocity was 0 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 number 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 wor·k of 12-foot and 16-foot Aermotor.<J in a year. 

Mean wind movement at Dodge, Kansas, Horsepower 

1889-1893. Total hours. 

Month. ~-

0 to 5 6to10 11 to15 16to20 21 to25 26to30 31+ hours. 12--foot 16-foot 

miles. miles. miles. miles. miles. miles. miles mill. mill. --~ 

-----------------

H1·s. Hrs. Hrs. Firs. Hr.~. Hrs. Hrs. January_--------~_ 200.9 253.0 156.2 74.4 37:2 14.9 7. 4 744 250.5 358.0 

February ...... ____ 176.0 230.1 128.6 74.4 40.6 20.3 6. 8 677 251.6 361.5 

March _. _ .. _. ~ . _ ... 126.5 208.3 178.6 119.0 59.5 29.8 22.3 744 386.6 558.9 

April ... ~---------- 115.2 172.8 158.4 115.2 72.0 43.2 43.2 120 461.2 611.3 

May-------- ____ .... 119.0 19o.5 171.1 119.0 74.4 37.2 29.8 744 433.9 629.4 June. ______________ 122.4 187.2 136.8 108.0 86.4 50.4 28.8 720 452.0 658.2 July _______ ~ _______ 141.4 215.8 178.6 119.0 59.5 22.3 7.4 744 389.8 489.3 

August ______ ------ 178.6 230.6 156.3 96.7 59.5 14.9 7.4 744 297.5 427.6 

September ________ 165.6 180.0 151.2 93.6 12.0 36.0 21.6 720 379.6 550.5 

October __ ----_ .. --- 20K3 2:30.6 141.4 74.4 52.1 22.3 14.9 744 294.0 423.5 November. ________ 194.4 266.4 129.6 64.8 36.0 14.4 14.4 120 244.9 350.9 

December----· ____ 1H6.0 267.9 141.4 81.8 44.6 14.9 7.4 744 262.2 374.6 ----- Mean ______ .... ____ ------- ------- ------- ------- ------- ------- -----·- ............. - 337.8 487.8 

Horsepower 16-

foot mill ..... ---- ------- 0.13 0.56 1.25 2.00 3.15 ------- -------- ----- --·- Horsepower 12- foot mill. _______ ------- 0.10 0.41 0.85 1.36 2.12 ------- -------- --------

1 Some Climatic Features of the Arid Region, by Willis L. Moore. Washington, 1896. 
MURPHY.) :M:ATHEMA'l'IOAIJ DISCUSSION. 119 

The work done by these mills is greatest at this place in April 

( 461 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 a51 horsepower hours for the 16-foot). rrhe mean mont,hly 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 

vdll 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 hourR a 

day for 26 days a month. It must be remembered that the wind 

velocity on the Great Plains is conEtiderably greater than in the eastern 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 determine 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 

Pl. XVI, B. It is made of wood, the parts being fastened together 

with bolts. The diameter is 7. 75 feet; length of sails, 11t feet. There 

are 8 sails, each made of two boards 11 t 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 3t feet long, and is made so as to fit on t~e end of 

the shaft. Oil was freely used on the brake. It was not found practicable to use loads greater than about 6 pounds on a 35-inch arm, as 

t,he friction burned the shaH; 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 It-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 t,han the friction of 

motion. The 0 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 11t 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 t,here were 8 sails, 

6ach having an area of Ilt feet by 8 inches; that is, each sail was 

only half as wide as those used in the first set of tests. In the t,hird 

set of tests the sail area consisted of 4 sails, each lit 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 

VELOCITY OF WIND IN MILES PER HOUR. 

10 11) 

0 

I 

v 

4/Z 

/ 

I I 

wheel. This inclined 

surface had a length of 

7 feet and formed an 

angle of II o with the 

horizontal. 

Test No. 1.-In Pl. 

XVI, B, the mill is 

shown with 8 sails, each 

lit feet by IG inches. 

Fig. 6I shows the number of revolutions of 

the wheel per half mile 

FIG. 61.-Diagram showing revolutions of wind wheel of mill of wind for t~wo loadsNo. 55---7.75-foot Jumbo. Curve marked 0 is for no brake 0 and 4. 5 pounds-on a · load; curve marked 4t is for a brake load of 4.5 pounds. 

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 I2 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 r~sults of these tests are as follows: 

Results of tests of Jumbo mill No. 55 with 8 sails 11.J;; feet by 16 inches. 

I Revolutions of wind wheel per Horsepower at given wind velociti:l minute at given wind velociLoad ties (per hour). (per hour). 

Load per rev- on olution 00 00 00 00 00 00 .,; rt ri brake. of wind ~ <V 

~ ~ 00 <V ~ <V <V 

wheel. <V :;:::: <V ] :;:::: :;:::: ] "§ s ] "§ s s ¢;! 00 00 M M ~ ~ 00 ~ ;:; ~ ~ 

Lbs. Ft.-lbs. 0 0 11 24 3.'3 41 49 -------- ---· ---- ------- -------- ------ ---- 1. 75 32.0 22 30 38 45 0.022 0.030 0.036 0.04.} 2.5 45.8 20 28 36 43 -------- 0. O'ZS 0.039 0.050 0.060 

L4.5 82.5 17 25 33 40 -------- 0.043 0.063 0.082 0.1~ 
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- Ji-FOOT JUMBO. 
MURPHY.] MATHEMATICAL DISCUSSION. 121 

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= 2?T RnL 7 

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), 

?T = 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 equi\1 to 2?TR 7 33,000: 

P0 = K X 41 (revolutions) X 0 (L) = 0 

P1 = K X 33 (revolutions) X 4.5 (L) = 148.5K. 

P2 = K X 26 (revolutions) X 8.5 (L) = 221.0K. 

P3 = K X 22.5 (revolutions) X 10.5 (L) = 236.3K. 

P4 =K X 20.75 (revolutions) X 11.4 (L) =238.6K. 

P5 = K X 19 (revolutions) X 12.5 (L) = 237.5K. 

