IC-NRLF

SB 3E TOO

AERONAUTICS

UNIVERSITY OF CALIFORNIA LIBRARY

LIBRARY

OF THE

UNIVERSITY OF CALIFORNIA.

Class

ELEMENTARY AERONAUTICS,

a

Artificial and Natural Flight. A Practical Treatise

on Aeroplanes, &c. By Sir HIRAM MAXIM. With 95

Illustrations. 5s. net.

CONTENTS. Air Currents and the Flight of Birds Flying of

Kites Principally Relating to Screws Experiments with

Apparatus Hints as to the Building of Flying Machines

Shape and Efficiency of Aeroplanes Some Recent Machines

Balloons Appendices Index.

" This is a thoroughly practical book ... it is to be highly recommended to all

those studying the question." Aeronautics.

" The book is well illustrated, and contains a great deal of very useful informa-

tion." Aeronautical Journal.

A Pocket = Book of Aeronautics. By H. W. L.

MOEDEBECK, in collaboration with O. Chanute aud others.

Translated from the German by Dr W. MANSERGH

VARLEY. With 150 Illustrations. 10s. 6d. net.

CONTENTS Gases Physics of the Atmosphere Meteorological

Observations Balloon Technics Kites and Parachutes

On Ballooning Balloon Photography Photographic Sur-

veying from Balloons Military Ballooning Animal Flight

Artificial Flight Airships Flying Machines Motors

Air Screws Appendix Index.

" Will be highly welcome to all aeronauts. It may be said to be the only complete

work practically dealing with such matters. We have no hesitation in thoroughly

recommending this as an absolutely indispensable book." Knowledge.

'' It is without a doubt the best book that has appeared on the subject." Aero-

nautical Journal.

" The present volume ought certainly to be possessed by every student of Aero-

nautics, as it contains a vast amount of information of the highest value." Glasgow

Herald.

Electric Ignition for riotor Vehicles. By W.

HIBBERT, A.M.I.E.E. With 62 Illustrations. Is. 6d.

net.

" A most comprehensive little volume, and one that it will be well for motorists to

buy if they wish to really understand this most important subject." Motor Boat.

" It is not too much to say that Mr Hibbert has really succeeded in writing an

explanation of the electrical ignition of internal combustion engines." Autocar.

WHITTAKER & CO., LONDON, B.C.

ELEMENTARY AERONAUTICS

OR

THE SCIENCE AND PRACTICE OF

AERIAL MACHINES.

BY

ALBERT P, THURSTON, B,Sc. (Lend.)

LATE ENGINEER TO SIR HIRAM S. MAXIM ; LECTURER IN AERONAUTICS,

EAST LONDON COLLEGE (UNIVERSITY OF LONDON); MEMBER

OF THE AERONAUTICAL SOCIETY OF GREAT BRITAIN.

WITH 126 ILLUSTRATIONS.

WHITTAKER & CO.,

2 WHITE HART STREET, PATERNOSTER SQUARE

LONDON, E.G.,

AND 64-66 FIFTH AVENUE, NEW YORK,

1911,

PREFACE.

THE author has been persuaded to publish this work in

the hope that it may be useful in leading others to the

scientific study of aeronautics.

The aim of the author, therefore, has been to present

to the reader a simple and concise account of the action of

air upon moving planes, aerocurves, propellers, bars and

the like, and the application of these principles to practice.

The theory of the normal and inclined plane and aero-

curve is dealt with in Chapters I. and II.

An introduction to the important problem of stability

has been given in Chapters III. and IV. The theories and

results deduced in Chapters III. and IV. appear largely to

have been confirmed by various experimenters and scientists

since these conclusions were arrived at.

The theory of the propeller and helicopter, and the

calculations relating to the design of a flying machine, are

set out in Chapters V., VI. and VII.

The principal instruments and apparatus used in an

aeronautical laboratory are described in Chapter VIII., and

the rest of the book is devoted to a description of the chief

types of flying machines and engines.

