MILITARY AEROPLANES
GUOVEK C. LOENING
T n
MILITARY ALROPLANLS
AN EXPLANATORY CONSIDERATION OF THEIR CHARAC
TERI5TIC5, PERFORMANCES, CONSTRUCTION,
MAINTENANCE AND OPERATION, FOR
THE USE OF AVIATORS
BY
GROVER C. LOENING, B. Sc., A. M., C. E.
Author of "Monoplanes and Biplanes"
Member, Society of Automotive Engineers
Director, Institute of Aeronautical Engineers
Member of Committee on Engineering. National Advisory Committee for Aeronautics Formerly Aeronautical Engineer U. 5. Army
SEVENTH EDITION
Sffi*
COPYRIGHT BY G. C. LOENING ALL RIGHTS RESERVED
Printed by
W. S. Best Printing Company
Boston, Mass.
1917
TABLE OF CONTENTS
CHAPTER I Introduction 9
CHAPTER II Types of Aeroplanes 13
CHAPTER III Primarily for Reference 25
CHAPTER IV Air Resistances 41
CHAPTER V Inclined Surfaces 57
CHAPTER VI Aerodynamic Theory 69
CHAPTER VII Characteristics of Aerofoils 73
CHAPTER VIII Characteristics of the Aeroplane 89
CHAPTER I X Stresses and Safety Factors 105
CHAPTER X Assembly and Construction 121
CHAPTER XI Marine Aeroplanes 139
CHAPTER XII Flying, Stability and Airworthiness 147
CHAPTER XIII The Eyes of the Army and Navy 171
CHAPTER XIV Conclusion. 175
PREFACE TO SECOND, THIRD AND FOURTH EDITIONS
Although great strides have been made in the application of military aeroplanes to problems of strategy and tactics, actual war lessons show that the principles of design, construction, and flying remain the same. Many important improvements in details, however, are given great im- petus by the exacting and inspiring rivalry of war.
The object of this book, in assisting military aviators to acquire a more intimate knowledge of their machines, appears to be attained, in that at the military and naval aviation schools of several nations it has been adopted.
These new editions are corrected, more conveniently re-arranged and somewhat enlarged.
Boston, June, 1917.
PREFACE TO FIFTH, SIXTH AND SEVENTH EDITIONS
The war in Europe, having resulted in many developments of im- portance, this new edition has been revised in several places and illus- trations of the most recent types of fighting aeroplanes have been incorporated.
The author is greatly indebted to the British Air Board, and several distinguished members of the Royal Flying Corps and the Royal Naval Air Service for valuable suggestions and assistance, given him on his recent trip to Europe.
New York, October, 1917
PREFACE
That military or naval aviators should desire to acquire a sound knowledge and just appreciation of the machines to which, day after day, they entrust their lives, is but natural. And at the suggestion of the officers of the Signal Corps Aviation Section, the writer has gathered together some information acquired in practical experience, into the form of a text-book for flyers.
Based, in its composition, on questions asked and information sought by military aviators, and written practically on the field, at the largest aviation center in this country, with unusual facilities for inspection, test, flying and discussion of aeroplanes — every effort has been made in this work to permit this practical atmosphere to permeate its pages.
It is to be noted that enlargement on or repetition of any matter contained in the author's previous work, "Monoplanes and Biplanes," has been avoided. There is presented here a new text-book, limited to the practical consideration of Military Aeroplanes in a manner particularly applicable on an aviation field, and containing knowledge that every aviator should have.
Occasion is taken to point out that the considerations of flying, stability, airworthiness and performances, are based on experiences of the author himself, in acting as observer, noting aeroplane move- ments, reading instruments and taking observations, in flight (a specialty to which the writer has devoted scores of hours in the air), particularly in the extensive experimental flying on the Signal Corps aeroplanes designed by him and piloted by Lieut. T. DeWitt Milling. To the latter, the author wishes to express appreciation of much valuable co-operation and assistance; and he is also indebted to Capt. Town- send F. Dodd, Lieut. Walter R. Taliaferro, George Hallett, and Oscar A. Brindley, expert aviator, for many valuable suggestions and assist- ance in proof reading, and to Capt. Arthur S. Cowan, in command, for every encouragement in this work.
Opportunity cannot too often be taken by aeronautical engineers to recognize and pay tribute to the great work of the Aerodynamical Laboratories, and in particular to the labors of the eminent French engineer, Gustav Eiffel, whose exhaustive tests and their splendid presentation form a basis for accurately predicting performances that one cannot help but marvel at. This work, and the reports of the British Advisory Committee, have been freely consulted, and refer- ence frequently made to information they contain.
Coronado, Cal., May, 1915.
MILITARY AEROPLANES
CHAPTER I.
INTRODUCTION
Although Aviation is a new field of human endeavor, its appli- cation to the art of warfare is already becoming a specialty. Only recently has it been appreciated, that military requirements have a most vital and important influence on many features of aeroplanes — not only in the art of using them in military operations, but in their fundamental design and construction.
It is planned, therefore, to give particular attention here to the military aeroplane, as we find it today — emerged from a crude state of invention and development into a more or less finished product, which, in the greatest war of history, has gloriously demonstrated its strategical and tactical importance.
It is no longer necessary to speculate on the uses of aeroplanes in warfare. What has actually been accomplished in directing artillery fire, in reconnaissance, in dispatch-carrying, and in offensive work has opened a new phase of warfare, as significant as it is surprising.
The technique of the use of aeroplanes in strategy and tactics, is decidedly a subject for the military expert, but the general design and construction of aeroplanes to accomplish certain definite purposes, and their operation and maintenance in the field, are subjects that may properly be considered here.
In addition to expert ability in their operation, it is found that a sound and practical knowledge of the design and construction of aeroplanes is exceedingly helpful to the military aviator.
A full consideration, therefore, is given to elementary theory and practice applied in aviation, and the information used is primarily designed to be of definite service, in the field, where many unforeseen difficulties constantly arise.
Before taking up the determination of its elements, it is neces- sary, clearly, to distinguish the aeroplane from other craft designed to navigate the air.
Aircraft may be divided into the following classes :
10 1. FLOATING AIRCRAFT.
The "airship," is distinctly a lighter-than-air machine, con- sisting of a balloon or gasbag, containing a gas — hydrogen for example — lighter than air, which by displacement of an equal volume of air, gives a notation, the magnitude of which is de- termined by the kind of gas, the size of gas container, and atmos- pheric conditions. The ordinary free balloon is, in short, nothing more than a harnessed "bubble," and the dirigible, or airship, is a balloon of elongated shape, fitted with steering apparatus and propelling mechanism.
The Kite Balloon — This type of balloon is used for artillery observation both on land and at sea. It is "Captive," in that it is held by a cable, which is let out from a mechanism on the ground permitting the balloon to float up to an altitude of a thousand feet or so. It has no motor and its peculiar shape, makes it very handy and stable in winds, pulling up steadily on its cable and preventing it from spinning around, hence the name "Kite Balloon."
A Kite balloon floating on its line. The basket contains the observer.
Central News Service
A "k. b." after being hauled down by its attendant motor car auxiliary.
Airships are constructed mainly in three different types, the "Rigid," the "Semi-Rigid" and the "Flexible or Non-Rigid." These designations refer, entirely, to the manner of combina- tion of gas container and framework carrying the weights of en- gines, etc. A flexible gas container, held in shape only by the pressure of gas within and to which the load is hung, character- izes the "Non-Rigid" system. A gas container, held in shape by gas pressure, with an additional stiffening keel to which the weights are attached, is descriptive of the "Semi-Rigid." Whereas, in the "Rigid" system, a stiff, braced frame-work or hull, carrying di- rectly the motors and loads, is formed to contain within it numer- ous separate, drum-shaped gas containers instead of balloons. The stiff frame provides, in itself, that necessary rigidity of hull, which interior gas pressure on the envelope provides in the other types.
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A Zeppelin "Rigid" airship and above it an aeroplane. The airship can float at rest but an aeroplane must acquire speed in order to fly.
The Zeppelin airship was the first successful development of the rigid system, and is useful in a naval fleet unit.
The "Blimp" - This type of air ship is a small scouting type used very largely for short range coast defense reconnaissance. It is a typical example of the Flexible dirigible system.
Close view of the car of a Blimp, similar to a trac- tor aeroplane fuselage.
A " Blimp " dirigible starting out. The rudders at the rear may be noted.
2. FLYING MACHINES.
The Aeroplane — In distinction to the airship, supported in the air by a buoyant gas, the aeroplane is. supported by an upward wind pressure, generated by its own speed through the air. This lift- ing pressure is obtained on specially formed wing surfaces, which are set at an inclined angle, and forced through the air at the re- quired speed by an air propeller. Suitable auxiliary surfaces and rudders are used to preserve the equilibrium of the craft and to enable the pilot to steer it.
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The Helicopter — Air propellers are similar in character to marine screw propellers, and not only are they made use of to 'push or pull an aeroplane, but it has been proposed, in operating them on a vertical axis, to use their thrust directly., in lifting loads. This type of flying machine is called the "Helicopter" or "direct lift" machine, and does not involve the principle of lift from the inclined arched plane, used in the aeroplane.
The Ornithopter — Nature's flying machines — the birds — are neither screw propelled aeroplanes nor helicopters. They derive their support from the wind pressure on their outstretched wings pre- cisely as does the aeroplane, but for propulsion, the bird flaps its wings in a rowing, weaving motion, which gives a forward push. When an aeroplane glides, it resembles in character the soaring of a bird, with wings outstretched, but attempts to de- rive propulsion from a reciprocating movement of wings, have not been successful, as yet. Machines of this type are called " Ornithopter s" or "Flapping-wing" Machines.
Although little has been accomplished with them, the possibil- ities of the helicopter and Ornithopter have by no means been fully investigated, and whether or not a combination of "direct lift" and aeroplane, often called the "gyroplane," has any future, is still a sub- ject for study.
Airships, on the other hand, are very highly developed, and al- though they are difficult to handle and very expensive, they are looked upon as "battleships" of the air. Their design and construction are full of interesting, and difficult, engineering problems, and it is planned to give them consideration elsewhere.
In this connection it is important to point out, that the oft-stated "principle," that aeroplanes are limited in size, due to a proportionally greater increase in weight as the size is increased, is a fallacy, and, as a matter of fact, recent work on large-sized machines, appears to demon- strate, that in proportion to the weight of the machine, as the size increases, a greater excess load can be carried. (In later chapters this feature will be further investigated.) Aeroplane "battleships" are, by no means, an impossibility. The consideration of large-size aircraft, therefore, becomes merely an efficiency comparison of the lift by gas bag and the lift by air pressure on planes. If the dirigible balloon lifts more "live load," per pound head resistance, at the same speed than does an aeroplane, the dirigible is apt to survive. As yet, it has not.
Of the various kinds of aircraft, only one type of flying machine is to be considered here, primarily, because we find the aeroplane, at present, the most successful, the most economical and the best developed means of navigating the air.
CHAPTER II. TYPES OF AEROPLANES
At the present time the early inventive stage in the development of the aeroplane is gradually but perceptibly giving way to a state of more precise engineering. And, in this step in its progress, aviation is but following the course taken by almost every other art and sci- ence. Any classification of aeroplanes, therefore, is subject to modi- fication as newer craft are developed, and old ones rendered obsolete. But the general principles of the machines do not change as rapidly as do their concrete interpretations.
The principle of sustentation of an aeroplane from the upward push of air flowing past it, has been stated, and, in the following chap- ters, will be analyzed. The support being derived from the free air, an aeroplane is readily subject to loss of balance, due to air disturb- ances, gusts, convection currents, etc. It follows, therefore, that many features designed to overcome loss of balance, are used on aero- planes. Organs are also introduced to give the pilot control over the craft within definite limits.
An aeroplane consists, therefore, of lift-generating surfaces at- tached to a frame carrying motor, fuel, pilot and equipment, and in combination with devices to balance and steer the craft.
Flying freely, in the air, an aeroplane has three axes of rotation.
1. It may ascend or descend, by virtue of changes in its longi- tudinal path. The nosing up and nosing down of an aeroplane is termed "pitching," as in boats.
2. An aeroplane, in flight, may change its direction of travel. This is termed "yawing," as in boats.
3. In addition to these, an aeroplane can tip over to either side, on a transverse axis, and this movement is termed "banking" or "roll- ing." In making turns, it is necessary to "bank" up an aeroplane, sidewise, sufficiently to overcome the centrifugal force, and prevent skidding. This "banking" is obtained by manipulating the lateral control.
The locomotive driver, is steered by the tracks, and has to give his attention, only to the control of the speed of his engine; an auto- mobile driver, controls his motor, also, but in addition must steer his machine; whereas the aeroplane pilot both steers and operates his engine, and in addition must give his best attention, continually, to balancing the machine, fore and aft and side to side.
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Like every science, Aviation has a language of its own, and a method is used here of expressing this language in photographs. Study of the explanatory caption and of the photographs themselves, there- fore, is equal in importance to the reading of the text.
The types of aeroplanes considered here are typical ones of dis- tinct features, and a more detailed discussion of their merits will be found in later chapters.
THE "TRACTOR" AND THE "PUSHER"
An aeroplane, that is pulled through the air by a propeller situ- ated at the front of the machine, is called a "tractor."
On the other hand if the propeller is back of the main lifting planes, the machine is called a "pusher." These terms are very expressive and very widely used.
The single propeller "tractor" is the most widely used type now, but the "pusher" type, particularly for gun-carrying, has still a "raison- d'etre."
The term "biplane" refers to an aeroplane with wings, super- imposed, and "monoplane" to a single deck type of plane.
THE CONTROLS.
Since there are three axes about which an aeroplane may rotate, it follows that three controlling organs are required :
1 . The ' ' elevator, ' ' for pitching ;
2. The "rudder," for steering or "yawing;"
3. The "lateral" or "rolling" control.
The principle of the air force derived from an inclined plane, is used in all of these controls. The "elevator" is inclined up or down, to lift or depress the tail of the machine. The rudder is turned so as to permit the wind to blow on it, to one side or the other, whereas the lateral control consists, merely, in giving a difference in angle to the two sides of the wings, causing one side to lift more than the other.
There are three general means of lateral control :
1. "Ailerons," or separate small planes, on either side independ- ent of the main lifting surface ;
2. "Wing flaps," or portions cut out of the main surface and hinged thereto;
3. "Warping," which consists in twisting the main lifting sur- face, so as to get a greater angle of inclination to the wind on one side and less on the other.
In the construction of rudders and elevators, the necessary change in angle to alter the wind pressure, is accomplished either by pivoting the entire surface, or by turning a flap hinged to a fixed surface in front of it.
The Sopwith tractor biplane — a very widely used type. The side view at the top shows right to left, the motor and propeller at the front, the machine gun shooting thru the propeller, the wings> and at the end of the body the control surfaces, the " rudder " is the vertical one, the " elevator " the horizontal one. The top wing is set ahead of the lower wing and therefore" staggered." The bend up across the wings shown in the lower cut is the " dihedral."
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THE TRACTOR BIPLANE.
The form of aeroplane that at present approaches the nearest to a standardized type is the Tractor Biplane.
The main lifting surface, as may be seen from the photographs, consists of two super-imposed planes, with their widest dimension across the flight path.
The main planes are attached to a long, fish-shaped body, termed the "fuselage," which, in effect, is the backbone of the machine, since it carries the motor and propeller at the front and the seats near the center, while at the extreme rear are mounted the rudder and elevator.
The use of an enclosed fuselage in a tractor type is almost uni- versal, and greatly increases the efficiency of a machine, by reduction of head resistance in the wind. The disposition of the seats in the body gives excellent protection to the aviators. It will be noticed that two seating arrangements are shown — "tandem," one ahead of the other, and "side by side." The former is good for military scouting, and the latter possibly for training.
In the types of tractor biplanes shown, the chassis is mounted to the body, as is also the center section of the wings. By taking the outer wings off, this type is readily made transportable by road.
In the photograph of the biplane tractors in flight, several de- tails show up clearly, — particularly, angles of view of the pilot, whose vision is interfered with by the lower plane.
PUSHER BIPLANES.
The older types of machines, particularly the early Wright and Curtiss, were pusher types — the Wright, however, had two propellers and the Curtiss only one. These types were open-bodied, entirely unprotected, and with the motor to the side of or behind the aviator.
A few years of development, led to the adoption of either a na- celle — short fuselage, protecting seats and motor only, — or a fuselage. In using a fuselage on a "pusher" machine, it becomes necessary either to mount a propeller at the extreme rear "torpedo" fashion, to mount a propeller on either side, or to have a propeller running on a large bear- ing around the fuselage. In "pusher" flying boats the propeller tips just clear the boat.
The earliest Wright machine had the elevator in front, so that to ascend the elevator was turned up, thus lifting up the nose, and vice versa; whereas, when it was later changed to the rear, for reasons of stability, to ascend it became necessary to turn the elevator the opposite way, thereby pressing down the tail. This distinguishes "front elevator" and "rear elevator."
17
Underwood and Underwood
The Spad tractor aeroplane — a typical European fighting scout, with a high speed of over 130 miles an hour. The biplane wings are mounted to the body at the front, and in examining the controlling surfaces at the rear it will be seen that the horizontal elevator flaps are turned down. This has lifted the tail off the ground and the machine is just starting to fly.
Underwood and Underwood
The Nieuport scout— a fast French type which is very nearly a Monoplane, because of the small size of the lower wing.
IS
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"PUSHER" BIPLANES
Above— Left— Wilbur Wright, the inventor, and the early type of Wright double pusher biplane, with elevator out in front. Right — Double screw pusher Wright biplane, of later pattern, elevator in rear.
Center — Twin screw, pusher fuselage biplane, with engine in front.
Bottom — Left — Early Curtiss open body, pusher — one screw, three wheel chassis rudders in rear. Right — Farman pusher biplane with nacelle or enclosed body.
A "fuselage" encloses motor seats, etc., but in addition serves as the main structural unit of a machine, whereas a "nacelle" serves merely for wind protection, since a separate frame carries the rudders.
The term "empennages" refers to the tail surfaces of a machine, whether they be "bal- anced" or "flap and fin."
The term "fin" largely replaces the term "keel." It will be noted that the early Wright machines have no fins or keels in the empennages.
The side surfaces of an enclosed fuselage are virtually keols.
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21 MONOPLANES.
It has often been the custom, distinctly to separate biplanes and monoplanes, as different types. This is hardly justified, since the only distinguishing feature is the use of a single deck, "king post" type of truss to carry the air pressure lifting load, in the monoplane, and a double deck, "Pratt" type truss, in the biplane. Biplane sur- faces, do interfere slightly with each other, but in tractors the disposi- tion of motor, wings, body, rudders and even chassis, is identical, whether biplane or monoplane.
A further misconception, in this connection, is that the monoplane is faster than the biplane. The more recent speed scout biplanes have proved the fallacy of this, and, in later chapters, it will be found that biplane and monoplane are both similar aeroplanes, differing primarily in wing surface bracing.
Several monoplane photographs are given on the opposite page.
Monoplanes, like biplanes, may be tractors, pushers, open-bodied, or have two propellers. Several European firms construct a body and chassis, complete with rudders, to which either monoplane or bi- plane wings may be mounted.