P4 is seen to be larger than any of the other values of P, and gives 

an approximate value of the 

power of the mill for that wind 

velocity (20 miles). 

We may find a more accurate 

value in an easier way. Let x 

VELOCITY OF WlND IN MILES PER HOUR. 

10 15 20 25 

be the load for maximum horse- .:l 401-----1-----1----.A--,.,L.....,,£---""71 

power in any given wind velocity. We have seen that 1 pound 

of load reduces the speed by 

1. 75 revolutions. Then we can 

write P= K (41-1. 75x) (x). 

For a maximum value of P we 

must differentiate P with respect to x, place the first differential coefficient 0, and solve 

for x. This value of x, according to calculus, makes the power 

a maximum. Differentiating, 

r;.;l 

r;.;l 

~ 

~ 

we have P + dx = 41-2 (1. 75x) FIG. 62.-Diagram showing revolutions of wind 

= 0. Solving for X we have wheel of mill No. 55-7.75-foot Jumbo. Curves 

marked 0, 1t, 2-t, and 4t are for brake loads of 

x = 11.7 pounds. The corre- o, 1.75, 2.5, and 4.5 pounds, respectively; .AB is 

sponding value of the revolu- for best load. 

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 pomids, and n = 16.5. 

In a similar way we get the load and revolutions for maximum power 

IRR 42-01--± 
122 'l'HE WINDMILL. [N0.42. 

for other wind velocities. T'hese and the corresponding horsepowers 

are as follows: 

Value..; for the curve DK (maximU'tnpower) fig. 63. 

. Wind 

1 

I velocity j 

i (miles per I i hour). 

8 

12 

16 

20 

25 

Load in 

pounds. 

I Revolutions of 

wind wheel 

perminnte. 

Horsepower. 

----------1----

3.1 

7.0 

9.4 

11.7 

14.0 

6.0 

12.0 

16 .. ') 

20.5 

J4.5 

0.010 

0.046 

0.086 

0.133 

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 

~ fii1 

!::: 

c 

VELOCITY OF WIND IN MILES ~ER HOUR. 

10 li'i 20 25 . :!o.-------.------r----r------. K 

I 

I 

.16t------if------t-----t---+----j 

I 

I 

t .12•t-------i-----+----·~----; if.! 

p: 

0 

III 

~ 

fii1 

~ -~t-------l----+,r--~~----; 

c 

s 

~ 

IJ 

FIG. 63.-Diagram showing horsepower of mill No. 55-7.75-foot Jumbo. '.rhe curves show the 

horsepower for brake loads of 1.75, 2.5, and 4.5 pounds, respectively; dotted curve DKshows 

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 2-!.-1 feet (the eireumference of t,he 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. 

Table showlng ratio between wind velocity and circumference velocity of wheel. 

w· Ill ct ,.e 1 oci ·t y per hour 

Load. 

8 miles. 12 miles. 16 miles. 20 miles. 25 miles. 

I I 

I 

No load ___________ . _ -·- ----- 0.38 0.55 0.57 0.57 

Best load -.. ---- - ---· ------ 0.21 0.27 0.28 0.28 

~ 7 

: 

From this we see that the velocity of the circumference of the wheel 

is ~ot more than 57 per cent of the velocity of the wind. For velocities above a certain amount it remains nearly constant for any load. 

It will be seen too t.hat the Rpeed of the wheel for best load is almost 

exactly half that for no brake load. 

Test No. 2.-Sail area, lit 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. 5S, with 8 sails lli feet by 8 inches. 

1'- Revolutions of wind wheel p minute at given wind velo 

ties (per hour). 

ui ui ui 00 00 Cll Cll .$ Cll 

,.!l :;::: :;::: '§ ] '§ s s ~ ~ ~ ~ I oo ~ [-

b>.-lb•. 

er Hor..,power at given wind velocities I CI- (per hour). 

00 • ui Cll Cll 00 Cll 00 00 Cll I ~ ] ~ ~ ~ 00 s ..... 

~ . ~ "' 0 

~ ~ 

~ 

P=~•·j 5g.6 ----~- 22 30 39 3.25 17 26 32 !b :::::::: -o: OOi ~ ~-0581· ·--o: ,r,.j-1 

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 4t-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-~ feet by 16 inchesevery other full sail removed. The results of this set of tests were 

almost the same as those of test No. 1. There was no measurable reduction in the speed of the wheel when every other full sail was 

removed. 'rhe 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-! feet by 16 inchesthe same as for test No. 1. There was an inelined surface (shown in 

Pl. XVI, B) for concentratin_g air on 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 diameters 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,! from which we infer that if galvanized-iron sails 

curved to a radius about twice the width and with the concave surface 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 test,s of Jumbo mills in the most practical form, we have the following as the proper sail area and the 

probable horsepower of wooden .Jumbo mills in a 16-inile wind when 

properly loaded, assuming the power to increase as the square of the 

diameter: 

Table showing proper sail area and probable horsepotoer of Jumbo wooden mills in 

a 16-mile 'mind. 

~meter of wheel. Number of Width of Length of Hor.epower.l sails. sails. sails. 

I Inches. Feet. 

I Sfeet - ·--- _ .. ___ ... ____ 4 12 12 0.09 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 isr P=F- (c-v) 2 

g (a) 

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 formulaB To 

rr=roBoT 

In this To is the absolute temperature in centigrade degrees. 

1 Kansas University Quarterly, Vol. IV, July, 1895. 

(b) 
MURPHY.) MATH EM A TICAL DISCUSSION. 125 

29 273 

From equation b we have r=0.08 X 30 X 301 =0.07 pound per square 

foot. From the table on page 123 it will be seen that for maximum 

power in a 16-milewind v=0.28c. Substituting in equation a we have, 

for the pressure on one sail1 

P=11.5x 32_

2 x0.07 (1-0.27)2 c2=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 4.1 x 3.6=14. 76 foot-pounds. 

This moment is equal to the moment of the brake load, and we have 

14. 76=35x, and x=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 Pl. 

