CHAPTER III THE FORM OR SHAPE OF FLYING MACHINES

CHAPTER VII ABNORMAL FLYING STUNTS AND SPEEDS

CHAPTER XII EXPERIMENTAL WORK IN FLYING

Copyright laws are changing all over the world, be sure to check the copyright laws for your country before posting these files!!

Please take a look at the important information in this header. We encourage you to keep this file on your own disk, keeping an electronic path open for the next readers. Do not remove this.

**Etexts Readable By Both Humans and By Computers, Since 1971**

*These Etexts Prepared By Hundreds of Volunteers and Donations*

Aeroplanes

by J. S. Zerbe***

September, 1998 [Etext #1445]

We are now trying to release all our books one month in advance of the official release dates, for time for better editing.

We produce about two million dollars for each hour we work. The fifty hours is one conservative estimate for how long it we take to get any etext selected, entered, proofread, edited, copyright searched and analyzed, the copyright letters written, etc. This projected audience is one hundred million readers. If our value per text is nominally estimated at one dollar then we produce $2 million dollars per hour this year as we release thirty-two text files per month, or 384 more Etexts in 1998 for a total of 1500+ If these reach just 10% of the computerized population, then the total should reach over 150 billion Etexts given away.

We need your donations more than ever!

For these and other matters, please mail to:

When all other email fails try our Executive Director:
Michael S. Hart <hart@pobox.com>

We would prefer to send you this information by email
(Internet, Bitnet, Compuserve, ATTMAIL or MCImail).

ftp uiarchive.cso.uiuc.edu login: anonymous password: your@login cd etext/etext90 through /etext96 or cd etext/articles [get suggest gut for more information] dir [to see files] get or mget [to get files. . .set bin for zip files] GET INDEX?00.GUT for a list of books and GET NEW GUT for general information and MGET GUT* for newsletters.

***START**THE SMALL PRINT!**FOR PUBLIC DOMAIN ETEXTS**START*** Why is this "Small Print!" statement here? You know: lawyers. They tell us you might sue us if there is something wrong with your copy of this etext, even if you got it for free from someone other than us, and even if what's wrong is not our fault. So, among other things, this "Small Print!" statement disclaims most of our liability to you. It also tells you how you can distribute copies of this etext if you want to.

To create these etexts, the Project expends considerable efforts to identify, transcribe and proofread public domain works. Despite these efforts, the Project's etexts and any medium they may be on may contain "Defects". Among other things, Defects may take the form of incomplete, inaccurate or corrupt data, transcription errors, a copyright or other intellectual property infringement, a defective or damaged disk or other etext medium, a computer virus, or computer codes that damage or cannot be read by your equipment.

If you discover a Defect in this etext within 90 days of receiving it, you can receive a refund of the money (if any) you paid for it by sending an explanatory note within that time to the person you received it from. If you received it on a physical medium, you must return it with your note, and such person may choose to alternatively give you a replacement copy. If you received it electronically, such person may choose to alternatively give you a second opportunity to receive it electronically.

THIS ETEXT IS OTHERWISE PROVIDED TO YOU "AS-IS". NO OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, ARE MADE TO YOU AS TO THE ETEXT OR ANY MEDIUM IT MAY BE ON, INCLUDING BUT NOT LIMITED TO WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.

INDEMNITY You will indemnify and hold the Project, its directors, officers, members and agents harmless from all liability, cost and expense, including legal fees, that arise directly or indirectly from any of the following that you do or cause: [1] distribution of this etext, [2] alteration, modification, or addition to the etext, or [3] any Defect.

[1] Only give exact copies of it. Among other things, this requires that you do not remove, alter or modify the etext or this "small print!" statement. You may however, if you wish, distribute this etext in machine readable binary, compressed, mark-up, or proprietary form, including any form resulting from conversion by word pro- cessing or hypertext software, but only so long as *EITHER*:

[*] The etext, when displayed, is clearly readable, and does *not* contain characters other than those intended by the author of the work, although tilde (~), asterisk (*) and underline (_) characters may be used to convey punctuation intended by the author, and additional characters may be used to indicate hypertext links; OR

[*] The etext may be readily converted by the reader at no expense into plain ASCII, EBCDIC or equivalent form by the program that displays the etext (as is the case, for instance, with most word processors); OR

[*] You provide, or agree to also provide on request at no additional cost, fee or expense, a copy of the etext in its original plain ASCII form (or in EBCDIC or other equivalent proprietary form).

[2] Honor the etext refund and replacement provisions of this "Small Print!" statement.

*END*THE SMALL PRINT! FOR PUBLIC DOMAIN ETEXTS*Ver.04.29.93*END*

Aeroplanes

by J. S. Zerbe

Scanned by Charles Keller with OmniPage Professional OCR software

AEROPLANES

This work is not intended to set forth the exploits of aviators nor to give a history of the Art. It is a book of instructions intended to point out the theories of flying, as given by the pioneers, the practical application of power to the various flying structures; how they are built, the different methods of controlling them; the advantages and disadvantages of the types now in use; and suggestions as to the directions in which improvements are required.

It distinctly points out wherein mechanical flight differs from bird flight, and what are the relations of shape, form, size and weight. It treats of kites, gliders and model aeroplanes, and has an Interesting chapter on the aeroplane and its uses In the great war. All the illustrations have been specially prepared for the work.

