WIND
MILLS
WOLFF
TJ
825
W86
VILEY & SONS

ARTES
LIBRARY
1837
SCIENTIA
VERITAS
OF THE
UNIVERSITY OF MICHIGAN
& PLURIBUS UNEM
الحذر الحلال
SI QUAERIS-PENINSULAM AMDENAMI
CIRCUMSPICE
DEPARTMENT
OF
ENGINEERING

THE WINDMILL
24469
Q
7
AS A PRIME MOVER.
BY
ALFRED R. WOLFF, M.E.,
CONSULTING ENGINEER, ASSOCIATE EDITOR "AMERICAN ENGINEER," MEMBER
AMERICAN SOCIETY OF MECHANICAL ENGINeers, etc.
NEW YORK:
JOHN WILEY & SONS,
15 ASTOR PLACE.
1885.
TJ
825
W86
COPYRIGHT, 1885,
BY JOHN WILEY & SONS.
ELECTROTYPED AND PRINTED
BY RAND, AVERY, AND COMPANY,
BOSTON, MASS.
PUL DE BAN
Bedicated to
MY FRIEND
DR. I. ADLER.
PREFACE.
THE aim of the author in preparing this work was, to pre-
sent, in one treatise, a consideration of the more important
features of windmill theory and practice, sufficient to enable
the engineer and the user to decide as to the actual state of
windmill construction, its history and progress, its probable
direction of development, and the degree of economy attained
as compared with that of other prime movers.
He was led to the preparation of the work because the
information on this topic was confined to articles in periodicals,
pamphlets, and transactions, together with brief treatises in
text-books; no one having as yet made a careful and complete
study of this important subject.
During the past nine years the author has had occasion, in
the course of his professional work, to pay close attention to
the theory and practice of windmill construction, and has pub-
lished, at various times, professional notes setting forth some
of the results of his investigations. These papers met with so
kind a reception from the engineering fraternity, that he was
induced to present them in a more connected form, and to
investigate the subject still farther; so that this first treatise
on the Windmill as a Prime Mover is now given to the public.
vi
PREFACE.
Many technical works have been consulted; and proper
credit has been given, as far as the author is aware, in every
case. His special thanks are due to a number of prominent
American steam-pump manufacturers for furnishing data of
durability and cost of their pumps. Without such data, it
would have been difficult to present the comparison in Chap.
IX. on "The Economy and Capacity of the Windmill," which
is deemed of some value to users in deciding upon the relative
economic bearing of the windmill as a prime mover.
Finally, it is but just for the author to express his thanks
to Messrs. John Wiley & Sons for the encouragement afforded
in the publication of a work which of necessity will have a
limited sale.
85 ASTOR HOUSE, NEW YORK,
June 1, 1885.
3
CONTENTS.
INTRODUCTION.
THE USE OF THE WINDMILL.
Windmills, economical motors.
Their great use and appreciation at the present
Number in use in America .
Number manufactured in United States
Windmills not antiquated motors.
The historical relation of windmills and steam-engines
Windmills the most economical motors for specific uses.
Power purposes of windmills as defined by wind
The specific uses of windmills.
Windmills for pumping and storing water.
Windmills for compressing and storing air
Windmills for driving dynamo-machines
•
•
•
CHAPTER I.
WIND: ITS VELOCITY AND PRESSURE.
Definition of wind .
Average movement and velocity of wind
•
Table I., showing average movement of wind in America
Velocity of wind required to drive windmills.
•
PAGE
I
I
I
2
2
~ N N
3
3
4
4
4
4
5
6
7∞
7
S
vii
viii
CONTENTS.
Average velocity of wind when driving windmills
Relation between pressure and velocity of wind
The effect of temperature on this relation.
Analytical investigation of this relation.
Loss by friction of particles of air in motion.
Table II., showing relation between velocity and pressure of wind .
Table III. (Rouse-Smeaton), showing relation between pressure and
velocity of wind
Weisbach on the relation of velocity and pressure of wind .
Rankine on the relation of velocity and pressure of wind
Hawksley on the relation of velocity and pressure of wind.
Field on the relation of velocity and pressure of wind
Gaudard on the relation of velocity and pressure of wind
Pole on the relation of velocity and pressure of wind.
Hagen on the relation of velocity and pressure of wind
Adoption of formula for relation of velocity and pressure of wind
Velocity of wind as affected by height of observation
Stevenson's formula for this relation
Archibald's formula for this relation
High wind pressures
Scott on high wind pressures
•
•
PAGE
8
8
∞
9
ΙΟ
12
14
15
16
17
18
•
18
19
20
21
•
21
21
22
22
22
22
23
23
24
•
25
Bender on high wind pressures across the Atlantic
Gaudard on high wind pressures in England and France
Trautwine on high wind pressures in America .
•
C. Shaler Smith on high wind pressures in America
Hartnup on high wind pressures in Great Britain (Table IV.)
CHAPTER II.
THE IMPULSE OF WIND ON WINDMILL BLADES.
Theoretical analysis
Theoretical mechanical effect of windmill sail
Application of Rankine's analysis
Errors in Weisbach's analysis .
26
28
28
29
CONTENTS.
ix
Adoption of formula for theoretical mechanical effect of windmill
sail
Best angles of impulse
Formula for obtaining best angles of impulse
PAGE
31
31
32
Formula for obtaining best angles of weather
32
Table V., showing best angles of weather.
33
Diagram showing best angles of weather and impulse
•
34
Best angles for ventilators, etc.
35
Theoretical mechanical effect of windmill of shape of sail for maxi-
mum effect
35
Loss of effect by friction of the shaft
Theoretical mechanical effect of windmill with plane sails
Actual mechanical effect of windmill with sails of best angles of
weather
38
39
39
Actual mechanical effect of windmill with plane sails.
Comparison of formulæ with results of Coulomb's experiments
40
40
CHAPTER III.
THE EARLY HISTORY OF WINDMILLS.
Beckmann on the early history of windmills
•
Windmills not used by the Romans .
43
44
Windmills not invented in the East.
Windmills probably first used in Germany
Their use in France in 1105
Their use in Northamptonshire in 1143
44
•
45
45
45
Their use by the Venetians in 1332
46
Their use in the Netherlands in 1393
Their use in Frankfort in 1442
German mills older than the Dutch
•
•
Mills of Dutch type invented in sixteenth century.
Windmills in Holland in fifteenth century
Claims of clergy and landlords in the fourteenth century as to pro-
46
46
46
47
47
prietorship of wind
•
48
X
CONTENTS.
CHAPTER IV.
EUROPEAN WINDMILLS.
PAGE
Description of horizontal mills.
Classification: horizontal and vertical mills
Disadvantages of horizontal mills
General description of vertical mills.
Illustration of windmill sails
엉엉
​50
50
52
53
55
Illustration of post or German mills .
57
General description of post or German mills.
58
Details of post or German mills
59
General description of Dutch or tower mills.
61
Detail of Cubitt's method of turning dome into the direction of the
wind
62
Development of governors for adapting surface of wind wheel to force
Cubitt's governor for reefing the sails
of wind
Meikle's governor for reefing the sails.
Comparison of European and American windmills
65
67
68
71
CHAPTER V.
AMERICAN WINDMILLS. SIDE-VANE GOVERNOR MILLS.
Magy
Comparison of American and European windmills
Superiority of American above European windmills
Classification of types of American windmills
General description of centrifugal-governor type
•
General description of side-vane governor type.
General description of other types
Comparison of centrifugal and side-vane governor types
The Corcoran Windmill.
Details of Corcoran Mill for railway water supply.
Details of Corcoran Geared Mill.
72
73
73
74
1
74
74.
75
76
79
80
CONTENTS.
xi
Details of plain tower for Corcoran Mill
The Eclipse Windmill
PAGE
81
85
CHAPTER VI.
AMERICAN WINDMILLS (CONTINUED).
Centrifugal-governor Mills.
General description of Halladay Windmill
Detail of iron-work of Halladay Windmill
Detail of fan of Halladay Windmill
•
Economy of Halladay Mill for railroad water supply
Detail of Halladay Geared Mill.
The Halladay Mill in Germany; applications of Friedrich Filler
The Althouse Windmill
The Althouse Pumping-Mill
The Althouse Geared Mill
The Adams Windmill
Details of the Althouse Mill
CHAPTER VII.
AMERICAN WINDMILLS (CONCLUDED).
Other types. Velocity Regulation, etc.
The Buchanan Windmill
The Woodmanse Windmill
The Stover Windmill
The Champion Windmill
The Regulator Windmill
The Strong Windmill
The Leffel Windmill.
·
92
94
94
86
89
90
91
☹ å å ä ☹ * *
96
97
98
99
ΙΟΙ
103
103
106
IOS
II2
116
xii
CONTENTS.
•
CHAPTER VIII.
EXPERIMENTS ON WINDMILLS.
No reliable American experiments.
Smeaton's experiments
Details of method.
•
Table VI., showing results of Smeaton's experiments
Smeaton's maxims
Discussion of Smeaton's results.
Coulomb's experiments.
Description of mills experimented on by Coulomb
Details and results of Coulomb's experiments .
PAGE
119
I 20
121
122
123
124
125
•
126
127
CHAPTER IX.
THE CAPACITY AND ECONOMY OF THE WINDMILL.
The standard of economy
•
129
The current expense of prime movers.
130
The capacity of the windmill.
131
The horse-power of windmills
132
Table VII., showing capacity of the windmill.
133
Economy of the windmill
134
Table VIII., showing economy of the windmill
135
The economy of steam-pumps
136
Relative economy of the windmill and steam-pump
136
Table IX., showing economy of steam-pumps .
137
Tankage required for windmills.
139
Its effect on the economy of windmills
140
The economy of the windmill and Ericsson's hot-air engine com-
pared.
140
Table X., showing economy of Ericsson's hot-air engine
141
Relative economy of the windmill and the gas-engine
141
The windmill the most economical prime mover
•
142
CONTENTS.
xiii
CHAPTER X.
USEFUL DATA IN CONNECTION WITH WINDMILL PRACTICE.
Allowance for friction of water in pipes
Table XI., showing loss by friction of water in pipes
Table XII., showing co-efficient of friction in axles
Table XIII., showing capacity of windmill pumps of different diame-
ters and strokes
•
Table XIV., showing class and proper diameter of pumps
Table XV., showing number of acres irrigated by windmills.
Table XVI., showing capacity of cisterns and tanks
Table XVII., showing dimensions, weight, etc., of wrought-iron pipes,
Index
PAGE
143
146
147
148
149
150
150
151
153
THE
WINDMILL AS A PRIME MOVER.
INTRODUCTION.
THE USE OF THE WINDMILL.
THE following questions have been frequently asked
by those interested in the study of windmills: "Why are
not windmills more generally used?" "Should they not
have an economic use; for example, to pump water?"
These questions, in various forms, but always to the
same intent, have been propounded, not only by laymen,
but even by professional engineers of noted ability and
wide experience in their specialties. The invariable
answer of the author has been to the effect, that in
truth windmills are not only economical prime movers for
specific purposes, but that such application and economy
are, in fact, better appreciated to-day than they have ever
been before; in other words, that there are more wind-
mills in use at the present time than at any other period
in the history of the world.
To place the number of windmills at work in Amer-
ica at several hundred thousand, is to give an estimate
I
2
THE WINDMILL AS A PRIME MOVER.
which those who have been interested in this department
of engineering, and who have travelled along the main
railroad lines of the country, must pronounce as low.
And when we further learn that in some single cities of
the Union over five thousand windmills are manufac-
tured, on an average, each year, it does seem remarkable
that so general a lack of acquaintance with the fact of
their extended use should be the rule with so many
otherwise well-informed and observant men.
That this is due to an impression that windmills
must be antiquated, from the nature of things, there
can be no doubt. There was a time when the natural
forces of wind and water were the only ones at the
command of man for industrial purposes, and when the
motors driven by these forces monopolized all indus-
trial pursuits which man did not accomplish by his own
physical exertion. Then came the recognition of the
value of steam as a motive power; and the era of Watt
practically introduced the steam-engine, with its great
amount of power concentrated in a small weight and
volume, with its reliability of action and its close regula-
tive qualities. This was certain to speedily and effec-
tively take the place of windmills in many industries.
Independent of the fact that it enabled the creation of
the most startling and important innovations, such, for
instance, as railroad traffic, and a host of others that
wind and water motors did not permit, its extended
use, its concentrated power, and its unceasing action
gave an appearance, in the popular mind at least, of
INTRODUCTION.
3
unreliability, clumsiness, and smallness of power, to wind
motors, sufficient to account for the general misappre-
hension under discussion.
Though the advent and general application of steam
replaced the windmill in many of its strongholds, and
restricted its use to a few specific purposes, such use
has become a very extended one, and will be still further
enlarged in the near future, as the true value of the
windmill as a prime mover becomes better appreciated,
and as electrical storage batteries become more of a
success.
For certain specific purposes, and, primarily among
them, for pumping water in moderate quantities, the
windmill is not only a thoroughly reliable, but at the
same time the most economical* prime mover, and, as
far as judgment can now be passed, will hold this place
for many years to come.
The power purposes which windmills are specially
fitted to subserve are circumscribed and defined by the
character of the motive fluid, wind. Though the wind
may be relied upon to blow with sufficient velocity to
drive a windmill to its average working capacity eight†
hours a day, it is evident that there are minutes and
hours of total calm.‡
Therefore the employment of the windmill is re-
stricted to two classes of use:-
* See chap. ix. p. 129.
† See pp. 8, 133.
See p. 8.
4
THE WINDMILL AS A PRIME MOVER.
I. TO WORK OF THAT NATURE WHICH ADMITS OF A
SUSPENSION DURING A CALM.
For instance, to work on a farm, such as shelling
corn and cutting feed, driving small sawmills, and the
like.
II. TO WORK WHERE ACCUMULATED POWER CAN BE
STORED FOR FUTURE USE.
Under this caption the windmill has its main use, and
three specific applications at once suggest themselves.
The first is that which now claims the extended employ-
ment of windmills.
1. For pumping and storing water. A few special
adaptations of this use may be mentioned. Water is
supplied to country houses and farms, to manufacturing
establishments, and to the upper stories of office build-
ings and domestic dwellings, when the pressure in the
reservoir is not sufficient to effect this; railway water
stations and tanks are supplied with water; and dry
lands are irrigated.
(Sand has also been raised, in place of water, and
has been applied to the driving of an overshot wheel.)
2. For compressing and storing air.
3. For driving dynamo-machines to charge electrical
accumulators. This was first suggested in 1881 by Sir
William Thomson. The application of the windmill to
this purpose will soon come actively into play when
storage batteries have been developed to a greater
success than is attained at the present time.
WIND: ITS VELOCITY AND PRESSURE.
5
CHAPTER I.
WIND ITS VELOCITY AND PRESSURE.
IN the treatment of this interesting topic, we have
in the main restricted ourselves to a consideration of
those data of importance in the theory and practice
of windmill construction and use. It is expedient to
mention this at the outset; inasmuch as this chapter
makes but slight mention of the effect of wind on other
than plane surfaces, and is therefore of but slight value
to those who are in search of information about the
effect of wind on bridges, in which the members are
curved and of complicated shapes.
In fact, the knowledge extant of the effect of wind on
other than plane surfaces is scanty, and on the whole con-
flicting. Undoubtedly, further experiments are needed
to definitely settle the problem of wind pressure on plane
surfaces; still, knowledge as to this particular is far more
accurate than is that relating to the wind pressure on
curved surfaces. This is evident from the records of
experiment, and the opinions of those authorities who
have given the matter their attention.
Definition of Wind. When the density of air is
uniform throughout, the atmosphere remains at rest; but
6
THE WINDMILL AS A PRIME MOVER.
as soon as this equilibrium is destroyed, a movement
results which takes the name of wind. If in one part
of the atmosphere the air becomes more dense, it rushes
towards that part whose density is less, in the same
manner that the air compressed in a pair of bellows
escapes by its orifice. These currents of air are caused,
directly or indirectly, by differences of temperature at
different times and localities, giving rise to changes of
density, and varying the production and condensation
of watery vapor.
Average Movement and Velocity. - Through the
courtesy of the chief signal-officer of the army, we are
enabled to present the following statement, showing the
average monthly movement of the wind, in miles, at
the below-named stations of the Signal-Service, United
States Army (computed and compiled from the records
on file at the office of the chief signal-officer of the
army).
WIND: ITS VELOCITY AND PRESSURE.
7

STATIONS.
No. of Years'
Data.
January.
TABLE I.
Average Movement of the Wind.
Chicago, Ill.
Cincinnati, O.
Denver, Col.
Eastport, Me.
II
6691
6219
•
12
4726 4639
7342 6859
5601 4835
4327
12
4708
4119
5415
II
9215 8583
9660
5288 5070
7341 6275
4538
4532
6422 5587 5314 5138 5588
4005 3576 3199
4178
6325
6177
6469
6178
3453
3963 4404
3924 4326 4622
4269
4304
4203
4560
4927
4718
4354
5456
7096
8735 8793
7096
Galveston, Tex.
12
7682
7245
Jacksonville, Fla.
12
4348 4665
7523 7794
5900 5436 5006
7332
6250
4949
Moorhead, Minn.
3
8684
7720
10088
8552 9029
6972
5820 5184 6486 7063 7989 7721
4692 4611 4635 5127 4687 4586
7647 7447 6944 7784 8298 8314
7007
4887
8123
New-York City
Omaha, Neb..
Portland, Oreg.
Prescott, Ariz.
St. Louis, Mo.
Salt Lake City, Utah
San Francisco, Cal.
*
Average each month.
•
9
7238
7292
8442
7001
6353
5683
5605 5423
6884
6318
7465 7659 6780
13
6807
6358
8035
7854
7092
5778
5200
5051
5557
6552
7084
6551 6493
12
4455
3470
3815 3402 3586
3358
3527
3033
3014
2951
3214
3471
3441
5
3002 3882
5155
6140
6072 5346 4283
3494
3621 4049
3552
2862
4288
•
12
7597
7005
8662
7690
IO
2923 2831
4336
12
5349
4961
5987
5642
7184 6406
4610 5008 4397 4283
6593 7236 8397 9083
6898 6431 6225 5520
5712
5532
6086
6920
7454
7454
6975
4282 3955
3631 2809 2602
3806
9578 9014
7129 5848 4420
4761
6864
5320 4996 5157 5611 5751
5719
General Average,* 5,769 Miles per Month.
* Computed by the author from data furnished by the chief signal-officer, United States Army.
Average* per
Month.
8
THE WINDMILL AS A PRIME MOVER.
It has been found by experience, that it requires, on
an average, a wind of a velocity of six miles per hour
to drive a windmill, and that the latter will run, on
an average, eight hours per day. From this it is safe
to assume that one-third the total movement of the
wind is lost, as far as the work of the windmill is con-
cerned, and the rest distributed on the eight hours of
work. Then, dividing 5769 X 2 = 3846 by 30 x 8 = 240,
3
×
we find the average velocity of wind, during the eight
hours of work of the windmill, to be equal to 3846
miles per hour; or, 16 × 1.463 23.5 feet
3
=
240
or 16
per second.
Relation between Pressure and Velocity of Wind.
In 1876* the author published the following method
of finding the pressure corresponding to a given velocity
of wind, when the wind impinged upon a plane surface
perpendicular to its course. It differed from other
methods more especially in taking into account the
effect of temperature. As will be seen farther on, a
variation in temperature from 0° to 100° F. produces a
difference in the amount of pressure for a given velo-
city, of over one-fifth the total amount. In making the
computations for a correct table, attention was paid to
the following facts:-
That the pressure depends upon both the velocity
and the density of the air; that this density depends
upon the temperature, the barometric pressure, and the
pressure due to the motion of the air.
* Engineering and Mining Journal, Sept. 23, 1876.
WIND: ITS VELOCITY AND PRESSURE.
9
Let p = barometric pressure, in pounds per square foot, at any level,
temperature of air being 32° F., absolute temperature t₁ =
491.4 degrees;
P
d₁
ང་
I
= pressure, in pounds per square foot, due to the motion of the
=
air;
barometric pressure (average) at the level of the sea;
density of air under pressure
degrees;
d₂ = density of air under pressure p,
density of air under pressure
¿
absolute temperature .
+ P when t₁ = 491.4
when t₁ = 491.4 degrees;
t,
+ P, the air being at any
(p + P)d₂
(p + P)d₂ × t₁
Then
d₁
and d =
(1)
I
pi x t
I
It has been found by experiment, that, for p, 2116.5
pounds per square foot, and t = 491.4 degrees (32°
F.), d₂ 0.080728 pound. Substituting these values
=
in equation (1),
0.018743(p+P)
d
(I.)
Let c
е
d
=
8 =
P
velocity of the wind, in feet per second;
volume of air carried along per square foot in one second;
density of air, as found above;
velocity, in feet per second, generated by gravity;
pressure of wind per square foot of surface.
Then
Р
d Qc
g
(2)
= c cubic feet per second; therefore, from equation
==
(2),
dc
P =
g
(II.)
IO
THE WINDMILL AS A PRIME MOVER.
Substituting value of d from equation (I.) into equation
(II.), we have
0.018743(p + P) c²
P =
tg
(3)
therefore
px 0.018743
P =
t x 32 /
0.018743
c²
(III.)
By substitution of values for the velocity c, the baro-
metric pressure at 32° F. for p, and the temperature
expressed absolutely for t in equation (III.), the theo-
retical pressure corresponding to these values is readily
ascertained. Now, some of this pressure is lost by fric-
tion of the particles of air in motion, so that the pres-
sures found from equation (III.) must be multiplied by a
co-efficient to make them identical with actual pressures.
To determine this co-efficient (or the ratio of the actual
pressure to the theoretical), a series of observations were
made, in which the actual pressure of wind, its velocity,
the temperature, and the barometric pressure, were
recorded at the same time. The co-efficient thus deter-
mined was 0.93. While exercising all care possible at
the time to insure accurate results, the methods used
were not such as to meet the author's entire satisfaction
at the present date; and this co-efficient is therefore
given with some degree of reservation, though it is
deemed to be not far from correct. Until more accurate
experiments shall have been made, it will be safe to use
this co-efficient in calculations for practical work. Multi-
WIND: ITS VELOCITY AND PRESSURE.
I I
plying equation (III.) by this co-efficient, we find equa-
tion (IV.), from which, by substitution of proper values
for p, t, and c, we can calculate P₁ = the actual pressure
corresponding to these values,
P₁
= t x 32 /
0.017431 X Þ
- 0.018743
(IV.)
c²
p
=
When 2116.5 pounds per square foot = average
atmospheric pressure at the level of the sea,
36.892887
P₁
=
t X 32 1/1/20
C²
- 0.018743
(V.)
By substitution in equation (V.) the following table
(Table II.) has been constructed. For any other baro-
metric pressure, the figures in Table II. must simply
be multiplied by the ratio of this barometric pressure
reduced to its value for temperature of air
3
32° F. to
barometric pressure at any
2116.5. Thus, letting
absolute temperature t, then p
must be multiplied by 2116.5
P
₤3 t
PX and the table
491.4
>
1
12
THE WINDMILL AS A PRIME MOVER.

VELOCITY OF
WIND.
TABLE II.
SHOWING RELATION BETWEEN VELOCITY AND PRESSURE OF WIND.
Pressure of WIND, IN POUNDS PER SQUARE FOOT OF PLANE SURFACE PERPENDICULAR TO ITS COURSE, WHEN P
WHEN P = 2116.5 AND
TEMPERATURE OF WIND =
Miles
per
Hour.
Feet per
Second.
0° F.
5° F.
10° F.
15° F.
20° F.
25° F.
30° F.
35° F.
40° F.
45° F.
50° F.
I
123456
1.463
2.933
4.393
5.8633
0.005371 0.005312
0.021482 0.021252 0.021025 0.020802
0.048335
0.005256 0.005201
0.005147
0.005094
0.005042
0.004990
0.004940
0.004889
0.004842
0.020586
0.020373
0.020165
0.019962
0.019761
0.019565
0.019374
0.047814 0.047305 0.046807 0.046318
0.045841
0.045372
0.044914
0.044465
0.044026
0.043591
0.085930 0.085006
0.084100 0.083214 0.082345
0.081495
0.080663
0.079847
0.079048
0.078264
0.077496
7.33%
0.134271 0.132824
0.131409 0.130024
0.128668
0.127339
0.126038
0.124704
0.123514
0.122290
0.121090
8.80
0.193354 0.191271 0.189239 0.187240
0.185287
0.183374
0.181500
0.179665
0.177867
0.176103
0.174374
78
10.263
0.263186 0.260353
0.257588 0.254863
0.252205
0.249601
0.247051
0.244552
0.242112
0.239703
0237350
11.733 0.343767
0.340066 0.336442
0.332895
0.329423
0.326023
0.322690
0.319427
0.316228
0.313093
0.310019
9
13.20 0.436283
0.430524 0.425829 0.421340
0.416945
0.412640
0.407823
0.404292
0.400243
0.396285
0.392385
ΤΟ
14.663 0.537188
0.531404 0.525741 0.520200
0.514772
0.509457
0.505124
0.499150
0.494151
0.489252
0.484429
II
16.13%
12
17.60
0.650036
0.773645
0.643035 0.636183 0.629476
0.622908
0.616477 0.610207
0.604003
0.597955
0.592026
0.586212
0.765308 0.757157 0.749171
0.741357
0.733608
0.726204
0.718857
0.711656
0.704600
0.697681
13
19.063
0.908020 0.898240
0.888667 0.879296
0.870122 0.861136
0.852335
0.843711 0.835260
0.826977
0.818857
14
15
16
456
20.533
1.053166 1.041821
1.030718 1.019849
1.010206 0.998769
0.988575
0.978572
0.968770 0.959162
0.949743
22.00
23.4623
17
24.93/
1.209087 1.196062 1.183314 1.170835
1.375798 1.360966 1.346460 1.332258 1.318354 1.304737
1.553273 1.536540 1.520160 1.504126
1.158616
1.146650
1.134928
1.123444
1.112190
1.101159
1.090344
1.291397
1.278330 1.265523
1.252964
1.240664
1.488425
1.473052
1.457991
I.443235
1.428786
1.414602
1.400706
18
26.40
19
27.8623
I 940634
1.741556 1.722792 1.704423 1.686444
1.919.720 1.899252 1.879215
1.668839
1.651599
1.634711
1.618167
1.501951
1.586058
1.569519
1.859596
1.840384
1.821564 1.803125
1.785056
1.767345
1.749982
20
29.333
25
36.66
30
44.00
2.150516 2.127337 2.104653 2.082447
3.362250 3.325986 3.290499 3.255761
4.845284
2.060705
2.039361 2.018555
1.997617
1.978095
1.958464
1.939225
3.221749
3.188486 3.155813 3.123847
3.092521
3.061819
3.032543
4.792984 4.742002 4.691710
4.642662
4.594628
35
45
80 8 4 A AU
51.33/3
6.600829
40
58.663
66.00
50
60
88.00
8.630351 8.537028 8.445701 8.356310
10.935522 10.817138 10.701289 10.587884
73-333 13.518265 13.371732 13.228340 13.087991
19.525304 19.313019 19.105299 | 18.902010
117.333 34.981530 34.598320 34.223330 33.856440
6.529525 6.459835 6.391739
4-547752 4.501482
4.456311
4.412038
4.368636
6.324565
6.259067
6.194814 6.132081
6.070498
6.010033
5.950698
8.268791
8.183131
8.099137 8.016896
7.936307
7.857321
7.777933
10.476877
10 368165
12.950585
12.816051
10.261687 10.157373 10.055155
12.684268 12.555160 12.428668
9.954978 9.856776
12.304691
12.183167
18.702993
18.508122
18.317252
18.130194 17.947145
17.767641
17.591679
33.497300
33.745730
32.801460
32.464240 32.133920 31.810220
31.493000
WIND: ITS VELOCITY AND PRESSURE.
13

