UNITED STATES GEOLOGICAL SUEVEY

CHARLES D. WALCOTT, DIRECTOR

EXPERIMENTS WITH WINDMILLS

'BY

THOMAS O. PERRY

WASHINGTON

GOVERNMENT PRINTING OFFICE 

1809
CONTENTS.

' Page.

Letter of transmittal.......................................................... 9

Introduction by F. H. Newell.................................................. 11

General statement ............................................................ 19

Apparatus................................................................ 21

Angle of weather ......................................................... 22

Artificial wind............ ................................................ 22

Dynamometer................................. .......................... 23

Method of experiment..................................................... 24

Starting forces............................................................ 25

Journal friction........................................................... 25

Comparative standard wheel .......... ............ ........................ 27

Results of original tests....................................................... 28

Tables and descriptions of wind wheels. ................*......--.. ......... 28

Wheel No. 1................................. .......................... 28

Wheel No. 2........................................................... 29

Wheel No. 3.............. ............................................ 31

Wheel No. 4............ .............................................. 33

Wheel No. 5................... ........................................ 34

Wheel No. 6...............:............. .............................. 34

Wheel No. 7........... ................................................ 36

Wheel No. 8..................... ...... ............................... 37

Wheel No. 9............. ............................................. 37

Wheel No. 10.... ................................................ .... 38

Wheel No. 11.......... ................................................ 38

Wheel No. 12.......................................................... 39

Wheel No. 13.......................................................... 39

Wheel No. 14.................................................... ...... 40

Wheel No. 15.......................................................... 40

Wheel No. 16..................................:................... .... 41

Comparative results with plain sails............. ...................... 41

Wheel No. 17.......................................................... 43

Wheel No. 18........................ ................................. 43

Wheel No. 19........................ .................................. 44

Wheel No. 23...... .................................................... 46

Comparison of several wheels..........................................;.. 46

Wheels Nos. 2 and 50.................................................. 46

Wheels Nos. 18,19,20, 21, and 22........................................ 47

Wheels Nos. 24,25,26,27, and 28........................................ 47

Wheels Nos. 29,30,31,32, and 33 ....................................... 49

Wheels Nos. 19, 20, and 34.............................................. 51

Wheels Nos. 35,36,37, and 38........................................... 51

Wheels Nos. 40,41,42, and 43........................................... 53

Wheels Nos. 40,41, and 42.............................................. 55

Wheels Nos. 35,39,40, and 44......... .............. ................... 57

5
6 CONTENTS.

Results of original tests Continued. Page. 

Comparison of several wheels Continued.

Wheels Nos. 45,46,47,48, and 49........................................ 59

Wheels Nos. 2,60, and 61........ *...................................... 61

Wheels Nos. 2, 49, 53,54, 55, 56, and 57................. .................. 64

Wheels Nos. 2,49, 51, 52, 58, and 59...................................... 65

Sails at best angles of weather ...... ...... .......... ...... ................ 65

Relations of three different velocities of wind............................. 66

Automatic brake adjuster................................................. 67

Theory of the action of the wind upon the sails of windmills.............. 69

Discussion of results .................... ...................................... 72

Thermometnc and barometric influences .............................. 72

Construction of tables ................................................ 73

Extreme results....................................................... 73

Influence of outside wind.............................................. 74

Standard of comparison............................................... 74

Corrections for axle friction........................................... 75

Aerial friction ........................................................ 76

Relation between spee'd and load ...................................... 76

Best speeds for wind wheels........................................... 78

Best loads for wind wheels............................................ 78

Conical deflector in center of wheels .................................. 79

Air-cushioned sail surfaces.................. .......................... 79

Obstructions en the back of sails............................ .......... 79

Waste of power due to the arms of wind wheels....................... 80

Twisted sails ......................................................... 81

Deflectors in front of sails ............................................ 81

Obstructions in front and in the rear of wind wheels .................. 82

Maximum products in different velocities of wind ..................... 82

Starting forces and loads at the maximum in different velocities of wind. 83

Speeds of unloaded wheels in different velocities of wind.............. 83

Action of air on the sails of a wind wheel ............................. 84

Theoretical efficiency of the wind wheel..................... .......... 84

Theoretical useful effort of wind.................................. .... 87

Aerial resistance to motion....... ...... .... ................ ...... ..... 89

Best number of sails.................................................. 90

Best relative areas of sail surface ..................................... 90

Actual efficiency of the wind wheel.................................... 91

Work of variable wind with variable load............................. 92

Regulation of wind wheels ................................ ........... 92

Limitation to size of wind wheels on account of weight................ 93

Efficiency of wind wheels as affected by diameter ..................... 94

Height of towers ..................................................... 94

Multiplication of wind power............................. ........... 95

Power of a 12-foot wind wheel ........................................ 95

Value of mathematical formula} in experimental investigations ........ 96

Index ........................................................................ 97
ILLUSTRATIONS.

PLATE I. Windmill pumping water for irrigation............................. 11

II. Reservoir and garden............................................... 12

III. Windmill and small reservoir....................................... 14

IV. Small irrigation reservoir........................................... 14

V. A, Homemade wind engine, as used on the Great Plains; B, The

Defender windmill and water elevator ............................ 16

VI. Elevation of apparatus used in wheel tests.......................... 20

VII. Plan of apparatus used in wheel tests................... ............ 20

VIII. Plan and elevation of dynamometer........................... ...... 22

IX. End views of dynamometer........................................ 24

X. Windmill and reservoir................................. ............ 78

XI. Windmill and reservoir ................ ................ ...... ...... 88

XII. Windmill on low tower on the Great Plains.......................... 94

FIG. 1. Vertical section through reservoir and outlet......................... 12

2. Windmills and circular reservoir..................................... 13

3. Steel windmill and tower carrying tank......................... .... 14

4. Irrigating ditch leading from earth reservoir filled by windmills...... 16

5. Distribution of water to small beds .................................. 17

6. Distribution system adapted to irregular land........................ 17

7. Elevation and section of wheel No. 2................................. 30

8. Outline of area not available......................................... 31

9. Elevation and section of wheel No. 3................................. 32

10. Dimensions of sails of wheel No. 3.................................... 83

11. Angles of weather of sails of wheel No. 3: A, Angle at inner ends of

sails; B, Angle at outer ends of sails............................... 33

12. Elevation and section of wheel No. 6................................. 35

13. Dimensions of sails of wheel No. 6...............'..................... 36

14. Dimensions of sails of wheel No. 18............. ...................... 44

15. Elevation and section of wheel No. 19................................ 45

16. Elevation and section of wheel No. 24...................... ......... 48

17. Elevation and section of wheel No. 29................................. 50

18. Elevation and section of wheel No. 35................................ 52

19. Dimensions of sails of wheels Nos. 35, 36, 37, and 38................... 53

20. Elevation and section of wheel No. 40................................ 54

21. Dimensions of concave sails of wheels Nos. 40, 41, 42, and 43.......... 55

22. Elevation and section of wheel No. 39................................ 56

v 23. Dimensions of sails of wheel No. 39................................... 57

24. Elevation and section of wheel No. 44................................ 58

25. Elevation and section of wheel No. 48................................ 60

26. Dimensions of sails of wheels Nos. 45, 46, 47, 48, and 49 ................ 61

7
8 ILLUSTRATIONS.

	PageFIG. 27. Elevation and section of wheel No. 60 ................................ 62

28. Elevation and section of wheel No. 61.... ............................. 63

29. Dimensions of sails of wheel No. 61 with obstruction on back........... 64

30. Action of wind on a sail................. ............................. 70

31. Action of air on the sails of a wind wheel............................. 84

32-35. Theoretical efficiency of the windmill...... ........................... 85

36-39. Theoretical useful effort of wind.................................... 87-88
LETTER OF TRANSMITTAL.

DEPARTMENT OF THE INTERIOR, 

UNITED STATES GEOLOGICAL SURVEY, 

DIVISION OF HYDROGRAPHY,

Washington, July 15, 1898.

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

Experiments with Windmills, prepared by Mr. Thomas O. Perry. 

These experiments, as described by Mr. Perry, were carried on during 

the years 1882 and 1883 for the United States Wind Engine and Pump 

Company, of Batavia, Illinois. As a result of these experiments radical changes and improvements were made in the windmills. As a 

matter of business policy the company did not desire that the results 

of these tests should be made known for some years. After the expiratibn of a certain time, however, the data have been placed at the 

disposal of the public through the kindness of the officers of the company and the efforts of Mr. Perry. Although as the result of this work 

great changes have been made in windmills, many of the suggestions 

made have not yet been put into practice and may serve as a foundation 

for further work along this line. The importance of the windmill as a 

means of utilizing the water resources of a part of the country is so 

great that all available information on the subject should be diffused 

and brought to the attention of persons who can make use of the facts. 

I respectfully request, therefore, that this manuscript, with a brief introduction, be printed as one of the series of pamphlets on water supply 

and irrigation.

Very respectfully,

F. H. NEWELL, 

Hydrographcr in Charge. 

Hon. CHARLES D. WALCOTT,

Director United States Geological Survey.

9

U_ S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 20 PL. I

WINDMILL PUMPING WATER FOR IRRIGATION.

INTRODUCTION.

By F. H. NEWELL.

During the progress of investigation of the extent to which the arid 

lands can be reclaimed by irrigation and of the related question of the 

occurrence of water underground attention has been continually drawn 

to the practical methods of bringing the underground water to the 

surface. Throughout a great part of the arid and semiarid region there 

are localities where water can be obtained at a short distance from the 

surface. The amount, although not large in the aggregate when compared with the quantity in some notable stream or lake, is yet inexhaustible by the ordinary methods of pumping. If, therefore, this 

water which exists from 10 to 50 feet beneath the surface could be 

cheaply raised, it would be practicable to utilize for agriculture tracts 

which otherwise have little or no value.

The irrigation of 20 acres in the midst of a section or township of 

land is, figuratively speaking, a mere drop in the bucket; but the 

reclamation of this small area generally means the utilization of adjoining lands. If, for example, 20 acres of some forage crop like alfalfa is 

made possible, this will result in obtaining a considerable amount of 

winter feed used in the sustenance of a herd which can be pastured 

upon the surrounding dry land. The successful cultivation of this 

20 acres may thus directly or indirectly support a family, and, with 

increased experience and adaptation to the surrounding conditions, 

the family may in turn give place to a rural community. Given the 

existence of sufficient water underground to irrigate the 20 acres, 

the first question is that of ways and means of bringing the water to 

the surface. -

The force which is ever present, making itself persistently felt 

throughout the Great Plains region, is the wind, which blows almost 

continuously. It carries the dust before it, cuts out the traveled roads, 

carries away the fine earth of the tilled fields, and builds up a fine 

loess, almost everywhere to be found. The wind, which has so long 

been considered as an annoyance and mischief-maker, has sufficient 

strength to perform the work of bringing water to the surface, if only 

suitable means of directing its energy can be discovered.

The windmill is the best-known method of converting wind energy 

into work. In one form or another it has been used from times an tell
12 INTRODUCTION.

I

dating the dark ages. In the twelfth century windmills, built either 

by individuals or by communities, were common. Some of these mills 

were of enormous size. In the German type the whole 

building on which the mill was placed was constructed 

in such a manner as to turn on a post in order to bring 

the sails into the wind. In the Dutch form the building was fixed, but the head of the mill could be turned 

into the wind. The most notable use of these early 

mills was in Holland, where the land was drained by 

pumping water from behind the dikes into the sea. In 

1391 the bishop of Utrecht, holding that the wind of 

the whole province belonged exclusively to him, gave 

to the convent at Windsheim express permission to 

build a windmill wherever it was thought proper. In 

so doing he overruled a neighboring lord who declared 

that the wind in the district belonged to him. Three 

years later the city of Haarlem obtained leave from 

Albert, Count Palatine of the Ehine, to build a windmill, using the wind of the country. 1

The huge, clumsy windmills of European make, one 

of which was erected at Lawrence, Kansas, within the 

memory of the present inhabitants, have within a few 

decades given place in this country to the light, 

rapidly running forms. Thousands of these have been 

made by various firms throughout the country. At 

first wood was used almost exclusively, but this is 

being rapidly displaced by metal, especially by thin 

steel plates and forgings. Although millions of 

dollars have been invested in the manufacture and 

purchase of mills and much attention has been given 

to the mechanical details and the saving in weight and 

cost, yet comparatively little study has been bestowed 

upon the actual efficiency of the various forms and 

upon their development toward theoretical ideals.

A view of gardens cultivated by water pumped by 

windmills is shown in the accompanying plate (PI. II). 

This picture has been taken from a windmill platform. 

In the foreground is a small reservoir, divided by a 

bank in the middle, so that one part may be used independently of the other. The part nearer the observer 

is the older; the second part is a recent addition, rendered necessary by the increase of the area cultivated. 

Without windmills the cultivation of the tract of country shown in this picture would be impossible. It is doubtful if a single 

cow could find subsistence on the area which now supports a family.

1 The Windmill as a Prime Mover, by Alfred R. Wolff, p. 51.
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 20 PL. II

RESERVOIR AND GARDEN,

INTEODUCTION. 13

Another small reservoir and windmill is shown on PL III. This 

reservoir is in the corner of a small suburban track farm, to which it 

furnishes water both for vegetables and trees. The owner has stocked 

a small pond with fisli and from it obtains an ample supply for his 

own use. On the right-hand side is shown the outlet gate, through 

which water is discharged into a ditch, and that in turn empties into 

furrows running near the fruit trees and traversing the cultivated 

ground.

In fig. 1 is given a section through one of these small reservoirs, 

showing at the bottom the puddled earth or clay that prevents the 

water from seeping into the adjacent ground. On this puddled earth 

the banks are built at a height of from 4 to 10 feet. These are usually 

built by plowing and scraping up the earth from the outside, the trampFIG. 2. Windmills and circular reservoir.

ing of the horses and the men serving to consolidate it. When the 

bank has been built to the proper height it is smoothed and sodded. 

On the right-hand side of the figure is the pipe or wooden flume from 

the windmill, and on the left-hand side is shown the outlet box, which 

is usually built of 2 inch plank. This is closed by some simple form of 

wooden gate or valve, either lifted by means of a screw or hinged so as 

to open outward, and is held in place by the pressure of the water 

against it.

The square reservoir is the form usually adopted. The mills, as in 

the other cases, are placed on each side, pumping through short wooden 

flumes over the bank. These reservoirs are not only used for holding 

water for irrigation, but, as before stated, with a little care serve as 

ponds for raising fish.

A view of one of these small square reservoirs is shown on the accom-
14 INTRODUCTION.

panying plate (PL IV). The banks are obscured by the luxuriant 

growth of weeds. The surface of the water is a little higher than the 

general level of the land, so that a supply can be drawn by gravity 

directly to the adjacent fields.

Fig. 2 gives a nearer view of one of these earth reservoirs, which in 

this case has been built nearly circular in form. The two windmills

which , supply the 

water are placed 

upon opposite sides, 

in order that the 

pumps may be as 

far apart as possible. 

In many instances 

threG or even four 

mills, each of moderate size, are placed 

around a reservoir 

of considerable size. 

The banks, made of 

earth, are covered 

with sod to protect 

them from washing 

by the rain and by 

the waves during 

times of high winds. 

Fig. 3 represents 

an adaptation of a 

windmill for use in 

domestic water supply or for furnishing 

water to a village 

or small town under 

considerable pressure. The wind engine is erected on the 

top of a high steel 

tower, which also 

supports a wooden 

tank with suitable 

cover to protect the 

water from loss by evaporation. This device is generally employed by 

railroad companies at stations on the Great Plains, where the wind may 

be depended upon to force a sufficient supply into the tank for use by 

locomotives or for the railroad shops and offices. Many towns also 

depend for their water supply upon a windmill pumping water into an 

elevated tank, particularly where the general surface is so nearly level

FIG. 3. Steel windmill and tower carrying tank.
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 20 PL in

WINDMILL AND SMALL RESERVOIR.

U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 20 PL. IV

SMALL IRRIGATION RESERVOIR,

INTRODUCTION. % 15

that it is impossible to construct a small earth reservoir within reasonable distance of the principal buildings.

The device shown in PI. V, JL, which has been employed to a considerable extent in the Great Plains region, is usually constructed by the 

owners. The merit of the device is its cheapness. It may be built 

mainly of old lumber and other material that can often be found about 

the farm, such as axles or other gear from old farm machinery, bale 

wire for staying the sails, and pieces of wood or* metal which may 

be classed as old junk. The machine can not be recommended on the 

ground of efficiency or economy. If a farmer has sufficient capital to 

purchase and erect a good windmill he will undoubtedly succeed better 

than by spending his time in making the cheaper device. On the other 

hand, in situations where, as is often the case in a dry region, the 

farmer has lost crops year after year, has exhausted his resources, and 

is on the verge of bankruptcy, a contrivance of this kind may serve to 

save a small crop and give him a new start. In such instances there 

usually will be found pieces of broken-down machinery about the farm. 

Time and labor are commonly of little value where the ordinary farming operations have been unsuccessful, so that by the exercise of a 

little ingenuity the material and energy that otherwise would be wasted 

may be turned to advantage.

The mill or engine consists of a shaft of wood or iron placed horizontally and supported at each end. *Upon this sails are fastened by arms 

extending out at right angles. On each end of the shaft is attached a 

crank, and each of these cranks in turn drives some simple form of 

homemade pump. The lower half of the mill is boxed in, and thus 

forms a small building without roof, above which project the arms carrying the sails.

As illustrating another homemade device, PI. V, B, has been introduced. This mill and water elevator, invented by the owner, has been 

successfully used to furnish water for irrigation, and, although not by 

any means an economical device, nor one that can be recommended, it 

has served its purpose. In other words, while as a rule it is economical 

to purchase the best, there are circumstances and times wheja for 

special reasons the best mill can not be had, but it is still practicable 

to construct a machine which will accomplish the desired end, that of 

getting water from the ground upon the land.

These examples might be almost indefinitely multiplied, but are sufficient to demonstrate the principle that with energy and ingenuity a 

start toward irrigation can be made. When, however, some experience has been had in irrigation and newer mills are being procured, it 

is highly essential for continued success that something better than 

the ordinary form of mill be obtained. Many of these have been 

designed for some other purpose than that of raising large quantities 

of water through a short distance for irrigation. Some, for example, 

have been built with the idea of pumping a small quantity from great
- 16 INTRODUCTION.

depth for watering stock. Such mills, as a rule, do not fill the requirements of the irrigator. Thousands of windmills are in use and thousands more will be purchased, involving expenditures on the part of 

farmers aggregating millions of dollars. A saving of even a small 

percentage in cost and economy is therefore a matter of considerable 

importance in the continued development of the water resources of the 

country.

Fig. 4 shows two windmills so arranged as to pump into a reservoir 

built of earth, placed upon the highest part of a farm. Running night 

and day the pumps supply such a quantity of water to the reservoir 

that when needed a considerable volume can be drawn at once, filling

FIG. 4. Irrigating ditch leading from earth reservoir filled by -windmills.

a ditch of as large size as is ordinarily built for irrigating a field of 

from 10 to 20 acres.

Fig. 5 illustrates one of the methods used to distribute small quantities of water, such as may be had from the tank or reservoir of a windmill. In the drawing the banks are represented as made of cement or 

of wooden planks, such as are used in portions of California, where 

water has especial value. The usual practice, however, within the 

Great Plains region is to make the ditches of earth and to place the 

little gates in wooden frames. Sometimes instead of using gates 

the irrigator controls the water bj shoveling earth into the ditches and 

furrows, backing up the water until it overflows the bank or comes out 

through on opening made by means of the shovel. As shown in the 

figure, the water flowing in the main stream from right to left is 

checked by small gates and forced to flow laterally through furrows.
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 20 PL. V

A. HOMEMADE WIND ENGINE, AS USED ON THE GREAT PLAINS.

B DEFENDER WINDMILL AND WATER ELEVATOR

INTRODUCTION. 17

and is again checked in these and forced out upon the beds lying on 

each side of the furrow. When a certain portion is wet the small 

gates are adjusted so as to force the water over other portions.

FIG. 5. Distribution of water to small beds.

Where land has a decided fall or is rolling and it is too expensive to 

terrace, a system of distributing the water must be devised suited to the 

contour of the ground. In the case shown by the accompanying figure 

(fig. 6) the water ejiters the distributing ditches at the upper left-hand

FIG. 6. Distribution system adapted to irregular land. 

/

corner and, dividing, flows through these and again into still smaller 

ditches, from which it is turned laterally into furrows. The flow is 

checked from point to point by little dams or temporary obstructions of 

IRR 20 2
18 INTRODUCTION.

earth. After the water passes out upon a Held any surplus is caught 

by a small trench shown in the figure as trending diagonally toward 

the right-hand lower corner, and from this in turn the water can be 

caused to flow out upon the lower fields, so that the excess or seepage 

from the higher portions is not wasted but is employed in the irrigation of the lower parts of the farm.

There are many other devices by which water pumped by windmills 

may be stored and distributed, but those briefly described above are 

among the most common. It is sufficient at this time to make mention 

of these in order to bring out the fact that experiment has demonstrated 

that it is practicable to irrigate land by water pumped by windmills. 

Many farmers in various parts of the United States are dependent for 

their living on this system of agriculture, and others are seeking to 

gain knowledge by which they may better their condition by providing 

a water supply for use in times of drought. This is true not only of the 

West, but of the East and the South, especially in regions where the 

soil, though fertile, is light and becomes dry if the rains do not occur 

with great regularity. Even on the Atlantic seaboard the early truck 

farmers are experimenting with devices of this character, copying 

methods which have already proved successful in Kansas. Modifications in mills and other machinery are doubtless necessary to suit local 

conditions. For a given purpose one mill may be far better than 

another, and of two wind engines similar in cost one may be actually 

worth two or three times as much as the other.

