AIRPLANE CHARACTERISTICS 
 
By the same author 
 
 The Principles of the Transformer 
 Direct and Alternating Current Manual 
 
 Experiments with Alternating Currents (being Part 
 II of Volume II of A Laboratory Manual of 
 Physics, edited by E. L. Nichols) 
 
 Alternating Currents : an Analytical and Graphical 
 Treatment for Students and Engineers (jointly 
 with A. C. Crehore) 
 
 Also, editions in French and German 
 
L* 
 
 
AIRPLANE 
 CHARACTERISTICS 
 
 A SYSTEMATIC INTRODUCTION FOR 
 FLYER AND STUDENT AND FOR ALL 
 WHO ARE INTERESTED IN AVIATION 
 
 BY 
 
 FREDERICK BEDELL, PH.D. 
 
 \ v 
 
 Professor in Physics, Cornell University 
 
 Member Aeronautical Society of America, Vice-President Amer- 
 ican Institute of Electrical Engineers, Fellow and Past General 
 Secretary American Association for the Advancement of Science, 
 Member the American Physical Society and Managing Editor 
 of The Physical Review. 
 
 FIRST EDITION 
 PRICE $1.60 NET 
 
 See Note in Regard to Publication on Following Page 
 
 TAYLOR AND COMPANY 
 
 ITHACA, NEW YORK 
 1918 
 
NOTE IN REGARD TO PUBLICATION 
 
 In view of the importance at the present moment of any contribution 
 to aviation, this first edition containing only part of the material con- 
 templated is issued now. The remaining part, referred to in the Preface 
 and Contents, is in preparation and this, it is expected, will be ready 
 for publication in 1919. 
 
 TAYLOR AND COMPANY, Ithaca, N. Y., will send copies of this book, 
 postpaid, upon receipt of $i .75 per copy. Copies may also be obtained 
 from The AERONAUTICAL LIBRARY, 299 Madison Ave., New York, 
 and from leading dealers generally. 
 
 COPYRIGHT 1918 
 
 BY 
 FREDERICK BEDELL 
 
 PRESS OF W. F. HUMPHREY, 
 
TO 
 
 FOUR NEPHEWS WHO ARE IN THE AIR SERVICE OF THE UNITED 
 STATES AND HER ALLIES, AND TO THE MEMORY OF 
 ONE NEPHEW WHO HAS DIED IN THAT 
 SERVICE, THIS BOOK IS DEDI- 
 CATED BY THE 
 AUTHOR 
 
 382818 
 
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 direc- 
 tion 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 volume is a contribu- 
 tion to such a codification, which, it is hoped, will prove 
 useful 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 air- 
 plane 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 made 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 air- 
 plane 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 AERONAU- 
 TICS, to study carefully the needs of such courses. He 
 has had occasion, also, to conduct several classes in aero- 
 dynamics 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 flying 
 experience only as passenger and would make no attempt at 
 specific flying 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. 
 
CHAPTER I. 
 CHAPTER II. 
 CHAPTER III. 
 CHAPTER IV. 
 CHAPTER V. 
 APPENDIX I. 
 APPENDIX II. 
 APPENDIX III. 
 APPENDIX IV. 
 
 CONTENTS 
 
 Sustentation 
 
 Relations in Flight 
 
 Resistance 
 
 Lateral Stability 
 
 Directional Stability 
 
 Glossary - 
 
 Thrust Characteristics - 
 
 Power Characteristics - 
 
 Control and Other Diagrams 
 
 PAGE 
 1 
 
 28 
 
 41 
 
 55 
 
 67 
 
 77 
 
 91 
 
 103 
 
 115 
 
 IN PREPARATION 
 
 The following chapters are in preparation: Thrust; Power; Climb- 
 ing; Gliding; Altitude; Single and Multiple Planes; Stability in 
 General; Longitudinal Stability. 
 
AIRPLANE 
 CHARACTERISTICS 
 
 CHAPTER I 
 
 SUSTENTATION 
 
 The first essential for flight is a sustaining force or sus- 
 tentation. 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 ornithopter, 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 lift 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 sustenta- 
 
 1 
 
2 AIRPLANE CHARACTERISTICS 
 
 tion 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 perpendi- 
 cular 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- 
 
 PRESSURIT P 
 
 AIR STREAM 
 
 DIRECTION OP MOTION 
 
 Fig. i. Pressure on flat surface. 
 
 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 would 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 
 
SUSTENTATION 3 
 
 plane. This is on account 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-the- 
 velocity," although not a general law that holds for all sub- 
 stances 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 found, 
 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 5, 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 units 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 * or air at normal 
 density; that is, 
 
 P = 0.003 SV 2 - 
 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 
 pounds per square foot. 
 
4 AIRPLANE CHARACTERISTICS 
 
 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 units 
 by 0.0408. 
 
 Variations 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 i n English 
 
 6 
 
 Fig. 2. Square with aspect ratio i; and rectangle 
 with aspect ratio 6. 
 
 units, K = 0.075 in 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 for K as 
 follows : 
 
 Length of side .I5m. -375m. .500111. .707111. i.oom. 
 
 Value of K .066 .0716 .0746 .0772 .0789 
 
 For rectangles of equal area (0.225 m. 2 ) and with different 
 aspect ratios (the aspect ratio is the length divided by width, 
 see Fig. 2) Eiffel gives: 
 
 Aspect Ratio I 3 6 10 20 30 50 
 
 Value of K .066 .0705 .0725 .0755 .0885 .092 .097 
 KR-J-KS i. 1.07 1. 10 1.145 I -34 MO M7 
 
 The last line, K R -4-K s , is the value of K for a rectangle 
 
SUSTENTATION 5 
 
 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. Turbulent region and rarefaction back of plane. 
 
 it being borne in mind that this value is only an approxima- 
 tion 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 compres- 
 sion 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 around 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. 
 
6 AIRPLANE CHARACTERISTICS 
 
 Back of the plane and near the edge is a turbulent 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 
 effect 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 
 performance 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. 
 
SUSTENTATION 7 
 
 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 
 
 Angle fcf Incidence 
 
 Fig. 4. Vertical and horizontal components 
 of pressure 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 upon a card 
 
 held in the hand oblique 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 
 
8 AIRPLANE CHARACTERISTICS 
 
 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. y 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 climbing 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. e. t a wing that is slightly curved from front to back) than 
 from a flat plane. 
 
 LIFT LIFT LIFT LIFT 
 
 ' ' A ' i 
 
 a bed 
 
 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 D, in such common use, may well be retained as a 
 symbol for dynamic or wing resistance; likewise, KD, formerly called the 
 coefficient of drift, may be retained as the coefficient of dynamic or wing- 
 resistance. 
 
SUSTRNTATION 
 
 9 
 
 sary to have power. Obviously it is desirable to have the 
 wing-resistance small, necessitating small thrust and small 
 power, and to have the lift 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 turbulent region 
 
 back of entering edge and the downward deflection 
 
 of air after leaving the plane. 
 
 This information cannot well be derived theoretically on 
 account 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 information, however, has 
 been found experimentally. 
 
 The total pressure P, the lift L and the wing-resistance D 
 all vary directly as the area 5, of the plane or wing, and as the 
 square of the velocity V; that is, 
 
 Total pressure = P = K P SV 2 ; 
 
 Vertical component or lift = L = K^SV 2 ; 
 
 Horizontal component or wing-resistance = D = K^SV*. 
 
10 
 
 AIRPLANE CHARACTERISTICS 
 
 We are particularly interested in the two components L 
 and D ; also in the two coefficients, K^ called the coefficient 
 of lift and K& called the coefficient of wing-resistance. 
 
 These coefficients have different values for each angle of 
 incidence. Their values, furthermore, will depend upon the 
 units used. 
 