VELOCITY OF
Wind.
TABLE II. Concluded.
SHOWING RELATION BETWEEN VELOCITY AND PRESSURE OF WIND.
Pressure of WIND, IN POUNDS PER SQUARE FOOT OF PLANE SURFACE PERPENDICULAR TO ITS COURSE, WHEN p= 2116.5 AND
TEMPERATURE OF WIND =
Miles
per
Hour.
Feet per
Second.
55° F.
60° F.
65° F.
70° F.
75° F.
80° F.
85° F.
90° F.
95° F.
100° F.
Ι
1 2
1.463
0.004796
0.004750
0.004705
0.004660
0.004617
0.004574
0.004532
0.004491
0.004450
2.93/3 0.019185
0.019001
0.018818
0.018642
0.018586
0.018294
0.018128
0.017964
0 017801
3456
4.393 0.043166
0.042751
0.042344
0.041944
0.041551
0.041166 0.040788
0.040717
0.040052
0.004410
0.017641
0.039694
5.863
7.333
8.80
0.076743
0.076008
0.075277 0.074568
0.073870
0.073185
0.072514
0.071854
0.071205
0.070568
0.119912
0.118758
0.117625
0.116515
0.115424
0.114355
0.113305
0.112274
0.111261
0.110267
0.172679
0 171017
0.169386
0.167786
0.166216
0.164675
0.163153
0.161678
0.160219
0.158784
78
10.263
0.235043
0 232780
0.230560
0.228382 0.226244
0.224148
0.222091
0.220091
0.218082
0.216140
11.73/3 0.307003
9
13.20
0.388570
IO
0.479739
II
12
17.60
13
19.06/
0.304050
0.384828 0.381159
14.663
0.470587
0.475121
16.133 0.580513 0.574923 0.569440
0.690824 0.684244 0.677718
0.810894
0.301150
0.298306 0.295514
0.292774
0.290086
0.287444
0.284852
0.377558 0.374025
0.370555
0.367153
0.363811
0.360529
0.282265
0.357305
0.466142
0.461779
0.457498
0.453295
0.449169
0.445118
0 441195
0.564058
0.558780 0.553600
0.548513
0.543527
0.538644
0.533815
0.671315
0.665032
0.658865
0.652815
0.646868 0.641032
0.635301
14
20.533
0.940507
15
22.00
1.079746
16
23.463
1.228542
17
24.933
1.387083
0.803085 0.795424
0.931449
0.922564
1.069347 1.059139
1.216763 1.205154 1.193758
1.373721 1.360613 I.347754
0.787909 0.780463
0.773296
0.766191
0.759216
0.752413
0.745638
0.913850
0.905292
0.896879
0.888655
0.880567
0.872587
0.864814
1.049130
1.039309
1.029670
1.020208
1.010919
1.001797
0.992841
1.182589
1.171621 1.160853
1.150283 1.139902
1.129707
1.335135
1.322751 1.310628
1.298659 1.286939
1.275429
18
26.40
1.554854
1.540180 1.525506
1.511102
1.496765
1.483066 1.469435
1.456052 1.442909
1.429470
19
27.86/3
1.732957
1.716260
1.699882
1.683813
1.668046
1.652571
1.637380
1.622467 1.607822
1.593439
20
29.333
1.929357
1 901853
1.883702
1.865894 1.848420
1.831270
1.814436
1.797908
1.781722
1.765740
25
36.663
3.002206
2.973261
2.944892
2.917015
2.889683
2.862857
2.836526 2.810674
2.785290
2.760359
30
44.00
4.326079
4.284344
35
40
45
50
4.203242
51.33/3 5.892963 5.836055 5.780246 5.725495 5.671771
58.66% 7.703980 7.627948
7.484862
7.556501
66.00
9.760493 9.666070 9.573460 9.482606
73.33/3 12.004021 11.947178 11.832584 11.820187
4.243405
4.163832
4.125157
4.087178 4.049715
4.013315
3.979371
5.619046
5.568291
5.516483
5.466594
5.417590
7.414568
7.345581
7.277867
7.211390
7 146115
7.082012
9.393460
9.395975
9.220106 9.135806
9.053001
9.971746
60
88.00
80 117.33/3
11.609840
17.419165 17.250017 17.084114 16.921371 16.761700 16.605025
31.182030 30.877150 30.578199 30.284930 29.997260 29.715020
11.501614
11.392659
16.451238 16.300276
11.291064
11.188654
11.088085
16.151954
16.006591
29.438010 29.166110 28.899220
28.863716
14
THE WINDMILL AS A PRIME MOVER.
The relation between the pressure and velocity of
wind given above corresponds quite closely, when the
temperature is at about 45° F., with the following table,
originally communicated by Mr. Rouse to Smeaton, and
now quite generally adopted for ordinary calculations.
TABLE III.
THE ROUSE-SMEATON TABLE OF WIND PRESSURES.

VELOCITY OF THE WIND.
PRESSURE.
COMMON APPELLATIONS OF
so
Miles per
Hour.
Feet per
Second.
Per Square
Foot,
in Pounds.
FORCE OF WIND.
5
1 2 3 4 in
I
1.47
2.93
0.005
Hardly perceptible.
0.020
4.40
Just perceptible.
0.044
4
5.87
0.079
Gentle, pleasant wind.
7.33
0.123
ΙΟ
14.67
0.492
Pleasant, brisk gale.
15
22.00
1.107
20
29.34
1.968
25
36.67
Very brisk.
3.075
30
44.0I
4.429
35
51.34
6.027
High wind.
40
58.68
7.873
45
66.01
9.963
Very high storm.
50
73.35
12.300
60
88.02
17.715
80
117.36
31.490
100
146.70
49.200
Great storm.
A hurricane that tears up trees,
carries buildings before it,
etc.
Immense hurricane.
WIND: ITS VELOCITY AND PRESSURE.
15
The formula which, in its general form, applies alike
to Tables II. and III., is P = 4, equation (II.); or, for
&
45° temperature, P = 0.005c², equation (VI.), in which c
is velocity in miles per hour.
de
Inasmuch as the correctness of this formula has been
questioned by some engineers of standing, who have
maintained that the pressure is equal to being
equal to h), it is well to quote the following authorities
in support of the analysis given above:--
2g
2g 25
Weisbach ("Mechanics of Engineering," edition of
Eckley B. Coxe, 1882, p. 1030, § 510), presenting the
formula P = Fy, equation (VII.), in which denotes
an empirical number dependent upon the shape of the
surface, says this "general formula for the impulse and
resistance of an unlimited stream is also applicable
to the impulse of wind and to the resistance of the
air."
P=
2,2
In § 511 we learn, that, "according to Du Buat's
experiments, and those of Thibault, we can put, for
the impulse of water and air against a plane surface at
rest, ¿
= 1.86." It will be noted that this co-efficient
substituted in equation (VII.) gives the expression
= 0.93 Fy, or the same co-efficient, 0.93, by which
equations (II.) and (III.) were multiplied to obtain the
figures in Table II. In vol. ii. (edition of Du Bois,
p. 652, § 342) Weisbach again gives the value of P as
equal to 1.86Fy, and continues, "or, since = 0.0155,
P = 0.028830v2Fy; or, if we take the density of the
28
I
2g
16
THE WINDMILL AS A PRIME MOVER.
wind, y =
62.5
800
0.078125 pounds, P =
0.00225202 F:
therefore, if the area of the surface is one square foot,
the pressure of the wind is P = 0.002252v2 pounds."
v, in the above expression, equals feet per second.
Remembering that 1 mile per hour equals 1.46 feet
per second, the pressure of the wind, when c equals.
miles per hour, becomes
or
P = 0.002252 X 1.46 X 1.463c2,
same as equation (VI.).
P = 0.005c²,
Rankine ("A Manual of the Steam-Engine and
other Prime Movers," edition 1874, p. 163, § 144)
says,
(C
'The direction and amount of the pressure exerted by a jet or
stream of water [or of wind-A. R. W.] against a solid surface are
determined by the following principles, which are the expression of the
second law of motion as applied to this case : —
"1. The direction of that pressure is opposite to the direction of
the change produced in the motion of the stream during its contact
with the surface.
"2. The magnitude of that pressure bears to the weight of water
flowing along the stream in a second, the same ratio which the velocity
per second of the change in the motion of the stream bears to the
velocity generated by gravity in the second [viz., g = 32.2 feet per
second]."
by
On p. 164 the magnitude of the pressure is expressed
in which DQ is the weight of the flow of water
DOHC
8
WIND: ITS VELOCITY AND PRESSURE.
17
in a second, and HC represents the velocity of the
change of motion undergone by the jet during its contact.
with the vane. When the vane is at rest, then HC
equals the original velocity of the jet c, and Rankine's
formula becomes
P=
DQ c
g
or P =
Da
g
same as equation (II.).
Mr. T. Hawksley, past president Institution of Civil
Engineers ("Proceedings of the Institution of Civil En-
gineers," vol. lxix., 1882), referring to the pressure of
wind upon a fixed plane surface, maintained that the
general solution of the problem might be thus briefly
stated:
"Let v =
velocity of the current in feet per second;
h = the height through which a heavy body must fall to produce
the velocity of v;
w the weight, in pounds, of a cubic foot of the impinging fluid
[for atmospheric air, about 0.0765 pounds];
во
= 32, the co-efficient of gravity.
2g
“Then / = 2; and since p, the pressure of a fluid striking a plane
surface perpendicularly, and then escaping at right angles to its original
path, was that due to twice the height h (D'Aubuisson de Voisins'
Hydraulics, Rouse's Experiments), then
272
Р
са
(for atmospheric air
0.076522
32
2 | شرح
[R
very nearly,"
18
THE WINDMILL AS A PRIME MOVER.
v²
v²
or very nearly; or, if c equals miles per hour,
400
1.46 X 1.46 c²
I
P =
P=
or
nearly,
400
200
which is again equivalent to equation (VI.).
Mr. Rogers Field, in the same discussion ("Pro-
ceedings of the Institution of Civil Engineers,” session
1881-82, vol. lxix.), agreed with the above presentation
of Mr. Hawksley, but said that "this could not, of course,
be strictly accurate, because other factors must enter the
question, such as the density of the air, which would be
affected by the temperature of the air and the height
of the barometer."
It should be remarked, that the analysis and Table II.,
presented on pp. 8-13, originally communicated by the
author in 1876, take account of the very factors which
Mr. Field mentions.
"}
Professor Jules Gaudard, in his paper on "The
Resistance of Viaducts to Sudden Gusts of Winds"
("Proceedings of the Institution of Civil Engineers,'
vol. lxix., 1882), makes an analysis of the pressure of
wind, finds the same equal to P = s sin a, and says,
شرح
g
Πυ
g
“As is double the height which the column of water
would require to fall to attain a velocity v at the bottom
of fall, it follows that the dynamical pressure, in the
case of vertical incidence, may amount to double the
weight of the same column in a state of rest." In a joint.
discussion of his own paper and that of Mr. Charles
WIND: ITS VELOCITY AND PRESSURE.
19
B. Bender, Professor Gaudard said he "would come back
to the theory given in various treatises on mechanics,
such as Mr. Bresse's Hydraulique' (p. 311 of the 1860
edition), which theory, based on the extinction of the
amount of motion by the re-action of the ground, re-
sulted in representing the theoretical pressure by double
the height of the fall. The total dynamic effect should
really be more powerful than the simple weight of a fluid
column at rest: the rate of flow played an important
part. On the other hand, it should be remembered,
that the theory disregarded viscosity, the mutual shocks
of the liquid molecules during their fall, the clashing of
their motion inducing either vacuums or an admission
of air, all constituting disturbing causes, which doubt-
less notably modified the action, and rendered it neces-
sary to leave the last word on this subject to the result
of experience." True as are these remarks of Professor
Gaudard, it should be observed, that, when the fluid is
air, the disturbing causes of molecular action, viscosity,
and the like, will not represent a very large percentage
of the theoretical dynamic effect.
Dr. William Pole, in the same discussion, figured
the theoretical pressure as only one-half the amount.
given above, considering the dynamic pressure equal to
the statical weight of a column whose height equals
but added, that "there appeared reason to think, that,
when the force of the wind was actually received on flat
surfaces, the pressure was considerably in excess of these
amounts.'
20
THE WINDMILL AS A PRIME MOVER.
All of the above tends to give strong support to
the analysis presented on pp: 8-13; but there is one
great authority differing from the same, whose work is
deserving of the highest consideration and credit, and
the results of whose scientific observations, throwing
some doubt on the accuracy of the above analysis, should
be noted here.
*
Hagen (Berlin, 1874) gives, as the result of very
careful observations of wind of moderate velocities, the
following formula,
P (0.0028934 + 0.001403) SV²,
in which P = total pressure in pounds avoirdupois,
Р the outline or perimeter of the exposed surface in
feet, V = velocity in miles per hour, S = area in
square feet. The formula applies to plane surfaces (of
no considerable depth) placed normal to the incident
wind, and with the density of the air corresponding to a
barometric height of 29.84 inches and a temperature of
59° F. If S = 1 square foot, p
I
= 4, and Hagen's for-
mula becomes
P = 0.0035949 V² ;
while for 60° F., Table II. shows
P = 0.004750V²,
or, the pressure obtained experimentally by Hagen is
* Appleton's Cyclopædia, article Wind, by Professor Cleveland Abbe.
•
WIND: ITS VELOCITY AND PRESSURE.
2 I
over twenty-five per cent less than that recorded in
Table II.
Thus, while for the time being, adopting the analysis
and values recorded on pp. 8-13, supported by the
authority of D'Aubuisson de Voisin, Bresse, Weisbach,
Rankine, Hawksley, Field, and Gaudard, we feel that
the same must be experimentally verified before being
finally accepted as correct; and we note that the careful
scientific observations of one of the greatest specialists
(Hagen) give results differing considerably from the
data provisionally adopted. It remains to be seen
whether future experimental evidence will support these
results, or the formula given by Hagen.
Velocity of Wind as affected by Height of Observa-
tion. Mr. Thomas Stevenson, member of Institution of
Civil Engineers ("Journal of the Scottish Meteorological
Society," 1881), finds that the velocity of the wind varies
with the height above the surface of the ground, and
proposes the following formula for finding the velocity,
V, at any height, H (in feet), v equalling the velocity at
the standard height of fifty feet above ground:
V = vV
H+ 72
122
for one hundred feet above the ground,
100 + 72
Ꮴ
V = V
I 22
or nearly 1.20; for twenty-five feet above the ground,
22
THE WINDMILL AS A PRIME MOVER.
25 +72
V
Ꮴ
=
122
or nearly 0.9ʊ.
This range of twenty-five and one hundred feet, or
of 1.27 and 0.9v, constitutes the limits between which
Mr. Stevenson's formula may be said to apply to wind-
mill practice.
Professor E. D. Archibald ("Nature," No. 786)
records experiments on the velocity of wind at different
heights, by means of Biram's anemometers raised by
kites. His results favor the formula
Mr. Stevenson's formula for heights above fifty feet is.
(1)%.
V
ข
V
ข
(#), while
H
h
High Wind Pressures. Since windmills are, of
course, preferably located where they are most freely
exposed to the action of the wind, and since they
must be made strong enough to withstand the pressure
of the heaviest gales, information as to the highest velo-
cities and pressures attained becomes of interest.
Mr. R. H. Scott,* then secretary, now president, of the
Scottish Meteorological Society, estimates the velocity of
the wind in the greatest hurricane at 90 miles an hour.
Mr. C. B. Bender† states that the greatest progressive
motion of an Atlantic hurricane having been observed to
be 50 miles per
hour, and no change of direction taking
* Quarterly Journal of the Meteorological Society, 1874, vol. ii. p. 109.
† Proceedings of the Institution of Civil Engineers, vol. xix., session.
1881-82.
WIND ITS VELOCITY AND PRESSURE.
23
place, it may be assumed that the velocity of the wind
proper at its maximum was not more, or much more, than
100 miles per hour. Professor Jules Gaudard * quotes
Rankine's statement, that about 55 pounds is the greatest
wind pressure observed in England by anemometers or
dynamometers, which is confirmed by the fall of chimneys
and other buildings, and remarks that a pressure of 61
pounds on the square foot was recorded at Liverpool
during the storm of the 7th of February, 1868, and of 71
pounds on the 27th of September, 1875. In regard to the
highest wind pressures in France, M. Gaudard mentions.
the upsetting of a train between Narbonne and Perpi-
gnan, in December, 1867, as indicating a pressure between
30 pounds and 50 pounds, and other similar accidents
with empty wagons on the same railway, in February,
1860, and January, 1863, as indicating a pressure of from
25 to 33 pounds. He continues: "No other part of
France is exposed to such violent storms; nevertheless,
in considering the stability of lighthouses, Fresnel allowed,
for the possibility of wind pressures up to 56 pounds."
Trautwine † mentions the breaking of a gauge at Girard
College, Philadelphia, under a strain of 42 pounds per
square foot; a tornado passing at the moment within a
quarter of a mile. At the Central Park (New York) Ob-
servatory, in March, 1876, a wind of 28.5 pounds per
square foot pressure was recorded. On Mount Washing-
* Proceedings of the Institution of Civil Engineers, vol. lxix., session
1881-82.
†The Civil Engineer's Pocket-Book.
24
THE WINDMILL AS A PRIME MOVER.
ton, N.H.,* 180 miles per hour has been observed. Mr.
C. Shaler Smith † gives the following as the most violent
storms of which he has personal record, having visited
the tracks of many destructive storms as soon as possible
after their occurrence :
"First, East St. Louis, 1871: Locomotive overturned;
maximum force required, 93 pounds per square foot.
(C
Second, St. Charles, 1877: Jail destroyed; force re-
quired, 84.3 pounds per square foot.
Third, Marshfield, Mo., 1880: Brick mansion-house
levelled; force required, 58 pounds per square foot.
(C
Fourth, Havre de Grace, Md., 1866: Ten spans of
wooden Howe truss bridge, 250 feet each, blown over;
force required, 27 pounds per square foot.
"Fifth, Decatur, Ala., 1870: Two spans of combina-
tion triangular truss blown over; force required, 26
pounds per square foot.
"Sixth, Meredosia, Ill., 1880: One span wooden
Howe truss, 150 feet long, overturned; force, 24 pounds
per foot.
"Seventh, Omaha, Neb., 1877: Two spans iron Post
truss, 250 feet each, blown down; force required, 18%
pounds per square foot."
Mr. Smith, in the same paper, also presents the fol-
lowing table of "the highest pressures registered in Great
Britain, those recorded by Mr. Hartnup at the observa-
tory at Bidstone:"
* The Civil Engineer's Pocket-Book.
† Transactions American Society of Civil Engineers, vol. x., May, 1881.
WIND: ITS VELOCITY AND PRESSURE.
25
TABLE IV.

DATE OF OBSERVATION.
27th December, 1868 .
Greatest Velocity, in
Miles, between any
Hour and the Next
Hour Following.
Greatest Pressure
in Pounds on the
Square Foot.
92
80
13th October, 1870
82
65
9th March, 1871
79
90
27th September, 1875
81
70
23d November, 1877
80
64
28th December, 1879
59
38
While such high pressures as above recorded are ex-
ceptional, their enumeration may serve to point out the
necessity of windmills being so constructed as not only
to run under light winds, but also to possess sufficient
strength to withstand heavy gales. And equal care, in
this particular of strength to withstand heavy wind press-
ures, should be observed in the design and construction
of windmill towers, which are at times of great height
and comparatively small weight and base.
26
THE WINDMILL AS A PRIME MOVER.
CHAPTER II.
THE IMPULSE OF WIND ON WINDMILL BLADES.*
LET AB (Fig. 1) = c represent the direction of mo-
tion and the velocity of the wind; the latter in feet per
second. Let BC= v, perpendicular to AB, represent
the direction of motion and the velocity of any element of

E
A
N
C
la
B
FIG. I.
the sail; the latter in feet per second. AB is 1 to BC,
because the direction of motion of each point of the
surface of a windmill sail is perpendicular to that of the
wind. Then, the wind moving in the direction AB with
* The main portion of this chapter was originally presented by the author in
"A Dissertation on the Theory and Practice of Windmills," Engineering and
Mining Journal, Oct. 7 and 14, 1876.
THE IMPULSE OF WIND ON WINDMILL BLADES.
27
a velocity c, and the element of the sail moving in a
direction BC with a velocity v, the effect of these com-
bined motions would be the same as if, the air being at
rest, the sail moved in a direction BD with a velocity
equal to BD (c² + v²); or, as if the wind moved
in a direction BD and struck the sail with a velocity
(c² + v²), the sail being at rest.
=
Let the angle of impulse < ABE = a, let < DBA
=D;
then < DBE = a — D,
sin (a — D) = sin a cos D — sin D cos a.
AB = DB cos DBA
Let O
:: (c² + ~²) }
= c sec D.
quantity of wind, in cubic feet, flowing along per square foot
per second;
d = density of wind;
k = 0.93 = co-efficient of friction of particles of air in motion
(see p. 10);
S = surface of sail in square feet;
F = total pressure, in pounds, exerted by the wind normally to
the surface.
F
-
SkQd (c² + v²) ‡ sin (a — D).
g
бо
Substituting for Q its value c,
SKcd
c sec D (sin a cos D — sin D cos a) ;
F=
g
SKcdc
F=
(sin a
tan D cos a); tan D =
tan D = 2;
g
SKed
ข
• F=
(sin a - - cos a).
g
C
28
THE WINDMILL AS A PRIME MOVER.
To find what part of this pressure is useful in causing
rotation, we resolve it into two components, one perpen-
dicular to, and the other in the direction of BC. The
former produces no beneficial effect; on the contrary,
increases the pressure on the journals, and thus gives
rise to a loss of effect by friction. The component in
the direction BC, however, is that part of the pressure
exerted which is entirely utilized, and represents the use-
ful
pressure on the sail. Let this pressure be represented
by L. Then L = F cos a = Sked (sin acosa) cos a.
This multiplied by v, the velocity of the sail in feet per
second, gives for the theoretical mechanical effect of the
windmill sail,
SKc2d
g
Le Sked (sina - cosa) cos a.
Lv=
SKcd
g
ข
C
(I.)
Rankine, in his "Steam-Engine and other Prime
Movers," edition 1874, p. 170, finds the following value
for the theoretical mechanical effect due to the impulse
of water on a flat vane:
Pv=
DQvc cos (cos & v² cos² 8
When applied to windmills, it must be remembered that
the direction of motion of each point of the sail is per-
pendicular to that of the wind, and the following substi-
tutions can accordingly be made:
8 = 90-3 .. cos 8 = sin;
THE IMPULSE OF WIND ON WINDMILL BLADES.
29
and, since
a = 8, a =
8, a = 90 — 5,
-
.. ( = 90
(= - a
sin (
= cosa, cos (= sin a.
DQcv sin a cos a
v² cos² a
Pv=
;
g
and, substituting L for P, S for the area of surface in
square feet, and kcd for QD, “the weight of water flow-
ing along the stream per square foot in a second,"
Lv=
ข
Skde of sin a
(sina - 2
- cos a) cos 4,
g
C
which is the same as formula (I.), found directly as
above.
Weisbach deduces (see "Weisbach's Mechanics,"
edited by Walter R. Johnson, p. 354) a value for the
theoretical mechanical effect, of which the errors in solu-
tion can be best pointed out by quoting a passage: —
"Ifè = the velocity of the sail, Q = the quantity of wind striking
on CD per second, y = the density of the wind, and a = the angle CAH

मर
FIG. 2.
(Fig. 2) which the direction of the wind makes with CD, then, on the
assumption that the plane moves away in the direction of the wind,
the normal impulse of the wind on CD is N sin a Qy. Putting
=
g
30
THE WINDMILL AS A PRIME MOVER.
the section CN=G, then the quantity of wind Q coming into action is
not Gc, but G(ċ – v), as the sail moving with the velocity v leaves a
space Go behind it, which takes up a proportion of the quantity of wind
Ge following it, equal to Go, without undergoing any change of motion.
Hence the normal impulse may be put N = sin a(cv) Gy =
M
g
C
ข
g
sin a Gy; or, if F = area of the element CD, and we substitute
Fsin a for G, then N (c — ~)²
g
sin² aFy. Besides this impulse on the
face of CD, there is a counteraction on the back, inasmuch as one part
of wind passing in the direction CE and DF, at the outside of the
plane, takes an eddying motion to fill up the space behind, and conse-
quently loses pressure corresponding to the relative velocity (cv) sina,
(cv)²
and represented by sin² a Fy. If we combine these two effects,
28
we get the normal impulse on the element of the sail.”
On examination, it will be seen that the relative
velocity of cand v, i.e., the fact that while the wind is
moving with a velocity c, the sail moves with a velocity v,
and therefore the wind actually strikes the surface with
a velocity (cv), is erroneously allowed for, twice. In-
stead of the normal impulse N reading N=
(c — 2)² sin a Gy,
g
it ought to read N = (c) c sin a Gy: for, in deriving
C.
&
ข
g
the expression N = sin a, the fact of the quantity of
wind striking with a relative velocity (cv) is taken into
account; and it is a mistake to forget this, and to make
the same allowance for a second time. Besides this im-
pulse, Weisbach adds another term, which, as is explained
below, it is not correct to add.. He assumes correctly that
the wind rushing past the sail produces a partial vacuum
behind it, and that this must be replaced by air. But is
it not probable that the vacuum will be filled up by wind
THE IMPULSE OF WIND ON WINDMILL BLADES. 31
of original velocity, and that the wind which has lost
part of its velocity by impact, only tends to fill up the
empty space left by the wind of original undiminished
velocity? It is certain, that as soon as one "line" of
wind has struck the surface, it glides along the surface
with diminished velocity, and simply forms a moving
cushion on the sail, upon which the wind, with its original
velocity, impinges. These facts seem to us to challenge
the correctness of Weisbach's analysis.
From all of the above considerations, the author feels.
justified in adopting, as the THEORETICAL MECHANICAL EF-
FECT OF A WINDMILL SAIL, the expression
Lv =
Skdc²
g
ย
(sin
ย
sin a- COS
C
a
s a) co
cos a;
(I.)
and, in finding the actual mechanical effect of a vertical
windmill, merely to make a deduction for loss. of effect by
friction of the shaft, considering a vacuum to be formed
behind the sail, and therefore assuming the resistance of
the air to be equal to nothing.
Best Angle of Impulse. — From formula (I.) it is ap-
parent that the effect increases with the velocity and
with the area S, but it is not so evident how the angle of
impulse affects the mechanical effect produced. That Lv
may not be zero, sin a must be > cos a, and cos a must
be > O. If sin a > cos a, tan a >; and, as cos a > 0,
therefore a < 90°. There must, therefore, be a value of a
between the limit tan a > and a <90°, corresponding to
C
V
V
C
C
32
THE WINDMILL AS A PRIME MOVER.
a maximum value of Lv. To find the value, we solve the
expression (sin a — 2
ข
cos a
a)
cos a for a maximum by the
с
laws of calculus, and obtain
20
tan² a
tan a = I,
C
(II.)
2
ข
tan a =
+
I +
(III.)
C
втр
In this formula, equation (2),
a represents the angle of impulse of the wind upon the windmill blade
(or sail), at any point of the blade, for maximum effect;
v=the velocity of the blade (at such point), in feet per second;
<= the velocity of the wind, in feet per second.
The table on p. 33 has been computed on the basis
of equation (III.), and sets forth the best "angle of
weather," that is, the angle which an element of the blade
or sail makes with the plane of motion of the blade.
This angle, which we will term w, is the complement of
the best angle of impulse; that is, w= 90° — a.
Let / = total length of blade from centre of windmill shaft to outer ex-
tremity of blade.
velocity, in feet per second, of the blade or sail, at a distance
from the centre of the shaft.
Then, in the table, w, represents the best "angle of
weather" at a distance from the centre of the shaft,
w6, represent the best "angles of weather"
and w₁, w₂,
2)
THE IMPULSE OF WIND ON WINDMILL BLADES. 33
at distances
‡ 1, § 1, . . . 7, respectively, from
, respectively, from the centre of
1, § 1,
the shaft.
TABLE V.
SHOWING THE BEST ANGLES OF "WEATHER" FOR WINDMILL BLADES
FOR GIVEN RELATIVE VELOCITIES OF BLADES AND WIND.

