Skip to main content

Full text of "Natural sources of power"

See other formats

to make the world's books discoverable online. 


publisher to a library and finally to you. 

Usage guidelines 


We also ask that you: 

personal, non-commercial purposes. 




About Google Book Search 


at jhttp : //books . qooqle . com/ 



TTbe " TPOlestmfnster " Series 





j w w u • •> *• * 

• »o 




• • • 

• • « 

• • •• 

• • • • „•• 




Two departments of engineering and their applications 

to industry form the subjects of the following pages. 

While the subject of water power (which occupies the first 

and greater half of the volume) would be conceded to be 

more important than that of wind power, the latter has 

a wider application at the present time than is popularly 

^ assigned to it, for the demand for windmills was never so 

^ great as it is to-day, nor the trade of the manufacturer of 

;> such motors never so brisk, and there are unmistakable 

"? signs of abnormal expansion in the direction of their useful 

^ application in the great agricultural countries of the world. 

The author cannot be charged with any attempt to appraise 

the relative value to the industrial world of two natural 

sources of power so widely different in distribution and 

t/N. reliability, moreover in a given place the choice rarely lies 

between the two, as local conditions determine the pre- 

" ference should an alternative perchance exist. It may, 

however, be said that the use of power of either kind in 

small installations renders such comparison more likely 

.; to be effective, for at present large windmill installations 

^] do not exist, with which water-power plants of great 

2 concentrated pow^might be compared. 

| The principles which underlie this utilisation of natural 

sources of power are those comprised in a few elementary 

**> laws of mechanics, but the complex problems which the 



engineer has to face and which demand special and 
extensive treatment require extended space, and moreover 
they cannot be satisfactorily elucidated without recourse 
to the calculus. With therefore an imposed limit to the 
use of mathematics, the object in view has been mainly 
that of showing that if the available power be small it may 
nevertheless be well worth turning to account, and if the 
pages that follow confer upon the reader a sense of the 
potentialities of the smaller bounties of nature they will 
have discharged their office. The thanks of the author are 
due to many persons and firms for assistance rendered. 
Besides other acknowledgments made throughout the text 
he wishes to express his indebtedness to Messrs. Holman 
Bros, of Canterbury, who generously placed valuable draw- 
ings at his disposal, to the Council of the Boyal Agricultural 
Society for permission to reproduce illustrations of wind 
engines, to Mr. W. Halliwell for kind assistance, and to the 
proprietors of " Engineering " for permission to reproduce 
illustrations contained in a paper which he presented to 
the British Association, and for other articles contributed 
to their columns. He also gratefully acknowledges valuable 
advice from Mr. Talbot Peel, M.A., and Mr. Alph Steiger, 

Among the illustrations are many supplied by the 
following firms and engineers : Gilbert Gilkes & Co. 
Ltd., W. Gunther & Sons, Garrick & Bitchie, Theodor 
Bell & Co., Escher, Wyss & Co., Bickman & Co., Thomas 
& Son, and J. W. Titt, to all of whom the author extends 
his thanks. 

B. S. B. 




Units with Metric Equivalents and Abbreviations . . xiii 



The natural supplies of energy 1 

Water and wind power contrasted with that derived from fuel . 2 

The lasting nature of the former 2 

Transformation and conservation of energy 3 

Losses in machines for utilising natural energy .... 4 

Energy in various forms . . . 5 

Distinction between energy and power 6 

Power and units for measuring 9 

Efficiency of machines 11 

Relative efficiency of prime movers 13 

Water Power and Methods of Measuring. 

Water, its weight and physical properties .... 
Power of a waterfall defined and method of calculating 
Velocity under free fall and influence of air resistance 
The flow of water in closed pipes and the theorem of Bernouilli 
Illustration of theorem by pipe leading out of reservoir 
Pressure to which a pipe is subjected with water flowing through 


Relation between velocity and pressure in pipe . 
Measurement of water in streams and rivers 






Weirs and velocity (or current) meters 28 

Francis formula for the flow over weirs 31 

Tables giving the flow in litres and cubic feet over weirs of unit 

width for depths in inches and centimetres ... 33, 34 

The use of the engineer's level 36 

Adjustments of the instrument 39 

Method of running a line of levels 40 

Useful data and formulae pertaining to water . . .45 


Application of Water Power to the Propulsion of 

Antiquity of the use of water power for industrial purposes . 46 

Early introduction into England 46 

Types of water wheel — (1) Overshot ; (2) Breast ; (3) Under- 
shot ; (4) Poncelet 48 

Efficiency of water wheels . .53 


The Hydraulic Turbine. 

General description of the hydraulic turbine . . . .55 

Comparatively high efficiency of the turbine .... 55 

Contrasted with the steam turbine 56 

Various types of turbine according to direction of flow . . 57 

Table showing classification of turbines 71 

The draft tube 73 

Power in a jet of water issuing from a nozzle .... 75 

The pressure exerted by jets upon plane surfaces ... 76 

Energy in jet applied to propulsion of vanes .... 77 

Pressure upon surfaces inclined to the direction of impact' . . 79 

Pressure upon curved surfaces 80 

Identity of pressure on curved surfaces and centrifugal force . 82 

Outline of theory of the turbine 84 

Relation of guide vanes to runner vanes 85 

Proper angles for the vanes 85 

Practical design of turbines with reference to efficiency . . 88 

Losses in turbines 94 


Various Types of Turbine. 


Reaction mixed flow turbine as used for low falls ... 96 

„ „ „ at Niagara ... 98 

Girard turbines on horizontal shaft with partial admission . 103 

The Pelton wheel 103 

Methods of testing turbines 109 

Result3 of tests 115 


Construction of Water-Power Plants. 

Dams 120 

Water pressure upon retaining walls 121 

Gravity and arch dams 123 

Various kinds of dam 123 

Masonry dams 125 

Rules for designing low dams 126 

Ratio of height to width to resist overturning 126 

Concrete 127 

Construction of wheel pits 128 

Water-Power Installations. 

Great variety of turbine installations 132 

Descriptions of plants : — 

• Low fall installation of small power using a Francis turbine . 135 


Specification for one 50 brake horse -power turbine . 

Turbine operating under a head of 2 feet . 

The Lake Tanay installation (920 metres head) 

The Pikes Peak (Colorado) installation, 2,417 ft. head 

Friction in pipe lines . 

The cost of water power ..... 


The Regulation of Turbines. 


Importance of speed control for electric plants .... 167 

Inertia of the water in a pipe 169 

Methods of regulating the flow of water ..... 171 

The pendulum governor 180 

Action of the fly-wheel 184 

Regulation attained in practice 193 

Descriptions of various types of governor, mechanical and 

hydraulic 194 

Tests of governing mechanisms 210 


Wind Pressure, Velocity, and Methods of Measuring. 

Air currents 212 

Complexity of air movements 214 

Experimental investigations 216 

Anemometers 219 

Pressure recording instruments 226 

Records of wind velocity compared 230 

Laws connecting velocity and pressure 232 


The Application of Wind Power to Industry. 

Early history of windmills 241 

Improvements in construction and in mechanism . . . 244 

The tower mill 247 

Angles of weather 256 

Smeaton's rules 258 


Modern Windmills— Constructional Details. 


Difference between old and new types 261 

The " American " mill 263 

The wheel proper 268 

The veering mechanism 274 

Transmission gear 275 

Governing mechanism 284 

Stopping and starting gear 290 

Special types of mill 292 


Power of Modern Windmills. 

Estimation of power developed 295 

Royal Agricultural Society's trials on pumping engines . . 296 

Experiments by Mr. Perry 305 

Windmills applied to electrical installations .... 321 

The cost of power generated by windmills 328 

Appendices A, B, C 333 

Index 337 




Unit. Abbreviation. 

1 inch in. 

= 25*4 millimetres. 

= 2*54 centimetres. 

= 0-0254 metres, 
lfoot ft. 

= 304*8 millimetres. 

= 80*48 centimetres. 

= 0*3048 metres. 
1 yard . yd. 

= 3 feefc. 

= 0*914 metres. 
1 mile mile. 

= 5,280 feet. 

= 1,609 metres. 

= 1*609 kilometres. 
1 millimetre mm. 

= 0*0394 inches. 
1 centimetre cm. 

= 0*394 inches. 
1 metre m. 

= 39*37 inches. 

= 3*28 feet. 
1 kilometre km. 

= 0*621 miles. 



Unit. Abbreviation. 

1 square inch . . . sq. in. 

= 645*2 square millimetres. 

= 6*452 square centimetres. 
1 square foot sq. ft. 

= 0*111 square yards. 

= 0*0929 square metres. 
1 square } r ard sq. yd. 

= 0*836 square metres. 
1 square millimetre sq. mm. 

= 0*00155 square inches. 
1 square centimetre sq. cm. 

= 0*155 square inches. 
1 square metre sq. m. 

= 10*76 square feet. 


1 cubic foot cu. ft. 

= 0*0283 cubic metres. 

= 28*32 litres. 
1 cubic metre cu. m. 

= 1*308 cubic yards. 

= 35*31 cubic feet. 


1 pound . . lb. 

= 0*454 kilogrammes. 
1 ton (English) ton. 

= 2,240 lbs. 

= 1*016 metric tons. 
*1 tor. (American) 

= 2,000 lbs. 

= 0*907 metric tons. 
1 kilogramme kg. 

= 2*205 lbs. 

•* Unless otherwise stated, the " long " ton of 2,240 lbs. is used throughout 
this volume. It is about 2 per cent, greater than the metric ton. 


Unit. Abbreviation. 

1 ton (metric) ton (metric). 

= 1,000 kilogrammes. 
= 0*984 tons (English). 
= 1*102 tons (American). 

1 pound per square inch lb. per sq. in. 

= 0*0703 kilogrammes per square centimetre 

= 2*307 feet water column. 

= 2*036 inches mercury column. 
1 kilogramme per square centimetre . . kg. per sq. cm. 

= 14*22 pounds per square inch. 

= 0*968 atmospheres. 

= 10 metres water column. 
1 atmosphere* at. 

= 29*92 inches mercury column. 

= 760 millimetres mercury column. 

= 33*9 feet water column. 

= 14*7 pounds per square inch. 

= 2,116 pounds per square foot. 

= 1*033 kilogrammes per square centimetre. 

1 foot per second ft. per sec. 

= 0*682 miles per hour. 

= 0*305 metres per second. 

= 1*097 kilometres per hour. 
1 mile per hour ml. per hr. 

= 1*467 feet per second. 

= 88 feet per minute. 

= 0*447 metres per second. 

= 1*609 kilometres per hour. 
1 metre per second m. per sec. 

= 3*28 feet per second. 

= 2*24 miles per hour. 

= 3*6 kilometres per hour. 
1 kilometre per hour km. per hr. 

= 0*911 feet per second. 

= 0*621 miles per hour. 

* Barometric variation necessarily renders an " atmosphere " a purely 
arbitrary quantity. It is generally taken as above. 


Unit. Abbreviation. 

1 revolution per second rev. per sec. 

= 6*28 radians per second. 

1 foot per second per second . . . .ft. per sec. per sec. 
= 0*682 miles per hour per second. 
= 1*097 kilometres per hour per second. 

1 foot-pound ft. -lb. 

= 0*138 kilogramme -metres. 
1 kilogramme-metre kg.-m. 

= 7*233 foot-pounds. 
1 British thermal unit B.T.U. 

= 778 foot-pounds. 

= 0*252 calories. 

= 107*6 kilogramme-metres. 
1 calorie cal. 

= 426*9 kilogramme-metres. 

= 3,088 foot-pounds. 

= 0*001163 kilowatt-hours. 
1 kilowatt-hour kw. hr. 

= 2,655,403 foot-pounds. 

= 367,123 kilogramme-metres. 

= 859*975 calories. 

1 horse-power H.P. 

= 33,000 foot-pounds per minute. 

= 550 foot-pounds per second. 

= 76*04 kilogramme-metres per second. 

= 745*6 watts. 

1 horse-power (metric) H.P. (metric.) 

(force de cheval or Pferde-kraft) 

= 75 kilogramme -metres per second. 

= 0*986 horse-power. 

= 735*5 watts. 

N.B. — Physical constants and units relating to water are to be found in 
the table on p. 45. The weight of dry air at atmospheric pressure and at a 
temperature of 10° C. (50° F.) is 1,247 grammes per cubic metre, or 0*08 lbs. 
per cubic foot. 




The supplies of energy upon which the engineer draws 
for his wants are of several kinds, and though mutually 
convertible, are distinct in their natural states, and bear 
separate characteristics. To some of them it is necessary 
to apply a transformation process before they are in the 
form in which the energy can be used for the purpose 
in view. In other cases transformation is not necessary, 
and nature yields up her stores in what may be termed a 
manufactured form. This distinction, arbitrary as it is, is 
convenient for the purpose of introducing the subject, and 
for defending the title under which these pages appear, 
which expressly classifies the sources of power considered 
as "natural." In a sense, therefore, the "natural" 
sources, such as water and wind power, are those which 
the engineer utilises directly for propelling machinery, and 
which directly supply mechanical energy without any inter- 
mediate stage of transformation ; while fuels may, in contra- 
distinction, be placed in another classification comprising 

N.S. B 


those bounties of nature which have to undergo chemical 
decomposition by which heat energy is developed, which is 
again transformed into mechanical energy by some form of 
engine or appliance. 

Long before the birth of the great inventions, by which 
the engineer is enabled to use the stored sunbeams in coal, 
gas, and oil, and by means of which heat is transformed 
into mechanical energy, the natural sources were tapped 
to supply the comparatively small requirements of a 
period long antecedent to the present age. To these 
sources of power, inexhaustible as they are, the engineer 
will some day turn again when our coal measures are 
exhausted, our gas retorts cold and empty, and the oil 
wells of the earth dried up for ever. In the present age 
of fuel, when almost all mechanical ingenuity is directed 
towards the utilisation of coal and other natural fuels, when 
engineers make their reputations by devising machinery to 
accelerate the consumption of this black diamond, and at a 
time when our extravagance is at its height, scarcely suffi- 
cient thought is directed to these natural powers, water and 
wind, which will some day be in the ascendant again as they 
were in the past, when sailing vessels ploughed the ocean 
long before steam power was introduced with its accom : 
panying profligate waste of our fuel resources. Geologists 
have estimated with reasonable confidence the approximate 
time that will elapse before the last ton of coal is shovelled 
into the wasteful furnace, and while the sun itself is slowly 
shrinking, and therefore our source of water and wind 
power will one day come to an end, and with it all life upon 
the earth, the end of our fuel supplies is, compared with the 
length of time of any appreciable diminution in the energy 


radiated by the sun, as one day to thousands, perhaps 
millions, of years. The foregoing arbitrary distinction 
between water and wind power on the one hand, and that 
derived from fuel on the other will serve to explain why 
these pages are limited to the former, though the compre- 
hensive title would imply something more. Nevertheless, 
as all forms of energy are capable of being changed into 
other forms, the engineer who wishes to obtain the best 
results has to be conversant with the changes that are 
likely to occur, and the losses that he may be exposed 
to by the transmutation of energy into other forms than 
that in which it is directly used in his machines. 

Water and wind power are manifested in various forms. 
The evaporation of water from the ocean, descending in the 
form of rain upon high lands and plateaux, supplies the 
rivers from which we are able by means of water wheels to 
utilise this power that the sun incessantly provides. Ocean 
currents and tides, though but little utilised, also represent 
a large and continual source of power which may some day 
be turned to account. 

Then wind power, which has been employed for ages 
to drive our commerce over the seas, and which has 
recently been tentatively used through the novel form 
of wave motors, has had in the past a greater share 
of attention than at the present time, when power 
from fuel is occupying the chief place in the minds 
of engineers, and is such an important feature in our 
industrial life. 

The law of the conservation of energy teaches us that 
energy cannot be destroyed, but that it can only be changed 
from one form into another. The engineer however has 



frequent reason to regard energy as destroyed or lost to his 
purpose, as for instance when a steam engine expends 
energy in heating bearings, or in cylinder condensation. 
If these sources of loss were not present, the energy so 
expended would be put into useful work in helping to 
drive the machinery. The physicist would not regard these 
losses in the same light as the engineer who is accustomed to 
speak of them as such. In every application of natural 
energy to the industrial arts, heavy tolls are exacted and 
losses sustained in the process of application, and the skill 
of the engineer is mainly directed towards reducing these 
losses, which, according to their magnitude may mean 
success or failure of the enterprise upon which he is 
engaged. His chief occupation is to contend with the 
imperfections of hie own apparatus which allows part of the 
energy to drain away in the same manner that a leaky 
pitcher carried from the well to a distance loses part of its 
contents by the way. If the water it contained were valuable, 
special efforts would be directed towards the replacement 
of the leaky vessel by a sound one ; this however is always 
impossible in engineering, and the most the engineer can 
do is to diminish the loss by imperfectly plugging the leaks. 
With power derived from fuel upon which a high price is 
placed, the economy of the plant is an important con- 
sideration, and it is also becoming one of the chief factors 
in hydraulic power, especially where water privileges are 
retained at a high value. As the wind is free to everyone 
it is commonly supposed that windmill efficiency is a matter 
of little moment, but such is not the case, for the power 
obtained from the wind is so extremely small for the 
size of the wheel and the cost of the installation, that 


it has to be carefully safeguarded from leakage, and the 
extended usefulness of the wind wheel to day for pumping 
water is largely due to improvements in mechanical con- 
struction which are designed to prevent waste, and which 
therefore utilise the small power to the fullest extent. That 
the windmill is still a very inefficient machine will appear 
evident from what follows, while the hydraulic turbine is 
by far the most efficient prime mover that we possess, 
all heat engines taking a secondary place in this respect. 

In order to be able to make a comparison, both scientific 
and commercial, between the efficiencies of different forms 
of prime mover, it is convenient to introduce a few words 
concerning energy, and the various forms in which the 
engineer has to deal with it, and the way in which it is 

Though energy is manifested in various forms such as 
mechanical, heat, or electric energy, the common denomi- 
nator of them all is known, and whatever may be the 
form in which it appears, it may readily be converted 
into that most familiar unit, the foot-pound (in the metric 
system the kilogramme-metre), by a simple sum. Now the 
foot-pound is often defined as the amount of energy which 
is expended in raising a one-pound weight through one foot, or 
half a pound two feet and so on, the product of the weight 
and height always being unity. This definition, though 
correct, is misleading, for the most frequent use which the 
engineer has for measuring energy does not involve the 
lifting of weights at all, and therefore such a definition does 
not cover the majority of cases in which energy is measured 
or dealt with. The introduction of a pound or kilogramme 
into the unit is often mentally inseparable from the idea 


of weight, and this gives rise to a notion which the writer 
has observed, that the process of lifting weights is exclu- 
sively connected with the measurement of energy. In order 
to broaden the definition so as to meet the cases in which the 
engineer is chiefly concerned, it is necessary to say that 
a foot-pound is the energy expended in overcoming a force 
of one pound through a distance of one foot in the direction 
of the pressure, or in general, when a force of p lbs. is exerted 
through a space of s feet, p X 8 foot-pounds of work are 
expended, and if pounds and feet be replaced by kilogrammes 
and metres, p X s kilogramme-metres are expended. 

The definition of energy is thus independent of time, and 
a given number of foot-pounds may be expended during any 
period without invalidating the definition of the quantity of 
energy. This is the distinction between energy and power, 
for the latter involves the rate at which energy is expended. 

The relation that exists between mechanical and heat 
energy, or, as it is commonly called, the mechanical equi- 
valent of heat, is known to a high degree of accuracy. The 
great discovery of Joule and the subsequent accurate ex- 
periments which have been made by eminent physicists 
show that 778 foot-pounds converted into heat would be 
sufficient to raise the temperature of a pound of water 1° F. 
which quantity of heat is established as the British Thermal 
Unit. 1 Thus, the energy expended in overcoming a resistance 
of 500 lbs. through a distance of 2'7 feet at any speed is 1,850 
foot-pounds, or in British thermal units 



= 1735 .... B.T.U. 

1 The calorie is the amount of heat necessary to raise the temperature 
of one kilogramme of water 1° Centigrade. 


The imagination is no guide to the relation between the 
thermal and mechanical units, for it is difficult to accept 
the statement that the heat necessary to raise a pound 
of water one degree F. is actually equal to 778 foot-pounds. 
Possibly the explanation for this may lie in the fact that 
mechanical energy is more often the subject of tentative 
measurement by which our ideas are adjusted, yet there is 
probably no other experimental constant in physics upon 
which there is less doubt than the mechanical equivalent 
of heat, within the small limits of experimental error. 

The electrical units of energy x are more confusing than 
the mechanical, for the reason that the foot-pound does not 
involve any question of time, while a watt, including as it 
does the ampere or rate of flow of current, is essentially 
concerned with time, and is therefore allied to a power unit. 
For instance, 1,000 foot-pounds are not equal to 22*6 watts, 
and such an equation would be meaningless, but the power 
expressed by 1,000 foot-pounds uniformly expended in one 
minute is correctly expressed in electrical units by 22*6 watts; 
likewise 1 foot-pound = 1*36 watt-seconds, the second term 
of the equation being qualified by a statement as to the 
time during which the 1*86 watts are expended. A pressure 
of 1*86 volts acting through a resistance of 1*86 ohms for 
one second, causing a current of one ampere thereby, 
expends an amount of energy in one second which, in 
mechanical units, is measured by one foot-pound. Foot- 
pounds and watts are not therefore mutually convertible, 

1 The Joule, or watt- second, which was defined at the International 
Congress of 1893 in Chicago as equal to 10 7 C.G.S. units of work 
(ergs), is represented closely by the energy expended in one second 
by an international ampere against an international ohm. It is equal 
to 0*738 foot-pounds. 


neither are watts and thermal units, for the latter are 
definitely related to the foot-pound, and do not involve 
time or rate of expenditure of energy in any sense. 

The foregoing fundamental distinction between the foot- 
pound and the watt is so important, and at the same time 
so easily overlooked, that an explanation may be not out of 
place. The difficulty rests with the proper understanding of 
the unit of current — the ampere. It is unfortunate that 
we do not generally express a measure of current in any 
other way than by a single word which in itself hides 
the important element of time, 1 or that the definition is not 
conveniently susceptible of subdivision, further than to say 
that the ampere is the current which will deposit a certain 
weight of silver from a nitrate solution in a second. Taking 
the analogous case of hydraulic measurements, it is custom- 
ary to express flow in " cubic feet per second," which in 
itself is a compound expression, clearly including the unit of 
time, and also the familiar unit — the cubic foot. Moreover 
there is no short expression for "cubic foot per second" 
which would take the same place in hydraulic engineer- 
ing that " ampere" does in electrical. It is thus that 
the "ampere," and consequently the "watt," fail to make 
evident the important item of time, which is hidden away 
in these single words, there being no analogous electrical 
expression for "cubic foot." To express energy in electrical 
units we have therefore to use compound terms such as 
" watt-hour " or " kilowatt-hour." 

1 The unit of quantity of electricity, which however is seldom used, 
and is universally disregarded in practical engineering, is the coulomb. 
It is denned as " the quantity of electricity transferred by a current of 
one international ampere in one second," and is that quantity which 
will deposit 0001 118 grammes of silver in a voltameter. 



It cannot be too clearly stated that power involves the 
rate of expenditure of energy, and that without some know- 
ledge of the time in which a given amount of energy is 
expended, no estimate of power can be made. A given 
number of foot-pounds may, in the course of being ex- 
pended, mean millions of horse-power or a millionth of a 
horse-power according to the time or rate at which the 
expenditure takes place, and the power may vary between 
any limits during the process of expenditure. It is easy to 
see then how velocity enters into all questions involving 
power, for velocity is the rate at which the space varies 
with regard to the time. The unit of power — the horse- 
power — of the engineer is defined as a rate of expenditure 
of energy. It is incorrect to say that one horse-power is 
defined by the expenditure of 33,000 foot-pounds in one 
minute or 550 in one second. This is only true if the 
rate of expenditure is uniform throughout the time. 
Otherwise the power may vary widely during the time 
considered. A steam engine, nominally assumed to 
develope a certain horse-power, is continually varying in 
power, even in a single revolution of the crank. In con- 
sequence of the "rate" of expenditure being a measure 
of power, it would, for example, be meaningless to say 
that the power expended in moving a body against a 
resistance of 1,800 pounds through 8 feet was 14,400 
foot-pounds ; this would be the energy but not the power, 
and yet careless expressions of this kind are common 
in technical literature. If this movement was effected 
at a uniform velocity, and the observed time of travel 


over 8 feet was 4 seconds, the power in horse-power units 
would be — 

np _ PX v _ 1,800 X 4 _ ft .„ 
H - R " ^50~ - —550— - 6 55 ' 
The velocity may be constantly varying, as it usually is 
in practical problems, and the power therefore varies in 
direct proportion. Thus, though the energy expended in 
this example would always be the same, regardless of the 
speed, the power may have any value whatever depending 
upon the speed at any particular instant. 

Energy in any form expended at a given rate involves 
the expenditure of power. If, for example, eight British 
thermal units be absorbed by the water in a boiler 
in 3*2 minutes, and the rate of absorption is constant, 
i.e., 2*5 units per minute, the horse-power of which this is 
an equivalent would be— 

_ 2'5 X 778 
H -*-- 33,000 - 0059 ' 

It has been pointed out that the watt is a measure of 
power in itself, for it includes the ampere, which introduces 
the necessary time or rate of expenditure of energy. It is 
therefore correct to say that one horse-power is 745*6 watts 
(or 0*7456 kilowatts) in electrical units. At a first glance it 
would appear that something has been left out, but when 
it is understood that the watt involves time, the time 
qualification which must be added to a statement of 
mechanical energy in foot-pounds to render it in power- 
units will be seen to have no analogy in electrical units, in 
other words, 33,000 foot-pounds expended in one minute is 
expressed otherwise by 745*6 watts. If it is desired to 
express energy in electrical units, as it is frequently necessary 


to do in hydraulic engineering, the kilowatt-hour or watt- 
hour can be used. This indicates an amount of energy 
represented by the expenditure of one kilowatt continued 
for one hour, which might equally well be represented 
by that expended by 1*34 h.-p. in the same period. The 
kilowatt-hour is becoming an increasingly useful unit for 
practical purposes, and it is just as definite as a measure 
of energy as a foot-pound or kilogramme-metre, for it stands 
for a definite number of each of these units, and has, pari 
passu, an equivalent in heat-units. 

Efficiency of Machines. 
The value placed upon a prime mover by the engineer 
depends to a large extent upon its efficiency, i.e., the ratio 
of the energy derived from it to that put into it in another or 
the same form. But it will be evident that, as some forms of 
energy cost more than others, efficiency alone is not the factor 
that determines the commercial value of a prime mover. 
For example, the price of coal renders the efficiency of the 
steam engine a matter of greater importance than that of 
the hydraulic turbine supplied with abundance of water 
obtained at little or no cost. Likewise the windmill, using 
a free natural source of energy, is seldom measured by the 
ratio of the power obtained from it to that supplied by the 
wind. In the case of the steam engine a slight increase in 
efficiency often means a considerable reduction of the fuel 
bill, and establishes the success of the plant, while an 
increase in the efficiency of a motor supplied with a working 
fluid which costs nothing means an increased output, which 
could otherwise be obtained by an increase in the size of 
the engine, without material additional running cost. The 


efficiency of an engine may therefore in some cases be of 
great commercial importance, while in others it is not the 
determining factor in the installation of a power plant. 

The measurement of the efficiency of hydraulic and wind 
motors is simplified by the fact that the energy supplied is 
in the same form as that delivered, and therefore it is the 
ratio of the two that directly gives the efficiency. Thus the 
actual work done by an hydraulic turbine in a unit of time (the 
power) is measured in foot-pounds, as is also the theoretical 
power in the falling water. The ratio of the one to the 
other gives the efficiency. In heat engines, on the other 
hand, the energy in the form of thermal energy supplied, is 
converted into mechanical energy delivered by the engine, 
and one set of units must be converted into the other before 
the efficiency is known. For example, a steam engine uses 
1*29 lbs. of coal per h.-p. hour. The coal has a calorific 
value of 14,000 B.T.U. per pound, so that the value of the fuel 
necessary per hour for 1 h.-p. is 129 X 14,000 X 778 foot- 
pounds. As the energy delivered by the engine in an hour is 
60 X 33,000 foot-pounds, the efficiency, which includes the 
boiler, is therefore about 14 per cent. In this case the deter- 
mination of the efficiency requires that the energy given 
off in foot-pounds on the engine shaft must be converted 
into equivalent thermal energy, so that it may be compared 
with the energy in heat-units caused by the combustion of 
the coal supplied to the boiler, or the heat energy in the 
coal might be expressed as mechanical energy, giving 
the same result. The efficiency of the steam plant is 
also made up of the combined efficiencies of the boiler, 
pipe line, and engine, and, as engineers well know, it 
is frequently convenient to refer to the efficiency of the 


steam engine alone by an arbitrary standard of the number 
of pounds of water per hour in the form of steam at a 
certain pressure that are necessary to give a horse-power 
hour in mechanical energy on the shaft. Such computa- 
tions are simpler for water power, for the efficiency of a 
water wheel is directly found, and does not depend upon 
what is generally an assumption in the case of the steam or 
internal combustion engine — the calorific value of the fuel. 
The weight of the water passing through a wheel, and the 
height through which it has fallen being known, the power 
supplied is directly ascertained. As the efficiency of 
water wheels and wind engines will be dealt with elsewhere 
we may conclude by the statement that of all prime 
movers the water turbine is the most efficient machine that 
we possess, as it will convert fully 80 per cent, of the 
energy supplied to it into useful work, the internal com- 
bustion engine comes next with a performance Of about 
40 per cent., and lastly the steam engine and wind engine 
which rarely exceed 20 per cent., and are usually very 
much less. If electric motors were included in the category 
of prime movers, they would take first place, as the efficiency 
of large machines is well over 90 per cent., but as they 
cannot be described as prime movers, they cannot properly 
be classed in this connection. Nearly all the inventions 
and improvements made since prime movers were first 
introduced have been directed towards an improvement 
in efficiency, and with conspicuous success in the case of 
hydraulic machinery, though not less so in the mechanism 
of the steam engine, but the great heat losses in the boiler 
will, as far as it is now possible to foresee, always keep 
the efficiency of the steam plant low. Notwithstanding the 


use of steam turbines fitted with condensers, together with 
the various adjuncts to the steam plant, such as economisers, 
feed water heaters, and superheaters, the efficiency of the 
whole transformation process from heat to mechanical 
energy by this means is very low. 



The Physical Properties of Water. 

For a practical understanding of the subject of water 
power as known and applied by the engineer in his work, it 
is not necessary to step beyond the elementary principles of 
hydraulics and hydrodynamics. The rough-and-ready rules 
which are applied to problems met with in practice, 
many of which are to be found in handbooks, rest upon a 
few general principles in hydraulics, easily understood and 
easily applied. Notwithstanding the great fascination which 
the broader subject of hydrodynamics has for the student, 
as expounded by Professor Lamb x and others, the engineer 
who is called upon to apply principles rather than follow 
lines of absorbing investigation must perforce be content 
at leaving off where the real student of hydrodynamics 
begins. It is up to this point that the reader is taken 
in the following pages, and the principles contained in them 
are those which the hydraulic engineer is called upon to 
apply in his work. 

It is natural that the subject of hydraulics should open 
with a few facts concerning the physical properties of 
water. Let us first consider the density or weight of the 

1 Treatise on the Mathematical Theory of the Motion of Fluids, 
Professor Lamb. 


fluid. Unlike most other substances which vary in density 
in one direction with the temperature, water attains a maxi- 
mum density at 4° C, above or below which temperature 
the density diminishes, but to such a small extent as to 
be negligible to the engineer, but important to the physicist 
who is carrying on refined experiments. The following 
table shows this, in which the relative volumes at different 
temperatures are given 1 : — 


Volume (Rossetti). 

Wt. of lcc, in grammes. 





The unit weight of water will be taken to be 62*5 lbs. per 
cubic foot. Although the weight of a cubic foot of distilled 
water at the ordinary temperature is 62*4 lbs. nearly, 
impurities both dissolved and suspended somewhat increase 
the specific gravity, so that 62*5 lbs. may be used in what 
follows as the weight in British units, while in the metric 
units the cubic centimetre of pure water at 4° is, by defini- 
tion, the gramme. The simplicity of the metric system for 
hydraulic calculations is especially apparent, inasmuch as 

i The behaviour of water under enormous pressure such as that 
developed in the explosion chambers of modern artillery has formed 
the subject of recent investigation at the hands of a skilled engineer. 
It is asserted that under pressures of about 20 tons per square inch 
the fluid can be reduced in volume by several per cent. This does not 
do violence to the common and accepted hypothesis that water is an 
incompressible fluid, for under the ordinary pressures at the surface 
of the earth, and those with which the engineer is ordinarily familiar, 
it may be regarded as such. The sea-water upon the bed of the 
Caribbean Sea is exposed to a pressure of about 5 tons per square 



the kilogramme of water and litre represent the same 
quantity of water. The only logical measure in the British 
system is the gallon, which weighs 10 lbs., but the univer- 
sality of this is unfortunately destroyed \>y the fact that the 
United States gallon weighs 8*34 lbs., and therefore there is 
a likelihood of confusion. For this reason the gallon will be 
omitted, and where British measures, in contra-distinction 
to metric, are employed, the cubic foot shall be the chosen 
unit of volume for water, for it is generally used by 
hydraulic engineers as being more convenient than the 
gallon for calculations. 

The Power in Falling Water. 

It has already been pointed out how the horse-power is de- 
fined, and that it represents 550 ft. lbs. (or the equivalent 
in metric units of 76*08 kgms.) exerted during one second 
or, what is more correct, energy expended at this rate, for 
it is of course unnecessary that the expenditure of energy 
shall be continued for a second; all that is necessary to 
define the power is that the rate is a certain value. The 
value of the horse-power in metric using countries is 
75 kgms. per second, which is slightly less than the 
English and American unit. The French force de cheval 
and the German Pferdekraft have this value. When using 
the metric system it will be convenient to refer to this 
unit, as the difference is less than 2 per cent, between it 
and the horse-power of 550 ft. lbs. per second. If, there- 
fore, 75 litres of water fall through a distance of one metre 
every second, the fall is capable of yielding up continuously 
one horse-power, and if it were possible to convert all of 
this to our use by machinery, we would be reclaiming all 

N.S. C 


that is possible from such conditions of flow and height of 
fall. To express the power of a fall generally, where y is 
the weight of w r ater falling per second, and h the height 
through which it fells — 

w p _ y X h yxh 

according as y and h are expressed in British or metric units. 
For example, a stream, as found by measurement, discharges 
118 cu. ft. of water per minute, which falls through a 
distance of 9*25 ft., the horse power is therefore — 

^ ^ _ 118 X 625 X 925 _ - 

H - p - - wm - 2 L 

If, again, the discharge necessary to develop a given 
horse-power falling through a known height be required, 
it may be found as in the following case. Sixty 
horse-power is required from a fall of 9*37 metres, the 
discharge (d) per second in litres is therefore — 

d = 6 ° * 75 = 480 litres = 0480 cu. metres. 

As the efficiency of the water turbine may be taken as 75 
per cent., for rough calculations the following simple rule 
for obtaining the net horse-power of a fall in metric units is 
convenient — 

HP- yXh v 0-75 - yXfe 
H.-P. _ 75 X075- 1(J0 . 

Thus, by multiplying the litres per second by the height 
of the fall in metres and dividing the quotient by 100, 
the actual horse-power which is developed at a turbine 
shaft may be obtained. This rule is, of course, only 


approximate, involving as it does the assumption of an 
efficiency of 75 per cent, for the wheel. In the above case — 

„■ -d 480 X 9*37 AK 

H - p - = loo = 45 - 

From this it is evident that fifteen horse-power is absorbed 
by the friction of the water passing through the wheel and 
connections, and other losses. 

The following are convenient to remember in this 
connection : — 

(1) One horse power is developed by 8'8cu.ft. per second falling 1 foot. 

(2) „ ,, „ 75 litres per second falling 1 metre. 

(3) ,, ,, ,, 1 cu. ft. per second falling 8*8 feet. 

(4) ,, ,, ,, 1 litre per second falling 75 metres. 

A continuous stream of water is essential if the power be 
required for driving water wheels, and the measurements 
w r hich the engineer is called upon to make to ascertain the 
extent of the power at his disposal, involve the measure- 
ment of the flow, and the vertical height through which the 
water passes, or the estimated difference which will exist 
between the level of the water in the head and tail races 
when the works are completed. 

Velocity of Falling Water. 

It would seem almost unnecessary to call to the mind of 
the reader the relationship between the velocity of a falling 
body and the height through which it has fallen, but 
through this relationship the hydraulic engineer is enabled 
to reduce his calculations to simple formulae, and to speak 
of " head " of water, as a mechanical engineer, specifying 
the qualities of a boiler, would speak of the " pressure " it 
was designed to carry. If, then, a body be allowed to fall 

c 2 


freely through a height k, it will acquire a velocity!;, which 
bears the following relationship to h : — 

v = As /2ghorh=£-. 

The symbol g stands for the acceleration due to gravity, 
the value of which may be taken as 981 cms. or 32*18 ft., 
per sec. per sec, v being correspondingly expressed in 
centimetres per second or feet per second. For instance, 
the theoretical velocity of water falling through a distance 
equal to the height of Niagara (156 ft.) would be — 

v = J2X 3218 X 166 = 100 ft. per sec. approx. = 
68 miles per hour. 

The curve (Fig. 1) is plotted with heights of fall in feet 
as abscissae, and velocities as ordinates, the latter being 
calculated by the foregoing formula. For example, a fall 
of 25 ft. corresponds to a velocity of about 40 ft. per 
second. The straight line shows the relation between 
height of fall and horse-power for one cubic foot of water 
per second. For example, one cubic foot per second falling 
through 70 feet is seen to give about 8 horse-power. 

No account is taken of air resistance in this formula, 
or of the loss in velocity which inevitably occurs when 
water is constrained to move in pipes or closed channels. 
These losses in practice are considerable, and will be treated 
of later, but at present we are only concerned with the con- 
ditions prevailing where nothing exists to disturb the action 
of gravity, not even air resistance. A stream of water is 
rapidly broken up in falling through the air, and in the 
case of some high falls there is nothing but spray and moss- 




10 100 

9 90 

a eo 


7 70 

6 60 

5 SO 

4 40 


3 30 

2 20 


j£ Ft. 5 10 IS 20 25 30 35 40 45 SO 55 60 65 70 75 80 85 90 95 100 

Fig. 1. — Relation between height of fall and velocity of water. 

covered rocks to testify to the existence of a stream tumbling 
over a ledge some hundreds of feet above, to which 
phenomenon the tourist from the Grand Canyon of the 


Colorado can bear witness. The velocity of the falling 
water, dispersed into small globules or spray, may thus be 
reduced indefinitely by the action of the air or arrested 
altogether, and the speed of falling raindrops has formed 
the subject of mathematical investigation of a very recondite 
order. Inasmuch as the engineer who is contemplating the 
utilisation of the waterfall, lays his plans so as to confine 
the water for his purpose, the formula as given above may 
be applied to estimate the potentiality of the stream, or as 
a basis upon which to build his hopes of a financial return, 
coupled with the results of his measurements upon the 
volume of water which the stream discharges. 

The relation between head and velocity being expressed 
for a free fall, the one as a function of the other, it is clear 
that when one is known the other is easily ascertainable. 
Engineers are accustomed to allude to " velocity head " when, 
by examination, they have discovered the velocity corre- 
sponding to a certain height of free fall. The mean velocity 
of the water across a section of a pipe is, let us say, 
17*3 metres per second, consequently the velocity head 
is — 

/ ' = 2X 7 9ll = 15 ' 25metreS - 

■ This does not necessarily mean, and in practice it never 
does mean, that the open water level is 15*25 metres above 
that section of the pipe where the velocity is measured. 
The actual head is, in fact, greater than the velocity head, 
for reasons which will be made clear by a full examination 
of the theorem of Bernoulli. 


The Theorem of Bernouilli. 

This theorem, which was first demonstrated by the Swiss 
mathematician and physicist, Daniel Bernouilli, in 1788, 
covers all the problems which arise in the investigation of 
the flow of water in pipes, and very important principles 
and fundamental truths are set forth in the few symbols 
into which the comprehensive principles are compressed. 

The theorem may be stated in the following concise 
terms. If p a and v a be respectively the pressure and 
velocity of the water in a closed pipe at a section A, and 
h a the height of the section above a given horizontal line, 
and p b , v b , and h b be the corresponding quantities at a 
section B, then 

m JL* _l 5l i h - ft 4- ^ 4- h 

(1) y +20 + *'- y + 2g + K 

assuming that water is a perfect liquid, and that it is 

flowing through a frictionless pipe. But - is the head due 

to the pressure at the point under observation, i.e., it is the 

height of a column of the liquid that could be supported 

v 2 
at the point by the pressure there, also ~- is the further 

height to which the liquid would rise in virtue of its 
velocity, if suitably guided upwards, while h is the eleva- 
tion which it already possesses, so that the sum of these 
three quantities above the datum chosen represents the 
height which it is capable of reaching by reason of all 
three, and the theorem expresses the fact that this is the 
same at all points in the pipe running full of water. 
Assume that there is a pipe (Fig. 2) leading out from an 



open reservoir filled with water, and that by some arrange- 
ment for admitting water, the level is kept constant when 
water is drawn off at the bottom by the opening of the 
valve B. If h is the height of the water level above a 
datum chosen for convenience below the valve, then the 

Fig. 2. — Reservoir and pipe to illustrate the theorem of 

head of water above a section A is h = hi - h 2 , and there 
will be a static pressure in the pipe at the section due to 
the weight of water above it, when the valve B is closed 
and the water is still. The head h producing this pressure 
is conveniently referred to as the pressure head, and the 
pressure per square unit upon the walls of. the pipe at A is 
p = y h, where y is the weight of a cubic unit of water, 
#nd //, the head in corresponding units, 


If in equation (1), the suffix a refers to the point A on 
the pipe, and b to the surface of the water in the reservoir, 
then, since v a and v h , are each equal to zero, and p^ is the 
atmospheric pressure, we have 

SL + h b = A + K , or h b - h a = V^V, 
y y y 

but h b — h a is the static head of water on the section A, 
and p a - p b is the pressure at that point above the 
atmosphere, so that the theorem shows the truth of the 
simple law giving the relationship between static head and 
pressure of water. 

Now suppose that the pipe is open to the atmosphere at 
A for the water to discharge, and that the water level in 
the reservoir is kept constant by a supply equal to the 
discharge, then since v b .= o, and p a = p b (since at the 
surface and at B the pressure is atmospheric) we have 

but h b — h a is, as before, the head above the point A, and 
this head is now utilised in imparting kinetic energy to 
the water and the expression v a 2 /2 g may be referred to as 
velocity head. The discharge of the pipe into the 
atmosphere at A would be the velocity multiplied by the 
area of the pipe at that point. 

As an example, supposing h b — h a be 26*2 feet and the 
diameter of the pipe be uniformly 6 inches. The discharge, 
neglecting friction, would be 

Q =AX /V /2^(/7 & -/ io )=^x(l) 2 X ^2 X 3*2 x 26'2 

»= 8*05 cu. ft. per sec. 



open reservoir filled with water, and that by some arrange- 
ment for admitting water, the level is kept constant when 
water is drawn off at the bottom by the opening of the 
valve B. If hi is the height of the water level above a 
datum chosen for convenience below the valve, then the 


head of water above a section A is h = hi - h 2y and there 
and the water is still. The head h producing this pressure 
is conveniently referred to as the pressure head, and the 
pressure per square unit upon the walls olthe pipe at A is 
$nd Ji {ihe head in corresponding units, 


then, since v a and v b , are each equal to zero, and p* is the 
atmospheric pressure, we have 

St+h h = v -»- + K, or h - h a = &=a 
y y y 

atmosphere, so that the theorem shows the truth of the 
simple law giving the relationship between static head and 
pressure of water. 

Now suppose that the pipe is open to the atmosphere at 
the reservoir is kept constant by a supply equal to the 
surface and at B the pressure is atmospheric) we have 

this head is now utilised in imparting kinetic energy to 
velocity head. The discharge of the pipe into the 
atmosphere at A would be the velocity multiplied by the 
area of the pipe at that point. 

diameter of the pipe be uniformly 6 inches. The discharge, 
neglecting friction, would be 

Q = A X s /2gU< b -K) = ]L x (I) 2 x ^2 x 3*2 x 26-2 

5= 8*05 cu. ft. per sec. 


The foregoing are two extreme conditions employed for 
the purpose of illustration, but in practical problems the 
head is always divided between velocity and pressure head 
along a line of pipe, and the relation between the two is 
constantly varying as different levels are reached and 
different sizes of pipes are encountered in a system. 

Thus when a pipe, running full of water, is decreased in 
diameter at a point, the velocity is increased and the 
pressure declines. This principle is made use of in the 
Venturi meter which is an instrument for measuring the 
quantity of water flowing along a pipe, and which is exten- 
sively used in water supply systems, but is not employed in 
connection with water power plants. The pressure in a 
pipe may be less than the atmospheric as the above equation 
shows, but in service pipes this is not often the case. 

The effective head, which is constantly referred to by 
hydraulic engineers, is the head corresponding to the total 
energy that may be obtained at the turbine or other 
apparatus which is to be driven by the water. In other 
words, the effective head is the actual head, as determined 
above, less the losses which occur owing to the flow of the 
water, and which must therefore be deducted, as they 
reduce the total energy available at the place where it is 
required. Though this is the exact definition of effective 
head, the term is often incorrectly applied, as for instance 
to the actual difference in elevation between the head and 
tail water of a waterfall, which cannot all be utilised. 

But so far the problem has been simplified by the 
omission of the losses which are always present to the 
engineer, and which considerably modify the results. 
These losses of energy in flowing water are caused by 


the friction in the pipes, eddies at bends and round ob- 
stacles such as rivet heads or badly fitted spigots, also 
losses due to the friction of the particles of water between 
themselves owing to the fact that all the particles do not 
move with the same velocity. Again, there is considerable 
loss due to sudden reductions in the velocity, such as occur 
when a pipe is suddenly enlarged. The reduction of these 
losses to a minimum, and an accurate means of estimat- 
ing their magnitude when laying out new work form an 
important part of the subject of hydraulic engineering. 

By an examination of the foregoing equation it is seen 
that the pressure to which the pipe is subjected at a 
section cannot, under conditions of uniform flow, be greater 
than that due to the head of water above the section in 
question, and that it is greatest when there is no flow in 
the pipe, i.e., a static head. There is, however, a cause 
hereafter to be considered which may give rise to great 
momentary increase in the pressure, but at present the 
acceleration or retardation of the water in the pipe are 
left unconsidered, and we are dealing with uniform 
velocity throughout the pipe. Generally the diameter of 
pipes vary throughout a system, but where all the pipes 
are running full «i vi = 03 t' 2 = const., where a\ and 03 
are the areas of the pipe at two places and v\ and v 2 the 
velocities across the sections at these places. This relation 
is referred to by some writers as the equation of continuity 
and is self-evident, and as the areas are proportional to 
the squares of the diameters, the relation may be written 

An example to illustrate the preceding facts may be drawn 
from practice. A pipe carrying water down a mountain 



side to a turbine installation is 2 ft. internal diameter, 
and the water level in the reservoir is 420 ft. above the 
valve at the bottom. Again, assuming the losses to be 
small even when the turbine is working at full gate with a 
velocity of 7 ft. per second through the pipe, we will proceed 
to find the value of the velocity head for various velocities 
up to 7 ft. per second. This is shown by the following 
table, where the total head of water is variously divided 
between pressure head and velocity head. 

Velocity in pipe 

Velocity head in feet. 

Pressure head in feet. 


ft. per sec. 


lbs. per sq. in. 































The velocity of the water through the pipe when at the 
maximum means a slight reduction in the pressure of about 
0*88 lbs. per square inch, which is only about 0*17 per cent, 
of the pressure due to the static head, and except for illus- 
trating the principle, is of little value practically, as the pipe 
has to be designed for strength to withstand higher pressures 
than the static head. 

Weir Measurements. 

The simplest method of obtaining an accurate estimate of 
the quantity of water passing down a small stream is by 
means of a weir over which the water is allowed to fall (Fig. 3). 


The weir as usually used by hydraulic engineers consists of 
a flat panel set vertically across the stream out of which a 
rectangular notch is cut through which the water flows. 
The height of the water over the weir to be used for calcu- 
lating the flow is measured from the sill of the weir to the 
surface of the stream some feet above the weir, as, owing to 
the increased velocity of the water at the edge of the weir 
the surface at that point is depressed. Two precautions are 
necessary in making such a measurement : (1) To be 
certain that the sill or edge 
of the weir is horizontal. 
(2) To measure the head 
as aforesaid by means of 
a suitable gauge. 

If the stream is too wide 
to permit the use of a weir, 
or the banks render access 

for such a purpose impos- 

.iii, , i , t Fig. 3. — Weir for measuring the 

sible, the next best way of flow of a gtream 

obtaining the flow is by 

taking soundings across the section of the stream, and 

obtaining the superficial area of the cross section, then by * 

measuring the velocity by floats, the amount of water passing 

is obtained by taking the product of the cross section and 

the velocity expressed in the same units. The velocity of 

the water at all points across the section is not the same. 

The friction against the sides and bottom reduce the velocity 

somewhat, so that a float, carried down on the surface, would 

indicate a higher velocity than the true average for the 

whole cross section. The average velocity may be more 

closely attained by means of a loaded stick floating 


vertically, or a bottle which projects downward into the 
current beneath the surface. 

In all important hydrometric investigations velocity 
meters are used which may be lowered from a boat to 
any point, and thus from a series of such measures the 
mean velocity and flow can be calculated. It would take us 
too far to describe the various kinds of velocity meters and 
other appliances used for these measurements in large 
rivers, and to follow the reduction of the observations to 
the desired result. These current meters, which consist 
essentially of a small screw propeller with means for 
measuring the revolutions when it is immersed in a current 
of water, have to be carefully calibrated experimentally in 
order to determine the relation between the revolutions 
of the screw and the speed of the current. Some experi- 
ments were made in a tank at Haslar by Mr. E. Gordon, 
the results of which 1 show that the speed of the meter 
and that of the current are not directly proportional. 
Thus, for a speed of 1 ft. per second a certain meter 
makes 0'82 revolutions, while in a current of 4 ft. per 
second it makes 3*4 revolutions in the same time. In 
general it is expedient to obtain the constants and errors of 
current meters over a wide range of values, and to plot 
a curve from which the speed of the current may be directly 
read off when the revolutions of the meter are given. These 
are usually to be obtained from the manufacturers who 
determine them by dragging the meter through water at 
different velocities and noting the revolutions of the counter. 
Weir measurements constitute the most reliable guide to 
the flow in small rivers and streams, and among the 

i "Proceedings Inst. M. E.," May, 1884. 


investigations that have been carried out, those of Mr. J. B. 
Francis are most noteworthy. He has left us most 
complete records of experiments which were undertaken 
upon the flow of water over weirs, and they have so far not 
been surpassed in accuracy. While there is a variety of 
choice of weir formulae open to the engineer, the Francis 
formulas give results that cannot be gainsaid, and the weir 
tables and curves (Fig. 4) are based upon these formulae. 
The reason for the differences that exist between the results 
of different experiments is that the coefficient of flow has 
not a fixed value, and various assumptions are made for it. 
If h be the height of the surface of the water above the sill 
of a weir, and b the breadth of the weir in feet, the theo- 
retical flow (Q) in cubic feet per second is 

Q = | b yJZjh X h = 5-35 b ^¥. 

