Chapter I: Part 1

FLYING MACHINES TODAY

"Hitherto aviation has been almost monopolized by that much-overpraised and much-overtrusted person, 'the practical man.' It is much in need of the services of the theorist--the engineer with his mathematical calculations of how a flying machine ought to be built and of how the material used in its construction should be distributed to give the greatest possible amount of strength and efficiency."

--From the _New York Times_, January 16, 1911.

FLYING MACHINES TODAY

BY WILLIAM DUANE ENNIS

_Professor of Mechanical Engineering in the Polytechnic
Institute of Brooklyn_

_123 ILLUSTRATIONS_

NEW YORK
D. VAN NOSTRAND COMPANY
23 MURRAY AND 1911 27 WARREN STS.

_Copyright, 1911, by_
D. VAN NOSTRAND COMPANY

THE · PLIMPTON · PRESS · NORWOOD · MASS · U · S · A

To MY MOTHER

PREFACE

Speaking with some experience, the writer has found that instruction in the principles underlying the science and sport of aviation must be vitalized by some contemporaneous study of what is being accomplished in the air. No one of the revolutionizing inventions of man has progressed as rapidly as aerial navigation. The "truths" of today are the absurdities of tomorrow.

The suggestion that some grasp of the principles and a very fair knowledge of the current practices in aeronautics may be had without special technical knowledge came almost automatically. If this book is comprehensible to the lay reader, and if it conveys to him even a small proportion of the writer's conviction that flying machines are to profoundly influence our living in the next generation, it will have accomplished its author's purpose.

POLYTECHNIC INSTITUTE OF BROOKLYN,
NEW YORK, April, 1911.

CONTENTS

PAGE THE DELIGHTS AND DANGERS OF FLYING.--Dangers of Aviation.--What it is Like to Fly 1

SOARING FLIGHT BY MAN.--What Holds it Up?--Lifting Power.--Why so Many Sails?--Steering 17

TURNING CORNERS.--What Happens when Making a Turn.-- Lateral Stability.--Wing Warping.--Automatic Control.-- The Gyroscope.--Wind Gusts 33

AIR AND THE WIND.--Sailing Balloons.--Field and Speed 43

GAS AND BALLAST.--Buoyancy in Air.--Ascending and Descending.--The Ballonet.--The Equilibrator 57

DIRIGIBLE BALLOONS AND OTHER KINDS.--Shapes.-- Dimensions.--Fabrics.--Framing.--Keeping the Keel Horizontal.--Stability.--Rudders and Planes.--Arrangement and Accessories.--Amateur Dirigibles.--The Fort Omaha Plant.--Balloon Progress 71

THE QUESTION OF POWER.--Resistance of Aeroplanes.-- Resistance of Dirigibles.--Independent Speed and Time-Table.--The Cost of Speed.--The Propeller 101

GETTING UP AND DOWN; MODELS AND GLIDERS; AEROPLANE DETAILS.--Launching.--Descending.-- Gliders.--Models.--Balancing.--Weights.-- Miscellaneous.--Things to Look After 121

SOME AEROPLANES.--SOME ACCOMPLISHMENTS 143

THE POSSIBILITIES IN AVIATION.--The Case of the Dirigible.--The Orthopter.--The Helicopter.--Composite Types.--What is Promised 170