In general, the biplane carries more load, and the monoplane is simpler in construction. But even these differences are fast disap- pearing.
A distinct advantage of the tractor monoplane over the tractor biplane, is found when the wings of the monoplane are raised slightly above the body, thereby enabling the pilot to look under them and to have a free and unobstructed view.
AEROBOATS OR FLYING BOATS.
For the purpose of starting from and alighting on water, aero- planes of tractor, pusher, or any type are readily modified.
Merely adding pontoons to a tractor, in place of wheels, gives the hydro-aeroplane; and the construction of aeroplanes, fitted to receive either wheels or pontoons, as circumstances require, has de- veloped considerably. Craft of this kind are called "convertibles."
But in order to obtain greater sea-worthiness and better co-ordi- nation in design, a special type of aeroplane has been developed, suit- able only for over-water work. The keynote in its design is found in its treatment as a boat with wings, rather than an aeroplane with floats. The aeroboat, or flying boat, therefore, is primarily charac- terized by a staunch, boat-like body, around which the rest of the aeroplane is built. The photographs show several different types.
For further discussion of aeroboats and hydro-aeroplanes refer- ence is made to the chapter specially devoted thereto.
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23
THE "DUNNE" AEROPLANE.
In the preceding types, the auxiliary organs for pitching and yaw- ing are separated from the main planes and are distinct. In the Dunne aeroplane, there is only one set of controlling organs, and due to the peculiar shape and construction of the machine, the control of yaw- ing, pitching and rolling is combined and governed, only, by the double wing flaps. As may be seen from the illustrations, the main planes are set in a "retreating" position. Their position in plan, and their angle setting, give inherent stability characteristics, which will be taken up in a later chapter.
The "Dunne" principle of a retreating plane is used, though in a modified way, in the German aeroplanes, called "Pfeilfliegers" or "Arrowplanes," but the customary fuselage and rudders are retained. The German "Taubes" are monoplanes with pigeon-like retreating wings. (See p. 170.)
It may be stated here, that the "retreating" planes have much the same effect as a dihedral angle, on lateral stability, but are not so sensitive to side puffs. The effect on pitching stability, obtained on the Dunne, by the negative incidence at the tips, can be had, though in a lesser degree, on the more ordinary types of aeroplanes, by a nega- tive setting of the tail planes. While "inherent" stability is descrip- tive of that obtained by the construction of the aeroplane itself, in shape,
THE U. S. ARMY DUNNE TYPE BIPLANE
The changing wing section and reducing angle of incidence are clearly seen.
The bustle is used to deflect the air sideways. The wing flaps on upper and lower planes, are the only means of control. To ascend all flaps are turned up, and to de- scend they are all turned down. Inverse movement rolls the machine laterally, causing it to turn.
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wing setting, balance and fin disposition, a clear distinction is drawn between stability of this type and that obtained by adding to any aero- plane an auxiliary mechanism, designed to be actuated by movements of the aeroplane, and automatically operating the controls, for proper corrective effect. Such a mechanism is virtually an automatic pilot, and is often termed, a stabilizer. "Automatic" stability may be ob- tained, by use of a mechanism of this nature, on an aeroplane that is inherently lacking in stability.
There are many other types of aeroplanes, but their general features resemble those described, and the art moves too quickly to give them all consideration. A general idea, of the various types, having been given, a more detailed study of the aeroplane may be taken up.
A squadron of French fighting aeroplanes of high speed single seater type, armed with machine guns.
CHAPTER III. PRIMARILY FOR REFERENCE
As much as possible, mathematics are avoided in the technical parts of this work. Where formulae are of real help, however, in stat- ing clearly the relation between quantities, they are used and fully explained.
In a field like this one, so eminently practical in its nature, com- mon-sense is of much greater benefit than abstruse scientific knowl- edge. There is justification for decrying the vast amount of com- plicated mathematics that have been built up on fundamental assump- tions which the practical air pilot knows are wholly erroneous, but in doing so, let us not forget that scientists and the laboratories have contributed a great and valuable share, in advancing the aeroplane's efficiency.
It is praiseworthy in presenting a subject, to simplify it, and to avoid a too technical impression, but where this is at the expense of a clear and full understanding, it is inadvisable.
Aeroplanes, as machines, naturally involve many scientific ele- ments, and it is certainly best, at the outset, to realize this and to ac- quire a working conception of what they are.
1. It is necessary to know the simpler types of equations and why they are so handy.
2. The elements used in solving triangles, such as sines and cosines of angles, should be familiarized, and a logarithm table is sometimes very convenient.
3. Mechanics dealing with momentum, inertia, accelerations, centrifugal force, and gyroscopic force, should, at least, be understood, and a comprehensive review should be made of Elasticity, Stress and Strain, and Fluid Motion.
4. A clear conception of Work, Energy, Power and Power Ef- ficiency, is of fundamental importance.
5. Graphical representations, composition and resolution of forces, are constantly of use.
6. Various modes of representing variations of quantities on charts, serve as the basis of recording air pressure results, and should be fully appreciated.
7. The relative values and conversion factors of different sys- tems of units, are most useful, and areas, volumes, etc., are frequently called for.
Recalling these elements is made simpler, if a brief summary of the features particularly applicable to this study be given.
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FORMULAE.
To attempt to present a study of flight without any formulae would make it necessary to express relations between quantities in long paragraphs of words, that could more readily be stated in simple equations.
There is nothing mysterious about an equation. It is merely a sentence tersely expressed.
Thus, if it was desired to state the rule that the quantity A mul- tiplied by twice the quantity B is equal to C, the formula represent- ing this would be,
A x 2B = C
Each letter or symbol in a formula represents some factor that is substituted when its value is known. If A = 16 and B = 4, then C = 128, since, the rule interpreted, reads,
16 x 8 = 128
Besides equations, other relations may be represented by formu- lae. Thus, the sign "oc," signifying "varies as," would permit the statement that "wind pressure varies as the square of the velocity of the wind," to be expressed
P oc V2
Equations are of two kinds, derived and empirical. A derived equation is susceptible of proof, by use of mathematical processes based on proven assumptions.
An empirical equation is neither derived nor proven. It is merely a statement of the results of experiment, regardless of mathematical proof.
In many branches of engineering, empirical formulae are con- stantly used, and in Aviation, the lack of a satisfactory basic theory of air flow makes empirical formulae based on experiment, most neces- sary.
Empirical formulae are really experimental averages. As an example: The theory of long columns, has not as yet permitted of the mathematical derivation of a satisfactory set of formulae for the stresses. Very extensive experiments have been conducted therefore, on the loads necessary to deflect and break such columns. Grouping these experimental results together it is found that if 1/d denotes the length ratio of a certain column, and p, the stress per square inch of cross section, the average of the experiments, may be expressed as
p = 32,000 - 277 1/d
This is strictly an empirical formula. The engineer is interested in its practical application, not in its derivation, and when a column of this type is to be designed, for any value or 1/d he can find the value of p.
Formulae of empirical nature are fundamental in a study of Aviation.
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It is often found necessary, particularly in an experimental field, to introduce numerical constants, to balance the two sides of an equa- tion. It may be known, for example, that the horse-power of a pro- peller varies as the cube of the revolutions and the fifth power of the diameter, but we could not express this relation as an equation, capable of solution, until a numerical factor is found which gives a value to the h. p. (horse-power) for any r. p. m. (revolution per minute) or diameter, that agrees with the experimental results.
Thus the relation could be written,
H. P. = kN3D5
but unless k = 1, the equation cannot be solved until a value of k is found. Since the equation is empirical, it becomes necessary, actu- ally to try many propellers, until an average is found. As a matter of fact, k, in the above formulae, has been determined by experiment to be 0.54 when certain units are used. The formula becomes,
H.P. = 0.54 N3D5,
and is capable of simple arithmetical solution by substituting values for the letters. A term like k is called a "constant."
The majority of formulae for air pressures involve "constants," and the great advance in designing during the past two years may be traced directly to the determinations by the aerodynamic laboratories, of better values of these constants, for use in empirical formulae.
SOLVING TRIANGLES.
Every triangle has six parts, three sides and three angles, and if we know any three (including a side) the triangle may be solved — that is the other sides and angles may be determined.
Triangles may be solved in two ways :
1. By trigonometry.
2. By graphical methods.
In aviation work only the simplest trigonometry is used, and about the only functions of angles used are the sine, the cosine and the tangent. It is well to recall, here, that "sine" and "cosine" are merely numerical ratios, representing the fractions that certain sides of a triangle are to the hypothenuse.
The accompanying chart shows what these functions are, and also gives formulae for solving the triangles.
In later, chapters it will be found that in the representation and solution of forces, in the determination of angles of incidence, glides and climbs, and in stress determinations, many occasions arise for solution of simple triangles.
But in aeroplane work great accuracy of computation is not ne- cessary, so that a simpler way of solving triangles may, at times, be used, i. e., the graphical method. This consists merely in a mechani- cal process of laying off on a sheet of paper the known angles, by a
28
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VARIOUS MATHEMATICAL SIGNS — FORMULAE FOR AND GRAPHICAL SOLUTION OF TRIANGLES -AND FUNCTIONS OF ARCS
29
protractor, and the sides to some convenient measurement scale. By closing the triangle, all that is necessary in order to determine the other sides or angles, is to measure them off. At first sight, this seems to lack the value of preciseness, but if a large enough scale is used, it is 'surprising how quickly and correctly, triangles may be solved in this way.
In aeroplane studies the use of logarithms is rarely justified ex- cepting possibly in propeller determinations, where formulae involv- ing, for .example, the fifth power of the diameter, D5, are used.
It may be recalled that a logarithm is merely the exponent, like five in the above, to which it is necessary to raise 10, in order to pro- duce the given number.
It will suffice to give here, the method of determining powers of numbers. For example, in determining D5, a laborious calculation is avoided by looking up the log of D, multiplying it by five, and find- ing the number corresponding to the log represented by this quotient.
The occasion will rarely arise where logs have to be used, or even trigonometry, if graphical methods are pursued.
MECHANICS.
Mechanics is the most logical of sciences — the causes and effects are so evident. It is often defined as the science that treats of the ac- tion of forces upon bodies. And anything that concerns the action of air forces on aeroplane wings and bodies, is of vital importance here. It is almost needless to recall, that as long as the propeller is pulling or pushing, or the aeroplane gliding, it is storing up momentum, which is defined as the product of the mass m by the velocity v at any instant ; whereas, inertia is that property of a body by virtue of which it tends to continue in whatever state it happens to be, until acted upon by some other force.
Velocity and Acceleration.
Acceleration of a particle is the amount of increase or decrease of its velocity in a unit of time. In other words, while the velocity is rate of motion, acceleration is rate of change by velocity.
A force is equal to a mass multiplied by its acceleration, because it is universally agreed that a force be measured by its effect in chang- ing the velocity of a particle. When we measure weights in pounds, we actually measure the force of the earth's attraction, which is equal to the mass of the body times the acceleration of gravity, g, which increases the velocity of a particle 32 feet per second every second.
Therefore w = m x g. So that when the mass of a particle is considered, it must be recalled that it is equal to what we call the ''weight" divided by acceleration of gravity or
w
m = — g
30
A body falling freely under the action of the constant pull of the earth, disregarding the retarding effects of air resistance, is an example of uniformly accelerated motion. It must not be forgotten that in a vacuum all bodies, whether a feather or a piece of lead, fall at the same speed. Air resistance, alone affects rate of fall, in free air.
It is useful to recall, that a falling body attains a velocity v in feet per second, falling a distance h feet, represented by
v = \/2gh where g = 32 feet per second per second.
Rotary Motion and Centrifugal Force
In a circular orbit of radius r a particle making n revolutions per second, covers in each revolution the circumference, 2 TT r, so that its velocity in feet per second
v = 2 TT r n
The numerical value of this velocity is solved by the above equa- tion, easily enough, but the particle swingng in a circle is constantly changing the direction of its velocity. This change in v, involves an acceleration, and since the particle has mass, it follows that a force is introduced, which is constantly making or trying to make the particle hold its circular path. This is the centripetal force.
The force acting from without and tending to make a particle take a curved path is called centripetal force, and is the opposite to centrifugal force.
Since this acceleration towards the center of the circle is equal to v2/r, it follows that
v2 w v2 Centrifugal force F = m x -
r gr
where w is the weight in pounds, v is speed in feet per second, r is the radius of the orbit in feet and F is the force.
The Pendulum
What applies to the speed with which weights fall, applies also to the simple pendulum. No matter what the weight of the pendu- lum, it is the length of arm 1 alone, that governs the period of oscillation. This period,
p = 2 TT Vl/g Moment of Inertia.
Inertia has been defined, but "Moment of Inertia" must be con- sidered when we come to rotary motion.
Moment of inertia is the quantity obtained by multiplying the mass of each particle of a body by the square of its distance from the axis. Whether a propeller, a flywheel, or a wing spar, every object has a "moment of inertia" I, about any axis. It would be a laborious
31
computation to find I for various shaped bodies. Fortunately it has been done for us, and values are given later in a table. I is expressed in pounds X feet squared (Ibs. ft.2).
Angular Velocity
The "radian" is often used as the measure of a distance along the circumference of a circle. There are 2 TT or 6.28 radians, covered in one revolution of a circle. So that one revolution per second, r. p. s., equals 2 IT radians per second.
If w is called the rotational or angular velocity of a particle, and n the r.p.m., then,
w = 2 TT n
It has been indicated that acceleration of a rotating particle, due to change in direction, gives rise to centrifugal force.
But the rotational velocity of a particle, may increase or decrease. This is called angular acceleration and is a rate of change of angular velocity, called s.
Torque.
In linear accelerations, we have Forces, while in rotational accel- eration, forces are also to be considered, but instead they are called Torques.
Torque, T, also equals mass x acceleration, but in its case mass is the moment of inertia and acceleration is angular.
1
.'. T = Ix sx - 32
where T is in pounds weight x feet and s in radians per second per second.
The Gyroscope
Linear motion and rotating motion have been considered. The axis upon which a body is rotating can be moved in a linear motion.
In addition the axis of a rotating body may change its direction continually. This brings us to the gyroscope.
An unbalanced force is of course necessary to change the direc- tion of linear motion of a particle.
In the same way an unbalanced force is necessary to change the direction of the axis of a rotating body. When a wheel is set rotat- ing, the direction of the axle tends to remain unaltered, as long as no unbalanced external force acts upon it. But when an unbalanced force is applied suddenly enough the axle's fixed position in space gives rise to a curious phenomenon, not only resisting movement by this force, but actually causing the axle to move in a direction at right angles to the applied force. It is unnecessary here to take up the relation of this phenomenon to the earth's rotation or the derived formu- lae, representing it.
32
An example of gyroscopic force, however, may be given. If a bicycle wheel is held out in front of one, by one end of its axle, and set rotating clockwise as viewed by the holder, when the axle is pointed down the tendency is for it to swing around and point to the left, and any effort to point the axle upward, meets a pronounced resistance, the axle at the same time turning sharply to the right.
The effect of this phenomenon on the aeroplane's stability is taken up later. In steadying ships or monorail cars, or in stability devices for aeroplanes, the movement at right angles to the direction of the applied force of a sensitive "gyro" is made use of.
Elasticity — Stress and Strain.
The phenomena which are associated with the distortion of bodies due to stresses are excessively complicated, and one has but to think of the many familiar properties of brittle substances, like glass or chalk, elastic ones like spring steel or rubber, and plastic ones like clay or wax, to realize that this is in itself a formidable study, much too ex- tensive to be given anything but a meagre consideration here. The importance of the study of Resistance of Materials, to aviation, can- not be overestimated, since in the design of the aeroplane proper, this is the branch of engineering that solves the fundamental problem — to build light and yet strong.
This necessary combination is one that truly represents a cri- terion of the excellence of an aeroplane, as a structural engineering unit, and although it often does not, nevertheless, the aeroplane should involve the most refined, advanced and expert, structural features that engineering development has made possible. It has been a great detriment to aviation that so many of its devotees have failed to realize that the very best material obtainable, and the most ingenious and perfect construction, is still hardly good enough to bear the strains properly.
Of all the great variety of solid substances, having almost every imaginable degree of elasticity, softness, hardness and brittleness, we are concerned in later chapters, only with the behavior under stress of those which are used as materials of construction, such as steel, aluminum, brass, linen, spruce, ash, glues, paints and rubber.
Of the three classes of substances, solids, fluids and gases, let it be recalled, that an "elastic" solid, like spring-steel, can withstand a stress which tends to change its shape for an indefinite length of time, whereas a "plastic" solid, like wax, does not recover from strain when the stress ceases to act. One must qualify the above, however, since the best spring steel never completely recovers from distortion, and even wax is slightly elastic. A fluid is a substance which at rest has no power definitely to resist a stress, and when at rest it is always pressing, normally, on the sides of the vessel containing it. A gas is a
33
matter with no independent shape, adjusting itself to take the form of the vessel in which it is confined, and tending to diffuse and expand indefinitely.
Substances are of two kinds — grained and ungrained. Glass and water are examples of ungrained substances, while wood, steel, and practically all materials of construction, have a grained struc- ture. The grain in steel is well marked, and though often lost sight of, it is most necessary in aeroplane work, that care be taken not to put too great a stress across the grain of a steel plate.
Elasticity may properly be defined as the resisting property of a body to motion of its molecules.
Strain is the distortion of a body measured at a given point.
Stress is the force by which the molecules resist a strain at any point. Stresses are developed, and strains caused, by the application of external forces. Each stress is accompanied by its own character- istic strain.
Stresses are of five kinds — Tension, Compression, Flexure, Tor- sion and those induced by Fluid pressure. They are illustrated on an accompanying cut.
It is a fact of fundamental importance in the theory of elasticity, that however irregularly a body may be distorted, any small portion of the body suffers that simple kind of distortion which changes a circle into an ellipse, the change of shape consisting essentially of an increase or decrease of linear dimensions in three mutually perpendicular direc- tions, sometimes accompanied by a slight rotation of the small parts of a body.
The stress on a body is usually represented as pounds per square inch, or the force in pounds acting on a one-inch square part of the body. The total force P on a body divided by area A, of its cross- section gives this unit stress which is called "intensity of stress." The strain 1 accompanying this is not represented in actual inches or units of total deflection d, but is given as a fraction of the span L of the piece, such that strain 1 equals d/L.
The basic law of Resistance of Materials is that intensity of stress p is proportional to strain 1. And to balance the proportion into an equation, a constant is introduced, called E, giving the simple rule, that
p = P/A = d/L x E = 1 x E
This constant E, is called the "Modulus of Elasticity," and is of
the greatest convenience in indicating what the proportion of stress in a given material is to strain. Thus, it is readily seen that steel is stronger than aluminum, when it is learned that E for steel is 28,000,- 000 and for aluminum 1,700,000.
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KINDS OF STRESSES - GRAPHICAL FORCE DIAGRAMS - CHARTS AND
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35
For all materials, however, there is a limit beyond which the ratio of stress to strain or coefficient of elasticity E = p/1, does not hold. This region is called the ' 'elastic limit" of the material, and while con- siderable stress can be added beyond this, the material begins to stretch out of all proportion and rapidly reaches the breaking away point, which is called the "ultimate resistance."