This would be the flow if water was a perfect fluid, but 
actually it is less than that given by this relation, by 
a certain amount depending upon the coefficient of flow. 
This coefficient is variously estimated and this gives 
rise to numerous weir formulae according to the value 
assigned to it. Moreover, it is not a constant for the 
same weir, but varies with the height of water above 
the sill. This variation is noticed in the formulae used 
by some engineers, but for small weirs with heights up to 
2 ft. a sufficient degree of accuracy is attained by assuming 
a mean value for the coefficient. The formula of Brasch- 
mann, which is much used in Switzerland, takes account of 
the variation in the coefficient, but it is generally the case 
that in the ordinary course of the measurement of flow 
of small rivers and streams the refinement of a varying 

n ' 5^:. ^URCES OF POWEK. 

. ^ • ^**sairy. as it represents a questionable 

v » *v; I lie writer has used Francis' formula 

v >. ;vU-«a and most convenient for small 

. w v* „.t :Vr all conditions that arise in practice. 

■s v\ v^ixv* v>r ratio of the actual flow to the 

v. . ^. wUfK<i by Francis, is 0*62, so that the 

•. k, \ t ut\v<\i iu English units, is 

V - O'itt X 5-35 b y/h* = 3'33 b W . 

I o j^, it into a more convenient form, let d be the width 
>. itc war in inches h y as before, the height of the water 
, \vi i he *iU in feet, and Q the flow in cubic feet per 
'...'..m', thou we have 

Q = 16-65 d M . 
Tho curve (Fig. 4) is plotted from this formula. 
ii U and h be expressed in centimetres and Q in litres per 
minute, the equation becomes 1 

Q = 1-102 d M . 

The discharge shown on the curve is plotted from this 

The vertical ends of a weir deflect the passing water so 
that the width of the stream immediately below the weir is 
not equal to the weir width. This deflection is caused by 
the angularity in the approach of the water when the weir 

1 The transformation from English to metric units is effected by 
substituting the values for cubic feet, inches, and feet, in litres and 
centimetres — 


2tf-3 - 16 ' 65 X 254 X 30-48 X y^TiS 
Q = 1-102 b hi . 


does not extend across the full width of the stream. 
Francis allows for these end contractions in a modification 
of his formula, but unless the weir is less than 3 ft. wide 
the correction for the end contractions may justifiably be 
left out, and even for a less width the error by leaving it 
out is small. 

Weir Table. 

Depth on Weir (h) 

Cubic ft. per min. 

Depth on Weir (h) 

Cubic ft. per min. 

in inches. 

per inch length. 

in inches. 

per inch length. 









































































The accompanying tables and curves give the flow over a 
weir for a unit width. It should be noted that the quan- 
tity passing a weir of only 1 in. or 1 cm. in width would 
be somewhat less than that given by the table or curve, 
owing to the end contractions in such a case having a 
relatively great influence, but as it is seldom that a weir 
would be anything like as narrow, the flow per inch width 
or per centimetre width for such a weir is correct. 

N.S. D 



Example : A weir is 4 ft. 8 ins. wide and the height 
over the sill is 10 ins. The flow in cubic feet per 
minute is therefore 12*7 X 56 = 711'2 cu. ft.; or again, 
a weir 1*46 metres wide with a depth of water of 36 cms. 

Depth on Weir (h) 
in centimetres. 

Discharge in litres per 

min. per centimetre 


Depth on Weir (h) 
in centimetres. 

Discharge in litres per 

min. per centimetre 







































34 9 































































gives a flow in litres per minute of 239 X 146 = 34,894 
litres = 34*894 cubic metres per minute. 

It is important to obtain the height of the water over the 
sill some few feet up-stream to avoid the declivity of the 
surface owing to the velocity of approach. The hook 
gauge, as used in laboratories, is a very delicate means of 




^ _ . 20 40 60 60 Ao 120 140 160 180 200 220 240 260 280 300 320 340360 380*00 
§ ^ L,tr P Pff m l n - 8 iQ t2 ft , e ia 20 22 24 26 28 30 32 34 36 38 40 
^*Cubic feet per min. 

Fig. 4. — Discharge over weirs. 

measuring the height. The gauge consists of a wire 
turned up at the end in the form of a hook and pointed. 

d 2 


The hook is immersed and is adjustable by means of a 
screw and nut. The screw is turned until the point of the 
hook reaches the surface and the reading is then taken 
which is referred to the sill of the weir. A two-foot rule 
used a few feet up-stream is generally as accurate as 
occasion warrants. If the surface of the water be broken 
the hook gauge is troublesome. If, however, it is used in 
such cases it can be protected from disturbance by sinking 
a pipe inside which the gauge may be placed. 

Small streams with variable flow should be measured 
during the driest weather when the water passing may be 
taken to be the least throughout the year, and the plant 
may then be designed with a view to utilising this minimum 
flow in one wheel, so that it will be working at as near full 
load as possible, and therefore at the highest efficiency. 
Violent changes and fluctuations in the flow from hour to 
hour, which occur on small watercourses in rainy districts, 
are the most difficult to deal with, unless there is sufficient 
storage capacity above the fall to allow a steady discharge 
to be maintained. The effect of a heavy flood on such 
streams is often to diminish the effective head on the 
wheels by raising the tail water, and this may have the 
effect of shutting down the plant altogether, which may be 
serious if there be no substitute for furnishing the power 
or light. 

Levels and Levelling. 

A preliminary survey of a site for a proposed water- 
power plant should begin with a measurement of the 
height of fall available, allowing for the possible reductions 
at all stages of the river. If there be a natural waterfall 


the height may readily be measured from surface to 
surface by means of a plumb line, but if the development 
of the water power necessitates the construction of a dam 
or canal by which the fall is obtained, it is necessary to 
" run a line of levels " to ascertain the fall in the river 
from point to point, and by this means determine the 
height which the dam should be, or the length of canal 

Fig. 5. — The engineers' level. 

necessary to obtain the desired difference of elevation at 
the site of the proposed water wheel installation. The 
levelling is usually carried out by an engineers' level, an 
instrument which, in the hands of a skilled craftsman, 
will yield very accurate work. An ordinary level, such as 
that shown in Fig. 5, which is employed for the purpose 
of railway levelling, will, if in proper adjustment, yield a 
very accurate result in skilled hands. As an actual example, 
a line of levels was run for three miles which showed a 
difference of elevation between the two ends of the three- 
mile stretch of about 120 ft. The levelling was then repeated 
backwards with the result that there was only a difference 
of 0*75 ins. between the two results, or about 0*05 per cent. 



difference. Such a result is only possible by great care on 
the part of the operator, and would not be attained without 
considerable practice. For hydraulic measurement a 
much less accurate result would be satisfactory if the 
object was merely to ascertain the height of fall, which, is 
subject to such continual variation. 

The engineers' level consists of a telescope provided with 

Fig. 6.— Adjusting screws for levelling. 

a focusing arrangement and cross-hairs, the intersection of 
which mark a point in the field of view. Attached to the 
telescope and parallel with it is a spirit-level, so that when 
the bubble is in the centre of the tube, i.e., at the highest 
point, the telescope is horizontal. Levelling screws are 
provided for altering the inclination to the horizontal by 
which the telescope may be levelled. The whole arrange- 
ment is mounted upon a vertical axis about which it turns, 
and the instrument is supported by a tripod. It is 


essential that the level be properly adjusted before being 
put into use. The principal adjustments are (1) The 
parallelism between the optical axis of the telescope and 
the level. (2) The perpendicularity between the telescope 
and the vertical axis. This latter relation cannot usually 
be altered by the user, as the instruments leave the factory 
with the relation fixed, but the level is provided usually 
with lock nuts by which adjustment (1) may be easily effected. 

Fig. 7.— Method of levelling. 

The level proper is a glass tube, the upper surface 
of which is curved to a circle of several feet radius. 
It is filled with pure alcohol or a mixture of alcohol and 
sulphuric ether, and the bubble at the top spreads out 
over some divisions scratched on the glass, by which the 
position of the bubble relative to the centre line may be 
seen. The instrument is brought to a level when the tripod 
is planted, by adjusting three thumb-screws (Fig. 6). As a 
plane surface will always be level when two lines at right 


angles upon it are level, the most expeditious way of 
levelling is to level one line parallel to the line joining two 
of the screws and another line at right angles to this. 
When this is done, if the level be in proper adjustment, 
any position of the telescope when rotated about the 
vertical axis will be level — as shown by the unchanged 
position of the bubble. The actual process of levelling is 
illustrated in Fig. 7. It is desired to obtain the difference 
in height between two points A and B. The level is set 
up at any intermediate point, not necessarily between or in 
line with A and B. After the instrument is levelled, the 
observer reads the height a upon the graduated rod which 
is held by his assistant vertically upon the point A. This 
reading having been recorded, the assistant transfers the 
rod to the point B, where the reading (which is usually 
taken to one-hundredths of a foot) is also recorded. If the 
first reading a be 8*27 ft. and b be 4'87, it is clear 
that the difference in height between A and B is 
8-27 - 4-87 = 3*40 ft. The height of the instrument 
above the ground is not a factor in this case. Any con- 
venient height will do, since it is the difference of the 
readings that denotes the difference in elevation of the two 
stations. If, however, the difference in elevation is required 
between points which are too distant from each other to be 
sighted from one setting of the instrument, it is necessary 
to accomplish the levelling by a series of steps which are 
known as a line of levels. 

The telescope is of such power in the ordinary engineers' 
level that the small divisions on the rod may be discerned 
up to 250 or 300 ft., beyond which it is not possible 
to ensure accuracy, and therefore distances of more 


than 600 ft. must be covered by more than a single 
setting of the instrument. The method of taking a 
series of levels and recording the results is the same 
as for a single pair of stations, but some recognised 
plan for keeping the notes is necessary to avoid con- 
fusion. The diagram shows two stations A and B 
with the instrument levelled, from which readings a and 
b are obtained. These two readings are set down in the 
level-book in columns 2 and 8. They are known as back- 
sights and foresights, as, in the first reading the level is 
turned back upon a station while in the second it is turned 
forward to read the rod when placed upon an advanced 
station. It is also evident from the diagram that a, the 
backsight reading, is the height of the instrument above A, 
and this is frequently set down in level books as H. I., being 
the height of the instrument above the station to which a 
backsight is directed when the instrument is set up. A 
page of a level- book would appear thus : — 






H. I. 













The first column gives the name of the station, and H. I., 
the backsight reading on the first station is entered as 872 
in the second column. The elevation of this first station 
may be any arbitrary figure. Sometimes it is referred 
to sea level when its elevation is known, and is expressed in 
feet. If the elevation is not known it may be entered as 0. 


The foresight reading on B, which is 4 : 87, is set down in 
column 3 in the line opposite B, and the elevation of this 
station, being 827 — 4*87 = 340, is placed in column 4. The 
instrument being removed from the first position at X to a 
new position Y, a backsight is taken upon B which is the new 
height of the telescope above B. This reading is found to 
be 7 # 25. The rod is now placed at C and the foresight is 
349. C is therefore 7*25 - 3'49 = 3*76 ft. above B and 
340 + 3*76 ft. above the datum ; therefore its elevation is 
7*16. It will be seen that by adding up all the figures in 
column 2 and subtracting the sum of those in column 3, the 
elevation of the last station is directly obtained. In the 
example cited the last station is higher than the first and 
the ground rises steadily. If however it is surmised that 
the line of levels will be taken downhill, as when they are 
run in a down-stream direction on a river bank it is con- 
venient to assume an elevation to start with so that 
negative signs may be avoided. 

It is immaterial whether the backsights and foresights 
be equal in length or different unless the operator has 
reason to believe that the instrument is out. of adjustment 
by not having the optical axis exactly perpendicular to the 
vertical pin upon which the level swivels. If there is an 
error in this, the backsights and foresights ought to be as 
nearly as possible of equal length, for by so doing this error 
is diminished, and if exact equality could be attained it would 
be entirely eliminated. As this source of error in a level is 
not easily put right in the instrument — and levels subject to 
rough usage are liable to become deranged — it is safest for 
accurate work to take both sights as nearly as possible of 
equal length, and this is generally done on long lines of levels 


where a cumulative error might make a great difference 
from end to end of the line if, as is often the case, the line be 
some miles in length. Accuracy in the use of a level 
depends mainly upon the skill of the craftsman, who must 
know how to make the various adjustments, and the errors 
or bias of his instrument. The three legs, which are shod 
with metal, should be firmly planted in the ground and 
then, by means of the screws, the telescope brought to an 
exact level. The manipulation of the screws on a cold day 
is a trying experience, particularly when they are stiff, as 
they ought to be. By repeatedly turning the telescope 
through angles of 90° and correcting by the screws until 
no change of position in the bubble is observed for any 
position of the telescope, the instrument is prepared for the 
first reading. 

The rod in the hands of the rod-man should not be held 
rigid, but should be balanced upon the selected point on 
the ground, and sustained by the tips of the fingers on 
each side. By such means a vertical position of the rod is 
assured. Some practice on the part of the rod-man is 
necessary before he can balance the rod, especially in a 
high wind. It is usual to mark the stations upon a short 
survey by wooden pegs driven into the ground, upon the 
tops of which the rod rests when taking a reading. They 
also serve the useful purpose of preserving a record of the 
stations so that check levels may afterwards be made 
should there be any doubt about the accuracy of the first, 
or a desire to confirm the previous figures. As some 
stations may be placed at conspicuous or definite points of 
which the elevation is required, some means of permanently 
marking them is essential. Most of the stations or turning 


points, however, are merely links in the chain of levels, and 
their actual elevation is not a matter of note. If, however, 
the elevation of intermediate points be required, a stone or 
other solid rest for the rod may be used — anything, in fact, 
that will afford a rigid base during the time the man at the 
instrument can take a fore sight, move the level to a new 
position, and take a back sight, after which the rod-man 
goes forward to give the leveller a fore sight upon the next 

It is customary in taking levels along a river to select 
convenient points or bench marks of a permanent kind so 
that the elevation of the surface of the water may always 
be found at all stages of the river by reference to them. 
A notch at the base of an extended root of a tree, or a 
marked position upon a rock or firmly embedded stone, may 
be conveniently used as a bench mark from which the level 
at all stages of the river may be obtained, and if there are 
several marks of known elevation along the bank, the 
variation in the fall of the river at different stages of flow 
may be readily observed. This is especially important 
owing to the effect which heavy floods have on small rivers 
of diminishing the head, an example of which, at the site 
of a dam on a small river, is referred to elsewhere. With a 
heavy flow the tail water in this case was raised so as to 
seriously diminish the available head which the dam was 
designed to afford (see page 136). In this case bench marks 
of known elevation were fixed above and below the dam in 
such positions that the distance down to the surface of the 
water from each could be directly obtained by readings on 
a rod, and by taking a series of simultaneous readings, 
the actual difference of elevation between the water surface 


at the two places could be ascertained, from which an 
instructive table could be made out giving the available 
head for different depths of water flowing over the weir. 

Useful Data and Formulae Pertaining to Water. 

One English gallon weighs 10 lbs. = 0*16 cu. ft. 
One U.S. „ „ 8-34 lbs. 

One cubic foot 
One cubic decimeter 
One litre 
One cubic metre 

62-5 lbs. 
1 kilogramme. 
1 kilogramme. 
1 ton (metric). 

If v = velocity in feet per second, and h = height of 
free fall in feet, then 

v = A ^2gh = a/2 X 82-2 X h = 8 y/h approximately. 

If V = velocity in metres per second r and H = height of 
free fall in metres, then 

V = ^JZgH = 4*4 x/H approximately. 

A column of water one foot high exerts a pressure of 
0*43 lbs. per square inch. 

A column of water one metre high exerts a pressure of 
O'lO kg. per square centimetre. 

(One kilogramme per square centimetre = 14*2 lbs. per 
square inch.) 

One atmosphere = 14*7 lbs. per square inch. (Note how 
closely this coincides with a pressure of one kilogramme per 
square centimetre. This is of great convenience in making 
approximate and rapid calculations in the metric system.) 

For quantities of water per horse-power, see page 19. 



1. Historical sketch of the utilisation of water power and early types of 
wheels, with deductions concerning the power derived from them. 

Water power was applied to the propulsion of machinery 
more than two thousand years ago, and indeed there are 
evidences that the early Egyptians made use of the current 
in the Nile for corn grinding by contrivances the outlines 
of which have been engraved on enduring stone. The earliest 
exact record of a water-wheel applied to corn grinding is 
given by two authorities 1 as th^t of Antipater of Thessalonica 
in 85 b.c, and mention is also made by Strabo of a water- 
mill belonging to Mithridates King of Pontus. Later we 
find that there are evidences of watermills in Europe 
almost at the period of the Eoman Justinian Code, and 
from this time their use for the purposes of corn grinding 
began to extend. Many of these early mills consisted of 
barges moored in rivers, from the sides of which paddle 
wheels on horizontal shafts projected, and these were 
slowly turned by the current as it swept past. Even to-day 
this type of mill is used in Southern Europe, though they 
are fast being replaced by more modern forms of mill. In 
England the use of water power was fairly extensive a 
thousand years ago, for we find surveys of thousands of 

1 " History of Corn Milling,' ' by Eichard Bennett and John Elton. 


mills recorded in the Domesday Book, and the Norse mill 
was, it is stated, introduced into Ireland in the third 
century. This primitive mill consisted of a horizontal 
paddle-wheel mounted upon a vertical axis, to the upper 
end of which the mill stones were fixed, and this was 
employed instead of the quern, which had done service from 
remote times, and which was the only method employed 
for converting the grain into flour before the introduction 
of the watermill. 

It is natural that the water-wheel should have been 
almost entirely associated with flour milling from the 
earliest times, for any new method of obtaining power would 
first be applied to the production of the staple food and after- 
wards to other purposes, though it is possible that the lifting 
of water for irrigation purposes may have been performed by 
some of the earliest and crudest water-wheels. We are 
not, however, as much concerned here with the applications 
of water power as with the way in which the power may be 
developed by the use of wheels, and the various types of 
wheel that have been evolved as the outcome of experience. 
It is sufficient to suppose that the necessity created by the 
demands for cheap flour led to the use of water power, and to 
the extinction of the quern in countries favoured by Nature 
with rivers which could be utilised for the purpose. The 
wheel thus introduced to the service of man has been 
applied to all manner of purposes, and water power was for 
many centuries the only supplement to animal power that 
was employed, unless windmills were introduced much earlier 
than existing records would have us believe. With the intro- 
duction of steam, water power has taken a very secondary 
place in those countries where coal can be procured at a 



moderate price, but notwithstanding the competition of 
steam power, the vast improvements in the construction 
of water-power machinery and the utilisation of remote 
falls by electric transmission of energy, has led to a re- 
generation in the use of water .power, of which we cannot yet 
foretell the ultimate influence upon the industries of those 
countries favoured with great powers in rivers and lakes. 

It is very improbable that the reader would ever have 
occasion to design or construct a water-wheel of the type 

that preceded the introduc- 
tion of the turbine, and 
therefore it is only for the 
sake of historical continuity 
that space ought to be given 
to descriptions of them, for 
they are fast becoming 
obsolete in England, and 
in many cases have been 
removed to make way for 
the more efficient machine. 
In one sense the extinction 
of the water-wheel is to be 
regretted, for of all the mechanical contrivances in or about 
a mill, they were the most picturesque, and the old wheel, 
groaning and creaking as it revolved between moss-covered 
walls, was by no means the least pleasing feature of an 
English landscape, and such may still be seen in places 
where the mill proprietor has not become imbued with the 
idea of making the most out of the water in his mill 

Three types of wheel (shown in Figs. 8, 9, and 10), have 

Fig. 8. — Overshot water wheel. 


been used for many centuries, while that shown in Fig. 11 
is comparatively modern, and is called after the French 
inventor Poncelet. As the operation of this wheel involves 
principles which are employed in the modern turbine in 
their entirety, it forms in a sense a connecting link between 
the old wheel and the modern. 

The oldest and most extensively used wheel in England 
was the overshot wheel, constructed of a series of buckets 
of sheet-iron or wood set round the periphery of the wheel 
and supplied with water from a shute or head race extending 
over the top of the wheel, so that the water entered the 
buckets approximately tangential to the circumference. 
The dead weight of the water in the buckets on the 
descending semi-circumference supplied the torque for 
turning the wheel. It will be seen from the illustration 
that a descending bucket lost a large part of the water it 
contained before reaching the lowest diameter of the wheel, 
so that the effective fall of the water acting upon the wheel 
was considerably less than the diameter ; thus of a given 
fall of water, or difference of elevation between head and 
tail race, hardly more than half was utilised by this wheel. 
By shaping the buckets with care a greater amount of 
water could be retained than might appear from the illus- 
tration, which is purposely exaggerated to illustrate the 
loss which would inevitably occur in such wheels from this 
source. In order that the wheel should clear the water in 
the tail race it was designed so that the diameter would be 
slightly less than the difference between head and tail race. 
A farther loss of available power was the result of this 
restriction. Wheels of this class have been constructed 
80 feet in diameter, so that the head which could be utilised 

N.S. B 



would be about half this amount. This limitation prevented 
water wheels from being utilised to develop the larger water 
powers, and confined their application principally to small 
streams, upon the banks of which mills could be erected. 

Eankine * states that the efficiency of wheels of this kind 
is as high as 70 to 80 per cent, when properly designed and 
constructed, but later experience of water wheels, combined 
with accurate tests upon turbines, throw discredit upon 
such a statement, and it is doubtful if such high efficiencies 

Fig. 9. — Breast water-wheel. 

Fig. 10. — Undershot water-wheel. 

were ever attained with this form of wheel. If such were 
the case, they would compare favourably with modern 
turbines for low heads, but only within a limited range. 
The expense of maintenance, especially if constructed of 
wood, is considerably more than that of a turbine plant 
of the same size, and the loss by friction owing to the 
necessarily heavy gearing is also greater with the water- 
wheel, as the machine work is less exact. 

The breast wheel (Fig. 9) is so called in consequence of 

1 " Applied Mechanics," p. 628. 


the arc of masonry or wooden sheathing that closely con- 
forms to the periphery of the wheel from the point at which 
the water enters the wheel to the place of discharge, usually 
a little less than a quadrant. The water is confined in the 
wheel during the time of descent of the bucket by the breast, 
and acts upon the wheel chiefly by weight and to some extent 
by the velocity at which it leaves the head race. The 
maximum theoretical efficiency of these wheels may be as 
high as 80 per cent., notwithstanding the leakage of water 
between the wheel and breast, for close fitting was not a 
characteristic of the work of the millwright, as is shown 
by the old water-wheels. Eankine gives for the velocity 
of the periphery of wheels of the two foregoing classes 
3 to 6 feet per second, which corresponds to 2*3 to 4*6 
revolutions per minute for a 25 foot wheel, which may 
be taken as the average size of wheels used upon the 
mill streams. 

The undershot wheel (Fig. 10) has radial paddles against 
which the water impinges when issuing at the velocity due 
to the head from beneath the sluice gate. The dead weight 
of the water does not operate upon the wheel at all, and the 
theoretical efficiency of these wheels is only 50 per cent., and 
their actual efficiency about 25 per cent. They were never 
much used in England, as a more efficient wheel of the breast 
or overshot type could be adapted in most cases. In Southern 
Europe they were used to a greater extent, in many in- 
stances being placed directly in the current of a stream 
or supported from a floating barge, and many such wheels 
were employed on the Ehine for corn milling, the efficiency 
of which was not more than 20 per cent. 

The early forms of water-wheel were entirely constructed 

e 2 



of wood with the exception of the shaft, gudgeons, and the 
large gear for communicating the power to the machinery. 
The later wheels have cast-iron spokes secured to cast-iron 
bosses on a steel or iron shaft, and carrying at their outer 
ends the sole plate which formed the back of the buckets 
and the drum of the wheel. The buckets are made of sheet- 
iron in the best wheels, sometimes strengthened in the 
centre if the wheel is wide. The cast-iron toothed ring 
or gear, which meshes with a pinion, is bolted to one of the 

circular rims or "crowns" to 
which the spokes are fastened. 
Owing to the slow speed of 
the wheel, a high gear ratio 
is usually necessary between 
the wheel and mill shaft. The 
loss by friction in the gearing 
is heavy in consequence of the 
difficulty of keeping the gears 
in alignment, which prevents 
them from always meshing on 
their pitch diameters. This 
loss is considerably reduced in turbine transmissions, for 
the gears can be made with greater accuracy, sometimes 
cut gears being used instead of hard-wood teeth set into a 
cast-iron spider, which is a common mode of construction of 
the main gearing. 

The Poncelet wheel (Fig. 11) receives the water at a 
velocity which is not quite that due to the total fall under 
which it works. The vanes are curved so that the water 
enters and exerts a pressure by being deflected, and subse- 
quently it falls back along the vane and is discharged into the 

Fig. 11. — Poncelet water- 


tail race. The breast slopes away from the wheel so that the 
water may acquire velocity before entering the vanes. The 
diameter of the wheel does not depend upon the height of fall, 
and consequently these wheels may be constructed of any 
suitable size for a given fall. This type of wheel has been 
much used in France, and, according to Delaunay, it yields 
an efficiency of 56 to 60 per cent, under low falls, which 
is close to the maximum that has been reached by wheels 
of the types under review. The water leaves the wheel 
with a relatively low velocity owing to the curvature of the 
vanes, which impress upon it a velocity in a backward 
direction relative to the wheel. The water comes to rest at 
the top of the vane, and in descending exerts a further 
impulse in the direction of motion and flows away with a 
low absolute velocity, just sufficient to prevent backwater. 
A fraction of the head is lost in this wheel owing to the 
necessity of raising it above the water in the tail race so 
that it may revolve clear. 

Actual tests for proving the efficiency of the water wheel 
have been made, but as the testing involves special appli- 
ances they are not usually convenient, and wheels of these 
types are rarely used for dynamo driving, except inciden- 
tally, such as for lighting the mill which is driven by the 
wheel. If exclusively used for electric work, an accurate 
estimate of the power developed may be read off from the 
ammeter and voltmeter when the efficiency of the dynamo 
is known. From tests of such a kind reliable inferences 
may be made if the water is measured correctly. It would 
appear from such information as exists, and it is but little, 
that water wheels fall off very rapidly in efficiency at partial 
gate as contrasted with turbines. This might be expected 


from the heavy friction losses at full load, which are not 
sensibly diminished at partial gate, and therefore at partial 
gate there is a less proportion of the energy delivered to the 
mill shaft. With turbines the friction loss is less than in 
the mill-wheel, mainly, perhaps, owing to the cruder 
construction adopted by early millwrights. 



The modern turbine and conditions of utilisation. 

The turbine (which is superior to all other hydraulic 
motors) consists of a wheel with curved vanes or buckets 
through which water is allowed to flow. The wheel as con- 
structed is in the form of a disc or cone, to which the vanes 
are attached at equidistant intervals round the circumference. 
The vanes may be disposed with reference to the axis in 
various ways, and may also be large or small compared with 
the diameter of the wheel. There is consequently a great 
variety of turbines, those at one end of the scale bearing but 
a slight resemblance to those at the other. Like most great 
inventions, the modern turbine is the product of the work 
of many men, for while certain forms of wheel are directly 
assigned to the skill of inventors whose names they 
bear, the successive improvements which have been added 
to the original ideas have resulted in perfected machines, 
which at the present time are the most efficient prime 
movers that the engineer possesses. There is no difficulty 
in returning 75 per cent, of the actual energy in water 
to a useful purpose by means of the water turbine. The 
steam, gas, or oil engine, on the other hand, compare very 
unfavourably in this respect. The most approved gas 
engine is incapable of yielding 40 per cent, of the actual 
energy supplied to it in the gas, while the steam engine 


falls far short of this. In this connection it is expedient to 
refer to the steam turbine, if only by way of comparison 
with the water turbine. Though both machines embody 
the same essential principle of a series of vanes being set 
into motion by the movement of a stream of fluid across 
them, the comparison begins and ends with this statement, 
for the nature of the working fluid is so different in the 
two machines that the construction, principles involved, and 
results, bear but slight resemblance to one another. The 
hydraulic turbine utilises an incompressible 1 fluid, of com- 
paratively great density, moving with a velocity which at 
the most is but a small fraction of the high steam velocity 
in the steam turbine. The volume of water issuing from 
the hydraulic turbine is the same as that at entry, but the 
expansion of the steam through the stages of a steam 
turbine results in a discharge a great many times that of 
the original volume. The high vane velocity again calls 
for a mechanical construction of great strength, but at the 
same time extreme lightness, so that the mass of rotating 
metal may not induce dangerous stresses. Moreover, the 
special problems introduced by expansion in the metal at 
the high temperatures in the steam turbine are not present 
in the water turbine, not only because the extremes of tem- 
perature are not so far apart, but also because the fitting 
is less accurate for hydraulic machines. The hydraulic 
turbine is, on the contrary, comparatively heavy, and the 
disadvantage of weight in the steam turbine may be turned 
to advantage in low speed hydraulic turbines by serving 
the purpose of a fly wheel. The leakage of steam through 
the annular space between the vanes and casing in a steam 

1 See page 16. 


turbine is a serious item to be reckoned with in the con- 
struction of these machines, but leakage losses in water 
turbines are small, though the construction of the wheel 
and fit in the casing is of a much rougher description than 
that necessary in the steam machines. The expansion of 
steam necessitates a series of stages or rows of vanes be- 
tween which there is a small difference of pressure. There 
is nothing of this kind in the water turbine, as generally 

Fig. 12. — Radial outward flow 

Fig. 13. — Radial inward flow 

only one stage is employed, even in cases where the head 
of water is great. 

Various Types of Turbine. 

The pressure exerted by a stream of water upon a 
curved vane may be utilised in four ways to impart rotary 
motion to a shaft according to the direction of flow of 
the water relatively to the shaft. This gives rise to four 
types of turbine, designated respectively by the course 
which the water takes from entry to exit. They are as 
follows : — 

1. Eadial outward flow turbine (Fig. 12). In this 



wheel the water enters round 
the shaft and flows radially- 
outward through the wheel and 
is discharged round the outer 

2. Eadial inward flow turbine 
(Fig. IS). In this wheel the 
water takes the opposite direc- 
tion to that of No. 1. This is 
a more common type of wheel 
as the course of the water from 
outside to inside renders the con- 
struction simpler, for the guide 
vanes are thus outside the wheel 
and are easily accessible. 

3. Parallel flow turbine (Fig. 
14). The designation given to 

this type of wheel would indicate that the water enters 
and leaves the turbine parallel to the shaft. This 
however, not quite correct, for 
the course which the water actu- 
ally takes is that of a spiral or 
helix. The course of the water 
in Nos. 1 and 2 is also spiral, 
but in a plane at right angles 
to the shaft. 

4. The mixed flow turbine 
(Figs. 15 and 15a). This is a 
combination of 2 and 8. The 
water enters round the outer 
edge of the wheel, flows radially 

Fig. 14.— Parallel flow 


Fig. 15. — Mixed flow turbine. 



inwards, and then in a direction similar to that of No. 3, 
where it acts upon the vanes which are bent round for the 

Fig. 15a. — Mixed flow turbine. 

purpose of utilising the remaining kinetic energy in the 
fluid after it has passed through the radial vanes. 

Any of these types of turbine may have horizontal or 
vertical shafts, according to the conditions under which 
they operate. 


The foregoing classification of turbines would be incom- 
plete without the necessary division of all turbines into 
two systems, into one of which every turbine must be 
placed. The distinction between these two systems is 
somewhat confused by a misleading nomenclature which 
does not convey the true sense of the difference between 
the two types. The terms " impulse " and " reaction " are not 
sufficiently explicit, but on the other hand it is difficult to 
replace them by a short definition which will convey the 
essentials without an additional explanation. 

The subject is one which has received a new measure of 
importance since the steam turbine has entered the field as 
a prime mover, for the distinguishing features of the 
"impulse" or "reaction" water turbine are imitated in 
steam turbines of different types. As the words " impulse " 
and " reaction " have apparently come to stay we must 
perforce continue to make use of them until a more 
descriptive short definition be found. It will be re- 
membered that pressure head and velocity head, corre- 
sponding respectively to potential and kinetic energy, are 
the two forms in which the energy stored in water may be 
utilised in operating machinery. Water under high 
pressure has been used in service systems for driving 
hydraulic motors essentially similar to slide valve engines. 
The motor consists of a piston working in a cylinder, and 
the water is admitted through valves alternately at each 
end, and is then discharged during the return stroke after 
it has accomplished the work of driving the. piston forward 
against the resistance, whatever it may be. In such a case 
pressure head only is used, and the potential energy of the 
water is transformed into useful mechanical work upon 


the piston. Supposing that, instead of admitting the 
water under pressure to the cylinder, the supply pipe be 
disconnected and the stream directed against a wheel with 
a series of buckets arranged round the periphery. The 
pressure head is now converted into velocity head, and the 
work done upon the wheel is due to the kinetic energy of 
the stream. These represent the two extremes of action in 
hydraulic motors. All turbines, however, operate under a 
combination of the two principles, and are designated as 

Fig. 16. — Tourniquet to illus- Fig. 17. — Tank on wheels, to illus- 
trate the principle of trate the principle of reaction, 

" reaction " on the one hand, and " impulse " or " action " on 

the other, according to whichever principle predominates. 

The reaction caused by a stream of water is experimentally 

shown by Figs. 16 and 17. The first represents a tube 

with the ends turned at right angles in opposite directions. 

It is supplied with water through the pivot at the centre and 

it rotates in the direction of the arrow under the reaction of 

the issuing jets. This principle is directly applied to lawn 

sprinklers, for, by the rotation of the tube the water is 

scattered over a wider area than would be possible by 

means of a fixed nozzle. The tank supported on wheels, 


from which water issues through a hole at the end, would 
acquire an acceleration backwards under the reaction of the 
jet. This force or reaction may also be accounted for 
by the unbalanced hydrostatic pressure, for the end of 
the tank which is not pierced has thus a greater area for 
the water to press upon. By closing the orifice the area 
on the two ends is equalised and there is no resultant 
pressure. Turbines are so designated which utilise this 
principle of reaction ; but if the water is allowed to acquire 
the velocity due to the head before it enters the wheel, the 
turbine is working on the action or impulse principle and 
the pressure head is converted into velocity head. The 
pressure at the mouth of the nozzle through which 
water issues freely is almost nothing when the velocity 
is that due to the head, but when the water is confined 
in pipes or between the vanes of a reaction turbine, the 
pressure is maintained and the velocity is less than it 
would be if, as in an impulse turbine, the pressure 
did not exist. It is somewhat difficult to dissociate the 
two ideas of action and reaction in the abstract, but 
the difference between them is made clear by recognising 
in the impulse or action turbine a high velocity, and 
almost no hydrostatic pressure, and in the reaction 
turbine a low velocity with a pressure which is exerted 
against the containing walls or passages of the wheel, 
and which exists by reason of the fact that only part of the 
pressure head is converted into velocity head. The dis- 
tinction between the two systems is also heightened by the 
fact that reaction turbines work " drowned," by being com- 
pletely immersed in water. That means that the water 
entirely fills the passages, channels, and the spaces between 



the curved vanes, and there is no air within the wheel. 
The impulse turbine, on the other hand, is located above the 
tail race, and the water which passes through it only occu- 
pies a part of the volume between the vanes, the rest being 
taken up by air at atmospheric pressure. In certain cases 
the entire space may be filled with flowing water, but the 

Fig. 18. — Fourneyron turbine. 

discharge from the wheel is such that there is no back 
pressure exerted upon the vanes. 

In all turbines, whether reaction or impulse, it is necessary 
to guide the water before entering the wheel so that it shall 
enter without impact and therefore loss of energy. This is 
accomplished by the guide passages or nozzles— the angles 
of which are generally fixed in direction, but in many 
turbines are arranged so that they may be turned about 
an axis by the governing arrangement, and thus the speed 
of the wheel can be controlled. 


The French inventor Fourneyron (1802-1867) devised a 
turbine of the outward radial flow type to work as an im- 
pulse or reaction wheel, and his name has been universally 
applied to that particular form of wheel, still much used 
in France. Fig. 18, which is a sectional elevation of 
the Fourneyron wheel, illustrates the construction. The 
water enters through the penstock A, following the course 
of the arrow until it emerges from the guide vane B and 
enters the wheel C. The penstock may be either below the 
wheel, as in this turbine, or above it. "Where the turbines 
work under high heads the arrangement shown is adopted 
for convenience. This wheel may be so proportioned as to 
operate upon either system, and there are guide vanes 
sometimes only round an arc of the circumference, in which 
case the turbine becomes a partial admission wheel, which 
also implies that it is operating by impulse alone. The 
shaft to which the turbine is keyed passes out through a 
watertight gland, and may be either horizontal or vertical as 
convenience suggests. The Fourneyron wheel is not exten- 
sively used outside the country of its origin, and chiefly for 
the reason that the regulation required for electrical work, for 
which purpose the greater number of turbines are built at 
the present time, is more difficult with the radial outward 
flow arrangement, for there is little room inside the wheel 
for the necessary mechanism for operating controlling 
gates, or for tilting the guide vanes as required by a change 
of load or water level. These turbines are usually regu- 
lated by a cylindrical gate interposed between the wheel and 
guide vanes, which alters, according to the position it is 
caused to occupy, the width of the passages admitting water 
to the wheel. The weight of this cylinder is balanced by a 


counterpoise, so that the governing mechanism has only to 
overcome the inertia of the system when altering the flow 
of water to the wheel. 

The Fourneyron turbine, though it may be worked as an 
impulse wheel, is usually " drowned," and therefore operates 
under the " reaction " principle. Impulse wheels as a 
class bear the name of another French inventor, and are 
known all over the world as Girard turbines, which take 
various forms and designs according to the conditions under 
which they revolve. They may be outward-radial or 
inward-radial flow wheels, and also parallel or axial flow, 
and yet be properly designated by the name of the engineer 
who made a series of early experiments upon turbines, and 
devised wheels suitable for high and low falls. They all 
employ the impulse principle of working, and the water is 
allowed to attain the full velocity due to the head before 
entering the wheel. 

The illustration on page 66 shows a radial outward flow 
Girard turbine of 525 h.-p. for a fall of 95 ft. The 
external diameter of the wheel is 63 ins., and the water 
enters from below, and is discharged round the outer edge. 
The small horizontal shaft below the wheel proper is for 
the purpose of regulating, by adjusting the flow through 
the wheel. This turbine is now driving a textile mill, and 
the upright shaft, the lower part of which is seen in the 
illustration, is about 80 ft. long, at the upper end of which 
the power is taken off through bevel wheels on to a horizontal 
shaft. The weight of the vertical shaft and bevel wheel is 
partly borne by the hydrostatic pressure upon the wheel 
acting upwards, and it is for this purpose that the water is 
admitted below the wheel. This plan is frequently adopted 

N.S. F 



in large installations, and a very large part of the weight 
of the upper parts of the Niagara turbines are water-borne 



! -r ft 


' ' 1 \ I 



Fig. 19. — Radial outward flow Girard turbine of 525 h.-p. 

in this manner, which relieves the step or thrust bearings 
of a heavy pressure which would render efficient lubrication 



The reaction wheel extensively used in Europe for low 
falls is a parallel flow wheel which bears the name of Jonval. 






The water is, as usual, deflected by guide vanes, so that it 
enters the wheel making an angle with the shaft, and is 
discharged beneath into the tail race. These turbines 



operate satisfactorily under very low heads. There is 
one such wheel giving 40 h.-p. under a head of less 
than two feet. The wheel is very narrow axially, but 
of very large diameter and passes a large volume of 
water. It is divided into two concentric sets of vanes, 
so that when the conditions in the river allow a higher fall, 
one set of vanes may be shut to the passage of water. The 
Jonval turbine generally does not give as high an efficiency 
as the Girard except under very low heads, but it gives very 
good results down to about one-half gate. Fig. 20 shows 
a Jonval turbine arranged to utilise a low fall of water. 
The control of the water to the wheel is effected through 
the vertical shaft and hand wheel, and the pinion at the 
bottom meshes with a large wheel, which, by being turned, 
regulates the size of the openings to the guide vanes. These 
vanes are contained in a cast-iron ring embedded in a con- 
crete arch, which separates the head and tail races. The 
turbine proper is suspended from a hollow shaft through 
which a solid steel shaft passes. This latter shaft rests 
upon a pedestal at the bottom of the tail race, as shown in 
the illustration, and the bearing which sustains the weight 
of the rotating parts is thus placed well above the water 
line and is accessible for lubrication and examination. It 
would be best understood by imagining a thimble dropped 
over the point of a pencil, upon which it would be free to 
rotate. This method of supporting turbines is only possible 
for low falls, as otherwise the supporting solid shaft would 
be too long. Another method of supporting the weight of 
the turbine is shown in the illustration on page 137. In this 
case the bearing is also placed well above the water line, 
and is formed by a steel casting bolted to two heavy steel 


joists, which sustain the weight. The bearing plates, which 
are keyed to the shaft, run in oil, so that only occasional 
attention need be given to them, and the turbine hangs 
from this bearing, and is guided in the centre by a light 
bearing placed close to the top of the casing. A large 
number of turbines have been erected with a bearing 
below water constructed of lignum vitse, a hard wood 
which resists abrasion to a remarkable degree. It is, how- 
ever, becoming an obsolete practice in turbine design to 
place the bearing which sustains the weight below water, 
and the advantages of a perfectly lubricated thrust bearing 
in an accessible position are now fully appreciated. With 
a lignum vitse step bearing the water lubrication is 
sufficient, but with metallic rubbing surfaces an oil pump, 
with which oil is forced into a bearing below water, has 
been used, but with indifferent success. 

The type of reaction wheel at present most in use is the 
mixed flow turbine. The illustration on page 59 shows this 
type of wheel as usually constructed. It will be seen that 
the course of the water is radially inwards, and then in its 
descent it encounters a series of vanes which are disposed 
in the same manner as in the Jonval turbine, and thus a 
double effect is produced. As actually constructed, the 
radial and parallel vanes are formed in one piece, 
the radial vane being turned up at the end to form the 
parallel vane. They are usually made of sheet steel cast 
into the wheel, but are sometimes cast with the wheel, 
though in the latter case the two sets of vanes are con- 
structed separately, and the rings are turned, faced true, 
and bolted together. The best vanes, however, are those 
of sheet steel, as the smooth surface diminishes the loss by 


skin friction, and the sharp edges also tend to make the 
flow through the wheel more regular. 

This type of wheel will work under low and moderate falls 
with very high efficiency, and it is only under very high 
falls that its utility is contested by the impulse wheel. The 
diameter of these wheels for a given power is relatively 
small, but they are often made long in the direction of the 
shaft, so that they pass a large quantity of water. As all 
the water entering the wheel has to flow parallel with the 
shaft in the annular space within the wheel, the length 
shaftwise is limited for this reason. The shaft may be 
horizontal or vertical, and for high heads the horizontal 
position is frequently adopted, two wheels being placed 
together upon a single shaft. The design of the mixed 
flow turbine to develop a given horse-power under a specified 
head is a problem which can only be solved by the light of 
practical experience, rather than by rules and calculations. 
The manufacturers of turbines ordinarily require the 
following data from which to construct a wheel. 

(1) Available head under which the wheel is to work, 
and consequently the velocity of free fall of the water 
due to the head. 

(2) The variation in the head clue to the possible backing 
up of the water in the tail race during floods. 

(3) The quantity of water which is available at all seasons 
of the year in litres or cubic feet per second. If the flow is 
very variable, and it is desired to utilise as much of it as 
possible at all seasons, it may be necessary to install more 
than one turbine, the capacity of the units being such that 
the flow during the dry weather will be sufficient to keep one 
of them in operation at full load, and consequently at 






CO w 

I p 








-i * i 5 J 


o o a> fl j 


I -kg* 

g H » "'H 
S i S -T3 

7 hn at h 

co y ^ ^ » 

.2 & 

13 & 


CO fl 

•g ©c£ 

-u CO 


1'S * 


5)»5 r © 

'I: -g 





maximum efficiency. Sometimes the flow is superabundant, 
in which case the horse-power actually required throughout 
the year must be known. 

(4) The speed of the shaft from which the machinery 
is to be driven, and the kind of machinery that it is 
required to drive. The direction of rotation of the shaft is 
important for direct drives, but with gearing between the 
turbine and line shaft the required direction of rotation 
can usually be obtained by a suitable arrangement of the 
gears, and is thus independent of the direction of rotation 
of the wheel. The makers of wheels usually supply them 
to run in the direction of the hands of a clock (unless 
otherwise specified) for wheels with vertical shafts where 
the observer is placed above the wheel. 

The table on page 71 shows the variety of wheels with 
the names by which they are usually designated. Besides 
the general distinctive names by which turbines are classed, 
there are a host of " brands " favoured by the makers, which 
have generally some feature upon which they are wont to 
place great reliance, but which seldom sustain the often 
extravagant claims made for them by the would-be vendors. 

The writer has been assured of 95 per cent efficiency by 
a turbine maker, who doubtless considered himself safe 
from a disclosure of the real efficiency of his wheel by the 
fact that the process of carrying out tests on turbines to 
ascertain the exact facts is generally costly and seldom 
resorted to. In this respect the purchasers of turbines 
are entirely in the hands of an unscrupulous maker, 
and where a lack of technical knowledge ^exists on the part 
of the purchaser, he is likely to be governed by every 
other consideration than the right one in purchasing a 



wheel, and, be it said, there is only one suitable type and 
size of wheel for each particular case. To ascertain this 
correct type and size a knowledge of the site and purposes 
for which the wheel is desired are necessary, together with 
the discrimination of the experienced engineer. Many 
makers of turbines have their standard sizes and types, 
from which a selection may be made by the engineer of the 
purchaser, and often the result is quite as satisfactory as if 
a wheel were specially designed to fit the case in hand. It 
costs considerably more in the 
foundry and machine-shop to 
turn out a special wheel for 
which working drawings and 
patterns have to be made ; but 
this extra cost is sometimes 
completely justified by better 
adaptation, resulting in higher 
efficiency. For places where 
water is scarce, an extra 5 per 
cent, efficiency may mean the 
success of the plant, to secure 
which a slight additional first cost may be justly entailed. 
It is chiefly for small isolated plants that wheels are sold 
without adaptation to the requirements, for larger installa- 
tions are designed with attention to details and usually 
under skilled technical advice. The large Italian and 
Swiss installations are perfect examples of design generally, 
in which every part of the machinery is especially adapted 
to its duty and is cleverly executed. 

It is sometimes convenient to raise a turbine above the 
level of the tail water for a considerable height, and, to allow 

Fig. 21. — Cast iron draft tube. 


this to be accomplished and still work the wheel with all the 
parts full of water, draft tubes are used. These are either 
of cast iron (Fig. 21) or riveted steel, and are fastened beneath 
the turbine, and the discharge from the wheel passes through 
the tube into the tail race. The mouth of the tube dips 
beneath the surface of the water in the tail race so that air 
cannot enter, and as all the joints are made air-tight,* both 
turbine and tube are entirely filled with water while working. 
The effect of excluding the air is to create a suction, which 
exactly compensates for the raising of the turbine above the 
tail water, and thus there is no loss of head. Draft tubes 
are frequently referred to as suction tubes for this reason, 
and a turbine may, therefore, be located at any elevation 
above the tail water up to a height theoretically equal to 
that of a column of water which would be supported by 
atmospheric pressure ; l but practically, owing to leakage 
of air, suction is not efficient above 20 ft., which is the 
limit to the height above the tail water that the wheel 
may be placed and still utilise the full head. Generally 
the draft tube is much shorter than this, and is just suffi- 
cient to raise the turbine to a convenient level above the 
water, allowing for a possible rise in the level during floods. 
In the plant illustrated on page 67 a suction tube was 
unnecessary, as the normal tail water level is above the 
floor of the turbine pit and air cannot enter beneath, so that 
the turbine always works drowned. Draft tubes from 6 to 
10 ft. in length are common in turbines of such a design. 

1 A water barometer would have a height, were a perfect vacuum 

14*7 X 144 

possible, of — ^^ = 33*9 ft., corresponding to a mercurial 


barometer of 29*92 ins. 


Fig. 29, on page 99, shows a forked draft tube fitted to 
a Niagara turbine of 5,500 h.-p. 

Principles under which Turbines Operate. 

It has already been pointed out that the stored energy in 
a given mass of moving water is proportional to the square 
of the velocity, or to the height through which it has fallen, 
unless during the descent there be frictional resistances 
present, to overcome which part of the energy has been 
dissipated. But assuming that, instead of a mass of water, 
there be a continuous stream issuing as a jet from a 
circular orifice with a velocity v, it is desired to ascertain 
how we may apply the power in the best manner, and without 
undue loss, to the propulsion of a water wheel. If A be 
the sectional area of the jet, the weight of water passing 
per second will be A y v and the mass M will therefore be 
A y vjg. The power of the jet will therefore be 

2 xV1 l 2g X 

This expression appears to contradict the above assertion, 
as the square of the velocity is replaced by the cube, but it 
is easily seen that the weight of water passing a given 
section of the jet per second is proportional to the velocity, 
and that the above expression represents, according to the 
units chosen, the kilogramme-metres or foot-pounds which 
the water can yield up each second. If this quantity be 
divided by the horse-power constant (75kg.-m.or 550ft.-lbs.) 
the horse-power of the jet is ascertained. The simplest 
but at the same time the most wasteful way by which 
the power of the jet could be utilised would be by the 



insertion of a pressure board as shown in Fig. 22. The 

pressure upon the board might 
then be utilised to drive it for- 
ward, and by attaching a series of 
" these boards to a wheel in the 
manner of a paddle wheel, a part of 
the power might be successfully 
Fig. 22.— Jet impinging on reclaimed — but only a very small 
plane surface. fraction of the available supply. 

First as to the pressure upon the board caused by the 
impact of the water. The mass of water which strikes the 

board each second is — — , and the momentum of this 


A v v 
mass is — r — . The pressure caused by destroying this 

momentum per second is therefore 

The board is assumed to be held stationary in the stream, 
and the energy of the water is therefore expended in 
useless splashing, part of it being carried away with the 
fluid as it spreads out on the board in all directions. 
The efficiency therefore is zero when the board is held 
fast. Assuming that the stream has a sectional area 
of 4*2 sq. ins. and that the velocity, corresponding to a 
head of 18 ft., is 34 ft. per second, the pressure upon 
a stationary board would be 

p = ni x H! x (34)2 = 65 ' 4 lbs - 

In order to utilise this pressure the board must move in 
the direction of the stream. This movement, at a velocity 


which will be designated by V, causes a reduction in the 
velocity with which the water impinges, and this impinging 
velocity is v—V. The weight of water striking the board 
per second is no longer proportional to v but to v—V. The 
pressure acting on the moving board is therefore 

p = A -l ( V _ V) 2 
and the work done on the board would be 

PV = £- y (v - V) 2 V. 

This equation shows, first of all, what is manifestly true, 
that when the board is stationary, and V consequently 
nothing, the power is nothing. It now remains to 
ascertain what the speed of the board should be relative 
to that of the water so as to obtain a maximum power 
from the stream. This value of V is found to be J v by 
differentiating the above equation 1 , so that the maximum 
power which, under any circumstances, can be obtained by 
the board is attained at a velocity which is one-third that 
of the water. By substituting r/8 for V, and ascertaining the 
ratio of the power reclaimed to that imparted by the 
stream, the efficiency is disclosed. 

A _Z( V — -Y-- 
Efficiency = - g - ^ 3 ' B = f 7 = 29 ' 6 P er cent 

If there be a succession of boards, as in an undershot 

water wheel, the work done would be 

PV = A ^vV (v - V). 

1 See Appendix A. 


This would be a maximum when V = v/2 corresponding to 
an efficiency of 50 per cent, (see page 51). 