 The values of these coefficients that will give lift and wing- 
 resistance in pounds, for different angles of incidence, when 5 
 
 o 
 
 20 
 
 s to AS" 
 
 ANGLE OF INCIDENCE 
 
 Fig. 6. Coefficient of lift J L and coefficient of wing-resistance KO 
 
 for flat rectangle at different angles of incidence; aspect 
 
 ratio, 6, i. e., 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. 
 
SUSTENTATION 
 
 11 
 
 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. 1 1 . 
 
 The coefficient of wing-resistance also increases more or less 
 uniformly with incidence and reaches a value of about 0.003 
 at 90 ; but in no case is KQ zero, even at zero incidence. 
 
 e r 
 
 Is 
 
 i: 
 
 -|.40 
 
 30 
 
 20 
 
 10 
 
 5 10- IS* goo 
 
 ANGLE OF INCIDENCE 
 
 Fig. 7. Curves showing L/D ratio and D/L ratio for flat 
 rectangle; aspect ratio, 6. 
 
 Lifting efficiency 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, KL 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. 
 
12 AIRPLANE CHARACTERISTICS 
 
 it is obviously desirable to have the L/D ratio as large as 
 possible. It is seen that the L/D ratio is equal to K L -r- K-Q, 
 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 /D ratio. 
 
 In the case of a theoretical plane with a perfectly smooth 
 surface, the pressure P would be perpendicular to the surface, 
 so that D /L would be the tangent and L /D 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 perpendicular 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 D, 
 the resultant pressure being P = V L 2 + D 2 . 
 
 Center of pressure. 
 
 When the plane is perpendicular to the air-stream, i. e., 
 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 
 
SUSTENTATION 
 
 13 
 
 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 flat 
 plane the center of pressure moves forward from the center 
 
 UJ .10 
 
 ENTERING EDGE 
 
 TRAILING EDGE 
 
 15 
 
 30 45 60 
 
 ANGLE OF INCIDENCE 
 
 75 
 
 90 
 
 Fig. 8. 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, 
 
14 AIRPLANE CHARACTERISTICS 
 
 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 under- 
 stood 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 for 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 air- 
 plane 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-line flow; the wing then enters the air and leaves 
 the deflected air without disturbance, and eddies are elimin- 
 ated 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 the 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 (indi- 
 cated 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 
 
SUSTENTATION 
 
 15 
 
 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 curvature of the upper surface of a wing that is 
 most important, particularly its dip toward the entering 
 edge, often referred to as the dipping front edge. The curva- 
 ture of the lower surface is far less important; with a well 
 
 Fig. 9. Flow of air past a cambered wing; side view. 
 
 formed upper surface, a good wing can be constructed with a 
 perfectly flat lower surface. 
 
 An upward turn in the lower surface toward the entering 
 edge, corresponding to the dip in the upper surface and 
 making what is known as "Phillips entry", is not advan- 
 tageous. The wing shown in Fig. 14, which is accurately 
 drawn to scale, has a more effective entry than the wings 
 sketched in Figs. 9 and 10. 
 
 Incidence, chord, span and area of a cambered wing. 
 
 A wing section, or side view, of a cambered wing is shown 
 in Fig. 10. The chord of a cambered wing is a straight line, 
 as shown, tangent to its under surface at front and rear. 
 
16 
 
 AIRPLANE CHARACTERISTICS 
 
 The length of chord is the length of the projection ab of the 
 wing-section upon this chord. Similarly, the area of a 
 cambered wing is its area projected on a tangent plane. The 
 span or spread of a wing is the maximum distance from tip to 
 tip. The aspect ratio is the ratio of span to chord. The 
 angle of incidence of a cambered plane is the angle between 
 its chord and the relative air, as shown in the same figure. 
 
 AIR 
 
 STREAM 
 
 ANGLE COINCIDENCE 
 
 Pig. 10. Section of cambered wing, showing angle of incidence 
 
 between the chord and the air-stream, and the 
 
 components of pressure. 
 
 Wing structure. 
 
 The whole wing structure is often referred to as an aerofoil. 
 Wings are made in many ways; although no standard con- 
 struction can be shown, the one shown in Fig. loa is fairly 
 typical. Each wing is commonly built up of two spars, as 
 there shown, running from one end of the wing to the other. 
 Spars may be of I-beam section, double I-beam, box con- 
 struction, etc. Supported by these spars are the ribs, 
 extending fore and aft, each rib having the exact shape of a 
 wing-section. The top and bottom of each rib is commonly 
 made of strips of spruce, held in place and strengthened by a 
 thin web, which gives the rib an I-beam cross-section. The 
 
SUSTENTAT10N 17 
 
 web is partly cut away for lightness, as shown in the illus- 
 tration. 
 
 The camber of either surface of a wing is the greatest dis- 
 tance between the chord and that surface, and is usually 
 expressed as a fraction of the chord. The camber of the 
 bottom surface indicated in Fig. loa is about i /4o. Mean 
 camber is the mean between the top camber and the bottom 
 camber. 
 
 Components of pressure. 
 
 The pressure P is considered as having its point of applica- 
 tion at the point where it intersects the chord ab, as shown 
 
 CAMBER 
 
 BANGLE OP INCIDENCE 
 
 Fig. loa. Wing structure. 
 
 in Fig. 10. This point is called the center of wing pressure 
 and is located (unless the incidence is very small or negative, 
 see Fig. 13) a little in advance of the middle point of the 
 chord. 
 
 The pressure P is more or less perpendicular* to the chord. 
 The total pressure P is resolved into its two compon- 
 ents, lift L and wing-resistance D, which also have their point 
 of application at the center of pressure 0. The direction of P 
 
 *For a certain angle of incidence (when cotangent * = L/D), P coin- 
 cides exactly with the perpendicular to the chord. For a smaller angle 
 of incidence, P is back of the perpendicular, due to the relatively large 
 value of D compared with L. For a larger angle of incidence, P is in 
 advance of the perpendicular, due to the relatively larger value of L. 
 
18 
 
 AIRPLANE CHARACTERISTICS 
 
 can be determined by laying off L and D where these are 
 known; P = \/U + D 2 . In ordinary flight, D is so small 
 
 MAXIMUM LirT 
 
 AT BURBLE POINT !> 
 
 .003 
 
 ANGLE OF INCIDENCE 
 
 Fig. n. Lift and wing-resistance for cambered wing, U. S. A. 5. 
 Lift (in pounds) = K^SV 2 ; wing-resistance (in pounds) =K D SV 2 , 
 where 5 is in sq. ft. and V is in miles per hour. For wing-section, 
 see Fig. 14. 
 
 compared with L, as shown in Fig. n, that P and L are 
 practically equal, the difference being less than one per cent. 
 
SUSTENTATION 
 
 19 
 
 Variation of lift and wing-resistance with angle of incidence 
 of a cambered plane. 
 
 Each different wing-section will have its own characteristic 
 curves for lift and wing-resistance, but all such curves have 
 
 MAXIMUM 
 
 ANGLE OF INCIDENCE l 
 
 Fig. 12. Curves for L/D ratio and D/L, corresponding to Fig. 1 1. 
 
 the same general trend. Fig. n shows curves for the 
 coefficient of lift K L , and the coefficient of wing-resistance 
 T D , for a representative cambered wing, designated as 
 
20 
 
 AIRPLANE CHARACTERISTICS 
 
 U. S. A. 5 and shown in Fig. 14. These curves are typical 
 and will serve to illustrate certain general features that are 
 characteristic of practically all cambered wings. 
 
 The corresponding values for the L/D ratio (obtained by 
 dividing K L by K D ) are given in Fig. 12, the values for D /L 
 being shown by the dotted curve in the same figure. 
 
 The numerical values* from which these curves are plotted 
 are given in Table I. ; these values will be used in later cal- 
 culations. 
 