Every Boy's Mechanical Library

AEROPLANES

BY
J. S. ZERBE, M. E.
Author of Automobiles—Motors

COPYRIGHT, 1915, BY
CUPPLES & LEON COMPANY
NY

CONTENTS

INTRODUCTORY

CHAPTER I. THEORIES AND FACTS ABOUT FLYING

The "Science" of Aviation. Machine Types. Shape
or Form not Essential. A Stone as a Flying Machine.
Power the Great Element. Gravity as Power. Mass
and Element in Flying. Momentum a Factor. Resistance.
How Resistance Affects Shape. Mass and Resistance.
The Early Tendency to Eliminate Momentum.
Light Machines Unstable. The Application of
Power. The Supporting Surfaces. Area not the Essential
Thing. The Law of Gravity. Gravity. Indestructibility
of Gravitation. Distance Reduces Gravitational
Pull. How Motion Antagonizes Gravity. A
Tangent. Tangential Motion Represents Centrifugal
Pull. Equalizing the Two Motions. Lift and Drift.
Normal Pressure. Head Resistance. Measuring Lift
and Drift. Pressure at Different Angles. Difference
Between Lift and Drift in Motion. Tables of Lift and
Drift. Why Tables of Lift and Drift are Wrong.
Langley's Law. Moving Planes vs. Winds. Momentum
not Considered. The Flight of Birds. The
Downward Beat. The Concaved Wing. Feather Structure
Considered. Webbed Wings. The Angle of Movement.
An Initial Movement or Impulse Necessary. A
Wedging Motion. No Mystery in the Wave Motion.
How Birds Poise with Flapping Wings. Narrow-
winged Birds. Initial Movement of Soaring Birds.
Soaring Birds Move Swiftly. Muscular Energy
Exerted by Soaring Birds. Wings not Motionless.

CHAPTER II. PRINCIPLES OF AEROPLANE FLIGHT Speed as one of the Elements. Shape and Speed. What "Square of the Speed" Means. Action of a "Skipper." Angle of Incidence. Speed and Surface. Control of the Direction of Flight. Vertical Planes.

CHAPTER III. THE FORM OR SHAPE OF FLYING MACHINES The Theory of Copying Nature. Hulls of Vessels. Man Does not Copy Nature. Principles Essential, not Forms. Nature not the Guide as to Forms. The Propeller Type. Why Specially-designed Forms Improve Natural Structures. Mechanism Devoid of Intelligence. A Machine Must Have a Substitute for Intelligence. Study of Bird Flight Useless. Shape of Supporting Surface. The Trouble Arising From Outstretched Wings. Density of the Atmosphere. Elasticity of the Air. "Air Holes." Responsibility for Accidents. The Turning Movement. Centrifugal Action: The Warping Planes.

CHAPTER IV. FORE AND AFT CONTROL The Bird Type of Fore and Aft Control. Angle and Direction of Flight. Why Should the Angle of the Body Change. Changing Angle of Body not Safe. A Non-changing Body. Descending Positions by Power Control. Cutting off the Power. The Starting Movement. The Suggested Type. The Low Center of Gravity. Fore and Aft Oscillations. Application of the New Principle. Low Weight not Necessary with Synchronously- moving wings.

CHAPTEB V. DIFFERENT MACHINE TYPES AND THEIR CHARACTERISTICS The Helicopter. Aeroplanes. The Monoplane. Its Advantages. Its Disadvantages. The Bi-plane. Stability in Bi-planes. The Orthopter. Nature's Type not Uniform. Theories About Flight of Birds. Instinct. The Mode of Motion. The Wing Structure. The Wing Movement. The Helicopter Motion.

CHAPTER VI. THE LIFTING SURFACES OF AEROPLANES Relative Speed and Angle. Narrow Planes Most Effective. Stream Lines Along a Plane. The Center of Pressure. Air Lines on the Upper Side of a Plane. Rarefied Area. Rarefaction Produced by Motion. The Concaved Plane. The Center of Pressure. Utilizing the Rarefied Area. Changing Center of Pressure. Plane Monstrosities. The Bird Wing Structure. Torsion. The Bat's Wing. An Abnormal Shape. The Tail as a Monitor.

CHAPTER VII. ABNORMAL FLYING STUNTS AND SPEEDS Lack of Improvements in Machines. Men Exploited and not Machines. Abnormal Flying of no Value. The Art of Juggling. Practical Uses the Best Test. Concaved and Convex Planes. How Momentum is a Factor in Inverted Flying. The Turning Movement. When Concaved Planes are Desirable. The Speed Mania. Uses of Flying Machines. Perfection in Machines Must Come Before Speed. The Range of its Uses. Commercial Utility.

CHAPTER VIII. KITES AND GLIDERS The Dragon Kite. Its Construction. The Malay Kite. Dihedral Angle. The Common Kite. The Bow Kite. The Box Kite. The Voison Bi-plane. Lateral Stability in Kites, not Conclusive as to Planes. The Spear Kite. The Cellular Kite. Tetrahedral Kite. The Deltoid. The Dunne Flying Machine. Rotating Kite. Kite Principles. Lateral Stability in Kites. Similarity of Fore and Aft Control. Gliding Flight One of the Uses of Glider Experiments. Hints in Gliding.

CHAPTER IX. AEROPLANE CONSTRUCTION Lateral and Fore and Aft. Transverse. Stability and Stabilization. The Wright System. Controlling the Warping Ends. The Curtiss Wings. The Farman Ailerons. Features Well Developed. Depressing the Rear End. Determining the Size. Rule for Placing the Planes. Elevating Plane. Action in Alighting. The Monoplane. The Common Fly. Stream Lines. The Monoplane Form.

CHAPTER X. POWER AND ITS APPLICATION Features in Power Application. Amount of Power Necessary. The Pull of the Propeller. Foot Pounds Small Amount of Power Available. High Propeller Speed Important. Width and Pitch of Blades. Effect of Increasing Propeller Pull. Disposition of the Planes. Different Speeds with Same Power. Increase of Speed Adds to Resistance. How Power Decreases with Speed. How to Calculate the Power Applied. Pulling Against an Angle. The Horizontal and the Vertical Pull. The Power Mounting. Securing the Propeller to the Shaft. Vibrations. Weaknesses in Mounting. The Gasoline Tank. Where to Locate the Tank. The Danger to the Pilot. The Closed-in Body. Starting the Machine. Propellers with Varying Pitch.