C
11
Wo=
W₁ =
WI
W₂ =
202
W3=
W4=
2015
ws=
ة الله
//
//
0
//
•
•
་
こ
​"/
0.10
O.II
42 8 41
39 20 42
36 39 I
34 5 57
31 43 3
41 51 41
38 47 47
35 52 7
33 7 31
30 35 41
29 31 5
28 17 15
0.12
41 34 44
38 15 7
35 6 2
32 10 46
29 31 5
นา
27 7 23
7
27 30 14
26 12
24 59 6
0.13
41 17 48
37 42 46
34 20 49
31 15 51
28 29 17
26 I 22
23 50 46
0.14
41 • 55
37 10 44
33 36 32
30 22 32
27 30 14
24 59 6
22 47 22
0.15
40 44 4
36 39
I
32 53 10
29 31 5
26 33 54
24 O 23
0.16
40 27 17
36 7 40
32 10 46
28 41 25
25 40 12
0.17
40 10 33
35 36 40
31 29 21
27 53 31
21 49 4
23 5 4
22 12 59
21 48 5
20 52 48
20
I 15
0.18
39 53 53
35 6 2
30 48 56
27 7 23
24 0 23
21 23 55
19 13 7
0.19
39 37 16
34 35 47
30 9 29
26 22 57
23 14 4
20 37 43
18 28 10
0.20
39 20 42
34 5 57
29 31 5
0.21
39 4 12
33 36 32
28 53 40
0.22
38 47 47
33 7 31
28 17 15
0.23
38 31 25
32 38 56
27 41 50
0.24
38 15 7
32 10 46
27 7 23
25 40 12
24 59 6
24 19 34
23 41 35
23 5 4
22 30
19 54 10
17 46 8
21 48 5
19 13 7
17 6 47
21
813
18 34 24
16 29 56
20 30 16
17 57 51
15 55 21
19 54 10
17 23 20
15 22 53
0.25
37 58 55
31 43 3
26 33 54
0.26
37 42 46
31 15 51
26
I 22
22 30
21 56 18
о
19 19 48
16 50 42
14 52 21
18 47 3
16 19 50
14 23 36
0.27
37 26 43
30 48 56
25 29 46
21 23 55
18 15 52
15 50 35
13 56 30
0.28
37 10 44
30 22 32
24 59 6
20 52 48
17 46 8
15 22 53
13 30 56
0.29
36 54 50
29 56 35
24 29 18
20 22 54
17 17 46
14 56 36
13 6 46
0.30
36 39 I
0.31
36 23 18
29 31 5
29 6
24 0 23
19 54 10
16 50 42
14 31 38
12 43 54
2
23 32
19
19 26
32
16 24 51
14 7 55
12 22 15
0.32 36 7 40
28 41 25
23 5
10
0.33
35 52 7
28 17 15
22 38
38
+ co
4
18 59 58
16 Ο ΙΟ
13 45 21
12 I 43
IS 34 24
15 36 33
13 23 53
II 42 14
0.34 35 36 40
27 53 31
22 12 59
IS 9 48
15 13 58
0.35
35 21 18
27 30 14
0.36
35
6
2
27 7 23
0.37
0.38
34 50 53
26 44 57
21
21 48 5
21 23 55
O 28
17 46 8
17 23 20
17
34 35 47
26 22 57
0.39
34 20 49
26
I 22
20 37 43
20 15 37
0.40 34 5 57
25 40 12
19 54 10
0.41
33 51 12
25 19 27
19 33 21
0.42
33 36 32
24 59 6
19 13 7
I 23
16 40 13
TỐ 19 50
16 Ο ΙΟ
15 41 II
15 22 53
0.43
33 21 58
24 39 8
IS 53 29
0.44 33 7 31
24 19 34
18 34 24
0.45
32 53 10
24 O 23
18 15 52
0.46
32 38 51
23 41 35
17 57 51
15 5 12
14 48 8
14 31 38
14 15 42
0.47
32 24 48
23 23 9
17 40 21
14 0 17
14 52 21
14 31 38
14 II 47
13 52 45
13 34 30
13 16 57
13 O
0 6
12 43 54
12 28 19
12 13 19
II 58 53
II 44 57
II 31 32
13 3 25
12 43 54
12 25 16
II
II 23 43
66
12
7 29
II 50 28
II 34 II
11 18 36
IO 49 20
10 33 21
10 18 12
ΙΟ
9 49 37
3 32
II 3 40
10 49 20
10 35 35
10 22 23
ΤΟ
9 36 18
9 23 33
9 II 20
8 59 37
9 42
S 48 23
9 57 30
8 37 35
9 45 45
S 27 12
0.48
32 10 46
23 5 4
17 23 20
13 45 21
11 18 36
9 34 27
S 17 13
0.49
31 56 51
22 47 22
0.50
3 43 3
22 30
17 6 47
16 50 42
13 30 56
13 16 57
II
6 6
9 23 33
S 7 37
10 54 3
9 13 3
7 58 22
34
THE WINDMILL AS A PRIME MOVER.
The diagram* (Fig. 3) shows graphically the best an-
gles of impulse and of "weather," as determined above.
The ordinates represent the best angles of weather and
impulse, expressed in degrees; and the abscissas, the ratio

85°
80°
70°
SHOWING THE BEST ANGLES of
PAPPER"
60°
50*
40*
30°
BEST ANGLES
VING WHEL BLADES
ALPARLOR /2015-
20°
10°
5°
CORVE SHOWING THE BEST AND IF THE IMPULSE +
RATIO OF VELOCITY OF WING TO VELOCITY OF WHEEL
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5
FIG. 3.
of the velocity of the wind to the velocity of the wind-
رح
mill blades, Thus, assuming the velocity of the wind
to be 31.416 feet per second, the diameter of the wheel to
be 35 feet, and the number of revolutions per minute
to be made to equal 30, the velocity of the wind wheel at
* Originally presented by the author in the Engineering and Mining Journal,
Oct. 26, 1878. See also Appleton's Cyclopædia of Mechanics, 1880; Transactions
American Society Mechanical Engineers, 1882; American Engineer, April 22, 1882;
Journal of the Franklin Institute, July, 1882; Engineering, Aug. 18, 1882; Proceed-
ings Institution Civil Engineers, vol. lxx., session 1881-82, Part IV.
THE IMPULSE OF WIND ON WINDMILL BLADES. 35
a point 2.5 feet from the centre of the shaft will be 7.854
feet per second; at 5 feet from the centre, 15.708; at 7.5
feet, 23.562; etc. and the ratio of the velocity of the
wind to the velocity of the sail,, will at 2.5 feet from
centre of shaft equal 0.25; at 5 feet, 0.50; at 7.5 feet,
0.75; etc. The best angle of weather equals, therefore,
at a distance 2.5 feet from the centre of the shaft, 38°;
at 5
feet from the centre, 32°; at 7.5 feet, 27°; etc.: and
the best angle of impulse equals, at a distance of 2.5
feet from the centre of the shaft, 52°; at 5 feet from the
centre, 58°; at 7.5 feet, 63°; etc.
Since there is no difference in the amount of effect
caused by the blades moving against the air, and that
caused by the air (or wind) striking upon the blades
(assuming the same velocity in both cases), the angles
set forth in the table and diagram will be found to be
those of maximum efficiency for ventilating purposes as
well as for windmills.
Theoretical Mechanical Effect of Windmill of Shape
of Sail for Maximum Effect.
Having given the velocity of the wind and the number
of revolutions and the dimensions of the sail, the shape of
the surface producing the maximum effect, and the cor-
responding theoretical effect, can be readily found.
Let c
=
velocity of the wind, in feet per second;
12 = number of revolutions of the windmill per minute;
bo, b1, b2, . . . b, be the breadth of the sail at distances l。, 11, 12,
3,... 7, respectively, from the axis of the shaft ;
།
36
THE WINDMILL AS A PRIME MOVER.
Let lo
= distance from axis of the shaft to the beginning of sail proper ;
/ = distance from axis of the shaft to the extremity of sail proper;
v, be the velocity of the sail, in feet per second,
at distances l。, l₁, l2, l3, . . . l, respectively, from the axis
of the shaft ;
Vo, V1, V2, V39
αo, A1, A2, Az,
Then will
ax, be the angles of impulse for maximum effect
at distances l。, 41, 42, 43, . . . 4, respectively, from the axis of
the shaft.
V。 = 0.10472/n,
V₁ = 0.104721,n,
VI
V₂ = 0.10472/₂n,
Vx=0.10472/n;
and, from (III.),
0.10472n
0.10472/。n
2
tan a。 =
+
I +
C
C
0.10472/,n
0.10472/,n
2
tan a₁ =
+
I +
>
C
C
0.10472/₂n
0.10472/₂n
2
tan a₂ =
+
I +
с
C
0.10472/n
0.10472/1
2
tan ax =
+
I +
C
C
From these equations can be found the angle which
the direction of the wind must make with the sail at
any point on its surface, in order to give the best effect.
As the shaft of a vertical windmill is parallel to the
direction of motion of the wind, these angles represent
also those which the elements of the surface at distances
l。, 11, 12, . . . l, make respectively with the axis of the shaft ;
or, the elements of the sail must make the complements
THE IMPULSE OF WIND ON WINDMILL BLADES. 37
of these angles (angles of weather) with the plane of
motion of the sail. Having, therefore, found the angles
of impulse, as indicated above, the shape of sail for
maximum effect is determined. The theoretical effect
for this sail is computed by application of formula (I.),
Lv =
SKcd
g
مد
From (II.) we have
sin a
-
ย
a)cos
-cos a Icos a.
cos
SKdc3
Lv=
(tan a
cot a) sin a
2g
c tan² a
I
C
ข
|
2 tan a
2
(tan a cota).
Substituting this value of v in (I.),
ta) (sin
tan a
cot a
2
cos a)oosa,
SKdc3
Lu
tan a sin a cos a
cot a sin a cos a
20
tan a (tan a
cot a) cos² a
cot a (tan a
cot a) cos² a
+
2
2
SKdc3
tan² a cos² a
Lv =
sin
sin² a
cos² a
2
2g
tan a cot a cos² a
cot a tan a cos² a
cot² a cos²
+
+
2
2
2
SKdc3
sin² a
cos² a
cos² a
Lv=
sin² a
cos² a
+
+
28
2
2
2
cost a
2 sin² a
SKdc³/sin² a
cost a
SKde³/sin¹ a
cost a
Lo
20
2
2 sin² a
48
sin² a
SKde³/ (sin² a + cos² a) (sin² a
cos² a)
Lv=
48
sin² a
SKdc³/2 sin² a
48
sin² a
1)
38
THE WINDMILL AS A PRIME MOVER.
S = (1 − 1)B (B = mean breadth of sail),
and
Lv =
(1 — 1) Kdc³ 2 sin² a
-B-
I
48
sin² a
B(2 sin² a -
1)
= the mean of
sin² a
2 sin² a。
I
bos
sin² do
2 sin² ax
I
2 sin² a,
I
- b x
b₁₂
sin² ax
sin² a,
Therefore the theoretical mechanical effect of the
windmill of shape of sail for maximum effect (when
N = number of sails or blades of windmill) equals
-
N(1 − 1) Kdc³
48
2 sin² αo
X mean of
sin² αo
I
2 sin² a,
-bor
sin² a
I
I
2 sin² axIbx. (IV.)
sin² ax
Theoretical Mechanical Effect of Windmill with Plane
Sails.
If the sail is a plane, the angle of impulse a will be
a constant quantity; and hence we find from (I.), for
the theoretical mechanical effect of a windmill with plane
sails, the value
(l - l)kc²dN
g
sa)o.coś
× mean of [v. (sin a
[vo (sina - 20 cos a), co
С
COS a
. v. (sin a-2 cos a), cos a]. (V.)
e
THE IMPULSE OF WIND ON WINDMILL BLADES. 39
Loss of Effect by Friction of the Shaft.
In calculating the amount of friction, the whole weight
of the wheel is taken as bearing upon the neck gudgeon,
and the pressure upon the lower bearing is not consid-
⚫ered. This certainly seems, at first sight, like finding an
excess of friction, part of the weight evidently resting
upon the lower bearing; but it must be remembered,
first, that this excess is compensated by the fact that no
attention is paid to the axial component of the pressure
of the wind, and, secondly, by the fact of the considerably
greater diameter of the upper than of the lower bearing.
Let W = weight of wind wheel in pounds,
f*
= co-efficient of friction of shaft and bearings,
n = number of revolutions of the windmill per minute,
D = diameter of upper bearing in feet.
The work expended in overcoming the friction will
equal the amount of friction into the velocity with
which it is overcome. This velocity in feet per second
= 0.05236nD, and the loss of effect by friction = ƒW
X 0.05236nD, which, subtracted from (IV.), makes
The actual mechanical effect of a windmill, with sails of best angles of
weather, equal to
(1-1)kdc3
X mean of
2 sin² a。 I
sin² do
1bo
45
2 sin² ax
sin² ax
I
bx) -ƒW × 0.05236nD. (VI.)
* For the co-efficient of friction in shafts, see chap. x., p. 147.
40
THE WINDMILL AS A PRIME MOVER.
Subtracting the loss of effect by friction of the shaft
from (V.), we have, for the actual mechanical effect of a
windmill with plane sails, the value
(1 — l) kc²d N
g
Vx
го
of [% (sin a- cos a) d, cos a
of[
X mean of v。 (sin a
V x
C
X
(sin a- cos a) b, cos aƒ W × 0.05236nD. (VI.)
α
C
cosa]
Proof of Accuracy of Formula (IV.).
It is always well to put a formula, however evident it
may appear theoretically, to a practical test, to ascertain
its truth. The only practical test which can be applied in
this case is a comparison of the effect produced, given as
the result of Coulomb's* experiments, and the effect as
deduced from the formulæ. Coulomb found as the total
effect, including friction of the shaft, 1,000 pounds raised
253 pieds de roi = 269.6 English feet for a windmill of
the following dimensions and given conditions: Length
of sail = /= 33 French feet 35.171 English feet; dis-
tance from axis of shaft to beginning of sail = 1= 6
=
French feet = 6.395 English feet; breadth of sail =
about 6.2 French feet
6.6195 English feet; number of
revolutions per minuten = 13; number of sails N
= 4; velocity of wind = about 20.5 French feet per
second = 21.982 (or about 22) English feet per second:
angle of impulse at l nearly 60°, angle at 78°.
The intermediate angles are not given; but, judging by
=
* See p. 125.
THE IMPULSE OF WIND ON WINDMILL BLADES.
4I
the agreement of the angles of impulse at /, and 4, the
windmill can be considered as having sails very nearly
of shape for maximum effect.
Let lo= v。
6.395 ft. Then = 8.70590 ft. per sec., tan a。= 1.48861,.'.
4 = 11.171
12 = 15.987
13 = 20.783
(C
1₁ = 25.579"
15 = 30.375
"
1 = 35.171
V₁ = 15.23498
VI
V₂ = 21.76406
03
= 28.29314
=
24 34.82222
25= 41.35130
Vx = 47.88038
(2 sin² 56° 6′30″ — 1)
sin² 56° 6′ 30″
(2 sin² 62°46′38″ — 1 )
sin² 62°46′38″
= 0.54880,
ao
tana, 1.94388,..a₁
=
56° 6'30".
62°46′38″.
:.a₂
tan a₂ = 2.45017, .. a₂ = 67°45′26″.
tan aз
= 3.00713,
.. a3 = 71°36′20″.
tan a₁ = 3.54901, .. a₁ = 74°15′50″.
4
tana5 = 4.12235,..as = 76°21′54″.
tan ax = 4.70488,.. ax = 78° 0′ 2″.
(2 sin² 71° 36'20"
sin² 71° 36′20″
(2 sin² 74° 15'50"-1)
sin² 74° 15′50″
1)
0.88941,
=
0.92060,
= 0.71747,
(2 sin² 67°45′26″
I)
0.83275,
sin² 67°45′26″
(2 sin² 76° 21′ 54″
sin² 76° 21′54″
I)
= 0.94115,
(2 sin² 78°0′2″ — 1)
=
0.95483.
sin² 78° 0'2"
the mean value of which, according to Simpson's rule, =
0.84458. Substituting the above values in equation (IV.),
4 X 6.6195 X 28.776
Lo
X
4
0.93 X dc²
g
X 22 X 0.84458;
de
=
and assuming the average temperature at time of obser-
vation 50° F., and the barometric pressure = 2088.5
(at 32° F. this = 2116.5), 1.2, and Lv = 6.6195 X
28.776 × 0.93 X 1.2 X 22 X 0.84458 = 3949.9 foot-pounds
per second 236,994 foot-pounds per minute 1,000
pounds raised 236.994 feet per minute. It will be noticed
that the effect as here calculated from the formula is
=
=
*These angles can be obtained directly from diagram, Fig. 3, or Table V.,
without first finding value of tan a, as has here been done as a mere matter of
interest.
42
THE WINDMILL AS A PRIME MOVER.
smaller than the actual effect; while, on account of the
better angles of impulse, it should be somewhat larger.
But, if the barometric pressure had
(at 32° this = 2381.06), then
=
dc2
g
equalled 2349.81
1.35, and Lv =
6.6195 × 28.776 × 0.93 × 1. 35 × 0.84458 × 60 = 266,618
foot-pounds per minute 1,000 pounds raised 266.618
feet per minute; or, if instead of c = 22 English feet, the
velocity had been 23 English feet per second, x c =
X 23 = 30.36 (the barometric pressure
529
de
g
39.66977 I
I 5903.20 0.018743
being assumed = 2088.5), Lv = 6.6195 × 28.776 × 0.93
X 30.36 × 0.84458 4541.4 foot-pounds per second =
1,000 foot-pounds raised 272.486 English feet per minute,
which is slightly above the effect found by experiment.
Now, the barometric pressure at the time of the obser-
vations might have been 2381.6 pounds per square foot,
instead of 2088.5, no record of the same having been
kept. Also, judging from the method by which the ve-
locity of the wind was ascertained,* an error of one foot
per second was very easily possible; and it is even prob-
able that the velocity of wind found differed somewhat
from the velocity with which the wind struck the mill,
no anemometer having been employed. However, the
close approximation between the results as determined by
calculation and by experiment is immediately discernible,
and various formulæ extant tested by the writer in the
same manner failed to give nearly as satisfactory results.
* See p. 127.
THE EARLY HISTORY OF WINDMILLS.
43
CHAPTER III.
THE EARLY HISTORY OF WINDMILLS.
ALL of paramount interest pertaining to the early
history of windmills has been collated by Professor John
Beckmann in his "History of Inventions and Discover-
ies." The work of this distinguished "public professor
of economy in the University of Göttingen" has, as we
have found by careful search, been exhaustive; and it is
a pleasure, therefore, to acknowledge our indebtedness
to this valuable treatise, or more directly to the transla-
tion by Mr. William Johnston, London, 1817, for all the
facts detailed in this chapter.
In vol. i., under the heading "Corn Mills," p. 247,
we read,
"The intrusting of that violent element water to support and drive
mills constructed with great art, displayed no little share of boldness;
but it was still more adventurous to employ the no less violent but
much more untractable and always changeable wind for the same pur-
pose. Though the strength and direction of the wind cannot be any
way altered, it has, however, been found possible to devise means by
which a building can be moved in such a manner that it shall be
exposed to neither more nor less wind than is necessary, let it come
from what quarter it may.
"It is very improbable — or, much rather, false-that the Romans
44
THE WINDMILL AS A PRIME MOVER.
had windmills; though Pomponius Sabinus affirms so, but without any
proof.* Vitruvius,† where he speaks of all forces, mentions also the wind;
but he does not say a word of windmills. Nor are they noticed either
by Seneca or Chrysostom,§ who have both spoken of the advantages of
the wind. I consider as false also the account given by an old Bohe-
mian annalist, || who says that before the year 718 there were none but
windmills in Bohemia, and that water-mills were then introduced for the
first time. I am of the opinion that the author meant to have written
hand and cattle mills instead of windmills.
•
"It has been often asserted that these mills were first invented in
the East, and introduced into Europe by the Crusaders; but this also is
improbable, for mills of this kind are not at all, or very seldom, found
in the East. There are none of them in Persia, Palestine, or Arabia; and
even water-mills are there uncommon, and constructed on a small scale.
"Besides, we find windmills before the Crusades, or at least at the
time when they were first undertaken. It is probable that these
buildings may have been made known to a great part of Europe, and
particularly in France and England,¶ by those who returned from these
expeditions; but it does not thence follow that they were invented in
the East.**
* See Pomponius Sabinus, ut supra.
† Lib. ix. c. 9, lib. xc. 1, 13.
‡ Natur. Quæst., lib. v. c. 18.
§ Chrysost. in psalm cxxxiv. p. 362.
"
|| At the same period [718], one named Halek, the son of Uladi the Weak,
built close to the city an ingenious mill which was driven by water. It was visited.
by many Bohemians, in whom it excited much wonder, and who, taking it as a model,
built others of the like kind here and there on the rivers; for before that time all
the Bohemians' mills were windmills erected on mountains."
¶ See De la Mare, Traité de la Police, etc., ut supra; Description du Duché
de Burgogne, Dijon, 1775, 8vo, i. p. 163; Dictionnaire des Origines, par D'Origny,
v. p. 184. The last work has an attractive title; but it is the worst of its kind,
written without correctness or judgment, and without giving authorities.
**"There are no windmills at Ispahan nor in any part of Persia. The mills
are all driven by water, by the hand, or by cattle" (Voyages de Chardin, Rouen,
THE EARLY HISTORY OF WINDMILLS.
45
"The Crusaders perhaps saw such mills in the course of their
travels through Europe; very probably in Germany, which is the original
country of most large machines. In like manner, the knowledge of
several useful things has been introduced into Germany by soldiers who
have returned from different wars; as the English and French, after their
return from the last war, made known in their respective countries many
of our useful implements of husbandry, such as our straw-chopper,
scythe, etc.
"Mabillon mentions a diploma of the year 1105, in which a con-
vent in France is allowed to erect water and wind mills, molendina ad
ventum.*
In the year 1143, there was in Northamptonshire an abbey,
situated in a wood, which in the course of a hundred and eighty
years was entirely destroyed. One cause of the destruction 'was said
to be, that in the whole neighborhood there was no house, wind or
water mill built, for which timber was not taken from this wood.†
1723, 8vo, viii. p. 221). "The Arabs have no windmills: these are used in the East,
only in places where no streams are to be found. And in most parts the people
make use of hand-mills. Those which I saw on Mount Lebanon and Mount
Carmel had a great resemblance to those which are found in many parts of Italy.
They are exceedingly simple, and cost very little. The millstone and the wheel are
fastened to the same axis. The wheel, if it can be so called, consists of eight
hollow boards, shaped like a shovel, placed across the axis. When the water falls
with violence upon these boards, it turns them round, and puts in motion the mill-
stone, over which the corn is poured" (D'ARVIEUX: Merkwürdige Nachrichten
von seinen Reisen, Part III., Copenhagen and Leipsic, 1754, Svo, p. 201). “I did
not see either water or wind mill in all Arabia. I, however, found an oil-press at
Tehama, which was driven by oxen, and thence suppose that the Arabs have corn-
mills of the like kind" (NIEBUHR: Beschreibung von Arabien, p. 217).
* "Iisdem etiam facultatem concessit constituendi domos, stagna, molendina
ad aquam et ventum, in episcopatu Ebroicensi, Constantiensi, et Bajocensi, ad
augendos monasterii proventus (MABILLON: Annales Ordanis S. Benedicti,
tom. v., Lut., Paris, 1713, fol. p. 474).
↑ "Præterea non fuit in patria, aula, camera, orreum, molendinum venticium
sive aquaticum alicujus valoris plantata sine adminiculo aliquo boscorum Sanctæ
Maria de Pipewalla [so the wood was called] quot virge molendinorum venticio-
rum dabauntur in temporibus di versorum abbatum nemo novit, nisi Deus. Caussa
46
THE WINDMILL AS A PRIME MOVER.
}
"In the twelfth century, when these mills began to be more common,
a dispute arose whether the tithes of them belonged to the clergy; and
Pope Celestine III. determined the question in favor of the Church.*
In the year 1332 one Bartolommeo Verde proposed to the Venetians to
build a windmill. When his plan had been examined, a piece of ground
was assigned to him, which he was to retain in case his undertaking
should succeed within a time specified.† In the year 1393 the city of
Spires caused a windmill to be erected, and sent to the Netherlands for
a person acquainted with the method of grinding by it.‡
“A windmill was also constructed at Frankfort in 1442, but I do not
know whether there had not been some there before.§
"To turn the mill to the wind, two methods have been invented.
The whole building is constructed in such a manner as to turn on a post
below, or the roof alone, together with the axle-tree; and the wings are
movable. Mills of the former kind are called German mills; those of
the latter, Dutch. They are both moved round, either by a wheel and
pinion within, or by a long lever without. I am inclined to believe
that the German mills are older than the Dutch; for the earliest descrip-
tertia destructionis boscorum fruit in constructione et emendatione domorum infra
abbathiam et extra utpote grangus, orreis, bercariis molendinis aquaticis et venticiis
per vices. [The letter of donation, which appears also to be twelfth century, may
be found in the same collection, vol. ii., p. 459. In it occurs the expression,
molendinum ventritricum. In a character, also, in vol. iii., p. 107, we read of mo-
lendinum ventorium]" (Monasticon Anglicanum sive Pandicta Canobiorum, edit.
sec. London, 1682, fol. i. p. 816).
* De reditibus molendini ad ventum solvendæ sunt decimæ, Decretal Greg.,
lib. iii. tit. 30, C. 23.
† Gir. Zanetti, Dell' Origine di alcune arte appresso di Veneziani, Venez.,
1758, 4to, p. 74; Pro faciendo unum molendinum a vento; Le Bret, Geschichte
von Venedig, II. i. p. 233.
Lehmann's Chronica der Stadt Speyger, Frankf., 1662, 4to, p. 847: "Sent
to the Netherlands for a miller who could grind with the windmill."
§ Lersner, Frankf. Chronik, ii. p. 22.
|| Description and figures of both kinds may be found in Leupold's Theatrum
Machinarum Generale, Leipsic, 1724, fol. p. 101, tab. 41-43.
THE EARLY HISTORY OF WINDMILLS.
47
tions which I can remember, speak only of the former. Cardan,* in
whose times windmills were very common, both in France and Italy,
makes, however, no mention of the latter; and the Dutch themselves
affirm, that the mode of building with a movable roof was first found out
by a Fleming in the middle of the sixteenth century.†
"Those mills by which, in Holland, the water is drawn up and
thrown off from the land, one of which was built at Alkmaar in 1408,
another at Schoonhoven in 1450, and a third in Enkhuysen in 1452,
were at first driven by horses, and afterwards by wind. But as these
mills were immovable, and could work only when the wind was in one
quarter, they were afterwards placed, not on the ground, but on a float
which could be moved round in such a manner that the mill should
catch every wind. This method gave rise, perhaps, to the invention of
movable mills."
+
An interesting episode relative to the use of wind-
*"Nor can I pass over in silence what is so wonderful, that, before I saw it, I
could neither believe nor relate it, though commonly talked of, without incurring
the imputation of credulity. But a thirst for science overcomes bashfulness. In
many parts of Italy, therefore, and here and there in France, there are mills which
are turned round by the wind" (De Rerum Varietate, lib. i. cap. 10, in the edition of
all his works, Lugduni, 1663, fol. vol. iii. p. 26).
† This account I found in De koophandel van Amsterdam, door Le Long,
Amsterdam, 1727, 2 vols. Svo, 11, p. 584: "De beweegelyke kap, om de moolens op all
windens te zettens, is erst in't midden van de xvide eeuw door een Vlaaming uytge
vonden " ("The movable top for turning the mill round to every wind was first
found in the middle of the sixteenth century by a Fleming "). We read there that
this is remarked by John Adrian Leegwater; but of this man I know nothing more
than what is related of him in the above work, that he was celebrated on account
of various inventions, and died in 1650, in the seventy-fifth year of his age. See
also Beschryving der Stadt Delft door verscheide Liefhebbers en Kenners der
Nederlandsche oudhedin. Te Delft, 1729, fol. p. 623.
"De molens hadden doen (toen) vaste kappen zoo datze maar met eene wind
malen konde, waarom men op zekere plaats, om dit ongeval voor te kommen, een
molen op een groot vlot neder zette dat men dan naar din wind draide." See the
History of the city of Delft, above quoted.
48
THE WINDMILL AS A PRIME MOVER.
mills, of special interest to the school of political econo-
mists, who hold that any of the free forces of nature,
such as air, water, land, and the like, should, in their
natural, unimproved offering, be the equal property of
all, is noted by Beckmann, on p. 268, as follows:
"The avarice of landholders, favored by the meanness and injustice
of governments, and by the weakness of the people, extended this
regality not only over all streams, but over the air and the windmills.
The oldest example of this with which I am at present acquainted is
related by Jargow.*
"In the end of the fourteenth century, the monks of the celebrated
but long since destroyed monastery of Augustines at Windsheim, in
the province of Overyssel, were desirous of erecting a windmill not far
from Zwoll; but a neighboring lord endeavored to prevent them, de-
claring that the wind in the district belonged to him.
"The monks, unwilling to give up their point, had recourse to the
Bishop of Utrecht, under whose jurisdiction the province had continued.
since the tenth century. The bishop, highly incensed against the pre-
tender who wished to usurp his authority, affirmed that the wind of the
whole province belonged to him only, and in 1391 gave the convent
express permission to build a windmill wherever they thought proper.†
one.
*Jargow, Einleitung in die Lehre von den Regalien, Rostock, 1757, 4to, p. 494.
† "As our monastery had not a mill to grind corn, they resolved to build a new
When the lord of Woerst heard this, he did every thing in his power to
prevent it, saying that the wind in Zealand belonged to him, and no one ought to
build a mill there without his consent. The matter was therefore referred to the
Bishop of Utrecht, who, as soon as the affair was made known to him, replied in a
violent passion that no one had power over the wind within his diocese but himself
and the church at Utrecht; and he immediately granted full power, by letters-
patent, dated 1391, to the convent at Windsheim, to build for themselves and their
successors a good windmill in any place which they might find convenient "
(Chronicon Canonicorum regularium ordinis Augustini, capituli Windesemensis,
auctore Joh. Buschio, Antverpiæ, 1621, 8vo, p. 73).
THE EARLY HISTORY OF WINDMILLS.
49
"In like manner, the city of Haerlem obtained leave from Albert,
count palatine of the Rhine, to build a windmill, in the year 1394.
"*
*"Albertus notum facimus quod donavimus donamusque civitati nostræ
Harlemianæ ventum molarium a parte australi civitatis nostræ praiscriptæ hemi-
stadium versus inter Pacis fossam et sparnam." (THEOD. SCHREVELII: Harlemum
Lugduni, Batavorum, 1647, 4to, p. 181).
50
THE WINDMILL AS A PRIME MOVER.
CHAPTER IV. ^
EUROPEAN WINDMILLS.
EUROPEAN windmills have been divided into two gen-
eral classes, according to the inclination of the shaft:
1. Horizontal Mills, in which the sails were so
placed as to turn, by the impulse of the wind, in a hori-
zontal plane, and hence about an axis exactly vertical;
and
2. Vertical Mills, in which the sails turn in a nearly
vertical plane, i.e., about an axis nearly horizontal.
Horizontal Mills.
On account of the many disadvantages connected
with the horizontal mills, their use has been exceedingly
limited. They have been employed only in situations
in which the height of the vertical sails proved a serious.
objection; a rare and extraordinary occurrence. This
class of mill demands, therefore, but little notice on our
part. Its general construction may be outlined to this
effect: Six or more sails, consisting of plane boards, are
set upright upon horizontal arms which rest upon a tower,
and which are attached to a vertical shaft passing through
EUROPEAN WINDMILLS. ·
51
the centre of the tower. The sails, which are fixed in
position, are set obliquely to the direction in which the
wind will strike them. Outside of the whole is placed a
screen or cylindrical arrangement of board intended to
revolve, these boards being set obliquely, and in planes
lying in opposite course to those of the sails.
As a
result, from whatever direction the wind may blow against
the tower, it is always admitted by the outer boards to
act on the sails most freely in that half of the side it
strikes on, from which the sails are turning away; and
it is partly, though by no means entirely, broken from the
sails which, in the other quadrant of the side, are ap-
proaching the middle line. Fairbairn* reprints from the
columns of the "Practical Mechanic's Magazine" the fol-
lowing account of a horizontal windmill at Eupatoria in
Crimea, as it appeared when seen by the writer of the
article during the period of the Crimean War. This
description will well answer for the whole type. It
reads: -
"Around the town of Eupatoria, in the Crimea, there appeared to
be nearly two hundred windmills, chiefly employed in grinding corn;
and all which were in a workable state were of the vertical construction,
and only one horizontal mill, which seemed to have been out of use
for at least a quarter of a century. The tower of this mill was built of
brickwork, about twenty feet diameter at the base, and about seventeen
feet at the top, and twenty feet high. The revolving wings, which con-
sisted of six sets of arms, appeared to be about twenty feet diameter
and about six feet broad, fitted with vertical shutters which were
* Treatise on Mills and Millwork, by Sir William Fairbairn.
52
THE WINDMILL AS A PRIME MOVE
movable on pivots passing through the arms, the shutters being about
twelve inches wide by five or six feet high; and the pivots were fixed
at about one-third of the breadth from the edge of the shutters, in
order that the wind might open and shut them at the proper time
during the revolution of the wings. About one-third of the circum-
ference of the wings was surrounded by a segmental screen, to shelter
the arms and shutters while moving up against the wind; and the screen
seemed to have been hauled round with ropes, in order to suit the
direction of the wind."
The objections to the employment of the horizontal
windmill, which virtually debarred, and still debar it from
use in competition with the vertical mill, are, first, that
only one or two sails can be effectually acted upon at the
same moment; and secondly, that the sails move in a
medium of nearly the same density as that by which they
are impelled, and that therefore great resistance is
offered to those sails which approach the middle.
Smeaton* puts it thus :
"Little more than one sail can be acting at once, whereas in the
common windmill all the four act together; and therefore, supposing
each vane of a horizontal windmill of the same dimensions as each
vane of the vertical, it is manifest that the power of a vertical mill with
four sails will be four times greater than the power of the horizontal
one, let its number of vanes be what it will. This disadvantage arises
from the nature of things; but, if we consider the further disadvantage
that arises from the difficulty of getting the sails back against the wind,
etc., we need not wonder if this kind of mill is in reality found to have
not above one-eighth to one-tenth of the power of the common sort,
as has appeared in some attempts of this kind."
*Philosophical Transactions, 1755 to 1763.
}
EUROPEAN WINDMILLS.
53
While it is true, that, with a like area of sails, the
power of the horizontal is always much less than that of
the vertical mill, Smeaton's estimate of one to eight or
one to ten is too unfavorable, inasmuch as he overlooked,
as Sir David Brewster first showed, the loss in vertical
mills of one component of the wind's pressure.* The
ratio of one to four, given by Sir David Brewster, is,
however, about the correct figure, and presents a suf-
ficient explanation of the limited use to which horizontal
windmills have been put in the past, and a sufficient
cause why they should not be employed at the present
time, if the question of economy of motive power at all
enters the problem as a leading consideration.
Vertical Mills.
In vertical mills of the European type, the tower or
building which supported the windmill proper was either
of wood or stone: if of stone, the tower was commonly
in the form of a frustum of a cone. The principal parts
of the mill proper are:
1. An axle or shaft, either of wood or iron, in the top
of the building, inclined to the horizontal at an angle of
from ten to fifteen degrees, as observation has shown
that the impulse of the wind is usually exerted in lines
descending at such angles.
2. The sails attached to near the outer extremity of
the shaft, and turning in nearly a vertical plane. The
* See p. 28.
54
THE WINDMILL AS A PRIME MOVER.
planes of these sails are placed obliquely to the plane of
revolution; so that, when the wind blows in the direction
of the axle, it impinges upon their surface obliquely, and
thus the effort of the sail to recede from the wind causes
it to turn upon its axle. These sails consist of wooden
frames (arms and cross-bars), with canvas covering the
lattice or frame work. If four in number, as is the rule,
though five and six have been employed, the sails are
fixed in position at right angles to each other. They are
usually constructed from thirty to forty feet in length,
though fifty feet has often been exceeded.
3. A large toothed wheel upon the horizontal axle,
the teeth of which engage with those of a pinion
upon
4. A vertical shaft from which motion is imparted to
the machinery.
It will be understood that the horizontal shaft is
supported at its inner end near the centre of the base of
the dome or cone surmounting the mill, while its opposite
extremity passes through a perforation in one side of the
dome, where it has its main support, and projects far
enough to receive the ends of the long timbers or arms
of the sail. The pivot at the lower or inner end of the
shaft takes up but a small part of the weight and counter-
pressure.
The axle is constructed of some hard wood, like oak,
or of wrought-iron with cast-iron flanges of large diam-
eter keyed on the front, which are furnished with re-
cesses for receiving and holding the arms of the sails.
EUROPEAN WINDMILLS.
55
7.
C
Windmill Sails