AERIAL WARFARE 189

LIST OF ILLUSTRATIONS

PAGE

The Fall of Icarus _Frontispiece_
The Aviator 3
The Santos-Dumont "_Demoiselle_" 4
View from a Balloon 9
Anatomy of a Bird's Wing 10
Flight of a Bird 11
In a Meteoric Shower 13
How a Boat Tacks 15
Octave Chanute 18
Pressure of the Wind 19
Forces Acting on a Kite 20
Sustaining Force in the Aeroplane 23
Direct Lifting and Resisting Forces 24
Shapes of Planes 26
Balancing Sail 28
Roe's Triplane at Wembley 30
Action of the Steering Rudder 31
Recent Type of Wright Biplane 31
Circular Flight 33
The Aileron 35
Wing Tipping 36
Wing Warping 37
The Gyroscope 39
Diurnal Temperatures at Different Heights 45
Seasonal Variation in Wind Velocities 47
The Wind Rose for Mt. Weather, Va. 49
Diagram of Parts of a Drifting Balloon 51
Glidden and Stevens Getting Away in the "_Boston_" 52
Relative and Absolute Balloon Velocities 53
Field and Speed 53
Influence of Wind on Possible Course 54
Count Zeppelin 55
Buoyant Power of Wood 57
One Cubic Foot of Wood Loaded in Water 58
Buoyant Power of Hydrogen 59
Lebaudy's "_Jaune_" 60
Air Balloon 62
Screw Propeller for Altitude Control 66
Balloon with Ballonets 67
Construction of the Zeppelin Balloon 68
The Equilibrator 69
Henry Giffard's Dirigible 71
Dirigible of Dupuy de Lome 72
Tissandier Brothers' Dirigible Balloon 73
The "_Baldwin_" 74
The "_Zeppelin_" on Lake Constance 75
The "_Patrie_" 77
Manufacturing the Envelope of a Balloon 79
Andrée's Balloon, "_L'Oernen_" 80
Wreck of the "_Zeppelin_" 82
Car of the "_Zeppelin_" 84
Stern View of the "_Zeppelin_" 86
The "_Clément-Bayard_" 87
The "_Ville de Paris_" 88
Car of the "_Liberté_" 89
The "_Zodiac No. 2_" 92
United States Signal Corps Balloon Plant at Fort Omaha 93
The "_Caroline_" 94
The Ascent at Versailles, 1783 95
Proposed Dirigible 96
The "_République_" 97
The First Flight for the Gordon-Bennett Cup 99
The Gnome Motor 102
Screw Propeller 103
One of the Motors of the "_Zeppelin_" 104
The Four-Cycle Engine 105
Action of Two-Cycle Engine 106
Motor and Propeller 108
Two-Cylinder Opposed Engine 110
Four-Cylinder Vertical Engine 110
Head End Shapes 113
The Santos-Dumont Dirigible No. 2 115
In the Bay of Monaco: Santos-Dumont 117
Wright Biplane on Starting Rail 121
Launching System for Wright Aeroplane 122
The Nieuport Monoplane 124
A Biplane 125
Ely at Los Angeles 126
Trajectory During Descent 127
Descending 128
The Witteman Glider 130
French Monoplane 132
A Problem in Steering 133
Lejeune Biplane 134
Tellier Monoplane 135
A Monoplane 137
Cars and Framework 139
Some Details 139
Recent French Machines 141
Orville Wright at Fort Myer 143
The First Flight Across the Channel 144
Wright Motor 145
Voisin-Farman Biplane 147
The Champagne Grand Prize Flight 148
Farman's First Biplane 149
The "_June Bug_" 150
Curtiss Biplane 151
Curtiss' Hydro-Aeroplane at San Diego Bay 152
Flying Over the Water 153
Blériot-Voisin Cellular Biplane with Pontoons 154
Latham's "_Antoinette_" 155
James J. Ward at Lewiston Fair 156
Marcel Penot in the "_Mohawk_" 157
Santos-Dumont's "_Demoiselle_" 159
Blériot Monoplane 160
Latham's Fall into the Channel 161
De Lesseps Crossing the Channel 163
The Maxim Aeroplane 164
Langley's Aeroplane 165
Robart Monoplane 166
Vina Monoplane 167
Blanc Monoplane 170
Melvin Vaniman Triplane 171
Jean de Crawhez Triplane 171
A Triplane 172
Giraudon's Wheel Aeroplane 175
Bréguet Gyroplane (Helicopter) 177
Wellman's "_America_" 181
The German Emperor Watching the Progress of Aviation 189
Automatic Gun for Attacking Airships 193
Gun for Shooting at Aeroplanes 197
Santos-Dumont Circling the Eiffel Tower 199
Latham, Farman and Paulhan 202

FLYING MACHINES TODAY

THE DELIGHTS AND DANGERS OF FLYING

Few things have more charm for man than flight. The soaring of a bird is beautiful and the gliding of a yacht before the wind has something of the same beauty. The child's swing; the exercise of skating on good ice; a sixty-mile-an-hour spurt on a smooth road in a motor car; even the slightly passé bicycle: these things have all in their time appealed to us because they produce the illusion of flight--of progress through the intangible air with all but separation from the prosaic earth.

But these sensations have been only illusions. To actually leave the earth and wander at will in aerial space--this has been, scarcely a hope, perhaps rarely even a distinct dream. From the days of Dædalus and Icarus, of Oriental flying horses and magic carpets, down to "Darius Green and his flying machine," free flight and frenzy were not far apart. We were learnedly told, only a few years since, that sustention by heavier-than-air machines was impossible without the discovery, first, of some new matter or some new force. It is now (1911) only eight years since Wilbur Wright at Kitty Hawk, with the aid of the new (?) matter--aluminum--and the "new" force--the gasoline engine--in three successive flights proved that a man could travel through the air and safely descend, in a machine weighing many times as much as the air it displaced. It is only five years since two designers--Surcouf and Lebaudy--built dirigible balloons approximating present forms, the _Ville de Paris_ and _La Patrie_. It is only now that we average people may confidently contemplate the prospect of an aerial voyage for ourselves before we die. A contemplation not without its shudder, perhaps; but yet not altogether more daring than that of our grandsires who first rode on steel rails behind a steam locomotive.

The Dangers of Aviation

We are very sure to be informed of the fact when an aviator is killed. Comparatively little stir is made nowadays over an automobile fatality, and the ordinary railroad accident receives bare mention. For instruction and warning, accidents to air craft cannot be given too much publicity; but if we wish any accurate conception of the danger we must pay regard to factors of proportion. There are perhaps a thousand aeroplanes and about sixty dirigible balloons in the world. About 500 men--amateurs and professionals--are continuously engaged in aviation. The Aero Club of France has issued in that country nearly 300 licenses. In the United States, licenses are held by about thirty individuals. We can form no intelligent estimate as to the number of unlicensed amateurs of all ages who are constantly experimenting with gliders at more or less peril to life and limb.

A French authority has ascertained the death rate among air-men to have been--to date--about 6%. This is equivalent to about one life for 4000 miles of flight: but we must remember that accidents will vary rather with the number of ascents and descents than with the mileage. Four thousand miles in 100 flights would be much less perilous, under present conditions, than 4000 miles in 1000 flights.

There were 26 fatal aeroplane accidents between September 17, 1908, and December 3, 1910. Yet in that period there were many thousands of ascents: 1300 were made in one week at the Rheims tournament alone. Of the 26 accidents, 1 was due to a wind squall, 3 to collision, 6 (apparently) to confusion of the aviator, and 12 to mechanical breakage. An analysis of 40 British accidents shows 13 to have been due to engine failures, 10 to alighting on bad ground, 6 to wind gusts, 5 to breakage of the propeller, and 6 to fire and miscellaneous causes. These casualties were not all fatal, although the percentage of fatalities in aeronautic accidents is high. The most serious results were those due to alighting on bad ground; long grass and standing grain being very likely to trip the machine and throw the occupant. French aviators are now strapping themselves to their seats in order to avoid this last danger.