CHAPTER XI. FLYING MACHINE ACCESSORIES The Anemometer. The Anemograph. The Anemometrograph. The Speed Indicator. Air Pressure Indicator. Determining the Pressure From the Speed. Calculating Pressure From Speed. How the Figures are Determined. Converting Hours Into Minutes. Changing Speed Hours to Seconds. Pressure as the Square of the Speed. Gyroscopic:Balance. The Principles Involved. The Application of the Gyroscope. Fore and Aft Gyroscopic Control. Angle Indicator. Pendulum Stabilizer. Steering and Controlling Wheel. Automatic Stabilizing Wings. Barometers. Aneroid Barometer. Hydroplanes. Sustaining Weight of Pontoons. Shape of the Pontoon.

CHAPTER XII. EXPERIMENTAL WORK IN FLYING Certain Conditions in Flying. Heat in Air. Motion When in Flight. Changing Atmosphere. "Ascending Currents." "Aspirate Currents." Outstretched Wings. The Starting Point. The Vital Part of the Machine. Studying the Action of the Machine. Elevating the Machine. How to Practice. The First Stage. Patience the Most Difficult Thing. The Second Stage. The Third Stage. Observations While in Flight. Flying in a Wind. First Trials in a Quiet Atmosphere. Making Turns. The Fourth Stage. The Figure 8. The Vol Plane. The Landing. Flying Altitudes.

CHAPTER XIII. THE PROPELLER Propeller Changes. Propeller Shape. The Diameter. Pitch. Laying Out the Pitch. Pitch Rule. Laminated Construction. Laying up a Propeller Form. Making Wide Blades. Propeller Outline. For High Speeds. Increasing Propeller Efficiency.

CHAPTER XIV. EXPERIMENTAL GLIDERS AND MODEL AEROPLANES The Relation of Models to Flying Machines. Lessons From Models. Flying Model Aeroplanes. An Efficient Glider. The Deltoid Formation. Racing Models. The Power for Model Aeroplanes. Making the Propeller. Material for the Propeller. Rubber. Propeller Shape and Size. Supporting Surfaces.

CHAPTER XV. THE AEROPLANE IN THE GREAT WAR Balloon Observations. Changed Conditions in Warfare. The Effort to Conceal Combatants. Smokeless Powder. Inventions to Attack Aerial Craft. Functions of the Aeroplane in War. Bomb-throwing Tests. Method for Determining the Movement of a Bomb. The Great Extent of Modern Battle Lines. The Aeroplane Detecting the Movements of Armies. The Effective Height for Scouting. Sizes of Objects at Great Distances. Some Daring Feats in War. The German Taube. How Aeroplanes Report Observations. Signal Flags. How Used. Casualties Due to Bombs From Aeroplanes.

GLOSSARY

INTRODUCTORY

In preparing this volume on Flying Machines the aim has been to present the subject in such a manner as will appeal to boys, or beginners, in this field of human activity.

The art of aviation is in a most primitive state. So many curious theories have been brought out that, while they furnish food for thought, do not, in any way, advance or improve the structure of the machine itself, nor are they of any service in teaching the novice how to fly.

The author considers it of far more importance to teach right principles, and correct reasoning than to furnish complete diagrams of the details of a machine. The former teach the art, whereas the latter merely point out the mechanical arrangements, independently of the reasons for making the structures in that particular way.

Relating the history of an art, while it may be interesting reading, does not even lay the foundations of a knowledge of the subject, hence that field has been left to others.

The boy is naturally inquisitive, and he is interested in knowing WHY certain things are necessary, and the reasons for making structures in particular ways. That is the void into which these pages are placed.

The author knows from practical experience, while experimenting with and building aeroplanes, how eagerly every boy inquires into details. They want the reasons for things.

One such instance is related to evidence this spirit of inquiry. Some boys were discussing the curved plane structure. One of them ventured the opinion that birds' wings were concaved on the lower side. "But," retorted another, "why are birds' wings hollowed?"

This was going back to first principles at one leap. It was not satisfying enough to know that man was copying nature. It was more important to know why nature originated that type of formation, because, it is obvious, that if such structures are universal in the kingdom of flying creatures, there must be some underlying principle which accounted for it.

It is not the aim of the book to teach the art of flying, but rather to show how and why the present machines fly. The making and the using are separate and independent functions, and of the two the more important is the knowledge how to make a correct machine.

Hundreds of workmen may contribute to the building of a locomotive, but one man, not a builder, knows better how to handle it. To manipulate a flying machine is more difficult to navigate than such a ponderous machine, because it requires peculiar talents, and the building is still more important and complicated, and requires the exercise of a kind of skill not necessary in the locomotive.

The art is still very young; so much is done which arises from speculation and theories; too much dependence is placed on the aviator; the desire in the present condition of the art is to exploit the man and not the machine; dare-devil exhibitions seem to be more important than perfecting the mechanism; and such useless attempts as flying upside down, looping the loop, and characteristic displays of that kind, are of no value to the art. THE AUTHOR.

AEROPLANES

CHAPTER I

THEORIES AND FACTS ABOUT FLYING

THE "SCIENCE" OF AVIATION.—It may be doubted whether there is such a thing as a "science of aviation." Since Langley, on May 6, 1896, flew a motor-propelled tandem monoplane for a minute and an half, without a pilot, and the Wright Brothers in 1903 succeeded in flying a bi-plane with a pilot aboard, the universal opinion has been, that flying machines, to be successful, must follow the structural form of birds, and that shape has everything to do with flying.

We may be able to learn something by carefully examining the different views presented by those interested in the art, and then see how they conform to the facts as brought out by the actual experiments.

MACHINE TYPES.—There is really but one type of plane machine. While technically two forms are known, namely, the monoplane and the bi-plane, they are both dependent on outstretched wings, longer transversely than fore and aft, so far as the supporting surfaces are concerned, and with the main weight high in the structure, thus, in every particular, conforming to the form pointed out by nature as the apparently correct type of a flying structure.