Even if there were no losses in the machinery through 
which the power was conveyed to the point of useful 
application, less than 50 per cent, of the energy in the 
water could be usefully applied by this means. When the 
frictional losses are taken into account the efficiency drops 
to such a low figure as to render such water motors 
unworthy of the serious attention of engineers. It is not 
possible to apply pressure boards in practice in this manner, 
for if attached to a wheel the angle of inclination to the 
stream would be continually changing, and only at one 
point in their course would they be normal to the direction 
of flow. Moreover, tfceir velocity in the direction of flow 
would be continually changing also, owing to the arc 
swept through by the wheel while the board is acted upon 
by the jet. The undershot wheel described in the last 
chapter is the nearest practical application of this principle. ■ 

The most perfect form of apparatus for utilising the 
kinetic energy of moving water would be that from which 
the water leaves the pressure boards, vanes, or buckets, 
with minimum velocity, carrying away a small proportion 
of the original energy. Clearly, there must be some 
residual velocity so that the water, after having passed 
through the apparatus, may be discharged into the tail race. 
It is the aim of the turbine designer to keep the velocity 
of discharge as low as possible consistent with a free flow 
away from the wheel. The successful attainment of this 
desired end is not to be found in devices which employ the 
force of impact of moving water upon a plane surface, for, as 
we have seen, some of the energy is expended in breaking 


up the stream, and the rest is carried away by the high 
velocity of discharge along the face of the plane radially 
outwards from the point of impact. The effect of inclining 
the plane to the direction of flow is to reduce the normal 
pressure on the plane to P sin 0, where is the angle made 
by the plane with the direction of flow. 

The principle upon which the water turbine operates was 
foreshadowed in the Poncelet wheel, which is designed with 
curved buckets over which the stream of water is intended 
to flow. In this respect it constitutes a notable excep- 
tion to other forms of water wheel, which were caused to 
rotate by the preponderating effect of a full bucket on one 
side, against empty ones on the other, in the same manner 
that two cars upon a funicular railway, at the ends of a 
rope passing over a pulley at the top of the incline, are 
moved up and down by alternately filling the water tanks 
beneath the cars, thus providing a force for accelerating 
the mass and overcoming friction. In such a case the 
potential energy of the water, as distinct from the kinetic, 
is alone employed, and the parallel might be extended to 
the utilisation of the kinetic energy by imagining that the 
water, stored at the top of the incline, was allowed to 
descend in a stream and thus acquire kinetic energy to be 
used in this form to drive machinery to operate the cars. 
Now the turbine essentially depends upon the movement 
of water over curved vanes, and not upon buckets filled 
with stagnant water which, by their dead weight acting at 
the end of a lever, apply a turning moment to a shaft. The 
first principle has now entirely superseded the latter, and a 
much greater efficiency in hydraulic motors is the result of 
the change ; thus, by passing from a consideration of the 


older type of water wheel to the modern turbine, we pass 
from one principle to another. 

If a stream of water be flowing along a flat surface A B 
(Fig. 23), in the direction of the arrow, a slight but inconsider- 
able force is exerted upon the plane tending to carry it in 
the same direction as the water, due to the friction of the 
water upon the surface. But as the plane is supposed to 
be very smooth, this force will be so small as to be 
negligible. If the plane, originally straight from C to B, 
be turned up about a hinge at C so as to occupy the position 
C Bi, and the water is still flowing, a force is developed by 
the change in the direction of the water at C, and this 

a c b 

Fig. 23. — Deflection of stream of water. 

force may be resolved into two components, one at right 
angles to C B and the other in the direction of C B. 
It is the first of these components that is made use of 
in turbines, to act tangentially to the wheel and thus 
cause rotation. In general, therefore, it may be said that 
the force employed in turbines is that due to the resistance 
which a mass of moving water offers to an enforced 
change in the direction of motion, and this change in 
direction is obtained by the contour of the surface over 
which the water is flowing. If, instead of a plane surface 
as shown in the figure, the surface be curved, the direction 
of flow of the water in passing over it is constantly changing, 
and this results in a pressure upon the surface at every 


point. The water, during its passage through or over the 
moving vane, is constantly yielding up its kinetic energy, 
and if all the kinetic energy were given up it would 
come to rest in the vane, which of course is not possible in 
practice. There must therefore be a residual velocity 
sufficient to allow the water to escape, and the energy that 
is lost is therefore proportional to the square of this 
residual velocity. It is the aim of turbine designers to 
keep the loss from residual velocity as low as possible, and in 
practice it may be brought down to less than 6 per cent, of 
the theoretical velocity due to the head of water acting on the 
wheel. For instance, for a turbine working under a head 
of 22 # 8 ft., corresponding to a velocity of free fall of about 
38*3 ft. per second, the water leaving the wheel flows away 
at a speed of about 9*2 ft. per second. The proportion of 
the initial energy passing off in the discharge is therefore 
9-2 2 /38'3 2 = 5-8 per cent. 

The force which a mass of water moving with a velo- 
city v in a given direction exerts against a compulsory 
change in the direction of its motion varies with the 
degree of change of direction imposed upon it, and 
increases with the angle through which the stream is 
diverted. This force may be simply illustrated by the 
tendency of a free hose pipe to straighten when water is 
first admitted to it. Other examples, equally simple, 
will doubtless suggest themselves to the reader. Another 
way of stating the same fact would be that the water 
has an acceleration imparted to it in a direction 
other than the course of the stream, and the force necessary 
to effect this acceleration is the pressure between the 
moving water and the walls of the containing vessel, or of 

N.S. G 



the curved vane along the surface of which the liquid 
flows. This is precisely the same force which causes fly- 
wheels to burst unless they are properly designed, for each 
piece of the rim of the wheel is constantly compelled to 
change the direction of its motion in space as it rotates 
about the axle, and the effects of this force have to be guarded 
against by the skill of the designer in proportioning the 
parts of the wheel in such a manner that the stresses 
induced will not overcome the tensile strength of the 
material. As the phenomena brought about by considera- 
tion of the action of centrifugal force are familiar in prin- 
ciple, the forces utilised in the 
water turbine may, at the outset, 
be more easily explained by deal- 
ing with the water flowing along 
the curved vane and exerting a 
pressure thereon in the same 
manner that the centrifugal force 
of a rotating body may be com- 
puted. In the simplest case, that 
of a vane conforming to the arc 
of a circle, and charged with a 
stream of water moving at a velocity v and entering and 
leaving the vane tangentially, we have an exact parallel 
to the ordinary problems in centrifugal force familiar to 
the engineer. In Fig. 24 the stream, with a cross- 
section A, is shown following the course of the vane, 
and discharging at right angles to the direction of entry. 
Even with the smoothest vane possible and the most care- 
ful adjustment of the nozzle it would be impossible to 
avoid considerable friction loss, with a consequent reduction 

Fig. 24. — Pressure exerted 
on curved vane by 
stream of water. 


of velocity, together with eddies and whirls which would 
mean a loss of energy. But for the moment these will be 
assumed to be non-existent, and consequently the velocity 
of discharge will be the same as that at the point of entry. If, 
as before, y be the unit weight of water (unity in metric units 
or 62*5 in British) the weight of water entering the vane 
per second will be A y v . At any point B on the vane the 
weight of water over a unit of vane area will be y A, and, 
as v is the velocity of the water, the centrifugal force, at 
a radius r, or the pressure upon the vane at that point will be 

y A v 2 

V = L • 

9 r 

This same reasoning applies to all points of the vane, so 
that it will only be necessary to integrate all these pressures, 
which act at all points normal to the surface of the vane, 
to obtain the resultant or total pressure in magnitude and 
direction. If it is desired to obtain the total pressure in 
the direction x y normal to the initial direction of flow, 
consider the total pressure exerted upon the semi-circum- 
ference of a cylindrical boiler in which the unit pressure 
is p. This is easily shown to be 2 pr, or the total pressure 
upon a quadrant is pr. The total pressure therefore 
exerted by the water would be 

7 . y A v 2 y A « 

P = pr = - x r = - — X r 2 . 

9 r g 

As the quadrant shape for the vane is symmetrical, the 
total pressure acting at right angles, or in the direction of 
the inflow, is also the same. It will be observed that this 
pressure exerted upon the curved vane is the same as that 
calculated for the pressure board placed normal to the direc- 
tion of flow. In either case the stream is diverted through 

g 2 


an angle of 90°, and flows off with undiminished velocity and 
with the same energy as it originally had, except such as 
would be lost by splashing in the one case and eddies or 
whirls in the other. If the stream be diverted through an 
angle (less than 90°) which would happen if the vane 
terminated at B instead of C (Fig. 24), the pressure upon 
the vane in the direction of flow at entry would be obtained 
by taking the difference in momentum per second between 
the incoming and outgoing stream in the required direction. 
The pressure would then be 

P = rAi xr _yAi ( ,cos0)= *A x * (i - cos o). 

9 9 9 

Thus if be 57° and the conditions the same as in the 
example given for the flat board, the pressure P would be 

P = 65*4 (1 - cos 57°) = 65'4 (1 - 0*54) = 30 lbs. 

As the vane is assumed to be stationary and the water 
leaves without loss of energy, it is clear that no work is 
done. When, however, the vane is in motion, work is 
done by the water. This movement is supplied by the 
rotation of the wheel under the action of the force, and the 
product of the force and the speed of the wheel give a 
measure of the useful work accomplished. 

Without attempting to discuss the intricate questions 

involved in the design of turbines, as regards the correct 

angles and shapes for the vanes under various conditions 

of service, it will nevertheless be expedient to point out the 

i^. nature of the problems which the turbine designer has 

ful adjre him. They are vastly complicated by practical 

avoid corons which render abstract theory difficult, if not 

} e, in many cases, to apply with certainty, but 


there are applications of theory which have become indis- 
pensable in this connection, and, with their limitations 
known to the skilled engineer, they become useful tools. 

The pressure of water upon a curved vane has been 
deduced on the assumption that the vane was stationary. 
But if the vane be put into motion the pressure is no longer 
the same. The velocity with which the water impinges is 
reduced if the vane has any motion in the direction of the 
impinging stream, and consequently the pressure falls. 
At the same time the absolute velocity of the water also 
falls, and therefore part of the original kinetic energy is 
transferred into work done against the resistances to the 
motion of the vane, i.e., to drive the machinery to which 
the turbine is geared. To keep the losses as low as possible 
in a turbine, the water must enter the spaces between the 
vanes without shock. To ensure that the loss occurring 
from this source shall be small, the stream must meet the 
vane tangentially so that there be no impact. This in 
itself is a difficult condition to comply with owing to the 
variable speed of the wheel, so that, should the angle of 
injection be correct for one speed, it would not be so for 
another. In practice it is usual to adjust the angle so that 
at full gate the turbine may be running with maximum 

In Fig. 25 the edge of a moving vane AB is shown, 
the motion being in the direction of the arrow, and the 
water enters in a direction along the guide vane CD. It is 
then deflected by the contour of the surface of the moving 
vane AB, and is finally discharged at the other end, having 
sustained a loss in kinetic energy by the work done in 
propelling the vane forward against resistances. Supposing 



that the velocity of the stream in the guides be v, it is clear 
that if the vane were held stationary the correct angle of 
incidence for the stream would be HAG, so that the water 
would enter the vane tangentially. If, however, the vane 
acquires a uniform velocity V, this angle must be altered so 
that the water shall still enter parallel to the edge of the 
vane, and thereby no energy shall be lost by impact except 
that due to the unavoidable parting of the stream by the 
edge of the vane. The water before it enters the wheel has 


Fig. 25. — Moving vane of 
reaction turbine. 

Fig. 26. — Moving vane of impulse 

a velocity v due to the head. It is important to observe 
that this velocity is taken relatively to a fixed point and is 
therefore absolute. The component of this absolute velocity 
in the direction of motion of the vane is v cos a, and as the 
vane is itself moving in the same direction with a velocity 
V, the relative motion of stream and vane is v cos a— V. 
Moreover the force acting upon the vane depends upon 
the difference between the velocity of the stream and 
that of the vane. The injection of the water without 


shock can only be effected by adjusting the angles to 
the ratio between v and V, both of which are subject 
in practice to independent variation. The speed of the 
wheel, unless under the control of a governor of excep- 
tional excellence, will vary with the load, and in small 
hydraulic installations a variable head will cause fluctuation 
in the initial velocity. The angle a, though unalterable in 
many turbines, in some designs is capable of being slightly 
changed through mechanism operated by the governor. 
The result of this is to alter the flow to the wheel as well as 
to change the incident angle. This method of governing is 
fully dealt with in another place. 

The fixed or normal angle for the guide vanes is in all 
cases that which best satisfies the velocity ratio for the 
speed at which the wheel is designed to run. Clearly the 
angle 6 which the wheel vane makes with the direction of 
motion must be of such a magnitude that, with the wheel 
at the normal speed, the water shall enter tangentially, but 
as 6 and a are connected together by a definite relationship, 
a variation in the one renders a new value for the other 
necessary if the condition of entry without shock is to be 
adhered to. It is of course impossible in turbines to vary 
the angle 0. The wheel is designed with the vanes 
permanently fixed at an angle with the tangent which the 
conditions of service enjoin. The vanes, either of cast iron 
or steel plate, in the one case cast with the wheel, in the 
other cast into the wheel, are not capable of alteration 
after the wheel is set to work. Any alteration therefore in 
the angle a is not accompanied by a corresponding change 
in 0, and there is consequently a loss of energy at the 
entry owing to the imperfect guidance of the jet into the 


wheel. As v cos a— F is the component of the relative 
velocity of the stream to the vane in the direction of motion, 
and v sin a is the component at right angles, by dividing 
the one by the other the tangent of the angle is obtained, 

(1) tan 

v cos a — V 
(2) or sin (v cos a - V) = v cos sin a 

which, expressed in another form, is 

F__ sin (0 - a ) 
v ~~ sin 

The angle 6 varies in practice from about 150° to 0°. 
With reaction turbines it is generally somewhat greater 
than 90°, but many wheels are designed with the vane edge 
at right angles, though 95° is a common value. It should 
be remembered that the angle is here measured from the 
line of motion. Some writers use the line at right angles 
to measure from, in which case the common value as given 
above would be 5°. It is, however, more convenient to 
refer to the angle as measured from the line of motion. 
For impulse wheels the angle is often much less than 90° 
(Fig. 26), and for the impulse tangential wheel known as 
the Pelton it is 0°. For each value of there is, according 
to the above equation, a corresponding value of a which 
may be calculated when the ratio V/v is known. It can be 
proved from initial considerations that the best velocity 
for the wheel is one-half that of the water, but in practice, 
owing to friction, and the necessity for keeping the efficiency 
high over a considerable range in speed, the actual wheel 
velocity varies considerably from the theoretical, especially 


with reaction turbines, and, though frequently less than 
one-half that due to the head, is also often higher 
than that which theory points to as the most desirable. 
Mr. G. E. Bodmer x gives a list of turbines in which 
the actual speed of the wheel is compared with the velocity 
due to the head as derived by experiment. Of 18 wheels 
operating under heads which vary from 5'1 to' 18*1 ft., this 
ratio lies between 0*461 and 0*770. Of 14 other wheels made 
by a single Swiss firm, and operating under heads varying 
from 8-2 ft. to 1804*5 ft., the ratio varies from 0*377 to 0*68. 
Of these wheels, one has a speed which is exactly half that 
due to the head, seven revolve faster, and six slower, than 
the best speed according to theory, though at these speeds 
they are presumably yielding a maximum efficiency. 

Taking 0*77 for example, as the ratio between V and v 9 
and assuming that 6 = 90°, the value of a would be obtained 
by substitution in the foregoing equation or 

- __ sin (90° — a) OCk0 

sin 90° 
With = 29° and V/v = 0*48 we have 

0-48 = Sm (29 o ^r- ••• sin (29° ~ a ) = 0*48 x 0*48 
sin JLv 

sin (29°- a) = 02304. 

Therefore a = 15° 42'. 

This is a value attained in impulse turbines, v being the 
velocity due to the head. For reaction turbines the 
entering velocity is less than that due to the head. If 
= 0, as in the case of the Pelton wheel, it will be found 
by substituting in the equation (2) that a = 0, and this 

1 "Hydraulic Motors, Turbines, and Pressure Engines," G. R. 


value is independent of the ratio of V to r, showing that 
whatever speed the wheel may run at the angle of injection 
is always the same for conditions of no loss of head by 
shock. This is self-evident from the tangential relationship 
of the wheel and jet. It is therefore the only form of wheel in 
which, for varying speeds, the condition of no loss by shock 
at the vane is observed, and were it not that it has other 
drawbacks it would, by avoiding a loss inevitable to other 
types of turbines with varying speeds, have an advantage 
over them in efficiency. 

The angle at which the water enters the wheel obviously 
cannot be the same throughout the cross section of the 
stream, as the cross section diminishes towards the wheel 
in radial turbines in consequence of the reduced diameter 
of the circle as the wheel vanes are approached. The vane 
angles are therefore at best a compromise, and as a 
consequence there is always in practice a loss at injection 
consequent upon the impossibility of constructing a wheel 
which shall fulfil the above conditions in all respects. The 
calculated angle is that which would be correct for a very 
thin stream of water approaching the wheel, nevertheless in 
fixed vane turbines the angles are laid down within 5 or 6 
per cent, of the calculated angle as found by assuming a 
ratio of velocities. 

The water having passed over the vane is discharged at a 
velocity relative to the vane which will be called t?i (Figs. 25 
and 26). The value of i m i would be nearly that of the velocity 
of the water relative to the vane at entry (which is c g on the 
diagram or u), the difference being due to the energy lost in 
overcoming frictional resistances and in internal friction of 
the particles of water upon each other, as shown by the 


formation of eddies and whirls. If the wheel be held station- 
ary, u — vi is small, and t\ becomes the absolute velocity of 
the water measured in the same manner as v — i.e., relative 
to a fixed point, and as the vane is fixed it will be convenient 
to refer to v\ as the velocity at exit relative to the vane. Now 
let the vane be put into motion by the force which the water 
exerts upon it owing to the enforced change from its original 
direction, and immediately work is being done upon the 
wheel, and the water consequently must lose kinetic energy 
and therefore must suffer a reduction in the absolute velocity 
with which it issues forth from the vane. Eeferring 
to Fig. 25, the absolute velocity of the water may be 
graphically obtained by the simple geometric construc- 
tion shown. If 0i be the angle that the edge of 
the vane makes with the direction of motion of the 
vane, and V and v x be laid off to a convenient scale, and 
parallel to the respective directions of motion, the third 
side of the triangle formed by these two lines will represent 
in magnitude and direction the absolute velocity of the 
water. This line is x y in the figure. Assuming for the 
moment that u = v u which means that the friction is 
nothing in the vanes, it may be seen by an inspection of 
the triangle that, whatever the angle Q\ may be, the absolute 
velocity as represented by the length of the line x y 
would become equal to v when F = 0, that is, when the 
vane is fixed. As V is reduced the line x y approaches v 
in length until the area of the triangle becomes nothing 
and vi and x y are coincident. In the practical design of 
turbines the angle 0i is so chosen that, with the assumed 
values of i'i and V, the water shall leave the wheel as nearly 
as possible at right angles to the direction of motion. As 


will be evident from the designs of turbines, this direction 
is approximately radial in the case of radial turbines and 
axial with parallel flow wheels. The exact attainment of 
this object renders the loss due to the energy escaping with 
the water a minimum, for the line x y is shortest when 
at right angles to the direction of flow, considering V as the 
variable and 6\ and %\ as constants. 

The losses of energy which are inevitable in the utilisa- 
tion of water power are divided between the turbine proper, 
the gates and controlling apparatus, and the pipe, penstock, 
or flume, which conducts the water to the wheel, together 
with that carried away in the discharge. For the present 
we shall alone consider the losses in the turbine and 
discharge, so that the efficiency of the wheel is represented 
by the ratio of the power developed in the shaft of the 
turbine to that entering with the water into the guide 
passages. If P be the foot-pounds of energy per second 
exerted at the shaft, and W the weight of water in pounds 
entering the wheel per second, E s the efficiency is 

F- P 

Both P and W h may be expressed in horse-power by 
dividing by 550, but of course the ratio between them remains 
unaltered provided both are expressed in the same units. In 
hydraulic problems generally the rate of expenditure of 
energy is directly implied, because the velocity of water 
enters into the conditions. Thus the product of W and h at 
once expresses the power as a definite number of foot-pounds 
expended in a stated time, and by dividing by the usual con- 
stant it may be directly rendered into horse-power. It is not 
possible to lay too much stress upon the distinction between 


energy and the rate of expenditure of energy or power, for 

many writers employ a loose method of dealing with the 

subject of energy generally, to the confusion of those who 

are endeavouring to understand the relationship between 

the two. As we are here dealing with a known mass of water 

at a stated velocity or head the element of time necessarily 

comes in, and therefore the results are in power-units, 

generally foot-pounds per second. 

The loss of W h — P foot-pounds per second occurs both 

within the turbine and in the velocity with which the water 

is discharged therefrom. The latter loss is easily ascer- 

1 Wv\ 
tained, being 5 - . By deducting this from the total loss, 

the other losses, which are not directly ascertainable, iuay 
be estimated. The internal losses, due to impact and 
friction of the water on the vanes, eddies, and vortices in 
the fluid itself, and friction of the shaft in the journals and 
thrust-bearing, are the remaining sources of loss which 
complete the balance between losses and power delivered to 
the shaft on the one hand, against the total power received, 
which in some way must be accounted for either as a loss 
or as useful work on the shaft. 

The energy stored in the water where it enters the wheel 
may be partly in the form of kinetic and partly in potential 
energy. As a general investigation of the losses of energy 
does not involve a consideration of the relative amount of 
each kind, but rather the type of wheel, this will be reserved 
until the two different types of wheel are considered 
separately. As to the relative magnitude of the various 
sources of loss in a turbine, take the case of a wheel passing 
3,200 cu. ft. per minute and subjected to a head of 12*2 ft. 


(under which head the velocity of freely falling water is 
28 ft. per second), and that after passing through the wheel 
the water is discharged at 7*1 ft. per second, the brake-horse- 
power as measured on the shaft being 51*5. The loss of 
power due to the friction of the water within the wheel 
together with the journal friction of the rotating shaft 
would be the difference between the total loss and that- 
carried away in the discharge. 

Approximate loss 
in per cent. 

m . . 1U • , . 3,200 X 62-5 x 28 2 

(1) Available power m water is ^^2"^3p00 
. = 73-8 h.-p. 

(2) Total power lost = 73*8 - 51'5 = 22*3 h.-p. . 30 

(3) Power lost in discharge = j x ^ x ^^ 

= 4-7 h.-p 6'4 

(4) Frictional losses of all kinds, 22*3 — 4*7 

= 17*6 h.-p 23-9 

(6) Efficiency of wheel = ^ .... 69*8 


Meissner is quoted by the before-mentioned authority, 

who allocates the various friction losses comprised under (4) 

into three classes, as follows : — 

Per cent. 

(1) Sum of losses by friction and impact in 

guide apparatus and wheel . . 10*5 to 14 

(2) Loss by leakage through clearance space 

between the guide vane ring and wheel 4 # 5 to 4*5 

(3) Friction in air and water of bearings 2 to 3*5 

Total losses other than residual 17 to 22 

(4) Loss due to residual velocity . . 6 to 6 

23 to 28 


Other authorities give different results than these. The 
residual velocity may be reduced so that the loss under this 
head is less than 6 per cent., but it is usually close to this 
figure. The above figures are for a reaction wheel which, 
working entirely submerged, renders the friction loss 
greater than for a turbine which encounters only air 
•resistance as it revolves. 


various types of turbine. 

Reaction Mixed Flow Turbine as Used for Low Falls. 

The illustration shows a Francis turbine arranged for 
low falls. This wheel differs but slightly from that employed 
in the low fall plant which is described in Chapter VII. 
The guide vanes are hinged and may be turned through 
an angle sufficient to completely close the apertures between 
them against the entrance of water to the wheel, or they may 
be placed so as to afford a full opening for the admission of 
water. In Fig. 28 they are shown in full lines arranged for 
the admission of water to the wheel, but when turned into 
the position shown by dotted lines they act as an ordinary 
gate to completely shut off the water. As the angle of 
entrance to the vanes is consequently subject to alteration, 
the efficiency of the wheel suffers owing to the loss of energy 
by shock at entrance when the water is admitted at an 
unfavourable angle. The movement of the guide vanes is 
effected through the vertical rods A and B (Fig. 27), which are 
rotated by the sector bolted to the I joists which support the 
bearing C. This sector is moved by a worm, which in 
turn receives motion from the governing arrangement. 
The regulation is necessarily performed against great 
resistance. The movable vanes possess considerable 
inertia, and if the water carries impurities, the pivots 



are liable to become choked by foreign matter, which 
adds to the friction and renders sensitive governing a 

Fig. 27. — Mixed flow turbine as used for low falls. 

matter of difficulty. The submerged mechanism cannot be 
artificially lubricated, and cleaning can only be done by 
draining the pit, which is not always possible, where the 






Fig. 28. — Movable guide 

turbine is in constant use. The weight of the turbine is 
carried by a thrust bearing at the top of the shaft above the 
gear by which the power is usually taken off to the horizontal 
shaft. This arrangement of turbine is especially suitable 

for falls up to 10 feet. The cast 
iron ring at the bottom is em- 
bedded in the concrete of the 
arch which divides the head from 
the tail race, or it may be sup- 
ported upon a grillage of steel 
embedded in concrete. In some 
arrangements a wooden floor is 
substituted, the spaces between 
the boards being caulked with oakum, but the weight of the 
guide ring should nevertheless be carried by steel beams, 
and to preserve them from corrosion they should be pro- 
tected from the water by concrete well packed about them. 

Reaction Mixed Flow Turbine as Used at Niagara. 

The arrangement of a 5,500 h.-p. turbine, as installed 
at Niagara, is shown in the two next illustrations. As this 
famous installation is one in which the principles of 
turbine construction have been combined to form a highly 
successful and efficient plant, it may be used as an illustrative 
example of the way in which the engineer surmounts the 
difficulties which oppose his skill in designing water power 
plants in general, and the type of turbine which was adopted 
after careful consideration represents one of the best forms 
of wheel of the class. 

The illustration (Fig. 29) is a vertical section through the 
shaft of the turbine, including the draft tube which is forked 



Fig. 29. — Niagara mixed flow turbine, 5,500 h.-p. 

beneath the wheel chamber for the purpose of allowing an 
uninterrupted flow through the tail race tunnel, as otherwise 




Fig. 30. — Niagara turbines. 

the tube passing through the water would offer obstruction. 
The two branches of the tube are brought down on each 
side of the tail race and discharge their contents beneath 


the surface of the water in the race. The penstocks which 
convey the water to the wheel are shown in the second 
illustration to the left of the shafts, and by means of a 
quarter-turn bend the water is admitted within the casing 
A B which encloses the wheel C D (the letters are placed on 
the vanes) (Fig. 29) . The guide vanes E F, which completely 
surround the wheel, admit the water at a fixed angle to 
the wheel. The runner, which is cast entirely of manganese 
bronze, is cone-shaped, so that the water is deflected down- 
wards into the draft tube. The principal dimensions of 
this turbine and setting are as follows : — 

Diameter of wheel (runner), 5 ft. 4 in. 

Outside diameter of turbine casing, 3,810 mm. (12 ft. 6 in.). 

Uniform diameter of penstock from point of exit at canal 
to turbine casing, 2,285 mm. (7 ft. 6 in.) 

Approximate height of centre of turbine above water in 
tail race, 6 m. (19 ft. 8 in.). 

The normal speed of the wheel is 250 revolutions per 
minute, and under the fall of 44*5 metres (146 ft.) it 
develops 5,500 h.-p. 

The turbine, being a reaction wheel, works with all parts 
of the casing, wheel, draft tube, and penstock full of water. 
The draft tubes dip below the surface of the water in the 
tail race, and thereby the suction becomes effective. The 
wheel is controlled by a circular bronze gate which is 
interposed between the ring of guide vanes and the runner. 
This gate is moved up and down in the direction of the 
shaft by the governor located in the dynamo room 180 ft. 
above. Though the gate may be in such a position as to 
partially screen the wheel from the water, the latter is 
nevertheless still completely full whatever the position of 


the gate may be as determined by the governor. The 
spaces behind the gate become filled with stagnant water, 
but no appreciable amount of air is present at any place 
within the casing. The local conditions required that the 
dynamos should be located some 130 ft. above the turbines, 
which necessitated a very long shaft. This shaft is made 
of steel tubes 965 mm. (38 in.) diameter except at intervals 
where bearings are located. It is reduced at these places 
by cone-shaped castings to a smaller steel shaft. The 
thrust bearing is placed on the top deck, but to relieve this 
of as much pressure as possible, a large part of the weight 
of the turbine, shaft, and rotating field of the electric 
generator is balanced by the upward pressure of the water 
against a disc G H, shown below the turbine in Fig. 29. 
Water from the penstock is admitted by a pipe to the 
space below the disc, and the upward reaction almost balances 
the weights. A series of stuffing rings on the periphery of 
the disc prevents undue leakage, and air is prevented from 
entering the suction tube by the cover plate of larger 
diameter than the disc. The upward pressure exerted by 
the water is about 60 tons, but there is a slight difference 
between this and the weight of the revolving parts so that 
there may be always a small resultant pressure against 
the thrust block. The weight of the circular gate and 
mechanism is balanced so that the governor has only to 
overcome the inertia of the mass in the process of regula- 
tion. The peripheral speed of the outside of the runner is 
about 70 ft. per second, that of the water under a free 
fall of 146 ft. being about 97 ft. per second, so that the 
turbine speed is 72 per cent, of the velocity of free fall. 
Since this turbine was installed a wheel of 10,000 h.-p. 


has been designed, which is the largest unit in the 
world at the present time. 

Girard Turbines on Horizontal Shaft with Partial 

The accompanying illustration (Fig. 81) of two 72-in. 
horizontal Girard turbines is reproduced by the courtesy 
of the manufacturers, Messrs. W. Gunther & Sons, Oldham. 
One of the turbines is shown with the casing removed to 
disclose the runner vanes. The water enters through the 
flanged openings and is directed against the wheel from a 
series of vanes which are below the floor line, and which 
extend over a small arc of the circumference so that the 
turbine works as a partial admission wheel. The discharge 
into the tail race is at the lowest level of the wheel. 
These wheels drive a textile mill through ropes, the pulley 
for which is upon the shaft between them. Each of them 
yields 500 h.-p. under a fall of 520 ft. (158*5 metres) and is 
72 in. (1*83 metres) in diameter. These Girard turbines are 
most efficient when working under comparatively high falls, 
and may be compared with the Pelton wheel as being used 
under conditions favourable to both types. They are 
governed by an independent governor, not shown in the 

The Pelton wheel, which was first used in America, is 
a form of Girard or impulse turbine in which the vanes or 
buckets are arranged in such a manner that a jet of water 
from a nozzle is directed in the plane of the wheel 
tangentially to the circle described by the mean radius of 
the buckets. The buckets are constructed of cast iron, 









cast or pressed steel, and are made double, so that the jet 
of water, impinging on the central edge, is deflected in both 
directions. The angle through which the water would be 
deflected, were the wheel held stationary, would be almost 
180°, as the outer lips of the buckets are turned back so 

Fig. 32. — Jet issuing from nozzle at high velocity. 

that a tangent to them has only a slight inclination with 
the direction of the jet. With the wheel in motion the 
direction that the water takes on leaving the bucket is more 
nearly axial ; but if the lips of the buckets were turned com- 
pletely back the water would be discharged in the plane of the 
wheel, and the direction would not be affected by the speed. 


The minimum absolute residual velocity, corresponding to 
the highest efficiency, is zero when the speed of the wheel 
is one-half that of the absolute velocity of the jet. Such a 
condition is impossible in practice, as the water must be 
endowed with a residual velocity to clear the buckets. 
Especially for mining districts and in outlying places where 
water is plentiful and the cost of transportation and erection 
of a turbine renders it inexpedient to install a more elaborate 
plant, the Pelton wheel is a very useful form of motor. 
It is constructed in small sizes for rough work on a self- 
contained frame, and the only works necessary for the 
installation are the water pipe and a trough for the dis- 
charge. The range of head for which these wheels are 
suitable is from 50 ft. upwards, though at this minimum 
limit other forms of wheel become serious competitors. 
Even at 100 ft. it is very doubtful if this wheel can be con- 
sidered to be good engineering, unless efficiency is of little 
importance, for the claims of very efficient reaction turbines 
have to be argued away to justify their use under such 

The most powerful wheels of this type that have been 
built are those of the Eio das Lazes hydro-electric station 
of the Eio de Janeiro Tramway Light and Power Company. 
These wheels are 9,000 h. -p. each, and they operate under a 
head which ranges from 950 to 1,000 ft. Each wheel is 
supplied by four needle nozzles, and they run at 300 revolu- 
tions per minute. The efficiency is estimated at 82 per 
cent. Each wheel receives water through a 36-inch welded 
steel pipe which varies from 0*4 to 0*7 in. in thickness, 
depending upon the head. (See Appendix C.) 

The shape of the nozzle from which the water is 










discharged is important, as it is essential that there shall not 
be any dispersion of the jet. The water should issue in a 
solid jet as shown in Fig. 32, which is a photograph kindly 


placed at my disposal by Mr. H. E. Warren. It will be seen 
that the jet suffers considerable contraction in area close to 
the mouth of the nozzle. 

The wheels manufactured by Messrs. Gilbert Gilkes & Co., 
Ltd., Kendal, range in size from 6 in. up to 21 ft. in 
diameter, and Fig. 88, for which I am indebted to the 
firm, shows the construction of one of the largest. 
This 21 ft. wheel, designed to develop 200 h.-p. with a 
98 ft. fail at 36 revolutions per minute, drives tin plate 
rolls by direct connection. The large diameter results in 
slow speed so that gearing is avoided between the motor 
and machine. The smaller wheels are not as efficient as 
the larger, nor is the same wheel as efficient under low as 
under high heads. Two wheels, one 8 in. diameter and 
the other 72 in., will have a difference in efficiency of 
almost 2 per cent, under the same low head, while a 
wheel of the latter size will have a distinctly better 
efficiency under 700 ft. head than, say, 200. For extremely 
high heads, such as that of the Lake Tanay installation 
or the Manitou plant (3,018 ft. and 2,417 ft. respec- 
tively), the efficiency is somewhat less than that attained 
with moderate falls owing to the enormously increased 
friction losses. There is consequently a medium head, 
which experience shows is about 850 metres (1,148 ft.), at 
which a wheel of this type will give a maximum efficiency 
of about 80 per cent. The diameter of the wheel should 
be as large as possible to attain the best results, for the 
buckets are placed more advantageously in the stream, as 
they move with less angularity to the direction of flow. 
For heads of 200 to 1,500 ft., with a freedom of choice as 
regards the diameter of the wheel, it should be possible to 


obtain an efficiency at full load of 75 to 77 per cent, with these 
wheels when constructed by firms of repute. It is very doubt- 
ful if efficiencies exceeding 77 per cent, are often attained by 
them, though extravagant claims are made by some American 
makers. The difficulties of testing wheels render statements 
concerning efficiency safe from confirmation. 

Testing Turbines. 

The recorded tests upon hydraulic turbines are very few 
considering the thousands of wheels which are in continual 
use throughout the world. Even though efficiencies and 
output are specified by the purchaser's engineer when 
ordering a turbine, but few owners care to subject themselves 
to the expense of a test made by experts under scientific 
conditions, to prove the worth of the turbine when installed. 
If the purchase was a steam engine, a pair of indicators, 
gauges, and perhaps a Prony brake, would suffice to obtain 
accurately the characteristics of the motor, but the apparatus 
required for testing a turbine is more elaborate, and the 
expense entailed is much greater. 

The late Mr. J. B. Francis for many years conducted 
elaborate tests upon turbines which still remain the most 
valuable information on the subject, and the records of the 
Holyoke testing station are especially interesting in view of 
the variety of wheels which were subjected to critical 
examination. As far as the writer is aware, this permanent 
testing station upon the Connecticut River at Holyoke, 
Massachusetts, is the only thing of the kind in the world, if 
we except the hydraulic plants which usually form part of 
well-equipped mechanical laboratories in our educational 
isntitutions, but which are necessarily limited for the purposes 


of testing. The Holyoke testing flume is arranged so that 
a wheel may be fitted into it, supplied with water under a 
prescribed head within the limits of fall of the river, and 
the power measured by a brake. The amount of water 
discharged is measured accurately, and, from first to last, 
valuable information regarding the wheel is obtained. The 
flume was originally designed for testing wheels for a local 
company which controlled the power rights upon the river, 
but soon it became a recognised testing station throughout the 
country, and the manufacturers of turbines resorted to it to 
prove their wheels. 

The tests applied to a turbine are similar to those to 
which other prime movers are subjected, the principal one 
being efficiency, or ratio of power developed to power supplied. 
This, in a turbine as generally understood, is the ratio of the 
brake horse-power, as measured on the driving shaft, to the 
theoretical power of the water falling through a height 
equal to the head. As the power in the falling water 
depends upon the flow, it is essential that an exact quanti- 
tative measurement be made of the water passing through 
the wheel. The necessity for such a measurement forms 
one of the chief obstacles to testing, as it involves weirs and 
special appliances which are not often readily available. The 
power developed upon the shaft of the turbine may be 
measured by a mechanical brake, of which there are several 
kinds, or, if there be an electrical generator with known 
efficiency, it may be directly measured electrically. As 
nearly all electrical engineers require shop tests of generators 
to be made by the manufacturers, the efficiency is generally 
known with sufficient exactness from the curves supplied 
from the testing room. These curves show the efficiency 


for different percentages of load, and from them the power 

required to drive the generator for a given output may be 

readily obtained. Thus if W be the output in kilowatts of a 

generator coupled to a turbine, as measured directly by an 

ammeter and voltmeter, and e be the efficiency of the 

generator, the power required in horse-power on the shaft 

of the turbine will be p = 7 r=Tz- > and if P be the 

theoretical-horse power in the water as calculated from 
measurements on the flow, and E the efficiency of the 
turbine, we have : — 

F = £- W 

P 0-746 X e x P. 

As an example, a 800 kw. electric generator, directly 
coupled to a turbine, has an efficiency at full load of 89*5 
per cent. The horse-power necessary to drive it so as to 
obtain an output of 800 kw. is therefore 

_ 800 __ 

^"0-746 x 0-895 ~ 44y * 

The turbine passes 180 cu. ft. of water per second, works 
under a 28 ft. fall, and the theoretical horse-power is 

_ 180 x 62-5 x 28 _ 
F ~ 550 - 57d ' 

The efficiency of the turbine is therefore 

V 449 „ . 

ji = — = 78-4 per cent. 

The efficiency of the entire unit is the product of the 
efficiencies of both turbine and generator or 78*4 X 89*5 = 



70*2 per cent. An efficiency of 76 per cent, can be obtained 
from low fall turbines at full load, i.e. at best speed. Referring 
to the installation described on p. 135, the full load efficiency 
of the wheel is 76 per cent., of the electric generator 90 per 
cent., and the loss in transmission from the generating 
station to the place of distribution of the current 7*2 per 
cent. Allowing 10 per cent, loss in the gearing and shafting 
between turbine and dynamo, the efficiency of the installation 

Fig. 34. — Prony brake. 

would be :— 0-76 X 0*90 X 0'90 X 0'92'8 = 57 per cent., 
i.e. more than half of the actual energy in the falling water 
is available at the distributing board one quarter of a mile 
distant, when the turbine is working at full load. 

The simplicity of the electrical method of obtaining the 
efficiency of a turbine cannot always be hoped for, and if 
the wheel is to be used for other machinery, the output must 
be measured by some form of absorption dynamometer, the 
simplest type of which is the Prony brake illustrated in 
Fig. 34. 


It consists of a cast iron wheel A with a hollow cored rim 
through which a constant stream of cooling water is made to 
flow, B and C being the pipes connecting the rim to the 
hollow shaft, through the end of which the water is admitted. 
As all the power is converted into heat at the periphery of 
the wheel, an ample supply of cooling water is essential by 
which the heat may be carried off. The periphery of .the 
cast iron wheel, which is turned true, is surrounded by a 
series of hard wood blocks D, and these are pressed against 
the wheel by the wrought iron clamp bands which may be 
tightened by the screw and hand wheel E. If the wheel is 
caused to revolve in the direction of the arrow it will tend 
to lift weights placed in the scale pan F and to stretch the 
spring G, the tension of which may be measured on the 
spring balance dial. To maintain the arms H and J in 
their original position against the turning effort, it would 
therefore be necessary to add weights to the scale pan 
F until the tendency to turn, as produced by the friction 
between the rim and wooden blocks, is balanced. When 
this condition is attained, the weights and tension in the 
spring together with the speed of the wheel give a measure of 
the power, which may be readily deduced. For if W be the 
loads in pounds necessary to hold the balance against the 
turning moment, the power developed for N revolutions 
per minute is : — 

n p __ W x 2 7T r N 
~" 33,000 

The measurement of the power does not involve the size 
of the brake wheel A, but for brakes to absorb 200 h.-p. up 
to speeds of 300 revolutions per minute it would be about 
3 ft. 6 in. to 4 ft. in diameter, and the distance r 

N.S. I 


(0 J = H), or effective radius at which the loads are 
placed, would be about 4 ft. 6 in. 

Example. — A turbine running at 198 revolutions per minute 
delivers power to an absorption dynamometer in which 
r = 4 ft. 6 in., and the loads are 487 lbs. Therefore 

„ D 487 X 2 w x 4-5 X 198 _ QO . 

H " P - 33,000 82 6 - 

These dynamometers are unsatisfactory under rapidly 
fluctuating loads, for the beam becomes unsteady and 
oscillates. Moreover the wheel must run very true, or else 
a correct reading cannot be got. Plates of sheet iron 
screwed to the sides of the wooden blocks and overlap- 
ping the rim of the wheel are usually fitted to prevent 
motion parallel with the shaft. This dynamometer is 
similar to the electric generator in that the power is 
absorbed, but there are other forms in which the power is 
measured and transmitted, and which may therefore be 
temporarily applied to a turbine at work, but, compared to 
the absorption type, they are seldom employed. 

A new form of power-measuring device, by which the 
power passing through the shaft of a marine turbine may 
be measured, depends upon the twist which a shaft 
experiences when power is transmitted through it. By 
means of a delicate electrical appliance this twist in a long 
shaft may be measured, and the power calculated. It is, how- 
ever, necessary that a considerable length of shaft be taken 
to show the minute torsional deflection, and as long shafts 
are not often required in hydraulic turbine installations it 
is doubtful if it has any application to this department. 1 

1 For an account of the Denny and Johnson Torsion Meter, see 
Engineering, April 7th, 1905. 



That the high efficiencies claimed by turbine manu- 
facturers are attained by some of the leading firms, the 

200 fLP.Turbine 



'/a 'A % 'M % -?4 Va / 

Fig. 35.— Tests on 200 h.-p. turbine. 

records of actual tests show. The Swiss firm of Messrs. 
Theodor Bell & Co., Kriens-Luzern, have supplied the 
writer with some records, from which the curves shown in 
Fig. 85 are reproduced. 

i 2 






The two curves illustrate the variation in the efficiency of 
the wheel when working (1) at the most favourable speed ; 
(2) at the constant normal speed. The figures on the 
curve are the revolutions per minute. It will be seen that 








/_ — 1 









W -J 

o 1 





Gate Opening 100 

Fig. 36.— Tests on Pelton wheel. 

an efficiency of 88'5 per cent, is attained at the most favour- 
able speed between a gate opening of 0*625 and 0*75, while 
for the same gate opening at the constant normal speed it 
is almost 1 per cent, less, and for small gate openings the 
difference is more marked. The maximum efficiency is, in 



this case, not coincident with full gate, but the normal 
working of the turbine is between 0*625 and 0*75 full gate, 
and slight departures therefrom effect the efficiency very 
little. Electrical driving requires a constant speed, so that 
it is impossible to allow a wheel to revolve at the best speed 
for all positions of the gate. The lower curve would there- 
fore be the efficiency curve in such cases. 

The efficiency, load, and water supply to a Pelton wheel 

Per cent, of full gate opening. 

per cent. 

per cent. 

per cent. 

per cent. 

per cent. 

(1) Fall in metres 






(2) Flow in litres per second 






(3) Theoretical horse-power 






(4) Electrical output, kw. . 






(5) Efficiency of generator, 
per cent. 






(6) Horse-power of turbine 






(7) Efficiency of turbine, 
per cent. 






constructed by Messrs. Theodor Bell & Co. are shown in 
Fig. 36, and the table gives the same particulars, from which 
the curve is plotted. It will be seen that the wheel maintains 
an almost constant high efficiency from a gate opening of 
60 per cent, to full gate, and the horse-power of the 
turbine increases almost in direct proportion to the flow, 
as may be seen from the straight line showing the load. 
The power developed is proportional to the discharge 
as shown by the straight line marked " water," which gives 



the discharge in litres per second. The maximum efficiency 
of the wheel is attained with a gate opening of 60 per cent., 
and the combined efficiencies of turbine and generator, 
80*4 x 94 = 75*6, represents the over-all efficiency of the 
installation from theoretical hydraulic power to electrical 
energy put into the line by the dynamo. Line (3) in the 
table shows the hydraulic power, which is directly derived 
from (1) and (2) by dividing their product by 75 (75 kg.-m. 








&> 3/10 4/to */to *//0 VlO VlO S/jo I 

Fig. 37. — Tests on double Francis turbine. 

per second in a, force de cheval). The output of the generator 
in kilowatts is given in (4), and the horse-power of the 
turbine is obtained by dividing the equivalent horse-power 
in line (4) by the efficiency of the generator. The force de 
cheval is equal to 735*5 watts, thus, taking the electrical out- 
put at 60 per cent, gate opening, which is 1,134 kw., this is 
equivalent to 1,134/07355 = 1,543 h.-p. 

A series of tests were made by Professor F. Prasil upon a 
turbine constructed by Messrs. Escher, Wyss & Co., which 


show what may be obtained from a double Francis turbine 
with horizontal shaft supplied with water under a head of 
about 6*7 metres (22 ft.) and yielding a power of 200 h.-p. The 
power was measured by an absorption dynamometer in the 
form of a Prony brake, one metre in diameter and 25 cm. 
wide, and the flow was obtained from velocity meter records. 
The meters were immersed in the water at various points 
across the section of the channel and the mean flow was 
calculated from the readings thus obtained. The constants 
for the meters formed the subject of previous inquiry, and 
were determined with apparently satisfactory accuracy. 
From the various tests it was found that the efficiency 
of the wheel, when approximately 200 h.-p. was being 
absorbed by the brake, was 85*23 per cent. The mean 
speed was 141 revolutions per minute and the mean head 
6-67 metres (21*9 ft.). The curve (Fig. 37) shows the 
variation in the efficiency with the gate opening. 



To cover all the varieties of construction works for water- 
power plants that have to be adopted to suit local conditions 
would be impossible within the limits of the few pages at 
our disposal ; consequently a few of the more general and 
common features of the construction of works common to 
the majority of plants can alone be dealt with. As 
nearly all the small water-powers, especially in 
England, are obtained by damming up a river so as to 
produce a fall, the construction of dams will perhaps 
repay a little ^attention, as an improperly constructed 
dam may be a constant source of trouble, not to say 
of danger. 

The design of high dams involves calculations based 
upon assumptions as to the nature and incidence of the 
stresses set up by the water pressure. These assumptions, 
as recent discussions of the subject show, are not universally 
accepted, and may be at variance with what actually occurs 
in a mass of material acted upon by conjugate forces. Some 
engineers, whose authority is unquestioned, contend that 
the accepted principles for the construction of dams are 
faulty, and that the factor of safety ascribed to the section 
by current principles of design does not exist in the struc- 
ture, Into these and kindred hypotheses, upon which no 


direct proof is forthcoming one way or the other, we cannot 
enter ; suffice it to say that many high dams all over the 
world have not given way, though they are designed upon 
principles which some would, in the light of experimental 
evidence, condemn as faulty, if not as actually 

As a rule dams for impounding small heads of water 
are constructed very much wider and heavier than any 
accepted theory of stability would pronounce to be suffi- 
cient. Leakage, liability to destruction by floods, and 
possibly the necessity for a right of way along the top, 
determine in many cases the width rather than the resist- 
ance to overturning by hydrostatic pressure. The question 
of leakage is especially important, and the cross-section 
may be considerably modified from that which theory 
would assign, lest there be insufficient width at the base 
to prevent the seepage of water down-stream, for leakage, 
once begun, quickly grows, and involves the speedy dis- 
integration of the material, especially if the facing of the 
dam be backed by earth or rubble. 

It can be easily shown that, if a vertical wall sustains a 
pool of water, thus acting as a dam, the total pressure of 
the water on a vertical strip of unit width, irrespective of 
the extent of the pool up-stream, is half the depth of the 
water in feet multiplied by the weight in pounds of a cubic 
foot of water multiplied by the area of the strip. For 
example, a wall 5 ft. high sustains water, the level of the 
water being at the top of the wall. The total pressure 
on a strip of the wall 1 ft. wide is therefore \ X 5 X 
62*5 X 5 = 78125 lbs. Expressed as a formula, in which 
I is the length of the strip along the wall, h the head of 


water, and y the weight of the cubic unit of water, the 
total pressure — 

P = ± h x y x I h = 1 1 h\ 

The total pressure is, therefore, proportional to the 
square of the head of water, so that the tendency for a wall 
of uniform section to be overturned by the water pressure 
increases rapidly with the height of the wall. If h and I 
are expressed in metres, and P is measured in kilogrammes, 
since one cubic metre of water weighs 1,000 kgs. 
P = 500 I h 2 . 

The total pressure upon the wall can be resolved into a 
single force which acts at two-thirds the total depth of the 
water, measured from the water level downwards. If the 
dam were composed of a solid mass capable of being over- 
turned about the down-stream edge or " toe," this force 
would be considered alone. As, however, dams are made 
up of materials cemented together and capable of being 
broken along vertical and horizontal planes, a correctly 
designed dam must be proportioned so that it will resist 
splitting along any horizontal plane, and as the pressure 
of the water increases from the top downwards the cross- 
sections therefore must also increase, and this gives rise to a 
curved outline on the down-stream edge. This curved out- 
line can be arrived at by calculation to give a desired factor 
of safety; but dams are never constructed to the exact 
mathematical curve for structural reasons; and for low 
dams, such as the development of small water-powers 
require, purely arbitrary sections are chosen. It is not 
necessary to follow the theory of the design of structures 
of this kind here, which only apply to high dams where a 


saving in the weight of masonry is specially important. 
For low dams structural conditions render a departure 
from any theoretical plan necessary, and it is with such 
that we especially deal at present. It may, however, be 
noticed that dams are of two kinds — those which offer 
resistance to the water by their dead weight alone and 
adhesion to the foundations, and those which are arched 
up-stream so as to develop resistance by a thrust at the 
abutments on each bank. This latter principle is only 
utilised for high dams, and mainly on rivers with precipitous 
banks to which the arch thrust can be transferred. For 
low dams the gravity principle is alone used, and it is this 
kind of structure that we are now considering, in which 
the resistance required against displacement is provided by 
the weight and adhesion of masonry or earth to the founda- 
tions, which forms a homogeneous mass when carefully put 

As so much depends upon the nature of the material 
used, whether earth or stone, which varies in one place 
from another, and of the class of cement and method of 
gauging, it is not possible to lay down any rules which are 
applicable in all cases. 

Dams may be classified as follows : — 

(1) Earth dams. 

(2) Earth with masonry facing. 

(3) Masonry, which may either be ashlar, or rubble with 
a facing of cut stone. 

The earth dam is perhaps the oldest of all forms of dam, 
and is, by reason of its comparative cheapness and facility 
of construction, becoming a common form of structure for 
reservoirs designed to impound water at low heads, At 


the same time it has been employed for comparatively high 
heads, as for instance at the Yarrow dam of the Liverpool 
waterworks, which is some 90 ft. high. In the case of this 
dam the foundations had to be carried 97 ft. below the 
original surface to obtain a layer upon which the super- 
structure could rest which would be entirely impermeable 
to water. Such dams are constructed of clay "puddle," 
which has to be tamped down hard, so that the mass 
may be impervious to water. Dry clay will absorb con- 
siderable quantities of water, which varies according to 
the nature of the soil, and which is estimated by different 
authorities at 88 to 60 per cent, of its weight. 