Practically all of the accidents occur to those who are flying; but spectators may endanger themselves. During one of the flights of Mauvais at Madrid, in March of the present year, the bystanders rushed through the barriers and out on the field before the machine had well started. A woman was decapitated by the propeller, and four other persons were seriously injured.

Nearly all accidents result from one of three causes: bad design, inferior mechanical construction, and the taking of unnecessary risks by the operator. Scientific design at the present writing is perhaps impossible. Our knowledge of the laws of air resistance and sustention is neither accurate nor complete. Much additional study and experiment must be carried on; and some better method of experimenting must be devised than that which sends a man up in the air and waits to see what happens. A thorough scientific analysis will not only make aviation safer, it will aid toward making it commercially important. Further data on propeller proportions and efficiencies, and on strains in the material of screws under aerial conditions, will do much to standardize power plant equipment. The excessive number of engine breakdowns is obviously related to the extremely light weight of the engines employed: better design may actually increase these weights over those customary at present. Great weight reduction is no longer regarded as essential at present speeds in aerial navigation: we have perhaps already gone too far in this respect.

Bad workmanship has been more or less unavoidable, since no one has yet had ten years' experience in building aeroplanes. The men who have developed the art have usually been sportsmen rather than mechanics, and only time is necessary to show the impropriety of using "safety pins" and bent wire nails for connections.

The taking of risks has been an essential feature. When one man earns $100,000 in a year by dare-devil flights, when the public flocks in hordes--and pays good prices--to see a man risk his neck, he will usually aim to satisfy it. This is not developing aerial navigation: this is circus riding--looping-the-loop performances which appeal to some savage instinct in us but lead us nowhere. Men have climbed two miles into the clouds, for no good purpose whatever. All that we need to know of high altitude conditions is already known or may be learned by ascents in anchored balloons. Records up to heights of sixteen miles have been obtained by sounding balloons.

If these high altitudes may under certain conditions be desirable for particular types of balloon, they are essentially undesirable for the aeroplane. The supporting power of a heavier-than-air machine decreases in precisely inverse ratio with the altitude. To fly high will then involve either more supporting surface and therefore a structurally weaker machine, or greater speed and consequently a larger motor. It is true that the resistance to propulsion decreases at high altitudes, just as the supporting power decreases: and on this account, given only a sufficient margin of supporting power, we might expect a standard machine to work about as well at a two-mile elevation as at a height of 200 feet; but rarefaction of the air at the higher altitudes decreases the weight of carbureted mixture drawn into the motor, and consequently its output. Any air-man who attempts to reach great heights in a machine not built for such purpose is courting disaster.

Flights over cities, spectacular as they are, and popular as they are likely to remain, are doubly dangerous on account of the irregular air currents and absence of safe landing places. They have at last been officially discountenanced as not likely to advance the sport.

All flights are exhibition flights. The day of a quiet, mind-your-own-business type of aerial journey has not yet arrived. Exhibition performances of any sort are generally hazardous. There were nine men killed in one recent automobile meet. If the automobile were used exclusively for races and contests, the percentage of fatalities might easily exceed that in aviation. It is claimed that no inexperienced aviator has ever been killed. This may not be true, but there is no doubt that the larger number of accidents has occurred to the better-known men from whom the public expects something daring.

Probably the best summing up of the danger of aviation may be obtained from the insurance companies. The courts have decided that an individual does not forfeit his life insurance by making an occasional balloon trip. Regular classified rates for aeroplane and balloon operators are in force in France and Germany. It is reported that Mr. Grahame-White carries a life insurance policy at 35% premium--about the same rate as that paid by a "crowned head." Another aviator of a less professional type has been refused insurance even at 40% premium. Policies of insurance may be obtained covering damage to machines by fire or during transportation and by collisions with other machines; and covering liability for injuries to persons other than the aviator.

On the whole, flying is an ultra-hazardous _occupation_; but an _occasional_ flight by a competent person or by a passenger with a careful pilot is simply a thrilling experience, practically no more dangerous than many things we do without hesitation. Nearly all accidents have been due to preventable causes; and it is simply a matter of science, skill, perseverance, and determination to make an aerial excursion under proper conditions as safe as a journey in a motor car. Men who for valuable prizes undertake spectacular feats will be killed as frequently in aviation as in bicycle or even in automobile racing; but probably not very much more frequently, after design and workmanship in flying machines shall have been perfected. The total number of deaths in aviation up to February 9, 1911, is stated to have been forty-two.

What It Is Like to Fly

We are fond of comparing flying machines with birds, with fish, and with ships: and there are useful analogies with all three. A drifting balloon is like a becalmed ship or a dead fish. It moves at the speed of the aerial fluid about it and the occupants perceive no movement whatever. The earth's surface below appears to move in the opposite direction to that in which the wind carries the balloon. With a dirigible balloon or flying machine, the sensation is that of being exposed to a violent wind, against which (by observation of landmarks) we find that we progress. It is the same experience as that obtained when standing in an exposed position on a steamship, and we wonder if a bird or a fish gradually gets so accustomed to the opposing current as to be unconscious of it. But in spite of jar of motors and machinery, there is a freedom of movement, a detachment from earth-associations, in air flight, that distinguishes it absolutely from the churning of a powerful vessel through the waves.

