Airplane Characteristics

Front matter

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Preface

Any contribution to aviation, however small, needs today no justification. The airplane is an accomplished fact and concerning it there is no longer any room for apology or speculation. So far has the art of flying progressed that the principles of flight can in the main be set forth as definite and without surmise, and a collection of the essential elements can now be made that will apply to all airplanes, irrespective of type or structure. Not that there is nothing further to be learned or discovered in aviation — ^for, far from it, there is ample opportunity for discovery and invention in this direction — ^but a codification of the well-known ground work can now be made that may be an aid to those who are advancing the art, as well as to those who are learning it.

The introductory discussion in this voltune is a contribution to such a codification, which, it is hoped, will prove useftd not only to the flyer and designer, for whom the book is primarily intended, but to students and engineers and to others who have only a general interest in aviation. Indeed, so important is the place now taken by the airplane that there are many who desire a knowledge of the principles of its operation.

It is the author's purpose to present the principles of airplane sustentation and stability and the characteristics of an airplane in flight in a way that is direct and simple and at the same time reasonably precise, laying particular stress on that which is vital. Except in minor ways, no claim is made for originality other than in presentation; in fact, the aim has been to include only those things that are essential and are accordingly well known to those versed in the subject. To those not thus well versed, the characteristics of an airplane

PREFACE

are, however, not so well known as they should be ; discussion of the subject is apt to be either superficial and inadequate or involved and complicated. The author has endeavored to give a treatment that is adequate but simple, and without the use of higher mathematics.

Logical sequence, rather than historical development has been kept in mind and no attempt has been nnade to ascribe particular features to their inventor or author. Military uses of the airplane, as well as its history, are left to others who may more appropriately discuss such phases of the subject. The author has confined his attention to the principles of airplane flight and has given no discussion of materials of construction — ^very important, of course, in airplane building — ^nor of the gas engine, on which there are many specialized treatises.

The author had occasion, as a member of a commission for planning the courses in our Schools of Military Aeronautics, to study carefully the needs of such courses. He has had occasion, also, to conduct several classes in aerodynamics and the principles of flight, made up not only of those with a direct practical interest in flight, as future pilots and designers, but likewise of others with an indirect interest -students in civil and mechanical engineering and physics— who have been interested in the airplane as in any of the mechanisms of our present day civilization. He has noted particularly those parts of the subject that have proved vital and of interest to all, — ^no matter from what angle the subject is approached.

It is planned that the book — ^with the added chapters now in preparation — shall be self-contained and complete in its own field, i. e., as an introduction; final practical instruction for flyer or designer must needs be obtained at the flying

PREFA CE

field or in the designing room. The author has had fljdng experience only as passenger and would naake no attempt at specific fljdng instruction.

In view of the present emergency, it is thought best to issue the material contained in this first edition without delay, and to reserve for subsequent publication the material now in preparation (referred to in the Table of Contents) that is needed to complete the work. The author will be glad to have his attention called to any error or obscurity in this presentation and will particularly appreciate constructive suggestions from those practically engaged in airplane operation or development.

Ithaca, N. Y., July 30, 1918.

Preface To Second Issue Of First Edition

So close upon the heels of the first issue is this second issue that no general revision has been possible. Some corrections and additions are given on the following page. The author thanks those readers who have called his attention to errors and repeats his request for suggestions.

CORRECTIONS AND ADDITIONS

Page 27. In caption of Fig. 15, for "blown" read "flown."

Page 28. In caption of Fig. 28, for "Lift-weight" read "Lift = weight."

Page 37. The first sentence should read: "The power supplied by the engine has no direct efifect upon velocity; if the elevator is controlled so that the same angle of incidence is maintained, the same velocity will be maintained, irrespective of the power supplied by the engine."

Page 38. Last sentence should read: "It is seen that if power is increased or decreased .... the inclination of the flight-path is changed, but (provided the angel of incidence is not changed) velocity remains unchanged."

In an endeavor to lay emphasis on this important relation between velocity and incidence, the statements originally made in the text go too far; constant velocity results from constant incidence, but (generally speaking) this requires control of the elevator by the pilot. When added power is obtained by opening up the throttle, this power may be used either in climb or in increased velocity, or part may be used in climb and part in increased velocity, — as the pilot determines by his control of the elevator. The immediate eflEect of the opening up of the throttle is increased speed, and the pilot may continue at increased speed in horizontal flight by proper elevator control; or, as stated above, he may use part or all of the added power for climb.