Mr. Burr Bassell * states that " there are in use to-day 
22 earth dams exceeding 90 ft. in height, and twice that 
number over 70 ft. in height. Five of the former are in 
California and several of these have been in use over 
25 years." Furthermore, he avers that "he fails to 
appreciate the reason for limiting the safe height of earth 
dams to 60 Or 70 ft." The earthquake in California (April, 
1906) brought out the superiority of the earth dam to with- 
stand shocks of great severity, for though the great fault line, 
which formed a plane of shear in a N.W.-S.E. direction, 
passed directly across a high earth dam, the structure 
was not severely injured, as it would have been if it had 
been constructed of masonry, for in that case the fracture 
would have rendered it ineffectual for its purpose. 

The form of an earth dam, as usually constructed, is 
that of a truncated triangular section with a slope of 
about two to one on both faces, but as the requisite 
degree of slope varies with the quality of the material 

1 " Earth Dams " by B. Bassell. 


(being naturally steeper for a stiff clay), the cross- sections 
of such dams display a great variety of shapes depending 
upon the caprice of the designer. The surfaces of earth 
or puddle dams are best covered with a pitching of stones 
and may be covered with grass, as in the retaining banks 
for reservoirs, though in this case they form only part 
of a composite embankment to retain the water. The 
nature of the material is an important condition to the 
success of earthen dams, for some clays will not pack 
sufficiently hard to prevent the seepage of water through 
them. Engineers are not agreed as to the best qualities 
to be looked for in material for an earthen dam. It is 
suggested by some that a certain proportion of sand in the 
earth is beneficial, and earthen dams have been constructed 
with mixtures of earth and sand containing 20 per cent, 
of the latter ingredient. 

Masonry Dams. 

Notwithstanding the extra cost of stone dams over those 
constructed of clay, their increased durability and com- 
parative immunity from destruction by floods or freshets, 
besides the valuable feature of providing a spillway where 
required, render them the best form of structure for hold- 
ing back a few feet of water for a small plant. Neglecting 
for the moment the adhesion or anchoring of a masonry 
wall to a foundation, and supposing that the dead weight of 
masonry alone were to be employed to resist the hydro- 
static pressure, it is easily shown that a rectangular wall 
with a height of less than 2 # 8 times the width will withstand 
overturning. To prove this, take 165 lbs. per cubic foot for 
the approximate weight of granite or limestone masonry, 



and if d is the width of the wall (Fig. 88) and h the head 
of water sustained by it, the overturning moment is, for 
each unit of length of wall — 

M =^ x fc 2 x ~=10'4/i 8 

The moment of resist- 
ance offered by the dead 
weight of the wall to over- 
turning about the down- 
stream edge A is, for a unit 
j> length — 

Mi = 165 X d X h x ^ 


A = 82-5 d? h. 

Fig. 38.-Overtu™ingby hydrostatic Equating thege tw0 mo . 

ments we have — 
10-4 h* = 82-5 X h x d 2 

A = a/7'98 d or ft = 2*8 d. 

This shows that a rectangular wall of masonry in which 
the height is less than 2*8 times the width will resist over- 
turning by water pressure, whatever the actual dimensions 
may be. Such a wall, being unnecessarily thick at any 
section above the base for withstanding the hydrostatic 
pressure at that section, may be reduced in section, and 
thus a considerable weight of material saved. Other 
considerations than overturning enter into the problem, 
especially for high dams where the pressure produced upon 
the toe of the dam by the resisting moment, together with 
the dead weight of the masonry, may exceed the crushing 


strength of the material, and it is cases of this kind that 
give rise to problems of special interest in the design of 
large dams. The tendency of the dam to shear along a 
horizontal section, or to slide bodily down stream under the 
action of the water pressure, is resisted by the friction and 
adhesion of the masonry to the foundation, but this is 
ordinarily so great that it is unusual for dams to fail in this 
manner, especially as the width at the bottom is made 
greater than would for this reason be necessary, for the 
purpose of preventing leakage. The illustration on page 134 
shows a dam which can be constructed cheaply, and which, at 
the same time, serves as a spillway over the top. The face 
of the dam is constructed of pointed ashlar masonry, and 
the back is filled in with rubble, which in this case was well 
packed down so that the water passing over it would not cause 
displacement of the stones. The foundations of the wall 
are carried down about a foot below the bed of the river, 
and the ratio of width of the ashlar wall to the height 
is something less than two. Dams of this kind require 
occasional re-pointing at the face to keep them watertight. 
The experience of the writer points to this as being the 
most satisfactory dam for low falls. Other kinds of struc- 
tures may be used, some of which are made of wood, but 
which are of a less permanent kind. Two lines of sheet 
piling with the intermediate space packed with earth and 
stones forms a good dam, though again of a less permanent 
description. The necessity for flood-gates and sluices 
renders the masonry dam particularly adaptable, as they 
may then be built into the work. 

Concrete is a valuable material for the construction of 
dams and walls, and as it can be laid under water, the work 


of construction is often facilitated by its use. For the con- 
struction of such the following mixture is recommended : — 

Portland cement . . . One part. 

Clean sharp sand . . . Two parts. 

Crushed stone (2 ins.) . . . Five parts. 

In order to save expense in building heavy walls, which 
would thus take a large amount of concrete if only this 
mixture was employed, it is good practice to use large 
stones with the above mixture well tamped about them. 
The stones forming the concrete proper ought not to be 
more than 2 ins. along any dimension. This allows the 
concrete to be thoroughly mixed and thrown into the 
trench by hand. The crushed stone contains such a large 
proportion of small chips that the mixture is sufficiently 
plastic to fill up the interstices completely and to make 
the wall watertight. In fact, it has been found that the 
large proportion of very small chips and particles of 
granite in the aggregate as it comes from the crusher is 
sufficiently great to render the reduction of the above pro- 
portion of sand possible, which (especially if the sand is 
dirty) is beneficial, as it is replaced by a better material. 
It is not easy at places far from the coast to obtain really 
clean sharp sand, and an adulteration of clayey matter is 
fatal to the proper setting of the concrete. For the con- 
struction of wheel pits and works subject to the action of 
water concrete is also a very excellent material, and by 
making use of the compressive strength of concrete com- 
bined with the tensile strength of steel, beams and turbine 
pit floors may be constructed in a substantial manner. 

Turbine pits may be constructed of wood, and often 
are, for small wheels working under a low head. The 


planks forming the back and floor of the pit ought to be 
6 ins. X 3 ins., tongued and grooved, and the joints packed 
with tarred oakum, after which the surface is then served 
with a coating of hot tar. This helps to protect the wood 
from warping ; but it is necessary to use well seasoned 
timber, so that the joints will not gape after being some 
time in service. The weight of the wheel should be taken 
off the floor by approved arrangements as described on 
page 98, but the casing and guide vane rings have to be 
carried by the floor, which is supported in the usual manner 
by steel or wooden joists, all of which ought to be served 
with tar to protect them from the water. The opening in 
the floor for the passage of the draft tube into the tail race 
is a source of weakness in any form of wood construction, 
so that it is better practice to construct the floor of the 
pit as an arch or floor of ferro-concrete, while the water 
back may be made of wood, which is sustained against 
the hydrostatic pressure by either wooden or steel beams, 
for which purpose old railway iron is very well adapted. 

The best floor for turbine pits is constructed of ferro- 
concrete, which can thus be made flat, and the head room 
necessary for an arch is consequently saved. The thickness of 
the concrete ought not to he less than one-twelfth of the 
greatest span. For example, a turbine pit of 25 ft. X 20 ft. 
ought to have a thickness of floor (which includes the rein- 
forcement as the bars are imbedded in the concrete) of not 
less than 2*1 ft., for though the safe thickness of floor will 
depend upon the load to be carried, deflection must be 
guarded against, and a floor which would be calculated to 
safely sustain the load might deflect to an extent sufficient 
to cause serious trouble with the setting of the turbine. 

N.S. K 


In calculating the amount of reinforcement necessary, the 
load may be assumed to be that due to the weight of the 
water at the maximum height to which it can ever rise in 
the wheel pit, and by taking such a load evenly distributed 
over the area of the floor and adding the weight of turbine 
casing and guide wheel which rests upon it, and assuming 
this total load to be evenly distributed, the correct proportion 
can be given to the materials composing the floor. 

One of the chief requisites for concrete employed for such 
purposes is that it shall be watertight, and to attain this 
end the sizes of the aggregate comprising it must not 
exceed a certain size. The laws governing the impermea- 
bility of concrete were fully discussed and elucidated in an 
excellent paper contributed to the American Society of 
Civil Engineers by Messrs. Fuller and Thompson. 1 They 
point out that both theory and experiment prove that 
mixtures which give the greatest density when dry do not 
necessarily give the greatest density when mixed with 
cement and water. To illustrate this point they state that 
a cubic foot of fine or of coarse sand when dry will weigh 
almost exactly the same, whereas when mixed with cement 
and water the mortar made with the fine sand will occupy 
a bulk approximately 20 per cent, greater than that made 
with the coarse sand. As a general result of their investi- 
gations they found that strength and impermeability to 
water go together, and the greater the proportion of cement 
the more watertight the aggregate becomes. Another con- 
clusion arrived at was that concrete composed of sand and 
gravel, in which the grains were rounded, was, for the same 

1 Proceedings " American Society of Civil Engineers." Vol. xxxiii., 
Nos. 3 and 5. 


proportion of cement, less permeable than that made of 
broken stone and screenings, also the permeability decreases 
materially with the age of the concrete. 

The sluices and head gates most suitable for small 
installations are constructed of wood. A good form of 
construction consists of two uprights of 8 in. X 8 in. or 
12 in. X 12 in., grooved or notched to allow the gate to 
slide up and down. The latter is a batten panel, which 
is operated through a rack and pinion geared to a 
crank through a worm and wheel, for by the use of 
such gearing the gate will maintain itself in any position. 
Gates of this kind may be constructed and worked by one 
man easily up to widths of 12 ft., but for wider openings 
than this it is advisable to make them smaller, by putting 
two gates to the opening separated by a post. The 
obstruction to the water by a post in the race ought to 
be avoided if possible, but the gates become too cumber- 
some for hand working, and with the pressure of water 
against them, difficulty may be experienced in moving them 
without the aid of other power. On the large hydro-electric 
installations power applied through electric motors is 
employed to operate gates. 




So various are the conditions under which water-powers 
may be found in those countries to which the engineer is 
turning for the future supply of this natural power, that it 
would be impossible to do more than touch upon the main 
characteristics of installations, for they are designed to 
meet the necessities of each particular case. The subject 
may therefore be best dealt with by describing installations 
where different conditions of flow and head of water prevail 
and which give rise to special forms of machinery and 
appliances. The range of conditions under which water- 
power may now be profitably developed is ever widening, 
due to the improved apparatus at the disposal of the 
engineer. Before the introduction of the turbine in any- 
thing like the present form, the mill stream, falling 
through a few feet, represented the usual conditions 
from which there could not be a great departure, and 
which left but little choice for the engineer who had to 
select a suitable wheel for utilising the power running 
to waste, but now the range of utilised head ranges from 
more than 3,000 ft. down to 2 ft. A complete discussion of 
the subject at the present time would include not only such 
small powers as may be found upon the rivers of England, 
and gigantic powers of medium fall such as Niagara and 
Victoria Falls, but also of powers which make up for a 


very small discharge of water by an extremely high head 
such as the Lake Tanay installation in Switzerland or the 
Pikes Peak plant in Colorado. The smaller powers from 
which 100 to 500 h.-p. may be obtained are those which 
in the future will play an important part in the economy 
of power generation. It is true that Niagara, and probably 
the undeveloped Victoria Falls and the great Falls of the 
Iguazu in Brazil, will be the most important instances of 
the kind in the world, as they are natural powers of 
surpassing size, but the method of attacking these vast 
stores of power is essentially the same as that for many 
sites, where, with the same head the flow is not so great, 
and, as far as Niagara is developed, it may be considered 
to be an aggregation of units which find a parallel else- 
where, but which by their size, and the natural attractions 
of the locality, have gained a large measure of popular 

Nature supplies water-power in a variety of ways, some 
of which require, on the part of the engineer, a vast 
amount of work to be done before they can be reclaimed to 
use, while others are almost ready made and only require 
the installation of the machinery. Of the former kind 
there are rivers with a fall which is spread over a long 
stretch and which can only be utilised by the construction 
of a costly dam which causes the inundation of a tract 
above it and consequent storage of water in a reservoir. 
Other natural powers, such as that of Niagara, are formed 
by the precipitous descent of a river bed in one great step 
over which the water tumbles. The development of this 
kind of water-power is costly, involving as it does large 
preliminary works and the construction of wheel pits and 



tunnels. At Niagara these were bored through solid rock 
at great expense. Another mode of developing water- 
power, some splendid examples of which may be 'seen in 
Northern Italy, is by the construction of canals from one 
point on a river, to another lower down, between which 
points the river has fallen, so that there is a difference of 

Section/ of Wmir. 
FlO. 39. 

Fig. 40.— Plan of Weir. 

elevation between the canal and river sufficient for operat- 
ing water wheels. Then again, there is the lake high up 
on a mountain side from which the water is led out by a 
long pipe to the place of utilisation hundreds of feet below, 
or, if there be no natural lake, an artificial one may be 
produced by throwing a dam across a valley. 

Each of these general plans necessitates special know- 
ledge, some of which is quite outside the scope of this 


work, and if it were extended to include them it would 
become a work on civil engineering. It is nevertheless 
impossible to avoid touching upon some of the allied 
subjects which are included under the comprehensive 
subject. As the smaller water-powers will become increas- 
ingly valuable in view of the possibility of utilising 
them through the medium of electricity, it is best to repre- 
sent them by a description of a small installation which 
works under a head of about 6 ft. and from which some 
50 h.-p. is obtained. This installation upon the Newry 
Eiver at a point just above the town is built upon the site 
of an old dam, a section of which is shown in Fig. 89. It will 
be seen from the plan (Fig. 40) that the watercourse makes an 
angle where the dam is thrown across the stream. This 
dam is 167 ft. from bank to bank and of uniform cross- 
section, and before the water was drawn off for the 
turbine it passed over the top along the entire width. 
As shown in the section, the vertical up-stream face 
of the dam is made of rough masonry laid and pointed 
with lime mortar, and the long sloping back by boulders 
embedded in stiff clay. 

The problem to be solved in this case was to ascertain 
the capacity of the proposed installation, for the flow of 
water was very variable owing to the rapidity with which 
the river responded to a downpour of rain, and it was 
important to fix the capacity of the plant at such a figure 
that the maximum output would be as large as could be 
maintained without incurring a wasteful efficiency by 
operating for part of the time at greatly reduced load. By 
measuring the flow over the weir and applying the Francis 
formula the discharge was calculated for heights varying 



from 1 in. up to 30 in. and the results are shown plotted in 
curve A (Fig. 41). Thus for a height of 10 in. over the weir 
the discharge per foot of length would be about 150 cu. ft. per 
minute. The horse-power was not proportional to the dis- 
charge owing to a sharp turn in the river together with a 
restricted channel. It was observed that when the depth of 

water upon the weir 
was 3 in. the actual 
fall was 6 ft., and dur- 
ing an exceptionally 
heavy flood when there 
was 18 in. on the weir, 
the head dropped to 3 ft. 
From these data the 
horse-power was calcu- 
lated for the varying 
depths on the weir and 
the results are shown on 

Height, over Weir, Inches " CUr\ r e B. The equation 

Fig. 41.— Flow over weir arid horse- for the curve was first 
power. obtained from which it 

was plotted (see Appendix B.). The ordinates give the 
horse-power for inches of weir depth measured as abscissae. 
The actual available power is obtained by multiplying the 
value shown by the curve by the length of the weir in feet. 
As the flow corresponding to a maximum power would 
only be obtained by occasional heavy floods of short dura- 
tion, the capacity of the plant had to be far short of this ; 
and from records and observations of the flow at different 
seasons, it seemed feasible to operate a 50 h.-p. wheel for 
the greater part of the year, at or near full load. It was 








*• -5 


I r* 


- — 



3 o 





Koo C 






<%400 ^ « 




Q. t 





1 I/O 





$; V" 



? JL 



O 5*!** 







• ■ 





) J 


t J 




Fig. 42. — Plan and elevation of small turbine installation. 


therefore decided to put in a turbine of 50 brake h.-p. with 
an hydraulic efficiency of 76 per cent., thus utilising at full 
load a supply of 6,200 cu. ft. of water per minute under an 
effective head of 5 ft. 6. in. (It was furthermore stipulated 
that the efficiency should be well maintained throughout 
a wide variation in the effective head.) Allowing 10 per 
cent, for losses in gearing between the turbine and generator, 
the actual horse-power delivered at the armature-shaft 
would exceed 44, so that a generator of 30 kw. capacity, 
with an efficiency of 90 per cent., could be driven at full 

The turbine pit was excavated out of the weir, and a by- 
wash 12 ft. wide was provided so that when the wheel 
was not at work the water could be diverted by means of 
the gates on the up-stream side. The pit is flanked by 
two concrete walls which are carried up to a s height of 
several feet above the level of the water on the up-stream 
side of the dam. The turbine is supported upon a floor of 
concrete reinforced by steel as shown in the sectional 
elevation (Fig. 42), and the back of the head race is con- 
structed of 4 in. planking, tongued and grooved, the seams 
being caulked with oakum and served with tar and supported 
against the hydrostatic pressure by rails laid across and 
embedded in the side walls. The weight of the turbine 
is carried from the bearing above the level of the water 
and this bearing is supported by two 15 in. I joists placed 
across the wheel chamber at the floor level. By this mode 
of suspension access may be had to the bearing for lubrica- 
tion and examination. The turbine is a mixed flow wheel 
of the kind generally employed for low heads. 

The speed of this turbine is 55 revolutions per minute, 


and the horizontal shaft revolves at three times this speed, 
this being the ratio of the bevel gear and pinion. From 
this shaft an overhead countershaft is driven at 800 revo- 
lutions per minute, and the dynamo is driven off this shaft 
by a belt, the normal speed of the machine being 650 
revolutions per minute. The output of the dynamo is 130 
amperes at 280 volts, and it is a compound-wound four-pole 
machine with an overload capacity of 25 per cent. 

The foundations of the turbine house are carried down 
to solid rock at the tail race end of the house, and the 
concrete used was made up of one part of Portland cement 
to two parts of sand and four of granite chips, the largest 
of which would pass through a 6 in. ring. To decrease the 
cost of the work without materially diminishing the strength 
of the foundations, large boulders were embedded in the 
concrete, and the mixture was well rammed about them. 

Due consideration was given by the author to a storage 
battery system by which the voltage of a supply current 
for lighting and power could be kept constant regardless 
of the condition of the river and the load ; but it ultimately 
was decided to supply the line direct from the dynamo, 
and to provide a governor for maintaining a constant speed 
of the machine under all conditions. The governor, which 
is shown on the illustrations, and which is elsewhere 
described, is driven from the overhead counter- shaft, 
and the regulation is effected through a chain drive which 
operates a worm and sector, and the guide vanes of the 
turbine are rotated by this means. This type of governor 
requires occasional attention and must be kept supplied 
with oil, but when set it is entirely automatic, and the 
plant may be left throughout the* day without an attendant. 


A complete specification for a low fall vertical shaft 
turbine would be as follows: — 

Specification for one 50 Brake Horse-Power Turbine 


1. Size. — The turbine shall be capable of developing 
50 b.h.-p. at full gate when operating under an effective 
head of 5 ft. 6 in., with a flow of 6,200 cu. ft. of water 
per minute. This corresponds to an available power of 
64'5 h.-p., so that the efficiency of the wheel at full gate 
must be 77*5 per cent, to develop the stated power. The 
guaranteed efficiency of the wheel at three-quarters and 
half load, as well as at full load, must be stated. 

2. Type. — The turbine may be either a mixed or radial 
flow wheel with vertical shaft. The step-bearing which 
carries the weight of the wheel may either be located above 
the head water or in the tail race, but must be accessible 
for repairs or adjustment if placed in the latter position. 

3. Speed. — The speed at full load should preferably not 
exceed 65 revolutions per minute ; but it is not considered 
advisable that the manufacturer should modify the design 
of a standard wheel in order to come below this limit, and 
any reasonable departure therefrom will receive due 

4. Details. — In addition to the wheel, guide-wheel, casing, 
base-plate and shaft, the contractor is to furnish all the 
iron work necessary for the support of the turbine in the 
pit. This would consist of steel I joists let into the wall 
on each side, with cast iron distance pieces to ensure a 
rigid construction. The beams are to be drilled for all 
bolts, and the length of the beams will be determined by 


the width of the sluice-way, which may be taken as twice 
the diameter of the turbine casing. Sufficient length must 
be allowed for a good bearing on the wall, and the beams 
are to rest upon square pieces of J in. iron plate which are 
also to be furnished by the contractor. 

5. Gearing — The vertical shaft is to be provided with a 
mortice bevel wheel, made in halves, bored, and with keys 
fitted. A machine-moulded cast iron pinion to mesh with 
the gear is to be provided, but this will be fitted to a 
horizontal 3J in. shaft supplied by the purchaser. The 
pedestals and bearings for the horizontal shaft will be also 
supplied by the purchaser, but the contractor is to furnish 
the cast iron yoke and bearing for the top of the vertical 
shaft. This vertical steel shaft will be approximately 10 ft. 
long, the exact length to be determined later. The gear 
ratio is to be 3 to 1, the diameter of the gear to be stated 
in the tender, but which is not to exceed 5 ft. 

In addition to everything necessary for the proper 
operation of the turbine, a set of spare spanners is to be 
provided, together with a spare set of bushings for the 
main bearings. 

6. Governor. — As the turbine is to operate a constant 
potential electric generator, it is essential that an automatic 
governor be provided, which is to be guaranteed by the 
manufacturer to control the speed of the turbine within the 
following limits consequent upon the corresponding per- 
centage changes of load here stated : 

Sudden variations of load of 25 per cent. 4 per cent. 
„ ,, „ 50 per cent. 6 per cent. 

From no load to full load . . .10 per cent. 
The contractor is to state where such a type of governor 


as he proposes to furnish is in actual operation in con- 
nection with turbines of less than 100 h.-p., operating 
under a head not exceeding 6 ft., the successful operation 
of water-wheel governors under high heads being no 
criterion as to their reliability with such a small head as 
we have in this case. 

7. Hand Control. — The requisite mechanism for con- 
trolling the turbine by hand is to be provided and is to be 
arranged for shutting down the turbine without the 
necessity of lowering the sluice-gate at the mouth of the 
wheel pit. 

8. Materials and Finish. — The cast iron used in the 
construction of the turbine is to be of a hard, fine-grained 
quality, free from blow-holes, and the turbine vanes and 
guide vanes are to present a smooth surface to the water, 
and may be of steel cast into the wheel. All parts of the 
governing and controlling mechanism situated on the 
dynamo floor are to be well finished and neat in appear- 
ance, and the working parts are to be provided with oil 
cups of large capacity so that frequent attention may be 

9. Painting. — All parts of the turbine and supports 
which are exposed to the action of the water are to receive 
two coats of anti- corrosive paint, and the governing mecha- 
nism and other parts in the dynamo room are to be painted 
black, striped, and varnished. 

10. Drawings. — The contractor is to supply dimensioned 
drawings of the turbine he proposes to furnish, showing all 
overall and important dimensions from which the plan of 
the wheel pit and station may be prepared by the 



Turbines are worked satisfactorily under lower heads 
than 6 ft. There is a Jonval turbine in Worcestershire for 
driving a mill which operates under 2 ft. head, and at 

Fig. 43. — Jonval turbine working under a head of 2 feet. 

certain seasons of the year this is even reduced. The 
turbine is a parallel flow wheel with a vertical shaft, the 
diameter being 18 ft. 2 ins. (Fig. 48). It is made up of 
two concentric rings of vanes, and the inner set may be 


closed to the water by a system of covers so as to limit the 
operation of the wheel to the outer ring. 

At some periods of the year a head of 3 ft. acts upon the 
wheel and the 40 h.-p. required is got from the outer ring 
alone ; but when the head is only 2 ft. both rings are used. 
This wheel makes 14 revolutions per minute, and passes 
about 14,000 cubic feet of water in that time. A very 
small head of water may thus be turned to profitable 
account where there is a good discharge. The cost of a 
turbine of this kind, including shafting, gearing, and sluice 
gates would be approximately £30 per horse power, or 
£1,200 for a 40 b.h.-p. wheel. The cost of foundations 
and special works would have to be added to this, but as it 
depends upon local conditions it is impossible to assign a 
value applicable to all cases. 

The large gear upon the shaft of the turbine is 10 ft. 6 in. 
diameter, and has 132 cast iron teeth of 10 in. face. It 
meshes with a pinion 3 ft. 6 in. diameter, with 44 teeth, 
giving to the countershaft a speed of 42 revolutions per 
minute. This installation was designed by Mr. Alph. 
Stieger, M.Inst.C.E., and is a notable instance of a very low 
fall being successfully employed. There are many rivers 
upon which, at comparatively slight expense, a low fall 
might be utilised by such a wheel as this. The Jonval 
type is specially adapted for such a purpose, as the com- 
paratively narrow wheel enables it to be used, even where 
the fall is very low. 

An arrangement for driving an electric generator by 
three turbines on a vertical shaft is shown in Fig. 44. The 
water is admitted from the head race shown on the right, 
and the discharge from the wheels passes off through two 


channels. If the water is low the uppermost wheel is put 
out of action, while the two lower wheels are still working 
efficiently. This arrangement of wheels is not uncommon 
in Switzerland. The gate at the mouth of the turbine pit 
shuts the water off entirely, so that access may be had to 
all the wheels when desirable. 

Turbines with horizontal shafts are coming into favour, 
especially for electric driving. Such a unit is illustrated 
in Fig. 31, p. 104. There is an advantage in having the 
electric generator upon a horizontal shaft as thrust bear- 
ings are dispensed with, and the generator and turbine 
are placed on the same floor with short rods and links 
for the governing mechanism. 

The impulse turbine usually takes the form of the Pelton 
wheel for very high heads, some interesting examples of 
which are worthy of note. 

To Switzerland at present belongs the distinction of 
utilising the highest head of water for driving water wheels. 
This installation is at Lake Tanay, a mountain lake of 
about 7*5 sq. kms. surface, out of which the water is 
conducted by a pipe line down the mountain side, and is 
discharged at a point 950 metres (3.115 ft.) below the 
surface of the lake. Of this great fall 920 metres (3,018 ft.) 
is the effective head acting upon the wheels, which yield an 
efficiency of 75 per cent, at full load and which, for every 
litre of water per second, do work at the rate of 9*2 h.-p. 
This power is employed in generating monophase electric 
current at 5,000 volts for distribution in the district of 
Vouvry, the generators being direct coupled to the Pelton 
wheels. The water is drawn off from the lake through 
tunnels, from which it is conducted down to the power 

N.S. l 


house through pipes. The first section of this pipe has a 
diameter of 500 mm., and is 635 metres long, the thick- 
ness of the metal varying from 7 to 11*5 mm. At the 
lower end there is a junction of forged steel from which 
two pipes- of 340 mm. diameter convey the water the rest of 
the way. The water issues from the nozzles at a velocity 
of more than 100 metres per second and impinges directly 
upon the vanes of the wheels. At this high velocity it 
would be extremely dangerous to interrupt or check the 
flow except very gradually, consequently the governing of 
these wheels offers a problem of special interest, for while 
the working of the alternators demands close regulation, 
the safety of the pipe line is only ensured when the rate of 
change in the flow of water is kept low. It is pointed out 
in the next chapter how a destructive stress may be set up 
by checking the flow in a pipe line too rapidly, and the 
closing of the valve by hand in the ordinary way at the 
bottom of a pipe line such as this would be accompanied 
by disaster unless the pipe was made unduly heavy. The 
pipes in this installation are of welded open-hearth steel, 
and longitudinal joints are avoided. Such pipes have shown 
under test that they develop 100 per cent, of the strength of 
the steel, but it is customary to allow 80 per cent, only in 
making the calculations for thickness of material. The 
sections are joined by flange joints bolted together, and at 
the lowest point where the pipe has to withstand the 
greatest pressure the thickness is 18 mm. In order that 
the pressure due to the retardation of the mass of water in 
the pipe upon closing the valve should not exceed 5 kg. 
per sq. cm. (71 lbs. per sq. in.), it was made impossible 
for the attendant to close the valve in less than five seconds. 

Fig. 44. — Electric general 

driven by three turbines. 


To each Pelton wheel there are two nozzles, one of which 
is fixed and the other is automatically regulated by a 
centrifugal governor. The jets from the nozzles have a 
cross section of 2 sq. cm. each, that of the fixed nozzle 
being circular, and of the adjustable, square. With the 
full load of 500 h.-p. the wheel has a speed of 1,000 revo- 
lutions per minute under the action of both jets. The 
wheel has a diameter of 1*20 m., and should the governor fail 
to act and the speed rise to the maximum of 2,000 revolu- 
tions per minute, the centrifugal stresses would still be well 
within the tensile strength of the material. The wheel 
consists of a disc to the periphery of which the vanes are 
attached, alternately right and left. 

It is unquestionably true that wheels operating under such 
high heads are much less efficient than at moderate heads. 
The losses are due to friction in the pipes and to the fact 
that the water has a comparatively high residual velocity 
upon leaving the wheel buckets, and thus the kinetic energy 
is only partially used in useful work. Another interest- 
ing plant of the same kind is that of the Pikes Peak Hydro- 
Electric Co., at Manitou, near Colorado Springs. Pelton 
wheels are also used in this installation, the total head 
being 737 m. (2,417 ft.) which is the next highest head 
utilised to that at Lake Tanay. The entire length of the 
pipe line is 1,455 m., part of which consists of a light 
pipe on a small gradient, and the rest of a heavy pressure 
pipe 584 mm. internal diameter. Deducting the loss of 
head due to friction in the pipe, the effective head acting 
on the wheels is 671 m., and the pressure to which the 
pipe is subjected may therefore rise to about 1,000 lbs. per 
sq. in., to resist which it is made of $ in. steel plate with 

l 2 



seams of double-butt straps. An attempt was made to 
caulk the joints in this pipe with lead, but it was squeezed out 
in a thin film. Eventually an alloy of tin and lead was found 
to withstand quite well. The water strikes the wheel buckets 
with a velocity of more than 91 m. per second (204 
miles per hour), and the governing is effected by deflecting 

mk& x± - rifl 



^'^i* \ -* 

fc^^jT « 

— ■, *r' 

m^ V -^ ^ 

jPPn^ \j^^ 


y HI 

*- %, h, - 



1 ^ 


! --Si 

Fig. 45. — Riveted steel pipe lines for high pressure. 

the jet, the nozzle being hinged for the purpose. As the 
impact of the jet would quickly wear through hard sub- 
stances, the momentum is destroyed by directing the jet 
into a pool, the tail race having been so designed as to 
form a pool 40 ft. long through which the fierce jet expends 
energy, and terminates upon a cast-iron baffle plate at the 
end The valves are fitted with a slow worm and wheel 
attachment driven by an electric motor, so that it is outside 


the power of the attendant to close them in less than 25 
minutes. The steel pipe which is employed for installa- 
tions of this kind is shown in Fig. 45, though welded 
pipe is now being largely used instead of riveted. A 
riveted joint cannot be relied upon for more than 80 per 
cent, of the strength of the solid plate. 

The pipes are sometimes laid in trenches, and in many 
cases are surrounded by concrete. In others they are 
sustained in position by being supported upon piers of brick 
or stone, the flanges at the ends of the pipes being spanned 
by the piers, as shown in the illustration. An expansion 
joint or sleeve is necessary to prevent distortion and leak- 
age at the joints, and is usually made in the form of a 
telescopic gland which allows longitudinal play. 

Friction in Pipe Lines. 

In every pipe carrying flowing water there is energy lost 
in overcoming the friction of the water against the walls of 
the pipe, and the energy so lost varies with the character 
of the interior surface of the pipe. Thus for rough cast 
iron pipes it is greater than for steel, for riveted pipes also 
it is greater than for welded. Then again, as a pipe in 
service becomes incrusted and corroded, the friction is 
greatly increased and consequently the loss of energy also 
becomes more serious with the life of the pipe. In choosing 
the size of pipe necessary to effect a given discharge, or to 
obtain the loss of head due to friction in a pipe carrying 
water at a known velocity, formulae are used in which the 
constants have been determined by experiment. The most 
reliable series of experiments are those of Darcy, which 
were undertaken for the French Government, and by which 


the value of the constants was found. The formula which 
is perhaps most employed by engineers is that known as 
the Chezy formulae, by which the loss of head, h, in a pipe 
of length Z, and diameter d, may be obtained, when the 
water is flowing through it with a given velocity. If the 
velocity r is in feet per second, and all dimensions are in 
feet, the loss of head h is : — 

(1) For clean pipes, h = 0*0004 X (-A X r 2 . 

(2) For incrusted pipes, h = 0*0008 X (-;) x **• 

If v is in metres per second and all other dimensions are 
in metres, the loss of head h is : — 

<3) For clean pipes, h = 0*0013 (-v\ r 2 . 
(4) For incrusted pipes, h = 0*0026 (^\ 

The loss of head for incrusted pipes is taken to be twice 
that for clean pipes, the coefficient in equation (2) being 
double that in (1). These formulae, though not strictly 
correct for all velocities and all sizes of pipe, may be taken 
to be sufficiently accurate for the moderate velocities usual 
in pipes and penstocks, and for pipes from four inches in 
diameter upwards. 

If the pipe be riveted, and therefore offering greater 
resistance to the water, formulae (2) and (4) ought to be used, 
and it is sometimes expedient to calculate the possible loss 
of head for a new pipe by using the formula for incrusted 
pipes so as to anticipate the inevitable incrustation and 
clogging of a pipe in service. As an example of the use of 
the foregoing equations, suppose it is desired to obtain the 


loss of head occurring in 500 feet of 8 inch cast iron 
asphalted pipe when the velocity of the water is 4*8 feet per 

h = 0*0004 X (~) X (4-3) 2 = 5-52 ft. 

The highest head in use in England at the present time 
is employed to drive a Pelton wheel at the Croeser slate 
quarries in Wales. This installation formed the subject of 
a recent paper, 1 in which the author states that two natural 
lakes discharge into the Cwmfoel valley, and by building a 
dam across the valley about 12 acres of water have been 
impounded at an elevation of 860 ft. above the power house. 
The higher lakes may be used to supplement the storage of 
the reservoir, or may be applied directly to the wheels in 
the power house. The steel pipe line is 3,200 ft. long, and 
it conveys water to two wheels, one of 375 b.-h.-p., and the 
other of 25 b.-h.-p. To avoid dangerous water hammer, the 
pipe line is provided with an air-vessel of 30 cu. ft. capacity. 
The hydrostatic pressure being more than 25 atmospheres 
(367 lbs. per sq. in.), it was necessary to fill this vessel with 
air at the same pressure. Under a head of 861 ft. with a 
flow of 276 cu. ft. per minute, and a peripheral speed of 
40*7 per cent, of the theoretical velocity due to the head, 
the wheel is stated to have attained an efficiency of 87 per 
cent., which would place it far above any other type of 
prime mover as an efficient machine if all the losses have 
been properly charged up against it. As such efficiencies 
have been claimed by others for these wheels there appears 
to be some ground for supposing that, at the best velocity, 

1 The Institution of Civil Engineers. "The Application of Hydro- 
electric power to Slate-mining," by Moses Kellow, Assoc.M.Inst.C.E. 


and with a steady load, this efficiency may be momentarily 
realised, but if the wheel is working under the conditions 
that practice implies from day to day, the efficiency would 
fall short of this. 

The Cost of Water Power. 

The consideration most generally affecting the choice of 
power for a given purpose is the cost, both first cost or 
capital charge, and running costs or maintenance. When 
a supply of water from which power may be obtained is 
available, the choice may therefore rest between water- 
power on the one hand and power derived from fuel 
either through the steam or internal combustion engine on 
the other. As the influence of " convenience " cannot 
readily be measured, even for a specific case, and still less 
for a general comparison, the problem, as far as we are con- 
cerned at present, resolves itself into a question of relative 
cost between the two forms of power, as to which should 
be used where both are available. But there is an essential 
difference between an estimate for a steam plant and for a 
water-power installation. The former is but little different 
for plants of given power laid out at different places 
accessible by rail, while an estimate for the development of 
a water-power for one locality would be entirely wrong for 
another. Local conditions affect the one but slightly, 
while with the other they affect the question so seriously as 
to make the issue dependent upon the result of a careful study 
of the locality. It is not to be assumed that the cost of instal- 
lation of steam plants is quite independent of the locality, 
for often heavy ground rents, high charges for condensing 
water, taxes, and numerous restrictions and observances 


which municipalities impose upon a power company, 
render the power-supply close to a large market somewhat 
more costly than it would be if the power station were 
situated in a country district, but the machinery and build- 
ings would cost the same, irrespective of the locality, and it 
is with the cost of these that we wish to compare the cost 
of the works generally necessary for developing a water- 
power. These works comprise the excavation of turbine 
pits, digging canals or laying pipes and penstocks, building 
dams and deepening channels, in short all the work 
necessary before the turbine can be started, which may 
include any or all of the foregoing processes. Then there 
is the cost of the turbine and accessories, such as the gear- 
ing and devices for supporting it in the pit, with the thrust 
bearing and countershaft for taking off the power, and 
finally the cost of the building. As against these items the 
steam plant comprises a boiler plant with coal hoppers, 
and possibly mechanical stokers and ash conveyors, steam 
engines with the piping, condensers, air pumps, and coolers, 
and possibly a feed water heater, hot well, and also a steam 
superheater. The variety of appliances and machinery 
going to make up a large steam plant is legion, but for 
small installations, with which it is intended to compare 
water-power plants of similar sizes, many of these 
auxiliaries disappear, and some are replaced by manual 
labour. Then there are the heavy foundations for the 
reciprocating engine to damp out vibration, and the building 
for protecting the machinery from the weather. Steam 
turbine plants effect a saving in foundation costs, but as 
this substitute for the reciprocating engine is chiefly 
economical in units of large size, it is only in the 


consideration of large undertakings that it invites 

Engine foundations and buildings have their counterpart 
in the water-power installation in the works necessary for 
conveying water to the wheel, also the buildings or turbine 
house. The cost of the former may be directly ascertained, 
as the quantity of concrete or brick work to put down for 
an engine of given size is known, and can be obtained from 
the makers in the light of their experience. The same is 
not true for turbine foundations or pits, the design and 
size of which are dependent upon several conditions pre- 
vailing at the site. In some cases necessary precautions 
against floods necessitate heavy construction with founda- 
tions carried far below the bed of a river until a firm 
foundation is reached, and the cost of construction increases 
accordingly, especially when the work has to be kept dry 
by pumping, or is in danger of being washed away by rises 
in the river. Then again the extraneous works often 
necessary to obtain the requisite fall upon a river add 
greatly to the first cost of water-power installations. Such 
for instance would be a canal which opens out from a river 
at a point above the site of the plant and conveys the 
water to the turbine under a head equal to the difference in 
elevation between the water in the canal and that in the 
river at the point in question. Some such canals, which 
form essential features of many of the beautiful installa- 
tions in Northern Italy, and which convey water for several 
kilometres, have been so costly as to be quite prohibitive in 
coal mining countries where cheap steam coal may be 
obtained. In fact the writer ascertained that the interest on 
the first cost of one famous installation added to the cost of 


maintenance made the cost of power almost equal to that 
derived from high priced fuel in a large city to which the 
power was conveyed by transmission lines. True, the 
losses in transmission, amounting to 8 per cent., told 
against the water-power plant, but notwithstanding this, the 
difference in cost of a horse-power delivered from the two 
sources was barely sufficient to justify the enormous 
expense of a canal cut through rock for several kilometres. 
And so it is in many other instances where, at a great out- 
lay of capital, water power is delivered in competition with 
heat-engine power with very little difference in cost, owing 
to the heavy capital cost of the works necessary to develop 
it, though the running costs and maintenance charges may 
be extremely low compared with steam or gas power, The 
development of such water powers remote from the centre 
of distribution is a problem of a special kind, while the use 
of small powers located close to a manufacturing centre 
and in direct competition with cheap steam power is quite 
another. Without prejudging the question as to the dis- 
tance it is commercially practicable to transmit power (the 
maximum distance at present being 232 miles from the 
% De Sabla power-house of the California Gas and Electric 
Co. to Sausalito at 50,000 volts), the limitations to which 
are chiefly in the cost of the copper line, and the difficulties 
incident to the insulation of the line at very high potentials, 
it is clear that there is a limit which may be nearer than 
some of the extreme advocates of long distance trans- 
mission imagine. The price of copper tends to rise (it is 
now £118 per ton) ; there is yet no satisfactory means of 
insulating a line for pressures greater than 60.000 volts 
without enormous loss at the points of support ; the high 


tension direct current system is still in a tentative stage, 
so that much still remains to be done before a prophecy as 
to the maximum economic distance is worth anything. It 
is true that in some cases a heavy loss in transmission may 
be accepted, so that only 25 or 30 per cent, of the hydraulic 
power is available at the distribution end, and still be able 
to successfully compete with steam power, as the water 
may cost nothing. This argument may however be gainsaid 
by a glance at the other side of the balance sheet showing 
the interest on first cost of a large plant, the cost of main- 
tenance of a long pole line, with a continual liability to inter- 
ruption by the weather or by the acts of vandals, followed 
by serious charges against the power company for failure 
in the supply. As long distance transmission schemes vary 
so much in character and involve such a variety of special 
interests and commercial considerations, it is not possible 
within the limits of this little work to take up this great 
branch of the subject which the author hopes to enlarge 
upon in another place. For the present, therefore, to 
simplify the problem, we will omit the pole line and the 
electrical side of hydro-electric installations and confine 
our attention to the case of water power versus steam or 
gas power delivered at the shaft of a generator or other 
machine which is to be driven. 

The cost of a turbine and accessories necessarily varies 
with the power it is intended to develop, but also with the 
type of wheel, the head under which it is to operate, and 
the speed. As the speed or velocity of the buckets or vanes 
is a direct function of the head (in the impulse turbine 
being approximately one half that due to the free fall of 
water), this may be attained by wheels of various sizes with 



correspondingly varying angular velocities, the revolutions 
being inversely proportional to the diameter for a given 
speed of vane. But the cost of the wheel, accessories, and 
setting increases with the diameter, so that a fast running 
wheel for a given output under a stated head is cheaper 
than one with a lower angular velocity. The diameter, 

900 4 


700 3 

"§ 500 2 
% 400 
§.300 1 
2 200 






?• — 






L— i 




__ 3 







l r^ 






20 30 40 50 60 70 80 90 

Head in feet. 

110 120 130 HO 150 160 170 
Fig. 46. — Relation between the cost of a turbine and the head of water. 

however, must in all cases be sufficiently large to allow for 
the passage of the water without choking. As the speed 
depends upon the head it follows that the cost of a turbine 
decreases as the head increases. This is shown by the 
curve in Fig. 46, which is plotted from a price list taken from 
a manufacturer's catalogue, and which refers to a vortex 
turbine with horizontal shaft complete with accessories. 



































H>. 10 20 30 40 SO 

Fig. 47. — Relation between cost of turbines and 

€0 70 eo 

rated horse-power. 


The ordinates are pounds sterling per horse-power and are 
obtained directly from the list by dividing the cost of the 
turbine in pounds for a given head by 40, which is the rated 
horse-power of the wheel chosen. The short curve refers 
to another type of wheel, by which it will be apparent that 
the cost per horse-power decreases more rapidly with 
increase in head than with the other type of wheel, which is 
plotted for a range of head of 40 to 180 ft. The points 
represent the actual costs per horse-poiver, and the smooth 
curve drawn through them is designed to indicate the way 
in which the cost changes with the head. For instance, at 
50 ft. head the cost of the wheel is «£4'9 per h.-p., or, for the 
40 h.-p., £196. At 140 ft. head 40 h.-p. is obtained from a 
turbine costing approximately £2*9 per h.-p., or £116 for 
the wheel.. This decrease in cost per h.-p. is due to the 
fact that under an increased head a smaller volume of water 
is passed to develop the rated power, and the size of the 
wheel may therefore be reduced. The speed curves on the 
same sheet show that the speed of the wheels is not directly 
proportional to the head, for if it were the curve would be 
replaced on the diagram by a straight line. For the highest 
heads the speed is less than it should be if it were always 
proportional to the head. Fig. 47 is put in to show how the 
price of turbines of this type varies with the rated horse- 
power of the wheel. The curve A refers to wheels working 
under 24 ft. fall, and B is for the same type of wheel under a 
90 ft. fall. The abscissae are the rated horse-power of the 
wheels and the ordinates are pounds sterling. Taking the 
two curves it is seen at once that the curve B bends over more 
sharply than A, and is inclined at a lesser angle to the hori- 
zontal axis. This shows the reduced cost of a wheel of given 







7 H.P. tO 20 30 40 SO 60 10 8 





n be 


m cc 


f 50 


It di 







and size of machines. 


power working under a higher head, and also that the 
capital cost per horse-power is considerably less. 1 There is 
no difference in this respect between turbines and other 
kinds of machinery, for additional power costs less as the 
size of the machine or engine is increased, though it is 
perhaps more apparent in turbines than other classes of 
machinery. Fig. 48 is a curve showing the cost of slow 
speed electric generators per horse-power, the slope of which 
is again an indication of the way the price per horse-power 
varies with the capacity of the generator. The diminution 
of this figure as the size of the generator is increased is less 
rapid than for the hydraulic turbines. The prices of tur- 
bines taken from a single maker's catalogue are naturally 
of limited value to a purchaser, and are only introduced 
here to illustrate how the cost per horse-power is effected 
by the size of the unit, and are not to be taken as indicative 
of the state of the market for such machinery. The facts 
which they are intended to illustrate are, however, indepen- 
dent of the price of the machinery by any one maker or of 
any special design or type. The water-p#wer plant is 
therefore no exception to the general rule that the cost 

1 These curves may be referred to equations which take the form 
y = a rt". Accordingly the slope of the curve at any point is a direct 
indication of the price per horse-power, for this price is obtained by 
dividing y by x at any point, and as : — 

d v , , v a x n 

-— ^= a n x*- 1 and — = = a x n ~ l 

ax xx 

therefore -^ = - X -y^-. 
x n ax 

As -r^ is the slope of the curve, the variation in the price per horse 

power is therefore readily seen at a glance. 

N.S. M 


per h.-p. diminishes with the size of the unit, being 
greatest when the units are small. 

The works necessary to develop a small water-power (say 
50 h.-p.) comprise the excavation and construction of the 
turbine pit, the construction of the turbine house and the 
installation of the machinery, and in many cases the build- 
ing of a dam to obtain the necessary fall. As, however, dams 
are not always a part of the work, they may be regarded as 
extraneous for the purposes of making comparisons. The 
capital cost of such works completed, with the turbine ready 
for running, would be, for falls up to 8 ft., about ±'1,200 to 
£1,400, according to the state of the soil as affecting the 
depth to which the foundations have to be carried. This 
total cost would be made up as follows : — 


Turbine, with gearing, draft tube, gates, and 

step bearing (£11 per h.-p.) . . . 550 
Excavation of turbine pit and construction of 
arch or ferro-concrete support with water 
back, side walls, and turbine house . . 750 


Total capital cost per h.-p., £26. . 
The cost of operation and maintenance per annum of 
such an installation would be as follows : — 

£ 8. d. 

Interest on capital at 3J per cent. . . 45 10 
Depreciation at the rate of 4 per cent, 
(which allows for entire replacement 
of plant in 25 years) . . . . 52 

Carried forward . . . 97 10 

£ 8. 


. 97 10 



. 20 


Brought forward 

Proportion of wages of attendant, whose 
time is divided between the hydraulic 
plant and the care of other machinery 

Oil, waste, and other supplies and repairs . 

Total cost for 50 brake h.-p. per annum . 167 10 
Cost per horse-power per annum . .370 
If the plant be in operation for 12 hours per day, 300 days 
in the year, the cost per horse-power hour becomes 0*22rf. 

Compare this with the cost of operation of a steam plant 
of similar power consisting of a multitubular boiler set in 
brickwork with chimney, feed pump, etc. The engine to 
be of the slide valve pattern with throttle governor, and 
wide rim wheel for belt. 

£ s. d. 
Cost of plant on foundations with shelter 770 

Cost per h.-p 15 8 

The total cost of operation would be as follows :— 

£ s. d. 

Interest on capital at 3J per cent. . 26 18 

Depreciation at 5 per cent. . 38 10 

Wages of attendant (entire time) 78 

Oil, waste, supplies, and repairs . 38 
Coal at 10a. per ton for 3,600 hours 
(4 lbs. per horse-power per hour, 

including waste) .... 160 14 3 

Total cost for 50 brake h.-p. per annum £342 2 3 
Cost per horse-power hour = 0*46d. 

m 2 


The steam plant is therefore twice as costly per horse- 
power as the water plant, and unless the difference is made 
up in charges for water, which are not allowed for in the 
estimate, the price of a water generated horse-power ought 
to be one half that of steam generated power for small 
plants. It may be said that a liberal allowance is made 
for coal consumption, which is put at 4 lbs. per horse- 
power hour, but this includes the wastage, and no deduction 
is made for ash and non-combustible material, which, in a 
cheap steam coal, may be a large proportion by weight. 

The depreciation upon the water-power plant is based 
upon the entire cost, but as the machinery which is most 
liable to deterioration is only 42 per cent, of the whole 
capital cost, this allowance errs on the side of liberality. 
On the other hand, a boiler plant is subject to compara- 
tively rapid deterioration, especially when fed with a low 
grade fuel, with perhaps a feed water charged with impurities 
which form a hard scale of carbonate or other salts of lime 
upon the shell. When it is remembered that a scale 1*5 mm. 
thick on the plates of a boiler causes a loss of one-eighth 
in efficiency, it will be seen that a neglected boiler 
quickly raises the expenditure on fuel also. The 
foundations and setting for the steam plant are a small 
proportion of the total cost as compared with the water-power 


A steam or gas engine plant is sometimes necessary as an 
auxiliary to a water-power plant during times of low water 
in dry weather. As the use of artificial light is generally 
less at seasons of low water, water-driven electric plants may 
often be maintained throughout the year without the aid of 
auxiliary sources of power by proportioning the plant to the 


capacity of the winter lighting load. It will be observed 
from the above figures that the stand-by charges for a 
steam plant (i.e., the cost of the plant in capital charges, 
interest, depreciation, etc., irrespective of whether it is 
running or idle), relative to the total cost, is a smaller pro- 
portion than for the water-power plant. Allowing half-time 
for attendance and lubrication, etc., in each case when the 
plants are shut down, the stand-by charges for steam 
are 38 per cent, of the whole cost of operation, and for 
water they are 79 per cent. The total cost of operation 
of the steam plant is, however, one half that of the 
water plant. 

A gas engine, which consumes 20 cu. ft. of illuminating 
gas per brake horse-power per hour (and this figure may 
be taken as an average for engines up to 50 h.-p. using 
gas of the calorific quality of London gas), and which 
may be quickly brought into service at times of low water, 
has advantages over a steam engine where gas is available 
at a fair price. Taking the price at 2s. 6d. per thousand 
cubic feet, the cost of fuel alone for the gas engine works out 
at 0'6d. per horse-power per hour. The small gas producers 
will yield a supply of gas sufficient for a brake horse-power 
at a consumption of 1*5 lbs. of coal per hour. Indeed, 
some of the best forms of producer have brought down the 
consumption to less than one pound, but even taking 
1*5 lbs., the gas engine with producer, fuel alone considered, 
is a cheaper method of producing power than the steam 
engine for small sizes, even though a better quality of coal 
is necessary to yield the gas. With large size units where com- 
pound engines or steam turbines are used with super-heated 
steam at high pressure and condensers, the consumption of 


good coal has been brought down lower than one pound per 
horse-power per hour, but this has not been attained with 
small simple steam engines, and in this the gas producer 
and engine excels. The depreciation and maintenance of 
a producer plant bear comparison with that of steam boilers, 
though in general are somewhat greater. 