FIG. 4.
56
THE WINDMILL AS A PRIME MOVER.
The latter must be proclaimed as the better practice;
since, the diameter of the neck of the wooden shaft being
from one and a half to two feet, an iron one substituted
in its place need not be more than six to nine inches,
and thus the loss by friction* is materially decreased.
The sails are made plane, concave, or warped. The
latter, the most effective, have been in greatest use;
and the angles employed in the Dutch type of mill†
have, on the whole, approached very closely to those
which theoretical analysis proves to be most serviceable.
Where plane sails have been used, the bars have all had
the same angle of inclination, ranging between twelve
and eighteen degrees to the plane of revolution.
Reference to Fig. 4, taken in connection with the
description of the windmills experimented upon by
Coulomb, as well as the accounts and illustrations of
special types given in this chapter, will not render it
necessary to say more in a general way about the sails,
than that they are either of rectangular or (more usually)
of trapezoidal form, increasing in width as they approach
the outer extremity of arm; that the innermost cross-bar
is placed at about one-sixth to one-seventh of the length
of the arm from the middle of the shaft; and that its
length is about equal to this distance. So the canvas
lattice-work covers only five-sixths or six-sevenths of the
outer portion of the sails. In a sail about thirty feet long,
the arms near the shaft are about one foot thick and nine
* See p. 39.
See p. 125.
† See p. 40.
EUROPEAN WINDMILLS.
57
F
T
{

B
P
R
H
FIG. 5.
.
P
P
58
THE WINDMILL AS A PRIME MOVER.
:
·
inches wide, and at the outer end about six inches thick
and four and a half inches wide.
As the direction of the wind is changing perpetually,
some contrivance is necessary for bringing the shaft into
the direction of the wind, so that the sails will be acted
upon most effectively. According as this revolution is
effected, European vertical windmills have been divided
into two general types: -
1. The Post or German Mill, in which the whole
building which sustains the wind sails, shaft, and the
machinery is supported upon a vertical post or column,
upon which it revolves at will when actuated by a lever.
2. The Tower or Dutch Mill, in which only the
head, cap, or dome of the building, with the shaft which
it contains, revolves.
Post or German Mills.
It will be readily understood that not only are these
mills necessarily limited in their size, but the manual
labor their turning to the wind implies, led to their
effectual abandonment when the tower mills had been
made automatic in their regulation.
Fig. 5 shows a general view of a post mill, for which
we are indebted to "A Manual of the Mechanics of En-
gineering and of the Construction of Machines," by Dr.
Julius Weisbach, vol. ii., translation of Professor A. J.
Du Bois, 1880, p. 637.
AA is the upright standard, supported by the cross-
EUROPEAN WINDMILLS.
59
timbers BB and B₁ B₁, and by the braces C and D; all
these parts constituting the so-called post. On the head
of the post is firmly placed the saddle E, composed of
four pieces of wood fastened together. The mill house
is supported by the two cross-beams, FF, and by two of
the six cross-lying floor timbers, GG. It rests also upon
the strong cross-timber H, which turns, by means of a
pivot, upon the head of the post. The neck N of the
axle KL turns in a metal or stone (basalt) plumber
block, which rests upon the strong axle timber MM,
the latter being supported by the roof framework 00.
Fig. 6 gives a sectional view of a post mill, taken
from the "Encyclopædia of Arts, Manufactures, and
Machinery," by Peter Barlow, F.R.S., professor at the
Royal Military Academy, Woolwich; London, 1851. We
copy the following description of this mill, verbatim, from
the same source:
"AB is the wind shaft, one end of which has a bearing on the beam
C of the framing of the mill, and the other is supported in a similar way
by a beam D; the part of the shaft outside the mill is larger, and made
square, and has two square holes or mortises through it, into which the
whips or arms of the sails are fitted, and made fast by wedges, aa.
The wheel EE, which is termed the brake wheel, is attached to the
wind shaft; it has a rim of wood, bb, on its circumference, termed
the brake, one end of which is attached to a fixed part of the mill, and
the other by means of an iron rod, to a lever, cd; so that, by pressing
down the end of the lever, the brake is made to bind upon the cir-
cumference of the wheel, and thereby produces such a resistance that
the mill may be at any time stopped. The brake wheel is here
represented on the old construction; i.e., the face wheel, which is
supposed to work a trundle not shown in the figure.
60
THE WINDMILL AS A PRIME MOVER.
"The lower floor of the mill is made to receive the post P, upon
which the mill is turned round to face the wind. This post is a very
strong tree, which is held perpendicularly by fixing it upon the middle

M
Post Mill.
H
P
F
F
B
FIG. 6.
of two long timbers, which form a large cross upon the ground, and
which constitute the base of the whole mill. The post is secured in its
vertical position by four oblique braces, F, F, F, F, which extend from the
ground cross to the middle of it; leaving ten or twelve feet of the upper
part, which is made round, clear from the obstruction of the braces.
EUROPEAN WINDMILLS.
61
This round part of the post rises up through the middle of the lower
chamber, in the floor of which a circular collar is formed to the exact
diameter of the post. At the upper end of the post is a pivot or
gudgeon, which enters into a socket fixed to one of the strongest
beams, G, in the middle of the upper floor; this beam must necessarily
be very strong, as it has to sustain the whole weight of the erection.
In this way the mill is made to turn freely upon the pivot, while the
collet in the lower floor serves to keep it steady and in a vertical
position. I is a ladder for the purpose of ascending to the mill: it is
united by joints to the back part of the framing, and has a rope, M,
fastened to the lower end, which passes in an inclined direction into
the mill, so that, by a lever or pulleys, it can be raised at pleasure
clear of the ground. The ladder thus raised serves as a lever for
turning the mill round, which is usually done by manual labor: some-
times, however, more force is necessary, and a small capstan is provided,
This capstan is
to draw a rope attached to the end of the ladder.
movable, and can be fastened at pleasure to any of the posts which are
fixed in the ground for the purpose. When the mill is by these
means placed in the desired direction, the ladder is let down to the
ground; and, its position being on the opposite side to that of the sails,
it serves not only for ascent, and to keep the mill steady in position,
but acts as a stay to resist the tendency of the wind to overturn it,
occurrence which sometimes happens in mills of this description."
Tower or Dutch Mills.
an
In Dutch mills the dome only is turned, carrying the
axle and sails with it into the required position; while
the vertical toothed wheel merely travels about the pinion,
and the connection is not broken. In order to allow the
dome to turn, and at the same time secure it in position,
it is most usual to construct the tower open at the top;
this opening being strengthened by a wooden rim
62
THE WINDMILL AS A PRIME MOVER.
running completely around it. And on the upper surface
thus exposed is a groove in which small circular metallic
casters or rollers are placed, to turn on horizontal axes.
The dome is made with a corresponding groove on its
under side, so as to rest upon the rollers, and turn on
them; while it has also a flange, projecting downwards,
surrounding the rim of the tower, small vertical rollers.
being here also usually fixed between the two. Thus the
dome can be turned with a slight effort into any re-
quired position, and by appropriate means can be fixed if
desired.
The turning of the dome was formerly effected by
a toothed wheel which engaged in a rack on the inner
side, and which was turned by means of an endless cord
pulled by a man; but at the present time Cubitt's method
is employed. This consists of a set of small sails, or an
auxiliary windmill, placed in an upright position upon
a long arm or frame projecting in the plane of the hori-
zontal shaft, but on the opposite side of the dome; the
plane of the sails of the auxiliary windmill being nearly at
right angles to the plane of the sails of the windmill
proper. By their revolution, the sails turn a shaft and
pinion, and finally act upon teeth surrounding the exte-
rior of the dome, turning it until the wind no longer
moves the auxiliary windmill vanes, when the sails proper
will be exactly in their best position to receive the im-
pulse of the wind.
Figs. 7 and 8 represent the upper or distinctive
portion of the tower windmill, with Cubitt's method
EUROPEAN WINDMILLS.
63
of bringing the sails into the wind. AA are the sides
of the stationary part or body of the mill, which is
either built of brick or stone, or framed in timber.
CC

L
Tower Mill
M
C
S
BUL
B
C
IN
D
A
A
FIG. 7.
is a wooden curb attached firmly to the top of the wall,
and upon which the rollers of the cap revolve. It is
commonly secured either to timbers built in the brick-
64
THE WINDMILL AS A PRIME MOVER.
work, or to long iron rods which extend to a considerable
distance down the walls. BBB is the cap, or head, of
the mill, which is made of timber strongly framed to-
gether, with a circular curb at the lower part, which
revolves upon the one attached to the body of the mill.
SS is the iron wind shaft. DD is the driving-wheel,
gearing into the bevelled crown wheel N. The brake,
employed for stopping the mill entirely, is similar to
that described in the post mill, Fig. 5. RR, Fig. 7, is
the ring of rollers which supports the whole weight of the
cap, and by means of which it may be turned round upon
the curb CC with great facility, in any direction. The
rollers, aaaa, seen in Fig. 8, which is a plan of the cap,
are for the purpose of keeping it in its place. They are
attached to the upper curb, and revolve against the inner
surface of the lower one, which is made smooth and true.
In Fig. 7 is shown the self-adjusting cap which is turned
round by the force of the wind acting upon the auxiliary
fan, so contrived that the sails are always presented in the
proper direction. A small pair of sails, M, are attached
to the projecting framework, LL, of the back part of the
cap; it has a pinion upon its axle, which engages in a
wheel, b (Fig. 8), attached to the inclined shaft cc: and
at the other end of this shaft a bevelled pinion is fixed,
which works in the wheel e, on the vertical spindle of
pinion ƒ (Fig. 7). This latter pinion engages the cogs
on the outside of the rim of the fixed curb; and by
these means, whenever the fan M is turned, it moves
the head of the mill slowly round. It will be readily
EUROPEAN WINDMILLS.
65
seen, by examining the manner in which the sails of the
auxiliary windmill are constructed, that, when the plane
of these sails is in the direction of the wind, they will not
be put in motion by it; but, if the wind varies in the least
from the direction of the shaft of the windmill sails
proper, it acts obliquely upon the sails of the auxiliary

M
L
Ο
a
FIG. 8.
0
D
O
mill, and turns them round; so that, on whatever side the
wind may come, the motion conveyed to the machinery.
of the cap brings the main shaft again into the direction
of the wind.
Windmill Governors.
The variations in the intensity of the wind being con-
siderable, often so within a brief time, and sudden and
extreme, it is necessary that windmills be provided with
means of regulation, so that the motion of the machinery
66
THE WINDMILL AS A PRIME MOVER.
be uniform, and the work performed a constant quantity,
irrespective of the varying pressure of the wind. At one
time this was effected by the use of a friction strap
applied to the outside of the wheel on the wind shaft,
but this soon gave way to the method of regulation by
change of extent of surface offered to the wind by in-
crease or decrease of the amount of canvas of the sail.
The latter was formerly accomplished by having a rope
attached to each sail, or having the canvas made in three
portions, controlled by separate ropes; and much trouble
and delay were occasioned, as the mill required to be
stopped, and a man had to ascend the sails separately to
take in or let out the canvas. A description of such a
mill is given in Fairbairn's "Mills and Millwork,” as fol-
lows:
"The tower was of brickwork, and appeared to be eighteen feet
diameter at the base, and about fifteen feet at the top, and about twenty-
two feet high. The four wings were about thirty-five feet diameter, and
of a rectangular shape, about fifteen feet long and five feet broad. The
surface exposed to the wind was increased or diminished by the appli-
cation of canvas sails, whose spread could be raised by reefing or
twisting up the extreme end of the sails when the mill was in a state of
rest. The main axle, which was octagonal in form, was constructed
of oak, about fifteen inches diameter at the neck, and about ten inches
at the rear end. The front of the axle, which received the arms, was
square; and the two pairs of arms did not intersect the axle in the same
plane, the one pair being in advance of the other. All the arms butted
against the axle, and were united to it by side pieces, which were securely
bolted to the arms and through the axle, which rendered mortising
unnecessary, and preserved the strength of the shaft. The bearing in
which the neck of the axle revolved, seemed to be formed of some hard
EUROPEAN WINDMILLS.
67
wood, probably lignum-vitæ, and was lubricated with soft soap and
plumbago. The rear end of the shaft was fitted with an iron gudgeon,
about three inches diameter, secured by iron hoops and wedges.
About the middle of its length, this axle carried a face wheel about four
feet diameter, which was constructed entirely of timber; its arms were
mortised through the axle, and secured by iron hoops round the rim,
which formed the bearing-surface for the friction strap or brake for
arresting the speed of the mill. The teeth of this wheel, which were
about three and a half or four inches broad, and four and a half pitch,
geared into a trundle or pinion about fourteen or fifteen inches diam-
eter, fixed at the top of a long vertical wrought-iron shaft about two
and a half inches square, which was coupled at its lower extremity to
the rhynd on the top of the millstone spindle; the long shaft being
steadied by a bearing near the centre of its length, to prevent any jarring
or vibration being communicated to the revolving millstones. . . . When
the mill was set a-going, the wings performed twenty-nine revolutions
per minute when loaded; and the extremity of the sails acquired a
velocity of about thirty-two hundred feet per minute, or nearly thirty-five
miles per hour."
In 1780 Mr. Andrew Meikle devised, for reefing the
sails when the mill was in motion, an ingenious applica-
tion of the centrifugal governor; viz., a sliding piece,
which operated upon rollers placed transversely with the
arms, and wound up or reefed the canvas when the sails
attained too great a velocity. The unfurling of the sails
or increasing their speed was accomplished by a weight
which actuated a rod passing through the centre of the
main axle, and operated centripetally on the sliding-
frames, and then unwound the canvas when the motion
of the sails was too much retarded. Fairbairn defines
this as the first successful automatic reefing apparatus
68
THE WINDMILL AS A PRIME MOVER.
applied to windmills, and says, that, when the wind was
not squally, it imparted to the mill a precision of motion
little inferior to some of the then modern steam-engines,
and that, by varying the weights for unfolding the sail,
the power of the mill could be increased or diminished
with facility.
In 1807 Mr. William Cubitt devised an excellent
method of reefing the sails of windmills, by introducing
movable shutters in the sails of the mills; which shutters
were closed by a governor, operating upon a rod passing
through the centre of the main axle. These shutters
were suspended on points fixed almost one-third of their
breadth from one side; and, when the wind was blowing
too strong, it opened the shutters, and allowed a portion
of the wind to pass through them, and so also checked
the velocity of the mill.
Sir William Cubitt's devices for governing, which
were satisfactory and effective, are illustrated in Figs. 9,
Io, and II; which cuts, as well as the following descrip-
tion, we extract from Barlow's "Encyclopædia of Arts,
Manufactures, and Machinery."
(C
Fig. 9 represents a set of vanes, in which AA shows the valves
turned to the wind, and their surfaces exposed at right angles to it; BB
exhibits the vanes as close-reefed, with their edges to the wind, so that
it can have no effect upon them, except on their edges. In the drawing,
the vanes are exhibited as having the whip down the middle, with valves
on both sides; but it is evident that the vanes may be constructed with
the whip placed in the usual way, and have valves on one side only.
Fig. 10 is a section through the wind shaft, exhibiting the apparatus
for regulating the vanes. A is the wind shaft, which is bored through
纂
​EUROPEAN WINDMILLS.
69
!
the centre, to admit an iron rod, B, to pass freely through it; one end
of this rod has a knol or onion on it, which turns in a box, c, so that
it can be moved endwise while it continues to revolve. The box is
fastened to a toothed rack, D, whose teeth engage those of a pinion, E,