Birds fly in one of three ways. The most familiar bird flight is by a rapid wing movement which has been called oar-like, but which is precisely equivalent to the usual movement of the arms of a man in swimming. The edge of the wing moves forward, cutting the air; on the return stroke the leading edge is depressed so as to present a nearly flat surface to the air and thus propel the bird forward. A slight downward direction of this stroke serves to impel the flight sufficiently upward to offset the effect of gravity. Any man can learn to swim, but no man can fly, because neither in his muscular frame nor by any device which he can attach thereto can he exert a sufficient pressure to overcome his own weight against as imponderable a fluid as air. If air were as heavy as water, instead of 700 times lighter, it would be as easy to fly as to swim. The bird can fly because of the great surface, powerful construction, and rapid movement of its wings, in proportion to the weight of its body. But compared with the rest of the animal kingdom, flying birds are all of small size. Helmholz considered that the vulture represented the heaviest body that could possibly be raised and kept aloft by the exercise of muscular power, and it is understood that vultures have considerable difficulty in ascending; so much so that unless in a position to take a short preliminary run they are easily captured.

Every one has noticed a second type of bird flight--soaring. It is this flight which is exactly imitated in a glider. An aeroplane differs from a soaring bird only in that it carries with it a producer of forward impetus--the propeller--so that the soaring flight may last indefinitely: whereas a soaring bird gradually loses speed and descends.

A third and rare type of bird flight has been called _sailing_. The bird faces the wind, and with wings outspread and their forward edge elevated rises while being forced backward under the action of the breeze. As soon as the wind somewhat subsides, the bird turns and _soars_ in the desired direction. Flight is thus accomplished without muscular effort other than that necessary to properly incline the wings and to make the turns. It is practicable only in squally winds, and the birds which practice "sailing"--the albatross and frigate bird--are those which live in the lower and more disturbed regions of the atmosphere. This form of flight has been approximately imitated in the man[oe]uvering of aeroplanes.

Comparison of flying machines and ships suggests many points of difference. Water is a fluid of great density, with a definite upper surface, on which marine structures naturally rest. A vessel in the air may be at any elevation in the surrounding rarefied fluid, and great attention is necessary to keep it at the elevation desired. The air has no surface. The air ship is like a submarine--the dirigible balloon of the sea--and perhaps rather more safe. An ordinary ship is only partially immersed; the resistance of the fluid medium is exerted over a portion only of its head end: but the submarine or the flying machine is wholly exposed to this resistance. The submarine is subjected to ocean currents of a very few miles per hour, at most; the currents to which the flying machine may be exposed exceed a mile a minute. Put a submarine in the Whirlpool Rapids at Niagara and you will have possible air ship conditions.

A marine vessel may _tack_, _i.e._, may sail partially against the wind that propels it, by skillful utilization of the resistance to sidewise movement of the ship through the water: but the flying machine is wholly immersed in a single fluid, and a head wind is nothing else than a head wind, producing an absolute subtraction from the proper speed of the vessel.

Aerial navigation is thus a new art, particularly when heavier-than-air machines are used. We have no heavier-than-water _ships_. The flying machine must work out its own salvation.

SOARING FLIGHT BY MAN

Flying machines have been classified as follows:--

Lighter than Air
Fixed balloon,
Drifting balloon,
Sailing balloon,
Dirigible balloon
rigid (Zeppelin),
ballonetted.

Heavier than Air
Orthopter,
Helicopter,
Aeroplane
monoplane,
multiplane.

We will fall in with the present current of popular interest and consider the aeroplane--that mechanical grasshopper--first.

What Holds It Up?

To the researches of Chanute and Langley must be ascribed much of American progress in aviation.

When a flat surface like the side of a house is exposed to the breeze, the velocity of the wind exerts a force or pressure directly against the surface. This principle is taken into account in the design of buildings, bridges, and other structures. The pressure exerted per square foot of surface is equal (approximately) to the square of the wind velocity in miles per hour, divided by 300. Thus, if the wind velocity is thirty miles, the pressure against a house wall on which it acts directly is 30 × 30 ÷ 300 = 3 pounds per square foot: if the wind velocity is sixty miles, the pressure is 60 × 60 ÷ 300 = 12 pounds: if the velocity is ninety miles, the pressure is 90 × 90 ÷ 300 = 27 pounds, and so on.

If the wind blows obliquely toward the surface, instead of directly, the pressure at any given velocity is reduced, but may still be considerable. Thus, in the sketch, let _ab_ represent a wall, toward which we are looking downward, and let the arrow _V_ represent the direction of the wind. The air particles will follow some such paths as those indicated, being deflected so as to finally escape around the ends of the wall. The result is that a pressure is produced which may be considered to act along the dotted line _P_, perpendicular to the wall. This is the invariable law: that no matter how oblique the surface may be, with reference to the direction of the wind, there is always a pressure produced against the surface by the wind, and this pressure always acts _in a direction perpendicular to the surface_. The amount of pressure will depend upon the wind velocity and the obliquity or inclination of the surface (_ab_) with the wind (_V_).

Now let us consider a kite--the "immediate ancestor" of the aeroplane. The surface _ab_ is that of the kite itself, held by its string _cd_. We are standing at one side and looking at the _edge_ of the kite. The wind is moving horizontally against the face of the kite, and produces a pressure _P_ directly against the latter. The pressure tends both to move it toward the left and to lift it. If the tendency to move toward the left be overcome by the string, then the tendency toward lifting may be offset--and in practice _is_ offset--by the weight of the kite and tail.