XVI, A. It is used for grinding wheat. The I.ittle 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, however, 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 circumference. 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 circumference. 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 lOt inches long and 

6! inches wide, set at an angle of 27° to the radius. The radius of 

curvature of the sails is 7-! inches. The vertical shaft of the wind 

wheel has a beveled cogwheel, which gears into another beveled cogwheel on a short horizontal shaft. The latter has a pitman for working a pump. The horizontal shaft on which the brake was placed 
126 THE WINDMILL. (No.42. 

was geared back 43-:-13. The brake arm was 2 feet lO-t 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 con·esponding speed of the wind wheel is found by multiplying by 3:f. 

The results of the tests were as follows: 

J 

~ 

~ 

Re:mlts of tests of Little Giant mill No. 56. 

r- Revolutions of brake shaft per minute Horsepower at given wind velocities I at given wind veloci- (per hour). ties (per hour). 

Load. !1i ai 00 00 00 riJ 00 ai ai ~ <1l <1l 

~ 00 <1l <1l <1l <1l r.:: ~ ] <1l 

r.:: s s ] ] ] ] s s ~ <:C ~ ~ ~1 <:C 00 ..... ..... 00 ..... ..... ~ ~ -------------------

Pounds. Ft.-lbs. 

I 

l 

[ 

0 0 10 19 25 31 38 ··o:oo7- · ·o~ oi7- ·-o~wf ·-o~ooo· .................... 2 35.7 6 16 21 27 34 0.040 

4 71.4 .. ----- 11 18 23 30 ------- 0.024 0.039 0.050 0.065 

6 107.1 ............. 6 14 19 26 -------- 0.019 0.045 0.062 0.084 

Referring to fig. 64, the mill will be seen to start for no load in a 

VELOCITY OF WIND IN MILES PER HOUR. light Wind-abOUt 5 mileS an 

10 15 20 25 hour. More than half of each 

40,r----,----.----r----. speed curve is a nearly F:traight 

: ~------+------+----~~~~~ 

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 tanQ 

~ 

~ 

gent, shows the maximum power 

FIG. 64.-Diagram showing revolutions of wind of the mill. This curve passes 

wheel of mill No. 56-4.67-foot Little Giant. The 

curves marked o, 2, 4, and 6 are for brake loads t h r 0 Ugh the points y (horse-· 

of o, 2, 4, and 6pounds, respectively. power)=O when x (wind velocity)=5, and y=0.024 when x=l2. Hence, if we assume this curve 

DK to be a parabola, we have for its equationx2 = 4:96y+ 25. 

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. 127 

Horsepower of mill No. 56 at given w1:nd velocities. 

lx 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 0.06~ 

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 velocities are as follows: 

Table showing relation of circumference velocity of wind wheel to wind velocity. 

I w;nd vcloo;ty 

per hour. 

No load. Maximum load. Ratio of 

----,--1 ---------c~----1 :i~~~l~t 

Revolu- Circum- ~~~~~~~ Revolu-~ Circum-~ ~atw of maxitions of feren_ce ference tions of feren_ce ~~~~~~ mum load 

brake velocity . brake velocity . to revolushaft per in miles velo<:Ity shaft per' in miles veloc:;Ity tions at 

h to wmd . h I to wmd 1 l-------l-m-i_n_u_te_. -l-p_e_r_ou_r. velocity. mmute. per our velocity. no oad. 

8 miles _____ _ 

12 miles __ . __ .. 16 miles _____ _ 20miles _____ _ 25 miles . ____ _ 

10 

19 

25 

31 

38 

5. 2 o. 65 6 3. 1 1 o. 39 o. 60 

9.9 0.74 11 5.7 0.47 0.58 

13.0 0. 81 14 7. 3 II 0. 46 8: ~~ I ~u z:~z 16 

1 

8.3 0.42 ~ 

From this we see that for no load the greatest circumference velocit,y 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. 7 5. 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 J urn bo is only from 0. 55 to 0. 70 of that of the Little 

Giant for best load. 'rhe horsepower of the Jumbo is about 1.~ times 

that of the Little Giant; the ratio of the .Jumbo diameters is 1.67; 
128 THE WINDMILL. (N0.42. 

hence the ratio of the power is a little greater than that of the diameters. 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. 

Mill. 

Comparative data of Little Giant and Jumbo mills. 

Maximum horsepower at given wind velocities (per hour). 

tJ3 tJ3 tJ3 ,;, ,;, ~ ~ <ll ~ ~ ] ;,::: ] s s s ~ ~ ~ 10 00 IN 

--------

Circumference velocity for 

maximum load at given wind velocities (per hour). 

,;, ,;, 00 ,;, 00 (]) (]) (]) (]) 

<ll ;,::: ] ] ;,::: ;,::: s s s ~ "' ~ 10 00 ~ IN 

----------

7t-foot.Jumbo ------------ 0.010 0.046 0.086 0.1o3 0.190 1.7 3 .. 40 4.70 5.80 ------~ 4+-footLittleGiant _______ 0.007 0.024 0.045 0.066 0.100 3.1 5.70 7.30 8.30 ------ ------------------------- 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 governs 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 Am·motor No.5 (for description 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. 

Mill. 

Load 

per 

revolu- Sail 

Revolutions of wind 

wheel per minute at given wind ve- locities (per hour). Horsepower at given wind 

velocities (per hour). 

tion of area. l--:---:---:---1----,-------.-------:--~1 

W

whienedl. tJ3 ~ ] ~ ; .... ~ ] ~ ] ] ~ ·a a ] ·a s ·a 

I--------IF-t.--1-bs-.ii-S-q.-ft-. ~ ~ ~ ~ ~~___!___~ 8-foot Aermotor (No. I 

5).---------------·--- 45 34 62 84 99 115 0.084 0.115 0.138 0.158 

4!-foot 

(No. 56) 

Little _______ Giant 

-------~~-~-~-~~ 92 _0.024 0.039_ 0.050_~~~ ~ 

• Ratio----------- 1.96 i 0.6B 1.82 1.53 1.40 1.25 3.50 3.00 2.76 2.43 
MURPHY.] COMPARISON OF LITTLE GIANT .AND .AERMOTOR. 129 

It will be seen that the sail area of the Aer·motor is only 0.6:3 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 gr.3ater than the power of 

the latter. While the sail area of the Aermotor is only 0. 6:3 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 t.he 

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 advantage 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. 7 5 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 p~ssing out of the 

wind wheel as well as while passing 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 

~ 

1"1 

VELOCITY OF WIND IN MILES PER HOUR. 