SHAPE OR FORM NOT ESSENTIAL.—It may be stated with perfect confidence, that shape or form has nothing to do with the mere act of flying. It is simply a question of power. This is a broad assertion, and its meaning may be better understood by examining the question of flight in a broad sense.

A STONE AS A FLYING MACHINE.—When a stone is propelled through space, shape is of no importance. If it has rough and jagged sides its speed or its distance may be limited, as compared with a perfectly rounded form. It may be made in such a shape as will offer less resistance to the air in flight, but its actual propulsion through space does not depend on how it is made, but on the power which propelled it, and such a missile is a true heavier-than-air machine.

A flying object of this kind may be so constructed that it will go a greater distance, or require less power, or maintain itself in space at less speed; but it is a flying machine, nevertheless, in the sense that it moves horizontally through the air.

POWER THE GREAT ELEMENT.—Now, let us examine the question of this power which is able to set gravity at naught. The quality called energy resides in material itself. It is something within matter, and does not come from without. The power derived from the explosion of a charge of powder comes from within the substance; and so with falling water, or the expansive force of steam.

GRAVITY AS POWER.—Indeed, the very act of the ball gradually moving toward the earth, by the force of gravity, is an illustration of a power within the object itself. Long after Galileo firmly established the law of falling bodies it began to dawn on scientists that weight is force. After Newton established the law of gravitation the old idea, that power was a property of each body, passed away.

In its stead we now have the firmly established view, that power is something which must have at least two parts, or consist in pairs, or two elements acting together. Thus, a stone poised on a cliff, while it exerts no power which can be utilized, has, nevertheless, what is called potential energy. When it is pushed from its lodging place kinetic energy is developed. In both cases, gravity, acting in conjunction with the mass of the stone, produced power.

So in the case of gunpowder. It is the unity of two or more substances, that causes the expansion called power. The heat of the fuel converting water into steam, is another illustration of the unity of two or more elements, which are necessary to produce energy.

MASS AN ELEMENT IN FLYING.—The boy who reads this will smile, as he tells us that the power which propelled the ball through the air came from the thrower and not from the ball itself. Let us examine this claim, which came from a real boy, and is another illustration how acute his mind is on subjects of this character.

We have two balls the same diameter, one of iron weighing a half pound, and the other of cotton weighing a half ounce. The weight of one is, therefore, sixteen times greater than the other.

Suppose these two balls are thrown with the expenditure of the same power. What will be the result! The iron ball will go much farther, or, if projected against a wall will strike a harder blow than the cotton ball.

MOMENTUM A FACTOR.—Each had transferred to it a motion. The initial speed was the same, and the power set up equal in the two. Why this difference, The answer is, that it is in the material itself. It was the mass or density which accounted for the difference. It was mass multiplied by speed which gave it the power, called, in this case, momentum.

The iron ball weighing eight ounces, multiplied by the assumed speed of 50 feet per second, equals 400 units of work. The cotton ball, weighing 1/2 ounce, with the same initial speed, represents 25 units of work. The term "unit of work" means a measurement, or a factor which may be used to measure force.

It will thus be seen that it was not the thrower which gave the power, but the article itself. A feather ball thrown under the same conditions, would produce a half unit of work, and the iron ball, therefore, produced 800 times more energy.

RESISTANCE.—Now, in the movement of any body through space, it meets with an enemy at every step, and that is air resistance. This is much more effective against the cotton than the iron ball: or, it might be expressed in another way: The momentum, or the power, residing in the metal ball, is so much greater than that within the cotton ball that it travels farther, or strikes a more effective blow on impact with the wall.

HOW RESISTANCE AFFECTS THE SHAPE.—It is because of this counterforce, resistance, that shape becomes important in a flying object. The metal ball may be flattened out into a thin disk, and now, when the same force is applied, to project it forwardly, it will go as much farther as the difference in the air impact against the two forms.

MASS AND RESISTANCE.—Owing to the fact that resistance acts with such a retarding force on an object of small mass, and it is difficult to set up a rapid motion in an object of great density, lightness in flying machine structures has been considered, in the past, the principal thing necessary.

THE EARLY TENDENCY TO ELIMINATE MOMENTUM.— Builders of flying machines, for several years, sought to eliminate the very thing which gives energy to a horizontally-movable body, namely, momentum.

Instead of momentum, something had to be substituted. This was found in so arranging the machine that its weight, or a portion of it, would be sustained in space by the very element which seeks to retard its flight, namely, the atmosphere.

If there should be no material substance, like air, then the only way in which a heavier-than-air machine could ever fly, would be by propelling it through space, like the ball was thrown, or by some sort of impulse or reaction mechanism on the air-ship itself. It could get no support from the atmosphere.

LIGHT MACHINES UNSTABLE.—Gradually the question of weight is solving itself. Aviators are beginning to realize that momentum is a wonderful property, and a most important element in flying. The safest machines are those which have weight. The light, willowy machines are subject to every caprice of the wind. They are notoriously unstable in flight, and are dangerous even in the hands of experts.

THE APPLICATION OF POWER.—The thing now to consider is not form, or shape, or the distribution of the supporting surfaces, but HOW to apply the power so that it will rapidly transfer a machine at rest to one in motion, and thereby get the proper support on the atmosphere to hold it in flight.

THE SUPPORTING SURFACES.—This brings us to the consideration of one of the first great problems in flying machines, namely, the supporting surfaces,—not its form, shape or arrangement, (which will be taken up in their proper places), but the area, the dimensions, and the angle necessary for flight.

AREA NOT THE ESSENTIAL THING.—The history of flying machines, short as it is, furnishes many examples of one striking fact: That area has but little to do with sustaining an aeroplane when once in flight. The first Wright flyer weighed 741 pounds, had about 400 square feet of plane surface, and was maintained in the air with a 12 horse power engine.

