Transcriber’s Notes:
Text printed in italics in the original work has been transcribed
between _underscores_, bold text has been transcribed between =equals
signs=. Small Capitals in the original work have been transformed to
ALL CAPITALS.
More Transcriber’s Notes may be found at the end of this text.
ARTIFICIAL AND NATURAL FLIGHT.
=A Pocket-Book of Aeronautics.=--By H. W. L. MOEDEBECK. 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 Surveying 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.”--_Aeronautical Journal._
“The present volume ought certainly to be possessed by every student
of Aeronautics, as it contains a vast amount of information of the
highest value.”--_Glasgow Herald._
WHITTAKER & CO., LONDON, E.C.
ARTIFICIAL AND
NATURAL FLIGHT.
BY
SIR HIRAM S. MAXIM.
WITH 95 ILLUSTRATIONS.
WHITTAKER & CO.,
2 WHITE HART STREET, PATERNOSTER SQUARE,
LONDON, E.C.,
AND 64-66 FIFTH AVENUE, NEW YORK.
1908.
PREFACE.
It was in 1856 that I first had my attention called to the subject of
flying machines. My father, who was a profound thinker and a clever
mechanician, seems to have given the subject a great deal of thought,
and to have matured a plan identical with what has been proposed by
hundreds since that time. I was then sixteen years of age, and a fairly
good mechanician, and any new thing in the mechanical line interested me
immensely.
My father’s proposed machine, of which he made a sketch, was of the
Hélicoptère type, having two screws both on the same axis--the lower one
to be right hand and mounted on a tubular shaft, and the top one to be
left hand and mounted on a solid shaft running through the lower tubular
shaft. These screws were to be rotated in reverse directions by means of
a small pinion engaging a bevel gear attached to each of the shafts. His
plan contemplated large screws with very fine pitch, and he proposed to
obtain horizontal motion by inclining the axis forward. He admitted that
there was no motor in existence light enough, but thought one might be
invented, and that an engine might be worked by a series of explosions
in the cylinder, that is, what is known to-day as internal combustion;
but he was not clear how such an engine could be produced. He, however,
said that a flying machine would be so valuable in time of war, that it
mattered little how expensive the explosive might be, even if fulminate
of mercury had to be used. It is interesting to note in this connection
that the great Peter Cooper of New York thought out an identical machine
about the same time, and actually commenced experiments. It seems that
this gentleman regarded fulminate of mercury as altogether too feeble
and inert, because we find that he selected chloride of nitrogen as his
explosive agent. However, his work was soon brought to an end by the
loss of the sight of one eye, after which time he had no further
dealings with this lively explosive.
The many early conversations that I had with my father on the subject
kept the matter constantly before me, and I think it was in 1872, after
having seen Roper’s hot-air engine and Brayton’s petroleum engine, that
I took the matter up, and commenced to make drawings of a machine of the
Hélicoptère type, but instead of having one screw above the other, I saw
at once that it would be much better if the two screws were widely
separated, so that each would engage new air, the inertia of which had
not been disturbed. The designing of the machine itself was a simple
matter, but the engine gave me trouble. No matter from what point I
examined the subject, the engine was always too heavy. It appears that
the Brayton engine was shown at the Centennial Exhibition at
Philadelphia in 1876, and that Otto visited this exhibition. Up to that
time, he had been making a species of rocket engine--that is, an engine
in which an explosive mixture shot the piston upward and then sucked it
back, a rack and pinion transmitting movement to the rotating shaft by
means of a pawl and ratchet. He appears to have been much interested in
the Brayton engine, as it was evidently very much in advance of his own.