10 15 20 25 

~ .lli~----;-----~~~--r-----~ 

0 

~ 

FIG. 65.--Diagram showing horsepower of millN o. 

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. 

angle of 27° with the radius AP. CD is the shield, with the wing DE 

open. Let An 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 
130 THE WINDMILL. (N0.42. 

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 some,vhat. L4 is approximately the absolute 

path of the particle over the sail, and ±-5 is the direction of t,he particleat exit. B6 represents the absolute path of a particle of air as it 

moves over the sail BK. 'fhis 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 particle out of the wheel. It is evident, however, tJhat 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 si<le where the air enters. 
MURPHY.) INDICATED A.ND 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 distances actually passed over by the wind per hour. Fig. 67 shows the 

Robinson cup anemome- · 

teras used by the United 

States Weather Bureau. 

This instrument was invented in 1846 by Dr. T. 

R. Robinson , of Armagh, 

Ireland, and is now used 

by several meteorological bureaus for the meas· 

urementofwind velocity. 

It gives a continuous record 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 tlie dial, 

and there is an electrical 

device for recording 

each 250 or each 500 revolutions of the cups. 

Referring to fig. 68, let 

A =the upper and B = 

the lower cup of a Robinson anemometer rotating 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 1 = the 

pressure on the concave 

surface, and P2 = the 

c 

Fro. 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; l, 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 I; Jl, one of ten contact pins to aid in closing tbe electric 

circuit at the end of each mile of wind; p' , two of these pins 

connected, forming the tenth mill pin: w. contact spring; q, 

o,contactpointat the end of contact spring; t, small insulated 

tube connecting q with the insulated binding post. " and 

with the second binding post"· 

pressur() 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 surface is presented to the wind. The pressure on the moving cup A is 

P1=K1Fr(c-v) 2+2g, 1 and the pressure on the cupBisP2=K2Fr(c+ 

v) 2+2g_; Fbeingtheareaof the cup, K 1 andK2 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 P1 must equal P 2 ; if P1 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 1 Fr (c-v) 2+2g=K2 Fr (v+c)2+2g or 4 (c-v)2= 

(c+v)2. This equation can be put in the form 4 (x-1)2=(x+1)2. Solv.:. 

ing we have x=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 

2 X 22 6. 72 . d=-7

- X 12 X 3 X 500=5,280 feet, or 1 mile. 

Dr. Robinson believed that this ratio of wind velocity to that of 

c 

c' \ 

\ 

c 

c 

/ / 

........ "' 

/ 

I 

I 

/ 

FIG. 68.- Diagrammatic section of anemometer cups. 

cup center was true for 

all velocities, and consequently the makers of 

the instrument have 

mar ked the dial in 

miles. We shall see, 

however, from the rating of the one that we 

have used in these windmill tests that this ratio 

is not a constant. It 

will be seen that for 

wind of uniform velocity this ratio is a variable which has the value 

3 for 9 miles an hour, is 

greater than 3 for less 

velocities, and is less 

than 3 for greater velocities 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 

1 Church's Mechanics of Engineering, p. 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 anemometer 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 cogwheel 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 mea,ns 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 Revolu- Correction, tions of Trueveloc- velocity, in long arm i ty, in miles Correction, in miles, miles per in miles. for gusty hour. in t mile of per hour. wind. wind. 

6 15.5 6.20 +0.20 0 

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 

I 

20 13.8 18.40 -1.60 !J 25 13.53 22.55 -2.45 ') 

30 13.3 26.60 -3.40 . 

It will be seen that the indicated velocity is less than the true 

velocity for velocities less than 9 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. [No.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 

tlie 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 revolutrion, 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 Robinson anemometer, recording miles or half miles, does not show these 

sudden changes, but gives an average velocity for the wind. Its 

5 

1.5 

1.4 

1.3 

1.2 

1.1 

~ 1.0 

1:: 

0 

~ 0.9 w. 

~ 0.8 ~ 

~ 0. f"1 

7 

8 

~ 0.6 

~ 0.5 

0.4 

0.3 

o.:.. ~ 

0. ] 

~ 

/ 

~ """ 

VELOCITY OF WIND IN MILES PER HOUR. 

9 ll m M TI W 21 23 

fF 

E D B 

I J I L 

I vv L 

v L li_ l_v 

J ;'/ /v 

I v./ )r 

v l;j v 

/ 

v 

I I~ V.; v 

1/ ~ ~v 

J ~ ~ v ~ v 

I ~ v 

/ A~jj" 

~ P"" 

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; 

xB-140.6 AE shows power in average gusty wind; A F shows power from H. P. = 2

,

086 · 

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: (I) 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 anemometers. If t~he anemometer is rated in natural wind, then a correction ------.. -~~-~~----------

1 Anemometry, by C. F. Marvin. Washington, 1893. 2 The Internal Work of th(' Wind, by S. P. Langley. Washington, 1893. 
M!IRPHY.) COMPARISON OF EXPERIMENTS. 135 

must be applied, but its amount is uncert.ain. 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 instrument 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 difficulty 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- anemomet.er is now so generally used to measure 

wind velocity that it is better to express the speeds and powers of windmills 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; AFwould give its power if the power increased as the cube of 

the indicated velocity. 

COMPARISON OF WRITER'S EXPERIMENTS WITH THOSE 

OF O'l'HERS. 

Comparison with Smeaton' s experim,e,nts.-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 windmill sail, whether loaded, so as to produce maximum power, or unloaded, 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 somewhat 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 t.he wind velocity. Our experiments show that for a constant load the power increases as the square 

root of the wind velocity. 
136 THE WINDMILL. [N0.42. 