 TABLE I. WING U. S. A. 5 
 
 i 
 
 K L 
 
 K-D 
 
 L/D 
 
 C.P.f 
 
 -4 
 
 .000326 
 
 .OOOI5OO 
 
 1.58 
 
 
 2 
 
 .000346 
 
 .0000948 
 
 3.64 
 
 753 
 
 1 
 
 .000636 
 
 .0000830 
 
 7.67 
 
 566 
 
 
 
 .000910 
 
 .0000741 
 
 12.28 
 
 .498 
 
 1 
 
 .001145 
 
 .0000803 
 
 14.28 
 
 .444 
 
 2 
 
 001355 
 
 .0000863 
 
 1572 
 
 .415 
 
 3 
 
 .001565 
 
 .0000966 
 
 16.21 
 
 377 
 
 4 
 
 .001740 
 
 .OOOIO92 
 
 15.98 
 
 .348 
 
 5 
 
 .001950 
 
 .OOOI290 
 
 15.35 
 
 .337 
 
 8 
 
 .002470 
 
 .0001830 
 
 13.52 
 
 .315 
 
 10 
 
 .002870 
 
 .0002380 
 
 12.08 
 
 303 
 
 12 
 
 .003130 
 
 .0002890 
 
 10.84 
 
 .300 
 
 13 
 
 .003240 
 
 .0003290 
 
 9.84 
 
 .298 
 
 14 
 
 .003285 
 
 0003545 
 
 9.25 
 
 .288 
 
 15 
 
 .003235 
 
 .OOO39IO 
 
 8.28 
 
 .292 
 
 16 
 
 .003205 
 
 .OOO42IO 
 
 7-63 
 
 .298 
 
 18 
 
 .003150 
 
 .0006900 
 
 4.57 
 
 330 
 
 20 
 
 .002790 
 
 .OOO82OO 
 
 3-41 
 
 368 
 
 tDistance of the center of wing pressure from the leading edge, ex- 
 pressed as a fractional part of the chord. Shown by curve in Fig. 13. 
 
 *From tests made by Captains E. S. Gorrell and H. S. Martin, 
 abstracted by A. Kelmin and T. H. Huff; published in Aviation, Vol. II., 
 p. 256, 1917. These tests were made on a model, 18" x 3", made of 
 brass; density of standard air: 0.07608 Ibs. per cu. ft. ; wind velocity, 
 30 MPH. 
 
SUSTENTATION 21 
 
 Characteristic features of a cambered wing. 
 
 An inspection of the curves in Figs. 1 1 and 1 2 shows the 
 following : 
 
 Lift with negative incidence. A cambered plane exerts a 
 lift even at a small negative incidence. Zero lift is usually 
 obtained when the incidence is between 2 and 4 (in 
 Fig. ii at 3) but in extreme cases the incidence may be 
 decreased to 6 or 8 before zero lift is reached. Although 
 in most cases an airplane flies with a positive incidence, at 
 high velocities it may fly with zero incidence or with a small 
 negative incidence, but not within two or three degrees of 
 the point of zero lift. 
 
 In approaching the point of zero lift there is danger of 
 going too far, so that the air is allowed to strike the top sur- 
 face of the wing, causing the machine to take a nose dive. 
 
 Lift is a maximum at about 14. As the incidence is 
 increased, the lift increases rather uniformly and reaches a 
 maximum of more than 0.003 at an incidence of 14 or so, 
 according to the particular wing. The angle of incidence 
 at which K^ is a maximum is called the critical angle. Beyond 
 this maximum, which is also known as the burble point, the 
 lift decreases somewhat irregularly and again becomes zero 
 at an incidence of about 90. 
 
 Up to the burble point, *. #., for an incidence of less than 14 
 or so, the air-flow past the wing is to a certain extent smooth 
 and without eddies, as shown in Fig. 9. Beyond this point, 
 i.e., for an incidence of 14 to 90, there is a confusion of 
 eddies and a turbulance (such as was illustrated in Figs. 3 
 and 5), accompanied by a decrease in lift and an increase in 
 wing-resistance. ("Burble" means "confuse;" hence the 
 term "burble point.") 
 
22 AIRPLANE CHARACTERISTICS 
 
 Ususal range of incidence is about o to 10. It is seen that 
 the lift increases more or less uniformly with incidence, from 
 zero lift at 3 to maximum lift at + 1 4- (It is to be under- 
 stood that other wing-sections would give slightly different 
 values.) The range for practical flight must be within these 
 limits, without either limit being reached. 
 
 The lower limit of zero lift cannot be reached, inasmuch as 
 some lift is necessary for sustentation ; it may be approached 
 to a certain extent at high velocities, but too near an approach 
 may lead to a nose dive as already mentioned. 
 
 The upper limit of maximum lift is possible but in ordinary 
 flying it, too, is only approached, for as it is approached there 
 is danger of a stall due to increase of wing-resistance, leading 
 to a fall or tail slide. With the decreased velocity which 
 accompanies increased incidence, the stability of the machine 
 becomes less and may vanish entirely; as the power of 
 control depends upon velocity, the recovery of equilibrium 
 when once lost at low speed is difficult. Too great an 
 incidence is a frequent cause of accident. 
 
 Exact limits* can not well be set; but, roughly speaking, 
 the range of incidence is between o and 10, limits which are 
 never greatly exceeded in ordinary flight. 
 
 (The angle of incidence may be increased beyond this 
 limit possibly up to the point of maximum lift f as a machine 
 
 "The question of power is taken up later. There is, for each machine, 
 a certain angle of incidence well within these limits at which the 
 power required is a minimum. If the incidence is either increased or 
 decreased, there is a very great increase in the amount of power required. 
 
 tAlthough the main wing-surfaces may thus in some cases be at their 
 maximum lift, the surfaces used for lateral control, called ailerons dis- 
 cussed later, should always be well below maximum lift. Otherwise 
 they would become inoperative, for lateral control depends upon increas- 
 ing the lift on one aileron and decreasing the lift on the other; if the 
 ailerons were at maximum lift, any change would decrease the lift on 
 both and would not give the desired control. 
 
SUSTENTATION 23 
 
 reaches the "ceiling," which is the highest possible altitude 
 a particular machine can attain ; also, when slowing down to 
 minimum speed just prior to landing.) 
 
 A flat maximum in the lift curve is very desirable, being 
 less dangerous than a sharp maximum in which the lift 
 decreases rapidly after the critical angle is reached. A flat 
 maximum is more readily obtained in a biplane or triplane 
 particularly if the planes are staggered than in a monoplane 
 for the maximum points for the separate planes may not 
 coincide, so that when the separate lifts are added together 
 to get the total lift the maximum point is broadened out. 
 
 Wing-resistance is small through usual range of incidence; 
 then increases rapidly. Wing-resistance, as already mentioned, 
 is in no case zero. It is small throughout the useful range of 
 incidence, gradually increasing throughout this range as the 
 incidence increases. As the incidence is further increased,, 
 the wing-resistance increases a little more rapidly until the; 
 burble point or point of maximum lift is reached ; after which 
 the wing-resistance increases very rapidly, finally reaching 
 a value of 0.003 (more or less) at an incidence of 90. 
 
 LID ratio has a maximum value of about 16 in middle range 
 of incidence. If the wing-resistance were constant, the L/D 
 ratio would be a maximum when the lift is a maximum. On 
 account of the increase in wing-resistance with incidence, the 
 L/D ratio reaches a well defined maximum before the maxi- 
 mum lift is reached. In Fig. 1 2 , this maximum of 1 6. 2 occurs 
 at +3. This is a good value for L/D. A slightly greater 
 value, 17 or 18, is obtained by some wings, at a sacrifice 
 perhaps of some other feature, such as stability or ease of 
 construction. 
 
 Comparison with flat plane. By comparing the curves in 
 Figs, ii and 12 for a cambered wing, with those of Figs. 6 
 
24 
 
 AIRPLANE CHARACTERISTICS 
 
 and 7 for a flat plane, it is seen that the cambered plane gives 
 more lift (the maximum value being about 50 per cent, 
 more), gives less wing-resistance and a much greater L/D 
 ratio, nearly three times as great. For these reasons a 
 cambered wing is always used. 
 