P
M
N
M
P
C
S
N
Τ
A
B
a
a
α
FIG. II.
a
FIG. IO.
W
F
A
FIG. 9.
upon the spindle of which is a sheave, F, with a groove on its circum-
ference to receive a rope, G, to which is hung the weight IV. This
weight serves to regulate the force of the wind upon the valves, and
may be adjusted to the nature of the work to be performed by the
mill. On the other end of the rod is fixed a plate of iron, K, with ears
70
THE WINDMILL AS A PRIME MOVER.
C
upon it, projecting from each side, in which are fixed the bridles or
leaders, L, L, which permit the levers M, M; to describe a curve with.
their ends, while the iron rod В moves in a straight line. N, N, are two
uprights or props, on the ends of which the levers M, M, move, and com-
municate the motion of the iron rod B to the racks P, P. These racks
engage the pinions Q, Q, on the axis of which (according to one method
here described, Fig. 10) is fixed a strong iron lever or crank, C: the
end of this is attached to a slider, S. Each vane has a small lever
projecting from it, which is fixed in the slider by a pin or gudgeon; so
that, by the motion of the slider, the vanes present a different angle to
the wind.
"The other method of regulating the vanes is shown in Fig. 11,
where, instead of levers, the vanes have a pinion attached to them,
which engages the teeth of a rack or slider, T.
"The operation of this apparatus will be readily understood by
imagining the rope G pulled down so as to cause about three-quarters
of a revolution of the sheave F. The pinion E will put in motion the
rack D and rod B, which brings the lever into the position represented
by the dotted lines. The rack P will have turned the pinions till the
slider S or T (according to whichever method may be used) brings
the vanes into such a position that their whole surface is presented
to the wind; therefore, if a weight be hung upon the line G, it will keep
the surface of the vanes to the wind until the strength of it is such as
to raise the weight, when the vanes will be more or less opened until
the pressure upon the inclined surface is reduced so as to balance the
weight. By this means the force of the wind beyond that sufficient to
raise the weight will not produce any additional velocity, and a degree
of regularity will be attained which can never be produced by the
ordinary method.”
Other methods of governing the area of the sails
according to the force of the wind have been devised
and put into practice; but, since the above suffice to indi-
cate the main types used, our object is accomplished, and
EUROPEAN WINDMILLS.
71
we feel justified in limiting our presentation of European
mills at this point. More especially is this permissible,
since windmills of the European type are rapidly and
deservedly being superseded by the American class of
mill, for reasons briefly outlined in the next chapter,
which treats more particularly of the various types and
of the construction of American windmills.
:
72
THE WINDMILL AS A PRIME MOVER.
CHAPTER V.
AMERICAN WINDMILLS.
Classification of Types. - Side-Vane Governor Mills.
mills,
AMERICAN windmills differ from the European
already described, most conspicuously in the form of
wheel receiving the impulse of the wind. Instead of the
small number of sails of large width, common to the
European or Dutch mills, the American wheel is made
up of a great number of blades or slats of small width.
This, of itself, gives an entirely distinct appearance to
the American wheel, since it resembles a closed surface
as compared to the large open spaces between the arms
of the European mill, though, of course, ample room is
provided between the slats to permit the free escape of
the impinging air. This division of the receiving-surface
of the mill into a large number of narrow sections, which
in turn are sustained by truss rods from an extension of
the main shaft, enables a much smaller aggregate weight
of parts for a desired strength, size, and capacity of mill;
so that the American windmill is lighter in weight, as well
as in appearance, than the European mill. The angles
employed are not as advantageous in the former as in the
AMERICAN WINDMILLS.
73
latter; but the surface presented for a given diameter is
so much greater in the American wheel, as to more than
No better proof of the
compensate for this defect.
superiority of the American windmill need be given than
the fact that it is rapidly replacing the Dutch type in
Germany, France, and England. In all of these coun-
tries the American type is now being manufactured on a
large scale, especially so in Germany. The American
windmill, too, is being extensively used in English col-
onies, on the recommendation of English engineers.
In presenting American windmill construction, it will
not be our aim to give an account of every special variety
of mill in the market, but rather to confine ourselves to
an ample illustration of the leading features of the several
types which distinguish American practice. Our atten-
tion will be directed mainly to the vertical mill, which
is the leading class in America, and which, in point of
economy and availability, of course so far surpasses the
horizontal mill, as to make it unnecessary to do more
than to give this brief reference to the latter type.
The several types of American windmills are charac-
terized by the form of wheel, and the method of regu-
lation or governing employed to vary the extent of the
surface presented to the wind, so that a uniform power
and a uniform rate of revolution may be obtained under
varying velocities of wind. The two principal types may
be distinguished respectively as the sectional wheel with
the centrifugal governor and independent rudder, and
*See p. 53.
74
THE WINDMILL AS A PRIME MOVER.
•
the solid wheel with the side-vane governor and inde-
pendent rudder. In both types, the rudder brings the
wheel into the direction of the wind. This rudder is a
large, strong vane, projecting opposite the shaft and the
wheel. The plane of the rudder is vertical, and perpen-
dicular to that of the wheel; so that the wind, however
shifting, acts directly upon the rudder to bring the plane
of the wheel normal to the wind. In the first type,
the flying-out or receding of weighted arms cause the
slats of the wheel to revolve, in sections, on pivots in
the windmill arms or frame, thus bringing the slats or
the surface of the wheel more or less normally to the
direction of the wind. In the second type, there is a
vane nearly in the plane of, and directly behind the solid
wind wheel, which vane is attached to the bearing of
the shaft. When the velocity of the wind increases, the
increased pressure on this side vane causes the wind
wheel to turn bodily away from the wind, the whole.
wind wheel and bearing rotating on a horizontal turn-
table, which forms part of the support of the mill. Thus,
less effective surface is presented to the wind until the
wind decreases, when the lowering of a counterbalancing
weighted lever, raised previously by the turning of the
wheel when the pressure was high, causes the wheel,
together with its accompanying side vane, to turn more
normally to the wind.
Besides these two leading types, there are others. In
a third type, a solid wind wheel is employed; but the
regulation is effected by placing the rudder, or its
AMERICAN WINDMILLS.
75
equivalent, at a slight angle to the centre line of the
shaft, so that the windmill is never entirely normal to
the direction of the wind. As the wind pressure increases
materially, the rudder is thrown more to the side, and the
wheel more out of the wind.
In a fourth type, no rudder at all is employed, and the
pressure of the wind on the wheel itself is relied upon to
bring the wheel into the proper direction. These latter
two types of governing are not at all sensitive, but
answer satisfactorily for smaller mills, to which their use
is restricted.
The two leading types, satisfactory in all sizes, are
the solid wind wheel with side-vane regulation, and the
sectional wind wheel with centrifugal governor regula-
tion;
both having independent rudders, to bring the
windmill exactly normal to the direction of the wind.
Either of these two types of governing is applied to
the smallest and the largest sizes of windmills, and acts
with sufficient accuracy and promptness to place the
American windmill in the rank of reliable automatic
engines.
It will be readily understood that the centrifugal
governor is somewhat speedier and more sensitive in
action than the side-vane governor, but the former type
of mill has the disadvantage of the wear and tear of the
pivots. Practically, however, the side-vane governor is
sufficiently sensitive and speedy in action; while, on the
other hand, the wear and tear of the centrifugal-governor
type, of proper construction, has not been found to be a
76
THE WINDMILL AS A PRIME MOVER.
material objection in use. As a fact, the choice between
these two types is narrowed to very close limits, and
both types are in use to an almost equal extent, and give
an almost equal degree of satisfaction.
The main point in the selection of a windmill, as far
as its reliability of action and durability are concerned, is,
to insist on the use of good materials and workmanship;
and, though both these requisites have a fair representa-
tion in this country, there is a sufficient amount of poor
work done to make it a necessity to call special attention
to this prime need.
Side-Vane Governor Mills.
The Corcoran Mill. Among this class of mill, there
iş none superior and justly more highly esteemed than
that manufactured by Mr. A. J. Corcoran of New-York
City.
Fig. 12 well presents the main features and details of
Mr. Corcoran's windmill for water supply. The iron-
work is indicated by numbers, and the woodwork by
letters. IJK represents a twelve-foot wind wheel, N
the side vane, M the flexible rudder, 26 the weighted
lever, 10 the connecting-link, 24 the slide; all concen-
trated in the iron frame 1. 17 is the supporting-piece,
faced on top, and bored out to receive the frame 1,
having flange on top to hold lubricating compound, and
being secured to the mast by four bolts. A flange also
extends halfway over the top of the mast.
At 18 is an

...
N.
7
I.
30
29
4
31
10
L.
K.
24
20
15
19
28.
23
126
17
21
18
D.
FIG. 12.
EWYORK
M
13
26
C.
78
THE WINDMILL AS A PRIME MOVER.
additional support, bored out to fit 1, and secured to the
post by two bolts. The main frame of the mill consists
of a piece of hydraulic tubing, with a bearing to support
the wind-wheel shaft, resting on an anti-friction washer,
which is held in place by cap 16. The object of this
tubing, coming down the mast as far as the windmill
arm I, is to give the main frame of the windmill a more
equal leverage with a strain brought upon the arm, and
thereby prevent any rocking motion of the mill on the
mast in unsteady winds. At 27 is the rudder bar, and
at 28 the truss rods which support the rudder vane.
The ends of the wrought-iron connecting-link 10 are
babbitted to fit steel pins on the crank wheel and slide.
The crank wheel has various centres, to admit of different
strokes of pumps, with a given
The wrought-iron lever 26 is
which works on the stud pin on the rear of the frame.
The chain 35 is connected to the stop rod 25, which is
secured to a small lever on the mast, near the ground.
By bearing down on the lever, the wheel is brought
around parallel with the rudder, thus presenting only the
ends of the slats to the wind. The arms I are bolted
to a centrepiece, 4, as shown; this spider form of
support 4 being a characteristic part of all American
vertical windmills. This form of wind wheel is known as
the "rosette' pattern. In high winds, the increased
pressure on the independent side vane causes the wind
wheel to gradually turn around, away from the wind.
raising the weighted lever 26. This lever, in turn, falls
diameter of wind wheel.
bolted to the piece 19,
AMERICAN WINDMILLS.
79

B
FIG. 13.
ска
4
80
THE WINDMILL AS A PRIME MOVER.
as the wind pressure again decreases, and thus the wheel
is again brought more normal to the wind. Thus a
uniform rate of speed is maintained, proportioned to the
position of the weight 13 on the lever.
The parts of this mill are accurately fitted to standard
gauge, and are therefore interchangeable.
In Fig. 13 is illustrated a Corcoran Windmill as
applied to railway water stations. A is the pump timber,
B the well curb, F the pump pitman, G the stopping-rod,
I the foot valve, 2 the suction valve, 3 the pump, 4 the
globe valve, 5 the delivery pipe, 6 the valve for emptying
tank, and 7 the overflow pipe. This illustration also
shows the wooden tower of the Corcoran Windmill for
sizes from sixteen to forty feet diameter of wheel, with the
camber of its side beams to secure stiffness and lateral
strength. A cheaper method of erecting a tower for wind-
mills of from eight and a half to fourteen feet diameter
of wheel is shown in Fig. 14, which explains itself.
Fig. 15 (p. 83) shows a Corcoran Geared Windmill,
designed for driving machinery. The windmill is made
in sizes of from sixteen to thirty feet diameter of wheel.
The illustration shows the method of transmitting the
power from the windmill by shaft No. 26 to the pulley
No. 13, as well as the general construction and appear-
ance of the ironwork, of which material the mill is
principally composed, the wind wheel and the rudder
vane being the only parts of wood.
The regulating or governing principle of this mill is
substantially the same as that of the pumping-windmill,

om
PLATFORM CLAMP.
10
10
Scale-
4 feet to an inch
c3
¥
WWW.
2
2
Detta Mar.
Rising Main 15
FIG. 14.
11
12
14
PLAN
SCALE INCH
TO LINCH
duy 100.
SIDE VIEW
82
THE WINDMILL AS A PRIME MOVER.
shown and described in Fig. 12; the balls and chain
attached to No. 16 of this mill being equivalent to the
weight bar No. 26, the weight No. 13, and the quadrant
No. 19, of the pumping-mill.
The regulation of this mill is accomplished independ-
ently of any of the parts used for transmitting the power.
All the parts of the same size of this mill interchange, all
journals are turned to measurement of solid calipers, the
bearings are babbitted on mandrels prepared for the work,
and the holes are drilled by template. The material em-
ployed consists mainly, of malleable iron. The shafting
is cold-rolled, and steel pins are used for all the joints.
In this mill, the upright and line shaft are all secured
in one iron frame, and so fitted that they cannot get out
of line during erection or during action, the weather not
affecting the same, as is the case where wood is em-
ployed for the main frame.`
Referring to the cut (Fig. 15), Nos. 4 and 5 are gears
made of Bessemer steel, and are graduated for speed at
the rate of one revolution to three. The vertical shaft
No. 8 revolves in Babbitt-metal bearings No. 6, and in
No. I at point shown by No. 3. No. 21 is a dome
enclosing Nos. 4 and 5. It is faced in a lathe, and bolted
to No. 1. No. 22 is secured to No. 21 by a flange and
bolts, same as that used for a shaft coupling, and is cone-
shaped, in order to prevent its getting out of line should
any of the bolts become loosened. Nos. 21 and 22 cover
the gears, protecting them from sleet or ice, or from the
entrance of any thing injurious. At the same time, they

31
認​款
​E
ZA
FIG. 15.
84
THE WINDMILL AS A PRIME MOVER.
1
form a strong and substantial support for the upper end of
the vertical shaft, also keeping No. 5 in place; and in the
event of repairs being necessary, or an alteration of the
shaft No. 8, the latter can be easily removed, without tak-
ing down the mill, by taking off the cap or dome No. 22.
The turn-table No. I rests and turns on a step
casting, No. 3, which has a deep recess for receiving the
end of No. 1. It also has a steel friction washer; and the
entire weight of the mill, supported by No. 1, rests and
turns on this steel friction washer, sustained by No. 3.
The windmill may be stopped and started by raising or
lowering a wooden rod connected with No. 16. This
lever is operated by a windlass placed in the bottom of
the tower; and, by raising the wooden rod and cross-head
No.. 16, the rings No. 19 and 20 move on the rods.
No. 18, the rings being connected by a chain with the
half-circle board E, a part of the rudder D.
The upright shaft 7-1, and the horizontal shaft 12,
are supported by a combined bearing; making it impos-
sible for either to get out of line. The upright shaft has
a steel lower end, revolving in a copper friction washer
No. 8. No. 12 is made of cold-rolled shafting or of steel.
An important feature of the mill is the safety lever
F, and the clutch coupling No. 14. No. 15 is a forked
lever, and works in a groove in No. 14. The shafts 7-1
and 8 are made in two pieces, united by the coupling
No. 14; the upper half working on a feather or spline,
and the lower half being firmly keyed to the coupling.
It is, of course, very important that there should be a
AMERICAN WINDMILLS.
85
•
means of stopping the motion instantly in case of acci-
dent, should the belt slip off, or for other reasons. Any
windmill can be stopped by pulling it out of the wind;
but, as this does not do away with its momentum, it is
some time before the line shaft 12 comes to a state of
absolute rest. With this mill, the safety rope G is brought
to a convenient point in the tower or shop, where any one
can pull down on it; and doing so separates the coupling,
lifting the upper half from the lower, and allows No. 8 to
revolve, while No. 7-1 and all below it stop instantly.
This method also makes it unnecessary to shift a
heavy belt to stop the machinery in the shop..
The number of arms A used in the wind wheel
depends upon its size, and varies from eight to twelve.
They are securely bolted to the hub No. 25, and sup-
ported by the front braces B, fastened to the brace head
No. 27, connected with main shaft No. 26, and supported
by girts C. The sections of the wind wheel-or fans,
as they are not uncommonly called - are connected, to
arms A by malleable iron clips 32, 33, 34, 35, making
from two to eight complete circles around the wind
wheel when all the sections are in place..
The Eclipse Windmill, manufactured by the Eclipse
Windmill Company at Beloit, Wis., is identical in prin-
ciple with the Corcoran Mill, just described, but differs
in its grade of construction, which is made to conform
to a cheaper class of trade. It is a good, reliable mill,
has a fair representation on the railroads of the country,
and is manufactured quite extensively in Germany.
86
THE WINDMILL AS A PRIME MOVER.
CHAPTER VI.
AMERICAN WINDMILLS (CONTINUED).
Centrifugal-Governor Mills.
Of the centrifugal-governor mills, the Halladay,
manufactured by the United-States Wind Engine and
Pump Company of Batavia, Ill., is most extensively used
in America; and its excellent record and extensive use
make it stand out pre-eminent among centrifugal-governor
mills.
Fig. 16 clearly shows the general construction and
method of operation of the mill. A, the bed plate, is
a strong casting, resting on, and firmly bolted to two
masts in the tower, and further secured by the two
braces E, E. Upon this revolves the turn-table B, held
in position by bolts K, with oblong heads, which reach
under the bed plate. The turn-table moves on rollers,
which allow it to turn freely as the wind changes its
direction. These rollers run on a lathe-turned track, and
both are protected from the weather by flanges on the
turn-table. The spider CC, to which are bolted the arms
or spokes of the wind wheel, is firmly keyed to the main
shaft, which rotates in Babbitt-lined boxes on the turn-
FLEEST
D
W
F
V
T
CILER-CO-CHE
Y
P
BH
G

Z
Y
FIG. 16.
R
M
H
K
C
Y
88
THE WINDMILL AS A PRIME MOVER.
table. On the inner end of this shaft is keyed the crank-
plate M, to which is attached the pitman L. By means
of the post attachments, consisting of sleeve box S,
swivel box X, and sliding-boss Z, connection is so made
between the pitman and the pump, that the revolving of
the turn-table upon the bed plate will not twist or cramp
the connections, or prevent sails being spread or furled,
by means of shut-off rod R.
The regulating-gear consists of the sliding-head D,
elbows Y, and their connections. The inner end of each
elbow is connected to the sliding-head by a link, the
connections from the outer ends to the sails being made
by means of regulating-rods.
On the outer ends of the regulating-rods are the
governing-balls or regulating-weights, the action of
which is the same as the governor on a steam-engine,
causing the sails to present less surface to the wind as
its velocity increases.
The weight W, on forked lever F, acts in opposition to
the regulating-weights, causing the sails to present more
surface to the wind as the power of the wind decreases.
The sails may be furled, and the mill stopped and made
to stand still, by pulling down on shut-off rod R. The
regulating-gear is comparatively simple, securing a direct
connection with each sail, and direct action of the regu-
lating-weights on the sliding-head and its connections,
thereby giving positive movement to all the parts.
Fig. 17 gives the detail of the iron-work in the Hal-
laday Mill. I represents the turn-table; 1a, the rear cap

8
со
10
Sa
9a
1
2a
10a
7a
За
10b
10c
14
9b
ба
6b
Ба
10d
4
12
FIG. 17.
2
HILST
ст
5
1d
la
5b
13a
6c
13
1c
lb
le
11b
15
1la
ifa
11

90
THE WINDMILL AS A PRIME MOVER.
on turn-table; 16, the front cap on turn-table; 1c, front
box on turn-table; id, rear box on turn-table; ie, clamp

11
116
11a
30°
FAN
FOR
12 FOOT MILL

(0)
FIG. 18.
bolt; 2, bed plate; 2a, anti-friction rolls and carriage; 3,
forked lever; 3a, weight on forked lever; 4, main shaft;
AMERICAN WINDMILLS.
91
5, spider; 5a, elbow; 56, elbow collar; 6, back plate; 6a,
shoes on back plate; 66, front-plate and slide-head rods ;
6c, link connecting back plate to elbow; 7, chain pulley;
7a, balance weight and chain; 8, crank plate; 8a, crank
pin; 9, pitman; 9a, top pitman box; 96, lower pitman
box; 10, stub end; 10a, sleeve on stub end; 10b, sliding-
boss on stub end; 10c, swivel box; 10d, sleeve box; II
(see also Fig. 18), regulating-rod; 11a, set iron on regu-
lating-rod; 116, regulating-weight; 12, angle box; 13,
tilt-bar socket; 13a, tilt-bar lever; 14, flat-bar connec-
tion; 14a, force-pump connection; 15, slide fork.
Fig. 18 represents the detail arrangement of the fan
of the 12-foot mill.
The angles of weather of the slats vary from 30 to 45
degrees, depending upon the size and kind of windmill.
In the geared mills the slats are set flatter than in the
pumping mills, as they are run more rapidly.
Fig. 19 shows the general arrangement of the geared
mills.
The Halladay Windmill is in more extensive use in
America for railway water stations than any other mill,
and the general view presented in Fig. 20 is therefore of
interest.
The manufacturers claim that hundreds of their wind-
mills have been in active use on railways for over twenty
years, at an expense not exceeding an average of five
dollars per year for oil and repairs. We see no reason
to question the correctness of this statement.
This mill is constructed in Germany, by Friedrich Filler

7
WIT
IXL
LADAY STANDARD
USWIND ENG!
BATAVIA
ઉન
FIG. 19.
11911
10


AZ
WE PO
BURNHAMS
FROST PROOF-
TANK
FIG. 20.
620
U.S.W.E.& P.CO.
94
THE WINDMILL AS A PRIME MOVER.
of Eimsbüttel, Hamburg, who does quite an extensive
business in its manufacture. We illustrate, in Figs. 21
and 22, a few interesting applications made by Mr. Filler,
which speak for themselves.

FIG. 21.
•
FRIED FILLER
DIMSBUTTEL HAMBURG
The Althouse Windmill. - Figs. 23, 24, and 25 illus-
trate the well-known centrifugal-governor mills, manufac-
tured by Messrs. Althouse, Wheeler, & Co., of Waupun,
Wis. The rudder is not shown in any of the cuts. Fig.
23 is a 10-foot mill, as constructed for pumping-purposes.
Fig. 24 is a 14-foot geared mill, as constructed for power
purposes. In this case the rudder is very small, and
placed in front of the wheel, and parallel to the main
AMERICAN WINDMILLS.
95
Like
shaft. Fig. 25 shows the iron-work in detail.
figures apply to like parts in the several illustrations.
I represents the bed plate; 2, the step; 3, the turn-
table; 37, turn-table roller block; 3e, turn-table rollers;

FIG. 22.
4, turn-table sleeve: 5, turn-table sleeve clip; 6, main
shaft; 8, spider; 9, crank wheel; 10, crank pin; 11, slide
head; 14, front slide; 17, chilled clutch ring (2 pieces);
20, clutch oil cup; 21, forked clutch bar; 24, weight
lever; 27, weight; 28, truss posts; 30, truss rod; 33,
pitman; 34, pitman upper box; 36, swivel; 37, swivel
collar; 38, wood-rod attachment; 39, section levers; 40,
section levers, links straight; 41, section levers, curved;
96
THE WINDMILL AS A PRIME MOVER.
14
7

34
זזתי
14.5
8
47
20
39
5
40
48
49
47
43
27
21
30
9
34 10
24
33
36
34
18
17
10
CHICAGO-ENG-ER
33
FIG. 23.
36
CA
37 38
~
1

www.
ALTHOUSE
::、- -ཟི
WHEELER & CO.
1
WAUPUN WIS.
FIG. 24.
98
THE WINDMILL AS A PRIME MOVER.
:
42, arms; 43, arm irons; 46, section fans; 47, section
centre-bar castings; 48, section inner-bar castings; 49,
section rods; 55, splice irons for wood rods; 56, wood
pitman rods; 57, pump attachment; 59, arm weight; `60,
hand lever.
The Adams Windmill, constructed by the Marseilles
Manufacturing Company, Marseilles, Ill., is shown in Fig.
26. It is identical in principle with the Halladay Mill,
with the exception that the centrifugal governor, consist-
ing of weighted lever, has no slide head as a counterbal-
ancing mechanism, but the regulating-rods leading from
the centre of the section bars are attached to a cylindrical
friction wheel placed on the rear of the hub. This fric-
tion wheel consists of a curved spring, set for a given
speed, which, when this speed is exceeded, is curled up,
and retards the motion of the cylinder to which it is
attached, thus causing the rods to pull the sails more out
of the wind. When the wind again decreases, the spring
uncurls, and the sections, actuated by the weighted lever,
again enter more into the wind.
AMERICAN WINDMILLS.
99

4
5
2
9
10
17
14
8
3-B
3 - A
34
28
7
3
36
33
37
40
20
43
59
38
39
47
21
48
FLETAAS
55
57
24
30
27
FIG. 25.
Uor M
100
THE WINDMILL AS A PRIME MOVER.

F
H
B
D
MY LE LABEL E
A
FIG. 26.
0
M
A
AMERICAN WINDMILLS: OTHER TYPES.
IOI
CHAPTER VII.
AMERICAN WINDMILLS: OTHER TYPES.
VELOCITY REGULA-
TION, ETC.
The Buchanan Windmill.
THIS wheel, shown in Fig. 27, belongs to the class
of mills which depend for their regulation upon the
natural tendency of the wheel to go into the direction it
turns, as the velocity of wind increases materially. In the
detailed view showing the mechanism, A is a wrought-
iron pipe, upon which the whole structure is supported;
B is the main frame which turns on the pipe A; D is
the governing device. As will be seen, a lug projecting
from the side of the lever bears upon the inclined pro-
jection on the main frame: so that, when the mill is
thrown out of the wind, the weight-lever is elevated;
and as the wind decreases from its high velocity, the
lowering of the weighted lever again brings the wheel
into the direction of the wind. G is the derrick сар, F
the cross-head, I a spring to cushion against the sudden
throwing of the mill out of the wind, - a necessity in the
class of mills which are governed by the velocity action
of the wheel itself.
102
THE WINDMILL AS A PRIME MOVER.
A feature of this mill different from all others is the
method of fastening the slats to the section bar of the

BUCHANAN
MICH
D.
A
F
B
H
G TE
C
Tus
FIG. 27.
wheel. While in other mills the slats are secured in
grooves in the section bars, by means of nails, the
AMERICAN WINDMILLS: OTHER TYPES.
103
slats in the Buchanan Mill are secured to the section bars
by wire clips.
The Woodmanse Windmill.
This mill, manufactured by the Woodmanse Windmill
Company, Freeport, Ill. (see Fig. 28), has a solid wheel,
and the rudder in the centre line of the main shaft, to
bring the wheel into the line of the wind. Its change of
extent of surface, according to the force of the wind, is
caused by a natural tendency of the wheel, running at a
high rate of speed, to move bodily in the direction that
the wheel turns. Of course this action is felt materially
only at high speed, which precludes the possibility of
such mode of regulation for large mills. In fact, it is
used with good effect only for small pumping-mills, where
it gives satisfaction.
It will be readily understood, that, as this wheel shifts
out of the wind at high speed, the weight shown in Fig.
28 is lifted. Its lowering when the wind decreases, again
brings the wheel into the direction of the wind. This
windmill is well constructed, and is therefore a good
machine of the type it represents.
The Stover Windmill.
The Stover Windmill, manufactured by the Freeport
Machine Company of Freeport, Ill., is similar to the mill
shown in Fig. 28, except that the rudder, instead of
being in the centre line, stands off from three to six
inches from the main shaft, but is parallel to it. . The

'ST 'OLI
474
1×6
food

23
་
་།་.
།།
24
5
22
22
22
13
15 16
17
19
22
12
--10
21
\20
CHAMPION WIND POWER
FIG. 29.
22
22
20
106
THE WINDMILL AS A PRIME MOVER.
distance between the planes of the rudder and of the
shaft increases with the size of mill.
This enables a speedier getting-out of the wind,
inasmuch as a larger portion of the wheel stands off
from the centre line of the rudder; but it has the disad-
vantage of the wheel never being fully in the wind.
This wheel runs to the left, while all other mills run to
the right.
The Champion Windmill.
Fig. 29 illustrates a ten-foot pumping-mill, in which
there is no rudder. This mill, known as the Champion,
is manufactured by Messrs. Powell & Douglas, Wauke-
gan, Ill. The regulation of the extent of surface is on
the centrifugal-governor plan. The mill is brought into
the direction of the wind by the natural tendency of the
wheel to turn into that position; the wheel being placed.
behind the mast, instead of in front, as is the customary
practice. Inasmuch as the face of the wheel is toward
the mast, and the sections turn in the same direction, the
wheel, as will be seen in Fig. 29, is a considerable dis-
tance from the axis of the mast; and consequently there
is an overhang, which has a tendency to bring an unequal
strain on the main bearing and turn-table. The face of
the wheel being behind the mast, and most of the regu-
lating-gear in front of the wheel, the wind is to some
extent broken before it strikes the wheel.
In Fig. 29, I represents the turn-table; 2, the bed
plate; 3, the step (two pieces); 4, main box; 5, cap of

.....
2
་ ་བ པ་ ་མ ཁས་
FIG. 30.
108
G
THE WINDMILL AS A PRIME MOVER.
main box; 6, crank plate; 7, connecting-rod; 8, cap of
connecting-rod; 9, pipe pitman; 10, pitman connection;
II, wood-rod splice; 12, pump connection; 13, twin levers;
14, slide head; 15, slide-head segments; 16, slide-head
ring; 17, spider; 18, outside hub; 19, spoke shield; 20,
socket on spoke end; 21, gudgeons of sails; 22, brace
connection on sail; 23, governing-weight; 24, fulcrum of
governing-lever; 25, tower-post weather shield.
}
In Fig. 30 is shown a geared wind wheel of the same.
type, in which a vane is placed at an angle to the centre
line of the shaft. The vane is to offset the tendency of
the wheel to go with the strain of the gear, and is found
a necessity in geared mills of this type. It is not neces-
sary in pumping-mills, with the crank motion, as the
strain then is entirely vertical.
The Regulator Windmill.
The Regulator Windmill, manufactured by the Sand-
wich Enterprise Company, Sandwich, Ill., shown in Figs.
31, 32, and 33, has a solid wind wheel, but no rudder,
and runs behind the mast, differing in the latter respect
from all other solid wind wheels. The regulating-gear
consists of a small vane on a large lever directly in front
of the wheel, the vane portion projecting outside of the
wheel. This vane is inclined to the plane of motion of
the wheel, being set at the same angle as the slats. In
addition, this vane has a projecting fan at right angles to
the vane itself, so as to make the vane catch the wind
•

FIG. 31.
་་་་་
LIMITATA EN
AKÄR LÄÄÄÄÄ Is dat the

FIG. 32.
२०७
AMERICAN WINDMILLS: OTHER TYPES.
III

•
NEMAWILDE
FIG. 33.
II2
THE WINDMILL AS A PRIME MOVER.
more effectively. As the velocity of wind increases, it
presses with greater force
greater force against this overhanging
vane, and tilts it, thereby raising a counterbalancing
weight. This lowering of the overhanging vane causes
the rotation of the turn-table to which it is attached, and
thus brings the wheel more out of the wind. As the
pressure decreases, the lowering of the counterbalancing
weight again brings the wheel and the vane more into
the wind. A point claimed for this windmill is the
method of transferring the motion from the crank on
the main shaft to the pitman which operates the pump.
This consists of links and levers which give an eccentric
motion, one-third of the revolution of the wheel causing
the downward, and two-thirds the upward stroke. It is
claimed that thus a lighter breeze moves the mill; but
we confess our inability to appreciate the reasoning upon
which this claim is based, while we do recognize the dis-
advantage of the increase of levers and joints which this
motion necessitates.
The Strong Windmill.
This windmill, the design of Mr. George S. Strong of
Philadelphia, belongs to the velocity-regulation type, the
wheel shaft being placed slightly out of line of the plane
of the rudder. Thus the pressure of the wind exerts itself
to push the wheel around the turn-table to the left, which
tendency is resisted by a counterbalancing weighted lever.
Referring to the accompanying cuts, Fig. 34 is a

A
A¹
T
السر
23-1
B
·-29"-
비
​H'
B'
B
E
Bi
201
N
FIG. 34.
T
X
W
K
R'
V
E'
AMERICAN WINDMILLS· OTHER TYPES.
113
side elevation of the mill, with wheel, arms, and rudder
broken off, showing the construction of wheel centre,
arrangement of governor, and connections of crank.
Fig. 38 is an elevation of the mill proper, showing the
construction of the wheel and rudder, or vane, without
any tower, which would come under the bed piece at T
Fig. 36 is a back elevation of Fig. 34. Fig. 39 is a

b
B
h
N
FIG. 35.
section through bed piece and turn-table, showing staple
connection with swivel guide. Fig. 35 is a plan showing
position of vane or rudder when full in the wind, and
arrangement of wire rope for shifting out of the wind
when it is desired to stop the mill. The smaller pieces
(Fig. 37) are clamps, and parts of wheel and rudder. R
represents the counterbalancing lever, having a swivelled
K
四
​
·
a
S
a
(7)
ليا
W
R
D
A
K
FIG. 36.