It actually developed, even at that time, one horse-power per hour for
every pound of crude petroleum consumed, but it was very heavy indeed,
very difficult to start, and not always reliable. The shaft that worked
the valve gear was parallel to the cylinder, and placed in the exact
position occupied by a similar shaft in the present Otto engine, but
instead of revolving only half as fast as the crank shaft, it made the
same number of revolutions. On Otto’s return to Germany, he evidently
profited by what he had seen, and made a new engine, which in reality
was a cross between his own and the Brayton; the result was a very
important invention, which has been of incalculable value to mankind. It
is this engine which is now propelling our motor cars, and it is the
only engine suitable for employment on a flying machine; but even this
motor was not in a sufficiently high state of development as far as
lightness was concerned, to be of any use to me. The drawings which I
made in 1873, although of little or no value, kept my thoughts on
artificial flight, and while I was away from home attending to business,
especially when in foreign countries, I often amused myself by making
mathematical calculations. Quite true, the formula which I used at the
time--Haswell’s--was not correct; still, it was near enough to the mark
to be of considerable value. Moreover, the error in this formula
affected the Hélicoptère quite as much as the aeroplane system, and as I
was working with the view of ascertaining the relative merits of the two
systems, the error, although considerable, did not have any influence at
all in the decision which I arrived at--namely, that the aeroplane
system was the best. The machine that I thought out at that time
contemplated superposed aeroplanes of very great length from port to
starboard. The size in the other direction was more for the purpose of
preventing a rapid fall than for a lifting effect. I saw that it would
be necessary to have horizontal fore and aft rudders placed a long
distance apart, so as to prevent rapid pitching, and it appeared to me
that the further these rudders were apart, the easier it would be to
manœuvre the machine. As I never had any doubts regarding the efficiency
of screw propellers working in the air, I decided to use two of these of
a large size rotating in opposite directions. Of course, all this
speculation was theory only, but I verified it later on by actual
experiments before I built my machine, and it is very gratifying to me
to know that all the successful flying machines of to-day are built on
the lines which I had thought out at that time, and found to be the
best. All have superposed aeroplanes of great length from port to
starboard, all have fore and aft horizontal rudders, and all are driven
with screw propellers. The change from my model is only a change in the
framework made possible by dispensing with the boiler, water tank, and
steam engine. In this little work, I have dealt at considerable length
with air currents, the flight of birds, and the behaviour of kites,
perhaps at the expense of some repetitions; as the resemblance between
kite flying and the soaring of birds is similar in many respects,
repetitions are necessary. To those who go to sea in ships, it is
necessary to know something of the currents they are liable to
encounter; if it be a sailing ship, certainly a knowledge of the air
currents is of the greatest importance, and so it is with flying
machines. If flights of any considerable distance are to be made, the
machine is liable at any time to encounter very erratic air currents,
and it has been my aim in discussing these three subjects--air currents,
birds, and kites--to bring them before the would-be navigators of the
air, in order that they may anticipate the difficulties they have to
deal with and be ready to combat them. Then, again, there has been
almost an infinite amount of discussion regarding the soaring of birds
and the flying of kites. Many years ago, after reading numerous works on
the subject of flight, I became a close observer myself, and always
sought in my travels to learn as much as possible. I have attempted to
discuss this subject in simple and easily understood language, and to
present sufficient evidence to prevent the necessity of any further
disputes. I do not regard what I have said as a theory, but simply as a
plain statement of absolute and easily demonstrated facts. During the
last few years, a considerable number of text-books and scientific
treatises have been written on the subject of artificial flight, the
most elaborate and by far the most reliable of these being the
“Pocket-Book of Aeronautics,” by Herman W. L. Moedebeck, Major und
Battaillonskommandeur im Badischen Fussartillerie Regiment No. 14; in
collaboration with O. Chanute and others. Translated by W. Mansergh
Varley, B.A., D.Sc., Ph.D., and published by Whittaker & Co. This work
does not, however, confine itself altogether to flying machines, but has
a great deal of information which is of little or no value to the
builder of true flying machines; moreover, it is not simple enough to be
readily understood by the majority of experimenters. In some other works
which I have recently examined, I find a confusing mass of the most
intricate mathematical calculations, abounding in an almost infinite
number of characters, and extending over hundreds of pages, but on a
close examination of some of the deductions arrived at, I find that a
good many of the mathematical equations are based on a mistaken
hypothesis, and the results arrived at are very wide of the truth. I
have shown several diagrams which will explain what I mean. What is
required by experimenters in flying machines--and there will soon be a
great number of them--is a treatise which they can understand, and which
requires no more delicate instruments than a carpenter’s 2-foot rule and
a grocer’s scales. The calculations relating to the lift, drift, and the
skin friction of an aeroplane are extremely simple, and it is quite
possible to so place this matter that it can be understood by anyone who
has the least smattering of mathematical knowledge. Mathematics of the
higher order expressed in elaborate formulæ do very well in
communications between college professors--that is, if they happen to be
agreed. When, however, these calculations are so intricate as to require
a clever mathematician a whole day to study out the meaning of a single
page, and if when the riddle is solved, we find that these calculations
are based on a fallacy, and the results in conflict with facts, it
becomes quite evident to the actual experimenter that they are of little
value. For many years, Newton’s law was implicitly relied upon. Chanute,
after going over my experimental work, wrote that Newton’s law was out
as 20 is to 1--that is, that an aeroplane would lift twenty times as
much in practice as could be shown by the use of Newton’s formula. Some
recent experiments, which I have made myself, at extremely high
velocities and at a very low angle, seem to demonstrate that the error
is nearer 100 to 1 than 20 to 1. It will, therefore, be seen how little
this subject was understood until quite recently, and even now the
mathematicians who write books and use such an immense amount of
formulæ, do not agree by any means, as will be witnessed by the mass of
conflicting controversy which has been appearing in _Engineering_ during
the last four months. When an aeroplane placed at a working angle of,
say, 1 in 10 is driven through the air at a high velocity, it, of
course, pushes the air beneath it downwards at one-tenth part of its
forward velocity--that is, in moving 10 feet, it pushes the air down 1
foot. A good many mathematicians rely altogether upon the acceleration
of the mass of air beneath the aeroplane which is accelerated by its
march through the air, the value of this acceleration being in
proportion to the square of the velocity which is imparted to it.