When relieved of stress, before reaching its elastic limit, a ma- terial will return more or less to its former state, but when the stress has exceeded the elastic limit the material takes a permanent set. The forces necessary to bring any material to the elastic limit, and the value of the ultimate resistance, are entirely matters of experi- ment, from which are derived empirical values.
Fluids and Gases.
In liquids the phenomena of surface tension, capillary action, cohesion, etc., are of but minor interest excepting in hydro-aeroplane studies. It is important to recall of liquids, however, that the pres- sure exerted on any part of an enclosed liquid, is transmitted undi- minished in all directions (air-pressure fuel tanks). When a fluid is in motion it is being acted upon by an unbalanced force, giving it velocity and by a pressure, or in other words, it has the energy of a "velocity head" and a "pressure head." Any increase in one is at the expense of the other.
A device very widely used for the measurement of velocities of both water and air is the Pitot tube, which measures the velocity head v = v 2 g h. It consists, merely of a bent tube with a nozzle, point- ing into the relative flow and measuring by means of the length of a column of liquid, the head h, which substituted in the above, gives the velocity v.
In considering liquids the losses in head in long pipe lines and the effects of expansion and contraction and of nozzles, are of inter- est with reference to the gasoline and radiator connections.
Buoyancy and Specific Gravity should be considered.
A body immersed in a liquid or a lighter gas immersed in air, is acted upon by a lifting force which equals the weight of the liquid or air displaced. In other words, the law of Floating Bodies is to the effect that a floating body will displace a volume of liquid of gas whose weight equals its own. A body immersed in pure water has a flota- tion of 62.41bs. per ft.3
The density of a substance is its mass per unit volume, while Spe- cific Gravity of a substance is its weight as compared with the weight of an equal "bulk" of pure water. So that, given the specific gravity of a substance, it is necessary to multiply by 62.4 to obtain its actual weight in pounds per cubic foot, since water weighs 62.4 Ibs. per ft.3 Specific gravity is sometimes referred to other substances — air for
36
example. The specific gravity of gold is 19.26. Its weight per cubic foot is consequently 1,200 Ibs. A table of weights and specific gravi- ties is given later.
Gases are highly compressible, in distinction to water and solids, and are perfectly elastic, though in distinction to solids their elasticity is one of volume and not of form.
It must be borne in mind, with reference to gases, that the tem- perature remaining the same, the volume of a gas is increased exactly in the same proportion as the pressure is decreased. Or, the product of volume X pressure equals a constant quantity.
The study of Aerodynamics which constitutes the major part of this work, takes up the mechanics of gases, making it unnecessary to give them further consideration here.
WORK, ENERGY, POWER.
Work is said to be done when a resistance is overcome, so that movement takes place through a certain distance. The air propeller which pulls against a resistance of 200 pounds, causing the machine to which it is fixed to move 80 feet, is doing work, inasmuch as it is continually overcoming this resistance.
The unit of work is the foot-pound, which is equivalent to the work performed in moving one pound of weight through one foot of space.
Work may be done in several ways — pushing or pulling weights, or working against pressures, such as the work performed by a piston in driving a fluid of gas before it, which is equal to the intensity of pressure X area of piston x distance traversed or stroke.
In the above example, the propeller is doing 16,000 foot pounds work by overcoming a resistance of 200 pounds and moving against it 80 feet.
Work, in whatever units it is expressed, is always "resistance overcome" multiplied by "distance traversed."
Energy is distinct from work, in that it represents capacity to do work, but not the actual work done. It is expressed in the same units as work.
There are two kinds of energy — Potential and Kinetic — since a body when at rest may have stored up "potential energy" due to its peculiar position or condition, and when in motion, a body is capable of performing work against a retarding resistance, due to its "kinetic energy."
A reservoir full of water, capable of turning a water wheel, if re- leased, is an example of potential energy, and another is the stored energy in storage batteries or gunpowder. The weight of the stored body x the distance through which it is capable of acting is the meas- ure of potential energy.
37
Kinetic energy or K. E. of a body, is equal to the work which must have been done upon it to have brought it to its actual velocity from a state of rest. While ^potential energy is due to the acquirement of "strategical position," kinetic energy is due to the acquirement of "tactical impetus" or velocity.
Kinetic Energy = wv2/2 g and is derived from the familiar rela- tion v = V 2 g h since K. E. equals the weight of the body X height from which it would have had to fall to acquire its velocity.
Finally, it becomes obvious that Energy exerted = Work done.
In referring to the amount of work done in a unit of time, it is necessary to consider Power, which may be denned as the rate of doing work. Whether the propeller in the above example traverses the 80 feet of distance in one second, or in one hour, the actual work done in foot pounds is the same, since time is not a dimension of work. Ob- viously, it would take more "power" to overcome any resistance in one second than in one hotir, and to measure power it is necessary not only to consider the resistance and the distance traversed, but also the time it takes to do it.
Power, then, is the number of foot pounds per second or per minute or the number of mile-tons per year, if we choose to use such units.
The customary unit of power is the Horse-Power.
One horse-power equals 33,000 foot pounds per minute, or, 1 h.p. = 550 foot pounds per second.
Thus, when a weight of 5.5 pounds is moved 100 feet per second, one horse-power is exerted.
An aeroplane,, with a resistance in the air of 200 Ibs., requires 29 h.p. when travelling at 80 feet per second, since 200 x 80 -*- 550 = 29 h.p.
It is interesting to note here, with reference to the possibility of man- power flight, that, for a few minutes a man can exert at the limit 200 ft. Ibs, per second, and for an hour about 100 ft. Ibs. per second, less than l/5th of one horse-power.
Although much energy is generated and expended, the fact re- mains that the sum total of all the energy in the universe remains the same. Mechanical energy and heat are converted one into the other, the heat of the boiler, taken from fuel coming from the earth, passes into the engine and into parts which do work against various kinds of friction, until finally the sum total of the mechanical energy has returned to the earth, from whence it originally came, as heat.
The law of the Conservation of Energy is the most firmly estab- lished of the laws of mechanics, and only by the creation of an addi- tional amount of energy in the universe, which is impossible by any known human agency, could perpetual motion be achieved, although some magnetic and atmospheric phenomena may be used very nearly to approach it.
38
POWER EFFICIENCY.
Any machine, in order to accomplish an amount of work in a given time, must have work put into it in proportion. Due to friction and other losses, it is always true that the power obtained from a machine is not as great as the power put into it.
Now, call P, the power delivered by a machine, and P' the power necessary to put into it, then the ratio P/P' will be less than unity, ordi- narily; it might be equal to 1, if the machine were a perfect one with no losses but never can it exceed one.
The ratio of the power delivered by a machine and the power it used in doing so is called the Power Efficiency of the machine.
We have used above an example of an aeroplane, with a flying resistance of 200 Ibs., which, when it was travelling at 80 feet per second, required 29 h.p.
If the h.p. of the engine were 50 h.p. then the efficiency would be 29/50 or 58%.
It is most important in this study clearly to understand the sig- nificance of Power Efficiency.
FORCES REPRESENTED GRAPHICALLY.
The development of a simple notion into an extensive science is well illustrated in Graphic Statics.
Based upon the elementary fact that a force can be represented by a line, — long enough to measure its magnitude to some convenient scale, and placed so as to indicate the direction in which the force acts with reference to some fixed point — there has been built up a com- plete science of the action of every kind of force, and in many cases simple solutions are obtained for problems that would require com- plicated mathematics.
For all ordinary engineering the numerical computation of the characteristics of forces has almost entirely given way to their determi- nation by machine-like graphical methods. In later chapters the particular application of graphical methods to determine the stresses in aeroplanes will be taken up.
It will suffice here to give a general idea of how the combined effect of several forces can be determined, — composition of forces : and how a single force can be split up into an equivalent set of forces — resolution of forces.
The single force, that would have the same effect at a point as a set of several forces, is called the Resultant.
Referring to the diagrams, illustrating the action of forces, it is indicated that two forces of 4 and 9 Ibs. are acting at a point o. It is desired to know what their combined effect is, so that a single force could be placed at o that would resist their combined action.
The mechanical process of finding their resultant consists merely in applying what is often called the "parallelogram of forces," p. 34.
39
Graphically, the mechanical process is as follows: Lay off AB parallel to the 4-lb. force, and from A lay off AC parallel to the 9-lb. force. Com- plete the parallelogram to E, and draw AE. Then choose some scale, such that AB when actually measured on the drawing measures 4 units, and AC 9 units. With this same scale measure AE. It scales about 10 y% units.
Therefore, its value is 10 ^ pounds.
Its direction is given by the direction of AE so that by drawing the force through o, parallel to AE, and making it 10 }/2 pounds long to scale, we completely determine it in direction, magnitude and point of application.
Finding the resultant of any number of forces, whether co-planar or not, consists in rinding the resultant of two, then finding the re- sultant of this resultant and one other, and so on.
Moments are defined on the diagram as merely the forces times their perpendicular lever arms, from the point about which moments are taken. If the force is expressed in pounds and the lever arm in feet, the moment is in foot-pounds. The unit is the same as in Work, but obviously, moment expresses what could be termed the Potential Energy of the force.
Scaling lever arms of forces, from diagrams to scale, is by far the easiest and quickest way to obtain them.
Of course, if a point is in equilibrium, all the forces pulling one way are balanced by forces pulling the opposite way. In the same way the sum of moments of all the forces will be zero. This is a very important conception to keep in mind.
The resolution of forces into parts or complements, along given directions or axes, is indicated in the diagram, and is, briefly, a reverse application of finding the Resultant.
The intricate-looking but simply-made stress diagrams of braced frames, like bridges, are made of an elaboration of compositions and resolutions of forces.
In all this graphical work, it is best to appreciate at the outset, the necessity of learning the mode of procedure of laying off the lines like learning to run a machine and then merely keeping the scales used clear and unconfused. Successfully to determine stresses it is as un- necessary to know the theory involved, as it is for the average taxi- driver to know the theory of why certain mixtures of gasoline and air are explosive.
40 Charts and Graphs.
The representation of the variation of something, as a graph on a chart, is merely a convenient way of tabulating results. Instead of having long, cumbersome tables, giving values, at certain intervals, it is far easier to represent them on a chart.
If it is but appreciated that a graph is a table with values for all intervals between the limits indicated, its convenience becomes very evident.
Diagrams are given, as an example, of two types of co-ordinates, the Rectangular and the Polar.
Graphs are used very extensively in studying Aviation, and the power curves for Aeroplanes bid fair to become as universal as the power curves for electric railway cars, etc.
The combination of several curves on the same chart is illustrated in the diagram, and consists merely in keeping the same cross lines, but assigning to them different scales.
SEVERAL VIEWS OF SEAPLANES HYDROPLANING AND FLYING
CHAPTER IV. AIR RESISTANCES.
The Aeroplane, having been described in a general way, and an outline having been given of the ordinary conceptions of science ap- plied to it, we can proceed with a detailed study of its various elements.
In considering the Aeroplane, three distinct features are pre- sented :
1. The determination of the reactions of the air on the parts of the moving machine, giving rise to resistances, lifting forces and thrusts.
2. The study of the construction of the machine to withstand these forces.
3. The investigation of the stability and manner of operation of the aeroplane, under the many conditions met with.
The determination of air reaction requires, at the beginning, a clear understanding of the nature of the air and how it may be expected to act.
It is well to realize that lifting forces and thrusts are no more im- portant than are the resistances, at the expense of which flight is ob- tained. And when it is found that for every ten pounds of air resistance saved there can be carried an additional load of almost one hundred pounds, the significance of low air resistance becomes apparent.
The late Edouard Nieuport, builder of the famous French mono- plane, made one of the greatest single advances in aeroplane construc- tion, in the past few years, by his practical development of aeroplanes with very low head resistance. And after the introduction of his ideas such rapid strides were made by constructors in the improvement of the aeroplane's efficiency, that load carrying capacity was almost doubled. Another lesson in the relative importance of the resistance to motion of an aeroplane, is found in the development of high-speed racing machines. It had been generally assumed that speed depended almost entirely on having added power, but the development of the Deperdussin monocoques proved that far better results could be ob- tained by systematic refinement and reduction in the resistances. It is needless to speculate on the speeds attainable in aeroplanes. The nature of air resistance and its increase with speed as considered in
42
this chapter, will lead to the realization that a high speed record of 130 miles per hour is not going to stand very long.
But it is not so much in the attainment of higher speeds that we are interested in air resistances, as it is in the reduction of the power necessary to fly. While fuselage and nacelle resistances are the largest, attention must be given to the air resistance of wires, fittings, struts, wheels, etc., the cumulative effect of which is surprisingly great. These resistances, however, are distinct from the resistance to motion of a wing that generates a lift.
The appreciation of the resistances of different forms and shapes is of great value in the field in determining their effect on the efficiency of a machine, and also on the stability, since changes in resistances are apt to affect the center of air resistance of the machine, and con- sequently the equilibrium of the air forces.
Occasions constantly arise in mounting bomb-dropping appar- atus, guns and other extra equipment, and in repair work, where in- formation of this kind is of value.
The Atmosphere.
The atmosphere is an ocean, consisting of a mechanical mixture of several gases with water vapor, and even on the highest mountain we are still living at the bottom of this ocean. The atmospheric en- velope has a definite extent, and at any point exerts a pressure which is given rise to by the weight of the amount of air above it. We are constantly carrying around, therefore, on our shoulders, on the roofs or buildings, everywhere, the weight of the column of air directly above. The higher up, however, the less is the weight of air, and, consequently, the less the pressure. Air being compressible this increase in pressure with decrease in altitude affects the weight of air per cubic volume. We would have quite an exact measure of height in, the atmosphere, in noting the corresponding pressure, were it not that this pressure is also affected by temperature and great wave movements of the air ocean, storms and winds.
As the temperature increases the density decreases, and the volume of a pound of air increases at the same pressure.
The unit of atmospheric pressure is the mean pressure of the air at sea level, at 60° F. and is called one "atmosphere." It value is 14.7 Ibs. per sq. in., and it causes the mercury in the barometer to rise 30 inches. Over one sq. ft., a pressure of one atmosphere is equiva- lent to a weight of 2,116 pounds.
43
For every 1000 feet increase in altitude the pressure decreases about y% Ib. per sq. in. At a height of 18,500 feet, atmospheric pres- sure is one-half of that at sea level, and at a height of 40 to 50 miles the air must be practically weightless.
At atmospheric pressure and 60° F., the weight or density of air is .081 Ib. per cubic foot.
It is convenient to recall that air is about 1 /800th as heavy as salt water, and 14 times heavier than hydrogen.
Nature of Air.
Since air has weight, it follows that, as a substance, it has inertia and momentum. The possibility of flight is due to the tendency of air to resist movement.
In addition to this, air is very elastic, but at aeroplane speeds, it may be considered, theoretically, as almost incompressible, like water.
Air is a "continuous" medium, each particle, naturally, tending to hold together with every other particle, and the tenuous manner in which any air disturbance influences adjacent air filaments is beau- tifully demonstrated in photographs of air flow.
Disturbances of the air cause up and down currents, complicated air vortices, aerial fountains, waves and pulsations, with changes in the velocity and direction of air streams; and just as water boils so will air boil, when heated. The action of the sun in boiling the air over a dry, open space, can be distinctly felt when flying.
In the consideration of air resistances, however, it is assumed that the air is uniform in flow, and at 60° F., and atmospheric pressure.
There is another very important conception, with regard to air resistance determinations. Disregarding the effects of inertia and acceleration of an object, the air pressures are the same in action, whether the object is moved against the wind, or the wind against the object.
Motion through the air gives rise to two distinct kinds of resis- tance :
1. Pressure, generated by the impact of the air on an object, and
2. Friction, generated by the flow of the air filaments past the surface of the object.
Characteristics of Air Flow.
Having defined air, the manner in which it flows may be con- sidered. Air either flows smoothly past an object in stream lines — continuous filaments — or it breaks up into swirls and eddies, due to too abrupt a change in flow. The accompanying photographs of air flow illustrate this.
44
PHOTOGRAPHS OF THE EIFFEL LABORATORY IN PARIS, SHOWING THE TESTING ROOM AND THE TWO WIND TUNNELS
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THE FLOW OF AIR
UPPER LEFT, A FLAT SURFACE - UPPER RIGHT, A SPHERE - LOWER LEFT AND RIGHT, STRUTS OF DIFFERENT FINENESS RATIO
45
It is apparent that a spindle or fusiform shape, gently dividing the air at the front, and gradually permitting the filaments to close together at the rear, will give a smooth flow, which amounts to the same thing as a very low resistance. It is also evident that a flat sur- face creates very great disturbance, and consequently high resistance.
The curve of the stream lines, necessary to prevent disrupting them, may be computed for any speed, by applying fluid dynamics. But it must be kept in mind that a form of this kind gives its low re- sistance, only at one particular speed, since the path of flow is affected by the speed. It is unnecessary here to take up the determinations of these forms. If the stream lines flow smoothly past an object, and close up again without eddies, it follows that the only resistance ex- perienced is frictional.
There are many ways of determining the manner in which the air flows past an object, such as noting the directions in which light silk threads are blown, or introducing smoke or particles into the air and photographing it. Ammonium Chloride is a very convenient smoke.
Importance of Visualizing the Air.
It is of great value in aeroplane work, to become accustomed to visualize the streamline flow of air, and ability to ''see the air" often solves many problems of stability and reduction in resistance, with- out any recourse to mathematics or measurements. Besides this, there is offered in the study of air flow by photography, a field of in- vestigation of great promise and absorbing interest.
It is a common experience that in a wind, at the front of a flat surface, there is a dead region of air, where no wind is felt. Photo- graphs show this air cushion clearly, and in Chapter VI this simple conception is found to hold a valuable theory.
In stability discussions, effect of following planes, interference, and propeller stream action, priceless secrets would be revealed if the air could be followed in its every movement.
Determination of Air Resistance.
The nature of the action of air on objects has been considered, but we must know in addition with what force in pounds P, the air pushes on an object when it passes it at velocity V.
Applications of Theory to determine the magnitude of air pres- sures, are given consideration in Chapter VI, but merely for reference, since the best measures of air resistance have been obtained by actual experiment.
46
Methods of measuring the resistance of the air that have been widely used, are the following :
1. Dropping surfaces from a height and measuring time of drop and pressure, used by Newton, and Eiffel in his earliest experiments.
2. The whirling arm, used by Langley, and consisting of whirling the surface at the end of a large arm around a circle of large diameter and recording the resistance automatically.
3. The moving carriage, an automobile, trolley or car, as used in the experiments of the Due de Guiche, Canovetti, and the Zossen Electric Railway tests.
4. By blowing or drawing air through a tunnel in which the object or a model of the object is placed. This method is the most modern and convenient, and permits of a uniformity of the air current, which cannot be obtained as easily in the open.
In wind tunnels, the best practice is to draw the air in, through screens and channels, that straighten it out, past the experimental chamber, and thence to the fan. Practically all the great Aerodynam- ical Laboratories use the wind tunnel method of experiment. The prominent ones are, the Eiffel laboratory in Paris, the National Physi- cal Laboratory in England, and the tunnel at the University of Goet- tingen. The speed of the wind in the Eiffel laboratory can be brought up to almost 90 miles per hour (40 metres per second), and its size permits of testing many objects such as struts, to full size, and complete models of aeroplanes to one-tenth full size. Such a magnitude per- mits of exceedingly val uable determinations, and the work of the laboratories is daily being applied with entire success to full-sized aero- planes, altho the higher speeds of aeroplanes require considerable cor- rection of wind tunnel results.