We may represent the two tendencies to movement produced by the force _P_, by drawing additional dotted lines, one horizontally to the left (_R_) and the other vertically (_L_); and it is known that if we let the length of the line _P_ represent to some convenient scale the amount of direct pressure, then the lengths of _R_ and _L_ will also represent to the same scale the amounts of horizontal and vertical force due to the pressure. If the weight of kite and tail exceeds the vertical force _L_, the kite will descend: if these weights are less than that force, the kite will ascend. If they are precisely equal to it, the kite will neither ascend nor descend. The ratio of _L_ to _R_ is determined by the slope of _P_; and this is fixed by the slope of _ab_; so that we have the most important conclusion: _not only does the amount of direct pressure (P) depend upon the obliquity of the surface with the breeze (as has already been shown), but the relation of vertical force (which sustains the kite) to horizontal force also depends on the same obliquity_. For example, if the kite were flying almost directly above the boy who held the string, so that _ab_ became almost horizontal, _P_ would be nearly vertical and _L_ would be much greater than _R_. On the other hand, if _ab_ were nearly vertical, the kite flying at low elevation, the string and the direct pressure would be nearly horizontal and _L_ would be much less than _R_. The force _L_ which lifts the kite seems to increase while _R_ decreases, as the kite ascends: but _L_ may not actually increase, because it depends upon the amount of direct pressure, _P_, as well as upon the direction of this pressure; and the amount of direct pressure steadily decreases during ascent, on account of the increasing obliquity of _ab_ with _V_. All of this is of course dependent on the assumption that the kite always has the same inclination to the string, and the described resolution of the forces, although answering for illustrative purposes, is technically incorrect.

It seems to be the wind velocity, then, which holds up the kite: but in reality the string is just as necessary as the wind. If there is no string, and the wind blows the kite with it, the kite comes down, because the pressure is wholly due to a relative velocity as between kite and wind. The wind exerts a pressure against the rear of a railway train, if it happens to be blowing in that direction, and if we stood on the rear platform of a stationary train we should feel that pressure: but if the train is started up and caused to move at the same speed as the wind there would be no pressure whatever.

One of the very first heavier-than-air flights ever recorded is said to have been made by a Japanese who dropped bombs from an immense man-carrying kite during the Satsuma rebellion of 1869. The kite as a flying machine has, however, two drawbacks: it needs the wind--it cannot fly in a calm--and it stands still. One early effort to improve on this situation was made in 1856, when a man was towed in a sort of kite which was hauled by a vehicle moving on the ground. In February of the present year, Lieut. John Rodgers, U.S.N., was lifted 400 feet from the deck of the cruiser _Pennsylvania_ by a train of eleven large kites, the vessel steaming at twelve knots against an eight-knot breeze. The aviator made observations and took photographs for about fifteen minutes, while suspended from a tail cable about 100 feet astern. In the absence of a sufficient natural breeze, an artificial wind was thus produced by the motion imparted to the kite; and the device permitted of reaching some destination. The next step was obviously to get rid of the tractive vehicle and tow rope by carrying propelling machinery on the kite. This had been accomplished by Langley in 1896, who flew a thirty-pound model nearly a mile, using a steam engine for power. The gasoline engine, first employed by Santos-Dumont (in a dirigible balloon) in 1901, has made possible the present day _aeroplane_.

What "keeps it up", in the case of this device, is likewise its velocity. Looking from the side, _ab_ is the sail of the aeroplane, which is moving toward the right at such speed as to produce the equivalent of an air velocity _V_ to the left. This velocity causes the direct pressure _P_, equivalent to a lifting force _L_ and a retarding force _R_. The latter is the force which must be overcome by the motor: the former must suffice to overcome the whole weight of the apparatus. Travel in an aeroplane is like skating rapidly over very thin ice: the air literally "doesn't have time to get away from underneath."

If we designate the angle made by the wings (_ab_) with the horizontal (_V_) as _B_, then _P_ increases as _B_ increases, while (as has been stated) the ratio of _L_ to _R_ decreases. When the angle _B_ is a right angle, the wings being in the position _a´b´_, _P_ has its maximum value for direct wind--1/300 of the square of the velocity, in pounds per square foot; but _L_ is zero and _R_ is equal to _P_. The plane would have no lifting power. When the angle _B_ becomes zero, position _a´´b´´_, wings being horizontal, _P_ becomes zero and (so far as we can now judge) the plane has neither lifting power nor retarding force. At some intermediate position, like _ab_, there will be appreciable lifting and retarding forces. The chart shows the approximate lifting force, in pounds per square foot, for various angles. This force becomes a maximum at an angle of 45° (half a right angle). We are not yet prepared to consider why in all actual aeroplanes the angle of inclination is much less than this. The reason will be shown presently. At this stage of the discussion we may note that the lifting power per square foot of sail area varies with

the square of the velocity, _and_
the angle of inclination.

The total lifting power of the whole plane will also vary with its area. As we do not wish this whole lifting power to be consumed in overcoming the dead weight of the machine itself, we must keep the parts light, and in particular must use for the wings a fabric of light weight per unit of surface. These fabrics are frequently the same as those used for the envelopes of balloons.

Since the total supporting power varies both with the sail area and with the velocity, we may attain a given capacity either by employing large sails or by using high speed. The size of sails for a given machine varies inversely as the square of the speed. The original Wright machine had 500 square feet of wings and a speed of forty miles per hour. At eighty miles per hour the necessary sail area for this machine would be only 125 square feet; and at 160 miles per hour it would be only 31-1/4 square feet: while if we attempted to run the machine at ten miles per hour we should need a sail area of 8000 square feet. This explains why the aeroplane cannot go slowly.

It would seem as if when two or more superposed sails were used, as in biplanes, the full effect of the air would not be realized, one sail becalming the other. Experiments have shown this to be the case; but there is no great reduction in lifting power unless the distance apart is considerably less than the width of the planes.