The author's thanks are due to the Editors of the

Aeronautical Journal and of Aeronautics for the loan of

blocks, and to his friends, Messrs S. E. R. Starling, B.Sc.,

and T. Kimpton, for kindly reading the proofs.

Most of the illustrations have been specially prepared,

and the author desires to acknowledge his great indebted-

ness to Messrs T. Kimpton and H. K. Pettet for valuable

help in the preparation of two or three drawings.

A. P. T.

London, 1911.

217108

CONTENTS.

CHAPTER I.

NORMAL AND INCLINED PLANES . . , Pages 1 to 14

CHAPTER II.

AEROCURVES . . ... . . . Pages 15 to 31

CHAPTER III.

AUTOMATIC LONGITUDINAL STABILITY AND

MANUAL AND AUTOMATIC CONTROL . Pages 32 to 40

CHAPTER IV.

AUTOMATIC LATERAL STABILITY . . . Pages 41 to 46

CHAPTER V.

PROPELLERS . . . . ->J; . Pages 47 to 59

CHAPTER VI.

HELICOPTERS . . . : .- . '. Pages 60 to 67

CHAPTER VII.

CALCULATIONS RELATING TO THE DESIGN OF

A FLYING MACHINE . . . . Pages 68 to 75

CHAPTER VIII.

LABORATORY INSTRUMENTS AND APPARATUS Pages 76 to 84

CHAPTER IX.

TYPES OF MACHINES . . . . Pages 85 to 100

CHAPTER X.

AERONAUTICAL ENGINES . . .. . Pages 101 to End

INDEX. 123

vii

ELEMENTARY AERONAUTICS

OR, THE SCIENCE AND PRACTICE OF

AERIAL MACHINES

CHAPTER I

THE atmosphere, " the sphere of vapour " which envelops the

earth, and which is commonly called air, has become of in-

creased importance and interest to man, since the discovery

of the flying machine has made it the highway of the future.

The density of the air is at its maximum at the

earth's surface, and rapidly decreases as the altitude

increases ; thus, at about 3J miles the density is only

one-half, and at 7 miles one-third of that at sea-level.

The height to which the earth's atmosphere extends is

not known with certainty, but it may be safely stated to

be not less than 50 miles. At this height the air is ex-

tremely rarefied, being about 25,000 times more rarefied

than at sea-level.

Air is nearly 800 times lighter than water: one cubic foot

of dry air at sea-level weighing about 1'29 ozs. or 0'08 Ibs.

It is with this light and subtle fluid, with its varying

currents and eddies, that we have to deal in the study of

aeronautics.

THE NORMAL PLANE

If a plane is placed at right angles, or normal to a

current of moving air, the air will strike the plane and will

exert a force upon it. If the velocity of the air is doubled,

then twice as much air will strike the plane every second,

and, since the velocity is doubled, every particle will strike

with double the force ; thus, the total force acting on the

normal plane will be four times as great.

Now, if the speed is tripled, then three times the

amount of air will strike the plane every second, and every

particle will strike with three times the force; thus, the

total force acting on the plane will be increased to three

times three, that is nine times.

Therefore, from theoretical reasons, we find that the

resistance of air to a normal plane varies as the square of

the velocity.

2

ELEMENTARY AERONAUTICS.

In the case of a current of air striking a normal plane,

the conditions are not so simple as we have assumed. It

will be seen from Figs. 23, 24 that some of the air in the

centre of the plane strikes dead on, and that the air at th^

sides is deflected ; also that the air passing over the sides

drags away some of the air from the back and creates a

rarefaction which is generally spoken of as a suction.

It has been found, as the result of many experiments,

PLANES.

that the resistance of a normal plane varies as the square

of the velocity. Thus we ID ay write :

Resistance = K A V 2 . Where K = constant.

A = area of plane.

At very high speeds, the resistance increases at a

greater rate than the square of the velocity, until a

maximum is reached at about the velocity of sound,

viz., 1100 ft. per sec., or 750 miles per hour, when the

resistance varies as the fifth power of the velocity. At

higher speeds than the velocity of sound, the resistance

decreases.