The dynamometric experiments carried on by Mr. Perry, as described 

in the following pages, have brought out many important points upon 

which depend the relative efficiency of various mills and the advantages 

of one type over another. Some of these points have already been considered and made use of in mills now on the- market, while others of 

equal or greater importance are awaiting practical application and 

ingenuity. It is hoped that by the publication of these facts interest 

will be aroused and inventors will be stimulated to continue work along 

various lines, leading to further improvement and to a consequent 

cheapening of the cost of "raising water by wind power.
EXPERIMENTS WITH WINDMILLS.

By THOMAS O. PERRY.

GENERAL STATEMENT.

The experiments with wind wheels described in the following pages 

were commenced June 1,1882, and concluded September 15, 1883. At 

that time wind wheels in this country were nearly all made with narrow 

wooden slats for sails, set at various angles with the plane of the wheel, 

ranging from 35 to 45 degrees.

The slats were usually placed as close together as possible without 

having their projections on the plane of the wheel overlap. The proportions of sail surface and their angles of weather were apparently 

arrived at without any well-defined purpose. The only experiments 

made in the United States, so far as could be learned, related to starting forces only. They did not include the measurement of work in footpounds. The only well-defined experiments with wind wheels, the 

records of which were available, were those made in England by John 

Smeaton, F. B. S., about one hundred and twenty-five years before. 

Smeaton's paper, On the Construction and Effects of Windmill Sails, 

was read before the Eoyal Society May 31 and June 14,1759, and to 

this day has remained the only definite available source of information 

on the subject treated. The paper was republished in Tredgold's Tracts 

on Hydraulics, a copy of which was received before these experiments 

were commenced.

It had been especially noted that Smeaton's angles of weather were 

much less than'those in common use in this country, and note had 

also bee,n taken of his statement to the effect that the work of a wind 

wheel is not increased, but diminished, by crowding it with sails so 

that their total surface exceeds about seven-eighths of the circular 

area containing them. The universal practice here was to crowd the 

wheel with slats until the total sail surface exceeded the total area of 

the annular zone containing them by more than one-fifth of the whole 

zone; according to Smeaton, this was adding to the greatest possible 

effective sail area more than 39 per cent additional area of worse than 

useless surface. If a large part of the material could be saved, and at 

the same time a considerable increase in power be effected, no slight

19
20 EXPERIMENTS WITH WINE MILLS. IHO.SO.

gain would be secured. Smeaton's experiments were made so long ago 

that they were disregarded, if they were ever noticed, by the builders 

of modern wind wheels. Our experiments fully confirmed Smeaton's 

results in regard to the greatest effective amount of sail area, although 

we do not necessarily accept Smeaton's judgment that it is not profitable to increase the total area of sails beyond about 37 per cent of the 

annular zone containing them.

In wheel No. 3 we followed closely Smeaton's angles of weather, but 

did not obtain so good results as with greater angles. In fact, we were 

not able to obtain the best results with weather angles so small as 

Smeaton's in any of our wind wheels. Nor did our sail speeds, as 

compared with wind velocity, nearly approach the speeds obtained 

by Smeaton. Even our unloaded wheels did not show the sail speed 

attained by the best of Smeaton's wheels when loaded for maximum 

work.

This difference in the ratio of sail speed to wind velocity constituted 

the greatest disagreement between his results and ours. Our loads at 

the maximum of work were smaller as compared with greatest loads, 

and the speeds of revolution at maximum work as compared with 

speeds of unloaded wheels were smaller for our wheels than for Smeaton's. The general laws established by Smeaton, as enunciated in his 

eight "maxims," were substantially confirmed by our experiments. 

The law of cubes pertaining to maximum products and the law of 

squares pertaining to greatest loads, or starting forces, were more 

exactly fulfilled in our experiments than in Smeaton's. The differences in results as regards angles of weather, speeds, and best toads 

might have been due to differences in the construction of the wheels.

Smeaton constructed his wheels after the manner of windmill construction in his time, and we constructed our wheels mostly after the 

methods adopted by American manufacturers at the time we experimented. Our methods of experiment were similar, though Smeaton's 

experiments were conducted on a much smaller scale with smaller 

wheels, and his appliances generally were crude as compared with 

our own.

Smeaton allowed about one-eighth of his total applied load as the 

equivalent additional load due to friction. This friction, as Srneaton 

determined it, was in reality friction at starting only, and it must have 

been much in excess of the friction under the rapid revolutions of his 

wheels, and helped considerably to swell his products.

Still another allowance must be made in comparing Smeaton's efficiencies with ours, on account of the relative shortness of the sweep, 

which carried his wheels in a circle against still air. The velocity of 

the centers of his wheels was taken as the equivalent velocity of wind. 

, As a matter of fact, some point beyond the center of the wind wheel, 

farther away from the axis of the sweep, should have been taken to 

represent wind velocity. The distance from the axis of Smeaton's
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 20 PL. VI

ELEVATION OF APPARATUS USED IN WHEEL TESTS.

U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 20 PL. VII

PLAN OF APPARATUS USED IN WHEEL TESTS,

PERRY.] APPARATUS. 21

sweep to the extremity of his sail as it revolved was, when greatest, 

nearly.double its least distance, and the energy of the wind acting on 

the tip of his sail was more than seven times as great at the maximum 

as at the minimum distance. To compute accurately the total wind 

energy intercepted by the wheel, after taking into account the various 

velocities of impingement, would be an interesting problem in integral 

calculus.

The differential expression for work is easily found, but the integration is not so simple. An approximate calculation shows that the wind 

energy intercepted by Smeatoii's wheel was more than 7 per cent in 

excess of what it would have been had all points of the wheel met the 

air with the same velocity as at the center. The difference is not so 

large as one would expect from1 the great difference in energy at extreme 

positions. We doubt whether anything should be deducted from 

Smeaton's products on this account, for only a very limited portion of 

the sails could have a proper relative velocity with respect to the wind. 

Our wheels were, of course, similarly affected, although in considerably less degree.

Weisbach's theoretical formulae for wind action, if correct, would 

cast a cloud over Smeaton's results; for he concludes his rather elaborate mathematical discussion with these words: "According to these 

experiments [Smeaton's] the action of the wind in general upon sail 

wheels is greater than is given either by the theory or by Coulomb's 

experiments." Coulomb's very incomplete experiments seem to have 

been a great source of consolation to those mathematicians whose 

theories would not permit the realization of efficiencies so great as 

Smeaton obtained.

Our own experience with wind wheels in actual use, in widely different lines of work, and the testimony of many persons using them, 

convince us that the efficiencies we obtained and which Smeaton 

obtained in artificial wind are not so great as those commonly obtained 

now in natural wind. We consider our experiments valuable principally on aecount of the comparisons made and th6 insight they afford 

into the causes of waste. Through the courtesy of Mr. H. .¥. Wade, 

manager of the United States Wind Engine and Pump Company, of 

Batavia, Illinois, we are enabled to reproduce the original records of 

our experiments on wind wheels as they were made in 1883.

APPARATUS.

Our experiments were conducted in a room about 36 feet wide, 48 

feet long, and 19 feet high from floor to roof trusses.

Pis. VI and VII represent, in elevation and plan, as a whole, the 

apparatus that was used and show portions of the roof trusses underneath which the sweep was suspended. The rear end of the sweep, 

not shown, carried a counter weight, which caused the whole apparatus 

to balance on the central shaft. Two rollers carried by the sweep on
22 EXPERIMENTS WITH WINDMILLS. [NO.20.

opposite sides of the suspending shaft ran lightly over a large circular 

track and prevented vertical oscillations. Pis. VIII and IX present 

enlarged views, showing the details of the dynamometer and its method 

of application.

These four plates and the illustrations of wind wheels Nos. 3, 6,19, 

24, 29, 39, 40, 44, 60, and 61 were recently prepared from data in our 

possession. The illustrations of wheels Nos. 2, 35, and 48 are reproductions of the drawings made for the original records, as are also all 

the other illustrative figures which are shown in connection with the 

original records. In computing the figures denoting efficiencies, shown 

in connection with the illustrations of wheels Nos. 3 and 6, axle friction 

was called 0.15 pound instead of the 0.3 pound given in the tables, as 

explained under the heading " Corrections for axle friction."

In these two cases, and also in computing the efficiency of wheel No. 

2, allowance was made for temperature as recorded and for atmospheric density, according to the records of the United States Signal 

Service station at Chicago for 2 p. m. on the days of experiments.

The efficiencies shown in connection with all the other illustrations 

of wind wheels were obtained by simply multiplying the efficiency for 

No. 2 by the ratios of products given in the various tables where direct 

comparison with No. 2 is shown.

The original records of 1883, immediately following, end on page 72. 

The comments following page 72, including the tables on pages 74 and 

77, have recently been prepared.

ANGLE OF WEATHER.

The term "angle of weather," used in connection with the following 

tables, means the angle made by the face of the sail with the plane of 

the wheel.

ARTIFICIAL WIND.

In conducting these experiments with windmills, it was necessary 

that results to be Compared should be obtained in wind' of uniform 

velocity. We therefore made use of artificial wind, obtained by carrying the wind wheels in a circle against still air on the end of a long 

sweep suspended beneath the roof trusses of a large room used for 

setting up tanks. The sweep was made to revolve horizontally around 

its vertical axis by means of gearing, pulleys, and belts connected with 

a line shaft driven by an 80-horsepower Keynolds-Corliss steam engine, 

which furnished the motive power for the works of the United States 

Wind Engine and Pump Company. The distance from axis of sweep 

to center of wind wheel was 14 feet, so that the velocity of wind against 

the wind wheel in miles per hour would be indicated very closely by 

the number of revolutions per-minute made by the sweep. To attain 

absolute accuracy the length of sweep should have been 14.006 feet. 

Hence it was only necessary to note the number of turns per minute
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 20 PL. VIII

PLAN AND ELEVATION OF DYNAMOMETER.

PERRY.] DYNAMOMETER. 23

made by the sweep in order to know the velocity of wind in miles per 

hour with sufficient accuracy.

For counting the number of turns of the sweep a toothed wheel, containing 80 teeth, was used, which was made to revolve at the same rate 

as the sweep. Thus the fractions of a turn could be easily determined 

to within 0.0125, and we made a practice of setting down the fractional 

turns to within 0.00125, thus securing relative accuracy in determining 

the velocity of the wind to within 0.00125 of a mile per hour.

The face of the wind wheel was set at right angles to the direction of 

the wind. The frame supporting the shaft of the wind wheel'was suspended^ about 3 feet below the sweep by four iron straps, presenting 

their thin edges to the wind, so that the action of the wind upon the 

wheel should be obstructed as little as possible by the sweep or otherwise. The motion of the sweep undoubtedly carried the air of the room 

with it to some extent, but not so as to produce a noticeable current.

DYNAMOMETER.

The ordinary Prony friction brake was used, with such modifications 

and additions as circumstances demanded.

The brake consisted of two pine blocks, clamped vertically upon a 

brass cylinder 5^ inches in diameter, attached to the shaft of the wind 

wheel. But instead of using two bolts, with thumb nuts'for adjusting 

the brake, one bolt was used as a hinge beneath the cylinder, and the 

adjustment was made by means of a cord passing across from one 

block to the other around small iron sheaves, which turned on common 

wood screws fastened into the tops of the two blocks, so that the pressure of the blocks against the cylinder corresponded to about sixteen 

times the tension of the cord.

The adjusting cord was carried back from the brake some distance 

in a direction parallel to the axis of the cylinder to a sheave fixed to 

the frame supporting the shaft of the wind whiel. From that point 

the cord was carried*by means of sheaves, levers, etc., up through the 

hollow shaft supporting the sweep and finally fastened to one end of a 

lever. The other end of the lever was hinged and provided with a 

sliding weight, by means of which the tension of the cord could be 

adjusted from the station of observation while the sweep was in motion. 

The brake was provided with a horizontal graduated arm carrying a 

weight, which could be moved in or out to correspond to any desired 

load. Suitable stops were provided, allowing a limited motion of the 

brake and - graduated arm, which could be conveniently watched from 

the station of observation, just beyond the reach of the sweep. The 

brake and graduated arm were balanced, as regards the action both of 

gravity and of centrifugal force, before applying the loads; which were 

balanced by the friction of the brake. The thrust of the rear end of 

the shaft of the wind wheel was sustained by :i ste*il point.
24 EXPERIMENTS WITH WINDMILLS. l»o.20. 

.METHOD OF EXPERIMENT.

For noting tha number of turns of the wind wheel, the rear end of the 

shaft was provided with a worm, with which a toothed wheel could be 

thrown in or out of contact at the pleasure of the operator from the 

station of observation. Each turn of the wind wheel would cause the 

toothed wheel to make 0.0125 of a revolution, as there were 80 teeth in 

the wheel, and the fractional turns could easily be estimated to within 

0.1 of a revolution of the wind wheel. The weight on the graduated 

arm was always expressed in pounds and decimal parts at 1 foot from 

the center of shaft of the wind wheel. During use the brake was freely 

lubricated with machine oil.

For a trial load the weight on the graduated arm was set at some 

number, say 1 pound. Then the counter which was to record the speed 

of the wind wheel was set at 0, as was also the counter which was to 

record the velocity of the wind. The sweep having been set in motion, 

the speed of the wind wheel was checked by the brake, which was 

adjusted from the station of the observer by regulating the tension of 

the adjusting cord until the-weight on the graduated arm was just 

lifted by the friction, and no more. As soon as the friction and weight 

were well balanced the counters which were to record the speed of the 

wheel and velocity of wind were thrown in by a single movement of a 

lever, and at the expiration of one minute they were both instantaneously thrown out. Then the sweep was stopped at the station of observation, the number of revolutions of the wind wheel recorded, and also 

the velocity of the wind.

To the load applied was added the friction of the journals, also 

expressed in pounds.at 1 foot from the center of the shaft. This sum 

made the total load, which was multiplied by the number of turns of 

the wind wheel.

Then a second product was obtained in precisely the same manner 

with a greater load applied; and if greater than the first, a still greater 

load was applied and the corresponding products-obtained. A succession of products were thus obtained corresponding to a succession of 

loads gradually increased until the products began to decrease on 

account of thje diminishing speed of the wheel. The greatest product 

corresponded to the best load for the wheel, and the actual work performed by the wheel in each case could be obtained by multiplying the 

product by 6.2832 feet, equal to the circumference of the circle whose 

radius is 1 foot. In obtaining these products measurements were taken 

several times for each load and the total load was multiplied by the 

avern ge turns of the wheel per minute. The average wind was also taken 

for record. The velocity pf wind was supposed to be nearly uniform, but 

varied slightly with the speed of the engine, and the variation was sufficient to affect results considerably in some cases; hence the necessity 

of recording the velocity of the wind in each case. In comparing
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 20 PL. IX

END VIEWS OF DYNAMOMETER.

PEBRT.] STARTING FORCES AND JOURNAL FRICTION. 25

results some allowance also had to be made for differences in velocities 

of wind.

In testing the speed of the wheel unloaded the brake was removed, 

making the load nothing but the journal friction.

STARTING FORCES.

The determination of starting forces was attended with some difficulty. In the first place, it became necessary to define what should 

be considered the starting force of a wind wheel whether it should be 

considered the greatest load under which the wheel would turn, or the 

greatest load which the wheel would balance without turning. It was 

also necessary to decide what motion of the wheel should be defined 

as turning. The wheel with a certain load would sometimes perform 

one revolution in ten or twenty minutes, if that could be called turning; between that and proper continuous turning there were many 

gradations. It was impracticable to decide when the wheel reached 

the lowest limit of speed which could properly be called turning. 

Therefore we have considered the starting force as the greatest load, 

the wheel would balance without turning. Our method of determining 

starting forces was to clamp the brake so tightly on the cylinder that 

the wheel could not turn, but could lift the load applied such small 

distance as was allowed by the stops which limited the motion of the 

brake. The sweep was then set in motion and timed for one minute, 

during which time the load on the graduated arm was watched, its 

alternating upward and downward movements were noted, and judgment was exercised as to the balance between the load applied and the 

starting force of the wind wheel. The average velocity of wind during 

these tests was always recorded after March 13,1883, but not always 

before that date.

In lifting the load the starting friction of the journals was also 

overcome by the wind wheel, but when the weight descended the load 

overcame the starting friction of journals in addition to the starting 

force of wind, and as the load almost constantly moved up and down 

when well balanced, nothing should be added to loads applied for 

friction in case of starting forces. Yet the friction has been added in 

the tables, the same as to other loads applied, in order to accommodate 

the statements at the head of columns for loads. On account of the 

starting friction being great and uncertain, and for other reasons, the 

starting forces recorded prior to March 13,1883, are not so much to be 

relied upon as those recorded after that date; nor were the later tests 

for starting forces nearly so accurate as those for products.

JOURNAL FRICTION.

For journal friction previous to March 13, 1883, see description in 

connection with wind wheel No. 11, page 38. After the date above 

given the journal friction was greatly reduced by the use of large anti-
26 EXPERIMENTS WITH WINDMILLS. [NO.20.

friction wheels in place of the front box, just behind the wind wheel 

and in front of cylinder, where the weight of the wind wheel and cylinder was mostly supported. In place of the rear box a small steel pin 

was inserted in the end of the shaft and turned in a brass box. The 

end thrust of the shaft, due to wind pressure and tension of the adjusting cord, was sustained by a steel point, as before.

As thus improved, one-half an ounce hung to a thread wound around 

the outside of wheel No. 37 overcame friction at very slow motion, and 

was almost if not quite equal to starting friction. The brake was 

removed during this test.

Let x weight 12 inches from axis required to overcome friction. 

30 inches = distance from axis to thread.

£ ounce = -3\ pound. 

12# = !f

x = 0.0785 = friction at very slow motion or at starting.

With brake and wind wheel removed 2i».50 ounces hung by a 'thread 

wound around the forward end of shaft 0.7969 inch in diameter over- 

.caine friction at very slow motion and was almost equal to starting 

friction, and 24.25 ounces hung in the same way overcame friction at 50 

turns per minute, and would not overcome friction when speed was much 

less. 0.8125 inch = diameter outside of thread, 0.4024 inch = radius 

to center of thread.

Friction at 50 turns per minute is to starting friction as 24.25 is to

f)A OK

26.50. Hence, 0.0785 x J^T: = 0.0714 pound = journal friction at 50

^u.oO

turns per minute, with wind wheel on and brake removed. The weight 

of the brake would, of course, add a little to the friction, which we have 

uniformly called 0.1 in the tables, as explained on page 28, under the 

table.

The 0.3-pound friction added to loads applied prior to March 13,1883, 

was friction at very slow motion and was undoubtedly much in excess 

of friction "at speed of wheels corresponding to maximum products, as 

is evinced by the fact that notwithstanding the great reduction of 

starting friction the tables do not show for the same applied loads, or 

even unloaded, very much increase of speed of wheels after March 13, 

1883, over speeds indicated previous to that date. If 0.1 pound had 

been added to applied loads previous to March 13,1883, the products 

at maximum and fort higher speeds of wheels would probably have been 

more nearly correct. It was this uncertainty and ignorance regarding 

friction at different speeds that led us to reduce as much as possible 

this source of error. However, the error thus arising does not greatly 

affect comparative values of products recorded prior to March 13,1883, 

although products affected by allowance of 0.3 pound lor friction should 

not, unless corrected, be compared with products recorded after above 

date.
PEHHY.] EXPERIMENTS WITH WHEEL NO. 2. 27

COMPARATIVE STANDARD WHEEL.

In the earlier stages of these experiments we acted on the supposition that only such variations in the state of the atmosphere as were 

indicated by the barometer and thermometer should aifect the work 

performed by a wheel tested at different times in wind of the same 

velocity. But? later we were convinced that the readings of the barometer and thermometer would not always account for variations in 

products given by the same wheel on different days. We were also 

convinced of the uselessness of speculating as to, or trying to understand and forestall, all the causes that might combine to affect results. 

Therefore we adopted the practice of comparing the maximum product 

of each wheel tested with the maximum product of wheel No. 2, obtained 

in close proximity as to time and under similar conditions in all respects. 

This could be done with a good deal of certainty, and no further trouble 

was experienced on account of contradictory results. After the best 

loads had been ascertained by trial, comparative tests were made by 

trying first one wheel and then the other in succession until a considerable number of measurements had been taken. Then as many measurements as possible, giving the same average velocity of wind for both 

wheels, were selected from each set of experiments.

In this, way the product obtained was usually the average of 8 to 10 

measurements of each wheel made under the same conditions of time, 

wind, weather, and whatever else might affect the results. The product of No. 2 was thus used as a standard qf measure, and the ratio of 

products indicated the relative value of the wheel compared.

For further particulars consult tables of experiments of later date 

than March 13, 1883.

Results of experiments performed in March and May, 1883, with wheel No. 2.

Velocity of 

wind per 

hour.

Miles. 

6.437

6.371 

6.381

8:417

8.403 

8.405

10. 898

11. 041 

10. 976

Load applied + 0.1 

for friction.

Pound*. 

0.1

1.1 

2.4

.1

1.9 

4.2

.1

3.3 

6.9

Turns of 

wheel per 

minute.

43.78

23.90 

0

59.05

32. 875 

0

77.85

41.06 

0

Product at 

maximum.

26. 290

62. 463

135. 498

Thermometer.

°F. 

62

54 

62

53

50 

53

46

60 

46

Date.

1883.

May 14

May 14 

Mav 14

Mar. 14

Mar. 14

May 21

May 17 

May 21

Previous to making the above experiments, March 13,1883, the dynamometer was improved by the addition of an automatic brake adjuster
28 EXPERIMENTS WITH WINDMILLS. [NO. 20.

and antifriction wheels, which reduced starting friction from about 0.3 

to about 0.08 pound, and made journal friction at 50 turns per minute 

about 0.071 pound. In the tablejriction was called 0.1 pound for convenience, as the absolute friction in each case could not easily be obtained, and the error does not materially affect comparative results. 