It must be borne in mind, however, that the air in a tunnel is con- fined and that all tunnel results are not perfectly adaptable to machines, unless suitable corrections are applied.
Measurements made in the laboratories consist of determining not only the magnitude, direction and position of the wind forces, but also in determining the distribution of air pressure over an object by measuring the pressures at different points.
Air Resistance varies as V2.
It has been found by very careful and extensive experimenting that the resistance of an object in an air stream is proportional to the square of the velocity of the air.
In other words, if the velocity is doubled, it follows that the re- sistance will be increased four times, or if velocity is five times as great, the force on the same object would be twenty-five times as great.
47
There are variations from this, however, due primarily to the fact that friction resistance alone, as distinct from impact resistance, varies as V1'8 increasing in less proportion than V2. On very large surfaces, and particularly on dirigible balloons, of streamline shape, the frictional part of the resistance is by far the greatest, and conse- quently makes the total resistance increase in a proportion less than V2.
For our purposes, however, the total resistance, of objects, in- cluding the pressures and frictions, are considered as varying with V2.
Air Resistance varies as S.
The size of the surface area, on which the air acts, S, gives a mag- nitude of air resistance that is in direct proportion to the size. If the area of the object is doubled, the air resistance is doubled, at the same air speed.
This experimental fact is also subject to modification, since, as the size of surface increases, the pressures are somewhat greater in proportion. But we can disregard this also without serious error.
Formula for Air Resistance.
It follows, therefore, from the above, that if we call P the force generated by the air movement at velocity V against an object of area S in cross-section, then P varies as SV2.
This at once leads to an empirical formula, for the air resistance,
P = kd S V2 This is the fundamental formula of Aerodynamics.
The units used will be S in square feet, V in miles per hour and P in pounds. The density of the air is d which varies with the altitude and k is a numerical value or "constant" determined by experiment, in order to express this relation as an equation.
In this chapter we are interested in the air resistance of various objects and parts made use of in flying machines — and in adding to the air resistance of these parts the air force on the wings, that must be overcome to obtain the lift, we obtain the value of the total resist- ance to motion that is overcome by the propeller thrust.
If experiments to determine k are conducted at sea level, the density d is fixed, so that kd can be combined into one term, which we call K, and which is the experimentally determined coefficient to use in the formula for the resistance of any body at sea level. At higher altitudes K would have to be modified, but for our comparative study, we will simplify it by considering the sea level condition only, and therefore the equation is written, P=KSV2.
In view of the above formula, it becomes necessary, merely, to review and average up the laboratory results, so as to obtain values of K for the various different objects, where K = kd at sea level.
48
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THE RESISTANCE OF VARIOUS]|SURFACES AND BODIES
49
Definitions.
In Aerodynamical studies it has become customary in denning objects to use unfamiliar terms.
Aspect Ratio — is a term used to define the shape of a surface, and is the long span of the surface across the wind divided by the width.
Fineness Ratio — is a term used to define the general shape of bodies, and is obtained by dividing the fore and aft length of the body by the. greatest width across the wind.
Master Diameter — is the greatest width of a body across the wind.
Fairing — is used to denote the additional "tail" or filler used to make a poorly shaped body more streamline in form, thereby reducing its resistance.
Diametral plane — is the plane, passed through a body, facing the wind perpendicularly, and cutting through at the master-diameter.
Normal plane — is another expression for diametral plane, and merely refers to the maximum cross-sectional projection of the body. It also refers to a flat surface held normal (perpendicular) to the air current.
Equivalent Normal Plane — is the size of normal flat surface, that would give the same resistance as does the body referred to.
It has been customary to refer to the air resistance of all bodies, as a percentage of the resistance of a flat square normal surface under the same conditions.
In this study, no such conception will be used, since values of K for each particular body are studied, and the flat square normal plane or surface is merely considered as one of several kinds of air-resist- ing bodies.*
Flat Surfaces,
Normal to the Air Stream. Square Planes —
In square planes, normal to the air, the value of K is .003 for sur- faces up to two or three feet square, and .0033 for very large surfaces like the sides of buildings.
It may be stated, therefore, for aeroplane usage, that P, the air resistance in Ibs., of a square surface, S sq. ft., in area, at a velocity V miles per hour, is
P = .003 S V2
Thus, for a surface 2 feet square, at 70 miles an hour: P = .003 x 4 x 4900 P = 58.8 pounds
* Attention is invited to the author's work "Monoplanes and Biplanes," Chapt. II, where a discussion of experimental results and many values of K are given.
50
In curve No. 1 p. 48, the graph gives values of P in Ibs. per sq. ft. for speeds up to 120 m. p. h. In the above example, at 70 m. p. h. the graph gives P = 14.7 Ibs. per sq. ft., or 14.7 x 4 = 58.8 Ibs., since S = 4 sq. ft.
Rectangles —
The aspect ratio of a square is one. Rectangles have aspect ratios above one, when presented normally to the air.
Up to an aspect of 5 or 6, K remains about .003.
An increase in the value of K is found for rectangles as the aspect ratio increases.
When the aspect ratio of the rectangles increases to 15, K becomes .0035 and on further increasing the aspect ratio to 30, K = .0038. This is shown on the graph, p. 48.
A flat rectangle, perpendicular to the air current, with its dimen- sion across the current, thirty times as large as its width, might be met with in rods, temporary struts, etc., and it is interesting to note how high the resistance would be.
Discs -
The shape of flat surfaces also affects their air resistance. Pass- ing from a square plane to a round disc, reduces K to .0028, so that the air resistance of a disc 2 feet in diameter, at 60 miles per hour, is P = K S V2 = .0028 x .7854 x 4 x 3600 P = 32 pounds
In general rounded edges may be expected to reduce K, for flat surfaces.
Parallel Normal Surfaces —
Discs or flat rectangles, placed one in front of the other, interfere with each other and exhibit a most important phenomenon. When the discs are separated by more than two diameters, both receive pres- sure; there is a pressure on the front disc somewhat greater than on a single disc, K = .0031, and a very slight pressure on the rear disc. But with spacing less than this, the rear disc ceases to have any pres- sure, and instead undergoes a suction effect, which action actually pushes it toward the front disc. The forward push of the rear disc naturally reduces the total resistance of the two discs to a smaller value of K, making it much less than a single disc, when the rear one is 1 J/£ diameters back of the front one. This phenomenon is given rise to by the nature of the air flow, which is illustrated in the diagram. A familiar application of this is where the racing bicycle rider follows in the wake of a motorcycle pace-maker.
Various Shaped Bodies. Cylinders —
Passing from the disc to the cylinder, with the circular base facing the wind, the resistance is found to be less as the length of cylinder
51
is increased, until the length becomes greater than 5 diameters, when the resistance is found to increase again. Some values of K are given on the chart. K for a cylinder 7 diameters long is .002.
When this cylinder is capped by hemispherical ends, the value of K falls to .0006, an interesting result.
When the cylinders are stood upon their bases various values of K are given. It is most important to point out that for the two cases corresponding with high aspect ratio — the cylinder with height very low in comparison to the diameter, and the long cylinder with diameter very small in proportion to height — the values of K are high.
Wires and cables are merely very long cylinders. Extensive ex- periments have been conducted on them, and values of K found. For smooth wires K = .0026, whereas cables are found to have considerably higher resistance with K = .003.
Thus, a machine having 200 feet of 1/8 inch cable, giving a pro- jected area of 200/96 = 2.08 sq. ft., will have an air resistance due to the cables at 80 miles an hour of
P = .003 x 2.08 x 6400 = 40 Ibs.
This high value immediately suggests the advisability of reduc- tion of cable resistances. In double cables, it would prove beneficial to tape them together, so as to streamline each other. A graph is given showing the reduction in resistance due to inclining the wires i. e., staggered planes.
Experiments indicate that the vibration of wires does not increase their resistance.
Spheres —
The resistance of the air on spheres presents a study of interest. The sphere is the simplest geometrical form, and, as a basic one, it should long ago have served as the unit form for air resistance. Lack of agreement in the experimental results of different laboratories was only cleared up when Eiffel discovered that an increase of speed of the air above 20 miles per hour caused a change of flow, due to the flatten- ing out of vortices back of the sphere, which reduced the resistance considerably. And that above this speed, the nature of the air re- sistance remained constant. K = .00044, for a sphere, at speeds above 20 miles per hour, whereas at very low speeds K becomes .001. In having a smoother flow at the higher speeds, less Ibs. of air are put in motion, which means that the resistance is less. This action of air, in tending to smoother flow with speed increase, is important to bear in mind.
For a hemisphere, convex side to the wind, K = .00083, and when turned so as to present the concave side to the wind, K increases to .0038.
52
P= f/0% rf$. of ont disc -by
indt'ccftf rfireclJon of
The bodies are placed in the order of their least resist- ances.
For the top one K = .00012 For the lower one K = .0002
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TOP LEFT - INTERFERENCE OF FOLLOWING DISCS - TOP RIGHT, THE BODIES TESTED AT GOETTINGEN - BELOW, BODIES TESTED
BY EIFFEL.
53
Streamline Shapes —
In this class may be included bodies of fusi-form or streamline form, shaped for least resistance. Their application to the design of tanks, fuselages, nacelles, hoods, etc., is of fundamental importance.
In a most interesting set of experiments, conducted by M. Eiffel, on streamline shapes, illustrated in the diagrams and chart on p. 52, the bodies consist of a nose, a cylindrical central portion, and a tail. The results of the experiments show that :
1. The blunter the nose, the greater the resistance.
2. The shorter the central cylindrical portion is, for the same nose and tail, the lower the resistance.
3. The effect of shortening up the tail is not very great, although slightly increasing the resistance.
In each case, however, measurements made at speeds up to 90 miles an hour showed that the resistance does not vary as V2, the value of K becoming constantly less with speed increase. This is a very sig- nificant determination, and may be explained on the ground that, in bodies of this kind, the major part of the resistance at high speeds is frictional and therefore increases at much less than V2. In addi- tion the effect of velocity increase is to flatten out the flow and suppress eddies.
The values of K for these bodies are given.
The Goettingen Laboratory conducted extensive experiments on the best shapes for dirigible balloons which it is important to consider. The models tested measured 3.75 feet long and .62 feet in diameter, giving a fineness ratio of 6. The shapes in their order of least resist- ance and values of K for 25 m. p. h. are given. At higher speeds, still lower Ks would be expected.
The form No. 1, having the least resistance, is, perhaps, the best form that has ever been tested in a laboratory, and at high speeds would give a resistance about I/ 25th of the normal pressure on its diametral plane. It is the form used in the Parseval non-rigid diri- gibles.
It is interesting to note in studying low resistance bodies, how closely they resemble the shapes of fishes, and of birds, measurements of a fast swimming fish showing an almost exact resemblance to this Parseval shape.
As a general rule, the best streamline body is the one having a fine- ness ratio of 6 and with the master diameter about 40% back of the nose, both nose and tail being fairly well pointed. Struts—
The application of fineness ratios, and shapes of least resistance, to improvement in the form of struts, has in many instances tremen- dously improved the performance of aeroplanes.
54
*INPL
THE RESISTANCE OF SEVERAL STRUTS OF DIFFERENT SHAPE
55
In addition to the form for least resistance, however, the weight of the struts and their strength are factors that must be considered in choosing the best shapes. We will confine ourselves here, how- ever, to a study of the resistance of various shapes.
A group of strut sections are given and K for each one. It is to be noted that the effect of yawing is greatly to increase these resist- ances by presenting the strut sidewise to the air, and it will be neces- sary later to consider the amount of this increase.
Inclining the strut to the vertical, as in staggered planes, has the effect of increasing the length of section in the air stream, and, con- sequently, the resistance does not decrease for streamline shapes, while for blunter shapes, inclination reduces the resistance considerably.
In struts, as in bodies, an increase of velocity is accomplished by a reduction in the value of K, that is more noticeable the greater the fineness ratio, i. e., the longer the section of the strut. This is again due, probably, to the preponderance of friction in the total re- sistance.
The results obtained in studies of strut resistance indicate the importance of having struts well made and of a uniform section. Just as in bodies, abrupt changes in contour must be avoided and atten- tion paid to a smooth curve on either side of the central portion.
It is found, in general, that a fineness ratio of 5 to 1 is best for use, where a fin effect is desired, and where not, — the best fineness ratio is 3 to 1.
Wheels -
The air resistance of chassis wheels is a considerable item in flight.
Experiments have been conducted on various-sized wheels, and the
results are as follows :
28y2" diameter by 2^"tire, K = .0025 24 " " " 3 " " K = .00265 21 " " " 3 " " K = .0018 18 " " " 2 " " K = .0021
When the wheels are covered in, it is found in almost every case that the resistance is halved, so that for the 24" x 3" wheel, when covered in, K = .00133. An average K for wheels would be .002.
As an example, it is desired to determine the resistance of two 26" x 4" wheels at 80 m. p. h.
The projected surface = 1.4 sq. ft.
.'. P = .002 x 1.4 x 6400 = 18 Ibs.
If the wheels were covered in at this high speed, about 9 Ibs. would be saved in resistance; this would permit of carrying about 60 Ibs. more load on an efficient machine, or would add 10 gallons more fuel.
56
Fuselages and Empennages —
The resistances of the bodies of aeroplanes, and of the tail pieces, constitute the major part of the resistance, and their importance and variations, with angles of yawing and pitching, make it necessary to give them separate consideration in a later chapter.
It may, however, be pointed out that the data on streamline bodies given, is readily applied to fuselages. The laboratories, however, have studied complete aeroplane models and fuselages, and have ob- tained valuable results.
Summary.
The data given in this chapter enables the air resistance of vari- ous shaped bodies to be computed for any speed V and any size sur- face S, where S is the maximum cross-sectional projection of the body, perpendicular to the air stream. It is merely necessary to supply the numerical values of K, S (in sq. ft.), and V (in m. p. h.), in the formula
P = K S V*
Where K = kd, d being the density of the air, and the values here being correct only for sea level and therefore largely comparative.
It is well, again to recall that the propeller of an aeroplane must give a pull or push great enough to overcome:
I. The resistance to motion of the struts, wires, body, wheels, fittings, skids, gas tanks and other attachments.
II. The dynamic resistance of the wings and rudders, called the Drift and generated by the same pressure that gives the Lift.
In this chapter the first has been considered. And a study of the second may now be taken up.
A TRACTOR AEROPLANE CLIMBING
CHAPTER V. INCLINED SURFACES.
In order to understand the mechanics of flying it is necessary to have a sound conception of the nature of air pressure on inclined surfaces. On a plane presented to the relative air current, at an angle less than 90°, the generated air pressure instead of acting straight back is inclined above or below the line of flow of the air.
Before discussing this, however, a few unfamiliar terms need to be defined.
Span is the dimension of a surface across the air stream.
Leading edge, is the first edge of the surface upon which the air impinges, whereas, trailing edge, is the rear edge of the surface.
Chord, is the dimension between the leading edge and the trailing edge of a surface. It is the depth of surface along the air stream.
Surfaces are of two kinds — flat in section and curved in section.
Camber, is the rise of the curved contour of an arched surface, above the chord line.
It follows from the above that for any inclined surface,
Span
Aspect Ratio
Chord
The explanatory diagrams on p. 60, are referred to, and it is seen that any inclined surface, is one in which the chord is inclined to the line of flow of the air.
This angle of inclination of the chord to the air stream is termed angle of incidence.
If the leading edge of a surface is presented to the air, above the trailing edge, the angle of incidence is said to be positive. And when the surface is inclined negatively to the air flow, it is meant that the air impinges on the top face of the surface, since the leading edge is below the trailing edge.
58
Lift and Drift.
The air acting on a surface presented to it with a positive angle of incidence generates a pressure, the line of action of which is pointed upwards and at the same time somewhat backwards. As the incidence of the surface is varied, of course, the inclination of this force above the horizontal is varied. But the important conception to grasp is, that the effect of inclining the surface below 90°, is to cause the total air pressure to assume an inclined position, with respect to the axis of flow of the air.
If the inclination is such that the total pressure points upward and backward, a study of the resolution of forces teaches that the verti- cal portion, or component, is equivalent to a force acting vertically upwards, capable of lifting weights, whereas the horizontal compo- nent of the same total air pressure is a resistance to motion.
It follows that in order to obtain this lifting component the hori- zontal one must be overcome, the two together corresponding to the resultant total pressure on the inclined surface.
Lift is the vertical component, called L.
Drift is the horizontal component, called D.
The resolution of the air pressure on an inclined surface into Lift and Drift, is the fundamental process in the mechanics of the aeroplane.
Drift is a drag or resistance to motion which is overcome by the thrust of the propeller, and at the expense of which a total inclined pressure is generated on the aeroplane surfaces, the vertical compo- nent of which is sufficient to support the weight.
Since Drift is a function of the pressure necessary to lift the weight, it now becomes apparent why Drift was classified as distinct from the head resistances of the various parts of a machine. The latter are due solely to their form and the speed of travel, and they exert no effect on the lifting power itself.
Consideration of this resolution into Lift and Drift, at once in- dicates that the characteristics to be sought for in a surface are great lift with a very small drift, so that for a minimum expenditure of power a maximum load carrying capacity is obtained.
The ratio of lifting power, L, to drift D, is a function widely used in considering the efficiency of surfaces, and the higher the value of L/D the greater is the weight that can be carried per pound of resist- ance.
It is well again to emphasize, that total resistance to motion is composed of two distinct items.
1. The air resistances of the various parts of a machine, such as struts, wires, wheels, bodies, etc.
2. Drift (in which is included the head resistance and f fictional resistance proper of the wings alone, at the particular angle at which they are presented).
59 Flat Planes.
It is necessary to draw a distinction between planes that have a flat cross-section, and surfaces that have a curved cross-section, be- cause the variations of the air pressures in magnitude, position, and dirction are quite distinct.
Let P90 represent the normal pressure on a surface set at 90° to the air stream and determined as explained in Chapter IV, pp. 49-50. And let Pa represent the total pressure on the surface when it is set at an angle of incidence A to the air stream.
It would be possible to express the variation of Pa, with changes in the angle of incidence a, as a percentage of P90 = K S V2. This would necessitate determining the ratio Pa/P9o, which is called the "ratio of inclined to normal pressure." Then
Pa = Pa/P90KSV2
where K is chosen for the particular aspect ratio used (see p. 50). This is the system ordinarily employed, but for our purposes it is consider- ably more convenient to return to the conception of having values of K tabulated for each separate item. So that we may call Ka the value of the constant in the expression
Pa = Ka S V2
and proceed to investigate the values of Ka for different angles of in- cidence, on the various surfaces. Thus, if we desire to determine the total pressure on a surface set at an angle of incidence, a = 6°, our system of notation becomes quite clear, in stating
P6 = K6 S V2 Lift and Drift.