In all present aeroplanes the sails are concaved on the under side. This serves to keep the air from escaping from underneath as rapidly as it otherwise would, and increases the lifting power from one-fourth to one-half over that given by our 1/300 rule: the divisor becoming roughly about 230 instead of 300.

Why are the wings placed crosswise of the machine, when the other arrangement--the greatest dimension in the line of flight--would seem to be stronger? This is also done in order to "keep the air from escaping from underneath." The sketch shows how much less easily the air will get away from below a wing of the bird-like spread-out form than from one relatively long and narrow but of the same area.

A sustaining force of two pounds per square foot of area has been common in ordinary aeroplanes and is perhaps comparable with the results of bird studies: but this figure is steadily increasing as velocities increase.

Why so Many Sails?

Thus far a single wing or pair of wings would seem to fully answer for practicable flight: yet every actual aeroplane has several small wings at various points. The necessity for one of these had already been discovered in the kite, which is built with a balancing tail. In the sketch on page 18 it appears that the particles of air which are near the upper edge of the surface are more obstructed in their effort to get around and past than those near the lower edge. They have to turn almost completely about, while the others are merely deflected. This means that on the whole the upper air particles will exert more pressure than the lower particles and that the "center of pressure" (the point where the entire force of the wind may be assumed to act) will be, not at the center of the surface, but at a point some distance _above_ this center. This action is described as the "displacement of the center of pressure." It is known that the displacement is greatest for least inclinations of surface (as might be surmised from the sketch already referred to), and that it is always proportional to the dimension of the surface in the direction of movement; _i.e._, to the length of the line _ab_.

If the weight _W_ of the aeroplane acts downward at the center of the wing (at _o_ in the accompanying sketch), while the direct pressure _P_ acts at some point _c_ farther along toward the upper edge of the wing, the two forces _W_ and _P_ tend to revolve the whole wing in the direction indicated by the curved arrow. This rotation, in an aeroplane, is resisted by the use of a tail plane or planes, such as _mn_. The velocity produces a direct pressure _P´_ on the tail plane, which opposes, like a lever, any rotation due to the action of _P_. It may be considered a matter of rather nice calculation to get the area and location of the tail plane just right: but we must remember that the amount of pressure _P´_ can be greatly varied by changing the inclination of the surface _mn_. This change of inclination is effected by the operator, who has access to wires which are attached to the pivoted tail plane. It is of course permissible to place the tail plane _in front_ of the main planes--as in the original Wright machine illustrated: but in this case, with the relative positions of _W_ and _P_ already shown, the forward edge of the tail plane would have to be depressed instead of elevated. The illustration shows the tail built as a biplane, just as are the principal wings (page 141).

Suppose the machine to be started with the tail plane in a horizontal position. As its speed increases, it rises and at the same time (if the weight is suspended from the center of the main planes) tilts backward. The tilting can be stopped by swinging the tail plane on its pivot so as to oppose the rotative tendency. If this control is not carried too far, the main planes will be allowed to maintain some of their excessive inclination and ascent will continue. When the desired altitude has been attained, the inclination of the main planes will, by further swinging of the tail plane, be reduced to the normal amount, at which the supporting power is precisely equal to the load; and the machine will be in vertical equilibrium: an equilibrium which demands at every moment, however, the attention of the operator.

In many machines, ascent and tilting are separately controlled by using two sets of transverse planes, one set placed forward, and the other set aft, of the main planes. In any case, quick ascent can be produced only by an increase in the lifting force _L_ (see sketch, page 24) of the main planes: and this force is increased by enlarging the angle of inclination of the main planes, that is, by a controlled and partial tilting. The forward transverse wing which produces this tilting is therefore called the _elevating rudder_ or elevating plane. The rear transverse plane which checks the tilting and steadies the machine is often described as the _stabilizing plane_. _Descent_ is of course produced by _decreasing_ the angle of inclination of the main planes.

Steering

If we need extra sails for stability and ascent or descent, we need them also for changes of horizontal direction. Let _ab_ be the top view of the main plane of a machine, following the course _xy_. At _rs_ is a vertical plane called the _steering rudder_. This is pivoted, and controlled by the operator by means of the wires _t_, _u_. Let the rudder be suddenly shifted to the position _r´s´_. It will then be subjected to a pressure _P´_ which will swing the whole machine into the new position shown by the dotted lines, its course becoming _x´y´_. The steering rudder may of course be double, forming a vertical biplane, as in the Wright machine shown below.

Successful steering necessitates lateral resistance to drift, _i.e._, a fulcrum. This is provided, to some extent, by the stays and frame of the machine; and in a much more ample way by the vertical planes of the original Voisin cellular biplane. A recent Wright machine had vertical planes forward probably intended for this purpose.

It now begins to appear that the aviator has a great many things to look after. There are many more things requiring his attention than have yet been suggested. No one has any business to attempt flying unless he is superlatively cool-headed and has the happy faculty of instinctively doing the right thing in an emergency. Give a chauffeur a high power automobile running at maximum speed on a rough and unfamiliar road, and you have some conception of the position of the operator of an aeroplane. It is perhaps not too much to say that to make the two positions fairly comparable we should _blindfold_ the chauffeur.