(See pages 25 and 26 for " Journal friction.'')

Average products of wheel No. 2, which was used as a standard for 

comparison, were obtained by selecting from numerous tests several 

numbers generally 8 to 10 which corresponded to wind of the same 

average velocity as wind for wheels compared in each case; the difference of averages in no case exceeded 0.001 mile per hour in the table on 

page 47.

Measurements for maximum products of two wheels compared were 

always taken as far as possible under the same conditions of wind, temperature, barometer, weather, time, etc.

RESULTS OF ORIGINAL TESTS.

TABLES AND DESCRIPTIONS OF WIND WHEELS.

WHEEL No. 1. Bexults of experiments.

Velocity of 

wind per 

hour.

Miles.

8.427

8.431

8.385

8.412

8.452

8.432

..........

Load applied +0.3 

for friction.

Pounds.

0.3

1.2

1.4

1.6

1.8

2.0

2.85

Turns of 

wheel per 

minute.

59.08

42.60

39. 90

35.69

31.69

28.02

0

Product.

17. 724

51. 120

55. 860

57. 104

57. 042

56.040

0

Experiments made June 1 and 2, 1882.

Load expressed in pounds applied 1 foot from center of wheel.

Circumference of circle whose radius is 1 foot, 6.2832 feet.

Work per minute at the maximum, 57.104 X 6.283 = 358.784 foot-pounds

Diameter of wheel, 5 feet.

Number of slats or sails, 30.

Length of slats, 18 inches.

Width of slat at outer end, 3.56 inches.

Width of slat at inner end, 1.344 inches.

Total area of slats or sails, 9.19 square feet.

Angle of weatKer, 35 degrees.

Portion of available annular space filled by sails, 0.5.

The spaces between are equal to the spaces occupied by the slats. This wheel is 

the same as No. 2 with one-half the slats omitted.

Slats, plain surfaces, made of white pine three-sixteenths.of an inch thick, with 

forward edges trimmed to an edge.
PERRY.] RESULTS OF ORIGINAL EXPERIMENTS.

WHEEL No. 2. Results of experiments.

29

Velocity of 

wind per 

hour.

Miles.

8.411

8.381

8.451

8.435

8.445

8.412

8.460

8.436

8.429

8.443

8.421

8.446

8.416

8.398

8.338

Load applied+0.3 

for friction.

Pounds.

0.3

0 Q

1.05

1.3

1.6

1.7

1.8

1.9

2.0

2.1

2.3

2.5

2.7

2.9

3.1

3.81

Turns of 

 wheel per 

minute.

57.95

49.00

47.00

43.08

40.80

37.30

35.85

34.89

33.43

31.33

27.60

24.48

21.70

20.00

15.80

0

Product.

17. 385

44. 100

49. 350

56.004

61. 200

63. 410

64. 530

66.291

66.860

65. 793

63. 480

61. 200 '

58. 590

58. 000

48. 980

0

Thermometer.

o jp_

69

77

73

70

78

72

78

69

73

75

76

Date.

1882.

June 7

June 7

June 7

June 8

Jane 8

June 8

June 8

June 8

Total area of slat sails 18.380 square feet.

Angle of weather, 35 degrees.

The same as No. 1, with double the number of slats that is, the projections of the 

slats upon the plane of the wheel equaled the entire available annular area. An 

area as shown in fig. 8 at each of the six arms constituted the space not available. 

Slats held in place by 12 straight notched pieces extending from arm to arm the 

same as in No. 1.
30 EXPERIMENTS WITH WINDMILLS. [NO. 20.

FIG. 7. Elevation and section of -wheel No. 2. (Sail area, 18.380 square feet; efficiency, 0.154.)
PEEEY ] RESULTS OF ORIGINAL EXPERIMENTS. 31

FIG. 8. Outline of area not available. 

WHEEL No. 3. Results o/ experiments.

Velocity of 

wind per 

hoar. ,

Miles.

8.476

8.435

8.441

8.428

8.447

8.436*

8.402

8.423

8.441

8.404

Loads applied+0.3 

for friction.

Pounds,

0.3

.95

1.05

1.1

1.2"

1.3

1.4

1.5

1.7

1.9 

2.4

Tnrns of 

wheel per 

minute.

90.48

69.40

64.90

62.15

59.65

55.36

51.10

47.48

41.00

32.00 

0

Product.

27. 144

65.930

68. 145

68. 365

71. 580

71. 968

71. 540

71. 220

69. 700

60. 800 

0

Thermometer.

0 F.

68

68

68

88

69

83

69

74

71

71

Date.

1882.

June 22

June 22

June 21

June 22

June 19

June 22

June 21

< June 19 

\ June 22

June 22

June 22 

June 22
EXPERIMENTS WITH WINDMILLS. [NO. 20.

FIG. 9. Elevation and section of wheel No. 3. (Sail area, 13.590 square feet; efficiency, 0.161.)

Diameter of wheel, 5 feet.

Numher of sails, 12.

Sails of lineal dimensions as shown in figs. 10 and 11, made of white-pine hoards 

three-sixteenths of an inch thick and fastened hy hinges near each end to 12 pine 

bands hent to arcs of circle and secured to the 6 arms.

Total sail surface, 13\59 square feet.

Sails concave toward the wind.
PERKY.] RESULTS OP ORIGINAL EXPERIMENTS. 33

/S.3J"

FIG. 10. Dimensions of 

sails of wheel No. 3. 

18 inches is the extreme length of sail.

FIG. 11. Angles of weather of sails of 

wheel No. 3. A, Angle of weather at 

inner ends of sails; -B, Angle of 

weather at outer ends of sails.

WHEEL No. 4. Results of experiments.

Velocity of 

wind per 

hour.

Miles.

8.354

8.372

8.375

8.324

8.461

8.467

8.465

8.366

8.386

8.369

Load applied+ 0.3 

for friction.

Pounds.

0.3

0.9

1.1

1.3

1.5

1.7

1.9

2.1

2.3

2.5

3.3

Turns of 

wheel per 

minute.

89.43

. 74. 54

70.03

62.75

60.72

55.93

48.75

42.78

38.50

29.13

0

Product.

26. 829

67. 086

77. 033

81. 575

91. 080

95. 081

92. 625

89. 838

88.550

72. 825

0

Thermometer.

°F.

76

76

76

68

73

73

73

68

68

68

Date.

1882.

June 29

June 29

June 29

June 29

June 28

June 28

June 28

June 29

June 29

June 29

June 29

Wheel the same as No. 3, except that the inclination of the sails was changed, making the angle of weather 20 degrees at outer ends of sails and 30 degrees at inner ends 

of sails.

20 3
EXPERIMENTS WITH WINDMILLS. 

WHEEL No. 5. Results of experiments, (a)

[NO. 20.

Velocity of 

wind per 

hour.

Miles.

8.444

8.499

8.479

8.493

8.419

8.422

8.468

8.465

8.456

8.414

8.424

8.440

8.491

Loads applied +0.3 

for friction.

Pounds.

0.3

0.9

1.1

1. 3

1.5

1.7

1.9

2.1

2.3

2.5

2.7

2.9

q O. 7 f

1 -L. Q<J

Turns of 

wheel per 

minute.

86.78

73.56

68.72

64.18

57.98

53.86

50.83

46.10

41.60

33.86

27.70

19.62

0

51.88

Product.

26. 034

66. 204

75. 592

83. 434

86. 970

91. 562

96. 577

96. 810

95. 680

84. 650

74. 790

56. 898

0

98. 572

Thermometer.

°F.

74

74

74

71

71

71

71

74

74

63

63

63

71

Date.

1882.

July 12

July 12

July 12

July 5

July 5

July 5

July 5

July 5

July 5

July 6

July 12

July 12

July 5

a See -wheel No. 44, p. 57.

Wheel the same as No. 3, except that the inclination of the sails was changed, 

making the angle of weather 22.5 degrees at outer ends of sails and 32.5 degrees 

at inner ends of sails.

WHEEL No. 6. Results of experiments.

Velocity of 

 wind per 

hour.

Miles.

8.373

8.355

8.348

8.405

8.317

a 8. 368

Load applied + 0.3 

for friction.

Pounds.

0.3

1.5

1.7

1.8

1.9

1.3

3.4

Turns of 

wheel per 

minute.

69.03

47.30

44.00

42.10

38.28

50.83

0

Product.

20. 709

70. 950

74. 800

75. 780

72. 732

66.079

0

Thermometer.

°F.

32

34'

34

35

35

38

33

Date.

1882.

Dec. 9

Dec. 9

Dec. 9

Dec. 9

Dec. 9

Dec. 9

Dec. 8

a, When reversed, so as to present its back side to the wind.
PERRY.] RESULTS OP ORIGINAL EXPERIMENTS. 35

FIQ. 12. Elevation and section of wheel No. 6. (Sail area, 10.688 square feet; efficiency, 0.163.)

Diameter of wheel, 5 feet. 

Arms and hands the same as in wheel No. 3.

Numher of sails, 24. Sails of lineal dimensions as in ng. 13; made of white-pine 

boards three-sixteenths of an inch thick, and hinged to the hands as in No. 3. 

Sails plain, with forward edges trimmed to an edge. 

Total sail surface, 10.688 square feet. 

Angle of weather, 30 degrees.
36 EXPERIMENTS WITH WINDMILLS. [NO. 20.

FIG. 13. Dimensions of 

sails of wheel No. 6.

WHEEL No. 7. Results of experiments.

Velocity of 

wind per 

hour.

Miles.

8.361

8.380

8.416

8.359

Loads applied + 0.3 

for friction.

Pounds.

0.3

1.3

1.5

1.7

2.8

Turns of 

wheel per 

minute.

73.60

52.50

47.40

40.74

0

Product.

22.080

68. 250

71.100

69.258

0

Thermometer.

°F.

42

39

40

40

42

Date.

1882.

Dec. 12

Dec. 12

Dec. 11

Dec. 12

Dec. 12

Wheel the same as No. 6, except that the inclination of the sails was changed, 

making the angle of weather 25 degrees.
RESULTS OF ORIGINAL EXPERIMENTS. 

WHEEL No. 8. Results of experiments.

37

Velocity of 

wind per 

hour.

Miles.

8.333

8.344

8.403

8.375

8.366

8.368

8.354

Loads applied + 0.3 

for friction.

Pounds.

0 ^

1.3

1.5

1.7

1.9

2.1

2.3

3.55

Turns of 

wheel per 

minute.

62.67

46.83

44.23

40.23

36.84

32.80

27.70

0

Product.

18. 801

60.879

66. 345

68. 391

69. 996

68. 880

63. 710

0

Thermometer.

°F.

48

48

39

41

47

47

Experiments made December 13, 1882.

Wheel the same as No 6, except that the inclination of the sails was changed, 

making the angle of weather 35 degrees.

WHEEL No. 9 Results of experiments.

Velocity of 

wind per 

hour.

Miles.

8.374

8.361

8.375

8.350

8.364

8.344

8.323

Loads applied + 0.3 

for friction.

Pounds.

0.3

1.3

1.5

1.7'

1.9

2.1

2.3

3.4

Turns of 

wheel per 

minute.

66.40

49.73

47.15

42.30

38.20

34.58

30.70

0

Product.

19. 920

64. 649

70. 725

71. 910

72. 580

72. 618

70. 610

0

Thermometer.

°F.

43

38

39

40

40

42

42

Experiments made December 14,1882.

Wheel the same as No. 6, except that the inclination of the sails was changed, 

making the angle of weather 32.5 degrees.
38 EXPERIMENTS WITH WINDMILLS.

WHEEL No. 10. Remits of experiments.

[NO. 20.

Velocity of 

 wind per 

hour.

Miles.

8.347

8.336

8.329

8.345

8.358

8.338

8.351

Loads ap- > 

plied + 0.3 

for friction.

Pounds.

0.3

1.1

1.3

1.5

1.7

1 Q

2.1

3.25

Turns of 

wheel per 

minute.

72.23

54.77

53.30

48.70

43.78

39.33

35. 06

0

Product.

21. 690

60. 247

69. 290

- 73. 050

74. 420

74."727

73. 626

0

Thermometer.

°F.

34

45

45

33

34

35

39

Date.

1882.

Dec. 15

Dec. 14

Dec. 14

Dec. 15

Wheel the same as No. 6, except that the inclination of the sails-was changed, 

making the angle of weather 27.5 degrees.

WHEEL No. 11. Results of experiments.

Velocity of 

wind per 

hour.

Miles.

8.415

8.353

8.391

8.401

8.410

Loads applied + 0.3 

for friction.

Pounds.

0.3

1.3

1.5

1.7

1.9

2.1

2.3

Turns of 

wheel per 

minute.

77.60

51.64

45.46

39.52

a 33. 14

(&)

0

Product.

23. 280

67. 132

68. 190

67. 184

62. 966

0

Thermometer.

°F.

41

39

40

40

41

a Started slowly and with difficulty, though well balanced. Once needed help to start. 

6 Ran slowly two or three minutes and stopped.

Experiments made December 18, 1882.

Wheel the same as No. 6, except that the inclination of the sails was changed, 

making the angle of weather 20 degrees.

A journal friction test made with wheel No. 11 by hanging a If-ounce weight by 

a thread wound around the ontside of the wheel showed that this weight did not 

overcome starting friction, but was sufficient to accelerate motion after the wheel 

was started at moderate speed.

Let x = journal friction, at 1 foot (12 inches) from axis. 

30 inches = distance of If-ounce weight from axis. .

1.75X30 = 12 x.

x = 4.375 ounces = 0.2734 pound = friction of journals at moderate speed.

The journal friction diminishes somewhat with the increase of speed, although 

authorities give the same coefficient of friction at all speeds. Some variation in 

journal friction is also dne to difference in weights of wheels and in lubiication; 

and as the above test was made with the brake removed, we have considered it 

approximately correct to call journal friction = 0.3 pound in all' cases. See, however, later conclusions.
PERRY.] RESULTS OF ORIGINAL EXPERIMENTS.

WHEEL No. 12. Results of experiments.

39

Velocity of 

wind per 

hour.

Miles.

8.405

8.385

8.376

8.341

8.376

Load applied + 0.3 

for friction.

Pounds.

0.3

.95

1.1

1.3

1.5

1.6

1.7

Turns of 

wheel per 

minute.

75.60

56.18

50.78

a 43. 88

635.42

(«)

0

Product.

22.680

53. 371

55. 858

57. 044

53.130

0

Thermometer.

o p_

44

40

40

41

42

a Started slowly. '

b Needed assistance to start in every instance, though without assistance it would barely move, at 

the rate, perhaps, of one turn in ten minutes. 

e Ean three minutes and stopped, after having been started at moderate speed.

Experiments made December 19,1882.

Wheel the same as No. 6, except that the inclination of the sails was changed, 

making the angle of weather 15 degrees.

WHEEL No. 13. Results of experiments.

Velocity of 

wind per 

hour.

Mileg.

8.369

8.377

8.353

8.352

8.407

8.375

8.328

8.351

Load applied + 0.3 

for friction.

Pounds.

0.3

1.7

1.9

2.1

2.3

2.5

2.7

2.9

3.1

3.2

3.7

Turns of 

wheel per 

minute.

56.33

37.13

34.10

31.30

28.70

25.38

20.63

17.25

(a)

(»)

0

Product.

16. 899

63. 121

64. 790

65. 730

66. 010

63. 450

55. 701

50. 025

0

Thermometer.

o p.

45

45

43

41

42

42

44

46

Date.

1882.

Dec. 20

Dec. 19

Dec. 20

Dec. 20

Dec. 20

Dec. 20

Dec. 20

Dec. 20

Dec. 20

Dec. 20

Dec. 20

a Ean very slowly after starting, and stopped several times. 

b Stopped and started occasionally.

Wheel the same as No. 6, except that the inclination of the sails was changed, 

making the angle of weather 40 degrees.
40 EXPERIMENTS WITH WINDMILLS. 

WHEEL No. 14. Results of experiments.

[NO. 20.

Velocity of 

wind per 

hour.

Miles.

8.327

8.335

8. 375

8.393

8.336

8.364

8.427

8.381

8.409

8.349

Load applied + 0.3 

for friction.

Pounds.

0.3

1.5

1.7

1.9

2.1

2.3

2.5

2.7

2.9

3.1

3.3

3.8

Turns of 

wheel per 

minute.

48.60

33.60

32.68

29.88

26.95

24.72

21.82

17.98

15.10

12.47

(a)

0

Product.

14.580

50. 400

55. 556

56. 772

56. 595

56. 856

54. 550

48. 546

43. 790

38.657

0

Thermometer.

o p

47

46

46

47

46

46

46

46

46

46

a Ran a minute or two, stopped, and afterwards started slightly.

Experiments made December 21, 1882.

Wheel the same as No. 6, except that the inclination of the sails was changed, 

making the angle of weather 45 degrees.

WHEEL No. 15. Results of experiments.

Velocity of 

wind per 

hour.

Miles.

8.444

8.402

8.429

8.479

8.457

8.443

8.440

8.438

8.406

Load applied +0.3 

for friction.

Pounds.

0.3

1.7

1.9

2.1

2.3

2.5

2.7

.3.1

3.3

3.5

3.95

Turns of 

wheel per 

minute.

46.84

29.36

27.40

25.30

22.92

20.17

17.71

10.20

(a)

(6)

0

Product.

14. 052

49. 912

52.600

53. 130

52. 716

50. 425

47. 817

31. 620

0

Thermometer.

0 F.

30

28

30

31

33

32

33

35

30

' 30

35

a Turned very slowly and irregularly. b Barely moved.

Experiments made January 5 and 6, 1883.

Wheel the same as No. 6, except that 1iie inclination of the sails was changed, 

making the angle of weather 47.5 degrees.
PEERY.J RESULTS OF ORIGINAL EXPERIMENTS. 

WHEEL No. 16. Results of experiments.

41

Velocity of 

wind per 

hour.

Miles.

8.443

8.444

8.440

8.385

8.447

8.419

8.505

8.426

8.484

8.257

8.426

Load applied + 0.3 

for friction.

Pounds.

0.3

1.7

1.9

2.1

2.3

2.5

2.7

2.9

3.1

3.3

3.55

3.9

Turns of 

wheel per 

minute.

42.40

27.75

24.92

23.27

20.67

18.45

16.23

a 12. 33

(b)

(f,\ \ L )

0

0

Product.

12. 720

47. 175

47. 348

48. 867

47. 514

46. 125

43. 821

35. 757

0

0

Thermometer.

0 F.

32

32

30

30.5

38

37

37

37

36

36

35

36

a Almost needed help to start, and once stopped within one minute.

6 Stopped after running one minute.

c Stopped after running very slowly a short time.

Experiments made January 6 and 8, 1883.

Wheel the same as No. 6, except that the inclination of the sails was changed, 

making the angle of weather 50 degrees.

Comparative results icith plain sails.

A

No. 

of wheel.

1

2

12

11

7

10

6

9

8

13

14

15

16

B

Angle of 

weather.

o

35

35

15

20

25

27.5

30

32.5

35

40

45

47.5

50

C

Velocity 

of wind 

per hour 

at maximum.

Miles.

8.412

8.429

8.341

8.391

8.416

8.358

8,348

8.364

8.366

8.352

8.336

8.479

S.385

D

Greatest 

load.

Pounds.

2.85

3.81

1.7

2.3

2.8

3.25

3.4

3.4

3.55

3.7

3.8

3.95

, 3.9

"E

Load 

at maximum.

Pounds.

1.6

2.0

1.3

1.5

1.5

1.7

1.7

1.9

1.9

- 2.1

2.1

2.1

2.1

F

Turns of 

wheel per 

minute 

at maximum.

35. 69

33.43

43.88

45.46

47.40

43.78

44.00

38.20

36.84

31.30

26.95

25.30

23.27

G

Turns of 

wheel per 

minute 

unloaded.

59.08

57.95

75.60

77.60

73.60

72.23

69.03

66.40

62.67

56.33

48.60

46.84

42.40

H

Products 

at maximum 

work,

E X F.

57. 104

66. 860

57. 044

68. 190

71. 100

74. 426

74.800

72. 580

69. 996

65. 730

56. 595

53. 130

48. 867

I

<ffl"otal sail 

surface.

Sq.ft.

9.190

18. 380

10. 688

10. 688

10. 688

10. 688

10.688

10. 688

10.688

10. 688

10. 688

10. 688

10. 688
42 EXPERIMENTS WITH WINDMILLS. [NO. 20.

No. 2 modeled after Halliday 10-foot mill, and contained 60 sails 18 inches long 

and 3.56 inches wide at outer end.

No. 1 contained 30 sails 18 inches long and 3.56 inches wide at outer end. 

Nos. 6-16 contained 24 sails 18 inches long and 5 inches wide at outer end.

If the separate tables are consulted, it will be found that in making out the comparative table, we have not taken the highest products for wheels Nos. 6, 9, 10, 13, 

and 14, in column H. As the angle of weather increases from 15 degrees to 47.5 

degrees, the loads at maximum should obviously increase or at least should not 

decrease in any case within those limits. This law would apparently have been 

violated if we had taken the highest products in the above-mentioned cases. So, in 

Nos. 6, 9, 10, 13, and 14, we have taken the loads and products immediately preceding those corresponding to maximum. By so doing we made column E appear con- 

"sistent with the law of increasing loads without materially changing the values of 

products in column H. For it will be noted that in no case does the product we 

have set down in column H fall short of the highest we might have taken by so much 

as unity.

The majority of the slight discrepancies in column H are clearly accounted for by 

the variation in wind as shown in column C. But in Nos. 9 and 10 there was evidently a slight fault in adjusting the friction of the brake to the load applied. 