 ENTERING EDGE 
 
 TRAILING EDGE 
 
 -5' !(> 'IS* 
 
 ANGLE OF INCIDENCE 
 
 20 
 
 Fig. 13. Position of center of pressure on a cambered wing 
 
 (U.S.A.5.) with aspect ratio 6, for different 
 
 angles of incidence. 
 
 Shifting of center of wing pressure with incidence. 
 
 The position of the center of pressure for the cambered 
 wing in question, U. S. A. 5, is shown in Fig. 13. All cam- 
 bered wings show a marked shifting of the center of pressure 
 toward the rear of the plane, when the incidence is small and is 
 decreasing, a bad feature for stability as discussed in a 
 later chapter. 
 
SUSTENTATION 25 
 
 In this one respect a cambered wing is inferior to a flat 
 plane, in which the center of pressure moves forward when 
 the incidence is decreasing, as shown in Fig. 8. 
 
 The shifting of the center of pressure shown in Fig. 13 is 
 much less than is found in the case of many wings, the section 
 of wing here used being in this respect satisfactory. 
 
 Wing-section. 
 
 There is no one type of wing that is best. The particular 
 wing, to which all the curves here given refer, is shown in 
 Fig. 14 and is fairly representative. But it will be under- 
 stood that in different machines different wings may best be 
 
 Fig. 14. Section of wing, U.S.A. 5. 
 
 used, according to the particular features to be emphasized; 
 high speed in one, large load-carrying capacity in another; 
 stability in one, quickness in maneuvering in another, and 
 so forth. 
 
 The characteristics of any particular wing-section are 
 shown by means of curves, such as those shown in Figs, n, 
 12 and 13. The usefulness of these curves in determining 
 the problems of flight will be brought out in the following 
 chapters. 
 
 Comments on wing sections. 
 
 A few comments on wing sections may here be made, 
 although the reader may find it well to postpone their perusal 
 until he has read some of the subsequent chapters describing 
 various relations and characteristics of an airplane in flight. 
 
26 AIRPLANE CHARACTERISTICS 
 
 Mechanical as well as aerodynamic considerations have to be 
 kept in mind by the designer ; there must be room for spars 
 and ribs of adequate strength. 
 
 For climbing and for heavy lift, a wing with deep camber 
 (particularly on the upper surface) and large value of K^ 
 should be used. For this purpose a deeply cambered wing is 
 flown at low speed, and at a large angle of incidence as shown 
 in Fig. 15. Such a wing, however, is utterly unsuited for 
 flying at high speed and small incidence, as shown in Fig. 16, 
 on account of its great resistance at small angles of incidence. 
 
 For speed, the wing should be flatter with only a little 
 camber, with less lift and with the least possible wing- 
 resistance at small incidence and high velocity. It is neces- 
 sary to sacrifice either speed or lift. A speed wing is sketched 
 in Fig. 17. 
 
 Again, both speed and lift may be sacrificed for stability. 
 As has been shown, the center of pressure on a cambered 
 wing, convexed upward, shifts with change of incidence (when 
 the angle of incidence is small) in the wrong direction for 
 stability. If a cambered wing were concave downward a 
 very bad wing for lift this shifting of the center of pressure 
 would be in the right direction for stability. The two effects 
 may be combined, in varying proportions, by giving a wing 
 a double curvature, as shown in Fig. 18. In this case, when 
 the machine starts to dive the air strikes the reversed curve 
 near the rear of the wing and restores equilibrium ; but this 
 means less lift and more resistance. 
 
 The characteristics of an aerofoil, although in a general 
 way shown by its section, are best shown by curves for its 
 performance, as in Figs, n, 12 and 13. 
 
 A high maximum to the K^ curve is of no advantage in a 
 high speed machine nor in ordinary flight; it gives, however, 
 
SUSTENTATION 
 
 27 
 
 the ability to climb to high altitudes and gives a low landing 
 speed, as brought out in the next chapter. 
 
 The L ID curve should show a good value, not necessarily 
 a maximum, at about the incidence for which the machine is 
 to be flown; thus, in a high speed machine, it is desirable to 
 have a large value for L /D at a very small incidence. This is 
 only another way of saying that wing-resistance D should be 
 small. 
 
 Fig. 15. Wing with high camber, suitable 
 for big lift and slow speed, when blown 
 at large angles of incidence as shown. 
 
 Fig. 1 6. Same wing at small incidence, 
 entirely unsuitable for high speed on 
 account of large wing-resistance due to 
 its camber. 
 
 Fig. 17. Flat, stream-lined wing with 
 little camber and small lift ; suitable for 
 high speed on account of its very small 
 wing-resistance . 
 
 Fig. 1 8. Wing with reversed curvature 
 toward trailing edge for increased sta- 
 bility. This is paid for by an increase in 
 wing-resistance and a decrease in lift. 
 
 In a high speed machine, which is to be flown at small 
 incidence and at small K^, it is desirable to have a curve for 
 KL that is not too steep as it approached zero lift; thus, it is 
 desirable to obtain a certain lift, when the plane, let us say, is 
 3 or 4 rather than i or 2 from the incidence of zero lift. 
 There is then less danger of a nose dive, when the machine 
 dips a little as it oscillates about its normal direction of flight. 
 
CHAPTER II 
 
 RELATIONS IN FLIGHT 
 
 Some interesting relations in regard to flight can be drawn 
 from the expressions derived in the preceding pages for the 
 lift and wing-resistance of a cambered plane. In this chapter 
 will be considered the significance of the lift equation, and 
 certain relations between velocity and incidence that may be 
 derived from it; wing-resistance will be considered in the 
 following chapter. 
 
 In horizontal flight, weight = lift = K L SV 2 . 
 
 We have seen that the lift that supports an airplane is 
 equal to the product of the area of wing 5, the square of the 
 
 LIFT 
 
 WEIGHT 
 
 Fig. 19. Lift- weight in horizontal flight. 
 
 velocity V, and a coefficient of lift K L that varies with the 
 angle of incidence : 
 
 Lift = L = K L SV 2 . 
 
 For sustentation in horizontal flight, see Fig. 19, the lift must 
 be just equal to the weight of the machine, including its load ; 
 we, accordingly, may write 
 
 Weight = W = K L SV 2 . 
 28 
 
RELATIONS IN FLIGHT 29 
 
 Weight acts downward through the center of gravity or 
 C. G. ; lift acts upward through the center of lift or C. L. 
 
 These two centers are never far apart, although they rarely 
 coincide exactly. When the center of gravity is in front of 
 the center of lift, there is a moment or couple tending to make 
 the machine nose down ; when the center of gravity is back 
 of the center of lift, there is a couple tending to make the 
 machine nose up. In neither case does the couple have any 
 affect upon the value of weight and lift (which are equal) , 
 although it does affect longitudinal stability. 
 
 Velocity equals square root of loading divided by square 
 root of K L . 
 
 The preceding equation, when transposed, gives the 
 important formula for velocity, 
 
 v = ^ik 
 
 This formula, although simple, is quite complete and will 
 bear careful study, for it leads to a number of interesting 
 conclusions, the appreciation of which is essential to a proper 
 understanding of flight. 
 
 The ratio W /S is the weight per unit area of wing and is 
 called the loading. It is the loading, rather than weight or 
 area, that effects the value of V. The formula shows that 
 the velocity of an airplane depends solely upon the loading 
 and upon K L . 
 
 The only possible way for changing the speed of a machine, 
 or for getting different speeds in different machines, is by 
 changing the loading or by changing the value of K L . In 
 practice there are of course limits to both of these changes. 
 For a machine in flight, in which the loading can not be 
 
30 
 
 AIRPLANE CHARACTERISTICS 
 
 changed, the only way for changing the speed is by changing 
 the value of K^. 
 