Suppose now that the aeroplane is thin and well-made, that both top and
bottom sides are equally smooth and perfect; not only does the air
engaged by the under side shoot downwards, but the air also follows the
exact contour of the top side, and is also shot downwards with the same
mean velocity as that passing on the underneath side, so if we are going
to consider the lifting effect of the aeroplane, we must not leave out
of the equation, the air above the aeroplane, which has quite as much
mass and the same acceleration imparted to it, as the air below the
aeroplane. Even calculations made on this basis will not bring the
lifting effect of an aeroplane up to what it actually does lift in
practice; in fact, the few mathematicians who have made experiments
themselves have referred to the actual lifting effect of aeroplanes
placed at a low angle and travelling at a high velocity as being
unaccountable. Only a few mathematicians appear to have a proper grasp
of the subject. However, three could be pointed out who understand the
subject thoroughly, but these are all mathematicians of the very highest
order--Lord Kelvin, Lord Rayleigh, and Professor Langley. In placing
before the public, the results of my experiments and the conclusions
arrived at, it is necessary to show the apparatus which I employed,
otherwise it might be inferred that my conclusions were guesswork, or
mathematical calculations which might or might not be founded on a
mistaken hypothesis; this is my excuse for showing my boiler and engine,
my rotating arm, and my large machine. I do not anticipate that anyone
will ever use a steam engine again, because any form of a boiler is
heavy; moreover, the amount of fuel required is much greater than with
an internal combustion engine, and certainly seven times as much water
has to be dealt with. However, the description which I am giving of my
apparatus will demonstrate that I had the instruments for doing the
experimental work that I have described in this work. In the Appendix
will be found a description of my machine, and some of my apparatus. The
conclusions which I arrived at were written down at the time with a
considerable degree of care, and are of interest because they show that,
at that date, I had produced a machine that lifted considerably more
than its own weight and had all of the essential elements, as far as
superposed aeroplanes, fore and aft horizontal rudders, and screw
propellers were concerned, common to all of the successful machines
which have since been made. The fact that practically no essential
departure has been made from my original lines, indicates to my mind
that I had reasoned out the best type of a machine even before I
commenced a stroke of the work.
I have to thank Mr. Albert T. Thurston for reading the proofs of this
work.
H. S. M.
CONTENTS.
CHAPTER I.
PAGE
Introductory, 1
CHAPTER II.
Air Currents and the Flight of Birds, 11
CHAPTER III.
Flying of Kites, 25
CHAPTER IV.
Principally Relating to Screws, 31
CHAPTER V.
Experiments with Apparatus Attached to a Rotating Arm--Crystal
Palace Experiments, 62
CHAPTER VI.
Hints as to the Building of Flying Machines--Steering by Means
of a Gyroscope, 77
CHAPTER VII.
The Shape and Efficiency of Aeroplanes--The Action of Aeroplanes
and the Power Required Expressed in the Simplest Terms--Some
Recent Machines, 99
CHAPTER VIII.
Balloons, 120
APPENDIX I., 125
APPENDIX II.--
Recapitulation of Early Experiments--Efficiency of Screw
Propellers, Steering, Stability, &c.--The Comparative Value of
Different Motors--Engines--Experiments with Small Machines
Attached to a Rotating Arm, 130
INDEX, 163
INDEX OF ILLUSTRATIONS.