The speed control of turbines has assumed an importance 
in recent years in consequence of the exacting requirements 
of the electrical engineer. While in every case where a 
turbine or other hydraulic motor is set to drive against a 
variable resistance some degree of speed regulation is 
desirable, if not actually necessary, the high degree of regu- 
lation necessary for dynamo driving has invited attention 
to the problems of regulation in general, and has resulted 
in successful achievement under most conditions. It is 
understood that the control to which reference is here 
made is that which is effected automatically by a mechanical 
arrangement designed to adjust the power supplied to the 
turbine by the water to the immediate necessities of the 
machinery to be driven, so that a constant speed of 
the machinery may be maintained at all times, whatever 
may be the fluctuations of the load on the one hand, or of 
the supply of water on the other. 

There is but little to guide the engineer in the study of 
the regulation of water turbines by similar work accom- 
plished for the steam engine. In the one case the working 
fluid is incompressible, possessing comparatively great 
inertia ; in the other we have the opposite to these physical 
attributes, which greatly simplifies the problem and renders 
steam engine regulation possible without cumbrous apparatus 


which wq must perforce employ in hydraulic installations. 
The centrifugal governor, which is usually employed alike for 
both types of prime mover regulation, represents the extreme 
limit to which analogy would lead us. In the case of the 
steam engine the centrifugal governor, directly applied to the 
throttle or cut-off gear, has sufficient influence to overcome 
the inertia and frictional resistance of the valves ; in the 
water turbine the movement of the governor is utilised 
indirectly in a relay to operate the heavy gates or con- 
trolling mechanism by which the flow of water is adjusted. 
Thus in the steam engine the flow of the highly elastic 
fluid is checked or increased by the movement of a delicate 
valve which is attached to the centrifugal governor and 
which moves therewith ; but in the water turbine the 
acceleration or retardation of large volumes of water 
necessitates the application of forces at the controlling 
gates greater than could be got directly from a centrifugal 
governor of reasonable dimensions. In large marine 
engines a steam relay valve is sometimes employed, by 
which the attendant, operating upon the throttle valve of 
a small engine, controls the main valve which is too heavy 
to be conveniently manipulated directly. Supposing such 
a valve to be under the control of a centrifugal governor 
which would keep the speed of the engine constant by 
acting as a relay, we would have a parallel to the relay 
arrangement customary in water turbine installations. 
There is indeed no other plan by which regulation can be 
accomplished satisfactorily, so that a relay is an indis- 
pensable adjunct to the governing mechanism. 

The sudden stoppage of a mass of water flowing in a 
pipe gives rise to a momentary pressure of great intensity. 


The magnitude of this pressure above the normal pressure 
when the flow is uniform has been investigated by theory 
and determined to some extent by experiment. The theo- 
retical investigation is somewhat too recondite to be 
entered into here ; moreover assumptions have to be made 
in the mathematical treatment of the problem which would 
divest it of practical utility, were it not that experiment 
has to a reasonable extent supported the conclusions 
arrived at. By assuming an absolute rigidity in the 
material of which the pipe is composed, it has been shown 
that there are waves of pressure induced in a pipe by the 
interruption of the flow, and the maximum pressure may 
be determined. 1 If p (expressed in pounds per square inch) 
is the pressure induced by the sudden interruption of the 
flow above the normal pressure, and v is in feet per second, 
the equation for water is p = 20 v. In metric units (metres 
per second and kilogrammes per square centimetre) this 
becomes p = 4*6 v. The instantaneous closing of the 
valve in the pipe is also assumed, but in practice such a 
rapid interruption of the flow would not occur, and there- 
fore the pressure liable to be induced in the pipe would 
be considerably less than the above ; but yet it has to be 
reckoned with in long lines of pipe, and methods have to 
be taken to guard against the possible destruction of the 
pipe from this cause. This may be effected by preventing 
water hammer altogether, such as by valves which cannot 
be rapidly closed, or by providing an air chamber on the 
pipe, or else by increasing the thickness of the pipe over 
that designed to withstand the hydrostatic pressure due 
to the head (see Appendix). Experiments carried out 
1 " Applied Mechanics," by Prof. J. Perry, p. 503. 



by Mr. Latting on a pipe line 2,395 ft. long and 8 ins. 
in diameter with a 2 in. jet gave some interesting results. 
Under 302 ft. head, when the valve was closed in 25 seconds, 
the pressure of 107 lbs. in the pipe rose to 143 lbs. Theory 
gives 139 lbs. The inference to be drawn from these 
experiments is that this phenomenon stands in the way of 
the close regulation of water turbines, for this pressure 
comes upon the gates and valves and upsets the regulation. 

For convenience in discussing the details of governing 
mechanism, hydraulic turbines may be divided into three 
classes according to the head under which they operate. 
The customary general distinction between Girard or 
impulse turbines on the one hand, and reaction or 
" drowned " wheels on the other, is not so relevant for 
the purpose as the head under which a wheel is designed 
to operate. The total range of head at present in use may 
therefore be arbitrarily divided into three parts, the division 
between one class and the next being necessarily obscure, 
but sufficiently definite for the purpose of allocating any 
turbine and designating it as : — 

(1) A low fall ; (2) a medium fall ; and (3) a high-fall 


Actual Range of Static 
Head in Feet 
(in Metres). 

Corresponding Range 

of Pressure. 

Lb. per Sq. In. 

(Kg. per Sq. Cm.) 

1. Low fall 

2. Medium fall 

3. High fall 

1.5 (0-457)— 30 (9-15) 

30 (9-15)— 300 (91-5) 

300 (91-5)— 3018 (92-0) 

0-65(0-046)— 13(0*915) 

13 (0-915)— 130 (915) 

130 (9-15)— 1310 (92-3) 

The mass of the movable parts of the regulating 
mechanism in turbines is very considerable, and the 


friction opposing the motion is also great, as they are of 
necessity constructed to withstand rough usage and cannot 
always be lubricated efficiently, especially when submerged. 
This friction and inertia together offer a great resistance 
which must be overcome by a considerable application of 
force on the part of the governing mechanism, for a rapid 
acceleration is required for accurate governing. 

The following four types of gate mechanism are employed 
for regulating the flow of water to turbines : — 

(1) A circular iron or steel gate interposed between the 
guide vanes and wheel, which may be raised or lowered 
parallel with the axis of the turbine. 

(2) Movable guide vanes capable of rotation through a 
small angle about a pivot near their geometrical centre or 
centre of gravity. (See Fig. 28, p. 98.) 

(3) Needle valves or deflecting nozzles as used with 
impulse wheels acting under high heads, particularly with 
the Pelton tangential wheel. 

In addition to these gates, which may be operated upon 
by the automatic regulating devices, there are also the 
usual forms of gate for closing down the plant or for 
shutting off the water preparatory to effecting repairs, but 
which are never connected with the automatic regulators. 

(4) In turbines constructed on the partial admission 
principle the flow may be regulated by gates which control 
the number of the openings between the guide vanes. 

The circular gate (1) is usually balanced by counterpoises 
so that the force necessary to raise or lower it is the same, 
and is that required to accelerate twice the mass of the 
gate in addition to overcoming frictional resistances. It 
may be noted that, to lift the gate at a given acceleration 


without a counterpoise, a greater force is necessary than with 

a counterpoise when the required acceleration is less than 

that due to gravity. Otherwise a counterpoise, by doubling 

the mass to be moved, would require a greater force. If 

W be the weight of the gate and a the acceleration, the 

force required to accelerate it against gravity and without 

a counterpoise will be : — 

F= — a + W. 

With a counterpoise : — 

F = a. 


As the friction is substantially the same in both cases, 
when a = g these two values of F are the same. The 
convenience of having a constant resistance for lowering 
and raising is such that a counterpoise is usually used. 
The Niagara turbines are equipped with gates of this kind, 
which, with their long connections to the regulators, weigh 
about 12 tons, all of which has to be put in motion every 
time the regulator operates (Fig. 29, p. 99). This form 
of gate has many advantages, and may be used with multi- 
section turbines, so that the position of the gate determines 
the number of rings of the turbine that are in operation at 
a given time. There is a loss of energy owing to eddies 
being formed round the edge of the gate, and also from 
leakage, as the clearance between guide vanes and wheel 
is necessarily large. The resistance offered by the water 
to the movement of this form of gate is small, for though 
submerged, the motion is edgewise and the pressures are 
balanced. It is not liable to become choked with impurities 
which may have passed the grating at the mouth of the 


penstock, and there are no joints or bearings exposed to 
the action of the .water which cannot be properly lubricated. 
The employment of movable guide vanes (2) in turbines 
of the Francis type is now very general, especially for 
low heads where the velocity is small. The vanes are 
arranged to rotate through an angle of about 20°, and 
the water may be completely shut off from the wheel 
by turning them so that the openings between them are 
closed as they touch (Fig. 28, p. 98). The resistance 
offered to the movement of this ring of vanes is com- 
paratively great, and in consequence they are generally 
actuated through a worm and wheel or a similar large 
reduction gear. The pivots upon which the vanes rotate 
are of steel or wrought iron, and are stepped into holes 
bushed with bronze with a loose running fit. The method 
of communicating the motion from the governor to the 
ring of vanes varies with different manufacturers. Some 
employ a steel ring with pins projecting therefrom in a 
direction parallel to the turbine shaft. These pins ride 
loosely in slots cut in the top of the guide vanes, and 
the rotation of the steel ring through a small angle by 
means of a sector and pinion is communicated to the guide 
vanes all round the circumference. Care must be exercised 
to prevent rubbish from being carried past the gratings 
when, with low falls, this form of gate arrangement is 
adopted. Stones and rubbish are liable to be carried along 
the bottom of the head race by the current, and, by entering 
between the vanes, would prevent regulation, if indeed 
serious damage was not done. To avoid this it is expedient 
to raise the turbine 3 ins. above the floor of the head race, 
and the rubbish may then be removed when the pit is drained 


by the closure of the main gates, which should be done 
from time to time. The pivots upon which the vanes turn 
are not placed exactly at the geometrical centre, so that the 
water pressure results in a turning moment which has to 
be overcome for rotation in one direction, and which assists 
rotation in the other. A vane which is suspended in a 
moving fluid on pivots located eccentrically tends to place 
itself with the long side down stream. In practice the 
pivots are closer to the inner edges of the vanes than to the 
outer, which is necessary so that the variation in the 
clearance between vanes and wheel may be as small as 
possible with the rotation of the 
vane. An objection to this form of 
regulation has already been alluded 
to, viz., the loss of energy by shock 

Fig. 49.-Needie nozzle. 0whl g to the Variable an 8 le ° f the 
guide vanes, for, with a certain 

speed of wheel, there can only be one angle at which 

the water enters tangentially, and therefore only one 

position in which there is no loss. 

The needle nozzle by which the stream of water for the 

Pelton wheel may be controlled is shown in Fig. 49. It 

consists of a nozzle, the interior contour of which is such 

that there is a minimum of dispersion in the jet as it issues. 

A spear is located axially inside the nozzle, and is capable 

of being moved longitudinally by the governor. When 

moved to the left the area of the passage for the water is 

diminished. For very high heads, where the interruption 

or partial suppression of flow by such an arrangement 

might be dangerous, deflection nozzles of various kinds are 

used. The nozzle is hinged in some cases and is moved by 


the governor, so that with a diminished load on the wheel 
part of the stream is diverted past the buckets. This is, 
of course, a wasteful method, but, generally speaking, 
water is plentiful in places where the Pelfcon wheel is found 
to be of service. Another form of deflection nozzle as used 
by Messrs. Theodor Bell & Co. is shown in Fig. 50. The 
nozzle is rectangular in section, the upper side being formed 
by the piece E pivoted at A. This is moved by the gover- 
nor attachment B so as to increase or diminish the area of 
the nozzle at the mouth. A secondary 
nozzle D is closed by a cap C, which also 
rotates about the pivot A, and is 
moved through the same angle as 
E by the action of the governor. As 
the two nozzles are the same width 
in a direction normal to the plane of the 
paper, a partial closure of the large fig 50. -Deflection 
nozzle is compensated for by an opening nozzle, 

of the smaller, so that the spouting area 
is always a constant, and therefore the flow is steady 
through the pipe, while the wheel receives that fraction 
of it which is required to maintain the speed constant 
at all loads. 

The regulation of the Pelton wheel involves a curious 
hydraulic paradox which explains why it has been noticed 
that in some cases a diminution in the spouting area of the 
jet causes an acceleration of the wheel, and vice versa. In 
other words, increasing the area of the nozzle involves a 
reduction in the kinetic energy of the jet, and closing it 
corresponds to an increase within certain limits. The 
explanation of this curious phenomenon was offered by 


Professor Goodman, 1 who showed that it depended upon 
the loss of energy due to friction in a long pipe con- 
veying water to the nozzle. If the friction be proportional 
to the square of the velocity in the pipe, and inversely 
to the diameter, any increase of area at the nozzle 
will, by augmenting the velocity, likewise augment the 
loss of kinetic energy by friction, so that the available 
kinetic energy of the jet may be diminished more than it is 
increased by the extra volume of water spouting from the 
jet of increased area. This balance between the loss of 
energy by friction on the one hand and increase on the 
other only occurs between narrow limits, and in cases 
where the pipe-line is long and the friction losses con- 
siderable. Should such conditions be favourable, a maxi- 
mum power in the jet does not correspond with the 
maximum spouting area of the nozzle. As the jet area is 
increased, the power increases up to a certain point and 
then diminishes with further increase of area. To avoid 
such behaviour for Pelton wheels supplied through long 
pipe-lines, careful adjustment of the different dimensions, 
such as pipe diameter and normal ratio of nozzle area to 
pipe area, are necessary. As far as the writer is aware, 
much still remains to be accomplished in this direction to 
guide the designer, so that the clumsy expedient of fly- 
wheels may not be necessary to prevent hunting. 

Speed ^Regulation of Prime Movers and Connected 

If the connection between a prime mover and the 
machinery which is driven by it be positive, any alteration 

1 See Article on " Governing of Pelton Water Wheels " by Professor 
Goodman, Engineering, Nov 4th, 1904. 


in the speed of the one implies a corresponding change in 
the speed of the other, and as it is chiefly with such con- 
nections that the electrical and mechanical engineer has to 
deal, it is sufficient to assume that slip is non-existent, 
even in cases where the prime mover is connected to the 
driven machinery by belting or other connection, which 
might, if improperly designed for the power to be trans- 
mitted, have a certain amount of slip. Except with direct 
connected machinery the angular velocity of the driven 
unit is not necessarily equal to that of the driver, but 
the linear velocity of points upon driver and driven pulleys 
must be the same when connected by a belt. Con- 
sequently, for ordinary connected machinery, either the 
angular velocity of the prime mover must be the same as 
that of the driver ; or, there may be equality between the 
linear velocities ; or again, in special cases, both may be 
equal. Unless otherwise stated, angular velocity will be 
referred to in what follows, for the linear velocity of rotating 
machinery does not express clearly the speed at all, but 
only that of one point of the rotating mass, while angular 
velocity is the same for all parts of a wheel, shaft, or any 
mass rotating about an axis. 

If any source of power, such as a water turbine, be applied 
to drive a machine, any constant speed at which the con- 
nected pair revolves will necessarily imply that the torque 
of the turbine is equalled by the opposing torque of the 
machine, together with that due to the frictional resistances. 
This speed may be termed the normal speed when the 
turbine or prime mover is working at full load, and any 
departure therefrom implies that the effort of the prime 
mover or the opposing resistances have changed. In 

N.S. N 


practice many conditions may arise to upset the balance 
between the torque of the prime mover and the driven 
machinery, and consequently the unit will accelerate 
or fall in speed until a new balance is maintained, and 
the function of a governing arrangement is to restore 
the balance as rapidly as possible when from any cause it is 

This disturbance may be caused by a drop or increase in 
the energy which the prime mover puts into the connecting 
shaft, or it may be due to a variation in the resistance 
offered by the connected machinery. In either case the 
result is that the unbalanced torque acts to accelerate or 
retard the rotating mass until an opposing torque is de- 
veloped to counteract it, when acceleration ceases and the 
speed again becomes uniform, either greater or less than 
the original speed, as the case may be. 

As an example, supposing a turbine be geared direct 
to an electric generator running at 300 revs, per minute, 
and that the torque or turning moment exerted by the 
turbine at full load be 800 lb.-ft. This turning moment, 
at constant speed, is partly resisted by the reaction of the 
strong magnetic field in the dynamo, and partly by friction 
losses in bearings, wind resistance, etc., and together they 
combine to form an opposing torque of 800 lb.-ft., equal to 
that of the turbine, and the speed is therefore uniform in 
consequence. The horse-power of the wheel at this speed 
would be — 

300 x 2 77 OA _ Atr „ 
33,000 X 80 ° = 45 ' 7 " 

Imagine that the gate of the turbine is closed down to 
such an extent as to reduce the torque of the turbine by 


25 per cent. There will now be an unbalanced torque of 
800-600 = 200 lb.-ft., which will oppose the motion of rota- 
tion, and which will reduce the speed until a new balance is 
effected between the driver and driven machinery. The time 
elapsing before the speed is again uniform will depend upon 
the law connecting the resistances of the driven machinery 
with the speed. As frictional resistances 'increase with the 
speed, an addition to the power of the turbine will result in 
an acceleration until these resistances have increased to such 
an extent as to effect a balance with the effort of the turbine. 
In the same manner a reduction of the turning moment 
will result in a declining speed, which will only be arrested 
when the balance between the two is again consummated. 
The function of a governing arrangement as applied to the 
prime mover is therefore to maintain at all times the balance 
between the turning effort of the turbine and the sum of the 
turning efforts opposing rotation when the unit is running 
at the definite speed for which it is designed. Complete 
success is only attained by an absolute invariability in 
the speed, but this is not to be expected from any governing 
arrangement, for it is only by an alteration in the speed 
that the governor is brought into action at all. 

The device known as the pendulum governor, consisting 
of rotating weights which occupy various positions according 
to the speed, forms the basis of turbine speed regulation. As 
these weights occupy a definite position for each speed, it is 
clear that absolutely constant speed is impossible with any 
governor using the pendulum principle as the key to its 
operation. In some forms of high-speed engine the governor 
is brought into action by a variation in the load. In such 
engines the belt pulley, instead of being keyed on to the shaft, 

n 2 



is attached thereto through the medium of springs, and as 
the belt pull, acting tangentially to the pulley, varies, the 
angular position of the wheel upon the shaft also varies, 
and this movement is communicated to the valve gear and 
changes the cut-off of the valve so that the turning effort of 
the engine may be increased or diminished proportionally, 
and thus a balance maintained. This form of governor 
is also subject to the same limitations as the pendulum 
governor, for before it is brought into action a change 

Fig. 5 1 . — Unloaded 
, governor. 

Fig. 52. — Loaded 

in the load or in the turning moment of the engine, 
and consequently in the speed, must have occurred. The 
pendulum governor, as used for hydraulic regulation, 
consists usually of two weights attached to a central spindle, 
and capable of being rotated, the position of the weights, 
which move in or out as the speed of rotation is diminished 
or increased, determining the position of the regulating 
mechanism. The governors may either be " unloaded " as 
shown in Fig. 51, or " loaded " (Fig. 52). In the latter 
case a mass A is attached to the linkage to which the two 
weights are attached, and this moves up and down upon 


the spindle as the weights are moved out or in. This 
weight has a very important influence upon the action 
of the governor, which can best be understood by referring 
to the forces which act when the weights are rotating about 
the spindle. 

To take a simple case. If a weight be suspended by a 
cord and rotated uniformly, so that the cord describes a 
cone, the position occupied by the weight, i.e., the distance 
of its centre of gravity vertically below the fixed point of 
attachment of the cord, will be such that the forces acting 
upon the weight are balanced. These forces are the tension 
in the cord, the attraction of gravitation, and the centri- 
fugal force. The position occupied by the weights is 
independent of their actual mass, and if h be the vertical 
distance of the centre of gravity of the weight below the 
point of suspension, corresponding to an angular velocity a, 
it will be connected to the angular velocity by the relation : — 

* = 4«— -v/I 

This shows that the height h varies inversely as the 
square of the angular velocity, or that the angular velocity 
varies inversely as the square root of the height of the 
weight of the governor. 

In the actual governor the ideal string is replaced by 
a linkage and a collar upon the spindle to which the 
regulating rod is attached, all of which exert frictional 
resistances, which may be regarded as a load acting to oppose 
motion in either direction. The sensitiveness of a governor 
is shown by the movement which takes place for a given 
change in the angular velocity of the weights, and this 
varies for the position of the weights. When the weights 



are far oat, tinder the influence of a high speed, a change of 
a certain number of revolutions in the velocity exerts a com- 
paratively small influence upon the height as compared 
with a change of the same number of revolutions when the 
speed is low. This is shown by the following table, in which 




















































a is increased in successive steps by the addition of 10 per 
cent. The second column shows the corresponding value 
of h, which decreases as a is increased. The third column 
(1 — h) gives the vertical height that the weights have risen 
above the plane that they were at when a = 1. The 
differences are shown in the fourth column, and it will be 
seen that, as the speed is increased, the rise becomes less 


for given increments of speed. The sensitiveness of a 
governor is therefore greater at the lower speeds, as the 
movement imparted to the valve is greater than at the 
higher speeds when an alteration of speed takes place. 

The inevitable friction in the joints of the governor, and 
also at the collar, together with the varying angularity of 
the links, renders an exact mathematical expression for the 
height very complicated, and at best only approxima- 
tions can be made to the true height for a certain speed. 
It is not necessary to enter into the theory here, but the 
influence of loading a governor should be referred to, as it 
has immediate practical applications. The sensitiveness 
may be greatly increased by the addition of a load, so that 
the motion of the loaded governor for a given change of 
speed is greater than in the case of the unloaded. The 
approximate increase in the sensitiveness by the addition 
of a weight 2TF, moving nearly at the same velocity as the 
ball, is : — 

1 + "d where B is the weight of one ball. 

The sensitiveness is therefore increased in the ratio of 

1 + : i. Thus if W = B the sensitiveness is doubled. 

With an unloaded governor a speed is soon reached which 
gives too small a height, and therefore it is necessary to 
load the governor if it is required for high speeds. By this 
means a greater height for a given speed is attained, and a 
greater movement for changes in speed. Springs are also 
employed on pendulum governors instead of weights, and 
for fly-wheel governors they are used to balance the centri- 
fugal force. The proper weight to be given to the balls 


will depend upon the amount of variation from the mean 
speed that is allowed before the governor begins to act, for 
it must exert a force at the collar greater than the friction 
and resistances. 

The pendulum governor is therefore the chief means by 
which an unbalanced condition between propelling effort 
and resistance is corrected in any motor attached to 
machinery. But there is also a valuable aid to the main- 
tenance of a constant speed in the inertia of the rotating 
parts, or what is known as " fly-wheel effect," and this has 
a steadying influence, as the inertia of the parts prevents 
too rapid an acceleration when the balance is, for any reason, 
upset. The fly-wheel, or rotating mass, which includes in 
the case of a turbine plant the turbine itself and connected 
machinery, must be such that the speed shall not be too 
rapidly increased or diminished by any changes of load or 
turning moment imparted by the motor. On the other 
hand, it is wasteful of power and costly in maintenance to 
have the mass of the rotating parts more than is necessary, 
and the attainment of a correct proportion for these masses is 
a problem which is often shirked by adding more weight 
than is necessary, and which remains, to outward appear- 
ances, solved, in the same manner that a foundation, which 
is more than sufficient to sustain the load which is to be put 
upon it, shows the excess in extra cost of useless material, 
while it serves the function of sustaining the building as 
well as if it were correctly proportioned. 

Some general remarks upon the subject of rotating 
masses will serve to illustrate the action of the fly-wheel as 
a regulator. 

The mass of a body, or its inertia, is measured by the 


force necessary to impart to the body a given acceleration, 
j and the well-known equation, F = M x a, applies uni- 

| versally. If, instead of the motion being in a straight line, 

the mass M is constrained to rotate about a radius r, a new 
relation exists which is represented by T = I x co, where 
1\ the turning moment, is equal to the product of the 
moment of inertia (I) and the angular acceleration co. It is 
easily seen that if a mass be rotating about a fixed point the 
turning moment necessary to accelerate it at a given rate 
depends upon the radius at which the mass is rotating, and 
/, the moment of inertia, takes the place of M, the mass. 
This constant, which takes the same place in the dynamics 
of rotation as mass does in linear motion, is therefore the 
moment of inertia or m r 2 , for a mass m rotating at a radius 
r. Engineers hardly ever speak of the moment of inertia ; 
it is generally expressed as ton-ft. 2 , lb. -ft. 2 , or kilogramme- 
metres 2 . The total moment of inertia of a wheel, or 
other rotating mass, is obtained by adding up the moments 
of the separate parts. This can be done for any geometrical 
figure, and the results are found in tables giving the formula 
for each figure. The engineer who is working problems in 
rotating bodies is chiefly concerned with rotating masses in 
the shape of cylinders or discs like grindstones or the rims 
of fly-wheels, and for these the moment of inertia, where i\ 
is the outside radius of the disc, and M the mass, is 

1 = M x~. 

If the disc has a large hole in the middle of radius r 2 , the 
moment of inertia of the rim is 

J = M x | (n a + r, 9 ). 


In this expression M is the mass of the rim. 

The radius of gyration, which is sometimes referred to, 
is the distance from the axis of rotation at which, if the 
entire mass of the rotating body were concentrated, the 
moment of inertia would be the same. For a circle this 
distance is 

4 = °' 707r - 

For simplicity it is usual to assume in calculations that 

the mass is concentrated at the mean radius or — ~ — - . 

For the same reason in calculations for weights of fly-wheels 
the spokes and hubs are neglected, as the rim, both by its 
position and relative weight, has an overwhelming effect, 
which makes the omission of the rest of little consequence. 
As an example, a cast-iron fly-wheel of 6 ft. outside 
diameter has a rim 8 ins. deep and 6 ins. wide (parallel 
to the axis). Assuming 450 lbs. per cu. ft. as the weight 
for cast-iron W= (28*27 - 17'10) x 0*5 x 450 = 2,513 lbs. 

32-2 ' 

g (n 2 + r 2 2 ) =i (9 + 5*45) = 7*225. 

I = 78*1 x 7*225 = 564 lb.-ft. 2 
By making the assumption that the mass of the wheel is 
concentrated at the mean radius of the rim 

= 78*1 x (■ 

3 + 2-333 \ 2 

= 78*1 x 7*11 = 555 lb. ft. 2 

This approximation therefore leads to a value of the 
moment of inertia, which is, in this case, within 2 per 
cent, of the actual. This is close enough for practical 



purposes, though it is but little extra trouble to obtain it 

The calculation of the total moment is complicated in 
turbine units by the inertia of the water passing through 
the wheel. This is especially the' case in large turbines 
passing a large volume of water, and therefore they tend to 
run more steadily than impulse wheejs which do not 
contain much water. Bodmer states that with some 
turbines (depending upon the vane angle) velocity of flow 
decreases as speed increases, while with others the contrary 

Fig. 53. — Turbine direct connected to generator, with fly-wheel. 

is the case. The ratio of the radius of entry to exit also 
has an influence. For impulse wheels the velocity of flow 
is constant whatever the speed of the wheel may be. As 
most reaction turbines are designed, the velocity of flow 
increases as the speed increases. In direct connected units 
it often becomes necessary to increase the inertia by 
the addition of a fly-wheel, as shown in Fig. 53, which is 
sometimes placed between the turbine and generator, and 
sometimes upon an extension of the shaft outside the out 
board bearing. This arrangement necessitates a heavier 
shaft to resist the bending moment. 


The armatures of electric generators are of necessity 
very heavy, and supply much of the needed inertia. In 
allowing for them they may be taken as a solid cylinder 
of metal of the air gap diameter, with an allowance for 
the ventilating ducts. With revolving field generators the 
calculation is not so simple, but the writer's practice is 
to omit the spokes, and bub and to calculate the weight of 
coils and poles as if constructed of solid metal. This gives 
a fair approximation to the true value. 

The coupling of an electric generator to a steam or gas 
engine is attended with special disorders which the hydraulic 
engineer does not experience. These are due to the uneven 
turning moment of the prime mover throughout the revolu- 
tion, caused by the varying angularity of the crank, and 
the expansion of steam or gas in the cylinder giving rise to 
a varying pressure. The uniform turning moment of the 
hydraulic turbine is a distinct advantage, by enabling the 
rotating mass or fly-wheel effect to be kept lower than that 
required for a steam engine. For this reason turbines may 
be advantageously used to operate alternators in parallel 
with greater success than attends steam or gas-driven units 
for the same mass in the rotating parts. The requirements 
of successful operation of alternators in parallel are such 
that the angular deviation of the armature from the normal 
position must not be greater than a certain fraction of the 
pole-pitch. This allowance differs, but among the large 
electrical companies 1 -200th is a usual figure. 

The unit shown in Fig. 53 consists of a turbine driving 
an alternator direct, with the exciter on the end of the shaft. 
If a fraction of the load is suddenly thrown off, as by the 
opening of a switch in the circuit or distribution system, 


the speed tends to rise, and supposing that there was no 
governor to restore the balance, the rate at which the speed 
would rise would be inversely proportional to the moment 
of inertia of the entire rotating mass. The addition of a fly- 
wheel will therefore serve to check the rate of change of 
speed, but cannot restore equilibrium. This latter function 
belongs to the governor. The difference between the fly- 
wheel and governor is, therefore, that the former allays 
the rate at which the speed changes when equilibrium is 
upset, and the governor effects the cure. The rate of 
change of speed (acceleration or retardation) may be made 
indefinitely small by the addition of metal, but there is an 
economical limit to this. Where turbines are connected to 
mills, the load is frequently changed slowly so that the 
acceleration is not constant, but in electric installations the 
throwing of a switch means that the turbine is instantly 
relieved of a fraction of the load and the resulting accelera- 
tion would be constant. In making calculations, constant 
acceleration or retardation is assumed, as it is impossible to 
obtain the law connecting the change in acceleration with 
change in the load owing to friction. The specifications to 
which governors are designed to conform are generally stated 
in allowable percentages of speed variation from the 
normal, for fractions of the load applied or thrown off. A 
good water-wheel governor ought to comply with the 
following conditions which would be considered necessary 
for the satisfactory operation of direct current generators, 
in conjunction with sufficient fly-wheel capacity to allow 
the governor time to act before the speed oversteps the limit. 
With sudden variations of load of 25 per cent, the change 
in speed ought not to exceed 3 per cent. 


With 50 per cent, load variation, speed variation 6 per 

With the entire load thrown off, speed variation 10 per 

Also with the load gradually thrown off during a period 
of not more than ten seconds the variation in speed should 
not exceed 4 per cent. 

These specifications, if adhered to, enable a generator to 
be coupled to a turbine and used for arc and incandescent 
lighting without the necessity for storage batteries. With 
hydraulic governors they are frequently surpassed, and on 
a large installation in Switzerland better results have been 
obtained for variations of 25 per cent, and 50 per cent, in 
the load. In such a case unlimited power is at the disposal 
of the engineer, so that the gates are operated rapidly. 
With small installations this is not possible if the power 
has to be derived from the wheel, which cannot be drawn 
upon suddenly for the power necessary for regulating. 

In order to comprehend the manner in which the speed 
changes with alteration in the load we must employ some 
suitable formula derived from elementary principles. If 
a shaft be rotating uniformly and transmitting power from 
the driver to driven machinery the relation between the 
torque, or twisting moment, in pound feet and the horse- 
power is expressed as 

TT _ 2 TT N 

H " P ' = 60 X 550 X i0r ^ e ' 

, . . , _, ,, , 5251 x H.-P 
from which T (torque) = ^ 

N being the number of revolutions per minute. 

If a> is the angular acceleration per second — i.e., the gain 


in revolutions per minute in one second — and p is the 
fraction of the load suddenly thrown off, 

5251 x H.-P. 60 
N x I 2?r r ' 

H -P 
or co = 50,140 jf-j-j x p, 

I being the moment of inertia of the rotating mass. 

If the fraction of the load p be suddenly thrown off, 
as for instance when a switch is opened, the opposing 
unbalanced torque of the turbine, if allowed to persist, will 
cause the speed to increase as given by this relation. As 
an example, a direct connected unit as shown in Fig. 53 is 
running at 180 revolutions per minute, 75 h.-p. being 
transmitted from turbine to generator. With the generator 
suddenly relieved of 25 per cent, of the load, the increase 
in speed can be calculated when the moment of inertia 
is known. This is found to be 20,120 (mass units), 
therefore : — 

w = 180 X 20,120 X °' 25 X 50 ' 140 = °' 26 - 

If no correction be made in the driving power by a 
governor, the speed will therefore have increased to 180 + 
0*26 x 60 = 195'6 revolutions per minute in one minute, or 
about 8*7 per cent. With greater fractions of the load 
thrown off, the rate will be correspondingly increased. A 
certain correction is automatically made by the increase in 
the frictional resistances, especially wind resistance, which 
increases with the speed, and this tends to keep down the 
speed, but its effect may properly be neglected. 

The increase in the speed, expressed in revolutions per 
minute, and percentage of the normal speed are plotted 



against time in seconds on the curve (Fig. 54). For 
example, with 50 per cent, of the load suddenly thrown off, 
it is seen that the speed has increased 5 per cent, in 17 
seconds, the increase being proportional to the time, and 
for 25 per cent, the increases are one-half those for 50 per 

If a disengagement governor were to be utilised to check 

the speed of the unit at 2 per 
cent, variation when 50 per 
cent, of the load was thrown 
off, we find from the curve 
that it would have to come 
into operation before 6'5 
seconds had elapsed since the 
acceleration began. Such a 
governor would never be 
employed to control the 
speed, for it is necessary that 
a check should be put upon 
the acceleration before the 
velocity had increased to such 
an extent, and this the hy- 
draulic and mechanical continuous governors do gradually 
from the moment the speed begins to rise above the 
normal. The action of a disengagement governor is 
shown by the dotted curve, and that of a continuous 
governor by the full line. Supposing 50 per cent, of 
the load be suddenly thrown off, the speed rises in accord- 
ance with the straight line, the slope of which shows the 
rate of rise. When the speed has increased 4 per cent, 
(to 187*2 revolutions per minute), which will be 14 

Fig. 54. 


-Acceleration curve. 



FVLLLGAO SPfBO J*#* *M.,tt0tO*D SP£E0 34IX0M 

seconds after the load is diminished, the governor acts, and 
the gates being gradually closed, the rate of gain in speed 
drops in consequence of the reduced driving torque. 
During this period the speed still rises, but at a decreasing 
rate, the point A upon the dotted line showing the maximum 
speed (188 revolutions per minute). As the driving torque 
has by this time been lowered by the shutting of the gates 
to such an extent that the resistance preponderates, the 
speed again drops as shown by the dotted curve. This drop 
is again checked when 
the governor goes 
out of action. The 
speed curve for a con- 
tinuous governor is 
shown as a full line, 
the rate of change in 
the speed beginning 
at the moment the 
load is thrown off, 
the maximum speed (186 revolutions per minute) being 
attained in 24 seconds (point B on the curve). 

Fig. 55 illustrates the action of a continuous hydraulic 
governor, and is a curve derived from a test made upon a 
500 brake horse-power turbine at an electricity works in 
Switzerland, for which the author is indebted to Messrs. 
Escher, Wyss, & Co. The full-load speed of the turbine is 
868 revolutions per minute, and the " no-load " speed 382 
revolutions per minute. The curve shows the effect upon 
the speed of suddenly throwing off the entire load. The 
abscissaB are seconds, and the ordinates percentages of the 
speed, the distance between the horizontal dotted lines 

Fig. 55. 

-Action of continuous hydraulic 



being 1 per cent. The curve shows that the actual speed 
oscillates about the " no-load " speed like a damped vibra- 
tion, each successive rise and fall being less than the 
preceding, until, about 18 seconds after the load is thrown 
off, the variation from the true " no-load' ' speed is very 
slight. This represents in general the action of the con- 
tinuous governor upon the speed, which oscillates about 
a mean value. 

A turbine by the same Swiss firm, working under a head 
of 14 metres (45*9 ft.) was tested for regulation with the 
following results. The wheel was a Francis turbine rotating 
upon a horizontal axis, and giving at maximum load about 
120 h.-p. The tests were made by a brake, and for a 
variation from 82 to 84 brake horse-power the increase in 
speed was 3*64 per cent., i.e. from 330 to 342 revolutions 
per minute. For a variation of 10 h.-p. (72 to 6*2) the 
speed variation was 1*78 per cent. Expressed as per- 
centages of full load, the variations show that the regulation 
was good. The governor operated upon the guide vanes of 
the wheel and was actuated by a hydraulic cylinder supplied 
with water at the pressure due to the head. 

Types of Water Wheel Governors. 

The earliest type of water wheel governor, which was 
applied to water wheels as well as to turbines, was a dis- 
engagement governor, which only came into action when 
an assigned departure from the normal speed was attained. 
Until this variation from the normal speed of the wheel or 
turbine was reached the pendulum governor was out of 
gear entirely with the mechanism for moving the gates, 
and it was only when a considerable displacement from the 



mean position of the weights was reached that the 
governor, by automatically engaging a mechanism, effected 
the opening or closing of the gates. These governors are 
still used even for electric work, and with some success 
when the fly-wheel effect is carefully proportioned to the 

Figs. 56, 57, and 58 show types of disengagement gover- 
nors. In that known as the Scholfield governor, there are the 
usual pendulum weights 
with spindle and collar. 
The shaft D (Fig. 56) is 
connected with the run- 
ning machinery, so that 
the eccentric E, which 
is keyed to it, shall be 
constantly in motion. 
At the end of the eccentric 
rod is a pin projecting 
from a rocking lever which carries two pawls, P and E, 
at its extremity. These pawls are arranged to engage 
the spur wheels A and B, but are opposed to each 
other so that they tend to rotate the shaft C in opposite 
directions when one or the other is allowed to engage with 
the spur wheels. The shaft C is connected with the 
regulating gate, and a rotation in one direction shuts off the 
water, and in the other opens the gate. S is a shield 
which is moved to the right or left by the action of the 
governor, and which raises one or other of the pawls off 
the goars and therefore allows the shaft C to be rotated by 
a succession of movements according to the revolutions of 
the eccentric. When the speed is normal the shield is in 


Fig. 56. — Disengagement governor. 


Fig. 57. — Disengagement governor. 


mid position and has no effect, so that the shaft C vibrates 
back and forth without any appreciable change on the gate. 
The sensitiveness of the governor would be measured by 
the distance the shield S has to move before coming into 
action with a pawl. 

Fig. 57 shows a governor of this type as made by 
Messrs. Gilbert Gilkes and Co., by whose courtesy I am 
enabled to produce the following description : — 

Motion is imparted from the governor to the guide blade 
shaft A by means of two sets of pawls B B (one set for 
opening and one set for closing) which work on to a ratchet 
wheel B keyed on to the guide blade gear shaft A. 

The position of the governor balls decide which set of 
pawls shall be in action. If the speed is high and the balls 
out, then the governor sleeve rising interposes a silencer or 
shield S between the opening pawls and the ratchet wheel. 
If the speed is low, the shield is interposed between the 
closing pawls and ratchet wheel. When the turbine, and 
consequently the governor, is at its normal speed, then the 
shield does not allow either set of pawls to work, and the 
guide blades are therefore stationary. It will be seen that, 
should the guide blades be full open, and the turbine for 
some cause below speed, the governor would endeavour to 
open the guide blades still further, and so break some- 
thing. Such a contingency is provided for by a knock-off 
arrangement, which consists of a scroll cast on to the 
ratchet wheel. As the ratchet wheel is revolved the scroll 
causes the wheel E to be rotated. 

Attached to E are two levers, so arranged that, when the 
guide blades are full open, one of the levers catches a pin 
and lifts the governor sleeve up, and of course at the same 



time causes the shield S to be interposed between the two 
pawls and the ratchet wheel, thus preventing any further 
opening of the guide blades. When the guide blades are 
shut, the other lever acts in a similar manner, pulling 
down the governor sleeve, and so preventing the guide 
blades from closing any further. 

Fig. 58 shows the Hartford governor, which is a con- 
tinuous governor in the sense that 
any change in speed whatever is 

Emet by a corresponding action of 
\\j/y the governor towards adjustment. 

A belt driven by the water wheel 
passes over two pulleys, one of 
which is a cone pulley. The belt 
is usually maintained tight by 
guide pulleys not shown. Each of 
these pulleys drives a bevel wheel 
(A and F) which mesh with the 
wheels D and B, and these wheels 
revolve in opposite directions. D 
and B are connected by sleeves 
with two similar bevel wheels which 
engage with C, and when revolv- 
ing with the same speed in opposite directions C merely 
revolves upon its own axis. When, however, owing to 
the position of the belt upon the cone pulley, D and 
B have different speeds, the shaft to which C is keyed 
moves round and, being connected to the gate mechanism, 
regulates the supply of water. The position of the 
belt upon the cone pulley, and hence the differential 
motion of the bevel gears, is regulated by the belt shifter 

Fig. 58.— Hartford dis- 
engagement governor. 



which is in connection with the pendulum governor. At 
the normal speed the belt is upon a diameter of the cone 
pulley equal to that of the cylindrical pulley, and hence 
there is no movement of the gate. The slipping of the belt, 
and the difficulty of always keeping it parallel to the 
normal to the pulley 
shafts, renders this 
form of governor slug- 
gish in action. The 
principle of the relay 
is adhered to in all 
these governors, for 
the force of the pendu- 
lum governor is only 
utilised to operate 
mechanism, either 
occasionally, as in the 
disengagement gover- 
nors, or continually, 
as in the belt-driven 
arrangement just 

Fig. 59.— Lombard-Replogle mechanical 

Fig. 59 shows another form of mechanical governor, as 
made by the Lombard-Eeplogle Company, of Akron, Ohio. 
The pulley A receives motion from the turbine, and the 
governor balls are located within it, the position of which 
effects the motion of the trip lever B. This lever is 
poised upon a movable fulcrum, and the first act of the 
governor is to shift the fulcrum so as to allow the speed 
governor to rest at a slightly lower speed for a short time. 
The lever actuates the rod C, upon which are carried two 

Fig. 60. — Niagara hydraulic governor. 


bevel pinions which are arranged to engage with the nut 
gear D. The rotation of the nut D draws a spherical 
pulley E out of centre with the two concave discs F and G, 
and as these discs are rotated in opposite directions by a 
quarter-turn belt connecting the two pulleys, the spherical 
pulley is given a rotation in one or other direction, and at 
the same time it tends to centre itself by the rotation of 
the screw in the nut D. The rotation of the shaft H effects 
the closure or opening of the gates according to the direc- 
tion of rotation. This differential motion is very effective, 
as it prevents the governor from over-running. 

Hydraulic governors have almost entirely suppressed the 
mechanical governor for purposes of close regulation in 
electrical installations. The mechanical governor cannot 
be made as sensitive as the hydraulic, the valves of 
which are directly controlled by the pendulum. Under 
the name of hydraulic governors all forms of apparatus 
using the pressure of a fluid to operate the gates are included. 
The fluid is usually water, and is often under the pressure 
due to the head acting on the wheel, but sometimes, for 
installations working at low heads, the pressure is obtained 
by pumps, and also oil is substituted for water where a 
closed system of piping can be maintained. The hydraulic 
governor used at Niagara, which controls the speed of the 
5,000 h.-p. turbines, is shown in Fig. 60. The position of 
the piston in the cylinder is regulated by the pressure of 
oil admitted through a valve controlled by the pendulum 
governor shown on the right of the illustration. Hand 
regulation is provided for by the bevel gears which are 
manipulated by the hand wheel outside the casing. This 
governor is placed on a platform about 125 ft. above the 



turbine, but the heavy connections are balanced, and it is 
extremely sensitive. The regulation of these governors is 

such that with the entire 
load thrown off the genera- 
tors as quickly as possible 
the increase in speed is less 
than 4 per cent, of the 
normal speedof 250 revolu- 
tions per minute. These 
governors are very much 
more satisfactory than the 
mechanical governors, and 
the speed variation under 
normal conditions (which 
would generally imply that 
less than 25 per cent, of the 
load would be at any time 
suddenly thrown off or on) 
is very satisfactory. The 
oil for operating these 
governors is supplied by 
pumps driven electrically. 
For small installations, 
operating under a low head 
of water, a governor of a 
different type is required, 
and the power consumed 
in operating the controlling 
mechanism must be derived 
from the turbine direct. If the wheel is of small power, 
that required to effect regulation makes a considerable 

Fig. 61.— Hydraulic governor for 
low falls. 


fraction of the whole, and must be considered in estimat- 
ing the output of the plant. The governor shown in 
Fig. 61 is designed to control turbines working under heads 
too low for the utilisation of the hydrostatic pressure, 
and oil is used as the working fluid. There is an advantage 
in oil, as the valves and passages escape the chance of 
becoming choked with sand and impurities carried by water. 
If water is used, strainers of close mesh are required to 
intercept such impurities. . The governor consists of a 
casing A, which is filled with oil, and two rotary oil pumps 
formed by close meshing spur gears in a tight case, one of 
each pair being keyed to the shaft C, which receives motion 
from the pulley D, driven direct from the turbine or 
counter shaft. These pumps are in mesh through a bevel 
gear with the bevel pinion E, which is keyed to a shaft 
communicating with the guide vane mechanism of the 
turbine. A valve G, worked by levers from the pendulum 
governor, controls the flow of oil to the pumps, and pro- 
duces regulation in the following way: — When the pump 
rotates in the direction of the arrow, the suction is at Q and 
the delivery at E. If E be closed so that no oil can escape, 
the wheels cannot rotate, and the casing must rotate with 
the shaft C. The aperture Q communicates with the main 
body A, and E with the valve G, which is so arranged that 
a small motion of the governor closes the connection from 
the upper or lower pump aperture E, and thus locks either 
the upper or lower pump. The locking of a pump causes 
the shaft F to be driven in one or the other direction 
according as it is the upper or lower pump thiit is fastened, 
and this motion is communicated to the guide vanes. A 
very small movement of the pendulum causes action. The 



oil in the chamber has to be renewed at intervals of some 
months, as otherwise it becomes thick, and is liable to clog 
the pumps and cause a slipping of the driving belt. 

The governing arrangement for a Pelton wheel is shown 
in Fig. 62, as made by Messrs. Gilbert Gilkes & Co., Ltd., 
Kendal. The function of the governor is to move the needle 

3- i 

Fig. 62. — Pelton wheel governor. 

in or out of the nozzle, and this is done by means of the 
pressure cylinder D, to which water is admitted through a 
double-ported valve E. The position of this valve is con- 
trolled by the pendulum governor. This method of govern- 
ing is extremely delicate, as there is no heavy gate 
mechanism to put into motion, and the action of the 
regulating gate is immediate. 

For mechanical governors of the best description, 10 
to 15 seconds is required for the entire closing of the 
gates, but with hydraulic governors this time is reduced 
to 2 or 3 seconds. With the Pelton wheel governors 















the action is instantaneous. This rapid closing of the 
outlet to a long pipe line would involve danger, and 
for this reason a deflection nozzle is preferable, in which 
case the pressure within the cylinder is applied to move 


the nozzle. Sometimes a butterfly valve is employed 
in the supply pipe, which is directly actuated by the 
governors. Fig. 63 shows a mechanical governor by Messrs. 
Gilkes & Co. applied to the control of a small Pelton wheel 
through a butterfly valve. These valves as a rule cannot 
be used with long lines owing to the danger from water 
hammer, but when actuated slowly with a small mass of 
water behind them, they afford a simple means of controlling 
the flow to the wheel. The mechanism of this mechanical 
governor is simple, and consists of an eccentric which 
oscillates pawls which engage with toothed wheels in the 
manner already described (page 195). The eccentric is 
always in motion, being driven through the bevel gears 
from the pulley shaft. Fig. 64 shows the same arrangement 
applied to a small double vortex turbine. Steadiness of 
running is further ensured by the small fly-wheel between 
the turbine and dynamo. 

Another form of regulating device for wheels of the 
Pelton type is the invention of Mr. CasseL The wheel to 
which this device is applied consists essentially of two discs, 
upon the peripheries of which the buckets are situated. 
These discs are free to slide along the shaft. The tension 
of certain springs holding the discs together is balanced by 
a weight. When the wheel is running at normal speed the 
springs keep the discs together, so that the two halves of 
the buckets come together, and the impinging stream of 
water is caught on the dividing projections down the centre 
of the bucket. Should the speed of the wheel increase, the 
weights, flying outwards by centrifugal force, draw the discs 
asunder and allow part of the stream to pass through 
between the two halves of the buckets. The closing of the 



Fig. 65. — Emergency governor. 

buckets takes place when the speed is again brought back 
to the normal, and so the wheel is controlled by allowing 
part of the stream to pass without doing useful work when 
the speed is above the normal. This controlling mechanism 
is therefore not unlike the deflecting nozzle, in that the 


excess water is wasted when not required for driving the 

Sometimes emergency governors have to be fitted in 
addition to main governors. In a plant for the Penhalonga 
Mines, in Southern Rhodesia, constructed by Messrs. Gilbert 
Gilkes & Co., emergency governors are employed, one of 
which is illustrated in Fig. 65. In this plant there are 
two Pelton wheels, which take their supply of water from a 
river 1440 ft. away, and 3.50 ft. higher than the power-house. 
The water is conveyed by a 22 in. riveted steel pipe, which 
branches into two 16 in. supply pipes inside the power- 
house, each branch supplying a 6 ft. Pelton wheel. The 
wheels are designed to run at 250 revolutions per minute, 
and each develops 375 h.-p. at normal speed. Each wheel 
is directly coupled to a three-phase generator supplying 
current at 440 volts and 50 periods when running at the 
normal speed. The pressure is raised by transformers in 
the power-house for the line. There are three governors 
fitted to these wheels. One is a sensitive hydraulic governor, 
which diverts the water from the wheels by means of steel 
slippers, which are machined to a knife edge, and the 
position of which in the jet is controlled by the main 
governor. The slippers are secured to levers keyed to a 
shaft passing under the covers of the wheels. One end of 
this shaft has a long lever keyed to it, which is worked 
from the governor. The governor has a spring loaded 
pendulum, which, through a system of levers, raises or 
lowers a valve controlling the water in the hydraulic 
cylinder, and thus moving the piston in or out, and the 
motion of the piston is communicated to the deflector shaft. 
A dash pot is provided, by means of which the speed of the 

N.S p 



slippers may be regulated. This governor is driven by an 
independent motor, which is supplied with current from the 
switchboard. By placing both wheels under the control of 
one main governor, the alternators, which are in parallel, 

will tend to remain so. 
In the event of a short 
circuit upon one of the 
generators, the emer- 
gency governor comes 
into action and at 
once shuts off the water 
from the wheel. 

The emergency 
governor consists of a 
loaded pendulum, 
which releases a cast- 
iron weight by means 
of a trigger if the 
speed should rise above 
a certain limit. The 
weight in falling oper- 
ates the deflector and 
causes the full jet to 
pass the wheel, and 
until released by hand 
the wheel cannot be supplied with water. 