It is a fundamental fact of aerodynamics, capable of proof, that, in flat planes, Pa is always perpendicular to the chord. This sim- plifies the consideration of inclined pressures on flat planes, since at any angle of incidence we know the direction in which the air pres- sure acts. Thus, a flat plane, set at an incidence of 10°, is acted upon by an air force, the line of action of which is pointed 80° above the direction that would be taken by the normal pressure.
This uniformity in the direction of Pa, with reference to flat planes, enables us to obtain very simple rules for finding the Lift and Drift of flat sections.
Obviously from the resolution of forces
Lift = Pa cosine a, = Ka S V2 cos a
Drift = Pa sine a, = Ka S V2 sin a In addition, the Lift-Drift ratio, L/D = cotangent a.
To determine the magnitude of the forces on flat planes, there- fore, it is merely necessary to know the appropriate value of Ka, as determined by mathematics or experiment. *
* In the author's work "Monoplanes and Biplanes," many relations for Pa are considered, in Chapter III.
60
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DEFINITIONS
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The definitions for flat and curved sections, given on p. 57, are shown at the top of the page.
Curve 2 shows the variation of Ka, for aspects of 1/3, 1. 3, and 6. Curve 3 shows the c. p. movement for the various aspect ratios.
61
The variations of Pa are affected by Aspect Ratio, and a very remarkable distinction between squares and rectangles in the man- ner in which Pa varies as the incidence is changed was discovered by Eiffel. At angles in the neighborhood of 40°, on square planes, Pa was found to have values very much greater than P90.
Values of Ka for several different aspect ratios are given in Curve No. 2, p. 60.
It will be seen from this graph, that an increase of aspect ratio above 1 is accompanied by increases of Pa, at low angles. But there is a general falling off of this at 15° to 20°, as the aspect ratio is in- creased. For efficiency, at low angles, on flat planes it is advisable therefore, to use the higher aspect ratios.
In all cases, S is the plan area of the surface.
Center of Pressure.
Although the direction and magnitude of forces on flat surfaces have been considered, these forces are not fully defined until determi- nations are obtained of their point of application.
The nature of the air reactions on a surface consists of a series of small impact pressures and friction rubs all over the surface; but their total effect can be represented graphically by a single force, in the resultant direction, and applied at a point about which all pres- sures balance.
This center of balance of air reactions is termed the "center of pressure," and if we draw thru it a force proportional to Pa, and in direction normal to the surface, we have completely defined the air reaction on that particular flat plane.
On flat surfaces it is indicated by Curve 3 that, as the incidence is decreased, the center of pressure moves forward until at 0°, it is very near the front edge, and at 90° it is at the center of surface.
The representation of position of center of pressure, c. p., as a percentage of the chord, is a convenient one that has become quite standard.
Example.
A typical example of the use of the data given for flat planes may prove of interest.
An aileron, flat in section, measuring 2 ft. chord by 12 ft. span (aspect 12 -T- 2 = 6), is pivoted 4 inches back of the leading edge. The aileron is moved to an incidence of 10° and the air speed is 60 miles per hour.
It is desired to find the corrective force on the balance of the ma- chine represented by the lifting force of the aileron, at 10° incidence.
62
Lift, L = Ka S V2 cos a. From the chart we find that for a plane with aspect ratio of 6,
Ka = .00175,
and Cos 10° = .985, S = 24 sq. ft., V2 = 3600, so that L = .00175 x 24 x 3600 x .985
= 149 Ibs.
In addition it is desired to know the moment of the total pres- sure Pa, about the pivot, at 10° incidence. From the graph it is found that
c. p. position = .33 chord = .33 x 24
= 8 inches from leading edge.
It follows, therefore, that the lever arm of the total pressure Pa about the pivot is 4 inches.
Pa = Ka S V2 = .00175 x 24 x 3600 = 151 Ibs. Therefore, the moment about the pivot is, = 151 x 1/3 = 50 foot Ibs.,
which would enable the pounds pull on a control mechanism to be determined, and leverages suitably arranged.
Curved Surfaces.
Although the general characteristics of the action of air on flat planes had been known more or less accurately for some time, the nature of air reaction on curved surfaces was not well appreciated until the pioneer work of Lilienthal and the Wrights disclosed it.
Lilienthal disco\ered that, at low angles, surfaces slightly cam- bered gave very much more lift and less drift, than did flat planes, at the same incidence, and that the resultant total pressure was not necessarily perpendicular to the chord, as on flat surfaces. In fact, he found that at certain low angles of incidence the total pressure on a curved surface was leaning considerably in front of the normal to the chord line, which meant that a smaller proportion of this total pressure was drift, and a greater portion was lift.
It is upon this discovery that the first practical demonstration of the possibility of flight may be said to have originated, and suc- ceeding generations are justified in hailing Otto Lilienthal, in view of his classic experiments, as the discoverer of modern flight.
The Wrights, in their gliding experiments, discovered that the center of pressure on an arched surface of Lilienthal type, did not change its position, in the same way as the c. p. on a flat plane, but that in- stead of moving steadily forward as the incidence was diminished the c. p. on the curved plane ceased to move forward at about 10°-15°, and retrograded, moving rapidly past the center of surface, towards the trailing edge as the angle grew smaller. This feature rendered Lilienthal's measurements somewhat inaccurate, but the corrections, readily applied, were used to make the old results applicable to the modern aeroplane.
63 KL and KD
Since the total pressure on the curved surface, which we will call Pi, is not necessarily perpendicular to the chord line its resolution by trigonometry into Lift and Drift is not possible unless we know its inclination with respect to the chord line. But, since this neces- sitates knowing its components, it becomes, at once, more convenient to study curved surfaces directly from measurements and data on Lift and Drift.
This is done throughout the study of curved surfaces and aero- foils (aeroplane sections), and in the laboratories it is customary to measure the vertical and horizontal forces on curved surfaces. The resultant of these determines PI, in magnitude and direction. But since we are rarely concerned with PI, where data is already available on L and D, its consideration is not so important.
To define L and D, it is most convenient to consider that
L = K SV*
D = KD S V2
and information on curved surfaces resolves itself into a study of the values of KL and KD for the various angles and shapes.
In this chapter, the simplest geometrical curved sections only are considered, as it is desired merely to bring out the main distinctions between flat and cambered sections.
The standard practice is adopted of referring to the camber of curved sections, as a fraction or percentage of the chord.
Forces on Cambered Planes.
The resolution of P into L and D is fully indicated in the diagrams on p. 64. The angle of incidence of the chord with the air stream is called i. But, since in cambered planes PI is not necessarily normal to the chord, it follows that the angle between PI and L is not neces- sarily equal to the angle of incidence i, as it is on -flat sections. This angle of the resultant with the vertical is called r, and from the con- struction of the triangle of forces it is apparent that tan r = drift/lift, and the ratio of L/D = cotangent r.
The nature and determination of "Lilienthal's Tangential" is not considered necessary in this study, although it is frequently dwelt upon in elementary aerodynamic treatises. *
Influence of Aspect Ratio.
The manner in which a change in Aspect Ratio affects the forces on circular arcs is shown in the charts on p. 64. It is found that not only the magnitude of L and D, but the movements of the center of pressure are influenced very much as on flat sections. For a circu-
* See "Monoplanes and Biplanes" Chapt. IV, p. 47.
64
To find D at any angle, divide values of L by corresponding values of L/D.
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Curve 4 shows coefficients Lift and Ratios of L/D for changes in aspect ratio, of a circular arc.
Curve 5 shows the c. p. movements for the same surfaces.
65
lar arc in which the camber is 1/13.5 of the chord (an average camber for good efficiency), the values of L and L/D steadily increase as the aspect ratio is increased from 1/3 to 6. The difference between aspects of 6 and 9, however, is not very marked, and it is indicated from these results that there is not much gained by increasing the aspect of an aeroplane wing above 6. With reference to the total pressure PI, it is found for cambered planes as it was for flat ones, that when the aspect ratio is 1 (a square), Pi rises to a value more than once and a half times the normal pressure P90 at an angle of about 40°.
The center of pressure chart shows that as the aspect is increased the reversal of movement at low angles becomes sharper, and the angle at which this reversal takes place falls from 45° for aspect 1/3 to 13° for aspect 6.
Effect of Depth of Curvature.
Alterations in the camber, i. e., in the depth of curvature of cir- cular arcs, greatly affect the magnitude of L and L/D, and the move- ment of the c. p. In the charts, on p. 66 there are plotted, the curves, showing the values of KL and L/D for arcs of 1/27 and 1/7 camber, with an aspect of 6, which are to be compared with the curve for a 1/13.5 camber, aspect 6.
It will be noted that the magnitude of L increases with the in- crease of camber, but the ratio of L/D is decreased by camber increase and the point of maximum L/D varied. This indicates that deeply cambered sections would prove to be inefficient wings for aeroplanes.
For the smaller camber, the c. p. movement is sharper, and the reversal point further forward.
The Reverse Curve.
Sections of cambered surfaces may, of course, be other than cir- cular. Combinations of straight lines and circular arcs, parabolic curves, spirals, and the like, have characteric pressures that differ from each other, but in so small an amount that it is hardly necessary to give them separate consideration — excepting in so far as they are taken up later in studies of aeroplane wing sections.
The reversed curve, however, is a distinctive geometrical section, to which attention should be given. These sections, as illustrated in the diagram, have the important property that the center of pressure continues to move forward as the angle is decreased, the character- istic retrograde movement, as found on circular arcs, being apparently absent. As will be explained later, this retrograde movement tends towards instability, and although the ratio of L/D and L are very greatly reduced by a reverse curve, it becomes necessary to bear in mind that for aeroplane wing sections the loss in efficiency may be worth while, in order to gain in stability.
66
.005
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.001
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Curve 6, shows the coefficients for Lift, and the values of L/D, for arcs of 1/7 1/13.5 and 1/27 camber, and the reverse curve section.
Curve 7, shows the c. p. movement for the same sections.
67 Aerofoils.
Only flat and the simplest geometrical sections have been con- sidered here. In aeroplane wings, it is necessary to have spars and ribs of considerable depth, in order to obtain suitable strength and rigidity of wing. This leads to sections of surfaces in which two cur- vatures must be considered — the top face and the bottom face.
An aeroplane wing section is, therefore, distinct from geometri- cal sections, and it is customary to refer to aeroplane types of sur- faces as Aerofoils. They are treated of fully in Chapter VII, since a knowledge of their characteristics, advantages and disadvantages enables the first essential step in the design of an aeroplane to be taken — the choice of a wing section that will give the weight-lifting, strength and speed combination desired.
Examples of the application of curved section pressures are taken up in several instances in the consideration of aerofoils, and many of them are deduced from actual practice as applied in well known types of aeroplanes.
Summary.
I. In flat surfaces.
The total pressure Pa is always normal to the section, and can be resolved into,
Lift = Pa Cos a Drift = Pa Sin a
The center of pressure moves forward as the incidence is decreased.
II. In cambered surfaces.
The total pressure Pi is not always normal to chord, and the pressures on a cambered plane are, therefore, more easily ex- pressed as
Lift = KL S V2 Drift = KD S V2
In the terms KL and KD, the same applies as in the previous chapter, the values given being the experimental ones determined at sea level, where actually KL = kLd, and KD = kDd, d being the density of the air. This must always be kept in mind. And at 18,500 feet, d being one half of its value at sea level, KL or KD would be one half the values given.
The center of pressure, on curved surfaces, moves forward up to a certain low angle where it reverses and moves rapidly to the rear' (except for reverse curved surfaces).
68
— 1
Photographs of air flow, showing air deflections, obtained at the author's labor- atory, by introducing chemical smoke into the air stream.
.s^--
&m
Normal Surface
Inclined Surface
DIAGRAMS OF AIR FLOW
Photographs of air flowing from left to right, on flat surfaces, made at the Kout- chino laboratory. Note the general deflection of the air stream, in the lower right hand photo, where the plane is at a low angle of incidence.
CHAPTER VI. AERODYNAMIC THEORY.
Although it is not 50 essential to consider the theoretical deriva- tion of formulae for air resistances in a work of this kind, a certain interest is attached to the application of the more recent experiments on the flow of air streams to the older conception of the mechanics of the air.
An outstanding experimental fact in air stream photographic studies, that vitiates many established aerodynamic derivations, is that the air stream, when it impinges against a normal surface, divides to pass around the edges, and in doing so actually imprisons a cushion of dead air against the surface, a phenomenon constantly met with in wind effects on moving vehicles, etc. Furthermore, in dividing, the air stream acts as if separated by two physical surfaces and takes a deflection of about 45°, instead of being turned thru an angle of 90°, as assumed in older hypotheses. Many photographs of air flow, in- cluding several taken in the writer's laboratory in New York, confirm this.
The mechanics of air flow on normal surfaces, if the air is con- sidered as deflected at 90°, may be stated as follows:
Moving air develops a pressure equal to its momentum, expend- ing its entire energy by impact. Momentum = mass X velocity. The mass of air = W/g, where W is its total weight, and equal to the unit weight or density of air w, x the volume of air moved, which is equal to S V, where S is the surface in sq. ft. and V the velocity in ft. per sec.
Supplying appropriate values we get for the total resistance,
P9o = w/g S V* = .0054 S V2
which is a formula of the form P = K S V2 in which K = .0054.
This value of K we know by experiment is quite incorrect, and it follows that we must consider the derived result worthless.
If, however, we start with the more correct hypothesis, that the air is deflected at about 45° (depending possibly on friction effects) instead of 90,° a derivation of this form would result.
70
Let A B, in diagram p. 68, represent the surface of area S, in an air stream of velocity V. Let ABC represent the imprisoned cushion of air, and A C and C B the surfaces of air along which the deflected stream flows.
Let s' and s" represent the normal projections of A C and B C.
The total energy of the air stream, before deflection, is represented by N' + N", where N' = w/g s' V2 and N" = w/g s" V2.
The resolution of N' into D' and F', indicates the probable state of affairs along the "deflection" plane A C. The force D' is parallel to and vanishes with the deflected air stream, and in fact represents the stream's energy. The force F', however, is perpendicular to the plane A C, and since its action is directed towards the surface it can be resolved into a force P', normal to the surface, and in the same di- rection as P90 and a force R', equal and opposite to R", which is entirely used up in compressing the air cushion. While a greater part of the energy of the stream D', D", goes away with it, a portion P', P", of the stream's force is "deposited" on the surface,
P90 = P' + p". Analysis shows that
N' = w/g S' V2 and N" = w/g S" V2.
AC = BC = S sin 45° and s' = AC sin 45° = S sin2 45° = S/2 = s' F' = N' sin 45°, F" = N" sin 45°, and P' = F' sin 45°, P" = F" sin 45°
Recalling that sin2 45° =0.5
P' = w/g S 0.5 V2 sin2 45° and P" = w/g S 0.5 V2 sin2 45° Hence using sea level and mean temperature, conditions, for w/g,
P90 = w/g SV2 sin2 45° = .0054 S V2 0.5 = .0027 S V2
which is so nearly in accord with experimental results, K = .003 as at once to lead to an appreciation of the value of considering the "air cushion, 45° deflection" characteristics of air flow, in any study of air pressures.
The experimental results on the pressures experienced by inclined planes show that at angles above 45° the change in inclination does not greatly affect the pressures. The division of the air in front of a plane inclined at angles greater than 45° is of the same character as in normal surfaces, and a similar theory when applied shows that the pressure remains constant from 90° to 45°.
71
Inclined Surfaces
Referring to the diagram, p. 68, the mathematics of this develops as follows :
AC = S Sin (a - 45°) and BC = S Cos (a - 45°)
/. S' = S Sin (a - 45°) Sin 45° and S" = S Cos (a - 45°) Sin 45°.
The normal pressures on the projected areas, S' and S", may be considered as the energy of the air stream, a proportion of which is ex- pended on surface AB as P.
Calling N' and N" these pressures, we have N' = w/g S' V2 and N" = w/g S" V2.
The force triangles show that, P = P' + P" and that P' = N' Sin (a - 45°) Sin 45° and P" = N" Cos (a - 45°) Sin 45°.
Supplying the values of S', S" and of the resulting N' and N", we get P = w/g SV2 Sin2 45° Sin2 (a - 45°) + w/g SV2 Sin2 45° Cos2 (a - 45°).
Since Sin2 + Cos2 = 1, and Sin2 45° = 0.5, and supplying values of w and g there is obtained,
P = .0027 SV2
From 35° to 45°, the inclined flat surfaces there is a region of un- steady flow, in which for squares the pressures become much greater than the normal.
Below these angles the air flow ceases to divide along deflection planes in front of the surface, and all of the air passes under the sur- face. In this case the pressure would be proportional to the sine of the angle of incidence, as outlined above, in forces F' P" and the formula
Pa = K S V2 sin a is found closely to agree with practice.
This theory, first proposed by the writer some time ago, is as rigid as any resolution into Lift and Drift. The hypotheses may be briefly summarized as the consideration of the division of the air along two deflection planes, which act like a surface on the air, and cause the energy of the air to be divided up into a force parallel to the deflected stream, which goes along with it, and a force normal to the layer of air, along which deflection takes place, which in turn is composed of a force compressing the air cushion and a force actually causing the resistance of the surface.
Proper consideration of air deflection is capable of determining c. p. position (by intersection of the deflection planes) and when ap- plied to curved surfaces, should give most interesting results. And, it would seem, that additional measurements by the laboratories, on the angles of the deflected currents, would make the data on surfaces more complete.
It is seen, therefore, that derivations based on a more accurate hypothesis of air flow, give much more satisfactory results. In a work dealing so largely with practice it is important to point out that unless the hypothesis of the physical air flow used in any theory is correct it
72
is far more practical to rely on observations and abandon formulae. The theory of propellers, and its lack of agreement with practice, is a field in which there is a most pressing need of a satisfactory basis for theoretical determinations.
The "Absolute" System of Units.
It has been indicated that K, in the formula P = K S V2 is a func- tion of w/g of air. For any body, if we introduce another constant C, we may write the air resistance formula in terms of density of air w, and acceleration of gravity g, as
P = C w/g S V2
Since the units in which P is expressed depend on the units used for w and g, S and V, it follows that C is a number independent of the system of units employed. For this reason it is called the absolute
coefficient, and its value is the same whether P is expressed in Ibs. or grams, providing the expression of w/g is made in the proper units.
The absolute system is used by the Goettingen and the N. P. L. (British) Laboratories. It is an inconvenient system for practical field use, but for the international comparison of scientific results it is admirably adapted.
The system used in this work is
P (pounds) = K S (sq. ft.) V2 (miles per hour).
Therefore, to translate results in the absolute system to these units the "absolute" values must be divided by 196.
"Absolute" values x .0051 = "m. p. h., sq. ft." units
The Metric System.
The Eiffel results are expressed in metric units,
P (kilograms) = K S (sq. meter) V2 (met. per sec.) so that Metric values x 8 = "absolute" values, and
Metric values x .041 = "m. p. h., sq. ft." units. Thus for K = .0033, we would have in "absolute" units
P = .64 w/g S V2 and in metric units, P = .08 S V2.
In the consideration of these conversion factors, atmospheric pressure at sea level and ordinary temperature conditions are assumed.
Summary.
The greater part of this chapter is presented for reference, but the different systems of units and the conversion factors are of import- ance, and should be understood, and borne in mind.