FIG. PAGE
1. Diagram showing the reduction of the projected horizontal
area, 2
2. Professor Langley’s experiments, 5
3. Eagles balancing themselves on an ascending current of air, 14
4. Air currents observed in Mid-Atlantic, 16
5. Glassy streaks in the Bay of Antibes, 17
6. Air currents observed in the Mediterranean, 18
7. The circulation of air produced by a difference in
temperature, 27
8. Kite flying, 29
9. Group of screws and other objects used in my experiments, 32
10. Some of the principal screws experimented with, 32
11. The three best screws, 33
12. Apparatus for testing the thrust of screws, 34
13. Apparatus for testing the direction of air currents, 35
14. The ends of screw blades, 36
15. The manner of building up the large screws, 39
16. A fabric-covered screw, 40
17. The hub and one of the blades of the screw on the Farman
machine, 42
18. Section of screw blades having radial edges, 43
19. Form of the blade of a screw made of sheet metal, 44
20. New form of hub, 45
21. Small apparatus for testing fabrics for aeroplanes, 50
22. Apparatus for testing the lifting effect of aeroplanes and
condensers, 51
23. Apparatus for testing aeroplanes, condensers, &c., 52
24. Cross-sections of bars of wood, 53
25. Sections of bars of wood, 54
26. A flat aeroplane placed at different angles, 55
27. Group of aeroplanes used in experimental research, 56
28. An 8-inch aeroplane which did very well, 57
29. Resistance due to placing objects in close proximity to each
other, 58
30. Cross-section of condenser tube made in the form of Philipps’
sustainers, 60
31. The grouping of condenser tubes made in the form of Philipps’
sustainers, 61
32. Machine with a rotating arm, 63
33. A screw and fabric-covered aeroplane in position for testing, 64
34. The rotating arm of the machine with a screw and aeroplane
attached, 65
35. The little steam engine used by me in my rotating arm
experiments, 66
36. The machine attached to the end of the rotating shaft, 68
37. Marking off the dynamometer, 69
37_a_. Right- and left-hand four-blade screws, 70
38. Apparatus for indicating the force and velocity of the wind
direct, 71
39. Apparatus for testing the lifting effect of aeroplanes, 73
40. Front elevation of proposed aeroplane machine, 77
41. Side elevation of proposed aeroplane machine, 78
42. Plan of proposed aeroplane machine, 79
43. Plan of a hélicoptère machine, 82
44. Showing the position of the blades of a hélicoptère as they
pass around a circle, 83
45. System of splicing and building up wooden members, 86
46. Cross-section of struts, 86
47. Truss suitable for use with flying machines, 87
48. The paradox aeroplane, 88
49. The Antoinette motor, 89
50. Section showing the Antoinette motor as used in the Farman and
De la Grange machines, 90
51. Pneumatic buffer, 91
52. Gyroscope, 94
53. Adjusting the lifting effect, 95
54. Showing that the machine could be tilted in either direction
by changing the position of the rudder, 96
55. Adjusting the lifting effect, 97
56. Adjustment of the rudders, 98
57. Diagram showing the evolution of a wide aeroplane, 102
58. In a recently published mathematical treatise on aerodynamics
an illustration is shown, representing the path that the air
takes on encountering a rapidly moving curved aeroplane, 104
59. An illustration from another scientific publication also on
the dynamics of flight, 104
60. Another illustration from the same work, 105
61. The shape and the practical angle of an aeroplane, 105
62. An aeroplane of great thickness, 106
63. Section of a screw blade having a rib on the back, 106
64. Shows a flat aeroplane placed at an angle of 45°, 107
65. The aeroplane here shown is a mathematical paradox, 107
66. This shows fig. 65 with a section removed, 107
67. Diagram showing real path of a bird, 108
68. The De la Grange machine on the ground, 111
69. The De la Grange machine in full flight, 111
70. Farman’s machine in flight, 112
71. Bleriot’s machine, 113
72. Santos Dumont’s flying machine, 113
72_a_. Angles and degrees compared, 115
72_b_. Diagram showing direction of the air with a thick curved
aeroplane, 118
72_c_. Aeroplanes experimented with by Mr. Horatio Philipps, 118
73. The enormous balloon “Ville de Paris,” 123
74. Photograph of a model of my machine, 130
75. The fabric-covered aeroplane experimented with, 131
76. The forward rudder of my large machine showing the fabric
attached to the lower side, 131
77. View of the track used in my experiments, 134
78. The machine on the track tied up to the dynamometer, 135
79. Two dynagraphs, 136
80. The outrigger wheel that gave out and caused an accident with
the machine, 137
81. Shows the broken planks and the wreck that they caused, 138
82. The condition of the machine after the accident, 139
83. This shows the screws damaged by the broken planks, 140
84. This shows a form of outrigger wheels which were ultimately
used, 141
85. One pair of my compound engines, 142
86. Diagram showing the path that the air has to take in passing
between superposed aeroplanes in close proximity to each
other, 144
87. Position of narrow aeroplanes arranged so that the air has
free passage between them, 145
88. The very narrow aeroplanes or sustainers employed by Mr.
Philipps, 146
89. One of the large screws being hoisted into position, 149
90. Steam boiler employed in my experiments, 157
91. The burner employed in my steam experiments, 157
92. Count Zeppelin’s aluminium-covered airship coming out of its
shed on Lake Constance, 161
93. Count Zeppelin’s airship in full flight, 161
94. The new British war balloon “Dirigible” No. 2, 162
95. The Wright aeroplane in full flight, 162
ARTIFICIAL AND NATURAL FLIGHT.