From a test of an hydraulic governor made by Messrs. 
Theodor Bell and Co., Kriens, the curves shown in Fig. 66 
are obtained. The turbine is a Pelton wheel of 2,500 h.-p., 
and the effect upon the speed of suddenly throwing off 600, 
1,120, 1,610, and 2,090 h.-p. is shown by the four lines. The 

Fig. 66.— Test curves of 2,500 h.-p 


distance between each horizontal dotted line represents 
1 per cent, of the mean speed, and it will be seen by the 
last diagram that in throwing off about 83 per cent, of the 
load the maximum speed variation is about 7 per cent., and 
the vibrations of speed above and below the mean value 
are quickly damped out, so that the uniform speed of 
806 revolutions per minute is soon attained. These curves 
are very instructive, for they show the excellence of the 
hydraulic governor as attained in modern practice. 




The currents of air which, in varying intensity and 
direction, blow over the surface of our globe have been 
employed by man from the earliest times as a motive power 
for propelling vessels over the seas, and, notwithstanding 
the introduction of steam, a large part of the carrying trade 
of the world to-day is done in ships propelled by the same 
natural element that filled the sails of craft thousands of 
years ago. It might therefore be supposed that the study 
of the winds and air currents which has been necessary to 
the mariner would have yielded results capable of scientific 
interpretation, and that this branch of meteorology would 
lead all the others in precise knowledge. But though the 
art of sailing has been practised for centuries, and our 
knowledge of prevailing winds over courses and at places 
on the surface of the earth is not without accuracy, certain 
features of the subject of air movements, which are chiefly 
useful to the power engineer, have defied the close attention 
which from time to time has been directed to them, and are 
still outside all scientific laws. It is only within recent 
years that studies of the wind have been made by experi- 
mental research, with a view to elucidating some of the 
points upon which the engineer especially desires knowledge, 
and about which we will treat in this chapter. 

The wind, at a given place on the earth's surface, is 


constantly varying in intensity and direction throughout 
the year. The change in direction may be either 
momentary, or it may be a decided change in the point of 
the compass from which it blows. The former changes are 
due to local influences, such as surrounding objects may 
exert by reflecting the wind from their surfaces, and the 
results of which are well known to the erecters of wind- 
mills, who have to choose a locality free from such disturb- 
ing influences. These sudden changes are seen in the 
oscillating movements of weathercocks and of the head of a 
windmill which is blanketed by buildings, trees, or other 
obstructions. The permanent changes in direction 
(permanent only in contradistinction to the above rapid 
changes), and which are accompanied by a corresponding 
change in the weathercock, have their causes in the varying 
distribution of heat on the earth's surface, which leads to 
upward currents of heated air at places, towards which the 
colder air moves to supply the vacancy thus created. While 
it is true that the contour of the surface of the earth at a 
locality has a great influence upon the prevailing direction 
of the wind at that place, at altitudes above the influence 
of the surface, the prevailing direction of the wind in many 
places is well defined, and at certain places these prevail- 
ing winds bear names such as the "trade" winds. In a 
mountainous country the wind naturally takes the direction 
of a valley either up or down, for the lateral ranges shut 
out winds which blow across the direction of the valley. 
The direction of the wind is different at different altitudes, 
the ocean of atmosphere being seemingly composed of layers 
or strata of air moving independently. Aeronauts take 
advantage of these currents of varying direction by rising 


or descending until the balloon enters a current moving in 
the desired direction, though they are not always successful 
in finding one quite suitable. If their desires were always 
gratified, controllable air ships would have become common, 
and the North Pole would have been reached ere this. 

But the surface of the earth presents such a rough and 
uneven bed over which a current of air has to pass that the 
current, instead of being made up of continuous parallel 
stream lines, becomes a boiling mass of eddies, vortices, 
and subsidiary currents, some of which even flow in the 
opposite direction to that of the main stream. It is out of 
this confusion that the physicist and engineer have been 
endeavouring to obtain some rules or laws which will guide 
them in predicting wind pressures from velocities and other 
important relations incidental to the flow of fluids. The 
motion of a leaf blown from a tree or other light object 
caught in the wind will illustrate the complex nature of the 
current, and how far from correct it is to assume that the 
movement of air is uniform and in parallel stream lines. 
Nor is there any evidence to show that the air current 
moves uniformly in the upper layers of the atmosphere, 
where, with the friction of the earth removed, such 
might be expected. There is, on the contrary, accumu- 
lated evidence to point to the conclusion that at any 
elevation the air moves in a manner quite different from 
that of water in deep rivers, which, though split up into 
eddies close to the bed or banks of the stream, flows along 
with a regular motion where such disturbing influence does 
not exist. The late Professor S. P. Langley, whose 
researches upon aerodynamics and the problem of flight 
form some of the most valuable contributions to the subject, 


refers to the complex character of the air currents in one 
of his monographs. 1 While making some observations with a 
light anemometer, his attention was attracted by the peculiar 
behaviour of the instrument, which registered an extreme 
irregularity of velocity in a wind which would have other- 
wise been classed as a feeble breeze. These irregularities 
suggested to him the possibility that a so-called steady 
wind is in reality made up of variable and irregular move- 
ments of great frequency which the inertia of the usual 
form of anemometer would hide. He accordingly made an 
anemometer especially for the purpose of observing this 
point more closely, which weighed only 5 grammes and had 
the small moment of inertia of 300 gr.-cm. a By means of this 
instrument he was able to compare observations with those 
taken by an ordinary weather bureau anemometer, with the 
result that his former conclusions were confirmed. A 
comparison of the two anemometers showed that the wind 
was registered on the light anemometer as very variable, 
while the ordinary instrument did not show the small 
variations at all. The record was taken over a period during 
which the wind would travel two miles, and the following 
are some of the observed results. 

In the words of the experimenter, " the velocity, which 
was at the beginning of the interval considered nearly 
23 miles an hour, fell during the course of the first 
mile to a little over 20 miles an hour. This is the 
ordinary anemometric record of the wind at such eleva- 
tions as this (47 metres) above the earth's surface, where 
it is free from the immediate vicinity of disturbing 

1 " The Internal Work of the Wind" (Smithsonian Contributions to 
Knowledge), by S. P. Langley. 


irregularities, and where it is popularly supposed 
to move with occasional variation in direction, as the 
weathercock indeed indicates, but with such nearly uniform 
movement that its rate of advance is, during any such brief 
time as two or three minutes, under ordinary circumstances, 
approximately uniform. This, then, may be called the 
* wind/ that is, the conventional ' wind ' of treatises 
upon aerodynamics where its aspect as a practically conti- 
nuous flow is alone considered. When, however, we turn to 
the record made with the specially light anemometer, at 
every second, of this same wind, we find an entirely different 
state of things. The wind starting with the velocity of 23 
miles an hour, at 12 hours, 10 minutes, 18 seconds, rose 
within 10 seconds to a velocity of 33 miles an hour, and 
within 10 seconds more fell to its initial speed. It then 
rose within 30 seconds to a velocity of 36 miles an hour, 
and so on, with alternate risings and fallings, at one time 
actually stopping, and passing through 18 notable maxima 
and as many notable minima, the average interval from a 
maximum to a minimum being a little over 10 seconds, and 
the average change of velocity in this time being about 
10 miles an hour." 

These experiments were primarily conducted to throw 
light upon the problem of flight as exemplified by the 
soaring of heavy birds which, without apparent muscular 
effort, sustain their weight in a current of air. Without 
entering into a question which would be irrelevant to the 
subject, it may be said that Professor Langley concluded 
that the energy requisite for sustaining a mass in the air 
having a specific gravity many hundreds of times that 
of the medium was obtained from these pulsations in the 


velocity. M. Mouillard, who has observed the actions of 
soaring birds very carefully, asserts that it is possible for 
them to advance against a wind without flapping their 
wings. 1 The solution of the problem of mechanical flight 
may, therefore, lie in the invention of a mechanical 
arrangement which will simulate the action of birds, by 
utilizing the rapid fluctuations in the speed of the air 
current of which a so-called steady wind is composed, and 
from which they derive energy. The lesson to be drawn 
from these experiments and others is that, in dealing with 
the action of wind upon sails or wings exposed to its 
influence, we have a problem of extreme complexity to 
solve, and which is but little understood. We must there- 
fore pass on to the practical questions of the measurement 
of wind velocity, while bearing in mind the limitations in 
our knowledge as proved by these experiments and others 
of a similar kind. 

The intensity of a wind is either referred to by an 
arbitrary name such as " breeze,"or else it is designated 
by velocity in feet per second, miles per hour, or kilometres 
per hour. The table on p. 218 gives, as far as the indefinite 
nature of the ordinary designation for wind will allow, the 
corresponding velocity in these units. 

It is customary among English engineers to use miles 
per hour, and in metric countries kilometres per hour, 
where wind is referred to in connection with windmills and 
the like. Some manufacturers in the United States use 
feet per second. 

The direct measurement of the velocity of the wind forms 
one of the principal records of a meteorological observatory, 
J L. P. Mouillard, " I/Empire de l'Air," Paris, 




Ordinary Designation. 

Miles per 

Feet per 

X»er Hour. 




Barely observable 




Just perceptible 




I Light breeze 





V Gentle wind 






. 12-9 





Fresh breeze 




Brisk blow 




Stiff breeze 




Yery brisk 




I High wind 




Very high wind 












Great storm 






j 146-7 



1 t Tornado 

and self-recording instruments are employed at most stations 
from which a continuous record of the velocity (and direction) 


of the wind is recorded for reference. These records are 
chiefly of value for predicting the weather over large con- 
tinents, when taken in connection with barometric observa- 
tions, and also for recording storms of unusual violence. 
The instruments with which observatories are usually- 
equipped are of two kinds : (1) the Eobinson anemometer (the 
invention of the late Dr. Eobinson) ; (2) pressure recorders. 
Of these two instruments the anemometer is the one most 
used. It consists of four semi-spherical hollow cups at the 
ends of arms pivoted to a vertical axis and capable of rotation 
about the axis with slight friction. The wind, acting on 
the concave side of one cup, and the convex side of the cup 
at the end of the arm opposite, produces an unbalanced 
turning moment, owing to the difference in the pressure 
exerted on the convex and concave sides. The linear 
speed of the cups gives a measure of the velocity of the 
wind, and in the recording forms of the instrument 
the motion of the cups is imparted to a drum, through 
suitable gearing, the rotation of which is indicated by 
a pencil pressing against the sheet of paper by which 
it is covered. The pencil is simultaneously moved by 
clock-work longitudinally (parallel with the axis of the 
drum) so that the slope of the line shows the velocity 
of the wind, and the sheets are periodically removed 
from the drum and may be filed for reference. There are 
other forms of this anemometer less elaborate than this 
which integrate the revolutions, the figures being read off a 
dial directly. The standard anemometers of the Eobinson 
pattern as used by the weather bureaus of different nations 
differ somewhat. The Kew pattern, which is the standard 
in Great Britain and in some other European countries, has 


brass cups made of No. 21 gauge metal 9 ins. in diameter, and 
clamped to § in. round steel arms with their centres 24 ins. 
from the axis of rotation. The weight of the cups is usually 
borne by steel wires attached to the top of the spindle which 
is extended above the plane of the cups. The United States 
Weather Bureau has adopted two instruments, one having 
brass cups and the other aluminium cups. They are 4 ins. 
in diameter and are mounted on square steel arms. The 
diagonals of the arms are set vertically and horizontally, 
and the centres of the cups are 6*72 ins. from the axis. 
The weight of the aluminium cups, including the spindle 
supporting them, is about 280 grams., and that of the 
brass cups 529 grams. There is another form of anemo- 
meter which was designed by Mr. Dines called the 
helicoid or air meter. It consists of a fan made of two 
aluminium blades like a screw propeller. One of these 
instruments, in which the fans have a radius of 8 ins., 
makes approximately two revolutions for each metre of 
wind registered by it. The weight of blades and spindle 
is about 15*5 grams. The necessity for low friction in the 
bearings has called forth the skill of the mechanician in 
making anemometers. The bearings of the best instru- 
ments are ball bearings or agate cups in which the weight 
of the instrument is supported, with means to keep them 
always well lubricated, and of such a pattern that they will 
run for a long time without attention or inspection, as 
anemometers are not always readily accessible, and con- 
sequently may be left for months without any attention. 

The speed of the cups of the Kobinson anemometer 
depends, of course, upon the velocity of the wind which is 
propelling them, and also upon certain constants depending 


upon the instrument itself. A certain pressure is necessary 
to overcome the statical friction of the moving parts of 
an anemometer in its bearings, which means that, before 
an anemometer will begin to move at all, a certain pressure 
or wind velocity must have arisen. In an anemometer of 
rough construction, with comparatively great friction in the 
journals, this velocity may be considerable before the 
pressure is sufficient to cause acceleration of the cups ; but 
with nicely made instruments the minim am wind velocity 
that is needed is very small. As the velocity of the wind 
increases the speed of the cups likewise augments, and 
for practical purposes the relation between the two may 
be taken as directly proportional, though in refined experi- 
ments, as we shall see, this is not quite correct. That is 
to say, if V be the velocity of the wind, and v the lineal 
speed of a cup, V = a v + b, where b is the constant before 
referred to, being the velocity of the wind which is just 
sufficient to communicate motion to the cups (if v = o in 
the equation, then V = b). The constant a, which is the 
number that the speed of the cup must be multiplied by to 
obtain the wind velocity, was stated by Dr. Eobinson to be 
three, or in other words, the speed of the cup is always 
one-third that of the wind. This factor has been used until 
recently by the Meteorological Office for reducing the 
anemometer observations to wind velocities, but it is now 
replaced by the factor 2'2, so that the cups of the standard 
Kew anemometer move with a speed somewhat less than 
one-half the velocity of the wind. This difference in the 
anemometer constant is accounted for by improvements 
in construction over the earlier instruments which have 
resulted in. reduced friction, and also by the results of 


accurate experiments. Mr. A. Lawrence Eotch, B.Sc, the 
accomplished director of the Blue Hill Meteorological 
Observatory, near Boston, Mass., 1 has conducted some 
interesting anemometer comparisons and tests, the results 
of which are recorded in the " Annals of the Astronomical 
Observatory of Harvard College. ,, As these experiments 
were carried out with great care, the results may be taken 
as authoritative in establishing some points concerning 
anemometers in general which are brought together for 
comparison in a convenient form, and from which some 
of the principal conclusions may be usefully extracted. 

The object of these experiments was to determine the 
mean differences between anemometers used as standards 
in different countries, so that wind velocities in one country 
might be directly compared with those in another. Besides 
the types of Bobinson anemometer used as standards 
in Great Britain and by the United States Weather 
Bureau, Dines helicoid anemometers were also tested. 
The mean differences that were determined are the differ- 
ences between the movements recorded by the anemometers 
during an interval of six minutes (one-tenth of an hour). 
The instruments were placed 26 ft. above the roof of the 
building upon a mast with cross arms, and were subjected to 
the same wind influences, so that the readings could be 
directly compared and the relative sensitiveness obtained. 
Preliminary comparisons of several anemometers, of exactly 
the same weight and size, showed differences that could not 
be accounted for, and careful measurements did not reveal 

1 The kite and ballonsondes experiments made at the Blue Hill 
Observatory upon air currents ia the higher strata of the atmosphere 
are described in " Sounding the Ocean of Air " by A. L. Eotch. 


sufficient variation in constructional detail between them 
to account for the differences in the observations. When, 
however, the round arms of the Kew instrument were 
replaced by flat arms with knife edges, the rate was found 
to have increased by 2 per cent. These tests proved the 
necessity of adhering to an absolute standard in the 
construction of an anemometer, even to the minutest 
details, if uniform accuracy is to be attained, or if a con- 
stant factor of reduction is to be universally applicable. 
The method of transmitting the motion of the cups to the 
recorder also affects the rate of the instrument. The most 
delicate arrangement is by the use of a mercury contact 
which closes a circuit periodically. Accurate experiments 
with whirling tables have been made by Mr. Dines and also 
by Professor Marvin. By means of a large machine 29 ft. in 
length, driven by a steam engine, Mr. Dines found that the 
factor for the Kew standard instrument was between 2*00 
and 2*27, instead of 3, and that it was practically con- 
stant. The whirling table upon which such experiments 
are made consists essentially of an arm pivoted at one end 
and capable of being rotated. At the other, or free, end 
the anemometer is fastened, and the arm is rotated at a 
speed which can be measured exactly. The anemometer is 
therefore moving in a wind the velocity of which is known, 
and the effect on the instrument is regarded as the same, 
whether the anemometer be stationary in a wind of given 
velocity, or whether the instrument as a whole be moved 
through still air at the same speed. Mr. Dines concluded 
from his experiments that, if 2*10 were taken as the factor, 
it would be within 5 per cent, of the correct value, and 
possibly within 2 per cent. 


The machine used by Professor Marvin was 28 to 85 ft. long 
and was turned by band. It was employed for determining 
the constants of the United States Weather Bureau instru- 
ments. The following formulae, deduced from the experi- 
ments, apply only to the Standard Weather Bureau 
instruments : — 

(a) V = '225 + 3-148 r - 0862 r 2 

(6) V = '268 + 2958 v - '0407 r 8 

(c) V = -466 + 2*525 r 

(rf) log V = -509 + -9012 log r 
in which V is velocity of wind in miles per hour, and r is 
velocity of the centres of the cups in miles per hour. 

Formula (a) was computed direetly from the whirling 
machine experiments ; (b) is the same formula adjusted to 
open-air conditions (for the experiments were carried on in 
a large room) ; (c) and (d) are empirical. 

Professor Marvin states that {b) is the formula which most 
closely fits the experiments for velocities of to 40 miles 
per hour, as 32 miles per hour was the limit to which the. 
experiments were carried. It will be observed that a term 
involving the square of the velocity is included, but this 
makes but little difference on the result, except in high and 
unusual winds, and the coefficient of r or 2 953 represents 
the constant for the instrument. Thus if v = 7, the velocity 
of the wind in miles per hour would be : — 

V = 0-263 + 7 X 2-953 — 1*994 = 18*94 miles per hour. 
Formula (c) gives V = 0*466 X 2-525 x 7 = 18'14 miles 
per hour. 

The average velocities, as recorded by the Kew instru- 
ments, are about 13 to 18 per cent, higher than those of 
the Weather Bureau. 


As a so-called steady wind is made up of alternate gusts 
and periods of calm, which is shown on a windy day by the 
rattling of window sashes ; an anemometer only registers 
a mean value for a velocity which may be rapidly 
changing between extremes. The degree in which this 
variable wind velocity is 
recorded by the instru- 
ment is a measure of 
its sensitiveness, and ex- 
periments reveal that 
the lighter the instru- 
ment is, the more 
readily will it respond 
to rapid fluctuations of 
velocity, as might be 
expected from the com- 
parative inertia of light 
and heavy cups. In 
this respect the U. S. 
Weather Bureau instru- 
ment, being of lighter 
make, is the more sensi- 
tive of the two, while 
the fan anemometers are 
still more sensitive. 
These rapid fluctuations of the wind, though of great 
scientific interest, in that many problems in aero- 
nautics and mechanical flight may be directly re- 
ferred to them, are not recorded by the anemometer, 
and as it is the pressure of the wind upon surfaces 
which chiefly concerns the engineer, the study of these 

N.S. Q 

Fig. 67.— Head of Dines Wind Pres- 
sure Eecorder (E. W. Munro). 


complex phenomena is somewhat outside our present 

Pressure-recording instruments indicate directly the 
pressure of the wind, which may afterwards be converted 
into velocity if necessary. One instrument of this type, 
which was invented by Mr. W. H. Dines, registers directly 
the pressure of the wind, so that the relation between 
velocity and pressure, about which there is so much 
ambiguity, does not enter into the record. The head, or 
part upon which the wind acts, is shown in Fig. 67. It 
consists of a short length of horizontal pipe, the open end 
of which is constantly kept turned against the wind by the 
vane. Two flexible metallic tubes connect the head with 
the recording apparatus, which may be placed at a con- 
venient distance. The vane is pivoted upon the top of a 
vertical tube. This vertical tube is surrounded by another, 
the exterior of which is perforated by four rings of holes 
placed close together round the circumference. A float 
made of a specially-shaped copper vessel closed at one end 
is placed with the open end downwards in a closed vessel 
partially filled with water. The inside of the float is con- 
nected to the vane pipe through one of the flexible tubes, 
so that an increase of wind pressure causes it to rise in the 
water. The outer perforated pipe below the vane is con- 
nected by the second flexible tube with the closed vessel. 
The effect of the wind blowing across the open holes is to 
create a suction which reduces the barometric pressure 
within the vessel and thus contributes to raise the float in 
the water. The pen, or recording apparatus, is actuated 
by the float through suitable mechanism, and thus the 
air pressure is directly indicated upon a chart, one of 

_ g 8 8 g 8 8 

? 8 



which is shown in Fig. 68, the paper being moved 
beneath the pen by clockwork. It will be seen from this 
record, taken in boisterous weather, that the pressure 
is incessantly changing. This is partly due to the 
inertia of the float and connections, and partly to the 
actual state of the barometric pressure within the tube 
caused by the rapid wave-like fluctuations in the actual 
barometric pressure at the mouth of the tube. When this 
instrument is used in cold climates the water is replaced by 
a mixture of spirit and glycerine, and the makers recom- 
mend the proportion of the two liquids to be one litre of 
glycerine to 1*28 litres of pure spirit. Pressure instru- 
ments will not always register the same for the same 
velocity of wind. With a low barometer and high tempera- 
ture, which means that the air is less dense, the registra- 
tion of pressure for a given velocity becomes correspondingly 
low. The maker of this instrument, Mr. Robert W. Munro, 
to whom the author is indebted for the illustrations of the 
apparatus, states that the corrections necessary from these 
causes are small. 

The principal advantages of this instrument are its 
simplicity, and the fact that it cannot be injured by 
high winds; moreover, it is more sensitive than any 
of the rotation anemometers, and extreme wind velocities 
registered by it are more nearly correct than with rotation 
anemometers. Mr. S. P. Fergusson, who conducted 
experiments at the Blue Hill Observatory, states that 
at low velocities, below eight miles an hour, the mean 
velocity appears to be very nearly correct, but the 
instrument failed to respond to sudden changes of velocity, 
and there were often differences of 100 per cent, between 


it and the cinemograph. In the lightest winds (below 5 
miles per hour) it was less sensitive than any of the other 
anemometers except the pressure plate. Another defect 
of this instrument is its liability to become choked with 
snow in cold climates. Notwithstanding these objections, 
this experimenter says that it is an excellent instrument 
for indicating maximum velocities, and the results are 
more likely to have a constant value than those of any 
other anemometer. 

An examination of anemometer records, as usually taken 
in an observatory, will reveal the prevailing direction of the 
wind, and the extreme variation in intensity and average 
velocity. The windmill engineer is not concerned to any 
extent with the direction of the wind, for all mills auto- 
matically adjust themselves so as to take advantage of wind 
coming from any point of the compass. It is the extreme 
wind velocities, and the average velocity over a period, with 
which he is chiefly concerned, also the way in which the 
wind varies from day to day or hour to hour. Before the 
erection of a windmill in any locality, a useful table may 
be made out from which the probable velocity of the wind, or 
the number of hours throughout the year that the velocity 
exceeds an assigned minimum, may be prophesied, as based 
upon the records of the nearest meteorological station. In 
hilly districts these prophecies are less likely to be accurate 
than over a flat country upon which an observing station is 

To illustrate the application of meteorological records to 
the purposes of the engineer, a record made at an observa- 
tory on the south coast of England during the month of 
January supplies the particulars as shown in the adjoined 



table : col. 1 gives the day of the month ; 2, the number 
of hours from midnight to noon that the velocity of the 
wind was 10 miles an hour or more ; 8, ditto, from noon 

Day of Month. 

Number of hours 

midnight to noon, 

10 m.p.h. or 


Number of hours 
noon to midnight, 

Total in 24 hours. 

10 m.p.h. or more. 
































































































to midnight ; 4, total number of hours in 24 hours that 
the wind velocity exceeded 10 miles per hour. Thus, 
from the point of view of the miller, the weather would 


have been good, with only two bad days, from the 4th 
to the 17th, while the latter part of the month would be 
comparatively calm. While 10 miles an hour is arbitrarily 
chosen, it is not to be inferred that wind velocities above 
it are necessarily good, and those below too low for the 
working of windmills ; but the number of hours of a wind 
of such velocity that can be counted on throughout the 
year is a fit measure of the suitability of the locality for 
the erection of a windmill. The danger of destruction by 
storms is not as great as formerly, since the automatically 
regulated steel mill came into use. The chief obstacle to the 
extension of windmills to all forms of industry is the un- 
reliable character of the wind and the number of hours of calm 
that prevail at a time in even the most exposed situations. 
Mr. James Eickman, A.M.Inst.C.E., a well-known authority 
on the subject of the use of the wind in England as applied 
to the modern steel mill, informed the writer that the 
longest period of absolute calm in his experience was only 
three days. Of course, there are many days in which, 
though not absolutely calm, the wind does not attain 
sufficient velocity to work a mill, but even then the number 
of such consecutive days in the calmest season of the year 
is small. Mean velocities of the wind are not as instructive, 
from the engineer's point of view, as the number of hours 
that can be counted on for a working wind. At some 
places, particularly the West Indies, a high average wind 
velocity is the rule, but this is the result of alternate 
hurricane and calm-^a most unsatisfactory condition 
from the engineer's point of view. The following 
table which is taken from the Meteorological Office 
reports shows the mean wind velocities at four stations 



for every month in the year, as recorded by Robinson 
anemometers : — 

Mean Wind Velocity at Four Stations for the Years 





January . 





February . 





March . . 





April . . 
May . . 









June . . 





July . . 





August . . 




















December . 





Valentia, on the south-west coast of Ireland, which is 
the most exposed of the four stations, has a mean velocity 
for these years of somewhat more than 10 miles per hour, 
while the Kew station is considerably less than that figure. 
The high Atlantic westerly winds which blow over the 
west coast make this situation one of the best for wind- 
mills, while an inland station does not benefit to the same 
extent, as may be seen by comparing the other three with 

Relation between Velocity and Pressure. 

The engineer is chiefly concerned with the pressure that 
the wind exerts upon surfaces exposed to it, whether he 
desires to build structures to withstand the wind, or whether 
he is engaged in problems pertaining to windmills. By the 


anemometer he may ascertain the velocity of a wind which, 
striking an exposed surface, results in a pressure upon it. 
What he most desires to know is the law that connects 
velocity and pressure, so that given the one he may readily 
deduce the other from it. The pressure which the wind 
exerts upon bridges, roofs, and all other forms of structure 
exposed to it necessitates extra precautions in construction, 
and it is important to know what this pressure may be so 
that the resisting powers of the structure may be sufficient 
to avert destruction in a high wind. The instruments for 
the direct measurement of pressure are not always available, 
and even if their readings could be relied on for accuracy, it 
is more convenient to be able to readily convert the common 
terms expressing the strength of a wind in velocity, direct 
into pressure. It is clear that the pressure exerted by a 
wind increases with the velocity, but it is not so evident 
that the pressure is not proportional to the velocity. Indeed, 
for a long time it was so regarded, until experiments con- 
ducted of late years have proved the contrary. If it were 
proportional to the velocity we should find that P = a V 
where a is a constant which is multiplied by the velocity V 
to obtain the pressure P. Thus if a wind of 25 miles an hour 
resulted in a pressure of 3*5 lbs. per square foot, a wind of 50 
miles an hour should produce a pressure of 7 lbs. per square 
foot, and the constant a would be 3*5/25, and P = 0*14 V. 
Such a relation is, in the light of recent experiments, far 
from correct, as it is found that the pressure increases more 
rapidly than the first power of the velocity, and while the 
exact function is not yet known, a nearer approach to 
accuracy than is given by a linear function has been 


The method of obtaining a value for the pressure of the 
wind upon an exposed surface for varying velocities 
necessitates (1) a correct measurement of the velocity ; (2) 
a measurement of the pressure by direct means. By 
observing the relation between these two quantities for a 
sufficient number of values, it is possible to obtain the law 
connecting the two, so that by interpolation the one may 
be derived from the other for all values. The anemometer 
may be used for obtaining the first of these quantities, and 
pressure boards for the other. The pressure boards which 
have been used are simply plane surfaces placed normal to 
the direction of the wind, and the pressure is registered 
on a gauge, the board being connected thereto so as to 
measure the pressure directly. The size of the board has 
an importance that in the early experiments was not fully 
considered, for it affects the pressure per unit of area to a 
great extent. As the exposed surfaces of structures are 
generally larger than could be conveniently experimented 
upon, it would appear that the results of experiments with 
large boards would, by simulating actual practice more 
closely, have the most value. 

The earliest formula connecting pressure and velocity is 
wrongly attributed to Smeaton, who obtained it from his 
friend Mr. Eouse, but he was so convinced of the accuracy 
of the relation that he adopted it, and it has been used in 
many countries since. If V be the velocity of the wind in 
miles per hour and P the pressure in pounds per square 

P = 0-005 V 2 

The following table gives in col. (3) the pressures worked 
out for various wind velocities according to this relation 


and the curve (Fig. 69) is plotted with pressures as abscissae 
and velocities as ordinates : — 





Miles per Hour. 

Feet per Second. 

Pressure per Sq. Ft. 
in lbs. (Smeaton). 

Pressure per Sq. Ft. 





























































































The accuracy of this formula has been assailed with 
success, and the latest experiments go to show that the 
pressures so calculated are somewhat too high for the 
•corresponding velocities, and other formulae are now 
regarded as more nearly true. The fact that the wind 
pressure varies as the square of the velocity is sufficiently 
proved, but the coefficient in the Smeaton formula should 
be smaller, as the best experiments clearly indicate. 

The late Sir Benjamin Baker conducted a series of 
experiments at the Firth of Forth to guide him in designing 



























P - 0005V 2 

Fig. 69. — Relation between wind pressure and velocity (Smeaton). 

the great structure that spans that estuary. He used three 
pressure boards, the largest of 300 sq. ft. and two smaller 


ones 1"5 sq. ft. each. His object in using boards of such 
varied size was to ascertain the difference in unit pressures 
derived from small experimental boards, and large surfaces 
comparable with those that the bridge would present to the 
wind. After two years of experiments conducted with 
great care he arrived at the conclusion that if the wind 
bracing were proportioned to withstand a maximum pressure 
of 56 lbs. per square foot, the structure would have an 
adequate factor of safety, as such pressures would not be 
attained under the highest winds. According to Smeaton's 
formula such a pressure would correspond to a wind of 106 
miles per hour, and though pressures of 70 lbs. per sq. ft. 
have been recorded in England they would be caused by 
momentary impulses which would have no effect upon a 
large and heavy structure. A tornado in the tropics at a 
velocity of 100 miles an hour might produce a steady 
pressure approaching 50 lbs. per square foot, but the 
practice of engineers in England and the United States is 
to design wind bracing for a pressure of 80 lbs. per square 

The experiments carried out by Mr. Dines with a whirling 
table, show that the coefficient in Smeaton's formula is too 
high and that the correct relation would be — 
P = 0-0029 V 2 

This value is practically confirmed by the experiments 
carried out at the National Physical Laboratory by Dr. 
Stanton, which, though made on very small pressure boards, 
were conducted with great care and skill. In these experi- 
ments a current of air was produced in a tube 2 ft. 6 in. 
diameter by a fan, and the velocity of the current was 
maintained constant throughout the section of the tube by 


introducing layers of gauze at certain points. By this 
means a fairly uniform current was set up all across the 
section, the velocity of which was measured by a Pitot 
tube of extremely ingenious construction, for the details 
of which the reader is referred to a paper 1 from which 
these particulars are drawn. It was found that discs up to 
2 ins. in diameter could be used for pressure experi- 
ments without being affected by the walls of the tube, and 
the plates used were, generally, not larger than this. The 
conclusions arrived at as a result of these observations were, 
that the pressure is greatest at the centre of the plate on 
the windward side, and diminishes towards the edges, while 
that on the leeward side is practically constant, being 
uniformly lower than the barometer, also that the pressure 
at the centre of the plate on the windward side is proportional 
to the density of the current and to the square of the 
velocity. It was also shown that for similar plates varying 
in size between the circumscribed limits of the apparatus, 
the mean intensity of the pressure for the same density of 
current was the same. For circular plates the diameter 
ranged from 0*5 in. to 2 ins., and this was the largest size 
of plate employed. Further experiments made upon large 
pressure boards mounted upon a steel tower show that the 
coefficient 0*003 is practically correct. 2 

The results, reduced to the same form as the other 
equations, give a coefficient of 0*0027, so that, compared 

1 The Minutes of the Proceedings of the Institution of Civil 
Engineers, vol. clvi., p. 78. 

2 The results of these further experiments were communicated to 
the Institution of Civil Engineers in a paper by Dr. Stanton read 
at a meeting on December 3rd, 1907. 



















Curve showing wind pressure according to the formula 
P= 0003 V 2 which is based upon the best experimental evidence. 

Fig. 70. 


with that obtained by Mr. Dines, it will be seen to agree 

(1) Smeaton P = 0005 V 2 

(2) Dines P = 0*0029 V 2 

(3) Stanton P = 0*0027 V 2 

The unit pressure obtained from experiments on small 
plates is higher than that obtained for large, for the reason 
that, where small plates are exposed to a current of air, the 
pressure at the down-stream side is less than the barometer 
over the entire surface, while with large plates this area of 
low pressure is confined to a zone round the back edge of 
the plate. It is probable, therefore, that the actual unit 
pressure upon structures is much lower than that given by 
(8), and that with the requisite factor of safety this formula 
would be quite safe. Probably the correct value is not far 
short of 0*003, so that P = 0'003 V 2 represents the best 
determination in the light of our present experimental 
knowledge. The experiments of M. Eiffel at the great 
structure in Paris which he has conducted with great 
care for several years substantially confirm these results. 
Pressure plates equipped with ingenious measuring appa- 
ratus were allowed to fall from the second stage of the 
tower and wind velocities exceeding 40 metres per second 
(90 miles per hour) were recorded. The pressures calcu- 
lated according to this rule are given in the fourth column 
of the table and are plotted in Fig. 70. 



The best available evidence upon the subject directs 
us to the conclusion that windmills were not used in 
England more than one thousand years ago, and the 
oldest authentic records that we have concerning the 
erection of a windmill bear the date of 1191. A strong 
testimony to the accuracy of this statement lies in the fact 
that the survey of mills in Domesday does not include 
windmills, which, had they been in existence, would 
have found a place in this complete record. There are 
however allusions by writers, long after that period, to 
windmills at an earlier date than 1086, but, in the opinion 
of two authors whose authority is unquestioned, 1 there are 
valid reasons for casting aside these references, and for 
accepting the account of the mill built by Dean Herbert in his 
glebe lands at Bury St. Edmunds as that of the first windmill 
to spread its sails aloft on English soil. Owing, however, 
to the fact that this mill was raised in defiance of authority, 
it was quickly destroyed by the order of an Abbot, and 
a report of the case, preserved in the Abbey, has come 
down to us. This mill, as indeed nearly all of those which 
dotted the landscape until the introduction of steam, 
was for grinding corn. From that time on the use of 

1 " History of Corn Milling," vol. ii. Kichard Bennett and John 

N.S. R 



windmills steadily increased in England and also in 
France, and it is on record that King Edward III. 
viewed the battle of Cressy from a windmill at the top 
of a hill (1846). In many instances the mills in 
England were the property of the Lord of the Manor, 
who exercised "soke" privileges, by which all the grain 
raised by his tenants over his estate had to be milled 
at his mill. The first mill, according to the best 

accounts, was a very crude 
affair when compared with 
those of later centuries, 
and the only character- 
istic which has survived 
until the present day was 
the number of the sails 
which, with a few isolated 
exceptions, has always 
been four. 

In order to follow to 
better advantage the 
evolution of the windmill 
from the earliest forms, a 
few words about constructional details are necessary. 

To begin with, there is the sail-shaft carrying the four 
sails, from which the power is transferred to the grinding 
buhrs through gearing. This shaft must be capable of 
being directed towards any point of the compass so as to 
present the sails to the winds from every quarter. This 
operation requires mechanism, which in the earlier mills 
was moved by hand, while later contrivances were devised 
to coerce the wind to accomplish the desired movement of 

Fig. 71.— Post Mill. 


the sail-shaft, so that it might always lie in the direction 
of the wind and thus be exposed to the full wind pressure 
upon the sails. The earliest type of mill, which is still to be 
found at work in England, is shown in Fig. 71. It was 
probably such a type as this that a great writer discovered 
while on a visit to the Azores and to which he referred in 
these words : " Small windmills grind the corn, ten bushels 
a day, and there is one assistant superintendent to feed 
the mill, and a general superintendent to stand by and 
keep him from going to sleep. When the wind changes 
they hitch on some donkeys, and actually turn the whole 
upper half of the mill around until the sails are in proper 
position, instead of fixing the concern so that the sails 
could be moved instead of the mill. ,,1 

The wooden building containing the machinery and 
stones is supported upon a wooden post, upon which it is 
free to turn. The miller, who has to watch constantly for 
a shift in the wind, turns his sails accordingly by laboriously 
turning the mill by means of the long baulk of timber which 
projects outward on the opposite side to the sails. The 
difficulties and danger involved in milling during a gale may 
well be imagined when the crude nature of the earlier fabrics 
is considered. Often with a howling tempest raging outside, 
and the crashing and creaking of the machinery within, we 
are told that the courageous miller would, like the dauntless 
sea captain, stand fast to his post. In vain he would apply 
rude brakes to stop the whirring shaft within, while all his 
corn hoppers would be opened to feed the rumbling mill 
stones, and thereby offer as much resistance as was possible 
to the impetuous motion of the machinery. Sometimes his 
1 " The Innocents Abroad." Mark Twain. 

R 2 


attempts would prove of no avail, and with a crash his 
dusty habitation would be blown over, and if he were 
fortunate enough to escape, he would see the wreck of what 
was for many years his pride, pleasure, and source of liveli- 
hood. In such mills wood was the chief material used 
in the construction, and fire, sometimes caused by an over- 
heated journal, was often an enemy to be reckoned with. 
The heavy sail-shaft, bored with two mortise holes at 
right angles through which the sailyards were passed, 
ran in rude journals, wrought-iron bands upon the shaft 
serving to reduce the friction to some extent. The 
gearing in the earlier types was that known as pin 
gearing, by which the necessity for nice adjustment 
between the gears was obviated, for the accurate alignment 
necessary for bevel gears was then beyond the powers of 
even the best millwrights of the period, and cast gears with 
wooden cogs were a later refinement which materially added 
to the efficiency of the mill by reducing the friction losses 
in the transmission of the power from the sails to the 

Chief among the improvements which contributed to the 
efficiency of the mill, and which relieved the miller from 
much misdirected attention, was an automatic apparatus 
for effecting the adjustment of the sails to the wind. The 
earlier devices for supplanting manual labour in this direc- 
tion were not wholly satisfactory. One form consisted of a 
wide fan projecting outwards on the opposite side to the 
sails, upon which the wind acted obliquely until the mill 
was turned in the desired direction. The mill, with the 
machinery and sacks of corn, was so heavy and the friction 
so great that this plan never found extensive acceptance 



in the early days, though, as will be seen later, it is now 
employed very generally upon the modern light steel mill. 
A later device consisted of a circular rack into which a pinion 
geared. The rack was attached to the revolving mill, which 
was thus turned by means of a rope and pulley similar to the 
apparatus used for rotating the dome in a modern observa- 
tory. But before a satisfactory change had been made 
in this direction the mill 
had undergone structural 
alterations, to some extent 
necessitated by the demand 
for mills of greater capa- 
city. Sweeps or sails of 
40 ft. from tip to tip were 
no longer the extreme limit, 
and 60 and even 80 ft. 
circles were swept by the 
great sails of canvas or 
wooden slats with which 
the mills were equipped. 
The post mill was not high 
enough for sails of such a 

Fig. 72. — Development of Tower 

size, and consequently the mill top, capable of rotation about 
a vertical axis, was mounted upon a short truncated cone 
of stone, brick, or wood, as illustrated in Fig. 72. In addition 
to the added stability and resistance to overturning in a gale, 
the basement afforded a convenient shelter and storage for 
sacks, and for receiving the flour as it came from the buhrs 
on the floor above. 

It is not difficult to follow the gradual evolution of the 
tower mill from this primitive form. The wooden house 


Fig. 73.— Tower Mill. 


or top gradually assumed the form of a cap to a sub- 
stantial tower of brick, stone, or wood, and was capable of 
rotating thereon and carrying with it the sail-shaft and 
connections. This process of development was slow, but 
during the sixteenth century the complete evolution took 
place, if, indeed, it is possible to indicate precisely the 
distinction between a tower mill so called and a mill having 
a somewhat enlarged rotating top placed upon a stone or 
brick pier. It is probable that the increasing necessity for 
capacity in a mill, coupled with augmented skill on the part 
of the millwright, were the contributory causes to a change 
which spread all over the country, to which the many ivy- 
clad remains of towers to-day bear witness. 

Thus from a mill entirely constructed of wood and subject, 
of course, to destruction by fire, the process of development 
culminated in a stone or brick structure, capped \>j a 
wooden frame and roof, and which readily lent itself to the 
demands for size by increasing the height of the tower and 
the length of the sweeps. The annexed picture shows one 
of these mills such as may still be seen at work in many places 
in the country, in which the various improvements in the 
details of construction and machinery are exemplified, and 
which, while marking the highest skill of the millwright's 
art in the construction of windmills for corn grinding, at 
the same time shows the last type of those picturesque struc- 
tures which the steam-driven roller mill has almost com- 
pletely driven out of existence. To some extent they are 
still used for grinding food for cattle, but, situated as they 
generally are, away from lines of transport and waterways, 
they can never hope to compete in any sense with the 
gigantic roller mills located at convenient places for the 



shipment of their product, and provided with a reliable 
and constant power. 

The interior arrangement of a tower mill varies according 
to the size. Some of the modern examples are more than 
100 ft. high, and are divided into three, four, or even five 
stories by floors, the ascent from one floor to the other 

Fig. 74. — Veering Mechanism. 

being made by wooden ladders. The automatic apparatus 
for rotating the top made it possible for the height to 
be increased to a great extent. In some of the larger mills 
an outside gallery surrounding the tower allowed access to 
the sails for making repairs, as they could not be reached 
from the ground. The mechanism of the device for automatic- 
ally adjusting the sails to the wind is shown in Fig. 74. A 
fan-wheel is pivoted at the end of a lattice arm on the 
opposite side of the tower to the sails, and the plane of the 
fan is at right angles to that in which the sails revolve. A 


bevel gear on the fan-wheel shaft meshes with a pinion, 
which, through a connecting shaft, rotates the pinion working 
in the annular rack upon the top of the tower. The top of 
the tower is free to move upon a series of rollers, and, as 
the fan- wheel is rotated by the wind, the top is moved round 
until the fan-wheel presents its edge to the wind and then 

Fig. 75. — Veering Mechanism. 

the sails are athwart the wind. With large and heavy 
mills there are two fan-wheels to render the self-adjustment 
more sensitive, but generally one is sufficient to keep the 
mill within a few points of the desired direction. Fig. 75 
shows another form of this arrangement. This was, 
perhaps, the most important invention in the art of wind- 
mill construction, but was of comparatively recent origin, 



and therefore has had a correspondingly short career of 
usefulness. Another plan, which, however, never was 
adopted extensively, also made use of the fan-wheel, but 
instead of being geared to the top of the tower it actuated a 
roller which was fixed at the end of a long projecting arm 

similar to that used in the post 
mill for gyrating the entire 
mill about the central post. 
This roller moved over a track 
in a circular orbit, and the mill 
top to which the beam was 
fastened was thus rotated. It 
was at the best a rude and 
clumsy makeshift, and is only 
interesting as a link in the 
stages of development of the 
mill from the one in which 
manual labour alone accom- 
plished the exacting and often 
dangerous task of keeping the 
sails full to the breeze. 

The "wind-shaft" or 
"round-beam," to give it the 
names conceded to it by millers, 
is in either case misnamed, 
for it is sheltered from the wind, and also usually has a 
square, hexagonal, or octagonal section ; in short, many 
sections, but circular. Sometimes these shafts were cut from 
a single piece of timber, but more often they were built up in 
layers with broken joints, and could thus be made up of short 
pieces of sound beech, oak, or pine. The main gear and 

Fig. 76. — Gearing for Mill 
with Single Pair of Stones. 


brake wheel, also of wood, was divided into sections, which 
were held together by bolts. This gear meshed into a small 
pinion, called a wallower, on a vertical shaft, which also 
carried a large gear at the bottom end, and this in turn 

Fig. 77. — Gearing for Four Pairs of Stones. 

meshed with a small pinion or " nut " on the top of the 
stone shaft. In some mills the top stone was driven, in 
others the nether stone. The arrangement of the machinery 
varied, of course, according to circumstances, and Fig. 76 is 
therefore only generally representative of the plan for a 
mill with a single pair of stones, and Fig. 77 shows how 
four pairs of stones may be driven from a single vertical 


shaft. The gear ratio at the sail-shaft was about 8 to 1, and 
at the stone shaft 4 to 1, so that the stone makes 12 turns 
to one of the wind-shaft. Most mills had two sets of 
stones, and others had edge runners for the grinding. 
The edge runners consisted of two large stones at the 
ends of a short horizontal shaft which was rotated in 
a horizontal plane by a vertical shaft through the centre. 
The stones rolled in a trough or pan, in which the raw 
material was placed, and was discharged through an 
opening when sufficiently pulverised. The amount of 
material that could be passed through a mill necessarily 
depended upon the wind and consequent speed of the 
stones. The authors before referred to quote the per- 
formance of a post mill with a length of sailyard of 
50 to 60 ft. from tip to tip. With a steady wind this mill 
would grind about twenty quarters of grist for cattle per 
working day, and on a very windy day twenty-four quarters 
of 480 lbs. (5*14 tons) ; and other mills of the same kind had 
a capacity of as much as twenty bushels of corn per hour. 
As the weight of contents of a bushel varies with the kind 
of grain, it is difficult to make correct comparisons between 
the performance of different mills. 1 Another post mill 
with a fairly steady wind is credited with six bushels 
of 60 lbs. per hour with one pair of stones, which would 

x The Imperial bushel contains 2,219*28 cu. ins., or 8018 lbs. of 
water at 60° F. and is equal to 36*368 litres = 1*032 Winchester 

The Winchester bushel contains 2,150*42 cu. ins., being the volume 
of a cylinder 18*5 in. internal diameter and 8 in. deep, and this is the 
standard in the United States. It = 60 lbs. of wheat, = 56 lbs. of 
corn or rye, = 48 lbs. of barley, = 32 lbs. of oats, = 60 lbs. of peas, 
= 35*24 litres, = 0*969 Imperial bushels, = 77*69 lbs. of water. 


appear to be a fairly correct estimate of the performance 
of such mills. The output of tower mills was only 
limited by the size of the sailyards. With one pair of 
stones 500 lbs. of grist per hour would be the output 
for a steady wind, but in a gale this might be doubled, 
while with a wind velocity of 13 miles an hour and 
sails making 11 to 12 revolutions per minute, 900 to 950 lbs. 
per hour was obtainable. The absence of exact data as to 
the spread of sail, velocity of wind, and other conditions 
entering into the problem render the figures of output some- 
what indefinite, and the condition of the stones also invests 
an estimate of the efficiency of the mill with uncertainty. 
As the mills were classified according to output in grist, the 
engineer of to-day, whose ideas of mechanical efficiency are 
of a finer order, cannot rightly appraise the value of a train 
of mechanism upon which a gust of wind acts on one end 
and at the other the useful work is measured in bushels of 

For this reason, and also because of our inexact know- 
ledge of the action of the wind of a given velocity upon a 
revolving sail, the mechanical efficiency of the corn-grind- 
ing windmill is unknown. If the pressure component in 
the plane of rotation acting on the sails at all points of the 
area exposed to the wind was known, it would only be 
necessary to multiply the pressure per unit of area by the 
velocity at which that part of the sail was moving to obtain 
the power put into the sail by the wind at that point, and 
the integral of these for the entire sail area would disclose 
the total power applied in torsion to the wind-shaft ; but 
attempts of such a kind to arrive at the power would be 


Haswell gives an empirical formula for estimating the 
power of a well-designed mill, which the writer has checked 
by reference to estimates made of the power of mills by 
practical millers. In every case where the data was suffi- 
cient for comparison the formula has proved fairly trust- 
worthy. If A be the total sail area in square feet and V 
the velocity of the wind in feet per second, the horse-power 
is given by the expression 

H-P = — A - — 

In one case a mill with four sails, each 24 ft. in length 
and 6 ft. in breadth, was estimated at 4 h.-p. with a wind 
velocity of 20 ft. per second (18'6 miles per hour). By 
applying the formula we have 

24 X 6 x 4 x (20)* _ 
ammMfm ~ 1,080,000 ~ V" 

The agreement in this particular instance is as close as 
could be expected, but in any case the formula must only 
be regarded as a rough guide and has no pretensions to 
accuracy, as it takes no account of weathering, length of 
sail, and the proportion of length to breadth of sail, all of 
which affect the power of the mill. As we have seen that 
the pressure of the wind upon a plane surface varies as the 
square of the velocity, the power developed must therefore 
vary as the cube, assuming that the speed of the sail is pro- 
portional to that of the wind. We have every evidence that 
this assumption is the correct one for plane sails as well as 
for the cups of the Robinson anemometer, which move with 
a speed proportional to that of the wind which acts upon 
them. It is not surprising, therefore, that in consequence 



of the very rapid falling off in the power developed at the 

wind-shaft when the wind drops by a 

few miles per hour, the requirements 

of the miller in the matter of wind are 

not such as can be satisfied by the 

weather every day. In the case before 

referred to, if the wind should drop from 

13*6 to 10 miles per hour, the power 

would fall from 4*27 h.-p. to little more 

than 1*68 h.-p. A wind of 8 miles per 

hour would not yield 1 h.-p., which would 

probably be insufficient for grinding even 

if the torque on the shaft at starting 

was sufficient to overcome the statical 

friction in the machinery and journals. 

Thus it was that for many days in the 

year the miller was forced to wait 

patiently for the wind to stir his sails 

while the sacks of corn accumulated on 

the mill floor. At length it would come, 

perhaps more than he desired, and for 

days and nights without ceasing the corn 

was converted into flour by the busy 

millstones, and his anxiety to make the 

most of that which the weather had 

brought him left him only time for an 

occasional nap throughout the long 

night spent amid the dust and whirr 

of the mill. 

If the wind increased sufficiently to become dangerous 
the mill was stopped by the application of the brake, or 

Fig. 78.— Sail as 
used on Tower 


the top was turned round out of the wind, and then the 
hazardous operation of reefing the sails was begun. On 
the smaller mills the sails were reached from the ground, 
but the tower mills, as shown in the illustration on p. 246, 
were provided with a balcony from which the miller could 
ascend the sail-arm and take in canvas in the manner of a 
sailor at the yard-arm. The sails of the more modern 
mills were constructed of wooden slats instead of cloth 
(Fig. 78), and the furling was at a later date accomplished by a 
train of mechanism from the interior of the mill, by which the 
weathering of the slats was altered. This mechanism was 
essentially the same as that adopted and still used on 
certain of the light mills of to-day to be described later. 
The chief advantage of the cloth sail was its comparative 
lightness, which was no small consideration in view of the 
necessity of losing as little power as possible. The dis- 
advantage, however, of the time lost in furling led to the 
adoption of the other principle, and eventually to the 
almost complete suppression of the cloth sail. In some of 
the mills equipped with the wooden sail the slats are laid 
parallel to the sail length and are simultaneously turned 
through the same angle in the manner of a Venetian blind. 
This method was the invention of M. Berton, a French 
engineer. They are also arranged in modern mills trans- 
versely to the sail, especially when the sail-arms are very 
long, as otherwise they would be unmanageable. More- 
over, the weathering of the sail at different distances from 
the centre is more accurately attained when the slats are 
athwart the sail length, as each member may be weathered 
more correctly for the radius at which it is placed. This 
may be understood by imagining that a Venetian blind is 


twisted out of the plane it would occupy if hanging free. 
The bars each suffer an angular deflection which may be 
supposed to increase towards the bottom, so that the last 
bar makes a considerable angle with its original position, 
while those near the top are but slightly changed in position. 
The bottom bar occupies a relative position analogous to 
that part of the sail nearest the wind shaft, while the top 
bar is at the extreme tip of the sail. To carry the analogy 
further, the reefing is represented by operating upon the 
hanging blind so as to change the angles which the bars 
make with a horizontal plane, such as by pulling upon the 
tapes with which Venetian blinds are usually provided. 