K
K
Α'
B
C
T
E
E'
E'
1
}
FIG. 38.
•
--16 ft
n
M
a
AMERICAN WINDMILLS: OTHER TYPES.
115
fulcrum at G, and coupled at its upper end by the link S
to the rudder. The fulcrum is supported on a bracket,
N, on the frame B of the mill. This lever resists the
action of the wind on the wheel until the pressure is



O
O
NO F
ALWIE
MIKIHUGE.
n
E8
FIG. 37.
p
greater than what the lever is loaded for, when the wheel
swings around on the turn-table, presenting its edge to
the wind, or partially so. As the wheel has an increasing
leverage on the governor as it swings farther around, it
is necessary that there should be an increasing resistance.
This is accomplished by a travelling-weight, K, on the
lever R. This weight is suspended at a point above
the fulcrum by the link V, on which it is adjustable, and
Uor M
་་་་


116
THE WINDMILL AS A PRIME MOVER.
4
can be moved up or down, to suit the velocity at which
the mill is required to run. As the lever R rises, this
link causes the weight K to travel out on the lever,
compensating for the positions of the wheel. The turn-
table is a pivot at the bottom of the bed piece, with a
collar at the top of the same, both of which are pro-
tected from the weather, and provided with abundant
oil cavities. The crank is back connected and coupled
through a staple to the pump rod, which is hollow, to
admit of a cable passing down through it, to throw the
mill out of the wind when it is desired to stop it. The
staple has a swivel guide at the top, so that it cannot bind
the crank pin.
The wheel consists of wrought-iron arms bent on
edge back on themselves, and clamped on a double-face
plate. There are twelve of these arms, with malleable
iron clamps, which slip over the arms, and clamp the rims
of the wheel. These rims are of hard wood, and sawed
out, to receive the sails; the inner and outer rims being
sawed at different angles, so as to give a screw shape to
the sails. The frame of the rudder is made of gas-pipe,
and trussed, and has malleable iron clamps to hold the
wood cross-pieces which secure the slats.
The Leffel Windmill.
The Leffel Windmill, manufactured by the Springfield
Machine Company, Springfield, O., is shown in Fig. 40.
It depends for its regulation on the fact that the centre.
B2
٤٠ارت
$

FIG. 39.
D
H'
+1·8″.
T
-2
f g
アイ
​FOL
-101″
118
THE WINDMILL AS A PRIME MOVER.
line of the wind-wheel shaft stands off somewhat from,
though it is parallel to, the plane of the rudder. The
wheel of the mill is a distinguishing characteristic.

POLLESO
NIZATDEMO
NEINIGED
furt
EMIL
DEBORAH LANJUTSTRESSINAT ANLAGE LENTUK ITUNE
FIG. 40. ·
The blades, which have a helical curve, are about three
feet long by two feet wide. They are made of No. 24
sheet-iron, fastened securely to curved iron ribs, and
bolted to a double set of one and one-eighth by five-
sixteenths inch iron arms.
EXPERIMENTS ON WINDMILLS.
119
CHAPTER VIII.
EXPERIMENTS ON WINDMILLS.
It is not pleasant to be obliged to make the admis-
sion, that, for experimental records of the efficiency of
windmills, we must have recourse to the foreign annals
of over fifty and over a hundred years ago. With the
exception of the data of capacity presented in Chap.
IX., which are the average records of experience rather
than the results of special experiment, America has con-
tributed no reliable* data relating to the performance
and efficiency of windmills. In this chapter we will
confine ourselves to an account and discussion of the
experiments of Smeaton and Coulomb. Originally the
intention was to reprint these papers in full; but the fact
that their main import can be presented in considerably
less space, and that their actual value at this time, though
comparatively of moment, scarcely warrants a complete
reproduction, has led to the abandonment of the first
idea. This statement is made with the full knowledge,
that, as a rule, these experiments are spoken of as if they
were possessed of no flaw, and also in apparent conflict
*The author has pointed out elsewhere that the windmill tests at the Penn-
sylvania Agricultural Exhibition, Philadelphia, 1884, were utterly unreliable, and
of no value whatever. See American Engineer, vol. 8, July 4, Oct. 17, and Dec.
26, ISS4.
120
THE WINDMILL AS A PRIME MOVER.
$
with the great respect which the author, like many other
engineers, has gained for Smeaton and Coulomb, by a
close perusal of their work in this and many other more
important departments of engineering. The fact remains,
however, that the angles recommended by Smeaton as
the result of his trials, as being "as good as any," cannot,
in the nature of things, be the most desirable angles, and
that, in Coulomb's experiments, only the velocity of wind
was specially recorded, while the total work performed,
and that lost, were in part calculated, and in part repre-
sented average annual performances. In how far this is
the case will appear in our account; and, while it is thus
the author's aim to warn against the too common blind
indorsement of the experiments under discussion as
being final, it is equally his pleasure to commend them
as the only experimental researches on record worthy of
study and consideration.
The hope may here be expressed, that American
windmill manufacturers may erelong see fit to institute.
such accurate experimental observations of the perform-
ance and efficiency of windmills as national pride should
dictate, as scientific accuracy demands, and as the mod-
ern methods of scientific investigation can readily secure.
Smeaton's Experiments.*- This series of experiments
with model windmills was instituted by the great English
engineer John Smeaton, to determine the best shape of
sail for a given area of surface. Of one set of wind-
mills experimented upon, the radius was 21 inches, the
length of cloth 18 inches, breadth 5.6 inches; making an
* See Philosophical Transactions, 1755 to 1763.
EXPERIMENTS ON WINDMILLS.
12 I
area of 100.8 square inches for each sail. In the second
set, there was added to each sail a triangular cloth whose
base was equal to one-half the breadth, i.e., 2.8 inches,
and whose height equalled 18 inches, the sail being
broadest at the extremity of the radius, or whip. Thus
the total area was 126 square inches. Number of arms
of windmills = 4.
On account of the uncertainty of the wind, the wheel
was moved, not by allowing or causing the air to move
against the wheel, but by turning the axis of the wheel
progressively around in the circumference of a large
circle, and thus causing the revolution of the wheel by
its impingement upon the air at rest. The effect was
then, of course, precisely the same as if wind of a like
velocity to that with which the air at rest was impinged
had acted by its impulse upon the wheel. This turning
of the wheel in the circumference of a large circle was
effected by giving a circular motion to an upright shaft
by means of a cord wound on a barrel upon the shaft,
which cord was operated by the experimenter. To this
shaft was framed an arm 53 feet long, at the end of which
was the seat of the windmill. The power of the wheel
was measured by a scale pan attached to a fine cord,
which latter wound about the shaft as it rotated, and thus
raised the scale and its weights. The scale moved up
and down in the direction of the upright shaft, and
received no disturbance from the circular motion. The
main results of his experiments are given by Smeaton in
the following table, and the principal deductions there-
from are expressed in the maxims on p. 123.
122
THE WINDMILL AS A PRIME MOVER.

TABLE VI.
EXHIBITING THE RESULTS OF NINETEEN SETS OF EXPERIMENTS ON WINDMILL SAILS OF VARIOUS
STRUCTURES, POSITIONS, AND EXTENT OF SURFACE. (SMEATON.)
THE DESCRIPTION OF SAILS MADE
Angle
at the
Turns
Turns
of the
Load
Ratio of
Greatest Ve-
Great-
Great-
Extent
of the
Sail at
at the
Prod-
locity to the
No,
est
est
of Sur-
Ratio of
Greatest
Load to the
USE OF,
Extrem-
ities.
Sail un-
the
Maxi-
uct.
Velocity at
Angle.
Load.
face.
loaded.
Maxi-
the Maxi-
Load at a
Ratio of
Surface to
the Product.
mum.
Maximum.
mum,
mum.
degrees. degrees.
lbs.
lbs.
8q. in.
Plane sails at an angle of 55º
I
35
35
66
42
7.56
12.59
318
404
10: 7.0
IO: 6.0
10: 7.90
12
12
Plane sails weathered according to
70
6.30
7.56
441
404
10: 8.3
IO: 10.10
the common practice
3
15
IS
105
.69
6.72
8.12
464
404
10: 6.6
10: 8.3
10: 10.15
4
18
18
96
66
7.00
9,81
462
404
10: 7.0
10: 7.1
10: 10.15
Weathered according to McClau-
5
9
26½
1
66
7.00
462
404
IO: 11.40
6
12
292
702
rin's method
7.35
518
404
10: 12.80
78
15
32%
63/2
8.30
I
527
404
1
IO: 13.00
15
120
93
4.75
5.31
442
404
10: 7.7
10: 8.8
10: 11.00
9
3
18
120
79
7.00
8,12
553
404
10: 6.6
IO: 8.6
10: 13.70
Sails weathered in the Dutch man-
ner, tried in various positions
ΙΟ
5
20
78
7.50
8.12
585
404
10: 9.2
10: 14.50
II
7/2
292
123
77
8.30
9.81
639
404
IO: 6.8
IO: 8.5
10: 15.80
12
IO
25
108
73
8.69
10.37
634
404
IO : 6.8
IO: 8.4
10: 15.70
13
12
27
100
66
8.41 10.94
580
404
IO: 6.6
10: 7.7
10: 14.40
Sails weathered in the Dutch man-
ner, but enlarged towards the
14
72
22/2
123
75
10,65 12.59
799
505
IO: 6.1
10: 8.5
10: 15.80
15
IQ
25
117
74
11.08
13.69
820
505
10: 6.3
IO: 8.1
IO: 16.20
16
12
27
114
66
12.09
14.23.
799
505
IO: 5.8
10: 8.4
10: 15.80
extremities.
17
15
30
96
63
12.09
14.78
762
505
IO: 6.6
IO: 8.2
10: 15.10
Sails being sectors of ellipses in
18
12
22
105
64½2 16.42
27.87
1059
854
10: 6.1
10: 5.9
10: 12.40
their best positions
19
12
22
96
64/2
18.06
1165
1146
10 : 5.9
10: 10.10
EXPERIMENTS ON WINDMILLS.
123
(6
The column marked Product" gives the relative
capacity of the mills.
In regard to the area of the sails as compared to the
circular area of the wheel, Smeaton found, that, beyond
a certain degree, the more the area is crowded with sail,
the less effect is produced in proportion to the surface.
By pursuing the experiments still farther than recorded
in No. 19 of Table VI., it was found by him, that though
in No. 19 the surface of all the sails together was not
more than seven-eighths of the circular area containing
them, yet a further addition rather diminished than in-
creased the effect; so that, when the whole cylinder of
wind is intercepted, it does not then produce the greatest
effect, for want of proper interstices to escape.
SMEATON'S MAXIMS.
1. The velocity of the windmill sails, whether unloaded, or loaded
so as to produce a maximum, is nearly as the velocity of the wind; their
shape and position being the same.
2. The load at the maximum is nearly, but somewhat less than, as
the square of the velocity of the wind; the shape and position of the sails
being the same.
3. The effects of the same sails at a maximum are nearly, but some-
what less than, as the cubes of the velocity of the wind.
4. The load of the same sails at the maximum is nearly as the
squares, and their effects as the cubes of their number of turns in a given
time.
5. When the sails are loaded so as to produce a maximum at a
given velocity of the wind, and the velocity of the wind increases, the
load remaining the same: first, the increase of effect, when the increase
of the velocity of the wind is small, will be nearly as the squares of those
124
THE WINDMILL AS A PRIME MOVER.
velocities; secondly, when the velocity of the wind is double, the effects
will be nearly as 10 to 27; but, thirdly, when the velocities compared
are more than double of that where the given load produces a maxi-
mum, the effects increase nearly in a simple ratio of the velocity of the
wind.
6. If sails are of similar figure and position, the number of turns in
a given time will be reciprocally as the radius or length of the sail.
7. The load at a maximum that sails of a similar figure and position
will overcome at a given distance from the centre of motion, will be as
the cube of the radius.
8. The effects of sails of similar figure and position are as the
square of the radius.
9. The velocity of the extremity of Dutch sails, as well as of en-
larged sails, in all their usual positions, when unloaded, or loaded to a
maximum, is considerably quicker than the velocity of the wind.
In relation to these maxims, it may be said that their
exactness is open to all the doubts which any experi-
ments made on a small scale, and without a commensu-
rate degree of accuracy, are subject to. Again: they do
not convey such specific information and exact relations
of the factors entering the problem as is the character-
istic demand of the present time. Altogether, the author
is led to attach less importance to the value of Smeaton's
experiments, for the solution of the efficiency problem of
the day, than is usually assigned to them.
Smeaton adds, in a note to his paper
I have found, by several trials in large, the following angles to
answer as well as any. The radius is supposed to be divided into six
parts; and one-sixth, reckoning from the centre, is called 1, the extrem-
ity being denoted 6. Nos. 1, 2, 3, 4, 5, 6, angle with the axis 72°, 71º,
EXPERIMENTS ON WINDMILLS.
125
72°, 74, 77, 83°. Angle with the plane of motion" [angle of
weather], "18°, 19°, 18° (middle), 16°, 124°, 7° (extremity).”
These angles are those quoted in all text-books and
engineering pocket-books as the best angles of impulse
and weather, as determined by Smeaton; but it must be
stated, in justice to Smeaton, that he does not term them
the best angles of impulse, but simply says they "answer
as well as any," possibly any that were in existence at his
time. Mathematical considerations* conclusively show
that the angle of impulse depends upon the relative.
velocity of each point of the sail and the wind, the angle
growing larger as becomes greater. It will be noticed
that Smeaton's angles do not fulfil this condition: the
angle of impulse at No. 2 being less than at No. 1, while
the velocity is twice as great; and the angle at No. 3
being the same as at No. 1, while the velocity is three
times as great. Thus an important discrepancy is dis-
covered, which should not be disregarded in a correct
and impartial estimate of Smeaton's work.
ย
C
Inasmuch as the best angles of impulse are dependent
upon the relative velocity of the wind and of the mill, and
as the velocity of the latter is to a great extent depend-
ent upon the amount of work to be done each revolution,
the determination of the best angles of impulse is of
necessity a matter of special study in each particular case.
Coulomb's Experiments are the record of careful
* See p. 31.
† Théorie des Machines Simples, Paris, 1821, par C. A. Coulomb.
126
THE WINDMILL AS A PRIME MOVER.
30479
observations made at Lille, in Flanders, to determine the
average effects produced by windmills the year around.
These mills, of which there were more than fifty near
Lille, were of the Dutch type, and were employed in the
extraction of oil from rape-seed. The following repre-
sents the main particulars of these mills: Radius of sail
= 33 French feet (pied de roi; 1 pied de roi = 32484
English feet); breadth of sail = 6.2 French feet, 5.2 of
which consisted of canvas covering framework; dis-
tance from axis of shaft to beginning of sail proper = 6
French feet; angle which element at this point made
with the axis of the shaft = 60°; angle which element at
the extremity of the sail made with the axis = 78°. In
regard to these angles, which increased quite regularly
from 60° to 78°, it is elsewhere shown* that they are those
of maximum effect; and, indeed, Coulomb, in speaking of
these mills, says, that, "by force of trial, the construction.
of these machines has reached a very great degree of
perfection." The shaft which was inclined from 8° to 15°
to the horizontal, was pierced by seven beams 42 inches
long, which acted as cams for raising seven stampers
twice during each revolution of the wheel. Of these 7
stampers, 5, used for pounding the rape-seed, were of
oak, 21 feet long by 10 inches square, provided with an
iron head 55 pounds in weight; each of the stampers.
weighing 1,020 pounds. The other two stampers, used
to clasp and slacken the wedges extracting the oil by
* See p. 41.
EXPERIMENTS ON WINDMILLS.
127
strong compression, were of the same length, but only
6.5 inches square, and weighed 500 pounds each. At
the time of the special observations herein recorded,
only one of these stampers was used. The velocity of
the wind was measured by light feathers, which the wind
carried along. Two men, placed on a small elevation in
the direction of the wind, and 150 feet from each other,
observed the time required by the feathers to pass the
150 feet. Of course this method involved the possibility
of a slight error in the matter of record, and presented a
chance that the velocity of wind recorded differed slightly
from that with which the wind actually struck the mill.
The velocity of wind thus obtained was 20.5 French feet
per second; the mill making 13 revolutions per minute, the
four sails having all their canvas spread. The barometric
pressure is not recorded. The actual mechanical effect
produced in one minute equalled (1020 X 13 X 10 + 500
X 13) pounds raised 1½ feet, or 1,000 pounds raised 218
feet per minute. The effect lost by the shock of the
cams and stampers was computed mathematically by
Coulomb, and found equal to 1,000 pounds raised 163
feet per minute. The loss of effect by friction (obtained
experimentally by giving motion to the windmill, while at
rest, by the application of weights at the extremities of
the sails) equalled 1,000 pounds raised 183 feet per min-
Therefore the total mechanical effect equalled the
raising of 1,000 pounds (218 + 163 + 183 =)253 French
feet per minute.
ute.
The above figures represent the average work of
128
THE WINDMILL AS A PRIME MOVER.
the windmills described. The velocity of the wind was
the only item specially obtained by Coulomb. Great as
is the value of Coulomb's record, it is meet to bear this in
mind, as well as the following extract from his work:-
•
"In these observations, I but followed in silence the work of the
miller (artiste), and I did not influence any thing in his operation. I
wished afterwards to have the disposition of the working of the mills,
so as to vary their action; thus, I would have procured a series of ex-
periments to establish the theory of these machines on the basis of a
great number of cases. But, when the proprietors learned what use I
wished to make of their machines, I could never induce them to lend
me the same for a few months' experimental work.”
Such data, the lack of which Coulomb deplored, are
still missing; but in view of the broader views which
manufacturers, in general, hold to-day in regard to the
value of scientific work, and of a correct analysis and
appreciation of their machines, it is not too hazardous to
give expression to the belief that it will not be many
years before such data are at hand.
•
1
THE CAPACITY AND ECONOMY OF THE WINDMILL. 129
CHAPTER IX.
THE CAPACITY AND ECONOMY OF THE WINDMILL.
The prime mover,
The Standard of Economy.
which develops and furnishes the desired amount of
horse-power for the least current money expense, is the
most economical. It is too often forgotten, that all the
separate running expenses of obtaining the power should
be expressed in money values, that these should be
added, and the sum regarded as the price of the power.
The smaller the price for reliably furnishing the required
power (or for performing the required work), the more
advantageous the use of the prime mover.
A glaring example of the damage done, and the
loss of money incurred, by a disregard of this standard
of economy, is seen in much of the present practice of
steam engineering. The amount of steam consumed
per horse-power developed is too often erroneously con-
sidered the sole test of economy, and the methods of use
of steam in engines made to conform to, and judged of
their relative value by, this test. The author has else-
where* pointed out some of the striking effects which
*The Most Economical Point of Cut-off in Steam-Engines, by James E. Denton
and Alfred R. Wolff; Transactions American Society of Mechanical Engineers,
130
THE WINDMILL AS A PRIME MOVER.
the more rational view of economy has on steam-engine
practice, and especially in the determination of the ratios.
of expansion of steam in cylinders, which will secure the
most economical working of the engines.
Even so great an authority as Sir William Thomson,*
when he originally proposed the use of the windmill for
storing electrical accumulators, urged, as a difficulty to
the adoption of the same in its present state of develop-
ment, that the first cost was too great. For the time
being, he overlooked the fact, that interest on capital,
and not capital itself, is one, and by no means the sole
item of current expense, by which the economy of prime
movers should be judged.
The current expense of any prime mover, or the cost
of obtaining the horse-power developed per unit of time,
which alone should form the basis of a comparison of
the economy of different prime movers, - consists prin-
1881; American Engineer, June, July, August, and November, 1881; American
Machinist, Aug. 6, 1881; Proceedings Institution of Civil Engineers, London, vol.
lxviii., session 1881-82, Part II. p. 75, and vol. lxix., session 1881-82, Part III.
P 44.
* Presidential address "On the Sources of Energy in Nature Available to
Man for the Production of Mechanical Effect," delivered before Section A of the
British Association for the Advancement of Science, 1881.
† In the same paper, Sir William Thomson, in estimating the cost of utilizing
the power of the Niagara Falls for electric lighting, correctly considers the interest
on first cost in determining the economical aspect of the question. The oversight,
noted in the text, becomes important and worthy of mention only, inasmuch as any
statement of so distinguished and justly esteemed an authority as Sir William
Thomson is apt to be accepted on the basis of authority alone; and it must be
added, that the great caution usually displayed by the most eminent living English
physicist entitles him prima facie to this mark of consideration.
THE CAPACITY AND ECONOMY OF THE WINDMILL. 131
cipally of interest, repairs, and depreciation of plant, cost
of fuel, oil, and attendance.
There are, of course, in addition, other expenses, like
insurance, engineers' stores, etc., which will suggest
themselves; but these are here considered of too trivial
import to be taken into account. The comparative
economy of the windmill and of other prime movers,
detailed in this chapter, is based on the sum of the
expenditures enumerated above.
The Capacity of the Windmill.—To judge of the
economy of the windmill, it is necessary to be acquainted
both with the items of current expense of developing the
power, and with the power developed by various-sized
mills, when driven by wind of specified average velocity.
It is to be regretted that there are not in existence such
serviceable data relating to capacity, obtained by dynamo-
metrical measurement of the actual horse-power of the
mill, and by simultaneous anemometrical measurement
of the actual velocity of wind. With the exception of
the experiments already referred to,* no direct accurate
measurement of the horse-power developed has been
published; and said results are not complete enough for
our purpose.
Fortunately, however, the author is enabled to pre-
sent reliable average performances, expressed in pump-
ing capacity or effect, of various sizes of a standard type
of American windmill.
Some eight years ago one of the most prominent
* See the experiments of Smeaton and Coulomb, pp. 120, 125.
132
THE WINDMILL AS A PRIME MOVER.
windmill manufacturers * came to the author with a few
scattered data of actual performances of his mills, which,
however, were sufficient, by means of deductions and
analogy from theoretical principles, to warrant the prep-
aration of Table VII., given on p. 133. From the quantity
of water raised to the specified direct elevation, it is, of
course, an easy matter to calculate the corresponding
horse-power; but it should be remembered that there is
a loss by the friction of the water in the pipes, so that a
slightly greater horse-power can be relied upon where
the windmill is used direct for power purposes. Inas-
much as the present principal application of windmills
is for pumping, the table of capacity, in the form
presented, will be found of the greatest use in practice.
Since the preparation of Table VII., over fifteen hun-
dred windmills have been sold on its guaranty; and in
all cases the actual results obtained, both in this country
and elsewhere, did not vary sufficiently from those pre-
sented to cause any complaint whatever, a proof that
the results as tabulated are correct, or certainly not too
high. If it be claimed that the horse-power developed
appears small,† from the stand-point of a (false) preva-
lent popular opinion, it should be observed, in response,
that the actual results noted in the table are in close
agreement with those obtained by theoretical analysis
* Mr. A. J. Corcoran. For description of the mill, see p. 76.
† Coulomb, in his experiments with a windmill of four sails seventy feet in
diameter, breadth of sails six and five-eighths feet, the wind blowing at a velocity
of fifteen miles per hour, obtained an actual useful result equivalent to about seven-
horse power. See p. 127.
THE CAPACITY AND ECONOMY OF THE WINDMILL. 133
of the impulse of wind upon windmill blades. The
manufacturer's own observations during the past eight
years have led him to conclude that they are correct.
A careful examination of a number of claims of the
development of greater horse-powers with the same
velocity of wind, led to the discovery that such claims
did not rest on a safe basis. In not a few cases, and
even in catalogues of foreign windmill manufacturers,
the nominal horse-power stated far exceeded those in
Table VII.; while the actual pumping effect recorded, as
found in practice, was considerably below that noted in
the table showing a lamentable discrepancy, and the
worthlessness of the claim of a horse-power exceeding
that theoretically possible.
TABLE VII.
SHOWING CAPACITY OF THE WINDMILL.