The following values of n are given by Major Squiers.

Where n is the index of the velocity in the equation.

n

Velocity

Feet per sec.

Miles per hour

2

3

5

3

2

1-7

1-5

Less than 790

Between 790 and 970

970 and 1230

1230 and 1370

1370 and 1800

1800 and 2600

Greater than 2600

Less than 592

Between 592 and 639

639 and 836

836 and 934

934 and 1227

1227 and 1773

Greater than 1773

There have been very many and various determinations

of the constant or coefficient K.

The following table gives a few values, the velocity

being taken in miles per hour.

-rr

Renard

0035

Langley

f '0039 to

1 '00326

Dines

0029

/ '0027 small planes

Stanton

j -00318 to

1-00322

\ large planes

Eiffel

003

The value '003 has been generally accepted as the best

all-round value for K.

ELEMENTARY AERONAUTICS.

. Resistance on a normal plane in Ibs. = P 90 = '003 A.V*

Where A = area in sq. feet ;

V = velocity in miles per hour.

SPEEDS AND PEESSUEES

(NORMAL PLANE)

Miles per hour

Feet per sec.

Metres per sec.

Lbs. per sq. foot

1

1-47

447

003

2

2-93

894

012

3

4-41

1-341

027

4

5-87

1-783

048

5

7-33

2-235

075

6

8-87

2'682

108

7

10-29

3-138

147

8

11-76

3-576

192

9

13-23

4-035

243

10

14-66

4-470

300

11

16-12

4-916

363

12

17-59

5-365

432

13

19-06

5-813

507

14

20-53

6-261

588

15

22-00

6-705

675

16

2347

7-158

768

17

24-94

7-601

867

18

26-41

8-050

972

19

27-88

8-497

1-083

20

29-35

8-945

1-200

25

36-70

11-376

1-875

30

44-00

13-411

2-700

35

51-32

15-646

3-675

40

58-68

17-881

4-800

45

6600

20-116

6-075

50

73-34

22-352

7-500

55

80-67

24-588

9-075

60

88-00

26-822

10-800

65

95-29

29-043

12-675

70

102-62

31-292

14-700

75

110-00

33-451

16-875

80

117-28

35-763

19-200

85

124-61

38-007

21-675

90

132-00

40-233

24-300

95

139-27

42-448

27-075

100

146-60

44-704

30-000

110

161-2

49-174

36-3

120

176

53-649

43-2

130

191

58-115

50-7

140

205-3

62-585

58-8

150

220

67-056

67-5

PLANES.

THE INCLINED PLANE

It now remains for us to consider the variation in the

pressure on a plane as we incline it in the direction of motion.

Sir Isaac Newton, from theoretical assumptions, ob-

tained an expression in which the pressure varied as

sin 2 where a = angle of inclination between the plane and

the direction of motion. This may be written :

Pa - P90 sin 2 a (Newton).

Where Pa = normal pressure on inclined plane at angle .

iZ

<f

*

\

>o is" to ** 3o as- * *r fo VF Co a* 70 7* go as so

FIG. 2. Curves of Eiffel Tower and Duchemin formulae

for inclined planes.

Lord Rayleigh showed that the pressure varied more

nearly as sin a.

Pa = P90 sin a (Rayleigh).

Colonel Duchemin deduced a formula which appears to

agree still more closely with actual practice :

Pa = P90 x 1 -, Sm " (Duchemin).

l+sm 2 a

According to the recent Eiffel Tower experiments,

Up to 30

and Pa = P90 Above 30

The plotted curves of the Eiffel Tower and Duchemin

formulae are shown in Fig. 2. In the case of the Duchemin

formula, the vertical component P cos a, i.e., " the lift,"

ELEMENTARY AERONAUTICS.

and the horizontal component Pa sin a, i.e., " the drift," are

also shown plotted.

Fig. 3 shows similar curves obtained by various ex-

perimenters. Figs. 31 and 32 also show further curves

FIG. 3. Curves for inclined planes. (Dines and Rateau.)