Smeaton found (maxim 6) that the circumference velocities of similarly 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 velocity for loaded sail, and about 1. 7 5 times the wind velocity for the 

unloaded sail. 

Comparison with Coulomb's experiments.-In this comparison indicated 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 minute 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. 

Revolutions CircumferMill. of wind ence velocity Horsepow wheel per in feet per minute. minute. 

er. 

0-foot mill - - . ~ - -,.. . - -- ~ ... --- ~ ... - --- 13 2,860 7. 0 

6-foot Aermotor _ . _ _ _ _ _ _________ 28 1,408 0. 

~ 

The circumference velocity of the large mill is more than twice that 

of the smaller one. The ratio of the powers is 7--;- 0.8 = 8.8. The ratio 

of the diameters is 70-716 = 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 horsepower 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 Griffiths'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.] CO:MP A RISON OF EXPERIMENTS. 137 

which may make the horsepower of one four or more times that of the 

· other. For example: Both mills hav~ a brake power of 1 horsepower; 

one mill works a pump which has an efficiency, under present conditions, 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 horsepo~er 

being 0.8, or four times that of the other. We have seen t};\~~Jor 

"'ind velocities above a certain amount the power increases near).y as 

the load, so that by doubling the load for the higher veloc~ties ~he 

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 greap 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. r.rhe 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 differences in load. In fact, most of his velocities ar·e 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 wjth low pump efficiency. 

Comparison of results of Griffiths's tests with those of writer's tests. 

I Outer di- Load per Wind ve-l Strokes of =l MilL ameter of stroke of locity. P::;fJuf:.r sail. pump. power .. 

Feet. Ft.-lbs. Miles. .. 

Griffiths's No. 1 ____ 22.3 480.0 7.0._ 6.8 __j}.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 

Writer's 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 

~ Griffiths's No. 6 ____ 9.8 30.7 6.0 12.5 2 

Writer's No. 47. ___ 10.0 37.0 6.0 7.0 8 

It will be seen from this table that the horsepowers of the mills tested 

by Mr. Griffiths are greater than the horsepower'S of the mills -we have 

tested. 'l.,he 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 eaperiments.-Professor King's measurements of the brake horsepower of a 16-foot Aermotor are given on 

IRR 42-01--5 
138 THE WINDMILJJ, [Nf>.42. 

page 20., Part I. These results are plotted in fig. 70, giving the curve 

AB. Th~ curve of maximum power for the 16-foot Aermotor No. 44 is 

redrawn in this figure a& 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 

Profe~Sor King's mill interfering with the anemometer, we have experitnent~d':With two anemometers, one located 29 feet directly south of 

the Wind! Wtieel of mili No. 44, the other located 27 feet. directly north 

of it, arid each recording, side by side, the wind velocity on an electri~ register. The hburly 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 following table: 

. Table showing wirul velocities during writer's experiments with anemometers on 

mill No. 44. 

Wind velocities. 

Hour. Direction 1--------1 

of wind.- Front ane- 1 Rear ane- mometer. I nrometer. 

I------------------I-~---I--M-il-es-.-~-M--~-ie-s.-- 11 --Pe_r_c_en-t.-

First __ . ~ . _ _ _ _ _ _ _ _ .. ____ . _ . . . SE _ . . . . .- 15. 0 10.2 0. 68 Second_ . ~ __ ~ __ . ___ . ________ .. ___ . do _ .. 18.0 13.4 0.74 Third . ____ . ______________ . _ __ __ _ do __ _ 18.0 13.5 0.75' Fourth _ . _______ . _ .. _ . ____ . _ _ _ . .. a.o . __ 19.5 12.8 0.66 

Fifth ____ . _ ... _ .. ________ . _. SW • ___ . 18.0 13.5 0.74 Sixth __ . ________ .. _ ... ____ .. _ . . __ . do _ . _ 16.3 12.6 ~.77 Seventh .... __ .. __ _ _ . ___ .. _ _ __ S _____ .. 15.2 10.0 0.65 

12.7 9.6 0.76 

10.5 7.5 0.71 Eighth ..... ---~-- ..... _______ SE .. ·--

Ninth .... ~·------------------ .... do __ _ 7.7 5.5 0.72 i 

7.2 7.2 1.00 : 8.6 8.6 1.00 i 

Tenth __________ ·--------- ........ do __ _ Eleventh ________ .. __________ -~--do --• Twelfth _____ ~"'"- _____ .. ________ .... do __ _ 

10.5 10.6 1.00 ; 

10.3 10.4 1.00 . Thirteenth_ ••. -.- .. __ ..• ____ . _ . _ .. _ . do __ .. 

Fourteenth-----·------ ______ .... do ___ 

·The direbtion of the wind is the mean -f{)r each hour, as shown by 

an Anemoscope.. When the wind was froni the southeast it occastonallY came for a short time ~~most ~irectly from the east_; and, agfin, 

'+.en from the southwest 1t occaswnally came for a time from ithe 

W!~St! ~ · , 

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 

·an of the tests were made when the wind came from the northwest or 
MURPHY.] COMP ARlSO::N. ·OJ!' EXPERIMENTS. 139 

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 act,ually existed, ~nd making the horB;epower greater than if the anemometer had been in front of the whe~l. 

In fig. 70 it will he seen ~hat an increase of from 5 to 25 pei· cent in 

Professor l{ing''s wind velocities would move his curve over to tbe 

right of our curve. r_rhese curves are found in very different waysL 

Professor King~s from 26 single observations, ours from more than.ltiO 

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 experim.ents.-Indicated velocities 

are used in this comparison. 

Some of ~Ir. 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 1i 

n:iiles ·an hour. Mr. Perry states 

that his results agree with those 

VELOCITY OF WIND IN MILES PER HOUR. 