CHAPTER I.
INTRODUCTORY.
It has been my aim in preparing this little work for publication to give
a description of my own experimental work, and explain the machinery and
methods that have enabled me to arrive at certain conclusions regarding
the problem of flight. The results of my experiments did not agree with
the accepted mathematical formulæ of that time. I do not wish this
little work to be considered as a mathematical text-book; I leave that
part of the problem to others, confining myself altogether to data
obtained by my own actual experiments and observations. During the last
few years, a considerable number of text-books have been published.
These have for the most part been prepared by professional
mathematicians, who have led themselves to believe that all problems
connected with mundane life are susceptible of solution by the use of
mathematical formulæ, providing, of course, that the number of
characters employed are numerous enough. When the Arabic alphabet used
in the English language is not sufficient, they exhaust the Greek also,
and it even appears that both of these have to be supplemented sometimes
by the use of Chinese characters. As this latter supply is unlimited, it
is evidently a move in the right direction. Quite true, many of the
factors in the problems with which they have to deal are completely
unknown and unknowable; still they do not hesitate to work out a
complete solution without the aid of any experimental data at all. If
the result of their calculations should not agree with facts, “bad luck
to the facts.” Up to twenty years ago, Newton’s erroneous law as relates
to atmospheric resistance was implicitly relied upon, and it was not
the mathematician who detected its error, in fact, we have plenty of
mathematicians to-day who can prove by formulæ that Newton’s law is
absolutely correct and unassailable. It was an experimenter that
detected the fault in Newton’s law. In one of the little mathematical
treatises that I have before me, I find drawings of aeroplanes set at a
high and impracticable angle with dotted lines showing the manner in
which the writer thinks the air is deflected on coming in contact with
them. The dotted lines show that the air which strikes the lower or
front side of the aeroplane, instead of following the surface and being
discharged at the lower or trailing edge, takes a totally different and
opposite path, moving forward and over the top or forward edge,
producing a large eddy of confused currents at the rear and top side of
the aeroplane. It is very evident that the air never takes the erratic
path shown in these drawings; moreover, the angle of the aeroplane is
much greater than one would ever think of employing on an actual flying
machine. Fully two pages of closely written mathematical formulæ follow,
all based on this mistaken hypothesis. It is only too evident that
mathematics of this kind can be of little use to the serious
experimenter. The mathematical equation relating to the lift and drift
of a well-made aeroplane is extremely simple; at any practicable angle
from 1 in 20 to 1 in 5, the lifting effect will be just as much greater
than the drift, as the width of the plane is greater than the elevation
of the front edge above the horizontal--that is, if we set an aeroplane
at an angle of 1 in 10, and employ 1 lb. pressure for pushing this
aeroplane forward, the aeroplane will lift 10 lbs. If we change the
angle to 1 in 16, the lift will be 16 times as great as the drift. It is
quite true that as the front edge of the aeroplane is raised, its
projected horizontal area is reduced--that is, if we consider the width
of the aeroplane as a radius, the elevation of the front edge will
reduce its projected horizontal area just in the proportion that the
versed sine is increased. For instance, suppose the sine of the angle to
be one-sixth of the radius, giving, of course, to the aeroplane an
inclination of 1 in 6, which is the sharpest practical angle, this only
reduces the projected area about 2 per cent., while the lower and more
practical angles are reduced considerably less than 1 per cent. It will,
therefore, be seen that this factor is so small that it may not be
considered at all in practical flight.
[Illustration: Fig. 1.--Diagram showing the reduction of the projected
horizontal area of aeroplanes due to raising the front edge above the
horizontal--_a_, _b_, shows an angle of 1 in 4, which is the highest
angle that will ever be used in a flying machine, and this only reduces
the projected area about 2 per cent. The line _c_ _b_ shows an angle of
1 in 8, and this only reduces the projected area an infinitesimal
amount. As the angle of inclination is increased, the projected area
becomes less as the versed sine _f_ _d_ becomes greater.]