The theory of air pressure presented, is purposely not expressed in terms of the usual theorems and laws of fluid dynamics, since it is desired to emphasize, merely, the importance of continually bearing in mind, that the resolution of air pressures, along the directions in which they act, is the correct fundamental conception of aerodynamics.
CHAPTER VII.
CHARACTERISTICS OF AEROFOILS.
The manner in which air pressures vary on flat and cambered surfaces has been considered fully enough to enable us to proceed with the study of aeroplane wings themselves. As already indicated, the necessity of having spars and ribs of considerable depth for the rigidity of an aeroplane surface, makes it necessary to use a section of a cer- tain thickness, and consequently two curvatures — the top face and the bottom face — must be taken into consideration.
Aeroplane wing sections are ordinarily referred to as aerofoils, and the study of the various aerofoils and their characteristics is of very real importance. While a good deal of the data on air pressures has been given by way of explanation and general information, the wing characteristics referred to here are of the greatest practical sig- nificance, and are every day being put to use and verified, on the avia- tion fields of the military world. The connection between the character- istics of a wing section and the operation of a great war would seem remote, but when it is appreciated that superior speed and climbing ability enables a hostile aeroplane to gather information quickly and escape from attack and pursuit, primarily because of the greater effi- ciency of its wing section, the importance of this study becomes ap- parent.
The development of wing sections has been along several lines. Originally geometrical sections were made thick enough to give room for spars and then rounded at the edges. Other pioneers, after de- ciding on the size of spar and thickness required, adopted a certain camber for the mean center line, and then proceeded to fill out a sec- tion that would streamline the spars. Still other investigators adopted parabolic and circular curve combinations, crescent shapes, etc., and finally the great laboratories took up the matter and systematized its study. The Eiffel, N. P. L., and Goettingen results are complete enough now to give a very firm basis for aeroplane design, and to en- able the effects of any changes in aerofoils to be quite accurately an- ticipated.
In general the features of an aeroplane wing that may be varied are:
1. Shape of Section, curvature, thickness, etc.
2. Shape in Plan, contour, aspect ratio.
74
In addition, the manipulations of the wing by warping or moving flap sections that are connected to it, modify the pressures, and there are further modifications of the air forces when the proximity of some other wing or body affects the air flow and interferes with the paths of the streamlines. Mutual interference of surfaces with each other is a formidable study, and is given special consideration.
The nature of air pressure on aerofoils is revealed by air-stream photographs, the most striking feature being the manner in which the rounded nose of the aerofoil in deflecting the air stream, causes the air some distance ahead to take a curvilinear path up to the aero- foil. This influence, frequently called the "phenomenon of the dip- ping front edge," is very pronounced for some aerofoils, and when generating an upward stream of this kind an aerofoil is virtually rid- ing on the crest of a wave. An explanation is found here for the greater lift and less drift of aerofoils, and the section that generates the most pronounced wave with the least break in the flow is naturally the most efficient.
Another feature that it becomes more necessary to consider now, in view of the separate nature of the top face, and the bottom face, is that the total air reaction, resulting in the forces on the aerofoil, consists of pressure, both positive and negative. Positive pressure is a compressive action, while negative pressure is a suction. In pre- vious considerations of air resistances, it has been unnecessary to draw this distinction, since we were interested, merely, in the total effect of the air reaction.
Lift by Suction on Top Face.
Careful studies of the distribution of pressure over the surface of typical aerofoils made by the great laboratories, have shown that the actual effect of the air flow at the usual flying angles is not only to generate a pressure (compression of air) on the lower face of the inclined surface, but also to cause a great suction on the upper face. Furthermore, measurements show that the value of this suction in pounds force is about three-quarters of the total air force on the aero- foil. In other words, the action of the air flowing past an aeroplane wing, primarily causes a partial vacuum on the top face, which tends to draw the surface up by suction. As long as this wave form suction type of flow continues, the surface is in its most favorable attitude for efficiency, but at higher angles than ordinarily employed in flying this type of flow breaks down, and a disruption of the streamlines follows, evidenced on the surface, by a great increase in resistance and fall in lift. The angle at which this change of flow occurs is called the critical angle.
While the distribution of pressure across the wing's chord is of the form indicated on p. 78, there is also good reason for investigat- ing the manner in which the pressures on a wing vary from the center
75
across the span to the tips. As the tip is approached the pressures reduce and the point of highest suction passes from the leading edge towards the trailing edge. The drift of the wing tips is found to in- crease and to be accompanied by a fall in L/D, as the tip is approached. The type of flow that produces the best L/D is found at the center of the wing, where the streamlines pass directly from front to rear. As the tips are approached, however, the streams of air begin to flow off sideways, endeavoring to escape out at the sides. Obviously, the higher the aspect ratio, the less in proportion is this sideways escape of air, and therefore the better the L/D.
General Characteristics.
Although the pressures, on the various sections differ consider- ably from each other, there are certain characteristic features that are common to the majority of the aerofoils.
At 0° incidence there is usually a certain lift A, and at a negative angle, anywhere from —2° to —9°, there is a point of no lift, H (see p. 78). The manner in which the Lift and L/D curves are plotted, on a basis of angles, is the same as in Chapter V, the Lifts being defined by values of KL in the formula, Lift = KL S V2. From A to C, on the Lift curve, is more or less of a straight line, the curve bending over at C, which point is called the point of maximum lift. From C to D, instead of continuing to increase, a critical state of flow has been reached, where further incidence increase is accompanied by a drop in the Lift. This is an interesting portion of the curve, and we will again have to refer to it when we take up the control of the aeroplane in this reversed pressure region. Where lift decreases in this way, it may be stated briefly, that the controls on an aeroplane would have to be reversed for flying in this region. To go up, it would be necessary to reduce the angle of incidence, and to descend, the elevator would have to be pulled back so as to increase the angle.
On the L/D curve from the point of F at 0°, the value of L/D increases to a maximum E, corresponding to a Lift of value B. From E to G, the L/D ratio again falls off. The ordinary regions of flight are limited to the peak region of the L/D curve.
In the study of the aeroplane, as a unit, taken up later, consid- eration will be given to the important relations that the maximum and minimum points of the L and L/D curves bear to each other.
Having, in a general way, considered the nature of air reaction on aerofoils, we may proceed with a study of the effect of alterations in shape and plan form and interference. The values of KL and L/D in the curves, refer to the combined action of whatever compression or suction is generated, unless otherwise noted. It is also well to re- call that L/D represents the ratio of the Lift force obtained from an aerofoil at the expense of the Drift D, a resistance that must be over-
76
come. "Efficiency" refers to L/D, and is higher, the greater the Lift obtained for resistance overcome.
ALTERATION IN SHAPE OF SECTION.
1 . Camber of Upper Face.
Increasing the camber of the top face from 1/40 to 1/6, on a form with a flat under face, shows that the maximum lift increases up to a camber 1/15 and then decreases. The ratio of L/D steadily im- proves up to a camber of 1/20. This camber appears the most efficient, as deeper cambers show a steady decrease in values of L/D.
On an aerofoil, having the under face arched considerably, when the camber of the upper surface is increased above 1/15, the Lift hardly varies, while the drift steadily increases with camber increase. For very thick sections, however, just as in spheres and cylinders, there is a critical flow, which, due to increases in speed, tends to smooth out and reduce resistance.
2. Camber of Lower Face.
Increasing the camber of the lower face, for a fixed upper face, shows that L/D does not vary very much, and that L increases ap- preciably with camber increase. Since the depth of spar is very greatly enhanced by keeping a flat underside, there is every reason for con- sidering rather flat under surfaces as advantageous. The increased depth of spar reduces the weight of framework in the wing necessary for a given strength, and would about compensate for the lift increase obtained by camber of the lower face.
The upper face, furnishes most of the lift and variations of lower face have very little effect on the upper side.
3. Thickness and Depth at Rear.
By keeping the same mean curve of a section, and adding to the top and bottom faces at the same time, the drifts are found to remain about the same, and a decrease in lift is found as the section becomes more and more a streamline body — due to the progressive bulging out of the section, both top and bottom.
For any particular curve a thickening of the rear alone to permit of a deeper rear spar, shows a decrease in L/D with increase in thick- ness and a slight decrease in Lift, but this is not so very marked, and sections can be deepened at the rear with ease, thus permitting of hav- ing the front and rear spars of the same depth.
4. Bluntness and Streamlining of Nose.
Substituting a blunt for a sharp leading edge, causes the ratio of L/D to fall off, but since L remains about the same there is indicated a pronounced increase in D. Bluntness of the nose may, therefore,
77
be considered a disadvantage. Pointing the nose of an aerofoil, to a streamline shape, designed to divide the air easier, often called a "Phillip's Entry," is frequently used. It is advantageous in decreasing the drift slightly at high speeds and low angles, but otherwise has little effect.
5. Changing Position of Maximum Ordinate.
The fraction of the chord at which the camber is the greatest is termed the position of maximum ordinate. It can readily be varied on aerofoils, and it is found that L/D increases as it is moved from the center of the surface, or .5 chord, towards the leading edge until it reaches the position of 1/3 chord, when further movement forward greatly reduces the efficiency of the section. The Lift is not affected very much at low angles by changes in the position of the maximum ordinate, but at high angles the lift of the section falls off when the greatest camber is at a point in front of 1/3 chord.
6. Reverse Curvature.
Reversing the curve of either face of an aerofoil, has a pronounced effect on the c. p. movement. The lower face of a deeply cambered aerofoil is readily made to reverse at the rear and meet the upper face. This is often done, and is distinctly beneficial.
More pronounced reverse curves in which both faces, at the rear, are turned up, have a very great influence on the air pressures. The advantageous feature of having a stationary center of pressure posi- tion for the various angles, is obtained by raising the trailing edge about .037 of chord — the curve starting from a point about .2 of chord from the trailing edge. But in doing this the maximum lift is reduced, and the range of lift restricted. There is also a speedy decrease in L/D, and, in general, this change leads to inefficiency, reducing lift by about 25% and max. L/D by about 15%.
7. Warping the Aerofoil.
"Warping" an aerofoil consists in twisting it in such a way as to have the various sections presented to the air at uniformly vary- ing angles of incidence. The section of wing remains constant, and since its characteristics for varying angles are known, the amount of pressure at the different sections could be found. In the ordinary range of warp in practice, on aeroplane wings, where one side is moved up and the other down equally at the same time, the Lift remains the same, as does also the position of the mean center of pressure, and tests show that computations on a basis of applying the ordinary data for the section to the different regions at their various angles gives correct results.
78
ASPECT RATIO TABLE
Values tabulated are the ratios of L and L/D at given aspect to values for an aspect of 6.
|
ASPECTS |
ANGLES |
||||||
|
3° |
6° |
9° |
|||||
|
L |
L/D |
L |
L/D |
L |
L/D |
||
|
2 |
.60 |
.47 |
.62 |
.54 |
.60 |
.55 |
|
|
3 |
.70 |
.58 |
.73 |
.64 |
.78 |
.72 |
|
|
4 |
.84 |
.73 |
.85 |
.77 |
.90 |
.83 |
|
|
5 |
.94 |
.86 |
.95 |
.90 |
.96 |
.92 |
|
|
6 |
1.00 |
1.00 |
1.00 |
1.00 |
1.00 |
1.00 |
|
|
7 |
1.05 |
1.06 |
1.04 |
1.10 |
1.04 |
1.09 |
|
|
8 |
1.08 |
1.09 |
1.08 |
1.16 |
1.08 |
1.15 |
|
|
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ftetreat PRESSURE DISTRIBUTION - TYPICAL CURVES —AND DEFINITIONS
79
ALTERATION IN PLAN FORM. Shape of Plane.
Cutting away the trailing edge at the tips, and rounding off the ends of the plane, is often resorted to for reasons of construction and appearance. It is found that this does not appreciably affect the pressures, and cutting away the tips slightly reduces the weight of wing. On the other hand, it is found that raking the ends of a plane or that the trailing edge is of greater span than the leading edge, does appreciably affect the pressures, the Drift being considerably reduced and the ratio of L/D improved. The gain in efficiency is due undoubt- edly to a better utilization of the sideways flow of air, in escaping past the edges. For the best results, where consideration is given to the strength of the wing, the ends should be raked at angles of 20° to 30°.
Aspect Ratio.
The influence of aspect ratio, on the pressures experienced by aerofoils is, of course, quite similar to its effect upon geometrical sec- tions. It becomes quite important for us to consider this, with refer- ence to aerofoils, in greater detail, since aeroplanes vary considerably in aspect. The "aspect" of an aeroplane is always considered as its total span -f- by the chord of wings, the wings not being considered separately from their attachment to the body.
Although Pa on flat planes is affected by aspect, the ratio of L/D is not so affected, since it is always a function of angle of incidence a, as outlined in Chapter V. But on aerofoils, not only does D vary, but there is a very pronounced change in L/D.
As the aspect ratio is increased from 2 to 8, the usual limits used in practice, the maximum lift coefficient remains at about the same value, but it occurs at smaller angles of incidence as the aspect ratio is increased.
The most marked change, due to aspect ratio variation, is in the value of L/D. This is found to be due mainly to an increase in the Drift, for the smaller aspects.
The average aeroplane, has an aspect of 6, which it is found is a good value, but an increase up to 8 and 9, is justifiable, since the limit in improvement of efficiency becomes pronounced only for these higher aspects. For very flat sections of camber 1/30, or thereabouts, the ratio of L/D is found to decrease at very low angles, when the aspect is increased above 5. At higher angles, higher aspects give better efficiency as in deeper cambered planes, but it would appear that for the flatter sections, used at low angles and very high speed, on the small fast scouting aeroplanes, there is justification for limiting the aspect ratio to about 5 — a feature that is structurally very advan- tageous.
80
The most convenient way to present data on aspect ratio has been a matter of question, and a system is adopted here which, it would seem, is the most practical for the use of the engineer and the aeroplane user. The data for wing sections given, is in every case, excepting where otherwise noted, reduced and corrected to correspond to an aspect ratio of! 6. In addition, accompanying . this, is a table which gives the factor by which to multiply values for any other aspect ratios from 2 to 8, the aspect ratio of 6, being considered as unity (see p. 78).
For example, at 3°, the L/D of N° 36 Eiffel surface is found from the graph to be 14.7 for an aspect of 6, and the corresponding lift co- efficient, KL is .0014. It is desired to know what the values would be for an aspect of 4. From the table, we find that L/D will be 73% of the value of 14.7, which is 10.7, and the value of KL will be 84% of .0014, which is .00118. If it is desired to know the values for angles between 3° and 6°, it is easiest to plot the values of 3°, 6°, 9° on the chart, and draw thru them curves entirely symmetrical and of the same character as the ones for the aspect of 6.
For field use, the table is put in a novel form, but one which it is thought is far handier than any hitherto published. The combined re- sults of all the laboratories were given consideration in deriving the values given.
Effects of Speed and Scale.
In stepping from model tests to full-sized machines, the best ap- proximation at present made appears to work out quite well in practice.
Lift values, of coefficient KL, are applied directly without any cor- rection.
Friction effects on Drift cause it to decrease with increase of speed, and, therefore, at speeds higher than the wind tunnel speeds, the value of L/D will be greater. The Eiffel results, however, were obtained in winds of 50 to 70 miles per hour and require no correction, and in or- der to bring the other results presented in accord, correction for speed has been made wherever necessary. The values given, therefore, may be applied without further correction to full-sized machines, at ordinary speeds, by supplying the values of S and V2.
Pressures are, of course, functions of V2 of the aeroplane, and the corrections mentioned apply only to the values of KL and L/D tabu- lated. Pressures are also functions of areas, and therefore vary as the scale of the model squared. In the wind tunnels pressures are meas- ured in pounds, let us say, and a particular pressure on an aeroplane model to 1/10 scale is found to be 1 pound, in a wind of 30 miles per hour. It is desired to know what the force on the aeroplane will be at 60 miles per hour. The observed value must be multiplied by 602 3600
- X 102,or x 100 = 400 pounds.
302 900
81
Typical Sections of Aerofoils.
Twelve aerofoil sections that represent a wide variety of actual practice are tabulated. The sections are drawn out all to the same scale, and the center of pressure graph is drawn for a distance of chord equal to that used in the drawings of the sections. This enables a rather more graphic conception to be obtained than has been possible heretofore. The values of KL and L/D are given in groups of four sections. The graphs look complicated, but they are merely con- venient methods of tabulating the results, and the curves can readily be distinguished with a little practice in reading off the values.
Among the sections given the Eiffel No. 13 bis, the one used on the Bleriot monoplanes, is a very widely adopted one, and because of its high lift and good efficiency it is one of the few of the older types of sections remaining in use. Many of the Royal Aircraft Factory biplanes, the Bristol biplane, several German and Italian aeroplanes, and the Martin biplane in this country, use a section of this type. Its most serious disadvantage is the lack of spar room, necessitating either a wide shallow and, therefore, heavy spar, or a lesser factor of safety on a well loaded wing. The efficiency at very low angles is not as good as in some of the newer types of sections, which permit of a greater range of speed though not possessing quite as good a maximum effi- ciency.
The Eiffel No. 31 section, of crescent shape, is Eiffel's most ef- ficient all-around wing, although its maximum L/D is exceeded by many other sections. The Lift at low angles is very high, and the wing is well adapted for load-carrying aeroplanes.
No. 32 Eiffel is essentially a speed range wing, for fast speed scouts, lightly loaded and with high-powered engines. The high value of L/D at low angles is particularly favorable to high speed.
No. 36, Eiffel is used on several military machines, and is a partic- ularly good wing for a meduim speed, military scout. The Lift is not run up very high, but the range of angles thru which a high L/D is maintained is favorable, not only to high speed, but also to climb, as will later be explained, when consideration is given to the complete aeroplane as a unit.
The Dorand wing, Eiffel No. 35, is similar to the Wright wing, and gives a very high lift, with a high L/D at angles from 3° to 6°. The small thickness of the section, however, does not make this wing very favorable from the standpoint of construction. In general, thinner wings are the more efficient, but spar room is a very necessary element, and efficiency and strength must be compromised.
82
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85
The Howard Wright wing, in which the contour is stepped, has been used on the White seaplanes, but its characteristics are not very advantageous, excepting in that the c. p. movement is practically stationary.
The Nieuport and Deperdussin are two standard wings, the lat- ter designed particularly for racing aeroplanes.
R. A. F. 6 is one of the more modern sections that has become standard on British Army aeroplanes, and also used on the huge fly- ing-boat "America." The effect of a reversal of the trailing edge on this section is shown also, and is of interest in connection with flaps on the trailing edge.
The N. P. L., No. 4 wing is a particularly deep one, in which the high Lift and fairly good L/D at angles of 3° to 6°, are advantageous for aeroplanes having a slow mean speed.
A new type of section, with a movable rear piece, is also shown, as a suggestion of improvement by the writer. The combination of low Lift and good L/D of a flatter section, at low angle, with facilities for changing to a deeply cambered surface, which would have a high Lift and also a high L/D at larger angles, could be made very greatly to extend the speed range of aeroplanes. Suggested curves of a pre- diction of the characteristics of a surface of this kind are indicated. It should be emphasized here, that several years ago the extent to which Lift and L/D could be varied on sections was not well known, and many investigators looked for an extension of speed range, by varying the size of the surface. The latest experiments indicate, however, that since a change in section can be made to vary the Lift and L/D, 100 per cent, or more, at different angles, much more is to be expected from a variable curvature section in extending speed range.