10 15 25 

5.-----,------.------.------, 

.B 

FIG. 70.-Diagram showing horsepower of two 

16-foot Aermotors. Curve AB slJOW.i!..."Q~ake 

horsepower of Professor King's 16-foot Aermotor; CD shows ma;x:imum power of writer's 

16-foot Aermotor No. 44. · 

of Smeaton. A comparison of our results wit,h Smeaton's has be~n 

given.on pages 135 and 136. . 

We will com par~ in detail the working of two of Mr. Perry's wh~els, · 

v~z, Nos. 44 and 48, with that of our 12-foot Am·motor 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, ea,ch_l.8 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 oute1· end. The air is more obstructed 

in its passage through this wheel than through the wheel of No. 21. 

The following are some of the results for these mills in an 8.5-mile 

wind, the only velocit.y which Mr. Perry gives for his IJ\ill. 
140 THE WINDMILL. [No.42. 

Comparison of results of tests of Perry's 5-foot mill No. 44 toith writer's tests of 

12-foot Aernwtor No. 27. 

Load Maximum load. No load. 

Wind 

Mill. Area veloc- per Revolu- Circum- Horse- Revolu- Circum- of sail. ity. revolu- tionsper ference power. tionsper ference tion. minute. velocity. minute. velocity. ----------------

sv_t. Miles. Ft.-lbs. 

mill No. 44 .. .6 8.5 11.3 44.4 8.6 0.016: 84.3 22.1 

Aermotor 

........................... 73.0 8.5 22.2 19.0 11.9 0.13 32.5 20.4 -------·--·------------- atios. ---- .... 5.3 -------- 19.6 ----............ 1.381 8.12 ....................... 0.92 

-~ 

It will be seen that the load, in foot-pounds, per revolution of wind 

wheel is 19.6 times greater and the circumference velocity for maximum 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. ~ehe 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. 48 with writer's test.'l of . 12-foot Aermotor No. 27 . . 

I Maximum load. Nol 

Wind Load 

Mill. Area veloc- per Horseof sail. ity. revo· Revolu- Circum- power. Revoln·l lution. tionsper ference ti<-!ns~er minute. velocity. mmue. 

· Sq. jt.j Miles. Ft.-lbs. • 

---1 

Perry's mill No.48. 14.2 11 23.3 66.8 17.4 0.047 1421 

10-foot No. 27 .............. Mrmotor 73.0 11 333 28.5 17.9 I 0.288 45 I 

Ratios---------- -5.2~-=~-::--==--1:005.00=== 

~ 

~t ference 

velocity. 

_:;;_I 

~ 

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-
M:UitPHY.) ECONOMIC CONSIDERATIONS. 141 

responding amount of obstruction the ratio of power would probably 

be 6.5 to 7. This ratio is greater even than 12 +_52=5. 76, the ratio of 

the sq nares 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 airnotably 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, sec.ond, that 

the power increases as the square of the diameter. Our tests of windmills 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 30-foot steel tower 

weigh about 4,250 pounds. rrhe 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 H)-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 factorscost 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, _ _ [N0.42. 

It has been shown that the steel mills, with' their few large sails, 

have much more .power than the w_ood.en ·mills with their many small 

sails. (See page 106.) A mill should have as few moving part.s 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 litt,le 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 shafting is much too heavy; apparently it is designed on the assumption 

that the mill will furnish several times more power than it really can. 

rrhe mill should be carefully erected, t.he 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 t11e smal1 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 wheeJ on ;t high tower than a large wheel on a low tower. An 

8-foot cwheel 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 

a:round it.. The tower shoulQ. 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 

graduaJly 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 

highe.r wind velocities, with a light load the mill will do {m~y a small 

fraction of the work it would do with a much heavier load. Theincrease in the load should be nearly proportional to the increase inthe wind velocity. (See page 113.) Until such a device is invented 

th~ 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 part!y 

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 ~:m the upstroke. 1,he descent of the weight 

assists the mill in lifting the water. Neither device is satisfactory. 

A p·umping 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 

hack 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, 101-10~ 

effect of air on sails of, diagrams showing ............................... 117,118 

effeet 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 

'vith .............................. 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 windmill, 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 

views of ............................ 28, 46, 131 

Back-geared steel windmills, comparison 

of direct-stroke wooden windmills 

with................................ 43 

Burnham,J.,invention of American windmill by............................. 11 

Carlyle windmill, test of, results of......... 17 

Centrifugal-governor method of regulation, 

explanation of...................... 14 

IRR 42-01--6 

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 • 

vie'v of................................. 98 

Cornell windmill, description of ........... 5!Hi0 

manufacturers of....................... 59 

tests of, results of. ................. . :c' 5!).-60, 64 

Cost of windmill plants ........... 28, aO, 31, 33,44 

Coulomb, C. A., windmill experiments by.. 16 

windmill experiments by, compared 

with Murphy's experiments........ 136 

Defender windmill, view of "water elevator" 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, comparison of back-geared steel windmills 

\Vith. ..... ..... ... .. ... ... . ... ...... 43 

Dodge, Kans., wind movement at ......... 70,118 

Dutch windmill, features of................ 14 

test of, at LillB, 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. ................ 00-51, 64,92 

where manufactured................... 50 

European windmill, compared with American windmill. .................. 11-12, 14 

early experiments with ................ 15-16 

European post windmill, section of . . . . . . . . 12 

European tower windmill, diagram showing 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 ................. ..,.. . . . . 24 

145 
146 INDEX. 

Page. 

Gem windmill, descriptions of. ............ 34-35, 

42-43, 43-44, 44-45 

manufacturers of ..... c................. 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, 64,94-96 

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, 0. P., tests of Frizell pumps by ...... . 24 

Horsepower, relation between wind velocity 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 

revolutio?s of wind wheel_ of, diagram 

showing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 

tests of, results of. 30-33,37-41,44,58,64,100-101 

views of. . . . . . .. .. . . .. .. . . .. .. .. . . .. . . 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 

horsepower 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 ...... 18-20 

windmill experiment!> by, compared 

with Murphy's experiment.;; ...... 137-139 

Langley, S. P., cited........................ 134 

Page. 