Slight errors of this nature are unavoidable, although they may be reduced to a 

minimum by the exercise of care and repeated trials. (See page 27.)

In the foregoing experiments seldom less than six measurements were made for the 

determination of each product and sometimes the unsteadiness of the wind required 

many more trials for the determination of a product. The variations in wind, though 

not great, sometimes made a difference of one or two turns of the wheel per minute. 

The indicator which registered the number of turns of the wheel was not originally 

intended to indicate fractions of a turn, although the fractional turns were actually 

set down by estimation to within one-tenth of a turn. But the indicator could not 

be counted on as absolutely correct to within less than half a turn, so that an error 

of half a turn too much or too little might sometimes account for a variation of one 

turn of the wheel. Since, however, the indicator was just as liable to make the 

fractional error one way as the other, the errors in average results would be probably diminished in proportion to the number of tests from which the averages were 

deduced.

Tho indicator consisted of a toothed wheel which was thrown in contact with a 

worm on the shaft of the wheel, and the teeth were liable to strike the worm so as 

to accelerate or retard the indicator to the extent of half the pitch of the teeth or 

less.

An examination of the several tables shows that there are generally three or four 

consecutive products corresponding to different loads, none of which vary much 

from the greatest product, and when the two highest products are nearly identical, 

as often happens, it requires but a very slight error in any one of two or three 

chances for variation to make the highest product correspond to either of two consecutive loads.
PEHHT.] RESULTS OF ORIGINAL EXPERIMENTS. 

WHEEL No. 17. Results of experiments.

- 43

Velocity of 

wind per 

hour.

Miles.

8.392

8.379

8.363

8.390

8.408

8.373

8.400

a 8. 391

a 8. 380

a 8. 374

a 8. 361

Load applied + 0.3 

for friction

Pounds.

0.3

1.3

1.5

1.7

1.9

2.1

3.05

.3

1.3

1.5

1.7

Turns of 

wheel per 

minute.

73.90

52.62

46.55

42.80

38.70

33.30

0

79.83

54.15

47.60

40.70

Product.

22. 170

68.406

69. 825

72. 760

73. 530

69. 930

0

23. 949

70. 395

71.400

69. 190

Thermometer.

op

32

30

30

31

31

31

32

32

32

31

32

a Reversed.

Experiments made January 10 and 11, 1883.

Wheel the same as No. 6, except that the sails were twisted, making the angle of 

weather 25 degrees at outer extremities of sails and 35 degrees at inner extremities 

of sails.

The twisting made the sails somewhat convex on the front side and concave on 

the reversed side.

WHEEL No. 18. Results of experiments, (a)

Velocity of 

wind per 

hour.

Miles.

8.430

8.370

8.362

8.386

8.397

8.393

8.357

8.368

8.419

8.440

Load applied + 0.3 

for friction.

Pounds.

0.3

1.3

1.5

1.7

1.9

2.1

2.3

2.5

2.7

3.4

Turns of 

wheel per 

minute.

75.58

53.48

50.64

48.08

43.31

39.42

33.65

628.31

c21.83

0

Product.

22. 674

69. 524

75. 960

81. 736

82. 289

82. 782

77. 395

70. 775

58. 941

0

Thermometer.

0 F.

37

37

38

38

39

40

39

40

37

38

a See table on p. 47.

b Started slowly.

c Started very slowly almost needed help.

Experiments made January 13 and 17, 1883.

Wheel contained 24 sails of lineal dimensions as shown in fig. 14, made of whitepine boards three-sixteenths inch thick, beveled on forward edges, and hinged to 

the bands the same as in wheel No. 6.

Total area of sail surface, 12.937 square feet.

Angle of weather, 25 degrees.
44, EXPERIMENTS WITH WINDMILLS. [NO. 20.

FIG. 14. Dimensions of sails 

of wheel No. 18.

WHEEL No. 19. Results of experiments, (a)

Velocity of 

wind per 

hour.

Miles.

8.375

8.375

8.466

8.475

8.379

8.422

8.439

8.400

8.397

8.392

8.370

8.329

Load applied +0.3 

for friction.

Pounds.

0.3

1.3

1.5

1.7

1.9

2.1

2.3

2.5

2.7

2.9

3.1

3.6

Turns of 

wheel per 

minute.

72.26

53.78

50.32

47.17

44.48

42.10

38.20

32.95

26.98

22.03

616.03

0

Product.

21. 678

69. 914

75. 480

80. 189

84. 512

88. 410

87. 860

82. 375

72. 846

63. 887

49. 693

0

Thermometer.

0 F.

33

34

28

28

29

30

31

31

31

32

32

32

« See table on page 47. b Needed assistance to start.
PBBBlf.] EESULTS OF OKIGINAL EXPEKIMBNTS. 45

FIG. 15. Elevation and section of wheel No. 19. (Sail area, 12.937 square feet; efficiency, 0.185).

Experiments made January 18, 1883.

Wheel the same as No. 18, except that the inclination of the sails was changed, 

making the angle of weather 27.5 degrees.
46 EXPERIMENTS WITH WINDMILLS. 

WHEEL No. 23. Results of experiments.

[NO. 20.

Velocity of 

wind per 

hour.

Miles.

8.422

8.420

8.428

8.486

8.444

8.400

8.402

8.382

8.434

8.399

Load applied + 0.3 

for friction.

Pounds.

0.3

1.3

1.5

1.7

1.9

2.1

2.3

2.5

a 2. 7

3.55

Turns of 

wheel per 

minute.

73.46

55.60

50.83

47.64

43.21

38.14

34.30

30.12

24.23

0

Product.

22. 038

72. 280

76. 245

80. 988

82. 099

80.094

78. 890

75. 300

65.421

0

Thermometer.

0 JF.

34

30

30

30

30

30

31

 31

32

32

a Needed assistance to start.

Experiments made January 25, 1883.

Wheel the same as No. 18, except that the angle of weather was 25 degrees at outer 

ends of sails and 30 degrees at inner ends.

COMPARISON OF SEVEKAL WHEELS. 

WHEELS Nos. 2 AND 50. Results of experiments.

No. of 

wheel.

2

2

2

50

50

50

Velocity of 

wind per 

hour.

Miles.

11. 022

11.054

10. 926

11.093

11. 054

10. 981

Load applied +0.1 

for friction.

Pounds.

0.1

3.3

6.8 

0.1

3.3

6.6

Turns of 

wheel per 

minute.

77.75

38.48

0

77.45

36.36

0

Date.

1883.

July 2

July 2

July 2

July 2

July 2

July 2

Wheel No. 50 was No. 2 with the center of wheel filled in by a cone whose base 

was 24 inches in diameter and whose slant height was 18 inches. Base of cone rested 

against the front of arms of wheel. Cone made of stiff paper, supported by light 

wooden frame.
PERRY.] RESULTS OF ORIGINAL EXPERIMENTS.

WHEELS Nos. 18 TO 22. Results of experiments.

47

No. of 

wheel.

18

18 

18

19

19 

19

20

20 

20

21

21 

21

22

22 

22

Angle of 

weather.

o

25

25 

25

27.5

27.5 

27.5

30

30 

30

32.5

32.5 

32.5

35

35 

35

Velocity 

of wind 

per hour.

Miles. 

8.516

8.485 

8.444

8.471

8.500

8.455

8.464

8.486

8.475

8.478

8.463 

8.400

8.498

8.461 

8.504

Load 

applied 

+ 0.1 for 

friction.

Pounds. 

0.1

1.5 

3

0.1

1.9 

3.3

0.1

1.9 

3.55

0.1

1.9

3.7

0.1

2.1

Q Q

Turns of 

wheel per 

minute.

77. 13

46.20 

0

74 94

39.57 

0

70.78

39.87 

0

67.97

38.72 

0

64.20

31.96 

0

Product 

at maximum.

69.300

75. 185

75. 753

73.568

67. 166

Product of 

No. 2 at 

maximum .

58. 083 

62. 719+

62. 966 

a62.225=

58. 957 

Batio of 

products.

1.193

1.204

1.203

1.182

1.138

Date.

1883. 

Apr. 10

Apr. 10 

Apr. 10

Apr. 12

Apr. 11 

Apr. 11

Apr. 14

Apr. 12 

Apr. 14

Apr. 16

Apr. 16 

Apr. 16

Apr. 17

Apr. 17 

Apr. 17

a The sign = indicates that the number affected needs no correction. 

'I hese wheels differed from each other only in angles of weather. 

WHEELS Nos. 24 TO 28. Results of experiments.

No. of 

wheel.

26

26 

26

24

24

24

25

25 

25

28

28 

28

27

27 

27

Angle 'of 

weather.

25

25 

25

27.5

27.5 

27.5

30

30 

30

32.5

32.5 

32.5

35

35 

35

Velocity 

of wind 

per hour.

Miles. 

8.455

8.434

8 448

8.428

8.426 

8.369

8 ^77

8.450 

8.425

0 JQ7

8. 391 

8.379

8.473

8.401 

8.454

Load 

applied 

+0.1 for 

friction.

Pounds. 

0.1

1.7

t> 9K

0.1

1.9

3.5

0.1

1.9 

3.7

d.i

2.1 

3.9

0.1

2.1 

4.1

Turns of 

wheel per 

minute.

75.38

43.74 

0

72.60

38.87 

0

69.00

38.95 

0

67.07

34.49 

0

63.65

33.74 

0

Product 

at maximum74, 358

73. 853

74.005

72. 429

70.854

Product of 

No. 2 at 

maximum .

a 62. 966+

a 60. 762 

1 61. 902 

c 61. 142 

..........

d 61. 370+

Eatio of 

products.

1.181

1.212

1.196

1.184

1.154

Date.

1883. 

Apr. 9

Apr. 9 

Apr, 9

Apr. 7

Apr. 6 

Apr. 7

Apr. 5

Apr. 6 

Apr. 5

Apr. 4

Apr. 4 

Apr. 4

Apr. 3

Apr. 3 

Apr. 2

a Wind, 8.432 miles per hour. 

& Wind, 8.455 miles per hour.

c Wind, 8.398 miles per hour. 

d Wind, 8.395 miles per hour.
48 EXPERIMENTS WITH WINDMILLS. [NO. 20.

FIG. 16. Elevation and section of -wheel No. 24. (Sail area, 15.000 square feet; efficiency, 0.187).

Wheels Nos. 24 to 28 differed from each other oiily in angles of weather, each 

having 24 plain sails 18 inches long, 7 inches wide at outer ends, and 3 inches wide 

at inner ends. Wheels otherwise the same as No. 6.

Total area of sail surface, 15.000 square feet.
PERRY.] RESULTS OF ORIGINAL EXPERIMENTS.

WHEELS Nos. 29 TO 33. Results of experiments.

49

No. of 

wheel.

33

33 

33

7 29

29 

29

30

30 

30

31

31 

31

32

32 

32

Angle 

of 

weather.

0

25

25 

25

27.5

27.5 

27.5

SO

30 

SO

32.5

32.5 

32.5

35

35

QK

Velocity 

of wind 

per hour.

Miles. 

8.434

8.401 

8.341

8.421

8.406 

8 454

8.348

8.429 

8.399

8.407

8.418 

8.422

8.410

8.454 

8 444

Load 

applied 

+0.1 for 

friction.

Pounds. 

0.1

1.9 

3.5

0.1

1.9 

3.7

0.1

2.1 

4.0

0.1

2.1 

4.1

0.1

2.1 

4.3

Turns of 

wheel per 

minute.

75.46

37.80 

0

73.10

39.10 

0

69.18

35.15 

0

66.73

34.94

0

62.90

33.43 

0

Product 

at maximum.

71. 820

74. 290

73. 815

73. 374

70. 203

Product of 

No. 2 at 

maximum.

a 62. 463 

b 61. 845 

c62. 478+

dQl. 864 

e61. 408+

Ratio of 

products.

1.150

1.201

1.181

1.186

1.143

Date.

1883. 

Mar. 14

Mar. 14 

Mar. 14

Mar. 27

Mar. 27

Mar. 27

Mar. 29

Mar. 28 

Mar. 28

Mar.- 30

Mar. 30 

Mar. 30

Mar. 31

Mar. 31 

Mar. 31

a Wind, 8.403 miles per hour. c"Wind, 8.427 miles per hour. 

6 Wind, 8.410 milea per hour. d Wind, 8.419 miles per hour.

e Wind, 8.440 miles per hour. 

1KB 20 4
50 EXPERIMENTS WITH WINDMILLS. [NO. 20.

FIG. 17. Elevation and section of wheel No. 29. (Sail area, 17.016 square feet; efficiency, 0.185.)

Wheels Nos. 29 to 33 differed from each other only in angles of weather, each having 24 plain sails 18 inches long, 8^ inches wide at outer ends, and 3-39^ inches wide 

at inner ends.

Total area of sail surface, 17.016 square feet. 

Wheels otherwise the same as No. 6.

Dynamometer improved by addition of antifriction wheels and automatic brake 

adjuster, first used March 13, 1883, with wheel No. 33.
PEKEY.] RESULTS OF ORIGINAL EXPERIMENTS.

WHEELS Nos. 19, 20, AND 3i. Results of experiments.

51

No. of 

wheel.

19

19 

19

20

20 

20

34

34 

34

Angle of 

weather.

o

27.5

27.5

27.5

30 .

30 

30

25,35

25, 35 

25,35

Velocity 

of wind 

per hour.

Miles. 

8.471

8.500 

8*. 455

8.464

8.486 

8.475

8.498

8.502 

8.487

Load 

applied 

+0.1 for 

friction.

Pounds. 

0.1

1.9 

3.3

0.1

1.9 

3.55

0.1

1.7 

3.5

Turns of 

 wheel 

per 

minute.

74.94

39.57 

0

70.78

39.87 

0

76.47

43.77 

0

Product 

at maximum.

75. 183

75. 753

74. 409

Product of 

No. 2 at 

maximum.

062.719+

b 62. 966 

061.655+

Ratio 

of products.

1.204

1. 203

1.207

Date.

1883. 

Apr. 12

Apr. 11 

Apr. 11

Apr. 13 

Apr. 14

Apr. 19

Apr. 18 

Apr. 19

a "Wind, 8.499 miles per hour. & Wind, 8.487 miles per hour. c "Wind, 8.501 miles per hour.

Wheels Nos. 19,20, and 34 differed from No. 18 only in angles of weather. 

The sails of No. 34 Avere twisted, making angles of weather 25 degrees at outer 

ends of sails and 35 degrees at inner ends.

WHEELS Nos. 35 TO 38. Results of experiments.

No. of 

wheel.

38

38 

38

36

36 

36

35

35 

35

37

37 

37

Angle of 

weather.

o

22.5

22.5 

22.5

25

25 

25

27.5

27.5 

27.5

30

30 

30

Velocity 

of wind 

per hour.

'Miles. 

8.524

8.488 

8.521

8.525

8.499 

8.413

8.413

8.424 

8.445

8.459

8.477 

8.473

Load 

applied

+ 0.1 for 

friction.

Pounds. 

0.1

1.5

2.9

0.1

1.7 

3.1

0.1

1.7 

3:4

0.1

1.9 

3.6

Turns of 

wheel 

per 

minute.

84.65

52,51 

0

80.67

47.05 

0

76.78

46.64 

0

73.12

40.41 

0

Product 

at maximum.

78.765

79. 985

79. 288

76. 779

Product of 

No. 2 at 

maximum.

a 63. 802=

& 62. 852 

063.726 

d 62. 928

Eat'o of 

products.

'

1.235

1.273

1.244

1.220

Date.

1883. 

Apr. 28

Apr. 28 

Apr. 28

Apr. 26

Apr. 26 

Apr. 26

Apr. 24

Apr. 25 

Apr. 25

Apr. 27

Apr. 27 

Apr. 27

a "Wind, 8.4S8 miles per hour. 

b Wind, 8.500 miles per hour.

c"Wind, 8.425 miles per hour. 

d Wind, 8.478 miles per hour.

Wheels Nos. 35, 36,87, and 38 contained 12 plain sails of lineal dimensions, as shown 

in fig. 19. Each sail made by fastening together 2 sails of No. 18. Wheels otherwise the same as No. 18, and differed from each other only in angles of weather.

Total area of sail surface, 12.937 square feet.
52 EXPERIMENTS WITH WINDMILLS. [NO. 20.

FIG. 18. Elevation and section of wheel No. 35. (Sail area, 12.937 square feet; efficiency, 0.192.)
RESULTS OF ORIGINAL EXPERIMENTS. 53

FIG. 19. Dimensions of sails of wheels. 

Nos. 35, 36, 37, and 38.

WHEELS Nos. 40 TO 43. Results of experiments.

No. of 

wheel.

41

41 

41

40

40 

40

42

42 

42

43

43 

43

Angle of 

weather.

0

25

25 

25

27.5

27.5 

27.5

30

30 

30

25,30

25,30 

25,30

Velocity 

of wind 

per hour.

Miles. 

8.461

8.496 

8.496

8.498

8.459 

8.519

8.491

8.464

8.475

8.528

8.476 

8.495

Load 

applied 

+0.1 for 

friction.

Pounds. 

0.1

1.9 

3.45

0.1

1.9 

3.75

0.1

1.9 

3.9

0.1

1.9 

3.6

Turns of 

wheel 

per 

minute.

84.70

46.81 

0

82.13

45.74 

0

77 Q5

43.15 

0

84.92

45.92 

0

Product 

at maximum.

88. 939

86. 906

81. 985

87. 248

Product of 

No. 2 at 

maximum.

65. 474=

62. 928 

61. 180=

62. 396=

Ratio 

of products.

1.358

1.381

1.339

1.398

Date.

1883. 

May 5

May 5

May 3

May 3 

May 3

May 7

May 7 

May 7

May 8

May 8 

May 8
54 EXPERIMENTS WITH WINDMILLS INO. 20.

Wind for No. 2 the same as for wheel compared in each case. Wheels contained 

12 angular concave sails of lineal dimensions as shown in fig. 21. Each sail made by 

fastening together two sails of No. 18 at an angle of 165 degrees so as to present concave surface to the wind. Wheels differed only in angles of weather. The sails of 

No. 43 were twisted, making the angles of weather 25 degrees at outer ends of sails 

and 30 degrees at inner ends. Total area of sail surface, 12.937 square feet.

FIG. 20. Elevation and section of wheel No. 40. (Sail area, 12.937 square feet; efficiency, 0.213.)
PEEEY.] RESULTS OF ORIGINAL EXPERIMENTS. 55

FIG. 21. Dimensions of concave sails of 

wheels Nos. 40,41,42, and 43.

WHEELS Nos. 40 TO 42. Results of experiments.

No. of 

wheel.

41

41

41

, 41 

41

41

40

40

40 

40 

40

40

42

42

42 

42 

42

42

Angle of 

weather.

o 

25

25

25 

25

25

25

27.5

27.5 

27.5

27.5

27.5

30

Qft

3fr 

30 

30

30

Velocity 

of wind 

per hour.

Miles. 

6.444

10. 963

6.459 

11. 022 

ft 104.

11.111

6.372

10. 890

6.371 

11.041 

R Af\q

10. 944

ft AXJl

10. 974

6.429 

10. 997 

6.411

11. 063

Load 

applied 

+0.1 for 

friction.

Pounds. 

0.1

0.1

1.1 

3.3 

2.0

5.6

0.1

0.1

1.1 

3.3 

2.1

6.3

0.1

0.1

1.2

3.7 

2.3

6.9

Turns of 

wheel per 

minute.

65.33

111. 10

35.07

55.45 

0

0

60.27

106.73

32.90 

56.32 

0

0

59.13

103. 50

29.65 

50.62 

0

0

Product 

at maximum.

38. 577 

182. 985

36. 190 

185. 856

35. 580 

187. 294

Product of

No. 2 at 

maximum.

28. 270= 

a!37. 346+

26. 290= 

135. 498=

26. 037= 

138. 897=

Ratio 

of products.

1.365 

1.332

1.377 

1.372

1.367 

1.348

Date.

1883. 

May 24

May L'9

May 24 

May 29 

May 24

May 29

May 14

May 21

May 14 

May 17 

May 14

May 21

May 23

May 23

May 23 

May 22 

May 23

May 22

a "Wind, 11.021 miles per hour.
56 EXPERIMENTS WITH WINDMILLS. [NO. 20.

FIG. 22. Elevation and section of wheel No. 39. (Sail area, 13.072 square feet; efficiency, 0.164.)
PERRY.] RESULTS OF ORIGINAL EXPERIMENTS. 57

WHEELS Nos. 35, 39, 40, AND 44. Results of experiments.

No. of

wheel.

35

35

35

39

39 

39

40

40 

40

44

44 

44

Anglo of 

weather.

o

27.5

27.5 

27.5

27.5

27.5 

27.5

27.5

27.5 

27.5

25,30

25,30 

25,30

Velocity 

of wind 

per hour.

Miles. 

8.413

8.424 

8.445

8.472

8.512 

8.431

8.498

8.459 

8.519

8.482

8.477 

8.475

Load 

applied 

+0.1 for 

friction.

Pounds. 

0.1

1.7 

3.4

0.1

1.9 

*3.7

0.1

1.9 

3.75

0.1

1.9 

3.6

Turns of 

wheel 

per 

minute.

76.78

46.64 

0

64 V>

35.57 o'

82.13

45.74 

0

84.88

44.35 

0

Product 

at maximum.

79. 288

67. 583

86.906

84. 265

Product of

No. 2 at 

maximum.

a&6. 726 

63.650=

62. 928=

60. 952=

Ratio 

of prodiicta.

1.244

1.062

1.381

1.382

Date.

1883. 

Apr. 24

Apr. 25 

Apr. 25

May 1

May 1

May 3

May 3 

May 3

May 9

May 9 

May 9

«"Wind, 8.425 miles per hour.