The wind shaft is set at an angle to the horizontal, which 
varies according to local conditions from 8° to as much as 
35°. There appears to be no other reason for this than 
that of allowing the sails to revolve clear of the tower, 
which usually has a batter of about 1 in 7, or 1 in 8, though 
it has also been ascribed to a supposed tendency of the 
wind to blow at an angle with the horizontal in a downward 
direction when on low ground. It is usual to make the 
sails rectangular with a ratio of length to width of about 
5 to 1, the whole sail surface not exceeding one-fourth 
of the circle swept by the sail arms. The rectangular sail 
is in some mills supplemented by a triangular addition 
upon which canvas is stretched also, as illustrated in 
Fig. 78. 

As it is doubtful if any of the readers of these pages will 
ever be called upon to design a windmill of a type which is 
so rapidly disappearing, it will not be advisable to take up 
much space in describing how the proportions of sails and 
" weathering " (angle which the sail makes with the plane 

N.S. S 


of revolution) were arrived at. Even if such a course were 
desirable, the information at hand is very scant and is of 
the rule-of-thumb kind. Smeaton left us a set of rules 
which were the outcome of a series of experiments, the 
results of which he communicated to the Royal Society in 
1759. Of these results the most important related to the 
angles which he pronounced to be the best for the weather- 
ing of the sail. His results are as follows : — 

Distance from centre of motion, 1, 2, 3, 4, 5, 6. 

Angle with plane of motion, 18°, 19°, 18°, 16°, 125°, 7°. 

Thus if the sail arm be divided into six equal parts, the 
angles which the sail makes with the plane of motion on 
the division lines are set forth, the angle decreasing towards 
the extremity of the sail until at the tip it is 7°. He also 
laid down the rule that the best speed for the tip of the 
sails should be 2'6 times the velocity of the wind, which 
implies that a point on the sail located at 38*5 per cent, of 
the radial distance moves at the same speed as the wind. 
Other angles have been used, which in some mills become 
almost 0° at the tip of the sail. The following angles are 
elsewhere given as an alternative : — 


Angle with plane of motion, 24°, 21°, 18°, 14°, 9°, 3°. 

The general conclusions to which Smeaton was guided by 
his experiments with wind velocities of 2*7 to 61 miles per 
hour are as given below. It is to be observed that these 
wind velocities would be regarded as too low for the practical 
operation of windmills, as a wind of 10 ft. per second (6*8 
miles per hour) was generally insufficient to drive a loaded 
mill, while 35 ft. per second (23*8 miles per hour) was con- 
sidered too high, and precautions had then to be taken by 


reefing sail to guard the safety of the structure in a gale of 
this severity. 

1. The velocity of windmill sails, so as to produce a 
maximum effect, is nearly as the velocity of the wind, their 
shape and position being the same. 

2. The load at the maximum is nearly as, but somewhat 
less than, 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 
as, but somewhat less than, the cubes of the velocity of the 

4. The load of the same sails, at the maximum, is nearly 
as the squares, and their effect as the cubes of their number 
of turns in a given time. 

5. When sails are loaded so as to produce a maximum 
effect at a given velocity, and the velocity of the wind 
increases, the load continuing the same — first, the increase 
of effect when the increase of the velocity of the wind is 
small will be nearly as the squares of those velocities ; 
secondly, when the velocity of the wind is double, the effects 
will be nearly as 10 to 27*5 ; but, thirdly, when the velocities 
compared are more than double of that when the given load 
produces a maximum, the effects increase nearly in the 
simple ratio of the velocity of the wind. 

6. In sails where the figure and position are similar, and 
the velocity of the wind the same, the number of revolutions 
in a given time will be reciprocally as the radius or length 
of the sail. 

7. The load, at a maximum, which 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. 

s 2 


8. The effects of sails of similar figure and position are 
as the square of the radius. 

9. The velocity of the extremities of Dutch sails, as well 
as of the enlarged sails, in all their usual positions when 
unloaded, or even loaded to a maximum, is considerably 
greater than that of the wind. 

modern windmills — constructional details. 

The Modern Windmill. 

The subject of this chapter is a type of mill somewhat 
different in construction and working from those which we 
have just considered. In a sense it cannot be said to be 
a replacement of the wooden mills, which are still used in 
rural districts for corn grinding, but it has a wider future 
and range of utility for pumping water and for driving light 
farming machinery and, to a very limited extent, for the 
generation of electricity. Indeed, so widely used are these 
mills in great agricultural countries like Australia and the 
western parts of America and the Argentine that the 
manufacturers have found difficulty in keeping pace with 
the demand, notwithstanding the fact that there are several 
firms that turn them out by the thousand, and who can 
always find a ready market for them. They are cheap and 
are well made, will work without much attention, and are 
admirably adapted to pumping water and to any service not 
requiring a continuous output of power. They are easily 
erected, require very light foundations, and repairs and 
renewals are a small item, as they are now made capable 
of withstanding the heaviest gales. 

In appearance they are strangely unlike the old mill. 
The heavy sweeps, sometimes 30 ft. or 40 ft. long, give place 



Fig. 79.— Steel Windmill and Tower. 


to a light disc made up of slats, not unlike the sections of a 
fan, and which is, in the largest mills, not greater than 
40 ft. in diameter, while the vast majority of these mills 
that are sold are not greater than 10 ft. to 12 ft. in diameter. 
Indeed the writer was informed by a leading manufacturer 
that the 10 ft. or 12 ft. mill is likely to be the standard size, 
and that a manufacturer who can turn these out well made 
and cheap has always a ready market for them. 

These mills are erected upon steel towers, which may be 
constructed to a height above ground of as much as 80 ft., or 
else they may be mounted on a house-top with a low tower 
sufficient to provide the necessary clearance from surround- 
ing obstructions, so that the sails may be fully exposed to a 
wind from any quarter of the compass. Fig. 79 is a typical 
example of a mill supported upon a steel tower built up of 
rolled shapes and braced diagonally by light tie-rods, so as 
to form a rigid structure. A ladder is provided for access 
to the platform at the mill, and the pump rod may be seen 
in the centre of the tower. Sometimes the tower is also 
the support for a water tank, in which case it is constructed 
somewhat heavier than if it is intended only to bear the 
weight of the mill and pressure of the wind. 

Where timber is cheap and good, wooden towers may be 
erected, but generally steel towers are the best for English 
mills, as there is but little difference in the cost, when the 
longer life of a steel tower is taken into account. The size of 
timbers used in the construction of a tower vary according 
to the size of mill. The Aeromotor Company, of Chicago, 
gives the following sizes for the construction of the head of 
the tower, where the four corner-posts come together, and 
to which a short steel head is attached. 



Details for Tops of Wooden Towers to which Short 
Steel Stub Towers are Attached. 

Size of Mill. 

Size of Timbers, 

8 and 10 ft. . 


12 ft. . . . 

4 x 4 or 4 x 6 

14 ft. . . . 

4 x 6 or 6 X 6 

16 ft. . . . 


x 6, 6x8 or 8x8 

20 ft. . . . 

8 x 8 or 10 x 10 

Where more than one size of timber is shown, the small 
sizes may be used if the timber is free from knots and 
shakes, and has a straight grain ; otherwise the second size 
is expedient and should always be used on the lower parts 
of towers when they are higher than 40 ft. 

The batter for wooden towers should be somewhat 
greater than for steel, and ought to be more than one-fifth 
the height. The Aeromotor Company recommends that the 
posts should be slightly sprung to an increasing batter and 
that they should be assembled with bolts, and not with 
screws or spikes, which are liable to work loose under the 
vibration. Attention should be directed to the bolts from 
time to time to ensure their tightness, and especially for 
the first few months succeeding erection, as the members 
are liable to be sprung and looseness developed at the 
joints. To prevent rot at the base of the tower it is 
necessary that the wooden anchors should be painted with 
a coating of hot pitch or asphaltum, and that the tower 
itself should receive a coat of paint composed of boiled 


linseed oil and white lead with the colour added, at least 
every second year. In the erection of wooden towers they 
may be assembled in a horizontal position on the ground 
and then raised to the vertical by means of blocks and 
tackle, and the mill afterwards hoisted into place. Heavy 
towers may be built up in a standing position. 

The foundations necessary for the tower, whether of 
wood or steel, are best constructed of concrete, in which the 
posts are embedded. The best proportions for the concrete 
are two parts of Portland cement, three parts of sand, and 
five parts of broken stone, both sand and stone being clean 
and sharp. After these ingredients are mixed dry by 
turning over and over, the water is added and the mass 
tamped into the form prepared for it. If the foundation is 
made in stiff earth wooden forms are unnecessary, and 
square holes dug to a depth sufficient to sink the foundation 
bolts are all sufficient. It is advisable to protect the top of 
the foundation bolts by long wooden casings, some 2 ins. 
square, which can be withdrawn when the concrete begins 
to harden. This allows the bolts to be moved laterally so 
that they may be correctly placed, and the space round the 
bolt can afterwards be filled with grout. The correct 
position of the bolts may be assured by a wooden template 
with holes through which their upper ends are passed. 

The steel towers are built up usually of light angle bars 
and, for the smaller mills, have sometimes only three legs, 
the ground plan being an equilateral triangle. The 
sections are fastened up with bolts, and are usually fitted 
together in the shop previous to shipment, so that when on 
the ground they may be quickly erected. In the large 
windmill factories the pieces are cut and punched to 


templates so that they are interchangeable, and a tower 
of a certain height is built up of members of standard sizes. 
After erection they receive a coat or two of paint, and are 
then ready for mounting the windmill. 

The wheels of the American mills are constructed of 
galvanised iron or of wood. Fig. 80 shows a metal wheel 
with curved sails supported by a circular band through 

Pig. 80.— Wind Wheel of Modern Mill. 

their centres, and by another at their inner extremities, 
and connected with the centre by six arms. The sails are 
riveted to the supporting pieces as it has been found 
difficult to keep bolts tight. Some makers construct their 
wheels of ash or maple, the slats being bolted to the arms 
and girts, and the tendency of the wind pressure to collapse 
the wheel is prevented by extending the axle and attaching 
guy rods by means of a star-shaped casting, which are 
fastened to the wheel at a radius from the centre. These are 

Fig. 81. — Windmill (30 ft. diam.) connected to Electric Generator. 


also used in metal wheels and are shown in the illustration. 
This makes a very strong construction, as the wind 
pressure is taken up by tension in the guy rods, which may 
be of small section, and by compression in the axle. 
Indeed these wheels, if presented broadside to the heaviest 
gales, will not suffer injury when constructed carefully, 
though the safety devices attached to most of these modern 
mills prevent them from being subjected to the severest tests. 
The essential parts of a windmill of this type, and which 
will be dealt with in the following order, are : — 

(1) The wheel proper. 

(2) The method of keeping the wheel abreast to the wind 
from whatever quarter it may blow. 

(3) The transmission gear for transferring the motion of 
the wheel to the pump or other machine it is required to 

(4) Safety devices for averting damage or destruction in 
a high wind, and for governing. 

(5) Gear for stopping and starting. 

The Wheel Proper. 

The wind wheel ranges in size from 6 ft. to 40 ft., 
though the latter is an exceptional size. Fig. 81 shows a 
wheel constructed by Mr. Titt, of Warminster, which is 
30 ft. diameter, and is mounted upon an hexagonal steel 
tower 35 ft. high. This wheel is used to drive an electric 
generator through gearing. Fig. 82 show T s an even larger 
wheel (87*5 ft. diameter) by the same maker, constructed 
for the Italian Government. It is erected at Margherita di 
Savoia, and is utilised for the purpose of pumping water from 
the sea for distribution in vaporising beds for the reclamation 

Fig. 82.— Windmill (37*5 ft diam.) employed for Pumping. 


of the salt. The dash wheel pump is worked through 
bevel gearing, which may be seen in the illustration. 

This wheel has 100 sails arranged in two concentric rings of 
fifty each. The sails are plane surfaces and are hinged about 
their front elements so as to be turned at any angle to the 
wind. When they are normal to the plane of the 
wheel the wind passes through without imparting a 
turning moment and the wheel is motionless. In the 
illustration they are shown in this position. 

In another installation by the Warminster firm, at Bury 
St. Edmunds, the wind wheel is 40 ft. in diameter, and is 
constructed with angle iron rims connected with the centre 
spider by ten tubular arms. It is fitted with fifty sails, each 
12 ft. long and 2 ft. 3 ins. wide at the extremity, tapering 
down to 1 ft. These sails are made with hard wood backs 
and light iron rims, and are covered with oiled sail cloth. 
They are connected with the main wheel by ball and socket 
joints, and are regulated through a system of levers. This 
engine is estimated to give 8 h.-p., with a wind velocity 
of 16 miles an hour. It is employed for pumping at a 

The foregoing are unusually large specimens of modern 
windmills, and for such sizes light material must be 
employed in the construction of the sails, as metal would 
be too heavy, though probably aluminium would be efficient 
were it not for the present high price of the metal. The 
risk of destruction in a gale consequent upon the difficulty 
of stiffening a large wheel has led to a reduction in the 
size of the wheel, coupled with a change in the material 
from wood and canvas to galvanised sheet iron or steel, 
which is the most extensively used material out of which 


sails are constructed. The mills used throughout the 
great agricultural countries are constructed of galvanised 
iron or steel and, as before stated, are for the most part 
about 10 or 12 ft. in diameter. 

The metal sail lends itself more readily to shaping than 
a wooden or canvas sail, and as a rule such sails are curved 
more or less like a screw propeller, so that the surface of 
the sail makes an angle with the plane of the wheel which 
is less as the distance from the centre is increased. In 
Fig. 88 the angle is the inclination of the line joining the 
edges of the sail with the plane of the wheel, and A divided 

Plane of Wheel 

Fig. 83. — Curvature of Metallic Sail. 

by B (sin 6) becomes less as the radial distance outward is 
increased. In an actual case the values of this ratio at the 
inner and outer extremities of the sail was such as to make 
the angles 89° and 84° respectively, the intermediate points 
having angles between these two extremes. 

The correct curvature is more a matter of trial than of 
deduction from any known law or rule, and while there 
may be a correct curvature on a sail for a wind of given 
velocity, an alteration in the velocity would require a 
corresponding change in the curvature, so that, with fixed 
sails, the angles at which they are set is, at best, a compro- 
mise. But, besides having the helical curvature, all metal 


sails are dished so as to present a concave surface to the 
wind. There is no reason for this except to add stiffness 
and convey strength to the sail, so that, supported as they 
are in some wheels only at their extremities, they may be 
able to resist the collapsing tendency of the wind pressure. 
The dished sail cannot strictly follow a helical surface, as 
different elements, at the same distance from the axis, are 
inclined at varying angles with the plane of the wheel, and 
only in so far as the line CD (Fig. 83) is inclined at an angle 
with the plane of the wheel, which would be correct for a 
helical surface of given pitch, can it be said that windmill 
sails are designed in accordance with any theoretical 
assumption ; for the rest, it is guesswork supported by such 
experimental evidence of the behaviour of mills in winds 
that is to be had. Experiments have shown that there is 
only a slight advantage in twisted sails over sails which 
have a constant angle to the plane of the wheel at all 
points. The rear edge of the sail should be nearly parallel 
to the plane of the wheel, while the forward edge should be 
at such an angle that the wind will enter parallel to the 
tangent, but by twisting the sail so as to effect the proper 
entrance of the wind, the rear edges from which the wind 
escapes are placed less advantageously, which reduces the 
benefits derived from a twisted sail. 

The best angle of weather, i.e., the angle that the sail 
makes with the plane of the wheel, has been determined for 
wheels in which the sails are made of plane slats. This 
angle ranges from 25° to 40°, depending upon the width 
of the sail and diameter of the wheel. As, however, the 
angle for metal wheels varies with the distance from the 
centre, the angle of weather cannot be stated exactly, but 


at the mean radius it is not far short of 36°. With fixed 
plane sails of wood or canvas it is usually smaller, and 
27° may he taken as a fair average. If a constant 
velocity of wind were assured the correct angle could be 
accurately determined, but nature does not assist in this 
respect towards the solution of the problem* The action 
of the wind upon the sails of a wheel is but little under- 
stood, which is not surprising considering the complex 
movements of currents of air. The energy contained in a 
moving stream of air is calculated in the same manner as 
that employed in ascertaining the energy in a current of 
water. Thus, if W be the weight of air passing a given 
point per second and v the velocity, the energy which the 
air current is capable of yielding up per second were it 
brought to rest would be 

1 W 2 

If y is the weight of a unit volume of air at a given tempera- 
ture and barometric pressure, then W = yvA, where A 
is the cross- sectional area of the current. By substituting 
this value for W we find that the energy yielded up per 
second is proportional to the cube of the velocity, or the 
power is expressed by 

P = £-A#. 

It is possible by means of this formula to determine the 
efficiency of a windmill, for, if the constants are known, 
and the power exerted by a wheel be measured by a brake, 
the ratio of the actual power exerted to the total power 
gives it directly. For example, a wheel 10 ft. in diameter 

N.S. T 


has a projected area of 78'5 sq. ft., which would be the 
cross-section of the stream of air intercepted by the 
wheel. The velocity of the wind is 12*3 miles per hour 
(18*1 ft. per second), so that the weight of air passing the 
wheel per second is: W= 0*08 X 78*5 X 18*1 = 114 lbs. 
The energy expended in bringing this current of air to rest 
per second would be 

1 114 

E = 2 X 3^2 X (18 ' 1)2 = 58 ° ft, ' lbs - per second 
or 1*05 h.-p. 

A brake test on the wheel showed that, when working at 
the speed which gave the maximum poWer, energy was 
given up at the rate of 84 ft.-lbs. per second. The efficiency 
would be therefore 


^ = 0*145 or 14*5 per cent. 

A large proportion of the air passes through the inter- 
stices between the sails without reduction of velocity, and 
that which impinges upon the vanes is only partially 
reduced, so that of the total energy in the air a small 
percentage actually is turned into useful work, part of 
which is lost in friction in the bearings of the wheel. 

Veering Mechanism. 

Various methods were devised for keeping the wind 
wheel abreast to the wind in the old types of mill. In the 
light metal mill there is only one device now employed — 
that of a tail vane upon an extended arm, upon which the 
wind acts until it causes it to rest in a position with its 
plane parallel to the direction of the wind. In so turning, 


the top of the mill, carrying wind wheel and gearing, is also 
moved round so that the wheel is set with its plane at right 
angles to the wind. This vane is shown in Fig. 1, which 
is representative of the type universally employed. Some 
makers hinge the tail vane arm so that when it is desired 
to stop the mill it may be drawn round by lanyards until 
the plane of the vane is in the plane of the wheel, and thus 
the wheel presents its edge to the wind. The tail vanes are 
made of sheet metal, and are supported by steel or iron rods 
riveted to them and to the head of the mill. The correct 
size for these vanes is derived from 
experience. If made too large they 
keep the mill perpetually oscillating 
in a high wind, and if too small the 
mill does not respond to slight changes 
in the direction. As the best mills are 
mounted upon roller bearings, the 
effort necessary to turn them is small, 
as the wind pressure on the sails is 
balanced unless in special cases to be 
referred to later. 

Fig. 84. — Transmis- 
sion Gear on Brant- 
ford Mill. 

Transmission Gear. 

The feature that most distinguishes 
one mill from another is the transmission gear for convert- 
ing the rotary motion of the wind wheel into a reciprocating 
motion for the pump plungers. In the trials that have been 
made of wind engines this feature has been the principal 
cause of superiority of one type over another, for the power 
of the wheels is so small that transmission losses should be 
reduced to as fine a point as possible in order that sufficient 

t 2 



power may be actually employed in pumping, and notwith- 
standing the care taken to reduce these losses between the 

Fig. 85.— transmission Gear on Brantford Mill. 

wind wheel and pump, they are still so large, even in the 
best mills, as to be one of the chief determining causes of 
the limited value of wind engines. 


For the purpose of transmission the familiar crank and 
connecting rod has certain disadvantages which, for this 
purpose, renders it objectionable. If a long stroke be 
desired for the pump the working of the mill is irregular 
owing to the leverage which the mill has to overcome in 
a long crank. In the Brantford mill (Messrs. Rickman 
& Co.) this difficulty is overcome by the mechanism 

Fig. 86. — Form of Transmission Gear. 

shown] in Figs. 84 and 85. The sail-shaft A carries a 
small pinion which meshes with a mangle rack B attached 
to the top of the pitman C. The mangle rack is in motion 
alternately up and down according as the pinion engages 
with B or Bi. At the end of the stroke two cams E, 
which are also keyed on to the sail-shaft, engage the 
rollers K and throw the rack over so that the pinion, 
riding round the semi-circular racks at the ends, engages 



alternately with the two straight racks. 


Fig. 86a. — Head of Mill showing Gearing. 

The acceleration 
the pitman is 
thus rapid, but, in- 
stead of the har- 
monic motion of an 
ordinary connecting 
rod gear, a uniform 
speed for the pump 
plunger throughout 
the greater part of 
the stroke is at- 
tained. The flanged 
rollers J riding upon 
the plate D guide 
the mechanism and 
This device has the 

constrain the gears to mesh properly. 

distinct advantage of working equally well whether the 

stroke of the pump be 8 ins. or as much as 36 ins. ; and 

the pump valves are 

rapidly opened and 

closed at the ends 

of the stroke, which 

helps the efficiency of 

the pumps materially, 

while with harmonic 

motion the operation of 

the valves is tardy, and 

in the case of large 

pumps has led to the 

use of mechanically 

operated valves. This 

Fig. 86b.- 

-Head oi Mill showing 


is the best mechanism so far devised for converting 
the rotary motion of the sail shaft into a reciprocating 

Another form of gear is shown in Fig. 86. The sail- 
shaft carries a pinion A at its extremity, which meshes 
with a gear B giving a reduced speed, the ratio being 4 or 
5 to 1. The pitman C is attached to a pin on the gear, 
and at the other end to a rocker arm D, swinging about a 

Fig. 87. — Elliptic Gear Transmission. 

bearing on the main casting, and the pump rod E thus 
partakes of the reciprocating motion. The throw of the 
pump is limited in practice with this mechanism t(x about 
18 ins., and with the exception of the fact that the motion 
of the pin F is not in a straight line, and that, therefore, 
the pitman oscillates through a small angle, the motion 
would be that of the ordinary crank and connecting rod. 
Figs. 86a and 86b illustrate this form of gearing. The 
gear shown in Fig. 87 consists of a pair of elliptic gears, 



one of which is keyed to the wind wheel shaft, and the 
other to a counter shaft. The pump rod is attached by a 
pin to the gear on the counter shaft, and thus receives a 
reciprocating motion, the up stroke being slow but the 
down stroke rapid, owing to the ellipticity of the gears. 
Thus, while the pump is drawing from the well the motion 

Fig. 88. — Transmission Gear. 

is slow, and the descent of the plunger then takes place 
rapidly. The advantages of this irregular motion are 
doubtful, and the device is used only to a limited extent, 
for the utility of the quick return is lost if the pump 
is forcing water against pressure. Another form of quick 
return mechanism is shown in Fig. 88. The shaft is driven 
from the wind wheel shaft by a spur wheel and pinion C 


and B, and the pin D, moving in the slot of the lever, gives 
the pitman a quick motion in descending, and a slow 
motion on the up stroke when the shaft is revolving in 
the direction shown by the arrow. The shaft has usually 

Fig. 89. — Crank and Connecting Rod Transmission Gear. 

about one-third the angular velocity of the wind wheel 
shaft. This device is used on the Hercules mill, and 
similar mechanisms are employed by other makers. These 
motions are all open to the objection of imparting a varying 
resisting moment at different parts of the pump stroke, so 
that in light winds the mill is at a disadvantage in starting, 



Fig. 90. — Bevel Gear Transmission. 


as the pump rods and plunger weights acting at the 
leverage of the length of the crank have to be overcome. 
Gearing is necessary unless the cranks, and consequently 
the stroke of the pump, be made very short. The straight 
line motion on the Brantford mill is free from these 
objections, as the pinion is small, and the length of the 
pump stroke is independent of the size of the gearing, but 
the speed of the pump is effected directly by the diameter 
of the pinion on the sail-shaft. 

Messrs. Thomas & Son, of Worcester, use a gearing on 
their " Climax " mills shown in Fig. 89, and the wind 
wheel makes 25 revolutions to one stroke of the pump rod. 
The connecting rod is a steel forging with gun metal head 
connection to the crank. The cross-head to which the 
connecting rod and pump rod are connected is fitted with 
rollers which travel in roll paths in the head casting. The 
bearings are gun metal and are lubricated by a revolving 
chain from an oil reservoir cored out of the casting beneath 
each bearing. These bearings will run for a considerable 
time without attention. 

The mills which are employed for various other purposes 
about a farm, such as corn crushing, chaff cutting, etc., do 
not require a transmission gear of a special kind, for the 
rotary motion of the sail-shaft can be directly communicated 
to the vertical shaft through bevel gears, and in the same 
manner the power may be taken off the vertical shaft or by 
a belt pulley at the lower end. An arrangement of bevel 
wheel and pinion on the head gear is illustrated in Fig. 90. 
The bevel pinion is placed above the gear on the vertical 
shaft, but it may also be placed below. The arrangement 
shown has the advantage that the gears tend to keep in 


mesh, while with the pinion below, any displacement of the 
vertical shaft acts to separate them. The shafts of this 
head gear are borne in roller bearings, and ball bearings 
are iised to take up the thrusts on both wind shaft and 
vertical shaft. As the chief value of these windmills is for 
pumping purposes, this form of transmission is less used 
than thosfc which convert the rotary into a reciprocating 

Safety Devices. 

Safety devices for averting damage to the mill in a 
high wind also perform the function of governors by 
regulating the sail area or the exposure of the wheel to the 
wind according to the strength of the wind. These devices 
are essential on all mills, which would otherwise be quickly 
shaken to pieces in a heavy gale if there were not some 
provision for automatic adjustment. In the old mill with 
long wooden sweeps covered with canvas the adjustment 
by reefing the sail was performed by the miller, but the 
inconvenience of constant attendance, and the fact that 
the prevailing pattern of mill has fixed sails, the area of 
which cannot be altered to suit the wind, render recourse 
to some other form of regulating arrangement necessary. 

The following methods of regulation are in use : — 

(1) Automatic alteration of the angle of weather, i.e., the 
angle the plane of the sail makes with the plane of the 
wheel, according to the strength of the wind. 

(2) Automatic change in the angle that the plane of 
the wheel makes with the direction of the wind, so that 
the wheel is not always normal to the direction of 
the wind. 


The system of regulation by altering the angle of weather 
has been used in mills of the type described in Chapter X., 
but it is not automatic. Some mills of the older types 
which are now used in England and elsewhere have sails 
made up of a series of wooden slats arranged across the width 
of the sail. These slats are capable of being rotated around 



Fig. 91. — Mechanism for Weathering Sails. 

an axis parallel to their long dimension, and are moved in 
unison by the mechanism shown in Fig. 91. The sail-shaft 
A is made hollow, through which the iron rod B passes, 
having at the rear end a rack into which a pinion meshes. 
By means of the linkage D the longitudinal movement of 
the rod B is communicated to the rods parallel with the 
sail arms G, and these rods are attached to the sails and 
rotate them all simultaneously through the same angle 



when the pinion is turned by the rope wheel on the pinion 
shaft. The necessity for watchful attendance on the part of 
the miller is not obviated by this plan, but Fig. 92 shows 
an automatic device, which is used on an American mill, 
the wheel of which is composed of radial sails D hinged at 

Fig. 92. — Automatic Weathering Mechanism. 

the ends of radial arms C and capable of being altered in 
position through the linkage and rod B. The weights E act 
to balance the mechanism, and also to assist regulation by 
the action of centrifugal force upon them, which causes the 
sail D to assume an inclined position upon which the wind 
will have less effect when the velocity increases. The 


regulation is at the same time effected by hand through the 
cord F and the bell-crank lever which moves the collar G 
upon the sail-shaft. 

This method of regulation is only of course adapted to 
mills with movable sails, and is therefore of very limited 
application. In fact it is confined to a class of mill which 
is numerically very much less used than the steel mill 

Eig. 93. — Governing Mechanism (Eclipse Mill). 

with fixed sails, and other systems of regulation have 
therefore come into use. 

One form of governing mechanism is shown in Pig. 98, 
which gives two views of the same mill (the Eclipse, made 
by Fairbanks, Morse & Co.). In this mill there is a small 
rudder vane, in addition to the usual tail vane for keeping 
the mill to the wind, but which is normally set with its 
plane parallel to that of the wind wheel but projecting out 
at one side of the wheel as shown. 

The vanes of the wind wheel in this case, as in the fore- 
going, are rigidly attached, and always present the same 



fixed angle to the wind whether light or heavy. When the 
wind increases in force it acts upon the vane shown to the 
right of the wheel in Fig. 93, and this vane is rigidly attached 
to the head casting by a stout rod. The result of the un- 
balanced wind pressure is to turn the wheel at an angle, so 

that it escapes the full force 
of the wind. A weighted lever, 
connected to the rudder vane 
through a pair of eccentric 
gears (Fig. 94), acts to re- 
store the wheel to the original 
position should the wind drop. 
This vane, the normal posi- 
tion of which is shown in the 
figure, should not be confused 
with the usual rudder vane to 
which it is set at right angles. 
Another expedient adopted to 
save the wind wheel from 
destruction in high winds is 
of a somewhat similar kind, 
though the unbalanced pres- 
sure necessary to turn the 
plane of the wheel is ob- 
tained by setting the centre 
of the wheel to one side of the vertical axis of rotation, the 
restoring couple being obtained by a spring or weight. 
When the wind pressure becomes too strong, it deflects 
the wheel, the latter is turned partially out of the 
wind, and thus prevents the speed of the wheel from becom- 
ing dangerously high. Another safety and governing 

Fig. 94. — Governing 
Mechanism (Eclipse Mill). 


Fig. 95. — Governing Mechanism on Brentford Mill. 
N.S. U 



device, as used on the Brantford mill, is shown to the right 
in Fig. 95. In the normal position the wheel is out of 
the wind, and the wind wheel and rudder vane planes are 
parallel. If anything should break in a high wind the 

wheel goes out of the wind 
and consequently stops, 
and to start the mill it is 
necessary to pull the wheel 
round to face the wind, it 
being held in this position 
by the lanyard manipu- 
lated from the foot of the 
tower. The mechanism 
for effecting this is clearly 
shown in the illustration. 
Another mechanism by 
which the weathering of 
the sails is altered is 
shown in Fig. 96. 

Gear for Stopping and 

The method for stop- 
ping and starting the mill 
with movable sails is to 
set the sails at right angles to the wind, or at the angle 
of weather. Fig. 96 shows a wheel through which the 
wind may pass without communicating any turning 
effort to it, though the tail wheel keeps it constantly 
abreast to the wind. The other, and most general method 
of stopping and starting, is by slewing round the tail vane 

Fig. 96. — Mechanism for Control by 




u 2 


through 90°, so that the planes of the wheel and vane shall 
be parallel. Almost all the makers of mills use this plan, 
the alteration in the direction of the vane being easily 
effected from the ground. The Brantford mill has this same 
method of starting and stopping, but, as we have seen, the 
tail vane is normally parallel to the wind-wheel and has to 
be pulled round to start the mill. Any system of brakes 
upon the sail-shaft is unsatisfactory, as the mill would be 
exposed to the full force of a heavy gale, unless the wind- 
wheel were turned edgewise to the wind, and kept in this 
position by the tail vane placed parallel to it. 

The American type of steel mill being now almost the only 
kind made to any extent, there is little to be said about 
other kinds of mill. Two special designs of mill may, 
how- ever, be described, as they possess novelty of design 
and construction. 

One of these windmills, which is fashioned somewhat after 
the Robinson anemometer, is shown in Figs. 97 and 98 and 
is the invention of the late Professor Blyth. The writer is 
indebted to his son, Mr. V. J. Blyth, for the use of the photo- 
graphs from which the illustrations have been made. Several 
of these mills have been erected, one at Marykirk and another 
at the Montrose Asylum. This latter mill suffered a frac- 
ture in the main 4-in. vertical driving-shaft and was not 

The reasons which led the inventor to adopt this type of 
mill are stated in a paper presented to the Boyal Scottish 
Society of Arts. 1 He states that he discarded the old type 
of mill because, when it was necessary to reef the sails, the 
mill had to be stopped, and just at the time when it should 
1 Transactions, Vol. xiii., part 2. 


Fig. 98.— The Blyth Windmill. 


have been going at its best. He then tried the American 
type of mill with metal sails, and, finally, in order to satisfy 
the following conditions, the anemometer type was chosen. 
(1) The mill must be always ready to go ; (2) it must go 
without attendance for lengthened periods ; (8) it must go 
through the wildest gale and be able to take full advantage 
of it. The machine he describes had four semi-cylindrical 
boxes attached to four strong arms, each about 26 ft. long. 
The opening of each box was 10 ft. by 6 ft., and the vertical 
shaft was an iron rod 5 ins. in diameter. At the lower end 
of the shaft the power was taken off by gearing, and the 
dynamo was driven by a belt. The turning moment was due 
to the difference in pressure of the wind upon the convex and 
concave surfaces of the sails at the ends of the opposite sail 
arms. Professor Blyth stated that the speed of the sails 
approaches a limiting value as the wind increases in violence, 
so that their velocity is not proportional to the wind velocity. 
Upon this the regulation of the mill depends, for a destruc- 
tive speed is automatically avoided. This same relationship 
is noticed in the anemometer at very high winds, the speed 
of the cups falling short of what it would be were the pro- 
portionality to prevail throughout the velocity range. 

Another novel type of windmill, known as the Eollason, 
has been working for some time. In this mill the sails are 
flat surfaces like paddles, projecting from a vertical shaft, 
and the wind is excluded from half of the wheel by a semi- 
circular shield which is kept in position by the tail vane. 
Thus half of the wheel is exposed to the wind, which, 
therefore, exerts pressure only on one side of the shaft and 
causes the wheel to revolve. 



The first point that an engineer requires reliable informa- 
tion upon in contemplating the use of wind-power is an 
estimate of the power it is possible to obtain from a mill, and 
the cost of the mill and the upkeep of the machinery. The 
size of the wheel alone is not sufficient to judge the power 
of the mill from, for an inspection of manufacturers cata- 
logues illustrates the difference that may exist in the power 
of different sized wheels actuated by a wind of a given 
velocity. Nor can the power of a wind-wheel be ascertained by 
calculation from the elements of the wheel, such as sail area 
and angle of weather, for even if it were possible to obtain 
the power put into the wind-shaft, that lost in the friction of 
the gearing has to be taken into account, if the net power 
applied to the pumps is to be accurately determined. 

In the previous chapter allusion was made to the available 
energy in a wind of given velocity, and how an estimate 
of the efficiency of a wheel might be calculated. As, 
however, the actual question of efficiency, i.e., ratio of power 
developed to power supplied, is of less importance than the 
power which a wheel of a certain size will develop, the 
latter is the usual form in which the value of a wind- 
wheel is gauged. It is therefore distinct in this respect 
from the usual designation for a steam engine or other 
form of prime mover in which the actual Lhermo-dynamic 


or mechanical efficiency is the most desirable means 
of estimating the worth of the machine. The efficiency of a 
wind-wheel may therefore be estimated by the power of 
a wheel of a certain diameter in a wind of given velocity — as, 
for instance, a 12 ft. wheel acted upon by wind of 16 miles 
per hour — and in this sense it is understood, though it is 
always necessary to state the velocity of wind, for numerous 
figures are used by the makers who often state the power of 
the mill without mention of the wind velocity. Moreover, of 
two mills which are to be compared, one may yield actually 
a greater power than the other for a certain wind velocity, 
while an increase in the wind velocity of a few miles an 
hour will reverse the position, the other mill developing 
more power. In other words, a mill with fixed vanes works 
best at a certain speed of wind, below or above which the 
power may fall off relatively, though most of the accurate 
tests made show that through a range of wind velocities 
the power increases with the velocity according to a law 
which is not directly proportional for the best wheels. 

The estimation of the actual power derived from wind- 
wheels rests entirely upon experimental data, of which there 
is not very much available. Of such as there is, some 
of the most interesting and accurate results so far obtained 
are collected together in the report upon the trials of wind- 
pumping engines carried out by the Eoyal Agricultural 
Society of England at Park Eoyal in 1903. These trials 
were conducted with great care and in connection with 
accurate anemometric observations, so that for the period 
during which the mills were under test accurate informa- 
tion concerning the wind was recorded. The wind pressure 
was measured by two Dines anemograph instruments placed 


with their vanes about 40 ft. above the ground. As the 
pressure fluctuated continuously the average wind velocity 
for a period was obtained from the diagrams of the instru- 
ment by drawing a mean line through the trace of the 
stylus (see Fig. 68, p. 227). A comparison between the 
records obtained in this manner and those of the Eobinson 
anemometers at Kew, not far distant, proved them to be 
very close, so that this method of measuring was sufficiently 
accurate for the purpose. 

The following are the regulations under which the wind 
engine makers competed, and which are taken from the 
report of the trials :— 

1. The wind engines must not exceed 4 b.h.-p. with an 
actual wind velocity of 10 miles per hour. They must be 
erected on towers so constructed that the centre of the vane 
is 40 ft. in height from the ground level. 

2. Each wind engine must be fitted with its own pump, 
provided with suitable suction and delivery tanks, and 
connections between same. Preparation must be made on 
the delivery pipe to receive a valve, to be provided by the 
Society, loaded to a pressure of 200 ft., through which the 
water will pass on its way to the delivery tank. 

3. The actual wind velocity will be registered by a 
recording Dines pressure tube fixed at a height of 
40 ft. 

4. The wind engines will run and be under continual 
observation for ten hours each day, when the wind velocity 
and horse-power developed by the engines will be noted. 

5. Each competitor may have a representative to attend 
to the oiling of the engine, etc., before starting ; but once 
it is set to work each day, any subsequent interference with 


the engine will be duly noted. The engine must not be 
interfered with after the day's work. 

6. Each competitor will use his own discretion as to the 
diameter of wind vanes and the speed at which the engine 
shall run. 

7. The points to which special attention will be directed 
are: — 

(1) Stability of tower and cost of foundations. 

(2) Eegulation and self-governing. 

(3) Ease of erection and maintenance. 

(4) Size of wind engine relative to power. 

(5) Price. 

8. Competitors will be required to erect the engines and 
provide their own foundations. 

9. The wind engines will remain in position until after 
the conclusion of the show. The competitors will not be 
required to pay for the space thus occupied. 

10. The trials of the wind engines entered will commence 
in the new permanent show yard on Monday, March 2nd, 
being continued, at the discretion of the judges, until 
April 30th, 1903. 

As the utility of a farm pumping wind engine depends 
upon other considerations than the power that can be got 
out of it, these were taken into account by the judges, and 
they are enumerated in clause 7 of the foregoing ; more- 
over, the efficiency of the pump was not excluded, and, 
therefore, a bad pump would affect the worth of the wind 
engine proper by affecting the entire plant. But as most 
wind engines of these types are employed for pumping, the 
pump efficiency may properly be taken into consideration, 
and the actual power, as measured by water lifted through a 


certain fixed height (in this case 200 ft.), may be taken as a 
measure of the power capacity of the windmill. 

Both engine and pump were expected to stand the strain 
of a run of two months with only the same attention that 
the plant would have in ordinary working, and any break- 
down occurring during that time necessitating the attention 
of the maker was regarded as sufficient justification for 
excluding the mill from further competition. 

Seventeen makers responded to the invitation of the 
Society by submitting twenty-two windmills, and these 
were erected in the Park in suitable positions so as to 
avoid blanketing each other. It would take us too far to 
describe all the details of the mills, which were the product 
of the leading manufacturers of the world. Besides the 
usual vertical wheel with tail vane, there was one in which 
the wheel was mounted upon the top of the tower like a 
mushroom on its stalk, which position it occupied when at 
rest or in a high wind. When working normally the axis 
was almost horizontal, but the action of a high wind would 
be to blow it up until it was edgewise to the wind. 

The laurel of the competition was awarded to the mill 
that contained the chief points of excellence, and it is 
significant that the wheel that showed the highest 
efficiency by pumping the most water was also the one 
that in general excellence of design, governing and other 
qualities, proved superior. The points specially worthy of 
commendation in this mill (the Brantford) were : — 

1. The general excellence of design, especially as regards 
the engine and pump. 

2. The efficiency as determined by the amount of water 


3. The successful governing. 

4. The arrangement for the automatic application of the 

5. Economy in upkeep, due to the slow motion of its 
moving parts, and good workmanship. 

6. Eeasonable price. 

The readings of the instruments were taken at frequent 
intervals during the trials, and the performance upon which 
the awards were based covered the full period under which 
the wheels were tested. Taking one of the readings at 
random we find that in a wind of 12 miles per hour the 
mill was pumping water against 200 ft., and by taking the 
amount of water pumped per unit of time the horse-power 
works out at 0'57. The efficiency of this wheel on the 
basis before outlined would be calculated thus : — The 
weight of air passing through a circular ring of 16 ft. 
diameter per second at a velocity of 12 miles per hour 
would be 283 lbs., and the energy expended per second in 
bringing this air to rest would be 1,369 ft. lbs. = 2*49 h.-p. 
The efficiency would, therefore, be 23 per cent., which is 
a high value. 

The general results of the trials are chiefly of interest as 
a basis of comparison between mills of different makers, 
but they are not complete in the sense in which an engine 
and boiler trial would be regarded as complete. The 
amount of water pumped during a stated period with an 
average wind velocity was the principal record obtained. 
As the water pumped is in direct proportion to the number 
of strokes of the pump, it forms a rough guide to the speed 
of the mill in a wind of known velocity, and by studying 
the way in which the water pumped during the period 












=5 5 








' < 







yr - 








5 £ 7 8 $ 10 II 12 13 14- IS 16 17 18 19 20 21 22 23 24 2S 
Wind Velocity - Miles per hour 

Fig. 99. — Relation between Wind Velocity and Speed of Wheel. 

varies with the wind velocity the law connecting the speed 
of wind and speed of wheel may be exposed. Taking two 


mills, referred to as (1) and (2) in Fig. 99, the traces show 
the variation in the amount of water pumped, and conse- 
quently the speed of the wheel with a varying wind velocity. 
The figures representing the speed of the mill are purely 
arbitrary, and the curve is therefore solely intended to 
point out the actual variation in wheel-speed with wind 
velocity. It will be seen that for both mills the trace, 
which is drawn through the points of observation and 
represents a mean value, is approximately straight, showing 
that the linear velocity of the sails is roughly proportional 
to the velocity of the wind. The curve No. 2 for a 30 ft. 
wheel dips down slightly at the upper end, indicating that 
at the higher velocities the speed of the wheel falls relatively 
to a slight extent. The same relationship for a 30 ft. mill 
is shown in Fig. 100, the curve representing a mean value 
of the observations. For low velocities the speed of the 
mill increases more than proportionally to the speed of the 
wind, but above 10 miles an hour the proportional law 
prevails. For the greater part of the range the wind velocity 
and wheel speed are directly proportional, as the line is 
straight for the most part. 

The design of each tower was carefully examined, and 
during the trial their stability was put to a severe test, for 
a wind of 45 miles per hour was recorded. This would 
correspond to a direct pressure of about 6*1 lbs. per square 
foot, which, acting upon a sail area of 150 sq. ft. at the top of 
a 40 ft. tower, represents an overturning moment of about 
36,600 lb. ft., which is resisted by the weight of tower and 
the tension in the foundation bolts on the windward side 
of the base, while the tendency to distort the tower is resisted 
by special diagonal wind bracing, which is shown in the 



























> J 




r < 









> < 


1 4 

\ I 

') i 

f 7 





f A 

? / 

3 ; 

* / 

5 I 

S 1 

7 1 

8 1 

9 2 


/ 2 

2 23 

Velocity - Af/7es yoer /101/r. 

Fig. 100.— Relation between Wind Velocity and Speed of Wheel 
(30 ft. wheel). 

illustration on p. 262. The pump attached to the Brant- 
ford mill is shown in Fig. 101, which is designed especially 


3fer- — p 

Fig. 101. — Plunger Pump for use with Windmill. 

for connection to wind engines. The stroke of this 
pump is exceptionally long, owing to the absence of 
a crank and connecting rod mechanism at the mill head iu 


this engine. The plunger works in a gun -metal tube within 
the main casting, the inlet and outlet valves being placed 
at the top of the pump. The action is clearly illustrated 
in the figure, and it will be noticed that there is no valve 
in the plunger, both inlet and outlet valves being contained 
in seatings in the casting. The air vessel upon the delivery 
system prevents any undue shocks being thrust upon the 
pump in the event of a stoppage in the pipe. The pump- 
rod end is fastened to a cross-head which works on 
guide rods, and the plunger makes one stroke to two and 
a half revolutions of the wind wheel, and it has a diameter 
of 4 ins. with a stroke of 22 ins. 

An important series of experiments carried out on wind- 
mills in the years 1882 and 1883 for the United States 
Wind Engine and Pump Company by Mr. T. 0. Perry, is 
now published by the Department of the Interior of the 
United States Government, and the writer is indebted to 
the Director of the Department, Mr. Geo. Otis Smith, for 
permission to make use of the information contained 
therein. 1 

The results of these experiments, conducted as they were 
for a private company, were not made known for some 
years, until they were eventually printed as one of the 
Government papers, but they have had an influence already 
upon the design of windmills in view of the important 
points elucidated. The demand for windmills in the arid and 
semi-arid regions of the West for raising water which could 
generally be found below the surface, led to a demand for 
improvement in construction, so that at all times and in all 

1 Water Supply and Irrigation Papers of the United States 
Geological Survey. 

N.S. X 


weathers the wind engine might be safely relied upon to 
supply the water necessary for the cultivation of the land. 

At the time these experiments were carried out the wind 
wheels were nearly all made with narrow wooden slats for 
sails, set at angles with the plane of the wheel ranging from 
35 deg. to 45 deg. The slats were usually placed as close 
together as possible without their projections on the plane of 
the wheel overlapping, and the proportions of sail surface and 
the angles of weather were very different, as there was no 
apparent rule by which they were proportioned. It was 
with a view towards learning something on these points 
that these dynamometric experiments were carried out. 
The angles of weather and other constants given by 
Smeaton more than a century ago were the chief source 
of reference in Europe, but American makers had departed 
considerably from the dicta of this eminent engineer. The 
universal practice in America was to construct the wheel 
with slats, so that the total sail surface exceeded the total 
area of the annular zone containing them by more than one- 
fifth of the whole zone. This was in direct violation of the 
principles of Smeaton, and these experiments showed that it 
pointed in the wrong direction, and that Smeaton's results 
could be copied as regards the sail area with beneficial results, 
though the angle of weather might profitably be different. 

The experiments were conducted in a room 36 ft. by 
48 ft. and 19 ft. high from the floor to the roof trusses, 
and Fig. 102 shows a plan and elevation of the appa- 
ratus employed. It consisted essentially of a revolving 
arm AB centered at A and counterbalanced by a weight 
on the opposite side which is not shown in the illustrations. 
This arm could be rotated by means of the gearing and 



Fig. 102.— Whirling Table for Testing Windmills (Plan and 

x 2 


belts at any desired uniform speed within the limits of the 
experiments. Two rollers C on opposite sides of the pivot A 
revolved upon a circular track so as to take the weight of 
the apparatus and prevent vertical oscillation. The wind 
wheel to be tested was supported at the outer end of the 
arm, and was thus exposed to a wind of definite velocity 
according to the angular velocity of the arm. The distance 
from the axis of the sweep to the centre of the wind wheel 
was 14 ft., so that the velocity in miles per hour would be 
given very closely by the number of revolutions per minute 
made by the sweep. As the air in the room was assumed to 
be quiescent, the actual wind velocity acting on the sails was 
that due to the speed of the sweeps ; for though the action 
of the sweep carried the air with it to some extent, it did 
not produce a noticeable current. The sweeps were caused 
to revolve by an 80 h.-p. engine. The revolutions were 
counted by an 80-toothed wheel, so that the fraction could 
easily be determined to within 0*0125 of a turn. For 
measuring the power a prony brake was used which was 
placed upon the wind-shaft. The brake differed in some 
respects from the customary type (see p. 112), the usual 
wheel being replaced by two pine blocks clamped vertically 
upon a brass cylinder 5*25 ins. in diameter, and the adjust- 
ment was made by a cord passing across from one block to 
the other round small iron sheaves, and then by means of 
sheaves and levers up through the hollow shaft supporting 
the sweep, and finally fastened to one end of a lever shown 
in the elevation, by means of which the tension in the cord 
could be adjusted from the station of observation while the 
sweep was in motion. The axial thrust of the wind wheel 
shaft was sustained by a steel point. 


The number of turns made by the wind wheel was 
observed on a worm and wheel gearing, the worm being 
placed upon the wind wheel shaft. Each turn of the wind 
wheel would cause the toothed wheel to make 0*0125 of a 
revolution as there were eighty teeth in the wheel, and the 
fractional turns could thus be estimated to within one-tenth 
of a revolution of the wind wheel. 

In making a test the dynamometer was loaded with a 
weight, say 1 lb., and both the counter for recording 
the speed of the wind wheel and that for wind velocity 
were set at zero. The sweep having been set in motion, 
the speed of the wind wheel was checked by the brake, 
which could be adjusted by regulating the tension in the 
cord. As soon as the friction * and weight were balanced, 
both counters were thrown in by a single movement of a 
lever, and, at the end, both simultaneously thrown out. 
The friction in the journals, expressed in pounds at 1 ft. 
radius was added to the load. This made the total 
load, which was then multiplied by the turns of the wind 
wheel per unit of time to obtain the power. A second 
determination was then obtained in the same manner with 
a greater load applied, and then another, until the maxi- 
mum was reached, for, with the diminishing speed of the 
wheel, there would be a value at which the product would 
begin to decline. The greatest product corresponded to 
the best load for the wheel, and the speed of the wheel at 
that load would be the best speed. 

This greatest product would therefore be the greatest 

1 A friction test made on the journals showed that 0*27 lbs. acting 
at 1 ft. radius was sufficient to accelerate the wheel when once started, 
but it was not sufficient to overcome the statical friction. 



power possible from the wheel when driven by a wind of 
given velocity, and would represent the maximum efficiency 
of the wheel. 

Some particulars of the wheels tested are set forth in the 
following table : — 


Angle of 

Sail Area. 




of Wheel. 


Sq. Ft. 

Per Minute 
at Maximum. 

Per Minute, 















24-5, 11-25 






20, 30 






22-5, 32-5 











































> > 











, f 
















25, 35 

































25, 30 





















. 27 


> » 





























> > 










25, 35 

12 : 94 





27 5 










Angle of 

Sail Area. 




of Wheel. 


Sq. Ft. 

Per Minute 
at Maximum. 