 The loading W /S is commonly about 6 Ibs. per sq. ft., 
 being less in slow machines and being more (8 and even 10) 
 in fast machines. The usual limits for K L are about 0.0008 
 and 0.003 2. 
 
 This gives us at once the speed variation, shown in Fig. 20, 
 for any machine irrespective of wing-section or other features 
 of design except loading. Each curve in Fig. 20 is for a 
 
 K, 
 
 ..0016 .0020 
 
 COEFFICIENT OS 1 LIJT 
 
 Fig. 20. Variation of velocity with coefficient of lift for any airplane, 
 when loading is 4, 6 (heavy curve), 8 and 10. 
 
 different loading. The heavy curve shows the change of 
 speed, with K L , for a machine with loading W /S = 6, this 
 being the plot of the equation V = \/ 6 -r- K L . The light 
 curves are for loadings 4, 8, and 10, an increase in loading 
 raising the curve and thus indicating a greater velocity. 
 
 It is seen that velocity increases as K L decreases; if K L 
 were zero, V would have to be infinite to create a lift equal 
 to the weight, as is necessary for sustentation. 
 
 Speed range. A machine that has a maximum speed of 
 100 miles per hour and a minimum speed of 45 miles per 
 hour is said to have a speed range of 55 per cent. The range 
 in speed depends upon the range in the value of K L . 
 
RELATIONS IN FLIGHT 31 
 
 Thus it is seen that, if we take the limits of K L as 
 0.0008 and 0.0032, the speed range for any machine is fifty 
 per cent. The curves in Fig. 20 are drawn solid between these 
 limits. Commonly the speed range is somewhat less than 
 fifty per cent., but in some cases is a little more. (A mini- 
 mum value of K L a trifle less than 0.0008 may be attained in 
 some instances; but a greater value, 0.0009 or more, is per- 
 haps a more usual minimum.) 
 
 By way of illustration, with limits 0.0008 and 0.0032 for 
 K L , a machine with loading W /S = 10 would have speed 
 limits as follows, the speed range being 50 per cent. ; 
 
 Maximum speed =\/ 10 * 0.0008 = 112 MPH. 
 Minimum speed =-\A -=- 0.0032 = 56 MPH. 
 
 As a further illustration, with limits 0.00074 and 0.0034 
 for K L , the speed range would be about 54 per cent. ; thus, 
 
 Maximum speed =\/io -r- 0.00074 = 116 MPH. 
 Minimum speed = \/io -f- 0.0034 = 54 MPH. 
 
 The speed range is the difference between maximum and 
 minimum speed, divided by the maximum speed; thus, in this 
 case, speed range = (116 54) -s- 116 = 0.54 or 54 per cent. 
 
 A greater speed can be attained only by increasing the 
 loading or by decreasing K L . For example, if a speed of 200 
 MPH. is to be attained: W /S must equal 29.6, if K^ 
 0.00074; W IS must equal 20, if K^ = 0.0005; W /S must 
 equal 10, if K L 0.00025; etc. 
 
 The advantage of a large speed range* not only a high 
 
 *Some early machines had a very small speed range, let us say from a 
 minimum of 35 to maximum of 50 miles per hour, giving a speed range 
 of 1 5 miles per hour. A gust from behind of more than 1 5 miles per hour 
 would reduce the relative air speed below the requisite 35 miles per hour 
 necessary for sustentation; so that the machine had no support. This 
 was one cause for the so-called holes in the air. 
 
32 
 
 AIRPLANE CHARACTERISTICS 
 
 maximum speed for flying but also a low minimum speed for 
 landing is obvious. To get a sufficiently low landing speed 
 is one of the problems of the designer. 
 
 .003 
 
 .0025 
 
 H '.002 
 
 & 
 
 I-J 
 
 s- 
 
 0015 
 
 g 
 
 8 . 
 
 .0005 
 
 MINIMUM VELOCITY 
 
 MAXIMUM LIFT 
 
 4 2. 7 5 MILES PER 
 HOUR 
 
 43.2 
 MPH. 
 
 8\.2 MPH. 
 97.1 MPH. 
 137.1 MPH. 
 
 ANGLE OF INCIDENCE 
 
 Fig. 21. Variation of coefficient of lift with incidence for a particular 
 
 wing-section; aspect ratio 6. Velocities are marked for several 
 
 points, assuming a loading of 6 Ibs. per sq. ft. 
 
 A given machine has a definite velocity for each angle of 
 incidence, and this is controlled by the elevator. 
 
 Since K L has a different value for each angle of incidence, 
 it is seen that the velocity of a machine varies with incidence 
 
RELATIONS IN FLIGHT 33 
 
 and, for a given loading, velocity depends only* upon incidence. 
 The angle of incidence is controlled by the pilot by means of 
 the elevator. 
 
 The variation of K^ with incidence, for a particular wing- 
 section, is shown in Fig. 21, reproduced from Fig. n of the 
 preceding chapter. The numerical values from which the 
 curve is plotted are given in Table I., page 20. 
 
 For any given loading, the values of V corresponding to any 
 point on this curve is readily determined. For example, 
 suppose W JS = 6. For an incidence of 4, from the curve 
 or table K^ = 0.00174; hence, V =\/6 -5- 0.00174 = 58.6 
 miles per hour. The values of V, determined in this way, 
 are marked for several points on the curve. It is seen that 
 for each incidence, the velocity has one definite value, f 
 
 *The density of the air is here assumed to be uniform; see a later 
 chapter on change of density and KL with altitude. 
 
 t Modification in complete machine. The lift curve for a wing is modi- 
 fied in a complete machine by whatever lift there is (either positive or 
 negative) on other parts of the machine body, tail and other surfaces 
 and, in a biplane or triplane, by an interference between the planes that 
 reduces the lift. This reduction is less when the gap between the planes 
 is large and when they are given considerable stagger than when the 
 gap is small and there is no stagger. Lift likewise increases with 
 aspect ratio, the ratio of wing span to chord. For the curves here 
 shown the aspect ratio is assumed to be 6, the usual standard value. 
 
 For simplicity a detailed consideration is not given here of these 
 features, for they in no way affect the general character of the conclu- 
 sions, although they do affect the precise numerical values. Proper 
 corrections have to be applied when exact numerical values are to be 
 obtained. 
 
 The net result of these corrections usually shifts each point on the 
 lift curve a little to the right, say a degree or so, so that a lift K^ = 
 0.00174 an d velocity 58.6 MPH. shown by the curve at 4 would, for 
 a complete machine, be at say 5, and so on for other points, the shift 
 being slightly different for different points. So far as lift and velocity 
 are concerned, the effect of these corrections is merely to change the 
 angle of incidence at which a particular value of lift and of velocity 
 occur. Put in a different way, at small angles (perhaps through the 
 working range) the lift curve is somewhat lowered and at large angles is 
 
34 AIRPLANE CHARACTERISTICS 
 
 Minimum velocity occurs at the point of maximum K L , 
 namely at the critical angle of incidence or burble point. 
 
 It is seen that the minimum velocity occurs when the value 
 of KL is a maximum, namely at the critical angle of incidence 
 or burble point. For any other incidence, KL is less and V is 
 correspondingly greater; in other words, when the angle of 
 incidence is either greater or less than the critical angle, a 
 greater velocity is required in order to produce the lift equal to 
 the weight, the condition necessary for horizontal flight. 
 
 Variation of velocity with incidence. 
 
 The variation of velocity with incidence is well shown by 
 the curves in Fig. 22, which correspond to Fig. 21 and refer, 
 therefore, to a particular wing-section, not to any wing- 
 section as was the case in Fig. 20. Curves for the variation 
 of velocity with incidence for other wing-sections would have 
 much the same general form. 
 