Wheel No. 39 contained 12 sails of lineal dimensions as shown in fig. 23, made by 

adding to the sails of No. 35, along their rear edges, strips as illustrated, so as to 

present concave surface to the wind, ttnt the line ab was considered the face of the 

sail as regards angle of weather. For No. 40 see previous description. Sails angular concave.

Wheel No. 44 was the same as No. 3 except that the angles of weather were 25 

degrees at outer ends of sails and 30 degrees at inner ends. Sails circular concave.

t-lct

FIQ. 23. Dimensions of sails of wheel No. 39.
58 EXPERIMENTS WITH WINDMILLS. [HO. 20.

. 24. Elevation and section of wheel No. 44. (Sail area, 13.590 square feet; efficiency, 0.213.)
PERKY.] RESULTS OF ORIGINAL EXPERIMENTS. 

WHEELS Nos. 45 TO 49. Results of experiments.

59

No. of 

wheel.

46

46 

46

45

45 

45

47

47

47

4«

48 

48

49

49 

49

Angle 

of 

weather, a

17. 5 at ah

20 at cd 

25 at ef

27. 5 at git, 

20 at ab

22. 5 at cd 

27. 5 at ef

30 at gh 

22.5ata&

25 at cd 

30 at ef

32. 5 at gh 

25 ata&

27. 5 at cd 

32. 5 at ef

35 at gh

f 27. 5 at ab

1 30 at cd 

35 at ef

37. 5 at gh

Velocity 

of wind 

per hour.

Miles. 

11. 025

10. 979 

10. 905

10. 918

11. 001 

11. 021

11. 026

10. 980 

10.944

11. 125

10.935 

11. 014

11. 187

10. 994 

10. 993

Load 

applied 

+0 1 for 

friction.

Pounds. 

0.1

2.7

4.8

V

0.1

2.9 

5.2

0.1

3.3 

6.0

0.1

3.7 

6.5

0.1

3.9 

6.6

Turns of 

wheel 

per 

minute.

160.90

85.19 

0

156. 63

79.99 

0

148. 68

73.31 

0

141. 97

66.79 

0

136. 30

58.82 

0

Product 

at 

maximum.

230. 013

231. 971

241. 923

247. 123

229. 398

Product of 

No. 2 at 

maximum.

6135. 201 

c!29. 195+

132. 264=

132. 033=,

127.116=

Ratio 

of products.

1.701

1.796

1.829

1.872

1.805

Date.

1883. 

June 25

June 25

June 21

June 20 

June 21

June 27

June 26 

June 27

June 27

June 28 

June 28

June 29

June 29 

July 2

a Letters in this column refer to flg. 26, p. 61. 

b Wind, 10.980 miles per hour.

e Wind, 11.000 miles per hour.

1.09 =- = # = ratio of velocity of wind to velocity 'of outer extremities of sails 

of No. 48 for maximum work. See page 71.
60 EXPERIMENTS WITH WINDMILLS. [NO. 20.

FIG. 25. Elevation and section of wheel No. 48. (Sail area, 14.159 square feet; efficiency, 0.283.)

Wheels Nos. 45 to 49 differed from each other only in angles of weather, and contained six sails of lineal dimensions as shown in fig. 26. Sails were made by gluing 

together several layers of paper which formed pasteboard about one-sixteenth of 

an inch thick. The backs of front and rear edges of each sail were bordered by thin 

pine strips. Backs of outer edges of sails were likewise bordered and held in shape 

by stiff curved pine pieces. The inner end of each sail was fastened securely to a 

thick curved pine piece, which was bolted against the outer end of a short ash arm, 

so that the sail conld be turned on the bolt and set at any desired angle of weather. 

Thus the arms did not extend beyond the inner ends of the sails. The outer corners of each sail were held in position by two fine brass wires extending to the front 

inner corner of the succeeding sail. The front and rear edges also curved somewhat, so that the sails presented double concave surfaces to the wind. In constructing these wheels we aimed at avoiding all unnecessary obstruction to the passage of 

wind between the sails.
PERRY.] JKE8ULTS OF OKIGINAL EXPERIMENTS. 61

PIG. 26. Dimensions of sails of wheels Nos. 45 to 49. 

WHEELS Nos.2, 60, AND 61. Eesults of experiments.

No. of

wheel.

60

-61

2

Velocity 

of wind 

per hour.

Miles.

8.451

8.452

8.452

Load 

applied 

-4-Otl for 

friction.

Pounds.

1.9

1.9

1.9

Turns of 

wheel 

per 

minute.

56.50

38.13

30.67

Product at 

maximum.

107. 350

a 72. 447

58. 273

Product 

of No. 2 at 

maximum.

58. 273 

58. 273=

58. 273=

Ratio of 

products.

1.842

1.243

1.000

Date.

1883.

Sept. 15

Sept. 15

Sept. 15

a This product may not have been a maximum, as only the one load, 1.9 pounds, was tried with 

No. 61.

Wheel No. 60 was the same as No. 48, except that the sails were considerably 

warped out of original shape from long standing and drying.

Wheel No. 61 was the same as No. 60, excgpt that along the back of each sail a
62 EXPERIMENTS WITH WINDMILLS. [NO. 20.

rectangular piece of pine 1 by 1£ by 17 inches was fastened to make an obstruction 

representing an extension of the arm, as illustrated in figs. 28 and 29.

The relative efficiency of No. 60 as compared with No. 61 is indicated by the 

equation

107.350

72.447 = 1.482

Fm. 27. Elevation and section of wheel No. 60. (Sail area, 14.159 square feet; efficiency, 0.284.)
PEBET.J RESULTS OF ORIGINAL EXPERIMENTS.

FIG. 28. Elevation and section of wheel No. 61. (Sail area, 14.159 square feet; efficiency, 0.191.)
64 EXPERIMENTS WITH WINDMILLS. [NO. 20.

FIG. 29. Dimensions of sails of 

wheel No. 61 with obstruction 

on back.

WHEELS Nos. 2, 49, AND 53 TO 57. Results of experiments.

No of 

wheel.

54

53

55

2

2

56

57

49

Angle of 

deflector.

0

30

45

60

50

" 50

Velocity 

of wind 

per hour.

Miles.

10. 989

11. 156

10. 985

11. 007

10. 975

10.968

11. 054

11. 032

Loads 

applied 

+ 0.1 for 

friction.

Pounds.

0.1

0.1

0.1

0.1

3.3

3.3

3.5

3.5

Turns of 

wheel per 

minute.

79.40

81.80

80.52

77.57

37.83

40.63

62.63

64.22

Date.

1883.

July 3

July 3

July 3

July 3

July 5

July 5

July 5

July 5

Wheels Nos. 53, 54, 55, and 56 were the No. 2 wheel, with stationary rectangular 

board, i by 9f| by 22 inches, placed in front of sails and with its face set at various 

angles with plane of wheel, as indicated in table, to act as deflector. Board supported by arm outside of wheel on side farthest from axis of sweep; its lower edge 

at height of axis of wheel, horizontal, and parallel to plane of wheel. Inner end of 

board 9 inches from axis of wheel prolonged.

Wheel No. 57 was wheel No. 49, with the same board, described above, similarly 

used as deflector, except that its lower edge was placed so as to clear the forward 

edges of sails by about 2 inches at each end.

In the case of Nos. 53 to 56 the center of board deflector was about 7 inches from 

center of sails.
PEBBY.] BEST ANGLE OF WEATHER.

WHEELS Nos. 2, 49, 51, 52, 58, AND 59. Results of experiments.

65

No. of 

wheel.

2

51

52

49

58

59

Position 

of 

obstruction.

Before . .

Behind. .

Before . .

Behind..

Velocity of 

wind 

per hour.

Miles.

11 141

11. 130

11. 045

10. 966

10. 972

10. 972

Load applied 

+0.1 for 

friction.

Pounds.

0.1

0.1

0.1

3.5

3.5

3.5

Turns of 

wheel 

per 

minute.

78.58

75.73

76.16

64.53

55.54

60.06

Date.

1883.

JulyS

July 3

July 3

July 5

July 5

July 5

Wheel No. 51 was No. 2, with"rectangular board J by 9^f by 22 inches placed horizontally in front of the side of wheel farthest from axis of sweep, its face parallel to 

plane of wheel so as to act as obstruction to wind. Board held at its outer end by 

means of an arm outside of wheel.

Distance from board to centers of sails, 8 inches.

Distance from inner end of board to axis of wheel prolonged, 9 inches.

Wheel No. 52 was the same as No. 51, except that the board was placed 8 inches 

behind centers of sails.

Wheel No. 58 was No. 49, with obstrution board above described similarly placed, 

8J inches in front of centers of sails.

Wheel No. 59 was the same as No. 58, except that the" board was placed 8J inches 

behind centers of sails.

SAILS AT BEST ANGLES OF WEATHEB. 

Efficiency of various wind wheels at best angles of weather.

1

o 

o

^

1

2

10

19

34

24

29

35

36

44

40

43

48

(H

3

It

8

^

Sq. ft.

9.190

18. 380

10. 688

12. 937

12. 937

15. 000

17. 016

12. 937

12. 937

13. 590

12. 937

12. 937

14. 159{

"S

15"-l

O

01s>

ua

<l

o

35

35

27.5

27.5

25,35

27.5

27.5

27.5

25

25,30

27.5

25,30

25, 27. 5 

32. 5, 35

§

a 

Ift

I

s. l>

Miles.

8.452

8.403

8.338

8.500

8.502

8.426

8.406

8.424

8.499

8.477

8.459

8.476

}lO. 935

Is

0

=1

01 a 

a 0

&

60.0

59.0

72.0

75.5

76.5

72.7

73.0

77.0

80.0

85.0

81.5

84.5

141.0

01

o

£

Ma ' G

Si

Lbs.

4.1

3.2

3.4

3.4

3.6

3.3

3.0

3.5

3.6

3.5

6.1

1

a

a

=3 s

O

^

Lbs.

1.6

1.9

1.7

1.9

1.7

1.9

1.9

1.7

1.7

1.9

1.9

1.9

3.7

 3 

as .

*,! o H

§a Sis 3 <*

H

31.69

32. 875

39.33

39.57

43.77

38.87

39.10

46.64

47.05

44.35

45.74

45.92

66.79

i

a

*t

 sa

s

£

50. 704

62. 463

66. 861

75. 183

74. 409

73. 853

74. 290

79. 288

79. 988

84. 265

86. 906

87. 248

247. 123

ii*-H

-^ s

§a 

1*CM

62. 463

1

a

4-1

o 

_o"S

M

1.000

62. 719

61. 655

60. 762

61. 845

63. 726

62.852

60. 953

62. 928

62. 396

132. 033

1.204

1.207

1.212

1.201

1.244

1.273

1.382

1.381

1.398

1.872

|1

in 43 as

rj O 0

>

0.0544

.0931

.0938

.0808

.0706

.0962

.0984

.1017

.1067

.1081

.1322

il

\%A ^ si

a^=2 S o o

K

30 B60 l]a

24S

24 Q

24$

240

24 M

wffl

12/B

12 2i

12 to

1203

I

1KB 20-
66 EXPERIMENTS WITH WINDMILLS. [NO. 20.

The velocities of wind given in this table are strictly correct only for products at 

maximum, though they are very nearly correct also for products of No. 2 at maximum. The velocities of wind are 'only approximately correct for turns of wheels 

unloaded and for starting forces. Nothing was added to starting forces for friction, 

and the 0.1 pound was added to starting forces in preceding tables only for convenience. 1 For further particulars consult preceding tables.

RELATIONS OF THREE DIFFERENT VELOCITIES OF WIND.

Relation of different velocities of wind to ^maximum products.

Angle 

of 

weather.

o

35

27.5

25

30

No. of 

wheel.

{ l

( 2

f 40

I 40

[ 40

f 41

41 

1 41

f 42 i S

"Wind per hour.

a

Miles.

6.371

8.459

6.371

6.371

8.459

6.371

6.459

8.496 

6.459

6.429 

8.464 

6.429

b

Miles.

8.459

11. 041

11. 041

8.45.9

11. 041

11. 041

8.496

11. 022 

11. 022

8.464 

10. 997 

10.997

Product at maximum.

A

26.290

62. 928

26. 290

36. 190

86. 906

36. 190

38. 577

88. 939

38. 577

35. 580 

81. 985 

35. 580

B

62. 928

135. 498

135. 498

86. 906

185. 856

185. 856

88. 939

182. 985 

182. 985

81.985 

187. 294 

187. 294

b 

a,

1.328 

1. 305+

1.733

1. 328 

1.305+

1.733

1. 315+

1. 297+ 

1. 706+

1. 317+ 

1.299+ 

1. 707+

(-)3 

Va /

2.342

2.223

5.199

2.342

2.223

5.199

2.274+

2.182 

4. 965+

2. 284+ 

2.192 

4.974

B

A

2.394

2.153

5.154

2.401

2.139

5.135

2.306

2. 057+ 

4.743

2. 304+ 

2. 284+ 

5.264

A \aJ

+0.052

 .070

 .045

+ .059

 .084

 .064

+ .032

 .125

 .222

+ .020 

+ .092 

+ .290

-(I)'

61. 571

139. 889

136. 682

84.757

193. 192

188. 152

87.724

194. 065 

191. 535

81. 265 

179. 711 

176. 975

Conclusion. Maximum products vary as the cubes of the velocities of wind. Some 

allowance must be made for the differences in time and condition of air under which 

the various products were obtained; considering these differences, there is no unaccountable variation from the law of cubes.

Relation of different velocities of wind to starting forces.

Angle 

of 

weather.

o

35

27.5

25

30

No. of 

wheel.

1 2

2

I 2

f 40

4 40

[ 40

1 ^

1 41

I 41

f 42

1 42

I 42

"Wind per hour.

a

Miles.

6.380

8.405

6.380

6.403

8.519

6.403

6.404

8.496'

6.404

6.411

8.475

6.411

b

Miles.

8.405

10. 989

10. 989

8.519

10. 944

10. 944

8.496

11. Ill

11. Ill

8.475

11. 063

11. 063

Starting forces.

A

Pounds.

2; 3

4.1

2.3

2.0

3.65

2.0

1.9

3.35

1.9

2.2

3.8

2.2

B

Pounds.

4.1

7.0

7.0

3.65

6.2

6.2

3.35

5.5

5.5

3.8

6.8

6.8

b 

a

1. 319 

1.307

1.722

1.330

1.285

1.709

1. 327 

1. 308 

1.735

1.322

1. 305 

1.725

CSf

1.740

1.708

2.965

1.769 

1.651

2. 921 

1.761

1. 711 

3.010

1.748

1.703

2. 976 

S

A

1.783

1.704

3.043

1.825

1.699

3.100

1.763

1.642

2.895

1.727

1.789

3.091

Conclusion. Starting forces vary as the squares of the velocities of wind.

1 See starting forces, " S," p. 25.
PEBBY.] AUTOMATIC BRAKE ADJUSTER.

Belation of different velocities of wind to speed of unloaded ivheels.

67

Angle of 

weather.

0

35

27i

25

30

Nos. of 

wheels.

2

2

2

40

40

40

41

41

41

42

42

42

"Wind per hour.

a

Miles.

6.437

8.511

6.437

6.372

8.498

6.372

6.444

8.461

6.444

6.454

8.491

6.454

6

Miles.

8.511

10. 996

10. 996

8.498

10. 890

10. 890

8.461

10. 963

10.963

8.491

10. 974

10. 974

Turns unloaded.

A

43.78

59.62

43.78

60.27

82.13

60.27

1 65. 33

84.70

1 65. 33

59.13

77.95

59.13

B

59.62

78.68

78.68

82.13

106.73

106. 73

84.70

111. 10

111. 10

77.95

103. 50

103. 50

b

a

1.322

1.292

1.708

1.334

1.281

1.709

1.313

1.296

1.701

1.316

1.292

1.700

B

A

1.362

1.320

1.797

1.363

1.300

1.771

1.296

1.312

1.701

1.318

1.328

1.750

1 Too great because of outside wind and perhaps other causes.

Conclusion, Speeds of unloaded wheels increase in somewhat greater ratio than 

the velocities of wind.

All wind wheels tested were 5 feet in external diameter, and all sails were 18 

inches long except in the case of Nos. 46 to 49 and Nos. 60 and 61, in which wheels 

the sails were 19 inches long, 1 inch being added for support at inner ends.

AUTOMATIC BRAKE ADJUSTER.

On March 13,1883, the dynamometer was improved by the addition 

of an automatic brake adjuster. Previous to this date the brake was 

adjusted as described on page 23 through regulating the tension of 

the adjusting cord by sliding a weight in and out 011 a lever attached 

to the cord.

This method required time and patience in order to get an exact 

balance between the load applied and the friction of brake, and it was 

also necessary to exercise judgment in determining when the balance was 

exactly even. Furthermore, an exact balance was not always retained 

during a test of one minute, as required for accuracy, and frequent 

readjustments were constantly necessary. The labor involved in adjusting and maintaining a proper balance of friction and load became very 

tiresome when kept up for from six to eight hours continuously, as was 

frequently the case; and weariness was detrimental to the perceptions 

as well as to the judgment. Therefore, an automatic adjuster became 

very desirable, both for relief to the mind and for the increase of 

accuracy.

The automatic brake adjuster, after various attempts and failures, 

was finally constructed as follows: The brake and adjusting cord were
68 EXPEEIMENTS WITH WINDMILLS. [NO.20.

left substantially as previously described on page 23; but one end 

of a short rod three-sixteenths inch in diameter was attached to the 

cord where it was brought back from the brake in a direction parallel 

to the axis of the shaft. The other end of this rod had a full thread, 

32 to the inch, and a nut which was fastened to a wooden wheel .A, 6J 

inches in diameter. This wheel was supported on a hollow tube through 

which the rod passed, and against the outer end of which the nut rested. 

The nut communicated tension to the adjusting cord, which was tightened by revolving the wheel A in one direction and loosened by turning the wheel in the opposite direction. This wheel A was driven by 

a small wheel U, 1£ inches in diameter, fastened to a large wheel (7, 5 

inches in diameter. This wheel C was driven by another small wheel 

D, 1-&- inches in diameter, fastened to a large wheel J57, 4 inches in 

diameter, the periphery of which was constantly in contact with another 

wheel F of the same dimensions. The wheels E and F were supported 

by a tilting frame which oscillated on a supporting rod passing through 

the centers of the wheels B and 0, but not touching them. The wheels 

E and F hung in close proximity to the rear end of wind wheel shaft, 1^- 

inches in diameter, so that a slight movement of the tilting frame would 

bring either of the wheels E or F in contact with the shaft; and if 

wheel E came in contact with the shaft while revolving, the adjusting 

cord would be drawn tighter, and if wheel F came in contact .with the 

shaft, the tension of the cord would be relaxed. The tilting frame was 

connected with the brake and partook of its oscillating motion, so that 

if the friction of the brake was too small to lift the load applied, wheel 

E would be in contact with the shaft and would cause an increase in 

the friction of the brake until the load was lifted and contact between 

wheel E and the shaft broken. If the friction of the brake was too 

great, the load applied was raised until wheel F came in contact with 

the shaft so as to cause a diminution of friction until contact of wheel 

F with the shaft was broken. It was very easy to tell at any time if 

friction of brake was too little or too great, by simply watching the 

direction of movement of wheels E and F. This did not require the 

exercise of judgment, as errors of balance were greatly magnified to 

the eye and made self-correcting. All contacts between the various 

wheels, J., -B, (7, D, J57, .F, and shaft were frictional. Wheels B, (7, were 

entirely supported by contact of peripheries with wheels A and D, and 

wheel E was so hung to a separately hinged support that its own weight 

produced a uniform pressure against wheel F. The entire automatic 

system was supported independently of the brake; the connection with 

the brake served only to give the necessary oscillatory movement to 

the tilting frame, which was also balanced both as regards the action 

of gravity and centrifugal force when the sweep was in motion.

Some power of the wheel was necessarily consumed by the automatic adjuster, but it may be ascertained, from the description and 

dimensions given, that a point in the wind wheel 1 foot from the center
ACTION OF WIND ON SAILB. 69

of shaft would move in tightening the adjusting cord about 67,019 

times as far as the threaded rod attached to the cord; from this it 

follows that the pressure of the brake against the cylinder was 67,019 x 

16 = 1,072,304 times as great as the force required at 1 foot from the 

center of shaft to produce the pressure, without considering the friction 

of the automatic system. And if we make the very liberal allowance 

of one-third additional force required to overcome the friction of the 

automatic system and call the friction of brake 0.05 of pressure, remembering that the diameter of cylinder was 5£ inches, we may readily find 

that the force required to produce friction of brake equal to any load 

would be only about TsieT Part of that load at the same distance from 

center of shaft. Hence, it will be seen that the power consumed by 

the automatic brake adjuster was too minute materially to affect products and called for no correction.

THEORY OF THE ACTION OF THE WIND UPON THE SAILS OF WINDMILLS.

Where a fluid moves along in a current, the direct force of the current is expressed in pounds by the formula MV, in which v represents 

the velocity of flow in feet per second and M is the mass of fluid which

W flows per second past a fixed point. M= , W representing weight in

y

pounds of fluid passing the fixed point per second, and g = 32.2, the 

constant for gravity. 1

Where a current acts against a surface and its direction is simply 

changed by the surface without impeding its velocity, a direct pressure = Mv is exerted by the impinging current in the direction of its 

motion, and an equal pressure is exerted by the current as it escapes 

from the surface, = MV, in a direction opposite to the direction of 

escape.