True, that machine was shot into the air by a catapult. Motion having once been imparted to it, the only thing necessary for the motor was to maintain the speed.

There are many instances to show that when once in flight, one horse power will sustain over 100 pounds, and each square foot of supporting surface will maintain 90 pounds in flight.

THE LAW OF GRAVITY.—As the effort to fly may be considered in the light of a struggle to avoid the laws of nature with respect to matter, it may be well to consider this great force as a fitting prelude to the study of our subject.

Proper understanding, and use of terms is very desirable, so that we must not confuse them. Thus, weight and mass are not the same. Weight varies with the latitude, and it is different at various altitudes; but mass is always the same.

If projected through space, a certain mass would move so as to produce momentum, which would be equal at all places on the earth's surface, or at any altitude.

Gravity has been called weight, and weight gravity. The real difference is plain if gravity is considered as the attraction of mass for mass. Gravity is generally known and considered as a force which seeks to draw things to the earth. This is too narrow.

Gravity acts in all directions. Two balls suspended from strings and hung in close proximity to each other will mutually attract each other. If one has double the mass it will have twice the attractive power. If one is doubled and the other tripled, the attraction would be increased six times. But if the distance should be doubled the attraction would be reduced to one-fourth; and if the distance should be tripled then the pull would be only one-ninth.

The foregoing is the substance of the law, namely, that all bodies attract all other bodies with a force directly in proportion to their mass, and inversely as the square of their distance from one another.

To explain this we cite the following illustration: Two bodies, each having a mass of 4 pounds, and one inch apart, are attracted toward each other, so they touch. If one has twice the mass of the other, the smaller will draw the larger only one-quarter of an inch, and the large one will draw the other three-quarters of an inch, thus confirming the law that two bodies will attract each other in proportion to their mass.

Suppose, now, that these balls are placed two inches apart,—that is, twice the distance. As each is, we shall say, four pounds in weight, the square of each would be 16. This does not mean that there would be sixteen times the attraction, but, as the law says, inversely as the square of the distance, so that at two inches there is only one-sixteenth the attraction as at one inch.

If the cord of one of the balls should be cut, it would fall to the earth, for the reason that the attractive force of the great mass of the earth is so much greater than the force of attraction in its companion ball.

INDESTRUCTIBILITY OF GRAVITATION.—Gravity cannot be produced or destroyed. It acts between all parts of bodies equally; the force being proportioned to their mass. It is not affected by any intervening substance; and is transmitted instantaneously, whatever the distance may be.

While, therefore, it is impossible to divest matter of this property, there are two conditions which neutralize its effect. The first of these is position. Let us take two balls, one solid and the other hollow, but of the same mass, or density. If the cavity of the one is large enough to receive the other, it is obvious that while gravity is still present the lines of attraction being equal at all points, and radially, there can be no pull which moves them together.

DISTANCE REDUCES GRAVITATIONAL PULL.—Or the balls may be such distance apart that the attractive force ceases. At the center of the earth an object would not weigh anything. A pound of iron and an ounce of wood, one sixteen times the mass of the other, would be the same,—absolutely without weight.

If the object should be far away in space it would not be influenced by the earth's gravity; so it will be understood that position plays an important part in the attraction of mass for mass.

HOW MOTION ANTAGONIZES GRAVITY.—The second way to neutralize gravity, is by motion. A ball thrown upwardly, antagonizes the force of gravity during the period of its ascent. In like manner, when an object is projected horizontally, while its mass is still the same, its weight is less.

Motion is that which is constantly combating the action of gravity. A body moving in a circle must be acted upon by two forces, one which tends to draw it inwardly, and the other which seeks to throw it outwardly.

The former is called centripetal, and the latter centrifugal motion. Gravity, therefore, represents centripetal, and motion centrifugal force.

If the rotative speed of the earth should be retarded, all objects on the earth would be increased in weight, and if the motion should be accelerated objects would become lighter, and if sufficient speed should be attained all matter would fly off the surface, just as dirt dies off the rim of a wheel at certain speeds.

A TANGENT.—When an object is thrown horizontally the line of flight is tangential to the earth, or at right angles to the force of gravity. Such a course in a flying machine finds less resistance than if it should be projected upwardly, or directly opposite the centripetal pull.

Fig 1. Tangential Flight

TANGENTIAL MOTION REPRESENTS CENTRIFUGAL PULL.—A tangential motion, or a horizontal movement, seeks to move matter away from the center of the earth, and any force which imparts a horizontal motion to an object exerts a centrifugal pull for that reason.

In Fig. 1, let A represent the surface of the earth, B the starting point of the flight of an object, and C the line of flight. That represents a tangential line. For the purpose of explaining the phenomena of tangential flight, we will assume that the missile was projected with a sufficient force to reach the vertical point D, which is 4000 miles from the starting point B.

In such a case it would now be over 5500 miles from the center of the earth, and the centrifugal pull would be decreased to such an extent that the ball would go on and on until it came within the sphere of influence from some other celestial body.

EQUALIZING THE TWO MOTIONS.—But now let us assume that the line of flight is like that shown at E, in Fig. 2, where it travels along parallel with the surface of the earth. In this case the force of the ball equals the centripetal pull,—or, to put it differently, the centrifugal equals the gravitational pull.

The constant tendency of the ball to fly off at a tangent, and the equally powerful pull of gravity acting against each other, produce a motion which is like that of the earth, revolving around the sun once every three hundred and sixty-five days.

It is a curious thing that neither Langley, nor any of the scientists, in treating of the matter of flight, have taken into consideration this quality of momentum, in their calculations of the elements of flight.

Fig. 2 Horizontal Flight

All have treated the subject as though the whole problem rested on the angle at which the planes were placed. At 45 degrees the lift and drift are assumed to be equal.