 The heavy curve in Fig. 22 shows the velocity for a loading 
 W IS = 6; the light curves, for loadings of 4 and 8, the 
 greater loading always corresponding to the higher velocity. 
 
 It is seen that there is a definite minimum velocity which 
 occurs at the critical angle of incidence in this case 14 
 when KL is a maximum, as was also shown in Fig. 21. If a 
 machine loses velocity below this minimum, it cannot sustain 
 itself and is said to stall, the critical angle of incidence being 
 also called the stalling angle. 
 
 somewhat raised, for at large angles the lift of the airplane body 
 becomes effective. 
 
 The lift curve for a complete machine may be determined by applying 
 proper corrections to the lift curve for the wing (which is of course the 
 chief factor) when data for these corrections is available; but it is best 
 determined by a wind-tunnel test with a complete model. Some of these 
 corrections are to be considered later in the chapter on Single and 
 Multiple Planes. 
 
RELATIONS IN FLIGHT 
 
 35 
 
 The velocity increases on each side of this minimum, with 
 change of incidence, so as to furnish the necessary sustenta- 
 
 140 
 
 100 
 80 
 60 
 40 
 20 
 10 
 
 85 
 
 *t 
 
 h 
 
 -5 e 5 i(J 15 20 
 
 ANGLE OF INCIDENCE 
 
 Fig. 22. Variation of velocity with angle of incidence for particular 
 
 wing-section, when loading is 4, 6 (heavy curve) and 8. These 
 
 curves correspond to the curve in Fig. 21. 
 
 tion, and would have to be infinite were K^ equal to zero, 
 namely if the incidence were decreased (in this case) to 3 
 or were increased to about 90; but, as already pointed out, 
 there are limits to the working range of incidence and velocity. 
 
 Usual working range. 
 
 Between the limits of o and 10 (corresponding to KI, = 
 0.00091 and K L = 0.00287) the curves are drawn as solid 
 lines; these limits would become -^3 and i2>, if the 
 limits of K L were taken as 0.0008 and 0.0032 as before. (It 
 is understood that precise limits cannot be set.) This shows 
 the usual working range : two or three degrees less incidence 
 would cause a dive; two or three degrees more incidence 
 
36 AIRPLANE CHARACTERISTICS 
 
 would cause a stall. An inclinometer is commonly used to 
 indicate the degrees angle of incidence (usually by a bubble) 
 and the advantage of its use is obvious. A stall indicator is 
 less frequently used to display a danger signal when the 
 stalling angle is approached. 
 
 Possibility of changeable wing-area or camber. 
 
 For mechanical reasons, wings are made with fixed area 
 and camber. A practical wing with either of these adjusta- 
 ble would do much to advance the art of flying, for it would 
 make possible a great increase in speed range, both by increas- 
 ing the maximum and decreasing the minimum speed. These 
 improvements have long been considered, the adjustable 
 camber now seeming the more promising of the two. 
 
 With adjustable wing-area, the pilot would use large area 
 for low speed and would use small area for high speed. 
 
 With adjustable camber, the pilot would use for low speed 
 such camber as gave maximum lift. For high speed he 
 would flatten out the wing and so get less lift without a 
 dangerous reduction in incidence. This flattening of the 
 wing would also bring about a reduction of wing-resistance, 
 a highly important advantage at high speeds. 
 
 For the present, however, it is necessary to be content with 
 wings of fixed area and camber. 
 
 Power has no direct effect upon velocity. 
 
 It has been shown that the velocity of a machine is depend- 
 ent only upon incidence (ignoring the possibility of a change 
 in wing-area or camber and the effect of altitude) , incidence 
 being controlled by the position of the elevator. It may well 
 be asked: What about power? What effect upon velocity 
 has the amount of power supplied by the engine? The 
 
RELATIONS IN FLIGHT 37 
 
 answer is : The power supplied by the engine has no direct 
 effect upon velocity, whatsoever; if the elevator is kept in 
 one position without change, the same angle of incidence is 
 maintained, and hence the same velocity, irrespective of the 
 power supplied by the engine. The effect of power is 
 shown in the following paragraphs. 
 
 Let us suppose, for example, a machine is flying with a 
 certain angle of incidence say, 4 determined by the 
 position of the elevator. The velocity of flight is then 
 definite, 58.6 MPH., if we use the data in Fig. 21. At a 
 definite velocity and incidence, the resistance of the airplane 
 (structure as well as wings) is definite in a certain instance 
 263 Ibs. to overcome which there must be an exactly equal 
 thrust (263 Ibs.) requiring the supply of a certain amount of 
 power (in this instance 42 horse power). But this definite 
 amount of power that is required may or may not be supplied 
 by the engine, for this depends on the throttle. Let us see 
 what happens when the engine does not supply this amount 
 of power. 
 
 Amount of power supplied by engine determines whether 
 machine climbs, glides or flies horizontally; but, if inci- 
 dence is not changed, does not affect velocity. 
 
 If the engine supplies just the right amount of power 
 required to overcome the total air resistance, the machine 
 flies horizontally, as in Fig. 23. If it supplies more power, 
 the machine takes an oblique path upward, as in Fig. 24, the 
 "surplus power" being used against gravity. If the engine 
 supplies less power than is necessary to overcome resistance, 
 the machine takes an oblique path downward, as in Fig. 25, 
 the necessary additional power being in this case supplied by 
 gravity. 
 
38 AIRPLANE CHARACTERISTICS 
 
 Thus, if the power required to overcome the total air 
 resistance is 42 H.P., there are the three cases: when the 
 engine delivers* 42 H.P., flight is horizontal; when it delivers 
 
 AIR : 
 
 5TREAM- 
 
 G FLIGHT PATH 
 
 Fig. 23. Horizontal flight. 
 
 more power, 47 H.P. for example, the machine climbs, auto- 
 matically taking a flight path inclined upward at such an 
 angle that the surplus 5 H.P. is used in overcoming gravity; 
 when the engine delivers 37 H.P., the machine takes an 
 oblique path downward at such angle that 5 H.P. is derived 
 from gravity. The angle of incidence the angle between 
 the chord and the relative air or flight path being the same 
 in the three cases, the velocity is the same irrespective of 
 whether the flight path is horizontal or oblique. 
 
 FLIGHT PATH 
 
 Fig. 24. Oblique flight, upward. The same incidence 
 and speed as in Fig. 23. 
 
 It is seen that if the power is increased or decreased, by 
 adjustment of the throttle, the inclination of the flight-path is 
 changed, but (provided the elevator is not changed) the angle 
 of incidence and velocity remain unchanged. Indeed, if the 
 power is entirely cut off, the machine takes an oblique 
 
 The power available for producing thrust, delivered through 
 the propeller, is here referred to. The question of propeller efficiency 
 is not here taken into consideration. 
 
RELATIONS IN FLIGHT 39 
 
 flight-path downward at a definite gliding angle, while the 
 velocity still remains unchanged. These relations will be 
 more fully discussed in subsequent chapters on Climbing and 
 Gliding. 
 
 When horizontal flight is to be maintained, velocity is 
 changed by a simultaneous adjustment of throttle and 
 elevator. 
 
 From the foregoing, it is seen that the one way to change 
 velocity is to change the angle of incidence by means of the 
 elevator ; furthermore, if horizontal flight is to be maintained, 
 the throttle must be adjusted at the same time so that the 
 amount of power required for horizontal flight is supplied by 
 the engine, otherwise the flight path will be oblique. The 
 pilot does not speed up and go faster merely by opening and 
 closing the throttle, as in an automobile. As a matter of 
 
 Fig. 25. Oblique flight, downward. The same incidence 
 and speed as in Figs. 23 and 24. 
 
 fact an airplane is, in normal flight, practically a constant 
 speed machine, flying usually at the one velocity correspond- 
 ing to a certain best angle of incidence for which the machine 
 is designed. 
 