If the current impinges against a surface which is itself in motion, 

the relative velocities of the impinging and escaping currents must be 

considered in determining the forces which act upon the moving surface. Of the two equal forces due to impingement and escape of current the sum of those components acting in the direction of motion of 

the surface constitutes the useful effort designated by P, and if the 

velocity per second of motion of surface is called u, the useful work 

yielded per second by the current will be represented by Pu. The

MV* Wv2 

actual energy of the current is represented 2 by ~2~=~2a~' The ratio

of useful work to actual energy is termed efficiency, and is represented 3 by the symbol 1 fc=

In deducing formulae to represent the action of wind upon the sails 

of windmills we have proceeded upon the assumption that the sail

1 See Rankine's Steam Engine, articles 14 and 144, Case III.

2 See Rankine's Steam Engine, article 31.

3 See Rankine's Steam Engine, article 92.
70 EXPERIMENTS WITH WINDMILLS. [NO. 20.

should be of such form as most effectually to change the air current 

into a direction as nearly as possible opposite to the direction of the 

sail's motion. We have also assumed, in accordance with principles 

stated by Rankine concerning the action of water on vanes, that the 

receiving edge of the sail should be tangent to the relative direction of 

the impinging current. These conditions are represented in fig. 30, in 

which DE = v = direction and velocity of wind, AE = u = direction 

and velocity of sail, and a = angle DEA, which the direction of wind 

makes with direction of motion of sail.

Then, DA = relative direction and velocity of current with reference 

to sail AB.

Let BG AD = relative direction and velocity of current as it 

escapes from the sail.

ft = angle BGF which relative direction of escaping current makes 

with direction of sail's motion.

Then

DC=v sin a.

AG=u vcosct.

AD= vV3 sin2 a+(u v cos a-)2.

G F= GB cos ft=AD cosyg. ____ _____

GF = cos ft Vv2 sin2 a+u2 2 uv cos a+v2 cos2 a.

GF= cos ft Vv2+u2 2uv cos a.

If Q= volume in cubic foot of air acting on sail in 1 second, and d = 

weight in pounds of 1 cubic foot of air, we have for useful effort

P= [cos fiVu2+v2 2uv cos a u+v cos a].

FIG. 30. Action of wind on a sail.

The expression for useful work becomes

Pu -L [u cos ft Vu2+v2 2 uv cos a u?+ uv cos a}. (A)

Dividing by = _ we have for efficiency 2 Zg
ACTION OF WIND ON SAILS. 71

Or letting -= 

v

l-lc=2x cos ft Vl+xz 2x cos «~2«2+2« cos a. (B)

By substituting cos y for cos ft in formula (A) the expression for 

Pu becomes the same as formula (6) on page 165 of Kankine's Steam 

Engine.

To find an expression for x corresponding to maximum efficiency, for 

general values of a and /3 would, as Eankine remarks, be more trouble 

than it is worth. But in the case of the windmill we know that 

a=90°, which makes cos o-=0. Hence, formula (B) becomes

2#2. (C)

The relation between x and ft corresponding to maximum and minimum efficiency will be expressed by the formula

From this it appears that if /?=0, as it should for maximum efficiency, 

x becomes infinite. That is, the theoretical efficiency of the windmill 

becomes greater as the speed of the sails increases indefinitely.

If /?=0 formula (0) shows that

For a?=l, l-fc=.828; for x=2, 1 fc=.944; 

For a?=3, 1 fc=.973; for a? =10, 1 fc=.0974;

or almost perfect efficiency when the speed of the sails is 10 times the 

velocity of the wind. Perfect efficiency, however, could not be reached 

unless #=oo .

Of course the formula does not take into account the retarding effect 

of friction, resistance of medium, and other causes which make it 

impossible to realize in practice anything like the efficiency indicated 

by the formula; and in practice ft can never equal 0 as it should for 

perfect efficiency.

Letting x=l and assigning more probable values to /?, formula (G) 

gives

For/3=10°, l-fc=.785.

For /5=20°, l-fc=.657.

For /5=30°, 1 fc=.449.

Theoretically the analysis of the action of wind on the sails of a windmill corresponds to the analysis of the action of water on a reaction 

wheel or turbine without guide blades.1 In the windmill, as commonly 

made, angle a in our formula (B) is necessarily 90°; but the formula 

suggests guide blades or deflectors corresponding to those of parallel1 See Rankine's Steam Engine, pp. 197 and 206.
72 EXPERIMENTS WITH WINDMILLS. [NO. 20.

flow turbine water wheels. For if we give to x and ft any probable finite 

values, we may find the values of angle a corresponding to maximum 

efficiency from the formula,

cos a = % (x +- x cos 2/3) (E) $/

in which 

For x = 3 and ft = 10°, a = 77° 46'; 

For x = 2 and ft = 10°, a = 73° 44'; 

For x = 3 and ft = 20°, or = 70° 00'; 

For x = 2 and ft = 20°, a = 68° 28'; 

For x = I and /3 = 20°, a 56° 03'.

These assumptions for x and ft are plausible, as x varies greatly 

between the outer and inner extremities of a sail, and ft should be 

assumed as the average angle of escape of the whole cylinder of air 

intercepted by the wheel, and not as the angle merely of that portion 

of air which comes immediately in contact with the sails, or which the 

sails directly intercept.

It is to be noticed that formula (B) does not take into account as such 

the angle of weather, which seems to be incidental to practice but not 

to theory.

As we have already pointed out, our formula (A) is substantially the 

same as Eankine's general formula for the action of water on vanes. 

But Eankine. instead of applying his general formula to windmills, 

breaks entirely away from it, and uses another formula specially deduced 

for the "case of a flat vane oblique to the jet," and which he calls the 

"easiest method of solution."1 But that his." easiest method" is erroneous even in the case specified, is evidenced by the fact that a very 

different result is obtained by the application of his general formula.

We pointed out the nature of Eankine's error in a paper dated 

December, 1881, which was submitted to Prof. E. H. Thurston, of 

Stevens Institute of Technology. Other writers on windmills have 

made the same mistake. The theory and formula which we have here 

given are abstracted from a paper also prepared for Professor Thurston, 

dated March 6, 1882.

Theoretical considerations were kept in view during our dynamometric experiments. It will be seen from the preceding tables of experiments how closely the results obtained in practice correspond to theory.

DISCUSSION'OF RESULTS.

THERMOMETRIC AND BAROMETRIC INFLUENCES.

The preceding pages are substantially an unchanged reproduction 

of the records made by the writer for the United States Wind Engine 

and Pump Company of Batavia, Illinois, during and immediately after 

the experiments in 1883. The only alteration we have presumed to

1 See Kankiae's Steam Engine, pp. 169 and 215.
PERBY.] EXTREME VARIATION. 73

make is in omiting«the records of barometric readings which were made 

during the earlier experiments. No barometric readings were taken 

or recorded after December 21, 1882.

CONSTRUCTION OF TABLES.

In tables on pages 28 to 46 results are recorded for a greater or less 

number of loads increasing usually by increments of two-tenths pound. 

Although the results are always given in the order of increasing loads, 

they were not' always obtained in that order, as is indicated by the 

marginal dates at the right-hand side of some of the tables. Enough 

tables were prepared in this manner to show how in general the speeds 

of revolution decreased as the loads increased, and how the products 

increased with the increasing loads up to a certain point, which marks 

the maximum, and then decreased continually with further increments 

of load until the vanishing point was reached. It was not necessary to 

try many different loads in order to find the best load corresponding 

to the maximum product. This could be ascertained by a few trials, 

and as our main object was to get at the relative merits of the wheels 

tested, we subsequently abandoned the practice of trying so many 

different loads, and confined our attention more strictly to the determination of maximum products, starting forces, and unloaded speeds; 

so that the remaining tables on pages 47 to 65 show in general only 

these three results for each wheel and comparisons of results with 

different wheels. Special explanations relative to special tables are 

given elsewhere.

EXTREME RESULTS.

In addition to the original tables already presented, we have collected 

together in the following table the maximum products given by wind 

wheel No. 2 at the various dates it was tested in connection with other 

wheels. It may be observed that the lowest maximum product was 

58.083, recorded on April 10, 1883, and that the highest product for 

wind of nearly the same velocity was 65.474, recorded on May 5, 1883. 

The products for the same wheel thus vary nearly 13 per cent on different 

days. Taking the temperature and barometric pressure of Chicago on 

the two days above mentioned as approximately the same as at Batavia, 

35 miles distant due west, we are able to account for but little more 

than 2 per cent of the variation. Kotice also that in wind of about 11 

miles per hour, the lowest maximum product was 124.839, recorded on 

July 5, 1883, and that the highest product was 138.897, recorded on 

May 22,1883. Here a variation of over 11 per cent appears for the 

same wheel on different days. In this case the difference in temperature and barometric pressure at Chicago might account for a little more 

than 8 per cent of the variation.
74 EXPERIMENTS WITH WINDMILLS.

Maximum product of wheel No. $ at different dates.

[NO. 20.

Velocity of 

wind 

per hour.

Miles.

8.485

8.499

8.487

8.463

8.461

8.432

8.432

8.455

8.398

8.395

8.403

8.410

8.427

8.419

8.446

8.501

8.488

8.500

8.425

Product 

at maximum.

58. 083 

62. 719+

62.966 '

62. 225

58. 957 

62. 966+

60. 762

61. 902 

' 61. 142

61. 370+

62. 463 

61. 845 

62. 478+

61. 864 

61. 408+

61. 655+

63. 802

62. 852 

63. 726 

Date.

1883.

Apr. 10

Apr. 11

Apr. 12

Apr. 16

Apr. 17

Apr. 9

Apr. 6

Apr. 6

Apr. 4

Apr. 3

Mar. 14

Mar. 27

Mar. 28

Mar. 30

Mar. 31

Apr. 18

Apr. 28

Apr. 26

Apr. 25

Velocity of 

wind 

per hour.

Miles.

8.478

8.496

8.459

8.464

8.476

8.512

8.477

8.452

11. 041

11. 054

11. 021

10. 997

10. 980

11.000

10. 980

10. 935

10. 994

10. 975

Product 

at maximum.

62. 928 

65. 474=

62. 928=

61. 180=

62. 396=

63. 650=

60. 952

58. 273

135. 498

126,984

137. 346

138. 897

135. 201

129. 195

132. 264

132. 033

127. 116

124. 839

Date.

1883.

Apr. 27

May 5

May 3

May 7

May 8

May 1

May 9

Sept. 15

May 17

July 2

May 29

May 22

June 25

June 20

June 26

June 28

June 29

 July 5

INFLUENCE OP OUTSIDE WIND.

Experiments were conducted in a closed room to insure the exclusion 

of all natural wind. The exclusion of wind from the inclosed space, 

however, was not perfect. The wind circling around the outside of the 

building undoubtedly at times caused a slight circulation of air inside, 

which may have been more potent in causing variations in results than 

either thermometric or barometric influences. The windows were 

always kept carefully closed during experiments, and the doors also 

were guarded as much as possible. The doors, however, were necessarily used, and we distinctly remember being obliged to discard many 

measurements on account of doors being opened during tests on windy 

days. But unless a door was opened during a test we considered that' 

errors from influence of outside wind were sufficiently guarded against 

by our practice of comparing all results with those obtained with 

wheel No. 2, under like conditions, as explained in the original records.

STANDARD OF COMPARISON.

As stated in the original record, wheel No. 2, which we always used 

as a standard for comparison, was modeled after the Halliday 10-foot 

wind wheel; that is to say, the slats, arms, etc., were the same in number
PBEET.] CORRECTIONS FOR AXLE FRICTION. 75

and of the same relative dimensions on a scale of one-half. There was, 

however, this difference, that the Halliday was what is called a section 

wheel, having pivoted sections for the purpose of regulation. Wheel 

No. 2 had all its parts rigidly fixed with reference to each other, and 

therefore was more like the solid wheels in common use at the time. 

The solid wheels were really copies of the Halliday, so far as the sails 

or slats and the arms were concerned. The only essential difference 

between section and solid wind wheels related to the method of stopping and governing their motion. Different makers of both styles of 

wheels had their own notions about angles of weather and proportions 

of sail surface. The Halliday 10-foot wheel had its slats set at an angle 

of 35° with the plane of motion. The slats were as thin as was consistent with safety, considering that their material was wood, and they 

were trimmed to a sharp edge, so as to cut the air as much as possible.

Nearly all wind wheels in use at the time of our experiments in 

1882-83 were made with narrow wooden slats, similar in general appearance to our wheel No. 2. Some makers adopted greater angles of 

weather than 35 degrees, and even let the sails overlap so as to boast of 

greater sail area for their wheels as a basis for claiming greater power. 

A 45-degree angle of weather was not uncommon, and the slats were 

often made thicker than those of the Halliday wheel; besides, they were 

not always trimmed to an edge in front.

In adopting as our standard of comparison a wheel modeled after 

the 10-foot Halliday, we believe that we made use of the best model 

available to represent wind wheels in general as then constructed.

CORRECTIONS FOR AXLE FRICTION.

in the earlier tables 0.3 pound was added to all applied loads. This 

0.3 pound was arrived at as explained after the table on page 38, and 

was in reality an estimate of frictional resistance to starting, or to 

slow motion. As authorities stated that friction was the same at all 

velocities, we adopted 0.3 pound as approximately representing the 

frictional resistance of the journals without regard to speed. We afterwards learned that the axial friction diminished greatly with increase of 

speed of revolution, as is made evident by comparing the speeds bf the 

same wheels after starting friction was greatly reduced with the speeds 

before reduction of friction under the same applied loads and also 

unloaded. (See original records after table on page 38.)

Wheels Nos. 2,18, and 19, especially, may be compared. Subtract 

0.3 from loads in the tables giving average results for wheels Nos. 2, 

18, and 19, on pages 29, 43, and 44, and subtract 0.1 in tables on pages 

27 and 47 to obtain applied loads. Evidently there is very little difference between the axial frictions in the two cases for unloaded wheels.

We can not now, after a lapse of more than fifteen years, undertake 

to assert what the axial friction previous to March 13, 1883, should 

have been called for different speeds. But if in the table on page 29 we
76 EXPERIMENTS WITH WINDMILLS. [NO. 20.

call friction 0.15 pound, we shall find the maximum product to be 

61.846 instead of 66.860, as there recorded. And as this correction 

would make this table agree substantially with the general results of 

the table on page 74, it seems probable that 0.15 pound is about the 

right amount to allow for friction in the first twenty-one tables to 

obtain maximum products.

If in the table on page 43 for wheel No. 18 we call friction 0.15 

pound, the maximum product will become 76.869, obtained January 13, 

1883. On April 10,1883, the -same wheel, No. 18, gave as maximum 

product 69.300, showing a variation of more than 12 per cent. But the 

United States Signal Service records in Chicago show for these two 

dates a difference of more than 1 inch in the barometric column, and 

about 39 degrees difference in temperature, which will account for a 

variation of about 12 per cent. Again, if in the table on page 44 for 

wheel No. 19 we call friction 0.15 pound, the maximum product will 

become 82.130, obtained January 18,1883. On April 11,1883, the same 

wheel, No. 19, gave as maximum product 75.185, showing a variation of 

over 9 per cent. The differences in temperature and barometric pressure as given for these two dates by the Signal Service records at 

Chicago would account for a variation in atmospheric density of just 

about 9 per cent. These three wheels, Nos. 2, 18, and 19, are the only 

ones tested both before and after the reduction of friction on March 

13, 1883. While the products as recorded In the tables in which 0.3 

pound was added to loads are all too large, their comparative values 

are not greatly distorted by the excessive allowance for axial friction.

The smaller allowance for axial friction will sometimes make the 

maximum product correspond to the next greater applied load, as in 

the case of wheel No. 19, page 44. But in the tables on pages 29 and 43, 

after allowing 0.15 pound instead of 0.3 pound for friction, the maximum 

products still correspond to the same applied loads and the same speeds 

of revolution as before.

AERIAL FRICTION.

So far we have not attempted to estimate the friction and resistances 

of the air itself, although the tables on pages 57,59, and 61 are very suggestive on this point, and theoretical considerations also indicate the 

great importance of this subject, as will hereafter appear.

RELATION BETWEEN SPEED AND LOAD.

The following table shows the relation between speed and load for 

various wind wheels:
PEEBY.] SPEED AND LOAD

Table showing the relation between

77

No. of 

wheel.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

Angles of 

weather.

o

35

35

24. 5, 11. 25

20, 30

22. 5, 32. 5

30

25

35

32.5

27.5

20

15

40

45

47.5

50

25, 35

' 25

27.5

30

32.5

35

25, 30

27.5

30

25

35

32.5

27.5

30

32.5

35

25

25, 35

27.5

25

30

22.5

27.5

A

Turns per 

minute at 

maximum.

31.69

33.43

47.48

55.93

46.10

42.10

47.40

36.84

34.58

39.33

45.46

43.88

28.70

24.72

25.30

20.67

38.70

39.42

38.20

39.87

38.72

31.96

43.21

38.87

38.95

43.74

33.74

34.49

39.10

35.15

34.94

33.43

37.80

43.77

46.64

47.05

40.41

52.51

35.57

.B

Turns per 

minute 

unloaded.

59.08

57.95

90.48

89.43

86.78

69.03

73.60

62.67

66.40

72.23

77.60

75.60

56.33

48.60

46.84

42.40

73.90

75.58

72.26

70.78

67.97

64.20

73.46

72.60

v 69.00

75.38

63.65

67.07

73.10

69.18

66.73

62.90

75.46

76.47

76.78

80.67

73.12

84.65

64.52

A 

B

.54

.58

.52

.63

.53

.61

.64

.59

.52

.54

.59

.58

.51

.51

.54

.49

.52

.52

.529

.56

.57

.50

.59

.54

.56

.58

.53

.51

.53

.57

.52

.53

.50

.57

.61

.58.

.55

.62

.55

C

Load at 

maximum.

1.65

1.85

1.35

1.55

1.95

1.65

1.35

1.75

1.95

1.75

1.35

1.15

2.15

2.15

1.95

2.15

1.75

1.95

2.15

1.9

1.9

2.1

1.75

1.8

1.8

.1.7

2.1

2.1

1.9

2.1

2.1

2.1

1.9

1.7

1.7

1.7

1.9

1.5

1.9

D

Starting 

force.

2.55

3.55

2.10

3.00

3.4

3.1

2.5

3.25

3.1

2.95

2.00

1.4

3.4

3.5

3.65

3.60

2.75

3.1

3.3

3.45

3.6

3.8

3.25

3.4

3.6

3.15

4.0

3.8

3.6

3.9

4.0

4.2

3.4

3.4

3.3

3.0

3.5

2.8

3.6

C 

Z>

.65

.52

.64

.52

.57

.53

.54

.54

.63

.59

.68

.82

.63

.61

.53

.60

.64

.63

.65

.55

.53

.55

.54

.53

.50

.54

.53

.55

.53

.54

.52

.50

.56

.50

.52

.57

.54

.54

.53

Sail 

surface.

Squarefeet.

9.19

18.38

13.59

13.59

13.59

10. 688

10. 688

10.688

10.688

10.688

10.688

10. 688

10. 688

10.688

10. 688

10.688

10. 688

12. 937

12. 937

12.937

12. 937

12. 937

12. 937

15.000

15. 000

15. 000

15.000

15.000

17. 016

17. 016

17. 016

17. 016

17.016

12. 937

12. 937

12. 937

12.937

12. 937

13. 072
78 EXPERIMENTS WITH WINDMILLS.

Table showing the relation between speed and load Continued.

[NO. 20.

No. of 

wheel.

40

41

42

43

44

45

46

47

48

49

Angles of 

weather.

o

27.5

25

30

25, 30

25, 30

20, 30

17. 5, 27. 5

22. 5, 32. 5

25,35

27. 5, 37. 5

A

Turns per 

minute at 

maximum.

45.74

46.81

43.15

45.92

44.35

79.99

85.19

73.31

66.79

58.82

S

Turns per 

minute 

unloaded.

82.13

84.70

77.95

84.92

84.88

156. 63

160. 90

148. 68

141. 97

136. 30

A 

S

.56

.55

.55

.54

.52

.51

.52

.49

.47

.43

O

Load at maximum.

1.9

1.9

1.9

1.9

1.9

2.9

2.7

3.3

3.7

3.9

D

Starting 

force.

3.65

3.35

3.8

3.5

3.5

5.1

4.7

5.9

6.4

6.5

O 

D

.52

.53

.50

.54

.54

.57

.57

.56 .58'

.60

Sail 

surface.

Square feet.

12. 937

12. 937

12. 937

12. 937

13. 590

14. 159

14. 159

14. 159

14. 159

14. 159

BEST SPEEDS FOR WIND WHEELS.

A

In the fifth column of the preceding table the decimal fractions ^

JD

indicate for the various wind wheels the ratio of speeds at maximum 

work to the speed of wheels unloaded.

By consulting the original tables on pages 28 to 46, it may be noticed 

that there are generally four or five products nearly as great as the 

maximum product for each wheel. Where the two greatest products 

are nearly the same, a very slight difference in velocity of wind, or 

other cause, may make the maximum result correspond to either of two 

different loads or two different speeds. This may account for certain

A C apparently rather wide variations in the columns g and jy

In general the best speed for most of these wind wheels is about 0.55 

of the unloaded speed, and a variation of speed between 0.45 and 0.70 

of the unloaded speed will not make a very great difference in the 

amount of work performed, provided the load is varied to suit the 

difference in speed.

BEST LOADS FOR WIND WHEELS.

In the eighth column of the preceding table the decimal fractions 

j= indicate the ratios of loads at the maximum of work to the greatest

loads that the wheels can start without continuous turning.

In collecting from the original tables the numbers D, which represent starting forces, the original figures were corrected so as to exclude 

what was originally added for axial friction. (See "Starting forces" 

on page 25.) Where 0.3 pound was added to applied loads prior to 

March 13, 1883, the figures were corrected for C in the sixth column
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 20 PL. X

WINDMILL AND RESERVOIR.