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 showing . . . . .. . . . .. .. . .. . .. .. .. . . .. .. . .. . 130 

comparisons of other mills with ....... 12-14, 

127-128,128-130 

description of ......................... 125-126 

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 windmills .............. 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 

Rhowing ........................... ; 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, 86 

manufacturers of....................... 86 

tests of, results of. ................ 17, 59, 64,86 

view of .. . .. . . .. . . . . . . . . .. .. . . . . . .. . . . . . 58 

working parts of, view of............... 85 

Perry, T. 0., comparison of Murphy's experiments 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, 

1:!8-130 

description of. .......................... 83-84 

difference between pumping mills and. 22 

economic considerations of .......... 141-143 

horsepower of, comparative diagram 

showing............................ 107 

method of testing..... . . .. . . . . .. . . . .. .. . 84-86 

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, diagrams showing .. . .. .. . .. . . .. .. .. .. 88, 91, 

92, 93, 94, 96, 98, 100,101, 105, 120, 121, 126 

revolutions of wind wheels of, comparative diagram showing . . . . . . . . . . . . . . 105 

tests of, results of. ............ 15-16,19,86-102 

useful work of. ....................... 118-119 
INDEX. 147 

Page. 

Power windmills, views of ....... 90, 94, 97, 99,120 

Pressure-tank system, description of ....... 68-69 

Pumping windmills, backgeared and directstroke, comparison of ............... 65-68 

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 testing .......... _. . . . . . . . . . . . . . . . . . . . . . 24-27 

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 showmg . . . 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 velocity, relations between, diagrams 

showing . . . . . . . . . . . . . . . . . . . . . . . . . . . 49, 88, 

91, 92, 93, 94, 96, 98,100,101,105,120,121,126 

Regulating devices of windmills, description of.............................. 14 

Robinson, T. R., anemometer experiments 

by ................................ 131,135 

invention of anemometer by........... 131 

Sail-wheel windmills, comparison of paddlewheel windmills and ............... 12-14 

Semiarid regions, mills and pumps for use 

in ................................... 71-72 

Smeaton, J., windmill experiments by .... 15-16, 

20,135-136 

Speed and horsepower, effect of tension of 

spring on . . . . . . . . . • . . . . . . . . . . . . . . . . . , 110 

0 

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 

vie'.v of................................. 30 

Stover windmill, test of, results of.......... 17 

Tension cf spring, effect of, on speed and 

horsepower.................. . . . . . . . 110 

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............................. 11 

Wind movement at Dodge, Kans., details 

regarding. . . . . . . . . . . . . . . . . . . . . . . . . . . 118 

relation between circumference velocity of wind wheel and ............ 122-125 

Wind velocity, relation between horsepower 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, 9'2, 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 Psrr~ i~. . . . . . . . . . . . . . . . . . . . 20 

Wonder pump, descnptiOR 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. ............. 51-52,55-5 7, 64 

Woodmanse Mogul windmill, descriptions 

of. ................ 27-29,51-52, 53-55,55-5 7 

manufacturers of.. . . . . . . . . . . . . . . . . . . . . . 27 

tests of, results of .............. 27-29, 53-55, 64 

views of................................ 28 

pump, etc.; of, view of.................. 54 

working parts of, view of............... 26 
•. 
11'09.:>. 

Sixteenth Annual Report of the United States Geological Survey, 1894-95, Part II, 

Papers of an economic character, 1895; octavo, 598 pp. 

Contains a paper on the public lands and their water supply, by F. H. Newell, illustrated 

by a large map showing the relative extent and location of the vacant public lands; also a revort on the water resources of a portion of the Great Plains, by Robert Hay. 

A ~eological reconnoissance of northwestern Wyoming, by George H. Eldridge, 

1894; octavo, 72 pp. Bulletin No. 119 of the United States Geological Survey; 

price, 10 cents. 

Contains 'a description of the geologic structure of portions of the Bighorn Range and 

Bighorn Basin, especially with reference to the coal fields, and remarks upon the water supply and agricultural possibilities. 

Report of progress of the division of hydrography for the calendar years 1893 and 

1804, by F. H. Newell, 1895; octavo, 176 pp. Bulletin No. 131 of the United 

States Geological Survey; price, 15 cents. 

Contains results of stream measurements at various points, mainly within the ariel regionJ and records of wells in a number of counties in western Nebraska, western Kansas, ana eastern Colorado. 

1S96. 

Seventeenth Annual Report of the United States Geological Survey, 1895-ll6,Part 

II, Economic geology and hydrography, 1896; octavo, 864 pp. 

Contains papers on '"l.'he underground water of the Arkansas Valley in eastern Colo· 

rado," by G. K. Gilbert; "The water resources of Illinois," by Frank Leverett; and "Pr~· 

liminary revort on the artesian areas of a portion of the Dakotas," by N.H. Darton. 

Artesian-well prospects in the Atlantic Coastal Plain region, by N. H. Darton, 

1896; octavo, 230 pp., 19 plates. Bulletin No. 138 of the United States Geological Survey; price, 20 cents. 

Gives a description of the geologic conditions of the coastal region from Long Island, 

N.Y., to Georgia,-and contains data relating to m:>uy of the deep wells. 

Report of progress of the division of hydrography for the calendar year 1895, by 

F. H. Newell, hydrographer in charge, 1896; octavo, 356 pp. Bulletin No.140 

of the United States Geological Survey; price, 25 cents. 

Contains a description of the instruments and methods employed in measuring streams and the results of hydrographic investigations in various parts of the United States. 

lS97. 

Eighteenth Annual Report of the United States Geological Survey, 1896-97, Part 

IV, Hydrography, 1897; octavo, 75(i pp. 

Contains a" Report of progress of stream measurements for the year 1896," by Arthur 

P. Davis; '"rhe water resources of Indiana and Ohio," by Frank Leverett; "New devel· 

opments in well boring and irrigation in South Dakota," by N.H. Darton; and" Reservoirs 

for irrigation," by J.D. Schuyler. 

lS99. 

Nineteenth Annual Report of the United States Geological Survey, 1897-98, Part 

IV, Hydrography, 1899; octavo, 814 pp. 