The Tail Planes.
The main wing surfaces determine in large measure the general characteristics of an aeroplane, but the Lift and Drift of the tail pieces or "empennages" are by no means negligible. The characteristic variations and values of L and L/D, that have been given, are sufficiently complete to enable us to determine their magnitude for these aux- iliary surfaces, when it is realized that the effect of the propeller stream, on the empennages is a powerful but more or less indeterminate factor.
Where balanced rudders are used, consisting of a flat surface of a certain aspect ratio, it is merely necessary to apply the data given on p. 60. And, as is often the case, where a pivoted balanced rudder is of a more streamlined section, as illustrated on p. 78, it is proper to consider the drift slightly reduced. Elevators or ailerons, con- sisting of a balanced surface of constant chord, span and section, pivoted
86
to take various angles of incidence, may be solved by the data given for their particular section.
On some aeroplanes, notably the early Wright biplanes, the ele- vator consisted of a normally flat plane that was quite flexible. This surface was fixed, at the leading edge, and so connected at the trail- ing edge that movement for control consisted of bending the ribs by moving the trailing edge up or down, thus causing the section to take various curvatures and angles. A surface of this kind is readily solved by applying the data given on p. 66, for sections of varying camber.
The more usual type of elevator, however, is the "flap and fin" type, in which movable flaps are hinged to the rear of a fixed surface. It has often been customary to consider these surfaces separately, but a moment's thought on the continuity of the air flow, shows that the proper conception is to consider a surface of this kind altogether as a single unit, which, when the flaps are in line with the fixed por- tion gives a flat surface of a certain aspect ratio. When the flaps are moved, there is obtained a section that is arched (though not circular), and in which the chord is a line from the trailing edge of the flaps to the leading edge of the fixed plane, with a camber depending on the amount the flap is turned. The data on curved sections given on p. 64 and 66, is then applicable, with the modification that the section being a pointed arch, instead of circular, will have a somewhat greater Drift, though the Lift may be taken as about the same.
INTERFERENCE OF AEROFOILS.
A study of the flow of the air stream about an aerofoil gives a clear indication that the streamlines are influenced and deflected quite a distance away from the surface, the rising streamline caused by the "dipping" front edge of an aerofoil being an example. In addition, the flow causes differences in pressure on an aerofoil, which, if affected, would modify the total forces on the aerofoil.
It follows that placing bodies or other aerofoils in proximity to any aerofoil will greatly affect its pressures. Interferences in flow are very interesting, and of most practical value, in their application to the aeroplane.
Biplane Effect.
When aerofoils are placed over one another, as in a biplane, there results an interference and modification of their air forces. It is cus- tomary to refer to the distance apart of the two superposed surfaces, as the gap, and the ratio of gap to chord, is used as a measure thereof.
Since the suction, on the upper face, is about three times as great as the compression on the lower face, of an aerofoil, the effect of plac- ing one over the other is greatly to reduce the Lift and efficiency of
87
the lower plane, but only slightly to affect the upper plane. This is evident when it is borne in mind that the compression on the bot- tom face of the upper aerofoil and the suction on the top face of the lower aerofoil merge into and mutually reduce each other, whereas the suction on the top face of the upper aerofoil and compression on the bottom of the lower aerofoil remain unaltered. The suction be- ing so much more important, it follows that the upper aerofoil must be much less affected. This is verified by the laboratories, and prac- tically the entire loss due to biplane effect is found in reduction of L and L/D of the lower surface. A deduction to be drawn from this is, that flaps on the upper plane are much more effective than flaps on the lower. Also, flatter planes; in which the suction is not so great, would be less interfered with when superposed. If the combination of high camber upper plane and a very much flatter lower plane, were used, it is evident that the interference would be reduced consider- ably. A table of biplane reduction coefficients for an average aerofoil is given.
N. P. L. BIPLANE TABLE. To obtain values for a biplane, multiply values for single aerofoil by factors given.
|
BIPLANE QPAPTNO |
LIFT |
LIFT/DRIFT |
||||
|
GAP CHORD |
6° |
8° |
10° |
6° |
8° |
10° |
|
0.4 |
.61 |
.63 |
.62 |
.75 |
.81 |
.84 |
|
0.8 |
.76 |
.78 |
.77 |
.79 |
.82 |
.86 |
|
10 |
.81 |
.82 |
.82 |
.81 |
.84 |
.87 |
|
1.2 |
.86 |
.87 |
.86 |
.84 |
.85 |
.88 |
|
1.6 |
.89 |
.90 |
.89 |
.88 |
.89 |
.91 |
Staggering.
The position of biplane surfaces over each other is subject to vari- ation, and the term stagger is used to describe the relative position referred to the vertical. For reasons of visibility, and minor consid- erations of construction and balance, it is sometimes convenient to stagger the upper plane ahead of the lower plane, as indicated in the sketch on p. 78. The effect of staggering, on the efficiency of the aero- foils, is again an illustration of the mutual reaction of the regions of suction and compression. When the upper plane is staggered for- ward, its Lift and L/D are improved, but at the same time the L/D on the lower plane is reduced. When the stagger is .44 of the chord
88
(a practical limit), the total effect is to cause the Lift, on the biplane as a unit at angles of 5° to 10°, to be improved by about 7% to 9% with practically no effect on the L/D.
Interference of Following Planes.
The air stream deflected from the main aerofoils of an aeroplane, takes a downward course, which causes the air flow past the empen- nages, or any surfaces in the rear, to be affected, and causing the angles of incidence of the rear surfaces (which are always the angles of the chord with the air stream) to be less than the angles of their chords with the horizontal flight axis. This is an exceedingly important ele- ment in the balance and stability of a machine, and is taken up, more fully, in considering the entire aeroplane as a unit further on.
Dihedral and Retreat.
Attention is called to the definitions of Dihedral angle and Re- treat, given graphically on p. 78. The effect of these features is con- sidered later with reference to stability. Within the limits used in practice their effect on Lift and Drift is negligible.
Summary
From a combined consideration of Aspect Ratio, Biplane effect and staggering, a biplane at 6° of aspect 6, stagger of .44 chord and gap equal to chord, would have about 89% of the lift of a single aero- foil (81% due to biplane effect and 8% increase due to stagger) and its L/D would be 81% of that of a single aeroplane of the same as- pect ratio. If this is compared with a single aerofoil of aspect 4.5, however, it is found that the Lift is practically the same, and only a slight difference is found in the efficiency. Likewise, a staggered biplane of aspect 8 and a large gap, is p'ractically the same as a mono- plane of aspect 6.
When a comparison, like the above, is made, the reference to single aerofoil means an equivalent monoplane of the same surface area as the biplane. To get the same lift with the same section and aspect, a monoplane would require less area than a biplane, by the amount of the biplane coefficient.
The data given on surfaces enables the lifting capacity and cor- responding wing resistance to be determined for the various sections. Examples indicating the manner in which this data is used, and a con- sideration of the aeroplane as a unit, may now be taken up.
CHAPTER VIII. CHARACTERISTICS OF THE AEROPLANE.
The surprising accuracy with which the performances of an aero- plane may be predicted from data on the lifts and resistances of its component parts, is, perhaps, the most striking indication of the great progress that has been made in Aeronautical Engineering, the past year or two. Constructors, fliers and the laboratories, have co-op- erated to advantage, and although many important features of the aeroplane remain to be explored, information that already has been obtained and verified, by the great work of the Laboratories, readily permits of establishing a working basis for the presentation of data of importance, relative to the aeroplane, — in a manner not only use- ful and intelligible to the aeroplane user, but at the same time capable of expansion as new conceptions develop.
It is proposed in this chapter to consider the aeroplane as a unit, with a view to determination of its total lifting capacity and resist- ances and the power necessary to fly. In a treatise on aeroplane de- sign, the matter considered here in a few pages would of itself consti- tute a text book, so that the limiting scope of this work makes it neces- sary to confine our attention to the military "field use" features capable of leading to an intelligent solution of problems in the modification of aeroplanes and their performances, as dictated by military neces- sity. Flying various types of machines, with greatly varying load conditions, radius of action, atmospheric conditions, and power varia- tions, presents a vast quantity of problems that often are solved best by the fliers themselves. That new kind of resourcefulness, in adapt- ing themselves to many changing requirements, that is demanded of a Flying Corps, is a criterion of efficiency and may be gauged not only by skill in maintenance, but also by the knowledge that the avia- tors and mechanicians have of the performances that may be expected of their machines.
It must be borne in mind that a manufacturer is required to fur- nish data on his machine in detail, and although a few examples are given here, information on the resistances, lifts, power available, and power required to fly, under definite conditions, of particular types, should come with each machine — the manufacturer in other words, interpreting the laboratory results applied to his type, for the benefit of the user. It is clear, therefore, that the military or naval user of an aeroplane must know how to read this data and how to apply it in a practical way.
90
In previous chapters, consideration has been given to the resist- ances of bodies, and the lifting efficiency of surfaces and aerofoils — completely enough, to explain the significance of the forces generated by an air stream, and with sufficient laboratory data to make the sub- ject matter of direct value for reference. We are now at liberty to combine these conceptions, and to give the definition of an aeroplane, (p. 11) a more technical wording — in that, an aeroplane consists of a combination of sustaining and balancing aerofoils, with a Lift deter- mined by the values of KL,V and S, and with power suitably proportioned to overcome the head resistance of the structure, and the Drift of the wings, at the expense of which the Lift is obtained.
Types of Aeroplanes.
Reference to Chap. II, gives a renewed significance to the photo- graphs of the various types of aeroplanes, and could profitably be re- considered with a view to fixing the relation of theory and practice. Thus, the wing section of the Curtiss Tractor, on p. 17, is none other than Aerofoil No. 36, of Eiffel, given on p. 82, and the wings of the monocoque on p. 20, have a section identical with Aerofoil No. 54, defined on p. 83. The several machines differ widely in values of the resistances of their various structural parts. Thus, the struts on the old-type Wright Aeroplanes, shown on p. 19, have something like five times the resistance of the struts on the Sturtevant tractor, p. 24, and the wheels on the Curtiss Tractor, p. 17, may be expected to have about half the resistance of the wheels on the Signal Corps tractor, shown below it, due to covering. The maze of wires and struts on the old types of pusher biplanes, are obviously more resisting than the simplified bracing and covered bodies of the later types. The dif- ference in aspect ratio of the Bleriot, on p. 20, and the upper plane of the Farman, on p. 19, is most noticeable. And, whereas, the Curtiss Model N has two staggered planes and a dihedral angle, the Deper- dussin, on p. 20, has a single surface with no dihedral. And yet if the surface section were the same, as is the case with the Bleriot, p. 20, and the Martin, p. 15, we would apply the same aerofoil data to both of them, with suitable corrections for Aspect Ratio, biplane interference and stagger. In addition, it may be noticed that the shapes of the fusel- ages, differ considerably, some tapering to an edge horizontally and others vertically, some square, others round, etc.
Each aeroplane, therefore, is bound to have particular character- istics of its own, for each of which the designer, if competent, had some particular object in view, towards either efficiency, stability, strength or convenience. To investigate them all would be a trespass on the domain of the aeronautical engineer. But not to appreciate what performances may be expected of any machine, is due to a lack of infor- mation, that it is the object of this work to supply.
91
From the standpoint of lifts, resistances and power required, the many different types all resemble each other in having a set of main supporting surfaces, auxiliary balancing surfaces, which may or may not exert lifting pressure, and certain structural resistances. In power available, there are differences of importance due to gearing of the propellers. Whereas, in characteristics of stability and operation, distinctions are most pronounced, and necessitate a full consideration later.
But whether tractors, pushers, staggered biplanes, monoplane aeroboats, etc., all aeroplanes have these characteristics in common:
I. A Lifting Capacity, determined by the surface characteristics,
and varying with speed and inclination of the machine.
II. A total resistance to motion, composed of
(a) The combined resistances of the various necessary structural parts, called the Structural Resistance, and varying with speed and inclination.
(b) The Drift, which is determined solely by the Lift char- acteristics and is, of itself, independent of speed.
III. A certain Power Required to fly, varying with the speeds
of the machine and its total resistances.
IV. A certain Power Available, due entirely to the horse-power
given out by the propeller, which, in turn, for various speeds is a certain proportion of the power of the engine, and there- fore must correspond to a certain fuel consumption. Flight is impossible unless the Lifting capacity exceeds the total weight, and the Power Available is greater than the Power Required. A study of these features enables the speed range, the glide, the climbing rate, the load-lifting capacity and the fuel consumption, to be determined in a most practical manner.
An Aeroplane of the Sturtevant type, the first built of steel construction, climbing off the ground.
92 Inclination of the Aeroplane.
The variations of the pressures on surfaces has been considered for changes in the angle of incidence. It is customary in aeroplanes likewise to refer to "angle of incidence," of the supporting surfaces, in defining the attitude of the machine. And the inclination of the body to the line of flight, and the line of the propeller axis, is referred to as the angle of incidence. If the wing is set at 5° to the axis of the body, and the angle of incidence of the machine is 5°, it follows that the body lies parallel to the air-flow. Whereas, if this same machine were presented to the air at 10° incidence, the body axis would make an angle of 5° with the air-flow. It is of importance, now, to realize that the entire aeroplane as a unit may be presented to the air at various inclinations.
On p. 13 the three motions an aeroplane is subject to — pitching, yawing and rolling — are defined. On practically all aeroplanes the lifting planes are fixed to the body, so that a variation in angle of in- cidence means pitching of the machine and is considered more fully here than either yawing or rolling, because of the effect change of in- cidence has on the surface characteristics. Yawing slightly affects the resistances, and rolling may affect the Lift, but both are more pro- perly considered under Stability.
The auxiliary surfaces, particularly the tail-planes, are in turn affected by the pitching of the machine, or, as we have defined it, by changes in the angle of incidence of the aeroplane. Where the ma- chine is so balanced that the tail lifts, then as the incidence of the aero- plane is increased the lift of the tail surfaces increases. And if the tail is set to receive a downward pressure, an increase of incidence causes this to be relieved.
As will be seen later, the variation in inclination of the structure, at the different angles of incidence, gives rise to alterations in the struc- tural air resistance, particularly of the fuselage, and in a staggered biplane an increase in the angle of incidence, increases the resistance of the struts and wires.
The Aeroplane as a combination, then, must be studied at various attitudes, and changes of inclination are expressed as changes in angle of incidence of the supporting planes. Where the special feature is involved of varying the angle of incidence as on some recent machines, inclination could be referred to the propeller axis. But it is more convenient in determining Resistances, and Lifts, to consider the chord of the wing as the base line.
Before proceeding with the study of Resistance and Power charac- teristics of an aeroplane, attention must be given to important features occasioned by combinations of lifting and 'auxiliary aerofoils, on the aeroplane frame.
Decalage, Wash-out, and Tail Interference.
The term "decalage" is used to define the difference in the angle of incidence between any two distinct aerofoils on an aeroplane. It is most often used to describe the difference between the setting of the main planes and the tail piece, and in a biplane the term is also used to denote a difference in angle of incidence between the upper surface and the lower one. Thus, on an aeroplane in which the body axis is in the line of flight with an angle of incidence of 5°, and with the chord of the elevator, inclined +2° above the body axis, the deca- lage of the elevator would be 3°. And in a biplane where, in order to gain slightly in efficiency, the upper surface is set at an incidence of 3°, when the lower one is at 5°, the decalage would be equal to 2°.
With reference to the decalage of the surfaces of a staggered bi- plane, laboratory experiments indicate that the effect of setting the upper surface at about 2° less incidence than the lower surface gives a pronounced increase in Lift and a slight gain in L/D over any other setting. This, however, is subject to modification where different wing sections are used, and a field of importance remains to be explored in the determination of the best combination of stagger, surface sec- tions and decalage, to minimize the effect of biplane interference and improve the Lift range of the biplane as a unit.
"Wash-out" is a term used to describe the progressive reduction in the angle of incidence, from body to tip, used on some aeroplanes for reasons of stability. Thus, on an aeroplane, in which the wings are set at an angle of incidence of 7° at the body, and then steadily reduced until the angle at the tip is only 3°, there is said to be a "wash- out" of 4°. With reference to the aerodynamic characteristics of this feature, laboratory results show that the approximation of considering the entire wing, as set at an incidence, equal to the mean of the angles at the body and the tip, is quite close enough. The stability features will be given consideration later.
The air that is thrown back from the front main surfaces of an aeroplane, onto the tail, is given a most pronounced downward trend, governed by the particular angle of incidence and surface section com- bination used. The tail pieces, consequently, are riding in air waves generated by the sustaining surfaces, and therefore are interfered with. "Tail interference" has only recently been given proper considera- tion, and its importance on the functioning of a machine requires parti- cular attention. Eiffel's experiments on this feature are particularly complete, and from them there can be drawn the general conclusion that the air, passing back from the sustaining surfaces, acquires a down- ward trend, dependent on their angle of incidence, which persists for some time, so that by the time this air region passes by the tail sur- faces it has straightened out to only a half to one degree less than the
94
actual angle of incidence of the sustaining planes. It becomes nec- essary, then, to distinguish between the apparent angle of incidence of the tail surfaces and their real angle with the direction of the air- flow past them. The apparent angle is the incidence referred to the line of flight, just as for the sustaining planes, whereas the real angle at which the air attacks the sustaining planes is the one for which all calculations of pressures on the tail surfaces must be made. A few examples will aid in making this clear. Let us consider an aero- plane, at an angle of incidence of 4°, in which the body axis is parallel to the line of flight/ and the tail surfaces of which have a decalage of 4°, with the sustaining surfaces. From our definition of decalage, the apparent angle of incidence of the tail surfaces would be 0°, i.e., they lie parallel to the body axis. But the air acquiring a downward trend from the main surfaces, of 4°, which gradually straightens out to 3°, as it passes the tail causes the real angle of attack of the air on the tail surfaces to be —3°. For the same case, if the tail surfaces are acted upon by the air stream, so that their real angle of incidence is 0°, it follows that the sustaining surfaces are at an angle of incidence of +7° and the body is inclined to the air flow at 4- 3°. For any particular machine, it is necessary to have special data on these features furnished by the designer.
Although other features causing modification of pressures on the various aerofoils may be met with, their importance would not re- quire special consideration here. The type of sustaining surface char- acterized by the "Dunne" class of aeroplanes, see p. 23, is readily solved when the laboratory data on this surface as a unit is furnished, — since the changing camber, and angle of incidence, would in no way alter the method of considering the values of L and L/D at different angles of inclination, precisely as for any other surface section. The sta- bility features of this type, however, require special consideration.
Having acquired a working conception of the aeroplane as a unit, we may proceed with a study of its probable performances, as out- lined on p. 91, and predicted from the laboratory measurements.