(Rateau) for flat and ship- shaped sections, where curve 1

is the lift, curve 2 is the drift, and curve 3 is the total

normal pressure. The pressure F in kilograms for any

angle is obtained from the following formula : F = <pSv 2 .

Where <p is the coefficient read from the diagram and S

is the area in square metres.

TABLE OF EQUIVALENT INCLINATIONS

Rise

Angle

in Degrees

Sin of Angle

1 in 30

1-91

0333

1 in 25

2-29

04

1 in 20

2-87

05

1 in 18

3-18

0555

1 in 16

3-58

0625

1 in 14

4-09

'0714

1 in 12

4-78

0833

1 in 10

5-73

1

1 in 9

6-38

1111

1 in 8

7-18

125

1 in 7

8-22

143

1 in 6

9-6

1667

1 in 5

11-53

'2

1 in 4

14-48

25

1 in 3

19-45

3333

PLANES.

POWER REQUIRED TO DRIVE AN INCLINED PLANE

If we wish to obtain a simple equation, showing the

energy required to propel an aeroplane, we can proceed in

the following manner :

90 = -003AV 2

Where A is the area of the plane in sq. feet, and V the

velocity in miles per hour :

. p X -003AV2

' ' Pa= "SO"

, ' . the drift, or the resistance = P sin

a X -003 AY 2 sin a

30

In addition to the resistance of the plane, there will be

a head resistance due to the body, struts, etc. If the

equivalent area of these, in square feet, equals S, then the

head resistance will = '003SV 2 .

.'. the total resistance or drift D will =

(003 S + sin a x -0001 A) V 2

.*. the horse-power will =

88 (-003 S + a sin a x "0001 A) V 3

33000

Thus, the power varies as the cube of the speed, if the

angle is kept constant.

As the speed increases it will be necessary, if the lift is

to be kept constant, to decrease the inclination of the plane,

and this will effect a corresponding reduction in the drift.

ASPECT

If an inclined plane is driven forwards, it will impress a

downward velocity on a certain volume of air.

The amount of air so depressed will depend upon

the size and " aspect " of the plane, and also upon its

inclination.

The aspect of a plane is the ratio rrrr. -^ ^he

width

8

ELEMENTARY AERONAUTICS

is at right angles to the direction of motion, the plane is in

" width aspect." If the length is at right angles to the

direction of motion, the plane is in " length aspect." The

amount of the lift of the aeroplane will depend upon the

amount of the downward momentum given to the

air

10" o

3*XI*.

FIG. 4. Curves for inclined planes in length

and width aspect. (Stanton.)

= MV, where M is the mass of air engaged and V is the

velocity given it.

Now, the energy given to the air, that is kinetic energy

or energy lost, = JMV 2 .

Suppose we have a given weight to support ; then, the

downward momentum to be given to the air in every unit

of time is known, and equals MV. We can make M as

small as we like in this expression, providing we make V

sufficiently large.

If we halve the mass acted upon, then

PLANES.

Plan

Consequently

Energy lost in second case _ JM x (2V) 2 2

Energy lost in first case MV 2 ~ i

i.e., by halving the mass of air acted upon, the power re-

quired to support the plane is doubled.

Hence, it is clearly advantageous to engage as much

air as possible.

This can be done

(1) By increasing the spread of the aeroplane, or by

mounting one plane upon another, thus in-

creasing the

amount of en-

tering edge.

(2) By increasing

the speed.

In Fig. 4, the curve

A shows the lift of an

inclined plane 3" x 1" in

" width aspect," and

the curve B, the same

plane in "length aspect."

These curves were taken

by Dr Stanton.* It will

be seen that the lift of

the plane between the

angle of and 10 in

" length aspect," is much

greater than in "width

aspect."

The superior lift of

the plane in " length

aspect" is almost wholly due to the fact that, in this

position ; it is able to engage more air than when in " width

aspect " ; also, when the plane is in " length aspect," there

is less escape of air at the sides, and this also adds to its

superiority.

To test this, Mr Dines, F.R.S., placed a plane, which was

provided with a number of pins carrying short ribbons, in

a current of air, and took a snapshot of it.