LIFT AND DRIFT.—The terms should be explained, in view of the frequent allusion which will be made to the terms hereinafter. Lift is the word employed to indicate the amount which a plane surface will support while in flight. Drift is the term used to indicate the resistance which is offered to a plane moving forwardly against the atmosphere.

Fig. 3. Lift and Drift

In Fig. 3 the plane A is assumed to be moving forwardly in the direction of the arrow B. This indicates the resistance. The vertical arrow C shows the direction of lift, which is the weight held up by the plane.

NORMAL PRESSURE.—Now there is another term much used which needs explanation, and that is normal pressure. A pressure of this kind against a plane is where the wind strikes it at right angles. This is illustrated in Fig. 4, in which the plane is shown with the wind striking it squarely.

It is obvious that the wind will exert a greater force against a plane when at its normal. On the other hand, the least pressure against a plane is when it is in a horizontal position, because then the wind has no force against the surfaces, and the only effect on the drift is that which takes place when the wind strikes its forward edge.

Fig. 4. Normal Air Pressure

Fig. 5. Edge Resistance

HEAD RESISTANCE.—Fig. 5 shows such a plane, the only resistance being the thickness of the plane as at A. This is called head resistance, and on this subject there has been much controversy, and many theories, which will be considered under the proper headings.

If a plane is placed at an angle of 45 degrees the lift and the drift are the same, assumedly, because, if we were to measure the power required to drive it forwardly, it would be found to equal the weight necessary to lift it. That is, suppose we should hold a plane at that angle with a heavy wind blowing against it, and attach two pairs of scales to the plane, both would show the same pull.

Fig. 6. Measuring Lift and Drift

MEASURING LIFT AND DRIFT.—In Fig. 6, A is the plane, B the horizontal line which attaches the plane to a scale C, and D the line attaching it to the scale E. When the wind is of sufficient force to hold up the plane, the scales will show the same pull, neglecting, of course, the weight of the plane itself.

PRESSURE AT DIFFERENT ANGLES.—What every one wants to know, and a subject on which a great deal of experiment and time have been expended, is to determine what the pressures are at the different angles between the horizontal, and laws have been formulated which enable the pressures to be calculated.

DIFFERENCE BETWEEN LIFT AND DRIFT IN MOTION.—The first observation is directed to the differences that exist between the lift and drift, when the plane is placed at an angle of less than 45 degrees. A machine weighing 1000 pounds has always the same lift. Its mass does not change. Remember, now, we allude to its mass, or density.

We are not now referring to weight, because that must be taken into consideration, in the problem. As heretofore stated, when an object moves horizontally, it has less weight than when at rest. If it had the same weight it would not move forwardly, but come to rest.

When in motion, therefore, while the lift, so far as its mass is concerned, does not change, the drift does decrease, or the forward pull is less than when at 45 degrees, and the decrease is less and less until the plane assumes a horizontal position, where it is absolutely nil, if we do not consider head resistance.

TABLES OF LIFT AND DRIFT.—All tables of Lift and Drift consider only the air pressures. They do not take into account the fact that momentum takes an important part in the translation of an object, like a flying machine.

A mass of material, weighing 1000 pounds while at rest, sets up an enormous energy when moving through the air at fifty, seventy-five, or one hundred miles an hour. At the latter speed the movement is about 160 feet per second, a motion which is nearly sufficient to maintain it in horizontal flight, independently of any plane surface.

Such being the case, why take into account only the angle of the plane? It is no wonder that aviators have not been able to make the theoretical considerations and the practical demonstrations agree.

WHY TABLES OF LIFT AND DRIFT ARE WRONG.— A little reflection will show why such tables are wrong. They were prepared by using a plane surface at rest, and forcing a blast of air against the plane placed at different angles; and for determining air pressures, this is, no doubt, correct. But it does not represent actual flying conditions. It does not show the conditions existing in an aeroplane while in flight.

To determine this, short of actual experiments with a machine in horizontal translation, is impossible, unless it is done by taking into account the factor due to momentum and the element attributable to the lift of the plane itself due to its impact against the atmosphere.

LANGLEY'S LAW.—The law enunciated by Langley is, that the greater the speed the less the power required to propel it. Water as a propelling medium has over seven hundred times more force than air. A vessel having, for instance, twenty horse power, and a speed of ten miles per hour, would require four times that power to drive it through the water at double the speed. The power is as the square of the speed.

With air the conditions are entirely different. The boat submergence in the water is practically the same, whether going ten or twenty miles an hour. The head resistance is the same, substantially, at all times in the case of the boat; with the flying machine the resistance of its sustaining surfaces decreases.

Without going into a too technical description of the reasoning which led to the discovery of the law of air pressures, let us try and understand it by examining the diagram, Fig. 7.

A represents a plane at an angle of 45 degrees, moving forwardly into the atmosphere in the direction of the arrows B. The measurement across the plane vertically, along the line B, which is called the sine of the angle, represents the surface impact of air against the plane.

In Fig. 8 the plane is at an angle of 27 degrees, which makes the distance in height across the line C just one-half the length of the line B of Fig. 7, hence the surface impact of the air is one-half that of Fig. 7, and the drift is correspondingly decreased.

Fig. 7. Equal Lift and Drift in Flight.

Fig. 8. Unequal Lift and Drift.

MOVING PLANES VS. WINDS.—In this way Boisset, Duchemin, Langley, and others, determined the comparative drift, and those results have been largely relied upon by aviators, and assumed to be correct when applied to flying machines.

That they are not correct has been proven by the Wrights and others, the only explanation being that some errors had been made in the calculations, or that aviators were liable to commit errors in observing the true angle of the planes while in flight.

MOMENTUM NOT CONSIDERED.—The great factor of momentum has been entirely ignored, and it is our desire to press the important point on those who begin to study the question of flying machines.

THE FLIGHT OF BIRDS.—Volumes have been written concerning observations on the flight of birds. The marvel has been why do soaring birds maintain themselves in space without flapping their wings. In fact, it is a much more remarkable thing to contemplate why birds which depend on flapping wings can fly.