Per Minute, 













































25, 30 






25, 30 






20, 30 






17*5, 275 

> j 





22-5, 32-5 






25, 35 






27-5, 37*5 




The fourth column of the table gives the revolutions per 
minute that the wheel made when it was putting the 
maximum power into the shaft, i.e., when the product of the 
revolutions and load was a maximum. The next column 
gives the speed with the wheel unloaded, and the succeed- 
ing column the ratios of these two speeds, which are, 
with few exceptions, about one to two. This result is 
largely independent of the angle of weather, though if 
any inferences are to be drawn it would appear that by 
decreasing the angle of weather the loaded speed rises so 
that the ratio is larger. Thus wheel No. 35 had an 
angle of 27"5 deg. and a speed ratio of 0*61, while No. 14 
had an angle of 45 deg. and a ratio of only 0*51. It may, 
however, with a fair degree of truth, be said that the 
loaded speed is about one-half that of the unloaded speed. 
Of course the friction is necessarily included in the 
unloaded speed which cannot be got rid of, though in these 


wheels it was reduced to a very low value by well-made 

We have seen that the energy stored in a mass of air M 
moving with a velocity V is proportional to M and to F 2 . 
But as M, the mass of air passing a given point per second, 
is also proportional to V, it follows that the power expended 
in bringing an air current to rest is proportional to V s . 
Consequently, if a wheel have a fairly constant efficiency 
over a range of wind velocities, the power indicated by the 
dynamometer ought to vary as the cube of the velocity of 
the wind. To ascertain how nearly theory and practice con- 
form in this respect, the experiment was tried by varying the 
wind velocities and recording the power corresponding to 
them. The power of the wheels taken was the maximum 
possible for each wind velocity, and it was obtained, as in the 
previous experiments, by varying the load on the dynamo- 
meter until the product of velocity and load was a 

In the adjoined table, the four wheels, which formed 
the subject of these experiments, are those designated by 
the numbers 2, 40, 41 and 42, in the foregoing table. 
Each wheel was first tried at a wind velocity (a) and then 
the speed of the sweep was increased to (b), the maximum 
products (power) being recorded (A and B) under each 
speed. Taking wheel No. 2 under a wind velocity of 6'73 
miles per hour we find that the maximum power is repre- 
sented by the arbitrary figure 26*290. By increasing the 
wind to 8*46 miles, the power ought theoretically to be — 

26-29 X [Hip = 61-6. 
The actual figure was (>2 , 930, from which it is seen that 










+ 1 i + 1 I + I I + + + 


+ + + 

•c| c 

+ + 4- 



1 + 1 + ++++++ 











SS?itHPv<»PP l P l P < ?*P 





8 ^pp^pp x P99 , ?9 < ? 

-n tH i-H t-HtH tHi-H i-H»H 


• t~coc-c~coc-coo«Ocococ© 
2 ^cbcbcbcbcbcbdo'i'cbdocb 


« « *S s =51 "§ = = 



o ITS l>» «5 © 

05 <N <N CO 



there is a close agreement between theory and practice. 

B ,b\* 

The differences in the tenth column, or 

A (a) ' are the 
discrepancies between the two, while the last column is 
the value of the power at the increased speed calculated 
from the lower speed according to the cube law. As the 
pressure upon the sails would theoretically be proportional 
to the square of the wind velocity, the starting forces ought 
therefore to vary as the square of the recorded wind velo- 
city, and the following table shows the result of experiment 
in this direction. Two velocities of wind, a and b, give 

starting forces A and B, and on this assumption —r ought 
Relation of Different Velocities of Wind to Starting Forces. 

Wind per Hour. 

Starting Forces. 

No. of 


















2 ) 
















,'.' 1 








40 \ 
















',', ) 








41 ) 
















„ i 








42 j 
















" i 








-J . The last two columns show the differ- 
ences between the two values which, considering the 


inevitable inaccuracies of experimental research, are suffi- 
ciently close to attest the truth of the rule that the pressure 
varies as the square of the velocity. The measurement of 
the starting forces is liable to inaccuracy ; moreover, as the 
author of the experiments states, they could not be defined 
or determined with the same accuracy as the maximum 
product of speed and load. It would seem that the measure- 
ment of a starting force would in itself be especially difficult, 
and the only absolutely correct method of determining it 
exactly would be to measure the angular acceleration pro- 
duced by the wind pressure. By exposing the wheel to a 
wind with a load, at first sufficient to prevent turning, and 
gradually decreasing the load until acceleration begins, a 
rough measure, depending upon visual observation, is 
obtained. An important result of these experiments upon 
wind wheels was the effect produced by cutting out obstruc- 
tions from between the sails which produced aerial resis- 
tance to motion. 

The conclusions arrived at regarding the sail area and 
best number of sails were, that wide sails do better than 
narrow ones, and that it is better to divide a given sail 
surface between a few sails than a large number. Thus 
one wheel with only six sails gave 2*5 times the efficiency 
of another with sixty sails. The reduction of the number 
of sails reduces the aerial resistance, and also leaves 
relatively fewer interstices for the air to flow through. 
Taking the total area of the zone formed by the space 
swept through by the sails as 100, three wheels were tested 
having respectively 75, 87*5, and 100 per cent, of sail area. 
Each wheel had the same number of sails differing only in 
width, and the maximum products are represented by the 


relative figures 1*204, 1*212, and 1*201. It is evident 
therefore that nothing was gained by making the total sail 
area more than 87 '5 per cent, of the zone area, and that 
75 per cent, was nearer the maximum than 100 per cent. 
The actual horse-power of these wind wheels of 5 ft. diameter 
is very small. Taking the result of one of the trials, we 
find that under a wind of 8*40 miles per hour the load 
(including 0*1 lb. for friction) at which the wheel gave the 
maximum power was 1'9 lb. applied at a distance of 1 ft. 
from the axis of the wind- shaft, and the wheel was making 
82*9 revolutions per minute with this load. The energy 
absorbed by the brake per minute would therefore be 
1-9 X 2 X 3*14 X 32*9 = 393 ft.-lbs. or about 1-2 per cent, 
of one horse-power. By taking the energy in the wind (see 
p. 274) and that spent at the brake the efficiencies of these 
wheels were determined. The highest efficiency on this 
basis for any of the wheels tested was 0*29. The maximum 
power obtained from any of the 5-ft. wheels was developed 
in a wind of 109 miles an hour, and was 1,553 ft.-lbs. 
per minute, or about one-twentieth of a horse-power. To 
obtain one horse-power from this wheel the velocity of the 
wind in miles per hour would therefore have to be 

' •««.«» X 10-9 = 80-2. 



As the areas of circles are to each other as the squares of 
their diameters, the sail area of a wind wheel likewise 
increases with the square of the diameter. But by increas- 
ing the size of the wheel its weight must be enormously 
increased to provide strength to withstand the increased 
wind pressure. If all the linear dimensions of a wheel were 


doubled its weight would be eight times the original, but at 
the same time the sail surface would only be four times as 
great. Consequently, there is a limit to the size, above 
which the wheel becomes so heavy that for light winds it 
is useless. For this reason small wheels are the 
best, as, without undue weight, they can be made sufficiently 
strong to withstand heavy wind pressure, and the cost of 
construction per unit of power is not any larger in small 
wheels than in large. This is at variance with other forms 
of motor to some extent, in which the cost per horse-power 
is greater for the smaller than the larger sizes. Mr T. 0. 
Perry, in referring to an experiment he made on a 22-ft. 
wind wheel in natural wind, states that, though the anemo- 
meter was placed as close to the wind wheel as possible, it 
was observed that the instrument would sometimes stop 
running when the wind wheel was actually accelerating, 
and that the wind could often be heard whistling through 
the sails on the opposite side of the wheel, while very little 
wind was felt on the near side close to the anemometer. 
In regard to the multiplication of wind power, he 
writes : " That for equal safety in storms, the weights of 
wind wheels of different sizes and like forms should be 
proportioned to the cubes of their diameters. It would 
require four 12-ft. wheels to equal the area and power of 
one 24-ft. wheel if the larger wheel is proportionately 
elevated. But the weight of the one 24-ft. wheel would 
be twice as great as the combined weight of the four 12-ft. 
wheels, and the weight of the one higher tower would 
probably be twice that of the four shorter towers combined. 
Hence it would seem that in proportion to the power 
obtained in each case, the one 24-ft. wheel would cost 


twice as much in material. The thought naturally presents 
itself that the four 12-ft. wheels ought in some way to be 
combined so as to act in unison for concentrating a great 
amount of power where it is desirable to use the power at 
only one point, as in driving one machine of large dimen- 
sions. If the four wheels were coupled together rigidly, the 
trouble from uneven reception of wind which is experienced 
in large wheels would be augmented. The problem has not 
been worked out, but we may imagine a number of wind 
wheels, each compressing air according to its own ability 
and delivering it at any distance into a common reservoir. 
Natural elevations would be selected as locations for wind- 
mills, and such a plant could not be rendered useless for 
the time by an accident to one or two of the wind wheels. 
There would necessarily be considerable loss in compressing 
air, but a low pressure system might be devised that would 
greatly reduce the waste. Some waste of power attends 
every mode of transmission. In seeking to make a gain in 
power of 100 per cent, in proportion to cost of plant, the 
loss of an extra 25 per cent, in transmission might well be 
tolerated. There may, however, be other and better 
methods for accomplishing the object in view than by the 
means we have ventured to suggest.' ' 

Assuming the cube law to hold, the power that may be 
derived from a wheel of the best construction at different 
wind velocities would be approximately as in the following 
table, though a word of caution is necessary lest the figures 
may be taken as expressing more than the available 
evidence on the subject justifies. The great variety of 
conditions and dimensions of wheels of different makers 
necessarily renders such an estimate only approximately 



reliable, but as a guide to an intending purchaser of a wind 
engine the figures may have some measure of significance : — 

Horse-Power of a 16-ft. Wind Engine at Various 
Wind Velocities. 

Wind Velocity. 

Horse-Power developed by 

Miles per Hour. 

16-ft. Wheel. 























To derive an estimate of the power that may be expected 
from a wheel of different diameter than 16 ft., multiply 
the horse-power as given in the table by the ratio of the 
squares of the wheel diameters. For instance, the power 
of a 12-ft. wheel in a 15-mile wind would be approximately 

1-00 X S = 0-56 h.-p. 

The increasing friction losses and aerial resistance, 
besides the wide difference in linear velocities of the outside 
and inside of the sails on large wheels, render these estimates 
for the power less accurate for wheels above 20 ft. in 
diameter, and, as far as experiments go to show, the power 



does not increase according to the same laws above that 
size. They are, therefore, applicable to the most generally 
used size of wheels, which range from 10 to 16 ft. in 
diameter. For a 10-mile wind the h.-p. of wheels from 
12 ft. to 30 ft. in diameter would be approximately as 
follows : — 

Diameter of Wheel. 














The following figures by Mr. Murphy are the result of 
laboratory tests on windmills at wind velocities ranging 
from 10 to 25 miles per hour : — 

Wind Velocity. 

Size of Mill. 

10 Miles 
per Hour. 

15 Miles 
per Hour. 

20 Miles 
per Hour. 

12 ft. 
16 ft. 

0-21 h.-p. 
0-29 „ 

0-58 h.-p. 
0-82 „ 

1*05 h.-p. 
1-55 „ 

For higher wind velocities it is found that the values fall 
much under the theoretical values. 

Mr. A. M. Orr records some careful prony-brake tests 
which show that in a 25-mile wind an 8-ft. wheel gave 



0*12 h.-p. in pumping water, and a 12-ft. wheel developed 
0*64 h.-p. The following are the results obtained from a 
30-ft. wheel which was employed to lift water into a tank 
through a distance of 135 ft. 

Velocity of Wind. 

Cubic feet of Water 
pumped per minute. 






The actual power at the wind-shaft was of course greater 
than these figures, as the friction in the pipe line and pump 
mechanism absorbs a large percentage of the power 
developed by the mill. 

Windmills Applied to Electric Installations. 

It might be supposed that cheap electricity would be 
possible with the windmill at our disposal to drive our 
dynamos, and that the acquisition of " power for nothing " 
would solve the problem of electric lighting, and banish the 
small isolated steam plant and internal combustion engine. 
But such is by no means the case, for, with few exceptions, and 
these expensive ones, the windmill electric installation has 
proved to be a failure so far, and has no compensating 
advantages for the doubtful virtue of obtaining power from 
the winds that blow, and thus avoiding a fuel bill. As 
dynamo driving requires a constant speed if the lamps on 
the circuit are directly connected to the machine, and are 

n.s. y 


to work at constant potential, it is clear that the machine 
cannot be directly connected to the windmill unless some 
sort of governing mechanism be provided whereby the 
fluctuation in speed shall be compensated by the field 
strength of the machine. This expedient has been tried, 
but without success, and we are therefore thrown back 
upon the storage battery as the only way out of the difficulty. 
With the introduction of the storage battery great com- 
plication ensues, besides the addition of an appliance which 
requires unceasing attention for its proper working. By 
such arrangements the dynamo supplies current to the cells 
only when the speed is up to an assigned amount, and the 
current is drawn off for the lamps at the proper voltage. 

The writer has received several letters from men who 
have tried installations of this character, all of which tell 
the same story. The irregular speed of the mill damages 
the accumulators rapidly, and as there is no other means of 
utilising the variable energy, they have been taken out in 
most cases. Devices for storing the mechanical energy 
have been tried, one of which consisted of a system of 
weights which could be raised by the windmill and which 
drove dynamos through a system of rope gearing during 
their descent in the manner of a clock weight. The 
enormous size of the weights necessary and the great 
friction-losses rendered this method unpractical. Supposing 
a drop of 60 ft. were possible it would necessitate a weight 
of 14*7 tons falling through that distance in an hour to 
give one horse-power, friction excluded. The loss in friction 
would probably require double this weight to obtain one 
horse-power at the dynamo shaft. Two such weights, with 
a very heavy structure to support them, would at least be 


necessary, so that when one was being raised by the mill 
the other would be giving out energy by falling. Such a 
plant would not be free from stoppage owing to low winds, 
and to increase the number of weights, so as to have one 
horse-power available at any time, would necessitate such 
an outlay as to be altogether prohibitive, even if absolute 
reliability were assured. 

The method of storage by raising water to be afterwards 
used in a turbine driving a dynamo is also quite prohibitive 
in cost. Supposing, for instance, sufficient water has to be 
stored so that it would yield one horse-power for 20 hours, 
and that the tank is placed 70 ft. above the turbine. 
The capacity of such a tank would have to be about 9,000 
cubic ft., and its dimensions 24 ffc. in diameter and 20 ft. 
deep. It is probable that scarcely more than half a 
horse-power would be obtained as electrical energy in view 
of the very low efficiency of a turbine and dynamo of such 
a small size, so that to obtain one electrical horse-power 
the tank would require to have double this capacity. 

The available power being exceedingly small, and a large 
proportion of it being lost in the gearing and generator, the 
actual energy put into a dynamo is very small for the size 
and cost of the plant. Taking a 12-ft. windmill giving 
0'17 h.-p. in a 10-mile wind, and driving a dynamo of 
80 per cent, efficiency, the electrical output would be 
0*17 X 0-8 = 0*136 h.-p. = O'lOl kw. This would be 
sufficient for a photometric power of 101/3*5 = 29 candle 
power constantly burning, assuming 3*5 watts per c.-p., or 
almost two 16 c.-p. incandescent lamps. It has been found 
that a 12-ft. wheel would provide a minimum of 19 lamp-hours 
(16 c.-p.) per day, while a 16-ft. wheel would give 35 lamp- 

y 2 



Fig. 103. — Windmill (35 ft. dia.) utilized for Pumping and Driving 
an Electric Generator. 


hours in the same time. This was ascertained from a plant 
consisting of a 12-ft. wheel driving a dynamo of 0*75 kw. 
capacity. As the cost of such an installation, including 
storage batteries, would be at least £200, the economy of 
lighting by a wind-driven plant is very questionable. 
Other devices than storage batteries have been interposed 
to maintain a constant voltage. One of these, an example 
of which is at work in Indiana, is connected to a 14-ft. wind- 
mill on a 50-f t. tower. The mill drives a plunger pump, which 
delivers water to a reservoir in which a constant pressure 
of 75 lbs. per sq. in. is maintained by weights on the 
plunger in the reservoir. This water under pressure is 
used to drive a 0*5 h.-p. turbine, which is direct connected 
to a 0*25 h.-p. 25 volt dynamo for charging a storage battery. 
The battery consists of eleven cells, and lights twenty 
8 c -p. lamps for three hours, or five 8 c.-p. lamps for six 
hours. By this means all the power of the windmill may 
be stored to be used in the turbine when desired. The 
author has been unable to obtain any information concern- 
ing the working of this installation which is of such a novel 
character. It is said that a windmill will run in this 
district for five hours a day. 

The first requisite to the success of a wind-driven electric 
plant is a variable speed dynamo, which, within a certain 
speed-range, will deliver current at a constant voltage, so 
that accumulators, if used, may be worked to better advan- 
tage. Several protracted attempts have been made to 
employ wind-power for dynamos, and in several cases every 
possible plan has been tried to make them successful. One of 
these, which is shown in Fig. 103, is situated on an eminence 
in the private grounds of Mr. George Cadbury, and has now 


been in service for thirteen years (though not all the time 
for electric lighting), and the canvas sails have been 
once replaced during that time. The canvas is treated 
with lead paint, which preserves the material very 
well. The motion of the sails is communicated to a 
counter shaft, from which a dynamo is driven. Another 
horizontal shaft takes off power through a pinion from 
the same gear, by which plunger pumps are driven. 
A clutch enables the pumps to be thrown out of gear when 
it is desired to work the dynamo. The irregularity in 
the speed and uncertain character of the driving power has 
resulted in the failure of the electric plant, and a gas engine 
is now installed for the purpose of lighting. The accu- 
mulators were found to wear out rapidly owing to the 
treatment to which they were exposed, and the plates 
buckled. The engineer in charge of the plant informed the 
writer that every possible expedient had been tried to 
make the plant a success, but without avail. The wind- 
mill is now used for pumping, for which purpose it is 
admirably adapted. It is 35 ft. in diameter, and is in an 
exposed situation. The governing of this mill is automatic, 
the sails being hinged so that the angle of weather is varied, 
and the tendency of the sails to turn edgewise to the wind 
is checked by a weight at the base of the tower, which hangs 
at one end of the furling lever, the other end being capable 
of being fixed into any desired position by means of a pin 
passing through holes in guides on each side. 

The engineer in charge of this plant had an experience 
which few men would have gone through without injury or 
loss of life. One day, during a gale of wind, he ascended 
the tower for the purpose of removing two broken sails. 



To accomplish his object he was obliged to stand on the 
outer circumference of the wheel, instead of on the platform. 
While in this position the wind carried one of the sails out 
of his hand, which dropped and struck the pin holding the 
furling lever in place. This pin was knocked out, the 
furling lever fell, and the sails were immediately turned 
for the wind to act upon, and the wheel consequently 
began to revolve. 
Hanging on with 
hands and feet as best 
he could, he was car- 
ried round several 
times before his 
shouts arrested the 
attention of a man 
who was 150 yards 
away and who stopped 
the wheel, but only 
just in time, for he 
was becoming ex- 
hausted, and his 
hands would have 

Fig. 104. — Transmission Gear between 
Windmill and Dynamo for obtaining 
constant Speed of the latter. 

been wrenched loose had he been exposed much longer to 
such a severe strain. 

Among the most satisfactory experiments that have been 
conducted upon the generation of electricity from wind 
power are those of Professor La Cour, which have received 
the support of the Danish Government. The experimental 
station was erected at Askov, and after a long period of 
trial it has been found sufficiently satisfactory to encourage 
the installation of plants at other places in Denmark, more 


than thirty of which are now in operation. The mill used at 
Askov is not built in accordance with American practice ; it 
is rather more like the old type of mill, with four arms 
carrying adjustable slats crosswise which are capable of 
being weathered by a system of rods and levers. These 
four arms are 7*4 metres long, and 2*5 metres wide, giving 
a sail area of 74 sq. metres. It is geared to two 12 h.-p. 
dynamos through a vertical shaft from which the power is 
taken off by bevel gearing on to a horizontal shaft which 
enters the house. From this shaft the dynamo is driven 
through an arrangement of pulleys as shown in Fig. 104. 
The shaft A receives motion from the windmill, and by 
means of the two pulleys the shaft B, which is suspended 
in a cradle D, is turned. By altering the weight W at the 
free end of the cradle the tension in the belt can be 
adjusted. By trial it is found that when the difference 
between the tensions in the tight and loose sides of the 
belt exceeds a certain value the belt starts slipping, and 
consequently the dynamo, C, has a limited speed. By an 
ingenious switch, the possibility of the cells discharging 
through the battery, if the dynamo voltage were to fall 
below the battery voltage, is prevented. The plant is 
assisted by a petrol motor to cover the periods of low 

The Cost of Power Generated by Windmills. 

The cost of wind-power is difficult to determine or to 
estimate with any approach to accuracy, for it depends very 
largely upon the point of view from which we regard it. 
Being a very unreliable source of power and altogether out- 
side of immediate control, if gauged by such a criterion it 


would be very costly indeed. If, on the other hand, we regard 
it as a means whereby water may be lifted for farm purposes, 
and which may therefore be independent of control, it would 
be regarded as a cheap and entirely satisfactory power. For 
most purposes where power is required reliability is the 
chief requisite, and it cannot be measured directly in 
money. For industries requiring a constant and unfailing 
power day by day wind wheels would necessarily be supple- 
mented by some other form of motor, such as a gas engine, 
and the cost of wind-power in such a case would be great, 
for the very small power to be obtained from wind wheels 
might be developed by the gas engine with a small increase 
in size and, consequently, very little extra capital outlay. 
The combination of wind wheels with other forms of motor 
is unsatisfactory, and it has none of the elements of satis- 
factory working that are brought about by the combination 
of an hydraulic turbine and heat engine. The capital cost 
of a wind wheel per horse-power is, relatively to other 
forms of motor, high, and there can, therefore, be no 
monetary advantage except in the absence of fuel charges, 
which, in a combined plant, are present almost to the same 
extent as if the heat engine were operating alone, because 
of the irregular and intermittent assistance rendered by the 
wind engine when exposed to the variable weather in our 
latitude. Most industries require power constantly and in 
unvarying amount, and for some of them excess power 
cannot be used advantageously and is therefore wasted when 
developed. Consequently, of the total number of horse-power 
hours developed per annum by a wind engine, or which could 
be developed if it were allowed to take advantage of the gales, 
a large part would ordinarily be wasted, just as if a gas 


engine driving a machine requiring 15 h.-p. were constantly 
operating at 25 h.-p., the difference being absorbed by a 
brake. The use of electric storage batteries prevents the 
waste of excess energy, but the cost of this extra plant must 
then be considered. The actual number of hours through- 
out the year at which a wind engine may therefore be relied 
upon to develop a full required power (which we will suppose 
would be developed at a wind velocity of 10 miles per hour) is 
disclosed by an examination of the weather charts, which 
shows how very different the average wind velocity is in 
different parts of the country. On the Atlantic coast there 
are a comparatively large number of hours during the year 
at which a velocity of 10 miles an hour or more may be 
counted, while at inland stations the average is very much 
less. Taking 3,600 10-mile hours for the year, the 
number of horse-power hours for a 16-ft. wheel would be 
0-30 x 3,600 = 1,080 h.-p. hours for the year. The cost 
of a 16-ft. wind engine erected on a 40-ft. tower would be 
approximately £65, so that the cost of power per horse- 
power hour would be as follows : — 

Interest @ 3J per cent. . . . 546tf. 

Depreciation @ 7 per cent. . . . 1,092c/. 
Upkeep, including occasional attendance 

and lubrication, £5 ... l,200d. 

Cost per h.-p. hour .... 2'6d. 

The assumptions upon which these figures rest will 
appear liberal when the meteorological records of English 
stations are examined. At most situations it cannot be 


assumed that, for one half the year, there is a wind velocity 
of 10 miles an hour. On the other hand, as against the 
wind engine, it is assumed that all velocities above 10 
miles an hour are grouped under that designation, so that 
for some part of the time the engine is developing power 
for which no account has been made. But, as previously 
explained, excess power above a predetermined amount is 
largely wasted, and a wind engine plant would be designed 
to give full load — at say 10 miles per hour — in the same 
way that a steam engine would be installed under a rated 
capacity. The cost per horse-power is therefore high for the 
wind engine, and there must be, therefore, some feature to 
counteract it to account for the rapid extension and enormous 
trade done in small windmills, especially for pumping 
water on farms in the great agricultural countries. The 
reason lies in the fact that, for water pumping, neither 
constant power nor power in a definite amount is 
necessary, as a pump can work under any wind down to a 
velocity sufficient to overcome the friction, and up to any 
speed which is only limited by the capacity of the machinery 
to escape damage. If the power developed and utilised 
by one of these pumping engines were integrated through- 
out a year it would probably be as low in cost per 
horse-power as in other forms of prime mover, though the 
distribution of the power makes it most undesirable for 
most purposes. Captain Scott in his notable voyage of 
exploration to the Antarctic regions took out a windmill on 
board the ss. Discovery for driving his electric lighting 
plant so as to effect a saving of valuable fuel. For such a 
purpose and in such a situation the windmill would appear 
to be ideally adapted as a supplement to other means of 



lighting the ship, though in this case the design of the 
mill was not properly adapted to the purpose. 

The initial expense of erecting a windmill is not great, as 
the only foundation necessary is four small concrete 
blocks for embedding the foundation bolts. In some mills 
the tower is the most expensive part of the outfit, and it is 
only with elaborately geared wheels that the cost of the 
engine exceeds that of the tower. The price of mills, 
erected upon towers 40 ft. high, would be approximately : — 

Approximate Cost of Mill Erected Complete on 
40-ft. Steel Towers. 

Diameter of Wheel. 

Price iu £ sterling. 

Horse-Power (10 Miles 
per Hour). 








The makers frequently express the power of a mill as the 
number of gallons raised per hour through a height of 100 ft. 
To reduce this to horse power, divide the number of gallons 
(Brit. imp. gallon of 10 lbs.) by 1980. 

The following is taken from a maker's catalogue : — The 
water raised through 100 ft. in gallons per hour by a 16-ft. 
mill under a wind of 10 miles per hour is 700. The 
horse-power is therefore 700/1980 = 0'35. 



To find the value of V in this equation which will render the 
power a maximum it is necessary to ascertain the rate of change 
in the power for different values of V. 

y (power) = ^ (v - V) *V. 
J*| = ^7[(„-F)2-2F(»-F)] 

/f = T 7 [ 8F '- 4 * F+ *'] 

The power is a maximum with such a value of V as will make 
d y 

Putting 8F s -4«F + « ! = o, 


and solving for V we obtain, as the roots of this quadratic, - and v. 


The power is therefore a maximum when V = - and a minimum 


when V = v. 


Experiments made at the weir at different stages of the river showed 
that when the depth on the weir was 3 in. the actual fall was 6 ft. ; 
and during an exceptionally heavy flood, when there was 18 in. of 
water coming over the weir, the head had dropped to 3 ft. Though 
the actual working head H and the weir-depth h are not connected 
by a linear law, the error in assuming such to be the case is small 
between narrow limits, so that we have 


where a and b are the intercepts on the co-ordinate axes of h and H 
respectively. The observations supply us with a means of obtaining 
values to insert for a and 6, for we have 

b -= 6 - 3 =2-4. 
a 1-5 - 025 


6 = 6+ (2-4 X 0-25) = 6'6 ; 
.-. H = 6-6 - 24 h. 
The horse-power per foot of weir length in terms of h will 
therefore be 

(1) H.-P. = 0-379 v/fc 3 (6*6 - 2*4 h). 
To find the value of h, which will make the horse -power a maximum, 
we have 

d (^-" R ) = 0-379 [9-9 7^-6 fcT] . 

Putting this = o, we have 

- 6 /$ + 9-9 hi = o. 
.-. 71=1-65 ft. = 19-8 in. 
We thus find that when the height of water on the weir is 19*8 in. the 
maximum horse-power is attained. Any further increase in h would 
not augment the horse -power, owing to the rapid rise of the tail- 
water and consequent diminution of effective head. The maximum 
horse-power for the full weir length under any conditions would 
therefore be 

H.-P. = 367 X 0-379 X 2-12(66 - 3-96) = 354. 


If t be the thickness of a pipe and r the internal radius expressed 
in the same units, the stress / per unit of area acting to tear the pipe 
asunder, when p is the unit pressure, is expressed by the following 

/= 0-+t)* 


In this formula the radius taken includes half the thickness of the 


pipe, but this may be neglected as t is always small compared with r, 
therefore — 

/= -p or —- = — where D is the internal diameter. 
J t t p 

The strength of the steel used in the manufacture of high pressure 
pipes may be taken as 60,000 lbs. per sq. in., or 4,220 kg. per sq. cm. 
= 42*2 kg. per sq. mm. If h is the head of water in metres acting 
on the pipe 

2> (kg. per sq. mm.) = j^. 

It is usual to assume a factor of safety of 4 so that the maximum 
allowable stress in the steel would be //4 = 42*2/4 = 10*55 kg. per 
sq. mm. 

We have therefore 

D _ 2 X 10*55 _ 21,100 

t ~ h ~ h ' 

If the pipe be riveted longitudinally, the resistance to rupture 
ought to be taken at 80 per cent, of that of the solid plate ; the thick- 
ness in millimetres would therefore be — 

t (riveted pipe) = __ X m = j^ + 3. 

For welded pipe 95 per cent, of strength of solid plate should be 

t (welded pipe) = ^ X ^ = £± + 8. 

The constant 3 is added to allow for the tendency of a large pipe to 
assume an oval form when lying on the ground. 

Example (1). Supposing a riveted pipe of 450 mm. diameter, made 

of open hearth steel, be subject to a hydrostatic pressure due to a 

head of 800 metres. What is the thickness required with a factor of 

safety of four ? 

. 450 X 800 . Q OK 1 . , • * i x 

* = — ia ourt h 3 = 25 mm. — 1 in. (approximately). 


Example (2). Supposing a welded pipe ot 750 mm. diameter, made 


head of 600 ft. (183 m.). What is the thickness required with a factor 
of safety of four ? 

. 750 X 183 . . ln 13 . 

^= WOOO - + 3=10mm * = 32 m ' 
If D and h are in inches and feet respectively, the two expressions 
become, for the thickness in inches — 

t (riveted pipe) = ^^ + 0*12. 
* (welded pipe) = ^g + 0-12. 



Abbreviations, xiii. to xvi. 

Abscissae, 136, 193 

Acceleration, angular, 315 

due to gravity, 20 
linear, 79, 81, 178, 

units of, xvi. 

Action turbines, 71 

Adhesion, 127 

Adjustments of level, 39 

Air chamber, 169, 305 

Air currents, 212 

Air resistance, 20, 319 

Air, weight of, xvi., 274 

Alternator, 146 

in parallel, 188 

American windmill, 261 

Ampere, 7, 8 

Anchor, 264 

Anemometer, 215, 317 

constant, 221, 224 
fan, 225 
helicoid, 220 
Robinson, 219 
tests of, 223 

Angular deviation allowance, 188 
velocity. See Velocity. 

Antipater, 46 


Applications of water power, 46 
Arch, 129 

dams, 123 
Area, units of, xiv. 
Armatures, 188 
Armature shaft, 188 
Ashlar, 123, 127 
Askov, 327 
Atmospheric pressure. See 

Automatic governor. See 

Axial flow, 65, 71 

Back pressure, 63 

Backsights, 41 

Baffle plate, 148 

Baker, 235 

Balancing, 65 

Ball and socket, 270 

Base plate, 140 

Bassell, 124 

Battery. See Storage. 

Bearing, ball, 284 

outboard, 187 
roller, 275, 284 
step, 66, 68, 140 

Bearing plates, 69 

Bench marks, 44 



Bernouilli, theorem of, 23 

Berton, 256 

Best speed, 88, 106, 116 

Blow-hole, 142 

Blue Hill, 222, 228 

Blyth windmill, 292 

Board, pressure on, 76 

Bodmer, 89, 187 

Boiler, 83 

depreciation on, 164 
thermal action of, 10 

Brake, Prony, 109, 112, 119,308,320 
wheel, 113, 251 

Brantford Mill, 275, 277, 283, 299 

Braschmann, 81 

Breast water wheel, 50 
efficiency of, 51 

British thermal unit, xvi., 6 

Buckets, 49 

Bury St. Edmunds installation, 

Bushing, 141 

By-wash, 138 


Cadbury, 325 

Calculation of power in water fall, 

Calibration of current meter, 30 

Calm, period of, 231 

Calorie, xvi., 6 

Canals, 37, 134 

Capital cost, 155, 161, 162 

Caribbean Sea, 16 

Casing, 129, 140 

Cassel governor, 207 

Cast iron, 52, 68, 73, 113, 142 

Cement, 128, 139 

Centrifugal force, 82 

governor. See Gover- 

Chezy, 150 

Classification of turbines, 71 

Climax mill, 288 
Coal, 2, 47, 164 

thermal value of, 12 
Co- efficient of flow, 31 
Compressed air system, 318 
Compressibility of water, 16, 56 
Concentric vanes, 68, 143 
Concrete, 98, 127, 138 

proportions of, 128, 139 
Conservation of energy, 3 
Construction of water wheels, 52 

power plants, 120 
Continuity, equation of, 27 
Copper, cost of, 155 
Corn milling, 46, 51, 241, 247, 252 
Cost of turbines, 144 

sfceam power, 163 
turbines as affected by 

head, 157 
turbines as affected by 

speed, 157 
turbines as affected by 

power, 159 
water power, 152, 162 
wind power, 328 
Counterpoise, 65, 172 
Countershaft, 139 
Cressy, battle of, 242 
Croeser, 151 
Crowns, 52 
Current meters, 30, 119 

water wheels, 46 
Curve of discharge, 35 
Cylindrical gate, 64 


Dams, 37, 120, 133, 135, 151, 162 
arch, 123 
earthen, 123 
gravity, 123 
puddle, 124 
stone, 125 



Dams — continued. 
wooden, 127 
Darcy, 149 

Dash -wheel pump, 270 
Data for turbines, 70 

pertaining to water, 19, 45 
Delaunay, 53 
Denny and Johnson, 114 
De Sabla, 155 
Density of water, 16 

air, xvi., 274 
Depreciation on water power 
plants, 162, 164 
on steam plants, 163 
Differential motion, 198, 201 
Dines, 220, 223, 225, 296 
Direct connection, 187 
Direction of rotation, 72 
Disc pressure, 102 
Discharge over weirs, 35, 136 
measurement of, 28, 186 
necessary for given power, 18 
Diversion angle, 84 
Domesday book, 47, 241 
Double-butt joint, 148 
Draft tube, 74, 98, 162 
Drowned turbines, 62, 65, 71, 170 
Dynamo, 53, 118, 139, 144, 178, 
cost of, 161 
constant speed, 321 
for testing, 110 
hydraulic system for driv- 
ing, 323 
three-phase, 209 
variable speed, 325 
weight system for driv- 
ing, 322 
Dynamometer, absorption, 114, 
119. See also 
transmission, 114 

Earthen dam, 123 
Earthquake, 124 
Eclipse mill, 287 
Economy in power utilisation, 4 
Edge runner, 252 
Effective head, 26, 147 
Efficiency, 5, 11, 12, 13, 50, 51, 
53, 55, 72, 76, 77, 89, 
92, 94, 103, 108, 110, 
115, 147, 333 
Jonyal and Girard tur- 
bines compared, 68 
of windmills, 253 
variation with gate- 
opening, 119 
Egyptian records, 46 
Electric generators. See Dynamo, 
motor, 148, 210 
efficiency of, 13 
lighting, 53, 139, 164, 190 
by wind power, 
Electrical energy, 5 

cost of, 325 
tests, 53, 110 
transmission, 48, 155 
units, xvi., 7, 10 
windmill installations, 
Elevation of station, 41 
Elliptic gears, 279 
End contractions, 33 
Energy, units of, xvi., 5 

conservation of, 3 
electrical units of, 7 
kinetic, 59, 75, 175 
losses of, 4, 19, 26, 78, 
81, 82, 85, 92, 112, 147, 
measurement of, 5 
potential, 60 

z 2 



Engineer's level, 37 
Equation of continuity, 27 
Errors in levelling, 42 
Expansion, 56 

joint, 149 


Fall, height of, 19 
high, 170 
low, 68, 70, 170 
maximum power from, 136, 
•*, medium, 170 
Falling water, power in, 17 

velocity of, 19 
Fergusson, 228 
Ferro-concrete, 129 
Flight, 216 
Floats, 29 

Floods, effect of, 36, 44 
Flood-gate, 127 
Flow. See also Discharge, 
co-efficient of, 31 
formula for weirs, 31 
measurement of, 8, 28, 119, 

velocity of, and speed of 
wheel, 187 
Flume, 92, 110 
Fly-wheel, 56, 82, 207 

and governor, differ- 
ence between, 189 
effect, 184 
governor, 179 
Fontaine turbine, 71 
Foot-pound, xvi., 5, 7, 75 
Force-de-cheval, value of, xvi., 

17, 118 
Foresights, 41 
Forked draft tube, 99 

Formula for flow over weirs, 31 
Formulae pertaining to water, 45 
Foundations, 127, 139, 154, 162, 

Fourneyron, 64 

turbine, 64, 71 
Francis, J. B., 31, 109 

formula for flow over 

weirs, 31, 135 
turbine, 71, 96, 119 
Friction in pipes, 149, 176 

losses by, 19, 26, 50, 52, 
54, 82, 93, 108, 147, 
statical, 221, 309 
Fuels, 1 

Full load speed, 140 
Funicular, 79 
Furling lever, 326 
iils, 256 


Gas engine, 2, 55, 164, 165, 188, 
326, 329 
producer, 165 
Gate, cylindrical, 64, 101, 171 

opening, 116, 118, 119, 140 
types of, 171 
Gauge, 34, 109 

Gearing, 52, 139, 141, 144, 162 
elliptic, 279 
pin, 244 

ratio for windmills, 252 
transmission, 275 
worm and wheel, 96, 
148, 309 
Gear-teeth, wooden, 52 
Generators. See Dynamo. 
Girard turbines, 65, 68, 71, 103, 



Gland, watertight, 64 

Goodman, 176 

Gordon, R., 30 

Governing by deflection, 148 
mechanism for, 96 

Governor (turbine), 139, 141 
centrifugal, 168 
continuous, 192, 198 
disengagement, 192, 

emergency, 208, 210 
hydraulic, 192, 193, 201 
loaded, 180 
mechanical, 192 
pendulum, 179, 209 
period of action, 204 
sensitiveness of, 182 
types of, 194 
unloaded, 180 
windmill, 284 

Grand Canyon of the Colorado, 

Grating, 173 

Gravel, 130 

Gravity, acceleration due to, 20 
dams, 123 

Gudgeon, 52 

Guide vanes, 63, 67, 96, 98, 101, 

Gyration, radius of, 186 


Hartford governor, 198 

Haswell, 254 

Head and cost of turbine, 157 

effective, 26, 147 

gate, 131 

highest, 145 

loss of, 53 

loss of by friction, 26, 147, 

Head, lowest, 143 
of water, 19 
pressure, 23, 24, 60 
race, 68, 144 
range of, 106, 170 
velocity, 22, 60 
Heat, energy, 5 

engines, efficiency of, 5 
mechanical equivalent of, 6 
Helicoid air meter, 220 
Herbert, 241 
Hercules mill, 281 
Holyoke, 109 
Hook gauge, 34 

Horse power and height of fall, 
definition, 9, 10 
test for, 111 
units of, xvi. 
Hose pipe, 81 
Hydraulic cylinder, 209 
motor, 60 

turbine. See Tur- 
Hydraulics, study of, 15 
Hydrodynamics, 15 
Hydrostatic pressure, 62, 65, 121, 
126, 138, 151 
balancing by, 65, 102 


Iguazu, 133 
Impact of water, 76 
Impulse turbine, 60, 64, 71 

best speed, 89 

vane angle, 88 
Inclined plane, 79 
Indicator, 109 
Inertia, 96, 102, 168, 187 

moment of, 185, 191 



Injection angle, 90 

Interest on first cost, 154, 162, 

Italian installations, 73, 184, 154, 


Jet, power in, 75, 176 

shape of, 105 
Joist, 129, 138, 140 
Jonval, 67 

turbine, 68, 71, 143 
Joule, 6 


Kbw, 219, 221, 224, 232 
Kilogramme-metre, xvi., 5 
Kilowatt, 111, 118 
Kilowatt-hour, xvi., 8, 11 
Kinetic energy, 59, 75, 175 


La Cour, 327 
Lamb, Prof., 15 
Langley, 214 
Lanyard, 275, 290 
Largest turbine, 103 
Latting, 170 
Lawn sprinkler, 61 
Length, units of, xiii. 
Level, accuracy of, 37 

adjustments of, 39 
construction of, 39 
the engineer's, 37 
Levelling, 36 

errors in, 42 

height of instrument, 

note -book for, 41 
Level rod, 40, 43 
Lignum- vitse, 69 

Lime-mortar, 185 
Line of levels, 37 
Liverpool waterworks, 124 
Loaded governor, 180 
Lombard-Beplogle governor, 199 
Long distance transmission, 155 
Losses of energy. See Energy. 
Low fall. See Fall. 
Lubrication, 66, 68, 138 


Machinery, efficiency of, 11 
Maintenance, 50, 155, 162 
Manitou, 147 
Marvin, 223 
Masonry, 123, 135 
Maximum head, 145 
power, 77 

of flow of streams, 28 

of head, 36 

of wind velocity, 219 
Mechanical equivalent of heat, 6 
Mechanism, governing. See 

Meissner, 94 
Meteorology, 212 

Method of levelling. See Level- 
Metric system, 

equivalents, xiii. to xvi. 

simplicity of, 16 
Mill shaft, 52 
Mill stones, 251 
Milling, 47 
Minimum head, 143 

velocity, 78 
Mining, 106 
Mithridates, 46 

Mixed flow turbine, 58, 69, 73, 



Modern windmills, 261 
Momentum, 76, 84, 148 
Mouillard, 217 
Moving vane, 85 
Murphy, 320 

Natural sources of energy, 1 
Needle nozzle. See Nozzle. 
Newry, 135 
Niagara, 20, 132 

draft tube, 74, 99 
gates, 172 
governors, 201 
turbines, 66, 98, 100 
No load speed, 193 
Norse mill, 47 
Nozzle, 62, 103, 146 

deflection, 175, 206 
needle, 106, 171, 174 
Nut, 251 


Oakum, 98, 129, 138 

Ohm, 7 

Oil engine, 2, 55 

pressure governor, 201 

pump, 69 
Open hearth steel pipe, 146 
Ordinate, 193 
Orr, 320 
Overshot water wheel, 49 

diameter of, 49 

efficiency of, 50 
Overturning of dam, 126 

Paddle wheel, 76 
Painting, 142 
Paradox, 175 

Park Royal experiments, 296 
Parallel flow turbine, 58, 71, 143 
alternators in, 210 

Partial admission, 64, 103 
Partial gate, 53 

Pelton wheel, 71, 103, 106, 145, 
175, 209, 210 
efficiency of, 108, 

117, 147, 151 
governor for, 204 
largest, 107, 108 
vane angle, 88 
Pendulum governor. See Gover- 
Penhalonga installation, 209 
Penstock, 64, 92, 101, 150 
Peripheral speed, 102 
Permeability, 130 
Pferde-kraft, value of, xvi., 17 
Pike's Peak, 147 
Pinion, 173 
Pipe, 106, 146, 148 
incrusted, 149 

lmes, friction in, 149, 150, 176 
thickness of,. 169, 334 
Pit. See Wheel Pit. 
Pitching, 125 
Pitman, 278, 279 
Pivot, 96, 173 

Poncelet water wheel, 49, 52, 79 
diameter of, 53 
efficiency of, 53 
Portland cement. See Cement. 
Post mill, 242 

Power. See also Horse- Power, 
cost of, 152 
defined, 9 
distinction between energy 

and power, 6 
economy in utilisation of, 4 
in jet, 75 
measurement of, 136. See 

also Dynamometer, 
units of, xvi. 
Prasil, 118 



Pressure, atmospheric, xv., 45, 
board, 76 
disc, 102 
head, 23, 24, 28, 
hydrostatic, 65, 102, 121, 

126, 138, 151 
hydrostatic unbalanced, 

on inclined plane, 79 
on curved vane, 82, 85 
on retaining wall, 121, 

of wind. See Wind, 
units of, xv. 
water column, 45 
Price. See Cost. 
Prime movers, 13 
Prony brake, 109, 112, 119, 308, 

Puddle, 124 
Pulley, 103, 198 

Pumps, windmill, 268, 278, 304, 
326, 331 

Quern, 47 



Radial inward flow turbine, 58, 
outward flow turbine, 57, 
Radius, effective, 114 

of gyration, 186 
Rails, 138 
Rankine, 50 
Ratchet and pawl, 197 
Rate of expenditure of energy. 
See Power. 

Reaction, 60 

best speed, 89 

turbines, 65, 71 

vane angle, 88 
Reefing, 256 

Regulation of turbines, 63, 64, 68, 
167, 176 
shaft for, 65 
Relay, 168, 199 
Reservoir and pipe, 24 
Residual velocity. See Velocity. 
Retardation of water in pipe, 27 

169, 146, 168 
Rhine, 51 
Rickman, 231, 277 
Rio das Lazes, 106 
Riveted pipe, friction in, 150 
Robinson. See Anemometer. 
Rod-man, 40, 43 
Rollason windmill, 294 
Roller mill, 247 
Rope drive, 103 
Rossetti, 16 
Rotch, 222 
Round-beam, 250 
Rouse, 234 

Royal Agricultural Society, 296 
Rubble, 127 
Runner, 98, 101 


Safety devices for windmills, 284 

factor of, 120 
Sails, 245, 255 

area of, 310 

best number of, 315 

curvature of, 271 

furling of, 256 

metallic, 271 

oiled cloth, 270 



Sails — continued. 

weathering of, 256, 272, 285, 
Sail-shaft, 242, 244 
Sand, for concrete, 128 
Scholfield governor, 195 
Scott, 331 
Sector, 96, 173 
Setting, turbine, 129 
Shaft, counter, 280 

horizontal, 65, 70, 103, 141 
sail, 242, 244 

vertical, 65, 70, 102, 141, 143 
Sheet piling, 127 
Shock, loss by, 85, 174 
Shop test, 110 
Skin friction, 70 
Slat, 262 
Slipper, 209 
Slope of curve, 161 
Sluice, 127, 181 
Sluice-way, 141 
Smeaton, 234, 258, 306 
Soaring of birds, 216 
Soke privileges, 242 
Sole-plate, 52 
Spear, 174 

Specific gravity, 16, 216 
Specification, 140 

speed variation, 189 

Speed, allowable variation in, 189 

best speed of turbines, 88, 

106, 116 
control. See Regulation 

and governing, 
of turbines, 72, 88 

and cost, 157 
of windmills. See Wind- 
variation in, 202 
Spillway, 125, 127 
Spouting area, 176 

Stand-by charges, 165 
Stanton, 237 
Starting force, 314 
Statical friction. See Friction. 
Steam engine, 60, 164, 188, 295 
efficiency of, 11, 12 

power of, 9 
regulation of, 167 
plants, relative cost, 152 

cost of, 163 
turbines. See Turbines. 
Steel, reinforcement, 138 

vanes, 69 
Step bearing. See Bearing. 
Stick, floating, 29 
Stone dams, 125 
shaft, 251 
Storage battery, 139, 322 
Strabo, 46 
Stream lines, 214 
Stuffing rings, 102 
Subaqueous foundations, 127 
Suction, limit of, 74 

tubes. See Draft tube. 
Sun, energy radiated from, 3 
Sweeps, 245, 255 
Swiss installations, 73, 133, 190 


Tail race, 67, 74, 148 

vane, 274 

water, rise in, 36 
Tanay, 145 
Tangential wheel, 71 
Tank, 61 
Tar, 138, 264 
Telescope on level, 38 
Template, 265 



Tests on turbines, 53, 72, 109 

on wind engines, T. O. 
Perry, 305 
Testing flume, 110 
Textile mill, turbines for, 65, 103 
Theorem of Bernouilli, 28 
Thermal units. See British 

thermal unit and calorie. 
Thrust bearing, 69, 98, 102, 145 
Tides, utilisation of, 8 
Time-element, 8 
Toe of dam, 122 
Tongue and groove, 129, 138 
Tornado, 218, 237 
Torque, 177, 178, 193 
Torsion meter, 114 
Tourniquet, 61 
Tower mill, 246 

size of, 248 
Towers, windmill, 263 
Transformer, 209 
Transmission of energy, 155 
losses in, 112 
Tunnel, 99 
Turbines (hydraulic), 

classification of, 71 

cost of, 144, 157 

data for, 70 

design of, 84 

efficiency of, 5, 11, 13, 18,50, 
68, 73, 92, 94, 103, 111, 
115, 147 

Fontaine, 71 

Fourneyron, 64, 71 

Francis, 71, 96, 119, 194 

gearing for, 139, 141, 144 

general description of, 55 

Girard, 65, 71, 103, 104, 170 

governing of, 167 

impulse, 61, 71 

Jonval, 67, 68, 69, 71, 143 

largest, 103 

Turbines (hydraulic), 

losses in, 81, 92, 93, 94 
mixed flow, 58, 69, 71, 98, 

parallel or axial flow, 58, 71 
Pelton, 71, 88, 103, 106, 107, 

117, 151, 175, 204, 209 
radial inward flow, 58, 71 
radial outward flow, 58, 71 
reaction, 61, 71, 98, 170 
regulation of, 63, 64, 65, 68, 

setting of, 129 
specification for, 140 
speed of, 72, 88 
step bearings, 66, 68, 69 
tangential wheels, 71 
tests on, 72, 109 
various types of, 96 
vortex, 71, 157 
Turbines, steam, 14, 56 
Turning moment, 113, 178 
points, 43 


Undershot water wheel, 51, 78 
United States, irrigation papers, 
Weather Bureau, 

220, 224 
Wind Engine and 
Pump Co., 305 
Units, electrical, 7 

table of, xiii. to xvi. 
transformation of, 32 
Unloaded governor, 180 

Valentia, 232 
Valve, butterfly, 207 

slow closing, 146, 169 



Vane angle, 87 

Vanes, concentric, 68, 143. See 
Tail vane, 
for turbines, 55, 69, 82, 85. 
See also Guide vanes. 
Variation in density of water, 

Veering mechanism, 248, 274 

absolute, 85, 86 

effect of, 28 

head, 22, 60 

meters, 30, 119 

minimum, 68 

of falling water, 19, 45, 75 

of water wheels, 51 

of wind, 218, 230, 232 

of wind and pressure, 232 

relation to power, 9 

relative, 77, 86, 90 

residual, 78, 81, 83, 93, 94, 
106, 147 

units of angular, xvi. 

units of linear, xv. 
Vibration, damped, 194 
Victoria Falls, 122 
Volume, units of, xiv. 

water, 16 
Vortex turbine, 71, 157 
Vouvry, 145 


Wall, pressure on, 121, 125 

Wallower, 251 

Water, as a natural power, 1 

compressibility of, 16 

data pertaining to, 45 

density of, 16 

impact of, 76 

physical properties of, 16 
Water column, pressure of, 45 
Water hammer, 151, 169 

Water power, 

application of, 46 

cost of, 152 

measurement of, 15, 17 

source of, 3 
Water power plants, 

efficiency of, 13 
construction of, 120 
description of, 132. 
Water-wheels, 46 

breast, 50 

construction of, 52 

overshot, 49 

Poncelet, 49, 52, 79 

undershot, 51, 78 
Watt, 7 
Watt-hour, 8 
Weathering. See Sails. 
Weight of water, 16 
units of, xiv. 
Weir tables, 33, 34 
Weirs, measurement of flow over, 

Welded pipe, 106, 149 
Wheel-pit, 128, 133, 138, 162 
Whirling table, 223, 306 

designation according to 
velocity, 218 

mean velocity of, 232 

measurement of velocity, 217 

pressure of and velocity, 232 

pressure recording instru- 
ments, 219, 225 

capacity in grinding, 252 

cost of power by, 328 

efficiency of, 4, 11, 273, 312, 

foundations for, 265, 332 

governor, 284, 322 

modern, 261