Broadly speaking, designers may be classed in one of two groups--those who, like the Wrights, believe in training the aviator so as to qualify him to properly handle his complicated machine; and those who aim to simplify the whole question of control so that to acquire the necessary ability will not be impossible for the average man. If aviation is to become a popular sport, the latter ideal must prevail. The machines must be more automatic and the aviator must have time to enjoy the scenery. In France, where amateur aviation is of some importance, progress has already been made in this direction. The universal steering head, for example, which not only revolves like that of an automobile, but is hinged to permit of additional movements, provides for simultaneous control of the steering rudder and the main plane warping, while scarcely demanding the conscious thought of the operator.

TURNING CORNERS

A year elapsed after the first successful flight at Kitty Hawk before the aviator became able to describe a circle in the air. A later date, 1907, is recorded for the first European half-circular flight: and the first complete circuit, on the other side of the water, was made a year after that; by both biplane and monoplane. It was in the same year that Louis Blériot made the pioneer cross-country trip of twenty-one miles, stopping at will _en route_ and returning to his starting point.

What Happens When Making a Turn

We are looking downward on an aeroplane _ab_ which has been moving along the straight path _cd_. At _d_ it begins to describe the circle _de_, the radius of which is _od_, around the center _o_. The outer portion of the plane, at the edge _b_, must then move faster than the inner edge _a_. We have seen that the direct air pressure on the plane is proportional to the square of the velocity. The direct pressure _P_ (see sketch on page 22) will then be greater at the outer than at the inner limb; the lifting force _L_ will also be greater and the outer limb will tend to rise, so that the plane (viewed from the rear) will take the inclined position shown in the lower view: and this inclination will increase as long as the outer limb travels faster than the inner limb; that is, as long as the orbit continues to be curved. Very soon, then, the plane will be completely tipped over.

Necessarily, the two velocities have the ratio _om_:_om´_; the respective lifting forces must then be proportional to the squares of these distances. The difference of lifting forces, and the tendency to overturn, will be more important as the distances most greatly differ: which is the case when the distance _om_ is small as compared with _mm´_. The shorter the radius of curvature, the more dangerous, for a given machine, is a circling flight: and in rounding a curve of given radius the most danger is attached to the machine of greatest spread of wing.

Lateral Stability

This particular difficulty has considerably delayed the development of the aeroplane. It may, however, be overcome by very simple methods--simple, at least as far as their mechanical features are concerned. If the outer limb of the plane is tilted upward, it is because the wind pressure is greater there. The wind pressure is greater because the velocity is greater. We have only to increase the wind pressure at the inner limb, in order to restore equilibrium. This cannot be done by adjusting the velocity, because the velocity is fixed by the curvature of path required: but the total wind pressure depends upon the _sail area_ as well as the velocity; so that by increasing the surface at the inner limb we may equalize the value of _L_, the lifting force, at the two ends of the plane. This increase of surface must be a temporary affair, to be discontinued when moving along a straight course.

Let us stand in the rear of an aeroplane, the main wing of which is represented by _ab_. Let the small fan-shaped wings _c_ and _d_ be attached near the ends, and let the control wires, _e_, _f_, passing to the operator at _g_, be employed to close and unclasp the fans. If these fans are given a forward inclination at the top, as indicated in the end view, they will when spread out exert an extra lifting force. A fan will be placed at each end. They will be ordinarily folded up: but when rounding a curve the aviator will open the fan on the inner or more slowly moving limb of the main plane. This represents one of the first forms of the _aileron_ or wing-tip for lateral control.

The more common present form of aileron is that shown in the lower sketch, at _s_ and _t_. The method of control is the same.

The cellular Voisin biplanes illustrate an attempt at self-sufficing control, without the interposition of the aviator. Between the upper and lower sails of the machine there were fore and aft vertical partitions. The idea was that when the machine started to revolve, the velocity of rotation would produce a pressure against these partitions which would obstruct the tipping. But rotation may take place slowly, so as to produce an insufficient pressure for control, and yet be amply sufficient to wreck the apparatus. The use of extra vertical rudder planes, hinged on a horizontal longitudinal axis, is open to the same objection.

Wing Warping

In some monoplanes with the inverted _V_ wing arrangement, a dipping of one wing answers, so to speak, to increase its concavity and thus to augment the lifting force on that side. The sketch shows the normal and distorted arrangement of wings: the inner limb being the one bent down in rounding a curve. An equivalent plan was to change the angle of inclination of one-half the sail by swinging it about a horizontal pivot at the center or at the rear edge: some machines have been built with sails divided in the center. The obvious objection to both of these plans is that too much mechanism is necessary in order to distort what amounts to nearly half the whole machine. They remind one of Charles Lamb's story of the discovery of roast pig.

The distinctive feature of the Wright machines lies in the warping or distorting of the _ends only_ of the main planes. This is made possible, not by hinging the wings in halves, but by the flexibility of the framework, which is sufficiently pliable to permit of a considerable bending without danger. The operator, by pulling on a stout wire linkage, may tip up (or down) the corners _cc´_ of the sails at one limb, thus decreasing or increasing the effective surface acted on by the wind, as the case may require. The only objection is that the scheme provides one more thing for the aviator to think about and manipulate.

Automatic Control

Let us consider again the condition of things when rounding a curve, as in the sketch on page 32. As long as the machine is moving forward in a straight line, the operator sits upright. When it begins to tip, he will unconsciously tip himself the other way, as represented by the line _xy_ in the rear view. Any bicyclist will recognize this as plausible. Why not take advantage of this involuntary movement to provide a stabilizing force? If operating wires are attached to the aviator's belt and from thence connected with ailerons or wing-warping devices, then by a proper proportioning of levers and surfaces to the probable swaying of the man, the control may become automatic. The idea is not new; it has even been made the subject of a patent.