I. THE LIFTING CAPACITY.
The data on surface sections furnished for any machine, together with suitable corrections for biplane effect, aspect ratio, stagger, deca- lage, etc., is the first essential — and perhaps the most convenient way to represent this is to have curves showing the corrected values of L and L/D as applied to the particular machine, on the same chart with the data on the wing section alone, examples of which are given on pp. 82-84. The corrected curves, then, give us direct informa- tion on the actual values of KL and L/D, to apply to the lifting sur- faces as a unit, corresponding to angles of incidence of the chord of the wings to the line of flight. Since the value of the surface area
95
S is given for a definite machine, and also information on the weight W to be carried, we can at once supply suitable values for solving
W = L = KL S V2
so that we may learn at what angles the machine must be flown, for given speeds, or, conversely, how fast and how slow we could go, with a definite range of angle of incidence. Since features of stability de- termine a safe limit of angles, the latter problem is the one most often met with.
Thus, for an aeroplane with 335 sq. ft. of surface area, in the form of a staggered biplane, of aspect 7, and gap equal to chord, and with a wing section corresponding to Eiffel No. 53, the values of KL and L/D corrected, would be shown, as indicated on p. 96. For this ex- ample, let us find the speed range corresponding to a range in the angle of incidence from 1° to 12°.
At the low angle 1°, we find by referring to the first chart that KL = .00085. Supplying values of S and L, equal to the weight, we obtain
W = KL S V2 = 1800 = .00085 x 335 x V2
from which it develops that,
V2 = 6320, and V = 79.5 miles per hour.
In the same way, reference to the chart of aerofoil characteristics shows that at 12°, KL = .0027, so that
L = 1800 = .0027 x 335 x V2 from which we obtain,
V = 44.6 miles per hour.
Since the required lifting power and area of the wing surfaces are fixed, it is hardly necessary to emphasize that, for any inclination, there is only one speed at which horizontal flight is attained with the given load. Each angle h,as its particular corresponding speed, and in the above example the angle range of 1° to 12°, corresponds to a speed range of 44.6 to 79.5 miles per hour, and to none other — unless the load is changed or the surface characteristics altered.
A simple way to record this process is to write the speeds cor- responding to the various angles on the curve for KL, as has been done in the example given.
This, then, is the first step in determining the aeroplane's char- acteristics, i. e. : — finding the speeds required in order to lift the weight, at various angles of incidence.
96
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II. TOTAL RESISTANCE TO MOTION.
As already indicated several times, the resistance overcome by the propeller consists of two distinct items: Structural Resistance and Drift.
Structural Resistance.
The air resistance of the structural parts of an aeroplane, such as the wheels, struts, wires, body, tanks, etc., all total up to a formid- able value, and are conveniently and properly classed together in one item, called the "Structural Air Resistance." This term, altho a new one, is deemed so much more expressive than the older terms, "body resistance," "parasite resistance," etc., that its introduction is cer- tainly justified. The term "parasite" is misleading, since a high drift is as much a "parasite" as an uncovered wheel.
In Chapter IV the determinations of the resistances of various shaped bodies were given consideration. For any aeroplane it is neces- sary to know the details of construction before a working total of the structural air resistances can be determined.
There are hardly any two types of aeroplanes with the same shape of body, so that this item, above all others, can be considered but from data given by the manufacturer. It may be of interest to note, how- ever, that the values of K, for the nacelle of the Farman (illustrated on p. 19), has been found by Eiffel to be .0014, and K for the Deper- dussin monocoque (p. 20), is .001. It has also been determined that in yawing and pitching the flat-sided fuselage has an appreciably greater resistance than a rounded one.
The resistance of the tail surfaces ordinarily should include some allowance for the drift of the tail, as determined by the particular shape and incidence used. Altho this should, perhaps, be considered in company with the wing resistances, its value is small for a well-bal- anced machine, and it is more convenient to include it in the struc- tural resistance until it assumes a greater value.
Altho the process of determining the Structural Resistance con- sists essentially of applying information on the values of K, for the various structural items, in the formula, P = K S V2, and adding up the result, we have found that a change in V for horizontal flight involves a change in the angle of incidence. This, in turn, means that at the various speeds the entire aeroplane assumes a "tail high — nose down," or "tail low — nose high" attitude. For the wheels, wires, etc., these incidence variations have but a slight effect, but the bodies, fuselages or nacelles are formed so as to give a least resistance in only one position — when the axis is in line with the wind. Any depart- ure from this due to a change in the angle of incidence, causes an in- crease in their resistance. So that at angles both above and below
99
the normal angle of incidence, the resistance of the body is higher, due to higher values of KL.
On p. 96 a typical resistance chart is given, and on it is shown a typical curve of structural resistance. The range of incidence of 1° to 12°, used as an example already, is, as indicated, accompanied by a rise in structural resistance from 60 Ibs. at 12°, to 195 Ibs. at 1°, since the speeds corresponding to these angles are 44.6 and 79.5 m. p. h.
Drift.
If we refer to the first chart showing KL and L/D, and recall that for any value of the angle of incidence the value of KL was read, to determine speed, it is seen that we can also read at the same time the value of L/D for that particular KL. Knowing the weight, this ratio at once gives us the Drift, since for horizontal flight,
Drift = Weight + L/D.
It becomes clear, now, why reasons of convenience lead to plot- ting the values of L/D in preference to the values of KD, to supply in D = KD S V2. Drift is always a fraction of Lift and, therefore, of the weight, but is in no other way concerned with the speed, V.
Thus, when the chart is referred to, to obtain the value of KL for 1°, the value of L/D = 13.6 could be read at the same time, and know- ing that the weight is 1800 Ibs. the Drift at that angle is immediately determined as, 1800 + 13.6 = 132 Ibs. In the same way the Drift at 12° is found to be, 1800 + 8 = 225 Ibs., and the least drift at about 4° is 1800 -f- 15 = 120 Ibs. Since these determinations are made in com- pany with the determinations of the air speeds corresponding to the various angles of incidence, we at once have obtained the values of the Drift for the various speeds — and, consequently, have solved for the second part of the Total Air Resistance. We proceed, then, to plot a curve showing the Wing Resistance, on the same chart, on which we have already plotted Structural Resistance, for different speeds.
The Total Air Resistance is the sum of these two. On a chart, curves drawn to the same cross lines are easily added graphically, by merely surmounting one value on top of the other. Thus, for 60 miles an hour speed, the value of the Wing Resistance, 120 Ibs. is added by means of dividers (in actual measurement) above the point on the Structural Resistance curve, which reads 105 Ibs., and this gives the total 225 Ibs., graphically. The same process is followed with other points, sufficient to establish the curve of Total Resistance to motion, which is the second characteristic to be determined.
100
III. POWER REQUIRED.
In Chapter III it was recalled that power expended corresponded to the exertion of foot pounds work at a certain rate, and that one horse-power = 550 foot pounds per second.
At any speed, therefore, the Ibs. Resistance x the speed in feet per second, gives the number of foot pounds per second used up by the aeroplane. Dividing this quantity by 550, will give us the Horse Power Required for horizontal flight at that particular speed.
If we call R the resistance and V the speed in miles per hour, then
R X V x 1.47 H.P. = -
550
since V in m. p. h. must be multiplied by 1.47, in order to express it in feet per second. Combining 1.47 + 550, we get the handier rela- tion that,
RX V Required H. P. = -
375
where R is the total Resistance in pounds read for any speed from the Resistance Chart, and V is the velocity in miles per hour.
A curve may then be plotted of Power Required to fly at the vari- ous speeds. This is done in the third chart, p. 96. It is to be recalled that in plotting the Drift on the resistance chart, the corresponding angles of incidence we^e marked on the curve.
This is also done on the Power Required Curve, the correspond- ence between Speeds and Angles of incidence being precisely the same as originally determined, when considering the first chart of KL and L/D.
As examples of the manner in which to determine Power Required, let us take the machine at incidences of 12°, 6° and 1°.
From the Resistance Chart we find that at 12°, corresponding to a speed of 44^ m. p. h., the Total Resistance is 285 Ibs. Therefore,
285 x 44.5 Required H. P. at 12° = - - = 33.8 h. p.
375
The same values read for 6°, give
215 x 54
Required H. P. at 6° = - - = 31 h. p.
375
And likewise for 1°, there is obtained
327 x 79.5
Required H. P. at 1° = - - = 69 h. p.
375
101
It is most important to note the general form of this curve, and as a "Characteristic" of the aeroplane, it is decidedly the most im- portant one. At angles below 10° there is a noticeable rise in Power Required, because the increase in Drift is so much greater than the decrease in Structural Resistance, corresponding to a slower speed. And the pronounced increase in Power Required, at angles below 6°, is due primarily to the greater preponderance of the increase in the Structural Resistance, as the speed increases.
At angles of 10° to 6°, corresponding to speeds of about 45 to 55 m. p. h., the Power required is at its lowest value and remains very nearly the same for this particular machine. Power required curves vary greatly for different aeroplanes, both in their contour and in the angles at which the low points are located. But the rise both above and below a certain speed where the power is least, is noticeable on all power curves, and leads to the general conclusion, that high drift at low speeds, and high structural resistance at high speeds, are the wasteful elements.
The establishment of all the points on the Power Required Curve, is made in the manner indicated, and we then obtain the third char- acteristic of the Aeroplane — which is the determination of the horse power, required for horizontal flight, at various speeds.
IV. POWER AVAILABLE FROM THE PROPELLER.
A certain horse power is given by the engine at various revolu- tions per minute, and a curve of this "Brake Horse Power," for cor- responding "r. p. m.," is as necessary and as easily furnished as in- formation on the size and weight of the engine. On p. 97, a curve for the particular motor taken as an example here is given.
But this power is not directly available, since its exertion on the air to move the aeroplane is thru the medium of an air propeller, which, unfortunately, is more or less wasteful of the power the engine gives to it.
The efficiency of the propeller, therefore, must be considered. Of all features of the aeroplane, propeller determinations from both theory and practice are exceedingly unsatisfactory. But laboratory experiments, notably Eiffel's, lately have given valuable informa- tion on a few good blades, in which the shape and section are left un- altered, and only the r. p. m. and diameter adjusted for different aero- planes. The theory of the "similitude of propellers," which permits of passing from one machine to another with the same type of blade, is at present the only really valuable basis for propeller determina- tions.
Experiment shows that the old notion of "pitch," etc., on a basis of screw propeller theory is poorly founded. Whereas, the more mod-
102
ern notion of a propeller, consists simply in a consideration of the blade as an aerofoil at a certain angle of incidence, moved against the air in a rotating path, and in which KL S V2, would represent the Thrust, and KD S V2, the Torque.
For purposes of aeroplane design, considerations of the propeller, its loading, deflections and strength, and its Thrust and Torque char- acteristics, are most important. For field use the strength question requires merely that a propeller never be run at a greater r. p. m. than has been proven safe, without information from the manufacturer as to the strength of that particular propeller; and that alterations, such as metal tipping, be done by the propeller maker, unless the propeller has already been designed therefor. But, we are very vitally inter- ested here in the suitability of various propellers, for different aeroplane performances, so as to enable us to pick out the propeller desired.
Since on any engine the power is determined from the r. p. m., by merely mounting any propeller in question on the engine and reading the r. p. m. for a given throttle, there is at once established the power used by the propeller. This is so readily and conveniently done in the field that for the present it is unnecessary to compute by extensive mathematics the power necessary to drive this propeller at a certain r. p. m. In the determination of the Power given out by the propeller in the air, however, no such convenient measurements can be made. We have recourse, therefore, to laboratory data furnished with the propeller.
This data is most conveniently given as a curve showing the Effi- ciency of the propeller, corresponding to values of the quantity v/nd.
The Efficiency of the propeller is merely the % of the power put into it, that is given out in Thrust Power by the propeller.
The quantity v/nd, is a convenient numerical relation, used by the laboratories to express the Efficiency of a propeller of definite shape and section for any combination of values of
(1) The velocity of the aeroplane in feet per second, v,
(2) The revolutions per second of the engine, n,
(3) The diameter of the propeller in feet, d.
The speed thru the air of the tip of the blade is determined in feet per second by the circumference = Trd, and the number of times a second it covers this distance = n. The quantity v/Vnd is the actual relation between the "tip speed" of the propeller and the speed thru the air of the entire aeroplane. Let us say, briefly, that it has been "discovered" that this relation definitely determines the efficiency of any particular blade.
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Our data on the engine gives us n, which is taken in this example as normally 1200 r. p. m. = 20 r. p. s. The diameter, d, in this example is 8 feet. For any speed of the aeroplane, v, therefore, we can com- pute v/nd, and on the Efficiency chart, p. 97, read % efficiency of the propeller. Knowing the horse power of the engine for the given value of n, we readily determine the actual horse power available from the propeller. As an example, at 60 m. p. h. speed, v = 60 x 1.47 = 88 feet per second, n = 20, and d = 8, whence v/nd = .55. Reading on the first chart p. 97, we find that for v/nd = .55, propeller efficiency = 76 %. On the second chart, p. 97, it is seen that at 20 revolutions per second, or rather 20 X 60 = 1200 r. p. m., the engine may be ex- pected to give 88 h. p. Our propeller Power Available, therefore, is 76%of88 = 67h.p., and is so plotted on the Power chart for 1200 r. p. m., on p. 96.
In the same way all the other points, not only for this same curve but for values of r. p. m. = 800, 1000, etc., are plotted, and we thus obtain the fourth characteristic — the thrust Power Available for any r. p. m., at the various speeds of the aeroplane.
PERFORMANCES OF THE AEROPLANE.
The characteristics of the aeroplane having been determined we may proceed with determinations of the performances that may be expected of it.
The Glide or Volplane
In horizontal flight the thrust of the propeller in pounds is just slightly in excess of the total Resistance of the Aeroplane. When the motor is shut off, however, this balance between power required and power exerted ceases, and a distinctly different condition of flight results. If some other force were not introduced to overcome the total resistance, which is still about the same as in the conditions of power flight,* the aeroplane would slow down and finally fall in some dangerously unbalanced condition. Such a force can at any moment be introduced, by merely inclining the path of the machine down- wards, enough to cause the gravity force, equal to the weight, to be- come the resultant of two forces — a Lift on the planes, less than the weight W, and a forward component of this gravity force, equal to the Total Resistance. The machine then descends, on a downward path, in which the power spent in descending the machine's weight at an inclined rate corresponding to a fall of a certain number of feet per second is equal to the power used up in overcoming the total Resist- ance, at the particular speed, on this downward path. The determi- nation of the slope of this path, becomes very easy. It is merely the ratio of the Weight of the machine to the Total Resistance, at the particular angle of incidence and speed assumed on the glide. This
* It is to be noted that in a tractor, the air propeller throws back a stream of air on the body that has a speed greater than the aeroplane's speed, so that shutting off the engine slightly reduces the Total Resistance.
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feature is considered again in connection with the Stability and Opera- tion of the aeroplane.
A curve of "gliding angles" is readily plotted on the Resistance Chart, by dividing the weight by the Total Resistance at any point. Thus, at 55 m. p. h., the Total Resistance is 215 Ibs. Therefore the gliding slope is 8.4 to 1. In other words, the aeroplane will travel 8.4 times as far as its vertical descent.
High Speed and Low Speed
It is apparent from a study of the Power Chart, p. 96, that the speed range is determined by the crossing points of the Power Re- quired and Power Available curve. Thus, at 1200 r. p. m., horizontal flight is impossible due to lack of power, above 82 m. p. h., and below 41 m. p. h. The speed ranges for other r. p. m. are also indicated.
Climbing Rate
Although atmospheric conditions vitally affect the rate of climb and height attainable of any aeroplane, it is possible to determine the initial climbing rate. The climbing of a machine is due to the exer- tion of an extra amount of power, which raises the Ibs. weight of the machine a certain number of feet per second, thereby using up a cer- tain horse power. This excess power is directly available, if the Power Available is greater than the Power Required. And a measure of this excels power is the difference between these two curves. Thus, at 56 m. p. h., the Power Required is 32 h. p., and the corresponding Power Available at 1200 r. p. m. in actual thrust, at that speed, is 63 h.p. Therefore, we have a reserve power of 31 h. p., which can be entirely made use of in climbing the machine. Since the weight is W = 1800 Ibs., the equation for climb becomes,
H. P. for climb = 1800 X climbing rate in feet per second, whence, Climbing Rate = H. P. in foot Ibs. per second + 1800 Ibs. weight. Therefore, for this example,
31 x 550
Climb in feet per minute = - - X 60 = 570 f. p. m., rate.
1800
Summary
Other curves giving the economy in fuel consumption and cor- responding engine speeds and aeroplane speeds, are explained on p. 97, and are of very practical value.
By the processes outlined in this chapter, the performances of an aeroplane may be predicted and recorded, with an accuracy and value that is, indeed, not only of great interest, but of real benefit to the aeroplane user.
It is seen that the characteristics of the aeroplane, from which the performances may be predicted so readily, are based on the data furnished by the laboratory tests on the aerodynamic features and the engine, so that the significance and importance of this informa- tion becomes evident.
CHAPTER IX.
STRESSES AND SAFETY FACTORS.
The nature and magnitude of the supporting and resisting pres- sures on aeroplanes, and their effect in determining characteristics and performances to be expected when the thrust power available and fuel consumption are known, constitute one feature of the study of the aeroplane, as outlined in Chap. IV., p. 41. We may proceed, therefore, with a consideration of the second feature — the study of the construction of the machine. And eventually, after having given attention to stability and operation, we will be at liberty to discuss the various military types of aeroplanes.
It is necessary to know the distributed loading on the aeroplane, of the air forces generated by the movement thru the air, before pro- per consideration can be given to the stresses and safety factors in its structure.
In gliding, the lifting forces on the wings are slightly less, and in climbing slightly greater, than in horizontal flight, but only in a small degree. When attacked by sudden puffs, the air forces are in- creased in various ways; banking on turns introduces extra stresses, due to the centripetal force; and in various maneuvers such as a sud- den recovery from a steep dive, looping the loop, flying with full power at very high angles, etc., additional loads are imposed on the structure of the machine, which must be withstood.
Safety Factor
The ratio of the breaking strength of any structural part to the load imposed upon it, is termed the safety factor of that part. Thus, if a wire requires a tension of 3000 Ibs. in order to break it, whereas the load it carries is only 300 Ibs., it is said to have a safety factor of 10. In ordinary engineering practice, the load that it is considered necessary for any part to carry is taken as the maximum load that the particular part will ever have to stand, and, in designing it, a safety factor is applied to this maximum possible load. Contrary to all good engineering practice, the structural parts of an aeroplane are gener- ally designed to have a certain "safety factor," with reference to the normal flying load, determined by the weight of the machine. The
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excess stress due to some additional maneuver is taken account of in the "safety factor" itself, so that in the engineering sense it is not a safety factor at all, but merely an allowance for extra stresses, in- duced by conditions other than ordinary horizontal flight. It is pos- sible to estimate what the maximum possible stresses are, and to deter- mine whether or not the aeroplane will collapse when they are im- posed. And in general an aeroplane is so designed that the strength of its weakest structural part will at least be great enough to with- stand a reasonable value of this maximum stress, without breakage, the real safety factor being very seldom as much as two. In most other branches of engineering a safety factor of at least ten is required. The object of a safety factor is to provide against the increased stresses of sudden impact shocks, which are difficult to estimate, and to take account of defective material