SB 3E TOO
UNIVERSITY OF CALIFORNIA LIBRARY
UNIVERSITY OF CALIFORNIA.
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.
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tion." Aeronautical Journal.
A Pocket = Book of Aeronautics. By H. W. L.
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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
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WHITTAKER & CO., LONDON, B.C.
THE SCIENCE AND PRACTICE OF
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
AND 64-66 FIFTH AVENUE, NEW YORK,
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.
NORMAL AND INCLINED PLANES . . , Pages 1 to 14
AEROCURVES . . ... . . . Pages 15 to 31
AUTOMATIC LONGITUDINAL STABILITY AND
MANUAL AND AUTOMATIC CONTROL . Pages 32 to 40
AUTOMATIC LATERAL STABILITY . . . Pages 41 to 46
PROPELLERS . . . . ->J; . Pages 47 to 59
HELICOPTERS . . . : .- . '. Pages 60 to 67
CALCULATIONS RELATING TO THE DESIGN OF
A FLYING MACHINE . . . . Pages 68 to 75
LABORATORY INSTRUMENTS AND APPARATUS Pages 76 to 84
TYPES OF MACHINES . . . . Pages 85 to 100
AERONAUTICAL ENGINES . . .. . Pages 101 to End
OR, THE SCIENCE AND PRACTICE OF
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
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
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,
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
The following values of n are given by Major Squiers.
Where n is the index of the velocity in the equation.
Feet per sec.
Miles per hour
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.
f '0039 to
/ '0027 small planes
j -00318 to
\ large planes
The value '003 has been generally accepted as the best
all-round value for K.
. 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
Miles per hour
Feet per sec.
Metres per sec.
Lbs. per sq. foot
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 .
>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,"
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
Sin of Angle
1 in 30
1 in 25
1 in 20
1 in 18
1 in 16
1 in 14
1 in 12
1 in 10
1 in 9
1 in 8
1 in 7
1 in 6
1 in 5
1 in 4
1 in 3
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
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
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.
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
The aspect of a plane is the ratio rrrr. -^ ^he
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
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
If we halve the mass acted upon, then
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-
amount of en-
(2) By increasing
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
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
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.
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
FIG. 6. Stream-line flow about an inclined plane.
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
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.
FIG. 8. Pressures on the back
and front of an inclined plane
at 60. (Stanton. )
THE DISTRIBUTION OF PRESSURE ON NORMAL AND
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.
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.
FIG. 10. Pressures on the back
and front of an inclined plane at
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
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
the suction from front to back varies at a greater
rate with decrease of inclination, than does the com-
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-
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.
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.
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
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.
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,
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.