Fig. 5 shows the direction in which the ribbons set

themselves. The inclination of the side ribbons proves

that the air escaped at the sides of the plane.

ie<*

*" /

1

\

s

/ /

I

\

\

/ /

I

\

\

/ /

j

\

\

/ /

1

\

\

Side..

FIG. 5. The direction and flow of air

about a plane.

* Proceedings of the Institution of Civil Engineers, vol. 156.

10 ELEMENTARY AERONAUTICS.

Fig. 6 is a stream-line photograph of the underside of

an inclined rectangular plane. The column of air is marked

by jets of smoke. It will be seen that the outer jets curve

round and flow over the sides, the greatest deflection taking

place at the front edge.

The loss by side leakage may be reduced by decreasing

the proportional length of the sides, i.e., by increasing the

"length aspect."

FIG. 6. Stream-line flow about an inclined plane.

LANGLEY'S LAW

Suppose we have a plane which is to lift a given weight;

(1st) at velocity v, and (2nd) at velocity 2v.

In the first case If M=mass of air engaged, the weight

supported will be oc to M.V, and work lost will be oo to

M*; 2 .

In the second case Since the velocity is doubled, twice

as much air will be engaged. Hence, it will only be

necessary to set the plane at such an angle that the air

will be forced down with velocity \v.

The weight supported will be o> to 2M- = Mv, and

work lost will be oo to

2M(|

PLANES.

11

Work lost in first case 2

Work lost in second case 1

i.e., by doubling the speed, we have halved the work done.

Consequently, " the power to drive an aeroplane varies in-

versely as the speed." This is Langley's law. It does not

hold in practice, because an aeroplane always has a certain

amount of " head resistance," which varies directly as the

square of the speed. Langley's law applies to the " sup-

porting momentum," and not to the head resistance.

Although the power required to drive an aeroplane is not

so favourable as Langley's law would appear to show, it

has been clearly demonstrated that it does not increase at

the same rate as for other means of locomotion, which

appear to vary directly as the cube of the velocity.

\

FIG. 7. Pressures on the back

and front of a narrow plane.

(Stanton.)

FIG. 8. Pressures on the back

and front of an inclined plane

at 60. (Stanton. )

THE DISTRIBUTION OF PRESSURE ON NORMAL AND

INCLINED PLANES

The variation of the distribution of the pressure with

change of inclination, has been well shown by the following

diagrams by Dr Stanton.

In Fig. 7, with the plane normal to the wind, the right-

hand curve shows the compression and the left-hand curve

the suction, on the front and back of the plane respectively.

The ratio of the maximum pressure or the windward side

to the suction on the leeward side of a circular plate was

found to be 2'1 to 1, whereas the ratio for a rectangular

plate (aspect ratio 25 to 1) was T5 to 1.

Fig. 8 shows the same plane inclined at 60 to the

current. The greatest compression and suction are now

toward the leading edge.

12

ELEMENTARY AERONAUTICS.

As the inclination is still further decreased to 45

(Fig. 9), the difference between the pressures at the

leading and trailing edge is still greater.

FIG. 9. Pressures on the back and

front of an inclined plane at 45.

(Stanton. )

FIG. 10. Pressures on the back

and front of an inclined plane at

30. (Stanton.)

When the plane is set at 30, as in Fig. 10, the air

receives a jerk when it meets the front edge of the plane.

This produces a great suction at first, but afterwards the

*0*

50'

50

-so

FIG. 11. The centre of pressure for various

inclinations of a flat plane. (Rateau.)

air springs back and causes a compression on the back of the

plane. It then rebounds again, causing a second suction.

It will further be noticed from these diagrams, that

PLANES. 13

the suction from front to back varies at a greater

rate with decrease of inclination, than does the com-

pression.

The variation of the distribution of the compression

and suction has the effect of causing the centre of pressure,

i.e., the point of action of the resultant force, to travel

towards the front edge as the inclination is decreased.

This was first noted by Sir George Cayley in 1809.