THE DOWNWARD BEAT.—It is argued that the downward beat of the wings is so much more rapid than the upward motion, that it gets an action on the air so as to force the body upwardly. This is disposed of by the wing motion of many birds, notoriously the crow, whose lazily-flapping wings can be readily followed by the eye, and the difference in movement, if any, is not perceptible.

THE CONCAVED WING.—It is also urged that the concave on the under side of the wing gives the quality of lift. Certain kinds of beetles, and particularly the common house fly, disprove that theory, as their wings are perfectly flat.

FEATHER STRUCTURE CONSIDERED.—Then the feather argument is advanced, which seeks to show that as each wing is made up of a plurality of feathers, overlapping each other, they form a sort of a valved surface, opening so as to permit air to pass through them during the period of their upward movement, and closing up as the wing descends.

It is difficult to perform this experiment with wings, so as to show such an individual feather movement. It is certain that there is nothing in the structure of the wing bone and the feather connection which points to any individual feather movement, and our observation is, that each feather is entirely too rigid to permit of such an opening up between them.

It is obvious that the wing is built up in that way for an entirely different reason. Soaring birds, which do not depend on the flapping motion, have the same overlapping feather formation.

WEBBED WINGS.—Furthermore, there are numerous flying creatures which do not have feathered wings, but web-like structures, or like the house fly, in one continuous and unbroken plane.

That birds which fly with flapping wings derive their support from the air, is undoubtedly true, and that the lift produced is due, not to the form, or shape, or area of the wing, is also beyond question. The records show that every conceivable type of outlined structure is used by nature; the material and texture of the wings themselves differ to such a degree that there is absolutely no similarity; some have concaved under surfaces, and others have not; some fly with rapidly beating wings, and others with slow and measured movements; many of them fly with equal facility without flapping movements; and the proportions of weight to wing surface vary to such an extent that it is utterly impossible to use such data as a guide in calculating what the proper surface should be for a correct flying machine.

THE ANGLE OF MOVEMENT.—How, then, it may be asked, do they get their support? There must be something, in all this variety and diversity of form, of motion, and of characteristics, which supplies the true answer. The answer lies in the angle of movement of every wing motion, which is at the control of the bird, and if this is examined it will be found that it supplies the correct answer to every type of wing which nature has made.

AN INITIAL IMPULSE OR MOVEMENT NECESSARY.— Let A, Fig. 9, represent the section of a bird's wing. All birds, whether of the soaring or the flapping kind, must have an initial forward movement in order to attain flight. This impulse is acquired either by running along the ground, or by a leap, or in dropping from a perch. Soaring birds cannot, by any possibility, begin flight, unless there is such a movement to change from a position of rest to one of motion.

Fig. 9. Wing Movement in Flight.

In the diagram, therefore, the bird, in moving forwardly, while raising the wing upwardly, depresses the rear edge of the wing, as in position 1, and when the wing beats downwardly the rear margin is raised, in relation to its front margin, as shown in position 2.

A WEDGING MOTION.—Thus the bird, by a wedge-like motion, gives a forwardly-propelling action, and as the rear margin has more or less flexure, its action against the air is less during its upward beat, and this also adds to the upward lift of the body of the bird.

NO MYSTERY IN THE WAVE MOTION.—There is no mystery in the effect of such a wave-like motion, and it must be obvious that the humming bird, and like flyers, which poise at one spot, are able to do so because, instead of moving forwardly, or changing the position of its body horizontally, in performing the undulatory motion of the wing, it causes the body to rock, so that at the point where the wing joins the body, an elliptical motion is produced.

Fig. 10. Evolution of Humming-Bird's Wing.

HOW BIRDS POISE WITH FLAPPING WINGS.—This is shown in Fig. 10, in which eight successive positions of the wing are shown, and wherein four of the position, namely, 1, 2, 3, and 4, represent the downward movement, and 6, 7, 8, and 9, the upward beat.

All the wing angles are such that whether the suspension point of each wing is moving downwardly, or upwardly, a support is found in some part of the wing.

NARROW-WINGED BIRDS.—Birds with rapid flapping motions have comparatively narrow wings, fore and aft. Those which flap slowly, and are not swift flyers, have correspondingly broader wings. The broad wing is also typical of the soaring birds.

But how do the latter overcome gravitation without exercising some sort of wing movement?

INITIAL MOVEMENT OF SOARING BIRDS.—Acute observations show that during the early stages of flight, before speed is acquired, they depend on the undulating movement of the wings, and some of them acquire the initial motion by flapping. When speed is finally attained it is difficult for the eye to note the motion of the wings.

SOARING BIRDS MOVE SWIFTLY.—Now, the first observation is, that soaring birds are swiftly- moving creatures. As they sail overhead majestically they seem to be moving slowly. But distance is deceptive. The soaring bird travels at great speeds, and this in itself should be sufficient to enable us to cease wondering, when it is remembered that swift translation decreases weight, so that this factor does not, under those conditions, operate against flight.

MUSCULAR ENERGY EXERTED BY SOARING BIRDS. —It is not conceivable that the mere will of the bird would impel it forwardly, without it exerted some muscular energy to keep up its speed. The distance at which the bird performs this wonderful evolution is at such heights from the observer that the eye cannot detect a movement.

WINGS NOT MOTIONLESS.—While the wings appear to be absolutely motionless, it is more reasonable to assume that a slight sinuous movement, or a rocking motion is constantly kept up, which wedges forwardly with sufficient speed to compel momentum to maintain it in flight. To do so requires but a small amount of energy. The head resistance of the bird formation is reduced to a minimum, and at such high speeds the angle of incidence of the wings is very small, requiring but little aid to maintain it in horizontal flight.

CHAPTER II

PRINCIPLES OF AEROPLANE FLIGHT

FROM the foregoing chapter, while it may be rightly inferred that power is the true secret of aeroplane flight, it is desirable to point out certain other things which must be considered.