The position of the elevator necessary for horizontal flight or for any particular incidence or climbing angle, is dependent upon several factors, — including the setting of the horizontal stabilizer, the relative positions of center of thrust and center of resistance and the amount of slip-stream, — the eflEects of which are variously influenced by velocity. Although the relation between incidence and velocity is definite and simple, a general relation between elevator position and incidence or velocity can not be so simply stated.

The foregoing relation between velocity and incidence is the relation in steady flight, and is modified by the inertia of the machine when velocity is changing. It is modified, also, when the flight path is greatly inclined.

Page 60, line 2. Add: "When the model is viewed from in front along the flight path, an increase in incidence of left or right wing is shown by an apparent increase in its area; a decrease in incidence of either wing by an apparent decrease in its area. The change in incidence of the raised and of the lowered wing of an airplane as it rolls is thus easily seen."

Page 64. Lines 8 and 9 from bottom: "as will occur with many wing sections" would better read "as will occur with practically all wing sections."

Page 64 or 65. Add the following paragraph: When a machine is banked, keel surface back of the center of gravity tends to turn the machine toward the lower wing and so aids in making a turn. This is due to the fact that a machine descends and side slips when banked on account of the decrease in the vertical component of the lift. There is, accordingly, an upward and side pressure on the keel, that swings the tail up and out. In other words the machine tends to nose down and to turn in toward the lower wing.

Contents

Sustentation Relations in Flight Resistance Lateral Stability Directional Stability Glossary - - -

Appendix III. Power Characteristics - Appendix IV. Control and Other Diagrams page 1

IN PREPARATION

Chapter I

The first essential for flight is a sustaining force or sustentation. This is obtained in balloons and in airships by the buoyancy of a light gas which makes the craft as a whole lighter than air and capable of flotation. In an airplane, or in any aircraft heavier than air, this sustentation must be obtained by the reaction of the air upon planes or surfaces which are moving with relation to the air and which force or deflect the air downward. The airplane is the only craft of this kind that has been practically developed and it alone will be discussed in this volume. Other types of flying machines have, however, been contemplated, among which may be mentioned the omitluqiter, with wings that flap like those of a bird and sustain the machine by forcing the air downward and at the same time backward; and the helicopter, equipped with propellers which revolve on a vertical shaft and Hft the machine by forcing the air directly downward.

A second essential for flight is stability, discussed in later chapters.

The sustentation of an airplane is due to the fact that the air it encounters is deflected downward by the wings; although this downward deflection is but little, it is sufficient to sustain the machine, for new air is being continually encountered and deflected. An understanding of sustentation will best be gained by a consideration of the pressure exerted by the air upon flat and curved surfaces moving rapidly with relation to it.

Flat Plane Perpendicular to Air Stream

We will first consider the pressure on a flat plane perpendicular to an air-stream.

Pressure varies as square of velocity.

If a thin plate or plane, say a book cover or the cover of a. cigar box, is held out from a moving automobile — well away from the body and windshield — so that the air-

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FRBSSURT P 1

DIRECTION OF MOTION

Fig. I. Pressure on flat stirface.

stream strikes the plane perpendicularly to its surface, as in Fig. I, a pressure is felt that is small at low speeds but which increases very rapidly as the speed increases. In fact, if accurate measurements were made, it would be found that when the speed is doubled the pressure becomes four times as great, in other words that the pressure varies as the square of the speed.

Furthermore, this same relation wotild be found to be true if the plane were held still in a wind or in the air from a blower, and so it is seen that the pressure depends not upon the absolute velocity of the plane or of the air but upon their relative velocity, as the air-stream strikes the plane. This is on accotint of the great mobility of the air particles, the effect being the same whether the air is stationary or moving. The law of the "square-of-thevelocity," although not a general law that holds for all substances and for all velocities, may be taken as practically true in air throughout the range of airplane velocities.

Pressure varies with plane area.

By using planes of different areas, it would be fotmd, likewise, that the total pressure on the plane increases with the plane area and (practically) in direct proportion to the area; for example, an increase of ten per cent, in area is accompanied by an increase of ten per cent, in total pressure on the plane. This relation, however, must be considered as only approximate, particularly when the planes compared differ greatly in shape or area.

General law.

The total pressure P, upon a"" surface S, normal to an air-stream with velocity V, may accordingly be expressed by the following law: —

P = KSV^.

Here K" is a number or coefficient, the value of which depends

upon the tmits used*. When the area 5 is given in square feet, the velocity V in miles per hour and the total pressure P

in pounds, a practical value for the coefficient K, that has been determined experimentally, is 0.003 for air at normal density; that is,

P = 0.003 SV^' The pressure per square foot of surface is thus seen to be

*Thus, when P is expressed in ounces per square foot, the numerical value of P, and so of K; is 16 times as great as when P is expressed in potmds per square foot.