1
2
3
4
DESIGNA-
TION OF
MILL.
Velocity of Wind, in
Miles
per
Hour.
Revolutions of Wheel.
R
5
6
7 8 9
10
11
12
GALLONS OF WATER RAISED PER
MINUTE TO AN ELEVATION OF
25
50
feet. feet. feet feet.
75 100 150 200
feet.
feet.
Useful Horse-Power
Average Number of
during which this
Developed,
Hours
Equivalent Actual
per
Day
Result will be Ob-
tained.
I.
81%-ft. wheel
16
70 to 75
6.162
3.016
0 04
00
II.
10-ft. wheel
16
60 to 65 19.179
III. 12-ft. wheel
16
55 to 60
33.941
9.563 6.638 4.750
17.952 11.851 S.485 5.680
-
0.12
0.21
00 00
8
IV.
14-ft. wheel
16
50 to 55
45.139
V.
16-ft. wheel
16
45 to 50 64.600
VI. 18-ft. wheel
16
40 to 45 97.682
VII. 20-ft. wheel
16
35 to 40 124.950
VIII. 25-ft. wheel
16
22.569 15.304 11.246 7.807 4.998 0.28
31.654 19.542 16.150 9.771 S.075 0.41
52.165 32 513 24.421 17.485 12.211
63.750 40.800 31.248 19.284 15.938 0.78
30 to 35 212.381 106.964 71.60449.725 37-349 26.741
1604/49
S
0.61
دی زیرم دارم
8
1.34
00
8
134
THE WINDMILL AS A PRIME MOVER.
These windmills are made in regular sizes, as high as
sixty-foot diameter of wheel; but the experience with
the larger class of mills is still too limited at this date to
enable the presentation of precise data as to their per-
formance.
If the wind can be relied upon in exceptional locali-
ties to average a higher velocity for eight hours a day
than that stated in the above table, the performance or
horse-power of the mill will be increased, and can be
obtained by multiplying the figures in the table by the
ratio of the cube of the higher average velocity of wind
to the cube of the velocity above recorded.
Economy of the Windmill.* The standard of
economy of prime movers having already been defined,
it is only necessary to particularize, that in windmills the
cost of fuel is zero, wind being a free gift of nature, and
that the attendance required for the leading American
types of self-regulating windmills amounts only to filling
the oil-cups three or four times a month, work which
any one
If any
can attend to in a few minutes.
account is to be taken of this service, an allowance of
fifteen cents a month would really be quite extravagant.
In the following table such allowance has been made.
Experience has shown that the repairs and depreciation
items, jointly, are amply covered by five per cent per an-
*Note on the Economy of the Windmill as a Prime Mover, by Alfred R.
Wolff; Transactions American Society of Mechanical Engineers, 1882; Engi-
neering, Aug. 18, 1882; American Engineer, April 22, 1882; Journal of the
Franklin Institute, July, 1882; Proceedings Institution of Civil Engineers (Lon-
don), vol. lxx., session 1881-82, Part IV.
THE CAPACITY AND ECONOMY OF THE WINDMILL. 135
•
num. Interest is calculated at five per cent per annum.
The oil used is a very small quantity, — a few gallons per
year, and is allowed for in the table according to the
size of mill. All the items of expense, including both
interest and repairs, are reduced to the hour by dividing
the costs per annum by 365 × 8 = 2920; the interest, etc.,
for the twenty-four hours being charged to the eight hours
of actual work. By multiplying the figures in column 6
by 365 × 8
584, the first cost of the windmill, in dollars,
100 X 0.05
is obtained.
TABLE VIII.
SHOWING ECONOMY OF THE WINDMILL

1
2
3
4
5
6
DESIGNATION
OF MILL.
7
8 9 10
11
Gallons of Water Raised
25 Feet per Hour.
Equivalent Actual Useful
Horse-Power Developed.
Average Number of Hours
per Day during which
this Quantity will be
Raised.
For Interest on First
Cost (First Cost,
including Cost of
Windmill, Pump,
and Tower. 5 per
Cent per Annum).
For Repairs and De-
preciation (5 per
Cent of First Cost
per Annum).
For Attendance.
For Oil.
Total.
EXPENSE OF ACTUAL USEFUL POWER
DEVELOPED, IN CENTS, PER HOUR.
Expense per Horse-Power,
in Cents, per Hour.
I.
82-ft. wheel
370
-0.04
8
0.25
0.25
0.06 0.04 0.60 15.0
II.
10-ft, wheel
1151
0.12
Co
8
0.30
0.30
10 06 0.040 70
5.8
III.
12-ft. wheel
2036
0.21
8
0.36
0 36
0 06 0.04 0.82
3.9
IV.
14-ft wheel
2708
0 28
со
0.75
0.75
0.06 0.07 1.63
5.8
V.
16-ft wheel
3876
0.41
8
1.15
1.15
0.06 0.072.43
5.9
VI.
VII.
18-ft. wheel
20-ft. wheel
VIII. 25-ft. wheel
5861 0.6r
8
1.35
1.35
0.06 0.07 2.83
4.6
7497 0.79
00
8
1.70
1.70
0.06 0.10 3.561 4.5
12743 1.34
8
2.05
2.05
0.06 0.10 4.26 3.2
The number of gallons pumped by the thirty-foot and
thirty-five foot mills and larger sizes, and the economy
of the mills, are not stated in the above table; for the
136
THE WINDMILL AS A PRIME MOVER.
number of larger mills in operation is not sufficient to
insure authentic precision of the results obtained. The
performance of the thirty-foot mill, as far as observed,
seems to gravitate to a pumping capacity equivalent to
2.4-horse power, and to an expense of 2.5 cents per
horse-power per hour.
The Economy of Steam-Pumps. In order to ascer-
tain the relative value of the windmill, its economy
must be compared with that of other prime movers.
Accordingly, the author has taken pains to secure from
the more prominent manufacturers actual data of cost,
durability, running-expenses, and the like, of the several
types of steam-pumps of same actual pumping capacity
as the sizes of windmills mentioned in Table VIII. On
these data, as a basis, he has prepared Table IX., show-
ing the economy of steam-pumps, being careful that the
data selected, and the results obtained, should represent
the best rather than average practice.
Relative Economy of the Windmill and Steam-Pump.
- By comparison of the figures in Column 11 of Table
VIII. and in Column 23 of Table IX., it appears, that,
even presuming the steam-pump to require no extra
boiler capacity, and no attendance whatever (or that no
extra expense is attached to extra attendance and boiler
capacity), the windmill is by far the most economical
prime mover. Averaging the several results, its economy
may be said to be about 1.5 times that of the steam-
pump when no charge is made for attendance and boiler
capacity for the latter prime mover.
-
THE CAPACITY AND ECONOMY OF THE WINDMILL.. 137

·
:
1
SHOWING
2
3
4
5
6
7
8
TABLE IX.
ECONOMY OF STEAM-PUMPS.
9
| 10
11
12
13
14
15
16
17
18
19
20
21
22
1.
370 0.04
15
0.17
0.17
0.41
0.15
0.05
0.44
1.02
19.77 | 10.39
7.27
5.71
4.15
3.67 3.36
II.
0.12
14
0 39
0.60
0.07
1.09
1.69
20.44
11.06
7.94
638
4.82
4.03
111.
2036 0.21
14
0.39
0.68
0.09
1.68
2.18
20.93
11.55
8.43
6.87
5.31
4.52
IV.
2708 0.28
14
0.43
0.81
0.81
0.11
1.95
2.71
21.46 12.08
8.96
7.40
5.84
5.05
V.
3876 0.41
13
0.51
0.90
VI.
5861 0.61
13
0.60
1.07
ཱ、。
0.90
0.14
2.49
3.27
22.02
12.64
9.52
7.96
7.02
6.40
5.92
5.61
1.07
0.18
4.30
23.05
13.67 10.55
8.99
8.05
7.43
6.95
6.64
VII.
7497 0.79
13
0.64
1.15
1.15
0.21
5.08 23.83
VIII.
12743
1.34
12
0.77
1.24
1.24
4.02
0.25
6.75 25.50 16.12 || 13.00
14.45 11.33
9.77
8.83
8.21
7.73
7.42
7.16 6.96
11.44 10.50 9.88
9.40
9.09
8.83
is b i o
Gallons of Water Raised
25
Feet per
Hour.
Equivalent Actual Useful Horse-Power Developed.
Pounds of Coal Consumed per Horse-Power of
Useful Pumping Effect per Hour.
For Interest, 5 per Cent of First Cost; Pump
without Boiler.
For Repairs and Depreciation, 5 per Cent of
First Cost; Pump without Boiler.
For Interest, 5 per Cent of First Cost; Pump
and Independent Boiler.
For Repairs and Depreciation, 5 per Cent of
First Cost; Pump and Independent Boiler.
For Coal, $5 per Ton of 2,000 Pounds.
For Oil.
For Interest, Repairs, Depreciation, Coal
and Oil, but no Attendance; Pump with-
out Boiler.
For Interest, Repairs, Depreciation, Coal
and Oil, but no Attendance; Pump and
Independent Boiler.
I
For Interest, Repairs, Depreciation, Coal and
oil, and Attendance of 1 Man at 18.75 Cents)
per Hour: Pump and Independent Boiler.
For Interest, Repairs, Depreciation, Coal and
Oil, and 1/2 Time of Attendant at 18.75 Cents
per hour; Pump and Independent Boiler.
For Interest, Repairs, Depreciation, Coal and
Oil, and 1/3 Time of Attendant; Pump and
Independent Boiler.
For Interest, Repairs, Depreciation, Coal and
Oil, and 1/4 Time of Attendant; Pump and
Independent Boiler.
For Interest, Repairs, Depreciation, Coal and
Oil, and 1/5 Time of Attendant; Pump
and Independent Boiler.
For Interest, Repairs, Depreciation, Coal and
Oil, and 1/6 Time of Attendant; Pump
and Independent Boiler.
For Interest, Repairs, Depreciation, Coal and
Oil, and 1/7 Time of Attendant; Pump
and Independent Boiler.
For Interest, Repairs, Depreciation, Coal and
Oil, and 1/8 Time of Attendant; Pump and
Independent Boiler
For Interest, Repairs, Depreciation, Coal and
Oil, and 1/9 Time of Attendant; Pump
and Independent Boiler.
For Interest, Repairs, Depreciation, Coal and
Oil, and 1/10 Time of Attendant; Pump
and Independent Boiler.
EXPENSE OF Actual USEFUL POWER DEVELOPED, IN CENTS PER HOUR.
138
THE WINDMILL AS A PRIME MOVER.

II.
III.
IV.
V.
VI.
VII..
VIII.
23
24
25
TABLE IX. — CONCluded.
26
27
28
29
30
31
32
33
34
EXPENSE PER HORSE-Power, in Cents per Hour.
For Interest, Repairs, Depreci-
ation, Coal and Oil, but no
Attendance; Pump without
Boiler.
For Interest, Repairs, Depreci-
ation, Coal and Oil, but no
Attendance; Pump and In-
dependent
Boiler.
For Interest, Repairs, Depreci-
ation, Coal and Oil, and At-
tendance of 1 Man at 18.75
Cents per Hour; Pump and
Independent
Boiler.
For Interest, Repairs, Depreci-
ation, Coal and Oil, and 1/2
Time of Attendant at 18.75
Cents per Hour: Pump and
Independent Boiler.
For Interest, Repairs, Depreci-
ation, Coal and Oil, and 1/3
Time of Attendant at 18.75
Cents per Hour; Pump and
Independent Boiler.
For Interest, Repairs, Depreci-
ation, Coal and Oil, and 1/4
Time of Attendant at 18.75
Cents per Hour; Pump and
Independent Boiler.
For Interest, Repairs, Depreci-
ation, Coal and Oil, and 1/5
Time of Attendant at 18.75
Cents per Hour; Pump and
Independent Boiler.
For Interest, Repairs, Depreci-
ation, Coal and Oil, and 1/6
Time of Attendant at 18.
Cents per Hour; Pump and
Independent Boiler.
.75
For Interest, Repairs, Depreci-
ation, Coal and Oil, and 1/7
Time of Attendant at 18.75
Cents per Hour; Pump and
Independent Boiler.
For Interest, Repairs, Depreci-
ation, Coal and Oil, and 1/8
Time of Attendant at 18.75
Cents per Hour: Pump and
Independent Boiler.
For Interest, Repairs, Depreci-
ation, Coal and Oil, and 1/9
Time of Attendant at 18.75
Cents per Hour; Pump and
Independent Boiler.
For Interest, Repairs, Depreci-
ation, Coal and Oil, and 1/10
Time of Attendant at 18.75
Cents per Hour; Pump and
Independent Boiler.
25.5
494.3
259.8
181.8
142.8
119.3
103.8
91.8
84.00
77.50
72.50
14.1
170.3
92.2
66.2
53.2
45.3
40.2
36.2
33.58
31.42
29.75
10.4
99 7
55.0
40.I
32.7
28.2
25.3
23.0
21.52
20.29
19.33
76.6
43.I
32.0
26.4
23.I
20.9
19.1
18.04
17.17
16.36
53.7
30.8
23.2
19.4
17.1
15.6
14.4
13.68
13.05
12.56
7.0
37.8
22.4
17.3
14.7
13.2
12.2
II.4
10.89
10.46
10.13
6.4
30.2
18.3
14.3
12.4
II.2
10.4
9.8
9.39
9.06
8.81
5.0
19.0
12.0
9.7
8.5
7.8
7.4
7.0
6.78
6.59
6.44
•
= 2920.
In the above table, the interest, as well as the repairs and depreciation, are charged to the eight hours of actual work by dividing these costs per annum by 365 × 8
dollars, of steam-pump and independent boiler, the figures in column 7 should be multiplied by 584.
To find the first cost, in dollars, of steam-pump without boiler, the figures in column 5 should be multiplied by
365 × 8
100 X 0.05
=
584. To find the first cost, in
THE CAPACITY AND ECONOMY OF THE WINDMILL. 139
As a fact, however, steam-pumps do require extra
boiler capacity, and some attendance.
A comparison of Column 11 of Table VIII. and of
Column 24 of Table IX. shows, that, allowing for an
independent steam-boiler, but for no attendance for the
steam-pump, the economy of the windmill averages about
1.75 times that of the steam-pump.
A comparison of Column 11 of Table VIII. and of
Column 34 of Table IX. shows that the economy of the
windmill averages about 2.25 times that of the steam-
pump, when there is included for the latter a charge for
boiler capacity, and for the services of one-tenth of the
time of one man. Of course, the exact relative economy
of the windmill and steam-pump can be obtained for
each special desired pumping effect by dividing the cor-
responding figure in Column 23 to Column 34 of Table
IX., respectively, as the case may be, by the correspond-
ing figure in Column 11 of Table VIII.
It should be remembered that the tankage required
by a windmill should be equivalent to two, or better
three days' average daily consumption of water, which
is larger than necessary to meet the demands when a
steam-pump is used.
is used. But the extra cost involved is not
sufficient to change the standing of the economy of the
windmill as compared to that of the steam-pump, though
its tendency is to decrease its ratio of superiority. The
question of cost of tank has not entered the above
comparison; since the tankage required is to a great
extent a matter of individual discretion, and dependent,
140
THE WINDMILL AS A PRIME MOVER.
too, on ever-varying local conditions and considera-
tions.
It is, however, an easy matter, if desired, to include it
in a comparison of the economy of the two prime movers
in any special case. All that is necessary is, to divide the
first cost, in dollars, of tank required for given pumping
effect of steam-pump, by 584; and the figure thus ob-
tained should be added respectively to the figures in
Columns II to 22, Table IX., and the corresponding
figure in Column 3, divided by the respective sums.
Thus will be obtained "the expense per horse-power, in
cents per hour," denoted respectively by Columns 23
to 34 for the special conditions stated, inclusive of tank-
age required.
Similarly, dividing the first cost, in dollars, of tank
required for given pumping effect of windmill, by 584, the
figure thus obtained should be added to Column 10 of
Table VIII., and the corresponding figure in Column 4
be divided by the sum: the result will be the "expense
per horse-power, in cents per hour," for the windmill,
inclusive of tankage required.
The ratio of the figures thus obtained for the wind-
mill and steam-pump will define the relative economy of
the two prime movers, the necessary tankage for each
being included in the comparison.
Relative Economy of the Windmill and Ericsson's
Hot-air Engine. - -The following table, based on data
of cost, consumption of fuel, and the like, published by
the manufacturers, has been prepared on the same prin-
THE CAPACITY AND ECONOMY OF THE WINDMILL. 141
ciples and advantageous footing characterizing the table
of "Economy of Steam-Pumps."
TABLE X.
SHOWING ECONOMY OF ERICSSON'S HOT-AIR ENGINE.

1
2
3
4
5
6
7
8
9
EXPENSE OF ACTUAL USEFUL POWER DEVELOPED,
Equivalent
IN CENTS PER HOUR.
Gallons of
Actual
Water
Useful
Raised 50
Horse-
Feet
per Power De-
Hour.
veloped.
For Interest
5% of First
Cost.
For Repairs
and Depre-
ciation, 5% of
First Cost.
For Coal, $5
per Ton of
2,000 Lbs.
Expense
per
Power, in
Horse-
For Oil.
Total.
Cents per
Hour.
I.
200
0.042
*0.34
0.34
0.63
0.05
1.36
32.38
II.
350
0.074
*0.43
0.43
0.83
0.05
1.74
23.51
III.
800
0.169
*0.57
0.57
1.50
0.06
2.70
15.98
IV.
1600
0.337
*0.86
0.86
3.00
0.10
4.82
14.30
A comparison of Column II of Table VIII. and of
Column 9 of Table X. reveals the fact, that the economy
of the windmill averages about three times that of the
Ericsson hot-air engine, when no charge for attendance
is made for the latter. Where gas is used, the cost for
fuel is somewhat greater than that above recorded; but
the attendance then practically costs nothing.
Relative Economy of the Windmill and the Gas-En-
gine. — A gas-engine developing 1.34 actual useful horse-
power, a performance equivalent to that of the 25-foot
windmill raising 12,743 gallons of water 25
of water 25 feet per
* Multiplying this figure by 584 gives first cost of prime mover in dollars.
142
THE WINDMILL AS A PRIME MOVER.
hour, includes in its operation the following minimum
expenses:
For interest, 5% on first cost
0.80* cent per hour.
For repairs and depreciation, 5% on first cost, 0.80
(6
(C
(C
0.40
For oil
For gas
Total
8.00 cents (C
(C
•
10.00 cents per hour.
Expense of gas-engine per horse-power per hour, 7.5 cents.
A comparison of this figure with 3.2 of Column 11
of Table VIII. shows, that, even making no allowance
for attendance in the running of the gas-engine, the
windmill is more than 2.25 times as economical as a
prime mover.
The comparison instituted in this chapter clearly and
conclusively proves that at the present time windmills
are the most economical prime movers for the purposes
outlined in the Introduction of this work, and for
powers and pumping-effects ranging from zero to 2.4-
horse power. The superior economy still maintains, for
an average pumping-effect equivalent to eight-horse
power, the highest power developed for an average of
eight hours per day by the largest-sized windmills de-
signed in America. The usual range is from 25 to
4 horse power, the latter being developed by a mill of
about 40-foot diameter of wheel.
* Multiplying this figure by 584 gives first cost of prime mover in dollars.
USEFUL DATA REGARDING WINDMILL PRACTICE. 143
CHAPTER X.
USEFUL DATA IN CONNECTION WITH WINDMILL PRACTICE.
In this chapter it is intended to supply some addi-
tional formulæ, rules, tables, and facts, which may prove
convenient in the practical application of windmills, more
especially for pumping-purposes.
Allowance for Friction of Water in Pipes.
The work required to overcome the friction of the
water in its passage through the pipes must be allowed
for in determining the proper size of windmill to be pro-
vided. The readiest way to express this friction is in
terms of the head of water required to overcome it.
Thus, if a given quantity of water per minute is to be
raised vertically 50 feet, but has to travel several hundred
feet through a given-sized pipe in the process of raising,
the power required will have to equal the raising of the
same quantity of water per minute, say 54, or 56, or 60
feet, as the case may be. The extra head can be found
approximately by the use of the following data, adapted
for the purpose from Weisbach's " Mechanics," vol. 2,
Coxe's edition, p. 868, et seq. :—
144
THE WINDMILL AS A PRIME MOVER.
?
The extra head in feet equals
h
=
0.1865/ Χ Χυ
d
xf,
(I.)
in which /= length of pipe in feet,
d = internal diameter of pipe in inches,
v =
183.34 × Q
d x d
Q = cubic feet of water raised per second,
d = diameter of pipe in inches, and
f=
0.0686 when v =
0.10,
"(
0.0527
0.20,
(C
(6
0.0457
0.30,
0.0415
0.40,
0.0387
((
((
0.50,
0.0365
(6
((
0.60,
(C
0.0349
0.70,
0.0336
0.80,
((
0.0325
0.90,
CC
(6
0.0315
1.00,
((
(C
0.0297
1.25,
0.0284
((
1.50,
0.0265
2.00,
0.0243
3.00,
0.0230
4.00,
(C
<<
0.0214
6.00,
66
(C
0.0205
8.00,
66
0.0193
= 12.00,
0.0182 (C
66
20.00.
(II.)
An example will best show the use of these data.
Let it be required to raise 125 cubic feet of water per
hour 25 feet, forcing the water through 500 feet of
USEFUL DATA REGARDING WINDMILL PRACTICE. 145
2-inch pipe; how many feet direct vertical rise will this
be equivalent to, the difference being due to friction of
water in the pipes?
125 cubic feet per hour =
125
60 x 60
cubic feet per second;
or, by equation (II.),
ย
183.34 X 125
3600 X 2 X 2
= 1.59,
for v1.59, f= about 0.028. Therefore, by equation
(I.),
h =
0.1865 × 500 X 1.59 X 1.59 × 0.028
3.3;
2
or, the power required would be the same as to raise the
125 cubic feet of water 25 + 3.3 28.3 feet direct ver-
tical height.
=
[A cubic foot of water weighs about 62.4 pounds. A
gallon of water measures 231 cubic inches, or 0.13368
cubic feet, and weighs 8.34 pounds. One cubic foot
contains 7.48 gallons of water.]
Substitution in equations (II.) and (I.) gives values
in close accord with the following table, prepared by Mr.
George A. Ellis, C.E. Mr. Ellis's table is, however, ex-
pressed in pounds pressure per square inch. By multi-
plying the figures in the columns headed "Sizes of Pipes"
by 2, the approximate head of water, in feet, correspond-
ing to friction, will be found for each 100 feet of length.
To obtain the approximate head, in feet, corresponding
to loss by friction, for any other length of pipe, multiply
146
THE WINDMILL AS A PRIME MOVER.
the figures in Mr. Ellis's table by twice that length, and
divide by 100.
TABLE XI.
FRICTION OF WATER IN PIPES.
Friction Loss, in Pounds Pressure per Square Inch, for each 100 Feet of Length in
Different Size Clean Iron Pipes Discharging given Quantities of Water per
Minute (G. A. ELLIS,* C.E.)

SIZES OF PIPES: INSIDE DIAMETER.
Gals.
per
Minute.
34 In.
I In.
1¼ In.
1½ In.
2 In.
2½ In.
3 In.
4 In'
6 In.
8 In.
10 In.
12 In.
14 In.
16 In.
5
3.3 0.84 0.31 0.12
IO 13.0 3.16 1.05 0.47 0.12
15 28.7 6.98 2.38 0.97
20
I
-
50.4 12.30 4.07 1.66 0.42
25 78.0 19.00 6.40 2.62
☺
-
0.21 0.10
1
I
}
18 In.
48.00 16.10 6.52 1.60
20.20 8.15
1
1
24.90 10.00 2.44 0.81 0.35 0.09
56.10 22.40 5.32 1.80 0.74
39.00 9.46 3 20 1.31 0.33 0.05
14.90 4.89 1.99
21.20 7.00 2.85 0.69 0.10
28.10 9.46 3.85
37.50 12.47 5.02 1.22 0.17
30
27.50 9.15] 3.75| 0.91
35
37.00 12.40 5.05
40
45
50
75
100
125
150
175
200
250
300
350
400
450
500
750
1000
1250
1500
1750
2000
2250
2500
3000
3500
4000
4500
5000
}
1
19.66 7.76 1.89 0.26 0.07 0.03 0.01
28.06 11.20 2.66 0.37 0.09 0.04
15.20 3.65 0.50 0.12
-
0.05 0.02
19.50 4.73 0.65 0.16 0.06
25.00 6.01 0.81 0.20 0.07 0.03
1
30.80 7.43 0.96 0.25 0.09 0.040 017 0.009 0.005
2.21 0.53 0.18 0.08
J
I
I
3.88 0.94 0.32 0.13 0.062 0.036 0.020
I
1.46 0.49 0.20
2.09 0.70 0.29 0.135 0.071 0.040
0.95 0.38
1.23 0.49 0.234 0.123 0.071
0.63
1
*Fire Streams and Hydraulics, p. 38.
0.77 0.362 0.188 0.107
1.11 0.515 0.267 0.150
0.697 0.365 0.204
0.910 0.472 0.263
0.593 0.333
0.730 0.408
USEFUL DATA REGARDING WINDMILL PRACTICE. 147
0.730 X 1200
100
-
Thus, let it be required to raise 5,000 gallons of water
per minute through 600 feet of 16-inch pipe. We note
in Table XI. the figure 0.730; by multiplying this by
twice 600, or by 1,200, and dividing by 100, we obtain
8.76, which represents the vertical rise of
water that the loss by friction is equal to. Therefore, if
the 5,000 gallons of water were to be raised 50 feet per
minute, being forced through 600 feet length of 16-inch
pipe, the power required would be the same as to raise
5,000 gallons of water per minute a direct vertical height
of 58.76 feet. By making the substitution as here noted
in Table XI., the results will accord quite closely with
those obtained by direct calculation from equations (I.)
and (II.).
TABLE XII.
SHOWING CO-EFFICIENT OF FRICTION IN AXLES.
(From Molesworth's "Pocket-Book of Engineering Formulæ.")

AXLE.
BEARING.
Dry.
Greasy Ordinary Lubricated
and Lubrica- Continu-
Wetted.
tion.
ously.
Lard and
Plumbago
Fatty
Matter.
Bell-metal.
Cast-iron
Bell-metal
C
Wrought-iron, Cast-iron.
0.097
0.049
0.25
0.19
0.070
0.050
0.09
CC
1
0.070
0.050
Cast-iron
Bell-metal
•
0.13
0.070
0.050
0.14
<<
Lignum-vitæ,
0.19
0.16
0.070
0.050
0.06
0.16
Wrought-iron,
Cast-iron
Lignum-vitæ.
<<
<<
CC
0.19
0.120
Cast-iron
0.18
0.100
•
•
•
0.090
0.14
0.110
0.15
Lignum-vitæ,
I
រ
0.070
J
148
WINDMILL AS A PRIME MOVER.
THE

TABLE XIII.
SHOWING THE NUMBER OF GALLONS DISCHARGED PER MINUTE BY A SINGLE-ACTING PUMP OF A GIVEN
DIAMETER AND STROKE AT TEN STROKES PER MINUTE.
LENGTH OF STROKE IN INCHES.
Inches.
1
2
3
4
5
6
7
8
9
10
12
14
15
16
18
20
24 In.
I
1
2
Diameter of Pump Barrel in Inches.
0.034 0.068 0.102 0.136 0.170
0.053 0.106 0.159 0.212 0.266
1½ 0.076 0.153 0.229 0.306 0.382
134 0.104 0.208 0.312 0.416 0.521
0.136 0.272 0.408 0.544
0.544 0.680
0,204
0.238 0.272 0.306 0.340
0.319 0.372 0.425 0.478 0.531
0.459 0.535 0.612 0.688
0.765
0.408 0.476
0.637
0.918
0.510
0.544 0.612
0.680
0.816 I
0.744
0.797
0 850
0.956
1.062 1.275 1¼
1.071 1.147
I.224
1.377
1.530 1.836
1½
22
0.212 0.425 0.637
0.850
0.850 1.062
3
0.306 0.612 0.918
1.224
1.224 1.530
32 0.416 0.833 1.249 1.666 2.082
2.499
2.915
4
42
5
5/2
6
78
0.544 1.088 1.632 2.176 2.720
0.688 1.377 2.065 2.754 3.442
0.850 1.700 2.550 3.400 4.250
1.028 2.057 3.085
3.085 4.114 5.142
1.224 2.448 3.672 4.896 6.120
1.666
3.332 4.998 6 664 8.330
2.176 4.352 6.528
19.584
a
9
2.754
24.786
ΙΟ
12
15
18
20
24
76.500 91.800 107.100 114.750 122.400 137.700 153.000 183.600 15
11.016 22.032 33.048 44.064 55.080 66.096 77.112 88.128 99.144 110.160 132.192 154.224 165.240 176.256 198.288 220.320 264.384 18
13.600 27.200 40.800 54.400 68.000 81.600 95.200 108.800 122.400 136.000 163.200 190.400 204.000 217.600 244.800 272.000 326.400 20
19.584 39.168 58.752 78.336 97.920 117.504 137.088 156.672 176.256 195.840 235.008 274.176 293.760 313.344 352.512 391.680 470.016| 24
The quantities given in the table are in gallons, and are calculated for single-acting pumps at 10 strokes per minute. The quantity for any other number
of strokes, per minute may be found by multiplying the quantity noted in the table by the ratio of 10 to the given number of strokes. For double-acting pumps,
the quantity noted in table should be doubled.
68.850
0.625 0.729 0.833 0.937 1.041 1.249
0.816 0.952 1.088 1.224 1.360
1.632
3.264 2
1.275 1.487 1.700 1.912 2.125 2.550 2.975
4.250 5.100 2/2
1.836 2.142
2.448
2.754 3.060 3.672 4.284
6.120 7.344 3
3 332 3.748 4.165 4.998 5.831
6.664 7.497 8.330 9.996
3.264 3.808
4.352 4.896 5.440 6.528 7.616
8.704 9.792
4.131 4.819 5.508 6.196 6.885 8.262 9.639 10.327 11.016 12.393
5.100 5.950 6.800 7.650
8.500 10.200 11.900
12.750 13.600 15.300
6.171 7.199 8.228 9.256 10 285
12.342 14.399
15.427 16.456| 18.513 20.570 24.684
7.344 8.568 9.792
11.016
12.240 14.688
17.136 18.360 19.584 22.032 24.480 29.376
9.996 11.662 13.328 14.994 16.660 19.992 23.324 24.990 26.656 29.988 33.320 39.984
8.704 10.880 13.056| 15.232
17.408
5.508 8.26211.016 13.770 | 16.524 | 19.278 | 22.032
22.032
3.400 6.800 10.200 13.600 17.000 20.400 23.800 27.200 30.600
4.896 9.792 14.688 19.584 24.480 29.376 34.272
39.168
44 064
7.650 15.300 22.950 30.600 38.250 45.900 53.550 61.200
1.457 1.562
1.666
1.874
2.082 2.499 134
1.904 2.040
2.176
2.448 2.720
3.187
3.400
3.825
4 590
4 896
5.508
6.247
3½
8.160
10.880 13.056
13.770 16.524
17.000 20.400
4
4/2
5
52
6
7
21.760 26.112
| |
30.464 32.640 34.816
39.168
27.540 33.048
38.556
41 310 44.064
50.572
34.000
48 960
40.800
47.600
51.000 54.400 61.200
43.520 52.224
55.080 66.096
68 000
78
8
9
81.600 IO
58.752 68.544
73.440 78.336 88.128
73.440 78.336 | 88.128| 97.920 |107.504 12
USEFUL DATA REGARDING
149
WINDMILL PRACTICE.