Some of the mathematicians have demonstrated by formulæ, unsupported by
facts, that there is a considerable amount of skin friction to be
considered, but as no two agree on this or any other subject, some not
agreeing to-day with what they wrote a year ago, I think we might put
down all of their results, add them together, and then divide by the
number of mathematicians, and thus find the average coefficient of
error. When we subject this question to experimental test, we find that
nearly all of the mathematicians are radically wrong, Professor Langley,
of course, excepted. I made an aeroplane of hard rolled brass, 20 gauge;
it was 1 foot wide and dead smooth on both sides; I gave it a curvature
of about 1/16 inch and filed the edges, thin and sharp. I mounted this
with a great deal of care in a perfectly horizontal blast of air of 40
miles an hour. When this aeroplane was placed at any angle between 1 in
8 and 1 in 20, the lifting effect was always just in proportion to its
angle. The distance that the front edge was raised above the horizontal,
as compared with the width of the aeroplane, was always identical with
the drift as compared with the lift. On account of the jarring effect
caused by the rotation of the screws that produced the air blast, we
might consider that all of the articulated joints about the weighing
device were absolutely frictionless, as the jar would cause them to
settle into the proper position quite irrespective of friction. I was,
therefore, able to observe very carefully, the lift and the drift. As
an example of how these experiments were conducted, I would say that the
engine employed was provided with a very sensitive and accurate
governor; the power transmission was also quite reliable. Before making
these tests, the apparatus was tested as regards the drift, without any
aeroplane in position, and with weights applied that would just balance
any effect that the wind might have on everything except the aeroplane.
The aeroplane was then put in position and the other system of weights
applied until it exactly balanced, all the levers being rapped in order
to eliminate the friction in their joints. The engine was then started
and weights applied just sufficient to counterbalance the lifting effect
of the aeroplane, and other weights applied to exactly balance the drift
or the tendency to travel with the wind. In this way, I was able to
ascertain, with a great degree of accuracy, the relative difference
between the lift and drift. If there had been any skin friction, even to
the extent of 2 per cent., it would have been detected. This brass
aeroplane was tested at various angles, and always gave the same
results, but of course I could not use thick brass aeroplanes on a
flying machine; it was necessary for me to seek something much lighter.
I therefore conducted experiments with other materials, the results of
which are given. However, with a well-made wooden aeroplane 1 foot wide
and with a thickness in the centre of 7/16 inch, I obtained results
almost identical with those of the very much thinner brass aeroplane,
but it must not be supposed that in practice an aeroplane is completely
without friction. If it is very rough, irregular in shape, and has any
projections whatsoever on either the top or bottom side, there will be a
good deal of friction, although it may not, strictly speaking, be skin
friction; still, it will absorb the power, and the coefficient of this
friction may be anything from ·05 to ·40. These experiments with the
brass aeroplane demonstrated that the lifting effect was in direct
proportion to the angle, and that skin friction, if it exists at all,
was extremely small, but this does not agree with a certain kind of
reasoning which can be made very plausible and is consequently generally
accepted.
[Illustration: Fig. 2.--Professor Langley’s experiments--_a_, end of the
rotating arm; _b_, brass plane weighing 1 lb.; _c_ _c_, spiral springs.
When the arm was driven through the air, in the direction shown, the
plane assumed approximately a horizontal position, and the pull on the
springs _c_ _c_ was reduced from 1 lb. to 1 oz.]
Writers of books, as a rule, have always supposed that the lifting
effect of an aeroplane was not in proportion to its inclination, but in
proportion to the square of the sine of the angle. In order to make
this matter clear, I will explain. Suppose that an aeroplane is 20
inches wide and the front edge is raised 1 inch above the horizontal. In
ordinary parlance this is, of course, called an inclination of 1 in 20,
but mathematicians approach it from a different standpoint. They regard
the width of the aeroplane as unity or the radius, and the 1 inch that
the front edge is raised as a fraction of unity. The geometrical name of
this 1 inch is the sine of the angle--that is, it is the sine of the
angle at which the aeroplane is raised above the horizontal. Suppose,
now, that we have another identical aeroplane and we raise the front
edge 2 inches above the horizontal. It is very evident that, under these
conditions, the sine of the angle will be twice as much, and that the
square of the sine of the angle will be four times as great. All the
early mathematicians, and some of those of the present day, imagine that
the lift must be in proportion to the square of the sine of the angle.