1.2 pounds at a velocity of 20 miles per hour, 4.8 pounds at a velocity of 40 MPH., 19.2 at 80 MPH., etc.

Metric units. — When V is velocity in meters per second,

5 the area in square meters and P the weight in kilograms, the value of K is 0.07 5 . To get K in English units of pounds, square feet and miles per hour, multiply K for metric tmits by 0.0408.

Variaticms in K.

The value of K is not strictly a constant. It varies directly with the density of the air, decreasing, therefore, with altitude, as discussed later, and changing somewhat from day to day. It varies, also, with the size and shape of the surface. The values given above {K = 0.003 ^ English

Fig. 2. Square with aspect ratio i ; and rectangle

with aspect ratio 6.

units, K = 0.075 ^ metric units) are for a square surface,

0.15 X 0.15 meters, in air of normal density. For squares of

different sizes, experiments of Eiffel give values f or K as

follows: —

For rectangles of equal area (0.225 m.^) and with different aspect ratios (the aspect ratio is the length divided by width, see Fig. 2) Eiffel gives: —

Aspect Ratio i

Value of K .066

.0705

.0725

.0755

.0885

.092

.097

1.07

1. 10

1.145

1.34

1.40

1.47

The last line, Kr -4- Ks, is the value of if for a rectangle divided by the value of K for a square. The percentage increase in K with change of aspect ratio, shown in the last line, will hold approximately for rectangles of other areas, for the effect of aspect ratio is almost independent of size of surface.

Somewhat different values hold for circular discs and other shapes. Considerable experimental data must be gathered before the precise value of K can be determined for a surface of any size and shape. Meanwhile the value 0.003 (English system) or 0.075 (metric system) will prove practically useful,

Fig. 3. Tiarbtdent region and rarefaction back of plane.

it being borne in mind that this value is only an approximation and that a closer value should be sought whenever it may be deemed desirable.

Eddies back of plane.

When a plane encounters an air-stream, there is a compression of the air on the front face of the plane. Immediately back of the plane there is a rarifaction, so that back of the plane air currents are set up that swing arotmd toward its rear surface. These air currents may be felt, by one riding in an open trolley car or in an automobile behind a wind shield, as a wind on the back of the neck.

These air currents are, in a crude way, visualized in Fig. 3.

Back of the plane and near the edge is a turbtilent region with complex eddy currents of air. These no doubt have a material effect upon the value of K, so that it is not surprising that K has different values for surfaces of different shapes and sizes, for in these the length of edge and the eddy-current eflEect is not proportional to the area.

Methods of experimenting.

Experiments on the air resistance of different surfaces or bodies may be made in various ways. The necessary velocity of the body relative to the air may be obtained by dropping it from a suitable tower or other height (employed by Eiffel), by carrying it on a fast moving vehicle, by carrying it at the end of a long rotating arm (employed by Langley), by exposing it to a natural wind, and finally by carrying it through the air in airplane flight.

The most convenient and approved method now in use is to expose the body to an artificial wind in a wind tunnel, first used by Eiffel* and now used in all aerodynamic laboratories. Air is forced through such a tunnel by means of a powerful fan; the body to be studied is held stationary, being attached to suitable devices for measuring the pressure and, in case of oblique surfaces, for ** weighing" the vertical as well as the horizontal component of the pressure.

In such a tunnel can be tested not only surfaces or bodies of various kinds, including wing sections, but even complete airplanes in model size; and it is important to note that the perf oniiance of wings and airplanes in flight is found to agree remarkably well with wind-tunnel tests.

•Eiffel's experiments are beautifully described in his book "The Resistance of the Air and Aviation," translated into English by J. C. Hunsaker.

Flat Plane Oblique to Air Stream

Let us next consider the action of a flat plane at an oblique angle with the air-stream; such a consideration will show at once the source of the sustaining force in an airplane.

Lift of an oblique plane.

If a plane be held so as to form an angle i (called the angle of incidence or the angle of attack) with the air-stream or

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Angle kit Inoidmoe

Fig. 4. Vertical and horizontal components of presstire on oblique plane.

"relative wind," as in Fig. 4, it will be seen that the total pressure P of the air against the plane has two components:*

A vertical component or lift, commonly designated by the letter L, tending to force the plane upward at right angles to the air-stream.

A horizontal component or dynamic resistance (called, in an airplane, wing-resistance,) commonly designated by the letter D, tending to force the plane backward in the direction of the air-stream.

These components may be observed by blowing upqn a card held in the hand obUque to the air-stream, or by moving the

*These two components are horizontal and vertical only in normal horizontal flight. More accurately defined, lift is the component of hand — slightly inclined — ^rapidly through water; in the latter case the upward lift may be distinctly felt.