SPEED AS ONE OF THE ELEMENTS—Every boy, probably, has at some time or other thrown small flat stones, called "skippers." He has noticed that if they are particularly thin, and large in diameter, that there is a peculiar sailing motion, and that they move through the air in an undulating or wave-like path.

Two things contribute to this motion; one is the size of the skipper, relative to its weight, and the other is its speed. If the speed is slow it will quickly wend its way to the earth in a gradual curve. This curved line is called its trajectory. If it is not very large diametrically, in proportion to its weight, it will also make a gradual curve in descending, without "skimming" up and down in its flight.

SHAPE AND SPEED.—It has been observed, also, that a round ball, or an object not flattened out, will make a regular curved path, whatever the speed may be.

It may be assumed, therefore, that the shape alone does not account for this sinuous motion; but that speed is the element which accounts for it. Such being the case it may be well to inquire into the peculiar action which causes a skipper to dart up and down, and why the path thus formed grows more and more accentuated as the speed increases.

As will be more fully described in a later chapter, the impact of air against a moving body does not increase in proportion to its speed, but in the ratio of the square of the speed.

WHAT SQUARE OF THE SPEED MEANS.—In mathematics a figure is squared when it is multiplied by itself. Thus, 4 X 4= 16; 5 X 5 = 25; and so on, so that 16 is the square of 4, and 25 the square of 5. It has been found that a wind moving at the speed of 20 miles an hour has a striking or pushing force of 2 pounds on every square foot of surface.

If the wind travels twice as fast, or 40 miles an hour, the pushing force is not 4 pounds, but 8 pounds. If the speed is 60 miles an hour the pushing force increases to 18 pounds.

ACTION OF A SKIPPER.—When the skipper leaves the hands of the thrower it goes through the air in such a way that its fiat surface is absolutely on a line with the direction in which it is projected.

At first it moves through the air solely by force of the power which impels it, and does not in any way depend on the air to hold it up. See Fig. 1, in which A represents the line of projection, and B the disk in its flight.

Fig. 11. A Skipper in Flight.

After it has traveled a certain distance, and the force decreases, it begins to descend, thus describing the line C, Fig. 1, the disk B, in this case descending, without changing its position, which might be described by saying that it merely settles down to the earth without changing its plane.

The skipper still remains horizontal, so that as it moves toward the earth its flat surface, which is now exposed to the action of the air, meets with a resistance, and this changes the angle of the disk, so that it will not be horizontal. Instead it assumes the position as indicated at D, and this impinging effect against the air causes the skipper to move upwardly along the line E, and having reached a certain limit, as at, say E, it automatically again changes its angle and moves downwardly along the path F, and thus continues to undulate, more or less, dependent on the combined action of the power and weight, or momentum, until it reaches the earth.

It is, therefore, clear that the atmosphere has an action on a plane surface, and that the extent of the action, to sustain it in flight, depends on two things, surface and speed.

Furthermore, the greater the speed the less the necessity for surface, and that for gliding purposes speed may be sacrificed, in a large measure, where there is a large surface.

This very action of the skipper is utilized by the aviator in volplaning,—that is, where the power of the engine is cut off, either by accident, or designedly, and the machine descends to the earth, whether in a long straight glide, or in a great circle.

As the machine nears the earth it is caused to change the angle of flight by the control mechanism so that it will dart upwardly at an angle, or downwardly, and thus enable the pilot to sail to another point beyond where he may safely land. This changing the course of the machine so that it will glide upwardly, means that the incidence of the planes has been changed to a positive angle.

ANGLE OF INCIDENCE.—In aviation this is a term given to the position of a plane, relative to the air against which it impinges. If, for instance, an aeroplane is moving through the air with the front margin of the planes higher than their rear margins, it is said to have the planes at a positive angle of incidence. If the rear margins are higher than the front, then the planes have a negative angle of incidence.

The word incidence really means, a falling upon, or against; and it will be seen, therefore, that the angle of incidence means the tilt of the planes in relation to the air which strikes it.

Having in view, therefore, that the two qualities, namely, speed and surface, bear an intimate relation with each other, it may be understood wherein mechanical flight is supposed to be analogous to bird flight.

SPEED AND SURFACE.—Birds which poise in the air, like the humming bird, do so because they beat their wings with great rapidity. Those which soar, as stated, can do so only by moving through the atmosphere rapidly, or by having a large wing spread relative to the weight. It will thus be seen that speed and surface become the controlling factors in flight, and that while the latter may be entirely eliminated from the problem, speed is absolutely necessary under any and all conditions.

By speed in this connection is not meant high velocity, but that a movement, produced by power expressed in some form, is the sole and most necessary requisite to movement through the air with all heavier-than-air machines.

If sufficient power can be applied to an aeroplane, surface is of no consequence; shape need not be considered, and any sort of contrivance will move through the air horizontally.

CONTROL OF THE DIRECTION OF FLIGHT.—But the control of such a body, when propelled through space by force alone, is a different matter. To change the machine from a straight path to a curved one, means that it must be acted upon by some external force.

We have explained that power is something which is inherent in the thing itself. Now, in order that there may be a change imparted to a moving mass, advantage must be taken of the medium through which it moves,—the atmosphere.

VERTICAL CONTROL PLANES.—If vertically-arranged planes are provided, either fore or aft of the machine, or at both ends, the angles of incidence may be such as to cause the machine to turn from its straight course.

In practice, therefore, since it is difficult to supply sufficient power to a machine to keep it in motion horizontally, at all times, aeroplanes are provided with supporting surfaces, and this aid in holding it up grows less and less as its speed increases.

But, however strong the power, or great the speed, its control from side to side is not dependent on the power of the engine, or the speed at which it travels through the air.

Here the size of the vertical planes, and their angles, are the only factors to be considered, and these questions will be considered in their proper places.