PEBBY.] OBSTRUCTIONS ON SAILS. 79

to correspond to an axial friction of 0.15 pound, as explained under the 

heading " Corrections for axial friction," page 75.

In general, it may be said that the ratio of best loads to starting 

forces is about 0.55, and that there may be a variation in the load 

between 0.50 and 0.65 of the starting force without serious impairment 

of efficiency.

CONICAL ^DEFLECTOR IN CENTER OF WHEELS.

Wheel No. 50 was tested because our attention was called to a windmill patent in which a conical deflector was shown. Besides saving 

the wind that otherwise would pass through the center of wheel 

unoccupied by sails, an advantage was also claimed because the air 

was made to act with greater leverage on account of encountering the 

sails farther from the axis. The experiment showed there could be no 

possible advantage from such an arrangement.

AIR-CUSHIONED SAIL SURFACES.

When wheel No. 39 was constructed, the narrow strips of board 

along the edges of the sails were intended not to obstruct the spaces 

between sails, but to afford air cushions on the faces of the sails against 

which the wind might act to better advantage than against plain surfaces. It had become apparent that plain sails were decidedly inferior 

to sails with concave faces, whether circular or angular. (Note experiments with wheels Nos. 40,43, and 44.)

It was contended by certain windmill experts that the narrow strips 

added to plain sails, as used in wheel No. 39, would answer the same 

purpose as the sail forms of wheels Nos. 40,43, and 44, and that wooden 

wheels could be more easily constructed in that way. One of the 

experts had constructed wind wheels similar to wheel 39. It was 

immediately due to the suggestion of another prominent windmill official that wheel No. 39 was made and tested. For ourselves, w»e had 

much more decided opinions after the test than before, notwithstanding 

the fact that our mathematical solutions as presented in this paper were 

written out and made public before any of our experiments were commenced. Whatever value there may have been in the air-cushioned 

sail faces of wheel No. 39, the advantage was more than nullified by 

the obstruction of spaces between sails and the bad contours of their 

backs.

OBSTRUCTIONS ON THE BACK OF SAILS.

Our experience with wheel No. 39 suggested that the arms and bands 

also might be detrimental to the proper smooth and peaceful flow of air 

between the sails. So we next constructed and tested wheels Nos. 45 

to 49, which have no bands and no arms along the backs of the sails. 

The results, as shown in the table on page 59, speak for themselves.

It may be noticed that wheel No. 47 carried 3.3 pounds as best load, 

the same as the best load of wheel No. 2, over which it shows a gain 

in power of about 83 per cent. The gain, therefore, in this case was
80 EXPERIMENTS WITH WINDMILLS. [NO. 20.

entirely in speed. Notice also the ratio between the speeds of the two 

wheels running- unloaded, iff ;ff =1.91. The denominator, 77.85, is 

taken from the table on page 27.

WASTE OF POWER DUE TO THE ARMS OP WIND WHEELS.

Two or three months after making the many experiments the summary of which is recorded on page 59, it occurred to us that it would 

be interesting to know and easy to ascertain something definite as to 

the gain in power effected by the removal of those portions of the arms 

which usually are made to extend along the backs of sails or between 

the sails of wind wheels. To represent the portions of arms previously 

removed, we prepared six pieces of pine wood 1 by 1^ by 17 inches. 

These could be quickly attached to the backs of the pasteboard sails 

by two little screws in each, and as quickly removed, as often as necessary.

We found, on retesting wheel No. 48 in September, that it showed a 

gain over wheel No. 2 of 84 per cent instead of the 87 per cent gained 

when tested in June. We attributed this small loss to the drying and 

warping of the sails, and therefore designated the retested wheel as 

No. 60. The same wheel, with the six pine strips above mentioned 

fastened to the backs of the six sails, was designated as wheel No. 61. 

We found by repeated trials, as usual, that wheel No. 60 required, for 

the wind velocity taken to produce a maximum product, a load of 1.9 

pounds.

This load was the same as the best load for wheel No. 2. The coincidence of best loads made the comparison of wheels No. 60 and No. 2 

merely a matter of recording speeds. No time had to be consumed in 

changing loads and readjustments of the brake, and the two wheels 

were replaced by each other alternately in rapid succession.

The same method was pursued in comparing wheel No. 60 with wheel 

No. 61, except that in this case, instead of removing from the axle and 

replacing the entire wheels, we merely placed and removed in succession the six strips of pine. The table on page 61 gives the averages of 

results.

It is possible that 1.9 pounds may not have been exactly the best 

load for wheel No. 61. To facilitate the speed comparisons and render 

mistakes of brake adjustment impossible, the load was not changed and 

the adjustment of the brake was left undisturbed during these alternate tests of the two wheels. We consider it altogether probable that 

an exact determination and application of the best load for wheel No. 

61 would not have materially changed the product as recorded. At 

any rate, simply removing the six strips of pine from the backs of the 

sails caused an increase in the speed of the wheel with the same load, 

from 38.13 to 56.50 turns per minute, or 48 per cent.
PEEEY.] DEFLECTORS IN FRONT OF SAILS. 81

TWISTED SAILS.

That the angle of weather of a sail should be greatest at the end 

nearest the axle and least at its outer end where its speed is comparatively great, seems self-evident, and the advantages to be gained by 

warping or twisting the sails so as to make the weather angles increase 

as they approach the center have always been recognized, at least in 

theory, by windmill manufacturers, although comparatively few American wind wheels are made with such sails. Our best results, as shown 

in the table on page 59, were obtained with warped sails, but it does 

not appear from previous experiments that the warping was by any 

means the most important feature of our best wheels.

The tables on pages 51 and 53 afford, in the comparisons of wheels 

Nos. 34 and 43, having twisted sails, with wheels as nearly like them 

as possible without twisted sails, an apparent test of the advantages 

gained by making the weather angles greater at the inner ends of the 

sails. Judged by these two wheels the advantage is very slight.

We are now satisfied that merely twisting the sails can not do much 

good for the reason that what is gained in .this way by better disposition of the forward or receiving edges of the sails is largely lost by the 

consequent less advantageous disposition of the rear edges from which 

the wind escapes.

As we have pointed out in the discussion of the theory of the windmill, the rear edge of a sail should be nearly parallel to the plane of 

motion without regard to radial distance, while the forward edge should 

be parallel to the relative direction of the impinging current of air, 

which depends on radial distance.

This theoretical disposition would make the angles of weather greatest where the sail speed is least, but is a very different thing from the 

twisting of the sails, as in wheels .Nos. 34 and 43.

Fig. 26, on page 61, shows a sail form more nearly in accord with 

our theory, which makes not only the angle of weather, but also the 

curvature of the sail, greater with nearer approach to the center of 

the wheel.

DEFLECTORS IN FRONT OF SAILS.

In our discussion of the theory,of the windmill on pages 71 and 72 we 

have called attention to the fact that our formula (E) indicates that the 

efficiency of a wind wheel might be increased if the air currents, just 

before meeting the sails, should be deflected so as to meet the plane of 

motion at a less angle than 90 degrees. In order to test somewhat this 

mathematical suggestion, the experiments recorded in the table on page 

64 were made. Only a single deflector was used, and that a plane surface. It may be noticed that when placed in front of wheel No. 2 at various angles the deflector caused some increase of speed in every instance, 

while the load remained the same. But when placed in front of wheel 

No. 49 its effect as an obstruction overbalanced its value as a deflector. 

20 6
82 EXPERIMENTS WITH WINDMILLS. [NO. 20.

It did not appear that deflectors would be advantageous in front of 

the most efficient wheel, nor of sufficient value in connection with the 

wheel of relatively low efficiency to justify the expense of such cumbersome appliances. W e did not, therefore, consider it worth while to 

experiment further with deflectors.

OBSTRUCTIONS IN FRONT AND IN THE REAR OF WIND WHEELS.

The experiments recorded on page 65 we were prompted to make on 

account of the contention by certain windmill experts, that an obstruction behind a wind wheel caused about the same loss of power as if 

placed in front.

Many so-called vaneless windmills had their supporting masts, or 

tower tops, in front of the wheels, while the ordinary mills with vanes 

had their supporting masts behind the wheels.

The obstructing boards described under the table on page 65 were 

intended to represent such obstructions as would be representative of 

supporting masts placed as indicated. In the case of wheel No. 2, 

unloaded, the obstruction when placed in front caused a loss of speed 

amounting to a little more than 3.5 per cent, and when placed behind 

the loss amounted to a little over 3 per cent.

In the case of wheel No. 49, loaded, the loss of speed from placing 

the obstruction in front amounted to nearly 14 per cent, and the loss of 

speed from placing the obstruction behind was nearly 7 per cent.

It may be observed that 3.5 pounds is less than the best load for 

wheel No. 49 (3.9 pounds), but it should be borne in mind that with all 

wheels a considerable variation in the load made but little difference 

with the product when near the maximum.

It might have been profitable if we had extended these experiments. 

It is evident that obstructions even when relegated to the rear are not 

obliterated.

MAXIMUM PRODUCTS IN DIFFERENT VELOCITIES OF WIND.

> 

The table on page 66 Indicates that maximum products vary as the 

cubes of the velocities of wind almost as exactly in fact as in theory. 

If there had been an exact correspondence between the results of

/b\ 3 

experiment and the law of cubes, the figures under( - ) would exactly

T> T>

equal those opposite under . The figures under -j are in some

A. A.

instances a little greater and sometimes a little less than those opposite

/^b\ 3 

under ( ) j as indicated by the plus and minus signs before the

T? / 7 "x *\

differences given under -,-_(_). The plus and minus signs happen

to be equal in number, showing a remarkable general agreement with 

the law of cubes. Again, the law of cubes would require that the
VELOCITY OF WIND. 83

numbers under ^i multiplied by ( _ ) should equal the correspond-

\Q> J

ing numbers under B. How nearly the law was actually fulfilled may

A 6 A 3 

be seen by comparing the last computed column, A x ( ) , with the \a>J

real products of column B.

STARTING FORCES AND LOADS AT THE MAXIMUM IN DIFFERENT VELOCITIES OF

WIKD.

Under the second table on page 66 we find the conclusion that " starting forces vary as the squares of the velocities of wind." If the law of

squares had been strictly confirmed, the computed ratios under 

would have just equaled the actual ratios of experiment as given

T>

under -^ . The agreement is quite close, but the numbers in column j\. T> 

- are more often greater than the corresponding numbers in column

So it appears that starting forces really increase in at least as *

great a ratio as would conform to the law of squares. But, as we 

have explained before, it should be remembered 'that what we have 

called starting forces could neither be defined nor determined with the 

same accuracy as was attainable in the case of maximum products. 

Nor could the loads corresponding to maximum products be determined 

so accurately as the maximum products themselves, since two or three 

different loads would generally give about the same product when the 

product was near the maximum. This fact made it all the more easy 

to ascertain the maximum products correctly, since a little variation 

from the best load was compensated for by the consequent variation in 

the speed of the wheel.

The table on page 77 shows, on the whole, a fairly constant ratio 

between loads at the maximum and starting forces, from which we may 

draw the conclusion that loads at the maximum vary as the squares of 

the velocities of wind.

SPEEDS OF UNLOADED WHEELS IN DIFFERENT VELOCITIES OF WIND.

7 T>

In the table on page 67 an inspection of columns and -*- will show u> .A

that in every case but two the counted turns of the unloaded wheel in 

the higher wind exceeds somewhat the number of turns computed on 

the supposition that the speed of an unloaded wheel should vary 

directly as the velocity of wind.' The two exceptional cases may be 

accounted for. We attribute this variation from the natural law in part 

to the fact, previously discussed, that the axial friction diminishes as the 

speed increases. Strictly speaking, the wheels, on account of unavoidable friction at the axle, could not be entirely unloaded.
84 EXPERIMENTS WITH WINDMILLS. [NO. 20.

ACTION OF AIR ON THE SAILS OF A WIND WHEEL.

In fig. 31, AB, AB are supposed to represent cross sections of two 

sails, one following the other as in a wind wheel. DE represents the 

direction and velocity of the wind with respect to the earth. AB represents the direction and velocity of the sail sections, at right angles to 

DE. Then DA represents the relative direction of wind with respect 

to the sails in motion, and the front faces AA of the sails are set parallel 

to DA. The rear faces of the sails B are set parallel to the plane of 

the wheel's motion, according to correct theory.

As one sail necessarily follows another in a wind wheel, the air can

JTio 31. Action of air on the sails of a wind wheel.

not escape in a direction exactly opposite to the sail's motion, and as 

the space between sails unavoidably contracts toward the rear edges 

these edges may in practice conform in some measure to the best pos- * 

sible direction of escape instead of being strictly parallel to the plane 

of the wheel. The placing of arms on the backs of or between the sails 

would render a necessary evil worse on account of further contraction 

of space. Besides, it should be noted that the backs of the sails, as well 

as their, faces, play an important part in deflecting the wind. For it is 

a well-known fact that air currents cling to and follow the surfaces 

along which they flow. Therefore, the backs of the sails should be 

smooth and free from obstructions. It is evident that all the air passing between the sails is deflected and not merely that portion which 

comes immediately in contact with the faces of the sails. The arrows 

and dotted lines in the figure indicate the relative direction and deflection of air as it flows through the wheel.

THEORETICAL EFFICIENCY OF THE WIND WHEEL.

Our general formulae and deductions previously given under theory 

of the windmill are presented just as they were originally recorded 

near the beginning of the year 1882. We now see no reason for alter-
PEBET.] THEORETICAL EFFICIENCY OF WIND WHEEL. 85

ing them in any respect, but there has been so much confusion among 

mathematical writers on wind action, that we wish to make the matter 

perfectly clear in its essential points.

It is not necessary to resort to the calculus, nor even to produce the 

general formulae (A) and (B) in order to arrive at the theoretical efficiency of a wind wheel. A very simple, graphical solution may be 

shown as follows: In figs. 32 to 35, AB represents the direction and 

velocity of the wind with respect to the earth; AC represents the direction and velocity of the sail, a section of which is represented by the 

curved line CD; the velocity of wind AB is the same for each of the 

four cases; and the several sail sections are supposed to be taken at 

the extremity of a sail in fig. 32, at a distance from the center of the 

wheel equal to two-thirds the radius in fig. 33, at one-third the radial 

distance in fig. 34, and at one-sixth in fig. 35. We have assumed that

Fig. 32.

Pig 33.

B

', .382

.61 8

K

Tig. 34. Fig. 35. 

FIGS. 32-35. Theoretical efficiency of the windmill.
86 EXPERIMENTS WITH WINDMILLS. [NO. 20.

the outer extremity of the sail travels three times as fast as the wind. 

That is to say3

AC = 3 x AB in fig. 32,

AC = 2 x AB in fig. 33, 

AC = 1 x AB in fig. 34, 

AC = £ x AB in fig. 35.

OB represents the relative direction and velocity of the wind with 

respect to the sail in each case. Neglecting friction, the relative velocity of the wind is not changed by contact with the sail. The air escapes 

from the sail at D with the same relative velocity it had at 0 ; but its 

course is changed so that it escapes in a direction parallel and opposite 

to that of the sail's motion. Now, since the sail is traveling with an 

actual velocity AC in one direction while the air is escaping with a relative velocity OB in the opposite direction, the difference between CB 

and AC = BK will represent the actual velocity of the air after it has 

escaped from the sail. The remnant of velocity BK is all there is left 

of the wind's original motion. The sail has absorbed the rest and converted into work a corresponding amount of energy. A certain quantity of wind started with a velocity AB and gave up all its energy 

except that corresponding to a velocity BK.

Now, the potential energy of the same quantity of air in motion 

varies as the square of its velocity, as in the case of any other substance. Hence a square constructed on AB and another square constructed on BK will represent relatively the original potential energy 

of the wind and the energy it still retains after encountering the sail. 

These squares are shown in the figures. The small squares represent 

the waste of energy or that not consumed by the sail. The relative 

areas of these squares may be readily computed. Taking the large 

squares as unity the small square equals 0.026 in fig. 32,0.056 in fig. 33, 

0.1,72 in fig. 34, and 0.382 in fig. 35. The efficiency is represented by 

the difference between the squares ; thus, the efficiency in fig. 32 is 

0.974; in fig. 33, 0.944; in fig. 34, 0.828, and in fig. 35, 0.618.

The small squares correspond to the letter & in the formula (B) on 

page 71. Compare these efficiencies with the values of 1 fc as originally obtained by a very different process. There would have been no 

difference if the decimals had'been equally carried out in both cases.

The potential energy of the wind, as well as the useful work resulting from its action on a sail, varies as the cube of its velocity, because 

the quantity of air coming in contact with the sail increases or diminishes with the change of velocity in the same proportion. It is only 

when we consider the result of a fixed quantity of air in motion, that 

its energy varies as the square of velocity and may be represented by 

square areas as illustrated above.
PEBEY.] USEFUL EFFORT OF WIND. 87

The work of the same quantity of air varies as the square of velocity, 

because its resultant reaction against the sail varies directly as the 

velocity and the sail also travels with the same proportional velocity. 

If, for instance, 1 pound of air, acting on a sail, has its velocity doubled, 

the sail travels with double velocity under doubled pressure, so that 

the work is increased fourfold; and, as in reality the doubling of velocity would cause 2 pounds of natural wind to meet the sail in the same 

time, the result is doubled again, making it eightfold in theory as well 

as in practice.

THEORETICAL USEFUL EFFORT OF WIND.

In the figs. 31> to 39, let AB represent the direction and velocity of 

wind with respect to the earth. In fig. 36 let AC = 3 AB represent 

the direction and velocity of the outer extremity of a wind wheel; in 

fig. 37 at two-thirds of the radius from center, AC = 2 AB; in fig. 38 

at one-third the radius from center, AC = AB, and in fig. 39 at onesixth the radius, AC = £ AB. The circular arc CD in each figure 

represents correctly what the cross section of the sail at each point 

should be according to theory. To make the calculation simple and 

specific, we will consider the action of 1 pound of air only, and that 

moving at an original velocity of 32.2 feet per second. *

We take this particular velocity because it requires the constant 

action of a 1-pound force to give to 1 pound of air, or to 1 pound 

of any substance, a velocity of 32.2 feet per second.

To give other velocities to the 1 pound of air, requires the impelling 

action of a force proportional to the velocity imparted in a second of 

time. That is to say, the force required to impart to 1 pound of air

i} 

any velocity, -», is represented in pounds by TjFig. 36.
88 EXPERIMENTS WITH WINDMILLS. [NO. 20.

-«-$«. D

Fig. 38. Fig. 39. 

TIGS. 36-39. Theoretical useful effort of wind.

The sail of a wind wheel moves at right angles to the direction of 

wind or in the direction AC, but the wind meets the sail in motion in 

the relative direction and with the relative velocity OB, and has with 

reference to the sail, due to the sail's motion, an opposite motion equal 

to OA in the direction 0 to A in addition to its original motion. The 

length of the line CB represents the velocity with which the air flows 

along the surface of the sail with undiminished relative velocity, 

neglecting friction, and the difference between CB and OA, or BK, 

represents the relative velocity acquired in a second by the air in a 

direction parallel to OA. That is to say, by action against the sail 

during one second, the 1 pound of air has acquired a relative velocity 

BK in a direction parallel to OA, in addition to the relative velocity 

0 A which it had before meeting the sail. This newly acquired relative 

velocity BK required for its generation a force reacting between the 

sail and the air proportional to the acceleration of velocity. If BK 

were equal to 32.2 feet, the reaction would be 1 pound. But the reaction is less than 1 pound in the same ratio that BK is less than AB, 

which we assumed to be 32.2 feet.

AB:BK:: 1 pound: Useful effort of wind.

BK So .-p. represents the ratio between original wind pressure in the
U. S. GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 20 PL. XI

WINDMILL AND RESERVOIR.

AERIAL RESISTANCE. 89

direction of its original motion and the useful effort which pushes the 

sail in the direction of its motion. If we lay off on BA prolonged 

AH=BK and complete the rectangles AOJH, the areas of the four 

rectangles in figs. 36 to 39, will represent relatively the work theoretically 

performed in each case. The effort AH may be readily computed. .For 

the action of 1 pound of air, at velocity of 32.2 feet per second, we find 

that the useful effort is 0.162 pound when the sail moves 3 times as 

fast as the wind, 0.236 pound when the sail moves twice as fast as the 

wind, 0.414 pound when the sail moves as fast as the wind, and 0.618 

pound when the sail moves one-half as fast as the wind.

AERIAL RESISTANCE TO MOTION.

It should be noted that by far the most striking and important results 

of our experiments with wind wheels were produced by cutting out 

from between the sails obstructions which produced aerial resistance to 

motion; and it should be profitable to study the causes which make 

these aerial obstructions apparently a matter of greater moment than 

all the other features of our investigation.

In the two preceding articles we have shown that the greater the sail 

velocities, theoretically the higher the efficiencies, and also that the 

useful efforts become smaller as the sail velocities increase.

When the sail travels three times as fast as the wind, the theoretical 

efficiency is 0.974, very close to perfection; but for a wind velocity of 

32.2 feet per second, each pound of air gives a useful effort of only 0.162 

pound. It is evident at once that while high sail velocity seems desirable, it does not require great aerial resistance to counteract a large 

percentage of the useful effort. -When the sail travels three times as 

fast as the the wind, a flat resisting surface of about 1 square inch set 

perpendicular to the direction of .motion would counteract entirely the 

useful effort due to the action of 1 pound of air. This is computed as 

follows:

At a velocity of 32.2 feet per second, 1 pound of air per second under 

ordinary conditions represents a stream of about 59 square inches area 

in cross section; from which it follows that 59 square inches of flat surface carried normally against still air at the rate of 32.2 feet per second 

meets with a resistance equal to 1 pound, and at a velocity three times 

as great meets with a resistance of 9 pounds. But the total useful 

effort in this case is only 0.162 pound.