It is the lift that holds an airplane up in flight, i, e., that gives sustentation; for an understanding of the airplane, therefore, a knowledge of what determines the lift is essential. Clearly for horizontal flight the lift must be just equal to the weight of the machine, otherwise the machine will either ascend or descend, — discussed later under clirnbing and gliding. The problem of horizontal flight is, therefore, the problem of securing a lift equal to the weight. As discussed later, this lift is better obtained from a "cambered*' wing (i. ^., a wing that is slightly curved from front to back) than from a flat plane.

LIFT LIFT LIFT LIFT a b c 4

Fig. 4a. Lift is inclined when machine is inclined.

In order to get the lift, the plane or wing must move rapidly through the air. But in order to move the plane or wing through the air it is necessary to overcome the wing-resistance and this is done by the thrust from the propeller. To drive the propeller, so as to obtain this thrust, it is neces-

total pressure that is perpendicular to the air-stream and that lies in the plane of symmetry of the machine; this plane is vertical as long as the machine does not roll. Lift is accordingly vertical in normal flight, but becomes inclined when the machine is inclined, as shown in Fig. 4a. Wing-resistance is, in all cases, the component of total pressure that is in the direction of the air-stream.

It is recommended by the U. S. Advisory Committee on Aeronautics that the word "drift," sometimes used as a designation for wing-resistance, be abandoned; see "drift" in Glossary, Appendix I. But the initial letter P, in such conmion use, may well be retained as a symbol for dynamic or wing resistance; likewise, I^d, formerly called the coefficient of drift, may be retained as the coefficient of dynamic or wing-resistance.

sary to have power. Obviously it is desirable to have the wing-resistance small, necessitating small thrust and small power, and to have the Uf t large so that the machine can sustain not only itself but some load in addition. But it is impossible to have the lift without the wing-resistance, and the wing-resistance has aptly been described as the price paid for the lift.

Variation of lift and wing-resistance with incidence.

Highly important is it to know how the values of lift and wing-resistance vary as the angle of incidence is changed.

Fig. 5. Flow of air past oblique plane, showing turbtdent region back of entering edge and the downward deflection of air after leaving the plane.

This infoniiation cannot well be derived theoretically on accotmt of the complexity of the problem, — due in part to the eddy currents in the turbulent region back of the entering edge, as indicated in Fig. 5. The infoniiation, however, has been fotmd experimentally.

The total pressure P, the lift L and the wing-resistance D all vary directly as the area S, of the plane or wing, and as the square of the velocity V; that is,

Total pressure = P = KpSV^;

Vertical component or lift = L = Kj^SV^;

Horizontal component or wing-resistance = D = Kj^V^.

We are particularly interested in the two components L and D\ also in the two coeflBlcients, Ki, called the coefl9icient of lift and Kj^ called the coefl9icient of wing-resistance.

These coefficients have different values for each angle of incidence. Their values, fiirthermore, will depend upon the tmits used.

The values of these coefl&cients that will give lift and wing-resistance in pounds, for different angles of incidence, when 5

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H

o

o o

ft* o t

ANGLE OF INCIDBNCB

Fig. 6. Coefficient of lift Ki^ and coefficient of wing-resistance Kn

for flat rectangle at different angles of incidence; aspect

ratio, 6, **. «., length -r- width = 6, as in Fig. 2.

is in square feet and V is in miles per hour, are shown by the curves in Fig. 6. These are plotted from data by Eiffel* for a flat rectangle with an aspect ratio 6.

For small values of incidence, it will be seen that the coefficient of lift increases nearly uniformly, in proportion to

Resistance of the Air," p. 122; size of rectangle 90 x 15 cm.

the angle of incidence; if the angle is doubled, the coefficient of lift is approximately doubled. After reaching a maximum value (in this case about 0.002) the coefficient decreases somewhat irregularly*, becoming zero at 90° incidence.

This maximum value is only two-thirds as great as the maximum value obtained by a cambered wing; see Fig. 11.

The coefficient of wing-resistance also increases more or less tmiformly with incidence and reaches a value of about 0.003 at 90° ; but in no case is Kj^ zero, even at zero incidence.

10 • 19^

ANBLX or IVCZSEtfCI

20^

Fig. 7. Curves showing L/D ratio and D/L ratio for flat

rectangle; aspect ratio, 6.

Lifting eflSiciency or L /D ratio.