 It takes more power to fly at low speed or at high speed 
 than at an intermediate speed. The amount of power 
 required to maintain horizontal flight, as shown in a later 
 chapter, increases very rapidly when the velocity is either 
 increased or decreased beyond a rather narrow range. Power 
 
40 AIRPLANE CHARACTERISTICS 
 
 as well as stability is, accordingly, a factor in many cases a 
 determining factor in deciding the range of velocity and the 
 limiting values for the angle of incidence and for K L . 
 
 To find out how much power is necessary for horizontal 
 flight, we must first know the thrust and this is determined 
 by the total resistance that is to be overcome. This will, 
 accordingly, be next investigated. 
 
CHAPTER III 
 
 RESISTANCE 
 
 Resistance is the force that impedes the progress of an 
 airplane through the air, this force being in the same direction 
 as the air-stream, and opposite to the direction of flight, as 
 
 THRUST 
 
 RESISTANCE 
 
 Fig. 26. Resistance is in direction of the air-stream 
 and is overcome by thrust. 
 
 shown in Fig. 26. Resistance is overcome by thrust from the 
 propeller, a force in the direction of flight, or nearly* so. 
 
 In uniform flight a machine assumes such a velocity and 
 attitude that resistance and thrust are exactly equal. 
 
 Center of resistance. 
 
 Thrust is a force forward through the propeller shaft, 
 applied at the center of thrust or C. T. The total resistance 
 of an airplane, the resistance of wings and structure all 
 included, may be considered as a single force backward in 
 the direction of the air-stream applied at the center of resist- 
 ance or C. R., which may coincide with the center of thrust as 
 in Fig. 26, or may be a little above or below it. When the 
 
 *When thrust is inclined with reference to the flight path, resistance is 
 overcome by the component of thrust in the direction of the flight path. 
 The small vertical component, when upward, supports part of the 
 weight so that correspondingly less lift is required of the wing for 
 sustentation; when downward, correspondingly more lift is required. 
 
 41 
 
42 AIRPLANE CHARACTERISTICS 
 
 center of resistance is above the center of thrust, there is a 
 tendency for the machine to nose up when power is on, and 
 when the center of resistance is below the center of thrust 
 there is a tendency for it to nose down. This affects longi- 
 tudinal stability but in no way affects the value of resistance 
 or thrust. 
 
 Wing-resistance and parasite resistance. 
 
 Airplane resistance falls under two heads: wing-resis- 
 tance, due to the wings; and parasite resistance, due to all 
 other parts of the airplane structure. (Parasite resistance is 
 sometimes called "structural resistance" or "head resist- 
 ance.") The sum of the two is the total resistance or drag; 
 thus, 
 
 Total Resist. = Wing Resistance + Parasite Resistance. 
 In English units, resistance is expressed in pounds. 
 
 Although expressed by very similar fundamental formulas, 
 each varying as the square of the velocity, wing-resistance and 
 parasite resistance have quite different characteristics: 
 wing-resistance depends upon incidence, the variation of the 
 coefficient of wing-resistance K^ with incidence having been 
 shown in Fig. n, page 18, of the first chapter; parasite 
 resistance, on the other hand, is practically independent of 
 incidence, except so far as incidence affects velocity. 
 
 Whereas parasite resistance always increases as velocity is 
 increased, wing-resistance decreases as velocity is increased 
 until a certain velocity is reached, after which it increases, as 
 brought out in the following discussion. 
 
 On account of their different characteristics, wing-resistance 
 and parasite resistance are considered separately. 
 
RESISTANCE 43 
 
 WING RESISTANCE 
 Fundamental relation. 
 
 Wing-resistance is equal to KnSV 2 , as shown in the first 
 Chapter, and is fundamentally determined by this formula. 
 A hasty inspection of the formula, however, might lead to 
 the erroneous conclusion that wing-resistance always increases 
 with velocity. This indeed would be true, if KD were con- 
 stant; but in fact, as mentioned above, the changes in the 
 value of KD with incidence actually cause wing-resistance 
 to decrease through a certain range of velocities, and then to 
 increase at high velocities. This is best shown by some 
 practical calculations and the plotting of curves. 
 
 Practical calculation. 
 
 Wing-resistance can be calculated directly from the formula 
 KvSV". The calculation, however, can be made more readily 
 from the L JD ratio for the particular wing in question. By 
 definition 
 
 L ID ratio = Lift -r- Wing-resistance. 
 Since Lift = Weight, in horizontal flight, we may write 
 Wing-resistance* = Weight -j- L /D ratio. 
 
 To get the wing resistance, it is merely necessary to divide 
 the known weight by the L/D ratio, the value of this ratio 
 being taken from a table or curve for the particular wing 
 section. 
 
 * Variation of wing-resistance with incidence. The formula given above 
 may also be written: 
 
 Wing-resistance = Weight x D/L ratio. 
 
 Wing-resistance is, therefore, proportional to D/L. A curve giving 
 the values for wing-resistance for different angles of incidence would 
 be similar to the D/L curve, Fig. 12, page 19, the only difference between 
 the two curves being the scale. 
 
44 AIRPLANE CHARACTERISTICS 
 
 Example. For example, the weight of a loaded machine is 
 2000 Ibs. The values for the L /D ratio for the wing used are 
 given by the Table I., page 20, or by the corresponding curve, 
 Fig. 12, page 19. Required to find the wing-resistance and 
 velocity for an incidence of 4. From the table, L/D = 16 
 (approximately); hence 
 
 Wing-resistance = 2000 -f- 16 = 125 Ibs. 
 
 It is seen that every 16 Ibs. of weight adds one pound to 
 the wing-resistance and will require one pound more thrust, 
 and a corresponding increase in power, to overcome it. 
 
 To determine the velocity corresponding to the wing- 
 resistance in the above example, it is necessary to know the 
 loading, for velocity depends upon loading. Thus, if the 
 loading is W /S = 6 Ibs. per sq. ft., using the formula of the 
 preceding chapter, we have 
 
 \w~ . - 
 
 = x / = \/6 -r- 0.00174 = 58.6 MPH. 
 V3*vL 
 
 Velocity 
 
 It is thus seen that when this particular wing-section is 
 used in a machine weighing 2000 Ibs., with loading 6 Ibs. per 
 sq. ft., the wing-resistance is 125 Ibs. at a velocity of 58.6 
 MPH. 
 
 Variation of wing-resistance with velocity. 
 
 The variation of wing-resistance with velocity is well shown 
 by the curves in Figs. 27, 28, and 29, the points being 
 calculated, in the manner just described, for different condi- 
 tions of weight and loading. 
 
 It is seen that with increase of velocity (decrease of inci- 
 dence) wing-resistance always decreases until a certain 
 velocity is reached, after which it again increases. The 
 minimum velocity for any wing-section is obtained at the 
 critical angle of incidence; a greater angle of incidence is 
 
RESISTANCE 
 
 45 
 
 beyond the range of practical flight. The critical angle for 
 the particular wing-section here used is 14, but the curves 
 have been calculated beyond 14 in some instances and are 
 shown by dotted lines. 
 
 350 
 
 2,0 
 
 100 
 100 
 
 OS 
 O 
 
 14- 
 
 20 ^0 60 8Q iOO 
 
 VELOCITY - - MILES PER HOUR 
 
 Fig. 27. Variation of wing-resistance with velocity. 
 The three curves show effect of changing weight 
 (W = 1000, 2000 and 3000 Ibs.) when loading is kept 
 constant (W/S = 6). 
 
 As incidence is decreased to o, -i, -2, etc., wing-resis- 
 tance and velocity both rapidly increase and both would 
 become infinite at the incidence that gives zero lift, in this 
 case at -3. 
 
 Effect of changing weight or loading. 
 