TABLE XIV.
SHOWING THE CLASS AND PROPER DIAMETER, IN INCHES, OF PUMPS SUITABLE FOR
SUITABLE FOR DIFFERENT
Desig-
nation
of Mill.
82-foot S
ELEVATIONS, AS BASED UPON ACTUAL RESULTS OF PRACTICE.
ELEVATION, IN FEET, TO WHICH WATER IS TO DE RAISED, FROM 10 FEET TO 200 FEET.
180
35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165] 170| 175| 180| 185| 190, 195] 200
10
15 20 25 30
S
ՄՐ
S SIS S
wheel. 42 4
24
SISIS
24
S
من
S
ين
32 34 3 2 223 2
SSS SS 9
10-foot D D
S
SSSSSS SS
wheel. 44 34 4 4 34 32 34 34 3 2¾¼ 2¾¼¼ 22½ 2¼2 2¼2 a
3
អ
DS S
12-foot D D D DS S SS SS SIS SSS SSS SSS SS SSSSS SS S SS SS
wheel. 6% 5 4½ 4 5 44 42 44 4 34 32 32 33 3 3 3 24 24 22 2%aa%a%2%22%2
14-foot D D DD DD S SSS SSS
SSS SSSSSSS S SS S SS SS
SSS SSSS SS SS SS SS
wheel. 6 5½ 4 4 3 5 44 42 44 4 34 34 32 32 33 34 3 3 24 24 24 22½ 22½ 2222222222222222
16-foot D D DD DD D D DDD D D D D D D D D D D D SS S SS
DDD DDD DDDD S SS
SSSSS
SSS SSS SSSSSS
SSS
wheel.
54%
74 6½ 52 5 42 44 4 34 32 34 34 3 32222222223333343 3 3 3 24 24 2 2 2 22½ 22½ 22½
18-foot D D DD DD D D
DDDDDD DD DDDDDD DDD DDDDDDDDDDDDDDD
wheel. 10% 8% 7% 6% 65% 5% 5 44 42 44 4 4 34 34 32 32 33 34 34 3 3 3 3 24 24 2 2 2 2% 2% 2% 2% 2% 2% 2% 33%
20-foot D D
DD D DDDDDDDDDDDDDDDDD DDD DDD DDDDDDD DD
DDD
wheel. 11% 9% 76% 65% 5% 54% 4% 4% 4% 4 43434343% 33% 343434 3 3 3 3 224 22¾¼ 2¾¼ 2¼2¾2½ 22½ 22½
25-foot D D
DDD D D D D D D D D D D D D D D│D│DDDDDDDDDDDDDD
DDD
wheel. 12 10 8 7 7 6 6 5 5 5 5 4 4 4½ 44 4 4 34 34 34 32 32 32 32 34 34 34 34 3 3 3 3 3 32242 24
30-foot
D DD DD D D DDDDDD DDDDDDD DDDDDDDDDDDDDDDD DDD D
15½ 13½ 12 11 10 92 98% 8 7 7 7 7 66½ 6 6 6 54545252555 5 5 5 44 444% 4% 4% 4% 4% 4% 4% 4
wheel. 19
D
D D
8
DDD
DDDDDD
Pump S referred to above, is a single-acting suction and force pump.
Pump D referred to above, is a double-acting suction and force pump.
150
THE WINDMILL AS A PRIME MOVER.
TABLE XV.
GIVING THE NUMBER OF SQUARE FEET AND ACRES THAT A FIRST-
CLASS WINDMILL CAN IRRIGATE ONE INCH IN EIGHT HOURS,
RAISING THE WATER 10 FEET, 15 FEET, AND 25 FEET RESPEC-
TIVELY, AS BASED UPON ACTUAL RESULTS OF PRACTICE.

SIZE OF WINDMILL.
10 Feet.
15 Feet.
25 Feet.
Square Feet. Acres. Square Feet. Acres. Square Feet. Acres.
82-foot diameter of wheel,
10
11736.34
37161.74
"
"
"
12
"
14
16
18
20
25
""
"
"
"(
44
30
0.269 7824.74 0.180
0.853
24774-75 0.569
66765.16
1.533
44509.85 1,022
85982.05 1.974 57321.11 1.316
120106.14 2.757 80070.76 1.838
192446.10 4.418 123164.58 2.827
238395.08
5.473 158930.31 3.649
410038.09 9.413 273359.24 6.275 163533-37
831686.24 19.093 561197.56 12.883 331752.96
4744.74 0.109
14767.83 0.339
26134.57
0.600
34757.03
0.798
49742.00 1.142
75215.14 1.727
96211.50 2.209
3.754
7.616
For two inches irrigation in eight hours, divide the figures in above table by 2, for three inches
by 3, etc. Eight hours represents the average running-time of the mills for irrigation purposes in a day
of twenty-four hours.
TABLE XVI.
SHOWING CAPACITY OF CISTERNS AND TANKS, IN GALLONS, FOR
TWELVE INCHES IN DEPTH.
EACH

Diameter in
Feet.
Gallons.
Diameter in
Feet.
Gallons.
Diameter in
Fect.
Gallons.
ICO
5.87
$6.5
248 23
II.O
710.90
2.0
-23.50
7.0
287.88
11.5
777.05
2.5
36.72
7.5
33048
12.0
846.03
3:0
52.88
8.0
376.00
13.0
3.5
71.97
8.5
424.48
14 0
992.91
1151.54
4.0
94.00
9.0
475.89
15.0
1321 92
4.5
118.87
9.5
530.24
20.0
2350.08
5.0
146.88
10.0
587.52
25.0
3672.00
5.5
177.72
10.5
647.74
30.0
5287.68
6.0
211.51
For
any
other depth, multiply the figures in the table by depth, in inches, divided by 12.
USEFUL DATA REGARDING WINDMILL PRACTICE. 151
TABLE XVII.
SHOWING DIMENSIONS, WEIGHT, ETC., OF WROUGHT-IRON WELDED
PIPE OF DIFFERENT DIAMETERS.

Length
of Pipe
Length
Inside Outside External
Diam-Diam Circum-
eter.
eter. ference.
per Sq. Internal External contain-
Foot of
Area.
Outside
Area. ing One
Cubic
of Pipe Weight No. of Contents
per Threads in Gal-
Foot of per Inch
Length. of Screw.
Weight
of Water
lons per
per
Foot of
Foot.
Length.
Surface.
Foot.
in.
inches.
inches, feet.
sq. in.
sq. in.
feet.
lbs.
lbs.
1/8
0.40
1/4
0.54
1.696
I.272 9.440
7.075
0.012
0.129 2500.00
0.24
27
0.049
0.229 1385.00
0.42
18
0.0006
0.0026
0.005
0.021
3/3
0.67
2.121 5.657
0.110
0.358 751.50 0.56
14
0.0057 0.047
1/2
0.84
2.652
4.502
0.196
0.554
472.40 0.84
14
0.0102
0.085
3/4
1.05
3.299
3.637
0.441
o 866
270.00
1.12
11½
0.0230 0.190
I
1.31
4.134
2.903
0.785
1.357
166.90
1.67
11/2
0.0408
0.349
14
1.66
5.215
2.301
1.227
3.164
96.25
2.25
11/2
0.0638 0.527
1/2
1.90
5.969 2.010
1.767
2.835
70 65
2.69
11½
0.0918 0.760
2
7.461
2.37
1.611
3.141
4.430
42.36
3.66
8
0.1632 1.356
22
3
2.87
9.032
10.996
3.50
1.328 4.908 6.491
30.11
5-77
CO
8
0.2550
2.116
1.091
3/2
4.00
12.566 0.955
+
if
4.50
14.137
0.849
7.068 9.621
9.621
12.566
19.49
7.54
8
0.3673 3.049
42
5.00
15.708
0.765
15.904
5
5.56
17.475
0.629
12.566
15.904
19.635
19.635 24.299
14.56 9.05
со
8
0.4998 4.155
II.31 10.72
9.03
7.20
12.49
CO
со
8
0.6528 5.405
0.8263 6.851
14.56
6
6.62
20 813
0.577
28.274 34.471 4.98 18.76
7
7.62
23.954
8
8.62
9
9.68
IO
0.505
27.096 0.444
30.433 0.394
10.75 33.772 0.355
38.484
45.663
3.72 23.41
50.265 58.426 2.88
28.34
63.617 73.715
2.26 34.67
78.540 90.792 1.So 40.64
со
00
со
1.0200
8.500
1.4690
12.312
1.9990
16.662
со
8
2.6110 21.750
S
3.3000 27.500
8
4.0810 34.000
1 inch and below are butt-welded, and proved to 300 pounds per square inch hydraulic pressure.
1¼ inches and above are lap-welded, and proved to 500 pounds per square inch hydraulic pressure.
To find the area of a circle in square inches, multiply
the diameter, in inches, by itself, and by 0.7854. To
find the circumference of a circle in inches, multiply the
diameter in inches by 3.1416.
|
:
INDEX.
PAGE
Accumulators, electrical, and wind-
mills
•
Acres, number of, irrigated by wind-
mills
Adams Windmill, description of.
Air, compression and storage of, by
windmills
•
Air, loss of pressure by friction of
particles of .
Air-engine, relative economy of wind-
mill and .
•
•
Althouse Windmill, description of
America, extent of manufacture of
windmills in
America, extent of use of windmills
in
America, movement of wind in
American experiments on wind-
wind
Area of circle
Average movement and velocity of
Average velocity of wind driving
windmill.
•
•
150
98
Average work of windmills.
4
IO
·
140
94
Barometric pressure, its effect on
wind pressure.
Batteries, storage, and windmills.
Bender, C. B., on high wind press-
ures
Best angles for ventilators
2 of impulse and weather
•
of impulse and weather (Smea-
ton's).
PAGE
151
6
∞ 3
8
II
4
22
35
31
2
125
7
Best ratio of sail to circular area of
wheel.
•
123
•
mills
American windmills, classification of
types of .
119
•
73
European
•
American windmills compared to
American windmills, durability of va- 76
rious types of .
Angles, best, for ventilators
•
best, of impulse and weather
Smeaton's.
Appreciation of the windmill
Archibald's formula for wind velo-
city
Area, best ratio of sail to circular
area of wheel
71
Blades, analysis of impulse of wind
on windmill (Rankine's)
Blades, analysis of impulse of wind
on windmill (theoretical) .
Blades, analysis of impulse of wind
on windmill (Weisbach's)
28
26
29
•
74 Buchanan Windmill, description of. 101
35
31 Calms, and the use of windmills
3
•
125 Capacity and economy of windmill. 129
I Capacity of cisterns and tanks
of windmill
150
131
22
of windmill pumps of different
diameters and strokes
123 Centrifugal-governor windmills
•
148
86
153
154
INDEX.
PAGE
Champion Windmill, description of
geared mill..
Champion Windmill, description of
pumping-mill
Description of Stover Windmill
•
108
of Strong Windmill
of vertical windmills
•
106
•
of windmill sails.
Character of wind, and the use of
windmills
3
151
149
Circle, circumference and area of
Class and proper diameter of pumps,
Classification of European windmills,
of types of American windmills 73
Comparison of American and Euro-
•
50
71, 72
pean windmills
Comparison of side-vane and centrif-
ugal-governor mills.
•
Corcoran Windmill, description of
for railway water supply
for water supply .
geared mill for power purposes
tower.
of windmills experimented upon
PAGE
• 103
II 2
53
•
56
:
126
by Coulomb
Description of Woodmanse Wind-
mill
Details of Smeaton's experiments
Diagram showing best angles of
impulse and weather
Diameter, proper, of pumps
Dimensions, weight, etc., of wrought-
iron pipes
. 103
120
•
34
•
148
•
75
151
•
mills
76 Disadvantages of horizontal wind-
80
52
•
128
77 Discussion of Coulomb's experi-
80
80
4
Corn, windmills used for shelling
Coulomb's description of mills ex-
perimented upon by himself. . 126
Coulomb's discussion of experi-
ments
Coulomb's experiments on
mills . .
. 128
ments.
Discussion of Smeaton's conclusions, 124
Dome, Cubitt's method of turning. 62
Durability of American windmills
Dutch or tower mills
Dwellings, domestic, and the use of
windmills
•
Early history of windmills
wind-
.40, 125
•
127
Eclipse Windmill
•
145 Economical motors, windmills
Coulomb's results of experiments
Cubic contents of a gallon
•
Cubic foot of water, weight of .
Cubitt's method of governing
of reefing windmill sails
of turning dome.
Current expense of Halladay Wind-
·
145 windmills the most.
69 Economy and capacity of the wind-
•
76
61
4
43
85
I
3, 142
68
mill
129
62
Economy of windmill as affected by
tankage
•
139
mill
•
91
Economy of windmill compared to
Ericsson's hot-air engine
•
►
•
140
Data, useful, in connection with wind-
mill practice
Economy of windmill compared to
143
gas-engine
·
141
Definition of wind .
5
Description of Adams Windmill
98
Economy of windmill compared to
steam-pump
•
•
136
of Althouse Windmill.
of Buchanan Windmill
of Champion Windmill
of Corcoran Windmill
•
76
of Eclipse Windmill
85
of Halladay Windmill
86
of horizontal windmills.
52
of Leffel Windmill.
116
of Regulator Windmill
108
94 Economy of windmill, standard of
IOI Effect, loss of, by friction of shaft
106
of barometric on wind pressures
of temperature on wind pressures,
of wind on plane surfaces
theoretical mechanical, of wind-
mill sail.
Effect, theoretical mechanical, of
windmill with plane sails.
·
129
•
39
II
8
တ
S
31
•
38
INDEX.
155
PAGE
PAGE
Effect, theoretical mechanical, of
windmill with shape of sail for
maximum effect
•
Efficiency of windmills
•
Electrical accumulators and the use
of windmills
•
Employment, special, of windmills
Establishments, manufacturing, and
the use of windmills
European windmills
description of sails
•
European windmill governors .
Expense, current, of Halladay Wind-
·
Gaudard on relation of velocity and
pressure of wind.
35 German or post windmills
119
4
Hagen on relation of velocity and
pressure of wind.
4 Halladay Windmill, current expense
of
Halladay Windmill, description of
fan of.
18
58
20
91
4
•
50
•
56
for power purposes.
91
65
for railway water supply
91
in Germany
2 8 8 ã ã *
86
90
94
91
iron-work of
•
89
. 130
·
25
·
17
mill
Expense, current, the basis of com-
parison of prime movers
Experiments on windmills, Smea-
ton's
•
Experiments on windmills, Cou-
lomb's
I 20
40, 125
Extent of manufacture of windmills
in America .
Extent of use of windmills in Amer-
ica .
Extent of use of windmills in the
world .
Farms and the use of windmills
2
2
Hartnup on high wind pressures in
Great Britain .
Hawksley on relation of velocity and
pressure of wind . .
Height of observation and velocity
of wind .
Height of observation and velocity
•
of wind, Archibald on
Height of observation and velocity
of wind, Stevenson on
History, early, of windmills
I Horizontal windmills.
compared to vertical
•
4
description of.
Feed, cutting, and the use of wind-
mills.
Field on relation of velocity and
pressure of wind
Filler's windmill
•
disadvantages of.
4 Hot-air engine, economy of Erics-
son's
21
22
21
43
50
53
50
52
•
141
18
Hot-air engine, Ericsson's, relative
94
23
economy of windmill and .
Hours, number of, windmills run per
•
·
140
39
day.
•
147
Impulse, best angles of.
IO
Smeaton's angles of
31
125
Fresnel on high wind pressures
Friction of axles, loss of effect by
table showing co-efficient of.
Friction of particles of air, loss of
pressure of wind by .
Friction of water in pipes, allowance
for .
Friction of water in pipes, table
showing loss by
Impulse of wind on windmill blades, 26
·
Rankine's analysis of
theoretical analysis of .
Weisbach's analysis of
28
26
29
•
150
. 116
•
143
146
Irrigation by windmills, table show-
Gallon, cubic contents of
145
ing capacity
Gas-engine, relative economy of wind-
mill and .
·
141
Leffel Windmill
Gaudard on high wind pressures in
England and France
Loss, by friction, of water in pipes. 146
•
23
of effect by friction of the shaft
·
39
156
INDEX.
PAGE
Loss of pressure of wind by friction.
of particles of air
Manufacturing establishments and
the use of windmills
Maxims, Smeaton's
ΙΟ
Pumps, capacity of windmill
class and diameter of windmill.
economy of steam
•
relative economy of windmill and
PAGE
. 148
•
149
136-138
4
steam .
. 136
•
123
Mechanical effect of windmill sail
•
31
Raising sand, windmills for
4
of windmill of shape of sail for
maximum effect.
35
Rankine on impulse of fluid on vanes,
Rankine on relation of velocity and
28
Mechanical effect of windmill with
pressure of wind
16
•
•
plane sails . . .
38
Ratio, best, of area of sail to circular
Meikle's method of reefing windmill
area of wheel
•
·
123
sails
67
Reefing windmill sails, Cubitt's
Movement of wind, average
6
in America.
7
method of
•
Pipes, weight of wrought-iron.
Pole on relation between pressure
and velocity of wind
Post or German windmills
Power, windmills for storing
•
•
151
Regulator Windmill
•
•
19
Practice, useful data in connection.
with windmill
143
method of
D
Reefing windmill sails, Meikle's
Relation between pressure and velo-
city of wind
. . . 8, 9, 12, 13, 15
58 Relation between theoretical and
actual wind pressures
4
II
•
•
Relative economy of windmill and
•
ΙΟ
•
·
•
140
Ericsson's hot-air engine
Relative economy of windmill and
gas-engine
22 Relative economy of windmill and
steam-pump
•
141
•
136
122
•
•
•
127
68
• 67
108
Pressure, effect of barometric on
wind
•
Pressure, high wind
high wind, C. Shaler Smith on.
high wind, Gaudard on
high wind, Hartnup on
loss of, by friction of particles of
air.
Pressure, relation between actual and
theoretical wind.
•
24
23
•
25
Results of Smeaton's experiments
of Coulomb's experiments
•
10
Sails, Cubitt's method of reefing
windmill..
68
10
Sails, description of European wind-
mill
56
9, 12, 13
Sails, Meikle's method of reefing
windmill.
67
Sails, plane, mechanical effect of
windmill with.
38
Pressure, relation between velocity
of wind and
Pressure, relation between velocity
20
17
of wind and, Gaudard on . . . 18
Pressure, relation between velocity
of wind and, Hagen on
Pressure, relation between velocity.
of wind and, Hawksley on
Pressure, relation between velocity
of wind and, Rankine on
Pressure, relation between velocity
of wind and, Weisbach on
Pressure, Smeaton's table of wind
Pumping water and the use of wind-
mills
•
Sails, shape of, for maximum effect. 32
shape of, for maximum effect,
mechanical effect of .
Scott on high wind pressures
•
16 Shaft, co-efficient of friction of
loss of effect by friction of
Side-vane governor compared to cen-
trifugal-governor windmills
15
•
14
I, 4
Smeaton's experiments, results and
discussion of
35
22
·
147
39
•
75
I 20
INDEX.
157
PAGE
PAGE
Smith, C. Shaler, on high wind press-
ures
•
Specific uses of windmills
Steam-engine, the windmill and the .
Steam-pumps, the relative economy
of windmills and . .
Stevenson on velocity of wind and
height of observation
Storage batteries and the use of
windmills
Storing air and the use of windmills,
water and the use of windmills
Stover Windmill
Strong Windmill
Supply, railway water, and the use of
windmills
Surfaces, effect of wind on plane.
Table I., showing average movement
of wind in America.
Table II., showing relation between
temperature, pressure, and velo-
city of wind
Table XIV., showing class and
proper diameter of windmill
pumps
24
3
•
149
2
Table XV., showing number of acres
irrigated by windmills
•
150
136
Table XVI., showing capacity of
cisterns and tanks
. 150
21
4
Table XVII., showing dimensions,
weight, etc., of wrought-iron
pipes.
4 Tankage required, and the economy
of windmills
4
103
Tanks, capacity of .
112 Temperature, its effect upon the
pressure of wind.
Theoretical mechanical effect of
•
151
•
139
•
150
•
12, 13
31
Theoretical mechanical effect of
7
windmill with plane sails.
Theoretical mechanical effect of
windmill with shape of sail for
maximum effect
38
48
windmill sail
•
12, 13 Thomson, Sir William, on the use
of windmills
Table III., showing (Rouse-Smeaton)
relation between pressure and
velocity of wind .
Table IV., Hartnup's compilation of
highest wind pressures in Great
Britain
Tower of Corcoran Windmill.
Trautwine on high wind pressures in
•
35
4, 130
So
14
or Dutch windmills. .
61
America.
23
25
Types, various, of American wind-
Table V., showing best angles of
weather.
mills
· 73
33
Table VI., showing results of Smea-
ton's experiments
I22
United-States Wind Engine and
Pump Company .
windmill.
the windmill
steam-pumps
Table VII., showing capacity of the
Table VIII., showing economy of
Table IX., showing economy of
Table X., showing economy of Erics-
son's hot-air engine
•
Table XI., showing loss, by friction,
of water in pipes.
Table XII, showing co-efficient of
•
friction in axles
Table XIII., showing capacity of
windmill pumps of different
diameters and strokes.
Use of the windmill
86
I
133
extent of, in America
specific
·
135
Velocity of wind
3
5
•
137, 138
·
141
•
146
•
147
on
as affected by height of observa-
tion
Velocity of wind as affected by
height of observation, Archibald
on.
Velocity of wind as affected by
height of observation, Stevenson
Velocity of wind, average in Amer-
21
22
21
•
148
ica.
7
158
INDEX.
Velocity of wind, relation between
PAGE
Wind, velocity required to drive a
windmill.
pressure and
Velocity of wind, relation between
• 9, 12-14
18
Adams
Windmill, acres irrigated by
Althouse
20
American
and steam-engine
•
•
17
appreciation of
average work of .
•
19
blades, impulse of wind on
16
kine on
•
blades, impulse of wind on, Ran-
Windmill blades, impulse of wind
pressure and, Field on.
Velocity of wind, relation between
pressure and, Hagen on
Velocity of wind, relation between
pressure and, Hawksley on
Velocity of wind, relation between
pressure and, Pole on
Velocity of wind, relation between
pressure and, Rankine on.
Velocity of wind, relation between
pressure and, Rouse-Smeaton
Velocity of wind required to drive a
windmill.
Velocity-regulation windmills
Ventilators, best angles for.
Vertical windmills .
compared to horizontal
general description of .
capacity of.
capacity and economy of.
•
14
on, Weisbach on .
Windmill, Buchanan
•
8
ΙΟΙ
•
•
•
35
33333333
53
53
Champion . .
PAGE
8
•
150
•
98
•
94
·
72
2
I
3
26
28
29
. IOI
131, 133
. 129
. 106
comparison of American and Euro-
pean
53 Windmill, Corcoran
Water, allowance for friction in pipes, 143
loss, by friction, in pipes.
weight of cubic foot
Weather, best angles of impulse
and
Wind, definition of.
effect of, on plane surfaces.
Coulomb's experiments on the.
71
76
•
40
Eclipse
•
85
·
146
economy and capacity of the
•
•
129
•
145
economy of the .
•
134, 135
•
14I
31
5
8
сол
effect of barometer on pressure of, II
economy of the, and gas-engine
economy of the, and hot-air engine, 140
economy of the, and steam-pump. 136
experiments on the .
experiments on the, Coulomb's
experiments on the, Smeaton's.
Halladay
effect of temperature on pressure
of .
8
Wind, high pressure of
22
Leffel
impulse of, on windmill blades
26
loss of pressure of, by particles of
pumps, capacity of
pumps, class and diameter of
Regulator.
•
•
獻
​119
•
. 125
•
I 20
. 86
. 116
148
149
. IOS
·
air in motion
ΙΟ
•
Wind, movement and velocity of.
movement of, in America
6
sails, Cubitt's method of reefing
68
•
7
relation between actual and theo-
retical pressure of
ΙΟ
sails, description of European
sails, Meikle's method of reefing. 67
sails, theoretical mechanical effect
•
•
55
Wind, relation between height of
•
observation and velocity of . .
Wind, relation between pressure and
velocity of
•
Wind, velocity and movement of .
21
9
•
6
of
Windmill sails, theoretical mechan-
ical effect of, shape for maximum
effect.
Windmill sails, the mechanical effect
31
35
velocity and
movement
of in
of plane.
38
America ..
7
Windmill, specific uses of the.
•
3, 4
Wind, velocity and pressure of
5
Stover
•
103
INDEX.
159
PAGE
PAGE
Windmill, Strong
use of the .
I
useful data in connection with
practice.
143
112 Windmills, horizontal.
horizontal, compared to vertical
horizontal, description of
horizontal, disadvantages of
50
53
50
52
Windmill, velocity of wind required
post or German
•
58
to drive.
8
sizes of .
134
Windmill, velocity-regulation.
ΙΟΙ
•
Thomson, Sir William, on
use
Windmill, Woodmanse
103
of .
4, 130
Windmills, Dutch or tower
61 Windmills, tower or Dutch.
61
early history of
economical motors
European
German or post
43
types of .
73
I
vertical
50 Woodmanse Windmill
58 Wrought-iron pipe, weight of
· 53
. 103
•
151

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