The ratio of lift to wing-resistance, is frequently referred to as the lift-over-drift ratio or the L /D ratio, or as the lifting efficiency of a plane or wing, and this ratio is of much significance. As it is desirable to have L large and D small,

*After 20®, Ki, increases slightly, having by Eiffel's data the same value at 30° as at 15°. The incidence at which the maximum occurs, and its value are different for different aspect ratios; but the curves are all of the type here shown.

it is obviously desirable to have the LjD ratio as large as possible. It is seen that the LjD ratio is equal to I^l -^ ^d» values for which are obtained from the curves in Fig. 6.

The values of the L /D ratio for a flat rectangle with aspect ratio 6, thus obtained from Fig. 6 for different angles of incidence, are shown in Fig. 7 . The maximum value for L /D is here seen to be a little over 6 at an incidence of 6®, — a rather poor lifting efficiency compared with an L /D ratio 16 or more for a cambered plane.

In Fig. 7, the values are also shown for D/L (see dotted curve); but, as these values approach infinity when L approaches zero, they are not so convenient to use. It is more usual, therefore, to make use of the L jD ratio.

In the case of a theoretical plane with a perfectly smooth surface, the pressure P wotdd be perpendicular to the surface, so that DjL would be the tangent and LjD the cotangent of the angle of incidence; and, at zero incidence, the resistance of the plane would be zero.

But in a practical case, the plate or wing that is used must possess an edge of definite thickness, and this with some skin friction (undoubtedly small) gives a certain resistance, even to a horizontal plate. The resultant pressure P, shown by the solid line in Fig. 4, is, therefore, not peri)endicttlar to the surface but is a little back of the perpendicular, — ^which is shown by the dotted line. Its direction and magnitude can be determined by laying off the two components L and Z?,

the resultant pressure being P — y/u + D^.

Center of pressure.

When the plane is perpendicular to the air-stream, i, ^., when the angle of incidence is 90°, the center of air pressure on the plane is at the center of the plane. When the plane is oblique, the center of pressure is found to be in advance of the center of the plane, moving more and more forward toward the entering edge as the incidence decreases. The position of the center of pressure for different angles of incidence is shown by the curve in Fig. 8. The position is somewhat different for different aspect ratios, but in all cases with a fiat plane the center of pressure moves forward from the center

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W.1DL

Id

.fiO

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l.CX)

ENTERING EDGE

CENTER UNE

TRAIUNG EDGE i

€P

Fig. 8.

15«

30*» 45« 60*»

ANGLB OF INCIDENCE

75«

Position of center of pressure on a flat plane, with aspect ratio 6, for different angles of incidence.

of the plane as the incidence decreases, thus becoming nearer to the front edge of the plane — ^which is called the entering edge or leading edge — and further from the rear or trailing edge.

Cambered Wing

Decreased turbulance when cambered wing is used.

A flat plane encountering an air-stream disrupts the air, the entering edge, and to a lesser extent the trailing edge, tending to produce air eddies. The turbulence produced by such a plane has been shown in Fig. 5, which as already explained indicates the phenomenon but should not be understood to be an accurate representation of it. It would seem that this turbulence would increase the wing-resistance and that it might decrease the lift; or, put another way, it would seem that, if the turbulence could be eliminated or reduced by any means — ^f or example by giving the wing more or less of a stream-line form, — an increase in lift and decrease in wing-resistance might be obtained. This indeed is the case, such a result being obtained by arching the wing from front to back. A wing thus arched is called a cambered wing and on account of its better performance is always used in airplane construction.

The flow of air past a cambered wing is shown in Fig. 9, which again is merely illustrative and is not exact in detail. The disturbance of the air by the wing is minimized by having the surfaces of the wing, throughout, more or less parallel to the stream-Une flow; the wing then enters the air and leaves the deflected air without disturbance, and eddies are eliminated so far as they can be.

Creation of lift.

It is to be borne in mind that it is the downward deflection of the air that creates the lift, it being the purpose of the designer to increase this lift and at thQ same time to decrease the wing-resistance. Lift is obtained to a certain extent by the positive pressure on the lower surface of the wing (indicated by p in Fig. 9) but to a much greater extent by the negative pressure on the upper surface, indicated by n; indeed, as much as three-fourths of the total lift may be due to this negative pressure. It will be seen that, in a cambered wing as shown in Fig. 9, the upward trend of the upper surface of the entering edge swings the air-stream upward over the wing before its final deflection downward; this decreases the pressure on the upper surface and so contributes materially to the lift.

The distribution of pressure on single and multiple planes is shown in a later chapter. See Appendix IV.

It is the curvatiu^ of the upper surface of a wing that is most important, — particularly its dip toward the entering edge, often referred to as the dipping ttoat edge. The curv;ature of the lower stuface is far less important; with a well