In Fig. 11 is shown Prof. Rateau's diagram for a flat

plane. The inclination of the plane to the wind is marked

FIG. 12. The centre of pressure for various inclinations of pressure

on circular diagram (Rateau, Wessel, Langley, Kummer).

off along the vertical, and the distance of the centre of

pressure from the leading edge, in terms of the width, is

marked off along the horizontal.

Between angles of 30 and 40 the curve is dis-

continuous.

Prof. Rateau's results agree very closely with a formula

obtained by Joessel in 1870 for water, and verified later by

Avanzini for air.

Joessel and Avanzini A = '3 (1 - sin a) L.

Where A = distance from the centre of area to the

centre of pressure, L = width, a = inclination in degrees.

Fig. 12 shows plotted on a circular diagram the results-

of various investigators on the centre of pressure.

14

ELEMENTARY AERONAUTICS.

The travel of the centre of pressure also varies with

the plan-shape of a plane. Thus, in Fig. 13 we see the

locus of the centre of pressure for a rectangular, semi-

circular and circular plane. Curves 1 and 2 show the

travel of the centre of pressure for the rectangular plane

in length and width aspect respectively. The aspect ratio

Distance, -prom Fronl" -edge. +*

FiG. 13. The centre of pressure for various inclinations of a

rectangular, semicircular and circular plane.

of the plane was 4'5 is to 1, and the distance from the

front edge is set out along the base line in terms of the

length of the rectangle. Curves 3 and 4 relate to the

semicircular plane with the diameter and the curve to

the wind respectively. The distance of the centre of

pressure from the front edge is set out along the base line

in terms of the diameter, which corresponds with the

length of the rectangular plane. Curve 5 is the centre of

pressure curve for the circular plane.

CHAPTER II

AEKOCURVES

THE wings of all birds are curved. Therefore it would

appear that this shape must possess some great virtue

not possessed by a plane surface.

It was left for Mr Phillips to make this discovery, and

to patent his invention in 1884. Every flying machine

now uses this invention.

If a diagram of the pressure on the back and front of

an aerocurve is taken, corresponding to Fig. 10, it will be

found that there is a particular angle at which the pressures

on the front edge are very small.

There is no shock entry upon the air, as is shown in

Fig. 10. The superiority of the aerocurve is due to the

fact that it is able to meet the air with a minimum of

shock, and to curve it round afterwards with a continuously

increasing velocity, until it is discharged at the trailing

edge, thus obviating a " surface of discontinuity." Further,

contrary to general belief, Sir Hiram Maxim has found

that, for minimum resistance, an aerocurve should be as

thin as possible, consistent with strength.

Otto Lilienthal, a Danish engineer, was one of the first

to appreciate the virtues of aerocurves, and the following

explanation of their superiority over a plane surface is due

to him.

Suppose we have a flat and a curved aeroplane

gliding down in the direction of the arrow, as shown in

Figs. 14 and 15. In the case of the flat plane, the result-

ant R may be resolved into components BA and BC,

parallel and normal to the plane. The parallel, or " tan-

gential " BA, always opposes motion. Lilienthal found

that with the curved plane (Fig. 15), the tangential com-

ponent AB of the resultant R 1 acted in the direction of

motion for angles between 3 and 30. The maximum

effect took place at 15, and then the component AB

equalled yoth the normal component or lift BC.

15

16

ELEMENTARY AERONAUTICS.

The Wright Brothers and other experimenters, have

verified the existence of the " tangential," although they

obtained different values for the constants.

The angle (Fig. 16) is known as the angle of incidence,

1A

FIGS. 14 and 15. Lilienthars explanation of the superior lifting

effect of a curved plane.

of attack, or of inclination ; the angle B as the angle of

entry, and the angle 7 as the trailing angle. A satisfactory

formula connecting lift with a, B and 7, does not appear to

have been obtained yet. It may be taken that a well-

made aeroplane, at an angle of 7, or 1 in 8, will lift 2'75 Ibs.

per sq. ft. at a velocity of 40 miles per hour.