Contains a" Report of progress of stream riteasuremonts for the calendar year 1897," by F. H. Newell and others;" The rock waters of Ohio," by Edward Orton; and "Preliminary 

report on the geol:lfb and water resources of Nebraska west of the one hundred and third 

meridian," by N. • arton. 1900, 

Twentieth Annual Report of the United States Geological Survey, 1898-99, Part 

IV, Hydrography, 1900; octavo, 660 pp. 

Contains a "Report of progress of stream measurements for the calendar year 1898," by F. H. Newell, and "Hydrography of Nicaragua," by A. P. Davis. 

WATER·SUPPLY AND IRRIGATION PAPERS, 1896-1899. 

This series of papers is designed to present in pamphlet form the results of stream meas- urements and of special investigations. A list of these, with other information, is given on the outside (or fourth) page of this cover. • 

Survey bulletins can be obtained only by prepayment of cost, as noted above. 

Postage stamps, checks, and drafts can not be accepted. Money should be transmitted by postal money order or express order, made payable to the Director of 

the United States Geological Survey. Correspondence relating to the publications 

of the Survey should be addressed to The Director, United States Geological 

Survey, Washington, D. C. 

IRR 42 
WATER-SUPPLY AND IRRIG.A.TION PAPERS. 

1. Pumping water for irrigation, by Herbert l\L Wilson, 1896. 

2. Irrigation near Phoenix, Arizona, by Arthur P. Davis, 1897. 

3. Sewage irrigation, by George W. Rafter, 1897. 

4. A reconnaissance in southeastern Washington, by Israel C. Russell, 1897. 

5. Irrigation practice on the Great Plains. by E. B. Cowgill, 1897. 

6. Underground waters of southwestern Kansas, by Erasmus Haworth, 18!l7. 

7. Seepage waters of northern Utah, by Samuel Fortier, 1897. 

8. Windmills for irrigation, by E. C. Murphy, 1897. 

9. Irrigation near Greeley, Colorado, by David Boyd, 1807. 

10. Irrigation in Mesilla Valley, New Mexko, by F. C. Barker, 1808. 

11. River heights for 18!l6, by Arthur P. Davis, 18!l7. 

12. Water resources of southeastern Nebraska, by Nelson IIoratio Darton, 1808. 

13. Irrigation systems in Texas, by William Ferguson Hutson, 18!18. 

14. New tests of pumps and wate1· lifts used in irrigation, by 0. P. Hood, 18!)8. 

15. Operations at river stations, 1897, Part I, Hl9S. 

16. Operations at river stations, 1897, Part II, 1898. 

17. Irrigation.near Bakersfield, California, by C. E. Grunsky, 1898. 

113. Irrigation near Fresno, California, by C. E Grunsky, 1898. 

19. Irrigation near Merced, California, by C. E. Grunsky, 1809. 

20. Experiments with windmills, by Tb.omas 0. Perry, 1899. 

21. Wells of northern Indiana, by Frank J_,everett, 1890. 

22. Sewage irrigation, Part II, by George W. Rafter, 18!1!), 

23. Water-right problems of the Big'1orn Mountains, by Elwood l\f ead, 1899. 

24. Water resources of the State of New York, Part I, by George W. Rafter, 1899. 

25. Waterresourcesofthet;tateof New York, Part II, l•y GeorgeW.Rafter, 18!J!l. 

26. Wells of southern Indiana (continuation of No. 21), by Frank Leverett, 189!). 

27. Operations at river stations, 1898, Part I, 1809. 

28. Operations at river stations, 1898, Part 1!, 1899. 

29. Wells and windmills in Nebraska, by Erwin Hinckley Barbour. 1899. 

30. Water resources of the Lower Peni mmla of Michigan, by Alfred C. Lane, 1899. 

31. Lower Michigan mineral waters, by Alfred C. Lane, 18!1!). 

32. Water rPsources of Puerto Rico, by H. M. Wilson, 1000. 

33. Storage of water on Gila H.iver, Arizona, by J. B. Lippincott, 1!)00. 

34. Underground waters of a portion of southeastern S.Dak., by ,J E. Todd, 1900. 

35. Operations at river stations, 18H!l, Part I, HJOO. 

36. Operations at river stations, 1899, Part II, 1000. 

37. Operations at river stations, 1809, Part III, 1900. 

38. Operations at river stations, 1899, Part IV, 1900. 

39. Operations at river stations, 1899, Part V, 1900. 

40. The Austin clam, by Thomas U. Taylor, 1900. 

41. The windmill: its efficiency ancl economic use, Part I, by E. C. Murphy, 1901. 

42. The windmill: its efficiency and economic use, Part II, by E. C. Murphy, 1901. 

In addition to the above, there are in various stages of preparation other papers relating to the measurement of streams, the storage of water, the amount available 

from underground sources, the efficiency of windmills, the cost of pumping, and 

other det'lils relating to the methods of utilizing the water resources of the coun- try. Provision has been made for printing these by the following clause in the 

sundry civil act making appropriations for the year 1896-97: 

Provided, That hereafter the reports of the Geological Survey in relation to the 

gaging of streams and to the methods of utilizing the water resources may be 

printed in octavo form, not to exceed 100 pages in length and 5,000 copies in nnm- ber; 1,000 copies of which shall be for the official use of the Geological Survey, 

1,500 copies shall be delivered to the Senate, and 2,500 copies !!hall be delivered to 

the House of Representatives, for distribution. (Approved, .T nne 11, 1896; Stat. L., 

vol. 29, p. 453.) 

The endeavor is made to send these pamphlets to persons who have rendered 

assistance in their preparation through replies to schedules or who have furnished 

data. Requests made for a certain paper and stating a reason for asking for it are granted whenever practicable, but it is impossible to comply with general 

demands, such as to have all of the series sent. 

Application for these papers should be made either to members of Congress or to 

IRR 42 

THE DIRECTOR, UNITED STATES GEOLOGICAL SURVEY, WASHINGTON, D. 0.