The Gyroscope

This device for automatic control is being steadily developed and may ultimately supersede all others. It uses the inertia of a fast-moving fly wheel for control, in a manner not unlike that contemplated in proposed methods of automatic balancing by the action of a suspended pendulum. Every one has seen the toy gyroscope and perhaps has wondered at its mysterious ways. The mathematical analysis of its action fills volumes: but some idea of what it does, and why, may perhaps be gathered at the expense of a very small amount of careful attention. The wheel _acbd_, a thin disc, is spinning rapidly about the axle _o_. In the side view, _ab_ shows the edge of the wheel, and _oo´_ the axle. This axle is not fixed, but may be conceived as held in some one's fingers. Now suppose the right-hand end of the axle (_o´_) to be suddenly moved toward us (away from the paper) and the left-hand (_o_) to be moved away. The wheel will now appear in both views as an ellipse, and it has been so represented, as _afbe_. Now, any particle, like _x_, on the rim of the wheel, will have been regularly moving in the circular orbit _cb_. The tendency of any body in motion is to move indefinitely in a straight line. The cohesion of the metal of the disc prevents the particle _x_ from flying off at a straight line tangent, _xy_, and it is constrained, therefore, to move in a circular orbit. Unless some additional constraint is imposed, it will at least remain in this orbit and will try to remain in its plane of rotation. When the disc is tipped, the plane of rotation is changed, and the particle is required, instead of (so to speak) remaining in the plane of the paper--in the side view--to approach and pass through that plane at _b_ and afterward to continue receding from us. Under ordinary circumstances, this is just what it would do: but if, as in the gyroscope, the axle _oo´_ is perfectly free to move in any direction, the particle _x_ will refuse to change its direction of rotation. Its position has been shifted: it no longer lies in the plane of the paper: but it will at least persist in rotating in a parallel plane: and this persistence forces the revolving disc to swing into the new position indicated by the curve _hg_, the axis being tipped into the position _pq_. The whole effect of all particles like _x_ in the entire wheel will be found to produce precisely this condition of things: if we undertake to change the plane of rotation by shifting the axle in a horizontal plane, the device itself will (if not prevented) make a further change in the plane of rotation by shifting the axle in a vertical plane.

A revolving disc mounted on the gyroscopic framework therefore resists influences tending to change its plane of rotation. If the device is placed on a steamship, so that when the vessel rolls a change of rotative plane is produced, the action of the gyroscope will resist the rolling tendency of the vessel. All that is necessary is to have the wheel revolving in a fore and aft plane on the center line of the vessel, the axle being transverse and firmly attached to the vessel itself. A small amount of power (consumed in revolving the wheel) gives a marked steadying effect. The same location and arrangement on an aeroplane will suffice to overcome tendencies to transverse rotation when rounding curves. The device itself is automatic, and requires no attention, but it does unfortunately require power to drive it and it adds some weight.

The gyroscope is being tested at the present time on some of the aeroplanes at the temporary army camps near San Antonio, Texas.

Wind Gusts

This feature of aeronautics is particularly important, because any device which will give automatic stability when turning corners will go far toward making aviation a safe amusement. Inequalities of velocity exist not only on curves, but also when the wind is blowing at anything but uniform velocity across the whole front of the machine. The slightest "flaw" in the wind means an at least temporary variation in lifting force of the two arms. Here is a pregnant source of danger, and one which cannot be left for the aviator to meet by conscious thought and action. It is this, then, that blindfolds him: he cannot see the wind conditions in advance. The conditions are upon him, and may have done their destructive work, before he can prepare to control them. We must now study what these conditions are and what their influence may be on various forms of aerial navigation: after which, a return to our present subject will be possible.

AIR AND THE WIND

The air that surrounds us weighs about one-thirteenth of a pound per cubic foot and exerts a pressure, at sea level, of nearly fifteen pounds per square inch. Its temperature varies from 30° below to 100° above the Fahrenheit zero. The pressure of the air decreases about one-half pound for each thousand feet of altitude; at the top of Mt. Blanc it would be, therefore, only about six pounds per square inch. The temperature also decreases with the altitude. The weight of a cubic foot, or _density_, which, as has been stated, is one-thirteenth of a pound ordinarily, varies with the pressure and with the temperature. The variation with pressure may be described by saying that the _quotient_ of the pressure by the density is constant: one varies in the same ratio as the other. Thus, at the top of Mt. Blanc (if the temperature were the same as at sea level), the density of air would be about 6/15 × 1/13 = 2/65: less than half what it is at sea level. As to temperature, if we call our Fahrenheit zero 460°, and correspondingly describe other temperatures--for instance, say that water boils at 672°--then (pressure being unchanged) the _product_ of the density and the temperature is constant. If the density at sea level and zero temperature is one-thirteenth pound, then that at sea level and 460° Fahrenheit would be

(0 + 460)/(460 + 460) × 1/13 = 1/26.

These relations are particularly important in the design of all balloons, and in computations relating to aeroplane flight at high altitudes. We shall be prepared to appreciate some of their applications presently.

Generally speaking, the atmosphere is always in motion, and moving air is called wind. Our meteorologists first studied winds near the surface of the ground: it is only of late years that high altitude measurements have been considered practically desirable. Now, records are obtained by the aid of kites up to a height of nearly four miles: estimates of cloud movements have given data on wind velocities at heights above six miles: and much greater heights have been obtained by free balloons equipped with instruments for recording temperatures, pressures, altitude, time, and other data.

When the Eiffel Tower was completed, it was found that the average wind velocity at its summit was about four times that at the base. Since that time, much attention has been given to the contrasting conditions of surface and upper breezes as to direction and velocity.