They reason it out as follows:--If an aeroplane is forced through the
air at a given velocity, the aeroplane in which the sine of the angle is
2 inches will push the air down with twice as great a velocity as the
one in which the sine of the angle is only 1 inch, and as the force of
the wind blowing against a normal plane increases as the square of the
velocity, the same law holds good in driving a normal plane through
still air. From this reasoning, one is led to suppose that an aeroplane
set at an angle of 1 in 10 will lift four times as much as one in which
the inclination is only 1 in 20, but experiments have shown that this
theory is very wide of the truth. There are dozens of ways of showing,
by pure mathematics, that Newton’s law is quite correct; but in building
a flying machine no theory is good that does not correspond with facts,
and it is a fact, without any question, that the lifting effect of an
aeroplane, instead of increasing as the square of the sine of the angle,
only increases as the angle. Lord Kelvin, when he visited my place, was,
I think, the first to mention this, and point out that Newton’s law was
at fault. Professor Langley also pointed out the fallacy of Newton’s
law, and other experimenters have found that the lifting effect does not
increase as the square of the sine of the angle. In order to put this
matter at rest, Lord Rayleigh, who, I think we must all admit, would not
be likely to make a mistake, made some very simple experiments, in which
he demonstrated that two aeroplanes, in which we may consider the sine
of the angle to be 1/4 inch, lifted slightly more than a similar
aeroplane in which the sine of the angle was only 1/2 inch. Of course,
Lord Rayleigh did not express it in inches, but in term of the radius.
His aeroplanes were, however, very small. We can rely upon it that the
lifting effect of an aeroplane at any practical angle, everything else
being equal, increases in direct proportion to the angle of the
inclination. In this little work, I have attempted to make things as
simple as possible; it has not been written for mathematicians, and I
have, therefore, thought best to express myself in inches instead of in
degrees. If I write, “an inclination of 1 in 20,” everyone will
understand it, and only a carpenter’s 2-foot rule is required to
ascertain what the angle is. Then, again, simple measurements make
calculations much simpler, and the lifting effect is at once understood
without any computations being necessary. If the angles are expressed in
degrees and minutes, it is necessary to have a protractor or a text-book
in order to find out what the inclination really is. When I made my
experiments, I only had in mind the obtaining of correct data, to enable
me to build a flying machine that would lift itself from the ground. At
that time I was extremely busy, and during the first two years of my
experimental work, I was out of England fourteen months. After having
made my apparatus, I conducted my experiments rather quickly, it is
true, but I intended later on to go over them systematically and
deliberately, make many more experiments, write down results, and
prepare some account of them for publication. However, the property
where I made these experiments was sold by the company owning it, and my
work was never finished, so I am depending on the scraps of data that
were written down at the time. I am also publishing certain observations
that I wrote down shortly after I had succeeded in lifting more than the
weight of my machine. I think that the experiments which I made with an
aeroplane only 8 inches wide will be found the most reliable. All the
machinery was running smoothly, and the experiments were conducted with
a considerable degree of care. In making any formula on the lifting
effect of the aeroplane, it should be based on what was accomplished
with the 8-inch plane. Only a few experiments were made to ascertain the
relative value of planes of different widths. However, I think we must
all admit that a wide plane is not as economical in power as a narrow
one. In order to make this matter plain, suppose that we have one
aeroplane placed at such an angle that it will lift 2 lbs. per square
foot at a velocity of 40 miles an hour; it is very evident that the air
just at the rear of this aeroplane would be moving downward at a
velocity corresponding to the acceleration imparted to it by the plane.
If we wish to obtain lifting effect on this air by another plane of
exactly the same width, we shall have to increase its inclination in
order to obtain the same lifting effect, and, still further, it will be
necessary to use more power in proportion to the load lifted. If a third
aeroplane is used, it must be placed at an angle that will impart
additional acceleration to the air, and so on. Each plane that we add
will have to be placed at a sharper angle, and the power required will
be just in proportion to the average angle of all the planes. As the
action of a wide aeroplane is identical with that of numerous narrow
ones placed in close proximity to each other, it is very evident that a
wide aeroplane cannot be as efficient in proportion to its width as a
narrow one. I have thought the matter over, and I should say that the
lifting effect of a flat aeroplane increases rather faster than the
square root of its width. This will, at least, do for a working
hypothesis. Every flying machine must have what we will call “a length
of entering edge”--that is, the sum of entering edges of all the
aeroplanes must bear a fixed relation to the load carried. If a machine
is to have its lifting effect doubled, it is necessary to have the
length of entering edge twice as long. This additional length may, of
course, be obtained by superposed planes, but as we may assume that a
large aeroplane will travel faster than a small one, increased velocity
will compensate in some degree for the greater width of larger
aeroplanes. By careful study of the experiments which I have made, I
think it is quite safe to state that the lifting effect of well-made
aeroplanes, if we do not take into consideration the resistance due to
the framework holding them in position, increases as the square of their