Therefore we obtain _F= ^ =?1.062 squareinches=flatresisting surface required completely to neutralize all useful effort of wind 

whose normal pressure against 59 square inches of flat surface equals 1 

pound. In like manner we find that F equals 3.418 square inches where 

the sail velocity is twice the wind velocity, 24.426 square inches where 

the sail velocity equals the*wind velocity, and 143.848 square inches 

where the sail velocity is one half the wind velocity.
90 EXPERIMENTS WITH WINDMILLS. [NO. 20.

Or if we let / be the percentage of wind area represented by F, we 

find that /= 0.018 when sail velocity is three times wind velocity, 0.059 

when sail velocity is twice the wind velocity, 0.414 when sail velocity is 

equal to wind velocity, and 2.472 when sail velocity is one-half wind 

velocity.

These percentages hold good for all velocities of wind and emphasize 

the necessity of reducing to the utmost aerial resistances to motion, if 

wo are to attain high efficiency in a wind wheel.

BEST NUMBER OF SAILS.

An inspection of the table on page 65 shows that wheel No. 35 was 

more than 3 per cent better than wheel No. 19, although the amounts of 

sail surface and the angles of weather were the same in both. Wheel 

No. 35 had exactly the same sails as No. 19, except that each sail of No. 

35 contained two of No. 19 placed edge to edge, making 12 broad sails 

instead of 24 narrow ones. By simply changing the angle of weather 

from 27.5 degrees to 25 degrees, we made No. 35 into No. 30 and thus 

gained nearly 6 per cent over No. 19. The wide sails did better with 

less angle of weather. Wheel No. 6, with the same number of sails as 

No. 19 but narrower, required a greater angle of weather, 30 degrees.

It is apparent that for a given total of sail area it is better to 

divide the surface between fewer sails. It may T5e noted that wheel 

No. 48, with six sails, gave, in proportion to total' sail area, nearly 

two and a half times the efficiency of No. 2 with 60 sails. Eeduciug 

the number of sails reduces the aerial resistance to motion due to the 

number of edges, and leaves relatively freer interstices for the flow of 

air between the sails.

BEST RELATIVE AREAS OF SAIL SURFACE.

Tables on pages 47 and 49 give the following results for wheels Nos.

J 9, 24, and 29:

Effect of area of sail surface on efficiency.

Square feet of sail surface ..................

No. 19.

12. 937

1.204

No. 24.

15. 000

1.212

No. 29.

17. 016

1.201

a Compared with wheel No. 2.

These three wheels were nearly of the same efficiency. As compared 

with the area of the zone containing the sails, No. 19 was about threefourths full, No. 24 was about seven eighths full, and No. 29 was what 

we call full, as the total area of the sails about equaled the area of 

the zone containing them. These -wheels all contained the same number of sails set at the same angle, and differed only in width of the 

sails. It is clear that nothing was gained by making the total sail 

area more than seven-eighths of the zone, and that very little was
PERRY.] ACTUAL EFFICIENCY OF WIND WHEEL. 91

gained by filling beyond three fourths of the zone surely not enough 

to pay for the extra material.

From the table on page 65 we obtain the relative values of these 

three wheels per square foot of sail surface, viz, for No. 19, 0.0931 j for 

No. 24, 0.0808; and for No. 29, 0.0706. Notice also the relative values 

per square foot of sail surface as given for other wheels in this table.

ACTUAL EFFICIENCY OF THE WIND WHEEL.

To obtain the actual efficiency of wind wheel No. 2, taking the result 

recorded in the table on page 27, we first obtain the maximum work 

performed by multiplying the maximum product by the circumference 

of a circle whose diameter is 2 feet. (See note under the table on 

page 28.)

62.463 =s maximum product in the table. 

6.283 feet = circumference of circle 2 feet in diameter. 

62.463 x 6.283 = 392.455 foot-pounds per minute ='work of wind

wheel No. 2 at maximum. 

The potential energy of the wind is expressed by the well-known

TIT* o 1/17" 2

formula v -^ X ^- in which we make W= weight of air inter- 2 g o2t.2> 2i

cepted per second by the total area of the wind wheel, v = velocity 

of wind in feet per second, and g = 32.2, the velocity acquired each second by a body whose motion is not resisted when impelled by a con 

stant force equal to its own weight. The temperature as recorded 

was 50° F., and on the same day at 2 p. m., in Chicago, the barometer 

stood at 28.983. Hence 0.075 pound may be taken as the weight of 

1 cubic foot of air, 19.635 square feet as the total area of the wheel 

which was 5 feet in diameter, and 12.286 feet per second, or 8.403 miles 

per hour, as the velocity of wind. Thus, W = 19.635 x 12.286 x 0.075

= 18.093.pounds per second, «,» = 150.946, and ^= 18'09? X *50°'946 2i g 2i x o2,2

= 42.4078 foot-pounds per second, or 2544.468 foot-pounds per minute. 

The portion of actual energy of wind utilized by wind wheel No. 2,

or its efficiency, is accordingly 0544 468 = ®'^^ + 

To obtain the efficiency of any other wind wheel whose maximum 

product is directly compared with maximum product of wheel No. 2 as 

shown in the tables of later date than March 13, 1883, it is only necessary to multiply 0.154, the efficiency of wheel No. 2, by the ratio of 

products obtainable from the various tables.

For example, in the table on page 59 we find 1.872 given as the ratio-of 

maximum products for wheels No. 48 and No. 2. Hence, 0.1.54 x 1.872 

= 0.288 is the efficiency of wheel No. 48. This is the highest efficiency 

attained by any of the wheels whose products are recorded in the preceding tables.
92 EXPERIMENTS WITH WINDMILLS. [NO. 20.

WORK OF VARIABLE WIND WITH VARIABLE LOAD.

In most localities the velocity of the wind is exceedingly variable. 

The average of velocity recorded for an hour by an anemometer gives 

no idea of the total actual energy of the wind.

It might in conception be actually of uniform velocity, but where the 

average velocity is 10 miles per hour it is quite as likely to blow onehalf the time at the rate of 20 miles and during the other half not at 

all. The potential energy of 20-mile wind for half an hour is four times 

as great as that of a uniform 10-mile wind for a whole hour, although 

the average velocity per hour in each case is the same.

This is taking an extreme case, but it shows how the wind as it 

blows may and does develop much more energy than could be derived 

from uniform wind of equal velocity as usually recorded,, It would be 

desirable, if possible, to have the load applied to a wind wheel vary as 

the square of the velocity of wind, in order that the work might be 

the greatest possible. Any fixed load which allows the wheel to run 

freely most of the time is generally altogether too small during much of 

the time as well as too great at other times. For most uses to which 

wind wheels are especially adapted an automatic regulation of the load 

to meet the varying wind would make the best form of wind wheel 

regulation.

REGULATION OF WIND WHEELS.

Ordinarily wind wheels in this country are made to regulate themselves automatically, so that they can not attain a very rapid rate of 

rotation. This practice of not allowing the wheel to run at more than 

a very moderate speed is due to the fact that our wind wheels have 

been developed mostly in connection with the operation of common 

reciprocating pumps attached directly to a crank on the. shaft of the 

wheel. Such direct connection necessitates a slow motion of the wheel, 

in order that the piston speed of the pump may not exceed its economical limit. The consequence is that many wind wheels are allowed to 

do only a small part of the work which they are capable of developing. 

Too much attention has been paid to restraining automatically the 

speed of wind wheels by means which involve a waste of power. So 

far as the safety of the wheel itself is concerned there should be no 

need of restraining its speed in any wind under 40 miles per hour; and 

it should be borne in mind that strains on the wheel, due to any given 

amount of work, may be diminished in the same ratio that the speed of 

the wheel is increased.

The gearing of a wind wheel, whether it is geared up or down, should 

be made to suit the work and the nature of the device through which 

the power of the wheel is applied to use. When the machine driven 

requires a high speed of revolution, much gearing up may be avoided 

if the wind wheel is allowed to revolve rapidly. Back gearing for slow 

running machines should be resorted to whenever a direct connection
PEBEY.] SIZE OP WIND WHEEL. . 93

with, the machine to be driven will not allow the driven mechanism 

and the wind wheel both to have their best speeds with reference to 

work and wind. 

For any given velocity of wind the speed of the wind wheel should 

not change, no .matter what the nature of the work or of the machine 

through which work is performed; but the gearing should be such as 

to suit the load to the wind.

LIMITATION TO SIZE OF WIND WHEELS ON ACCOUNT OF WEIGHT,

Probably in no other form of motor does a gain in efficiency effect so 

great a saving in weight as in the wind wheel. The strength of other 

motors needs to be proportional to their own power. A 4-horsepower 

steam engine for instance does not need to weigh more than four 

times as much as a 1-horsepower engine, as the strains to which it 

is subjected are only four times as great. But a 4-horsepower wind 

wheel needs to be eight times as heavy as a 1-horsepower wheel in 

order to resist equally well the violence of exceptional storms. It is 

the strains of storms, and not its own working strains, that determine 

the required strength of a wind wheel.

Consider a single sail A supported on the end of an arm fastened to 

a central spider. Let L = length of the arm from center of wind pressure on sail to point of attachment to spider. If the wind wheel is 

doubled in diameter, keeping the same proportions, L will be doubled 

and the area of A will be four times as great. Hence the arm needs to 

resist four times the wind pressure acting at double the former distance 

out from its point of attachment, and needs to have eight times its 

former strength. This eightfold strength is secured by doubling all 

lineal dimensions, as evidently should be done, when the diameter of a 

wind wheel is doubled.

But the doubling of all lineal dimensions makes the wheel weigh 

eight times as much, and as its area is only four times as great, it 

follows that, in proportion to its power, the weight of the wheel is 

doubled.

As actually made, all the dimensions of large wind mills do not conform strictly to the proportions of small mills, and often the large 

wheels are built after different models from small ones. But it is wellknown that the large wheels as built do not resist storms so well as 

small ones, and costly experience has taught manufacturers to make the 

weight of their large wheels at least approximately what calculation 

requires.

On account of the disproportionate weight of large wind wheels, the 

towers which support them also have to be made considerably heavier 

than would be the case if the large wheels required no more material 

in proportion to power than do small wheels. If the tower for a large 

wind wheel were of correspondingly greater height, the weights of towers 

would follow the same law that should control the weights of wheels.

It is evident that small wind wheels" are more efficient in proportion
94 . EXPERIMENTS WITH WINDMILLS. [NO. 20.

to weight than large ones, and that the cost of construction, as the 

wheels .are made larger, is increased in much greater proportion than 

the gain in power.

EFFICIENCY OF WIND WHEELS AS AFFECTED BY DIAMETER.

Another reason why small \yind wheels are more efficient than large 

ones is that the wind meets all parts of the area of a small wheel with 

greater uniformity of velocity. It needs no special acuteness of observation to discover that the wind strikes different portions of large 

wheels with great unevenness of velocity.

Before commencing the experiments here recorded we attempted to 

measure the power of a wind wheel 22 feet in diameter in natural wind. 

By way of preparation we made a special anemometer, which indicated 

at sight the velocity of wind. We placed the anemometer as near to 

the wind wheel as possible, expecting to be able to note where its 

pointer stood and know the wind velocity for a minute of time, during 

which the revolutions of the wheel carrying a known load might be 

counted. The first thing we learned was that the anemometer never 

pointed steadily to any uniform velocity of wind even for one-fourth 

of a minute, and we next observed that the anemometer would sometimes almost stop running when the wind wheel showed an extra spurt 

of speed; also the wind wheel would slow down while the speed of the 

anemometer was accelerated. We could often hear the wind whistling 

through the sails on the opposite side of the wind wheel, while very 

little wind was felt on the near side close to the anemometer. We were 

unable to obtain a single measurement which we considered worth 

preservation. We could not determine even the best load for any 

wind, to say nothing about comparative results. We do not doubt 

that localities might be found where the wind would blow with greater 

uniformity, but our experience in trying to measure the power of 

wind wheels in natural wind led us to provide for artificial wind before 

proceeding further. The slight variations in the best artificial wind 

we could command caused a great abundance of vexations, which 

made the obtaining of accurate average results a matter of tedious 

labor.

4

HEIGHT OF TOWERS.

Nothing like steady wind can be obtained near the ground in an 

inhabited country. Buildings, trees, and other obstructions set the 

wind to whirling and cause it to flow in sinuous streams of very uneven 

velocity, concentrated in one place at the expense of another.

There is no effective remedy except in the elevation of the wind 

wheels several feet at least above all obstructions, even if the obstructions are isolated and a thousand feet away. In order that a large 

wind wheel may be as efficient in proportion to its area as a small 

wheel, its height above the ground must be greater. So it is probably 

not far out of the way to say that the weights of the towers as well as
U. S GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 20 PL. XII

WINDMILL ON LOW TOWER ON THE GREAT PLAINS.
PEEBY.] POWER OF WIND WHEEL. 95

the weights of the wind wheels, for equal safety and efficiency, should 

be nearly proportional to the cubes of the diameters of the wheels.

\

MULTIPLICATION OF WIND POWER.

We have shown that for equal safety in storms the weights of wind 

wheels of different sizes and like forms should be proportioned to the 

cubes of their diameters. It would require four 12-foot wheels to equal 

the area and power of one 24-foot wheel, if the larger wheel is proportiorfately elevated. But the weight of the one 24-foot wheel would be 

twice as great as the combined weight of the four 12-foot wheels, and 

the weight of the one higher tower would probably be twice that of 

the four shorter towers combined. Hence it would seem that in proportion to the power obtained in each case, the one 24-foot wheel would 

cost twice as much in material. The thought naturally presents itself 

that the four 12-foot wheels ought in some way to be combined so as to 

act in unison for concentrating a great amount of power where it is 

desirable to use the power at only one point, as in driving one machine 

of large dimensions. If the four wheels were coupled together rigidly 

the trouble from uneven reception of wind which is experienced in 

large wheels would be augmented. The problem has not been worked 

out, but we may imagine a number of wind wheels, each compressing 

air according to its own ability and delivering it at any distance into a 

common reservoir. Natural elevations would be selected as locations 

for windmills, and such a plant could not be rendered useless for the 

time by an accident to one or two of the wind wheels. There would 

necessarily be considerable loss in compressing air, but a low-pressure 

system might be devised that would greatly reduce the waste. Some 

waste of power attends every mode of transmission. In seeking to 

make a gain in power of 100 per cent in proportion to cost of plant, 

the loss of an extra 25 per cent in transmission might well be tolerated.

There may, however, be other and better methods for accomplishing 

the object in view than by the means we have ventured to suggest.

POWER OP TWELVE-FOOT WIND WHEEL.

The maximum product of our best experimental wheel, No. 48, is given 

as 247.123 in the table on page 59, and the velocity of wind as 10.935 

miles per hour.

The constant 6.283 multiplied by products gives the foot-pounds of 

work per minute. Hence 247.123 x 6.283 = 1552.674 foot-pounds = work 

per minute of No. 48 in wind of 10.935 miles per hour.

The work of 5-mile wind compared with the work of 10.935-mile wind

f 5 \3 is ( IQ 935 ) or .0956. Hence, the work of "No. 48 is, in 5-mile wind,

1552.674 x .0956 or 148.345 foot-pounds. The work of a 12-foot wheel 

in 5-mile wind is 148.345 X ( -5- ) or 854.467 foot-pounds, which is equal 

to 0.0259 horsepower.
96 EXPERIMENTS WITH WINDMILLS. [NO. 20.'

It is, therefore, approximately correct to call the power of a 12-foot 

wind wheel in 5-mile wind equal to one-fortieth of a horsepower. Computing the power of other wind velocities according to the law of cubes, 

we obtain for the power of a 12-foot wheel, one-fortieth or 0.025 horsepower in 5-mile wind, 0.2 horsepower in 10-mile wind, 0.675 horsepower 

in 15-mile wind, 1.6 horsepower in 20-mile wind, 3.125 horsepower in 

25-mile wind, 5.4 horsepower in 30-mile wind, 8.575 horsepower in 35-mile 

wind, and 12.8 horsepower in 40-mile wind.

Most 12-foot wind wheels, as now made, are strong enough to staM 

the strain of furnishing 13-horsepower, and this we believe is not beyond 

the actual achievement of some 12-foot wind wheels in 40-mile wind.

VALUE OF MATHEMATICAL FORMULAE IN EXPERIMENTAL INVESTIGATIONS.

The formulae which Professor Eankine and other mathematicians 

have applied to wind wheels give for maximum theoretical efficiency 

only 50 per cent of the potential energy of the wind actually intercepted 

by the sails. Our experimental wind wheel No. 48 realized an efficiency 

of more than 44 per cent, if we consider only the wind which would be 

intercepted by a surface equal to the projections of the sails on the 

plane of the wheel. So, if we should accept previous mathematical calculations as correct, we have already made a wind wheel which utilizes 

88 per cent of the greatest possible theoretical result, and the remaining 12 per cent margin would not furnish very great incentive to 

attempts at improvement. Mathematicians hitherto have treated the 

sails of wind wheels as flat surfaces. Even, for flat surfaces their 

theoretical results have been entirely too small; but it is not our 

purpose to discuss previous mathematical errors. Wind-wheel sails of 

proper form are not flat, but curved surfaces, and in analyzing the 

action of wind on curved sails we have not contradicted Eankine's 

formulae, but have confined ourselves to making such suppositions as 

may be actually true in practice. Eankine's formulae for the action of 

fluids on curved vanes give as a theoretical result a maximum efficiency 

of 100 per cent. This is correct. It shows that we have not made a 

very efficient wind wheel yet, and affords hope for the attainment of 

still better results in the future. We know that there is a great waste 

of energy somewhere, even in the best wind wheels we have been able 

to produce, but we are encouraged to think that much of the waste can 

be avoided. We do not claim, therefore, that our experiments have 

revealed the whole truth. In fact we believe that only a beginning 

has been made, and fully expect to see our best results greatly surpassed. In our view, the results of our experiments, as here recorded, 

are far richer in the suggestions offered than in the efficiencies realized.
INDEX.

Page. 

Air, resistance of... ................... 71,76,80,89

Air currents, action of...................... 84

Air-cushioned sails, description of.......... 57, 79

American wind wheels, development of.... 19,

30,74, 75,92 

Anemometer, description of................ 94

Angle of impingement, theory of........ 70, 71, 72

Angle of weather, experiments with.... 22, 75,90

Theory of.............................. 72

Barometric influences, effect of .......... 27, 72, 76

Brake, automatic adjustment of...... 27, 67,68, 69

Description of...................... 23,24,67

Deflector, experiments with.......... 46,64, 79,81

Theory of.............................. 71

Dynamometer, description of............... 23

Efficiency of windmills, determination of... 22,

60,91,96 

Effect of area of sails on................ 90-91

Effect of diameter of wheel on.......... 94

Theory of........................ 69-72,84-87

Energy of wind. (See Wind.) 

Experiments with windmills, methods of... 24,

25, 26, 27,42 

Place of........................ 9,21,22,72,73

Friction, corrections for........... 25, 26, 38, 75-76

Friction hrake. (See Brake.)

Gearing of windmills, method of........... 92-93

Journals, friction of........................ 25-26

Loads of windmills, application of......... 23-24

Axle friction included in............... 24, 75

Determination of best............... 77-79, 83

Law of squares for..................... 66,83

Regulation of variable................. 92

Newell, F. H., introduction by.............. 11-18

Letter of transmittal by ............... 9

Obstructing edges, effect of................. 90

Obstructions before and behind wheels, 

effect of.................................. 65,82

Obstructions on sails, effect of .... 57, 61,62, 79,89

Power of wind wheel, determination of .... 95

Products, determination of maximum...... 24,

27,42,73, 76.82-83 

Effect of journal friction on............ 20,

22,24, 25, 26, 75, 76 

Effect of state of atmosphere on. 27, 72,76

Regulation of wind wheels, methods of..... 92-93

Results of experiments, variations in ...... 73

Sail area, determination of best......... 65,90-91

Sails, angle of weather of...... 22,41,42,51,52,90

Effect of twisting of ............. 51,53,57,81

Efficiency of............................ 85

Forms of................... 65,69,72,84,85,90

Inclination of. (See Angle of weather.) 

Number of............... ....... 28,29,65,90

Obstructions on. (See Obstructions.)

Speed of.......................... 59,71,89,93

Smeaton, John, experiments of.......... 19,20,21

Speed indicators, forms of .............. 23,24.42

Speed of wind wheels, determination of.... 25,

67,77,78,83, 93 

Starting forces, best angles for............. 40,41

Definition and measurement of. 25,66, 77-79,83 

Thermometric influences, effect of....... 27,72,76

Towers, height and weight of.............. 93-94

Wind, effect of circular motion on ...... 20,21,23

Efficiency and waste of................ 85

Energy of........:............ 69,86, 91,92, 95

Escaping currents of................ 69, 71, 72

Experiments in natural................ 92, 94

Impinging currents of.............. 60, 70,72

Theory of the action of............. 69,72,84

Use of artificial.................. 23,22,42,74

"Useful effort of......................... 87-89

Wind wheels, determination of power of .. 95 

Determination of speed of.. -25,67,77, 78,83, 93 

Dimensions of.......................... 93-94

Effect of obstructions on...... 28,29,60,64,80

Efficiency of. (See Efficiency.)

Forms of...................... 19,20,30,74,75

Methods of regulation of............... 92-93

Reversal of ............................ 34,43

Sail area for............................ 90

Size of................................. 93,94

Towers for............................. 93-95

Work of wind wheels, computation of... 24,91,95 

Graphic representations of............. 87, 88

In variable winds...................... 92

Law of cubes for.................... 66,82,86

Strains due to.......................... 92

Theoretical formula for ................ 69, 70

97

IKE 20-