velocity. Double their speed and they give four times the lifting
effect. The higher the speed, the smaller the angle of the plane, and
the greater the lifting effect in proportion to the power employed. When
we build a steamship, we know that its weight increases as the cube of
any one of its dimensions--that is, if the ship is twice as long, twice
as wide, and twice as deep it will carry eight times as much; but at the
very best, with even higher speed, the load carried by a flying machine
will only increase with the square of any one of its dimensions, or
perhaps still less. No matter whether it is a ship, a locomotive, or a
flying machine that we wish to build, we must first of all consider the
ideal, and then approximate it as closely as possible with the material
at hand. Suppose it were possible to make a perfect screw, working
without friction, and that its weight should only be that of the
surrounding air; if it should be 200 feet in diameter, the power of one
man, properly applied, would lift him into the air. This is because the
area of a circle 200 feet in diameter is so great that the weight of a
man would not cause it to fall through the air at a velocity greater
than the man would be able to climb up a ladder. If the diameter should
be increased to 400 feet, then a man would be able to carry a passenger
as heavy as himself on his flying machine, and if we should increase it
still further, to 2,000 feet, the weight of a horse could be sustained
in still air by the power which one man could put forth. On the other
hand, if we should reduce the diameter of the screw to 20 feet, then it
would certainly require the power of one horse to lift the weight of one
man, and, if we made the screw small enough, it might even require the
power of 100 horses to lift the same weight. It will, therefore, be seen
that everything depends upon the area of the air engaged, and in
designing a machine we should seek to engage as much air as possible, so
long as we can keep down the weight. Suppose that a flying machine
should be equipped with a screw 10 feet in diameter, with a pitch of 6
feet, and that the motor developed 40 horse-power and gave the screw
1,000 turns a minute, producing a screw thrust, we will say, of about
220 lbs. If we should increase the diameter of the screw to 20 feet, and
if it had the same pitch and revolved at the same rate, it would require
four times as much power and would give four times as much screw thrust,
because the area of the disc increases as the square of the diameter.
Suppose, now, that we should reduce the pitch of the screw to 3 feet, we
should in this case engage four times as much air, and double the screw
thrust without using any more power--that is, assuming that the machine
is stationary and that the full power of the engine is being used for
accelerating the air. The advantages of a large screw will, therefore,
be obvious. I have been unable to obtain correct data regarding the
experiments which have taken place with the various machines on the
Continent. I have, however, seen these machines, and I should say when
they are in flight, providing that the engine develops 40 horse-power,
that fully 28 horse-power is lost in screw slip, and the remainder in
forcing the machine through the air. These machines weigh 1,000 lbs.
each, and their engines are said to be 50 horse-power. The lifting
effect, therefore, per horse-power is 20 lbs. If the aeroplanes were
perfect in shape and set at a proper angle, and the resistance of the
framework reduced to a minimum, the same lifting effect ought to be
produced with an expenditure of less than half this amount of power,
providing, of course, that the screw be of proper dimensions. It is said
that Professor Langley and Mr. Horatio Philipps, by eliminating the
factor of friction altogether, or by not considering it in their
calculations, have succeeded in lifting at the rate of 200 lbs. per
horse-power. The apparatus they employed was very small. The best I ever
did with my very much larger apparatus--and I only did it on one
occasion--was to carry 133 lbs. per horse-power. In my large machine
experiments, I was amazed at the tremendous amount of power necessary
to drive the framework and the numerous wires through the air. It
appeared to me, from these experiments, that the air resisted very
strongly being cut up by wires. I expected to raise my machine in the
air by using only 100 horse-power, and my first condenser was made so
that it did actually condense water enough to supply 100 horse-power,
but the framework offered such a tremendous resistance that I was
compelled to strengthen all of the parts, make the machine heavier, and
increase the boiler pressure and piston speed until I actually ran it up
to 362 horse-power. This, however, was not the indicated horse-power. It
was arrived at by multiplying the pitch of the screws, in feet, by the
number of turns that they made in a minute, and by the screw thrust in
pounds, and then dividing the product by the conventional unit 33,000. I
have no doubt that the indicated horse-power would have been fully 400.
On one occasion I ran my machine over the track with all the aeroplanes
removed. I knew what steam pressure was required to run my machine with
the aeroplanes in position at a speed of 40 miles an hour. With the
planes removed, it still required a rather high steam pressure to obtain
this velocity, but I made no note at the time of the exact difference.
It was not, however, by any means so great as one would have supposed.
From the foregoing, it will be seen how necessary it is to consider
atmospheric resistance. Although I do not expect that anyone will ever
again attempt to make a flying machine driven by a steam engine, still,
I have thought best to give a short and concise description of my engine
and boiler, in order that my readers may understand what sort of an
apparatus I employed to obtain the data I am now, for the first time,
placing before the public. A full description of everything relating to
the motor power was written down at the time, and has been carefully
preserved. An abridgement of this will be found in the Appendix.