 In calculating the curves here shown, it was necessary to 
 know the weight and loading, inasmuch as wing-resistance 
 = weight -T- L/D, and velocity =\/\oa.dmg -5- K L . Dif- 
 ferent curves for the variation of wing-resistance with 
 velocity are accordingly obtained by changing either weight 
 or loading, or both, and in no other way, it being understood 
 that we are dealing with a particular wing-section flying in 
 
46 
 
 AIRPLANE CHARACTERISTICS 
 
 350_ 
 I 
 j 
 
 |3CQ 
 
 > 
 
 "250 
 
 jurf. 
 100 
 
 g 
 
 ^ 
 
 so 40 do BO ioa 
 
 VELOCITY - - MILES PER HOUR 
 
 Fig. 28. Variation of wing-resistance with velocity. The 
 three curves show effect of changing loading ( W/S = 4, 6 
 and 8) when weight is kept constant (W = 2000 Ibs.). 
 
 350 
 
 300 
 
 j 2ftO 
 I 
 
 S*oo 
 &5 XSO 
 
 gioo 
 
 O 50 
 
 666 
 
 ^..--- VV=I33J 
 
 20 40 60 80 100 
 
 VELOCITY - - MILES PER HOUR 
 
 Fig. 29. Variation of wing-resistance with velocity. The 
 three curves show effect of changing weight (W = 1333. 
 2000 and 2666 Ibs.) and loading (W/S = 4,6 and 8) in 
 proportion, wing-area being constant. 
 
RESISTANCE 47 
 
 air of constant density. It will be found that all the curves 
 are similar in form and differ only in scale. 
 There are three cases: 
 
 (1) when weight is changed and loading is kept constant; 
 
 (2) when loading is changed and weight is kept constant; 
 
 (3) when weight and loadmg are both changed. 
 
 (1) Effect of changing weight when loading is kept constant. 
 
 In this case machines with greater weight also have greater 
 wing area, the loading remaining constant. Wing-resistance 
 for different machines is then directly proportional to weight. 
 This is shown by the curves in Fig. 2 7 for three machines of 
 different weight. Any point on these curves, corresponding 
 to a particular incidence and velocity, is merely moved up for 
 a heavier, or down for a lighter, weight machine ; the heavier 
 the machine, the greater is the wing-resistance. 
 
 (2) Effect of changing loading when weight is kept constant. 
 
 In this case weight is constant and wing-area is changed so 
 as to give different loadings. Changing the loading, for a 
 certain weight, changes the velocity corresponding to a cer- 
 tain incidence, but does not change the amount of wing- 
 resistance, for that incidence. Hence, as shown by the 
 curves in Fig. 28, a change of loading shifts to right or to left 
 the point corresponding to a particular angle of incidence, the 
 velocity for that incidence being proportional to the square 
 root of the loading. 
 
 The loading which gives the least wing-resistance is differ- 
 ent at different velocities. Thus, for the case shown by the 
 three curves in Fig. 28 with loading 4, 6 and 8, up to about 55 
 miles per hour the wing-resistance is least for a loading of 4 ; 
 from 55 to 65 miles per hour, for a loading of 6 ; and above 65 
 miles per hour, for a loading of 8. 
 
48 AIRPLANE CHARACTERISTICS 
 
 (3) Effect of changing both weight and loading, wing-area 
 being constant. 
 
 This is a combination of the two preceding cases. A point 
 on any of the curves is moved up or down in proportion to 
 weight, and to right or left in proportion to the square root 
 of the loading. 
 
 The three curves in Fig. 29 show the effect of changing 
 weight and loading in proportion, wing-area remaining con- 
 stant; this might be brought about by taking up the same 
 machine at different times with different loads. It is to be 
 noted that, at the same angle of incidence, greater velocity 
 is required to sustain the greater weight; or, at the same 
 velocity, a greater angle of incidence is required. 
 
 Variation of wing-section. 
 
 For a given wing-section there are the three possible ways 
 just described for changing wing-resistance, by changing 
 the weight, the loading or both. If the wing-section is varied, 
 the number of possible variations is infinite. A wing that has 
 high camber in order to secure great lift, also has large resis- 
 tance, particularly, at small angles of incidence; while, as 
 already mentioned, a flatter wing with less camber and less 
 lift is better adapted for high speed, having small resistance. 
 But there are many intermediate forms and variations that 
 make an interesting field for study. 
 
 PARASITE RESISTANCE 
 Meaning and importance of parasite resistance. 
 
 The wings of an airplane are its first essential, for they 
 create the lift, but in creating lift they at the same time cause 
 a wing-resistance. Wing-resistance, therefore, although not 
 a cause of lift, is seen to be a necessary concomitant being 
 
RESISTANCE 
 
 49 
 
 the price paid for the lift. In a preceding example, it was 
 shown that, in a given case, every sixteen pounds of lift must 
 be paid for by one pound of wing-resistance. 
 
 Unfortunately this is not all. In addition to wings an 
 airplane must have other parts body, landing gear, struts, 
 wires, etc., all of which have a resistance; but unlike the 
 wings, these parts do not contribute to the lift. The 
 resistance of these parts is, therefore, with some appropri- 
 ateness called parasite resistance. 
 
 One of the important problems in design is to make this 
 parasite resistance as low as possible, for while small at low 
 
 Fig. 30. Air-flow past a cylindrical strut ; air eddies and 
 low pressure back of strut cause high resistance. 
 
 velocities parasite resistance is very great at high velocities, 
 being perhaps fifty per cent, more than wing-resistance at 
 ordinary maximum flying velocities. In airplane flight, while 
 about two-fifths of the power delivered through the propeller 
 by the engine is used in pushing the wings through the air, 
 three-fifths of the power, approximately, is used up in para- 
 site resistance. It is seen that parasite resistance is the 
 biggest obstacle to high-speed flight. 
 
 Streamline flow. 
 
 Fig. 30 shows the flow of air past a cylindrical strut or wire. 
 Behind the strut there is a turbulent space and a partial 
 vacuum, or negative pressure n, that tends to suck the strut 
 
50 AIRPLANE CHARACTERISTICS 
 
 along in the direction of the air-stream. A large part of the 
 resistance of the strut to motion through the air is thus due 
 to^'this region of low pressure behind it. 
 
 In Fig. 31, the space behind the cylindrical strut A is 
 partly filled by a piece B, so as to reduce the region of tur- 
 
 Fig. 31. Cylindrical strut A, backed up by a filler B of 
 a form that reduces, but does not entirely eliminate, 
 the air eddies and low pressure back of strut. Resist- 
 ance is thus reduced. 
 
 bulence and low pressure. The resistance to motion through 
 the air is thus greatly decreased. Struts are sometimes made 
 in this manner, a piece A for strength being backed up by a 
 piece B, of light material to save weight, and resistance may 
 be reduced in this way. 
 
 Although the shape shown in Fig. 3 1 is an improvement on 
 the cylindrical strut, it is by no means the best, for it does not 
 
 Fig. 32. Strut with air eddies and low pressure back of 
 
 strut further reduced, by approaching 
 
 a streamline form. 
 
 conform entirely to the streamline flow ; there is still a turbu- 
 lent region n, although this is much reduced. The more 
 
RESISTANCE 51 
 
 nearly a body conforms to streamline flow the less is its 
 resistance, the turbulence and suction back of the body being 
 then reduced to a minimum. Fig. 32 shows a strut more 
 nearly conforming to streamline flow. 
 
 Only a little is gained by tapering the front side of a cylinder 
 or strut. Note the blunt breast and tapering tail of a bird, 
 and the shape of a fast swimming fish that can dart through 
 the water with scarcely a ripple. 
 
 For low resistance, wheels and body should be enclosed; 
 these, as well as every strut and wire, should be streamlined 
 so far as they can be. It should be remembered that a small 
 cylindrical wire may offer much more resistance than a larger 
 wire that is well streamlined. 
 
 Parasite resistance varies as the square of the velocity. 
 
 The law for parasite resistance is summed up in the state- 
 ment, determined by experiment, that parasite resistance 
 varies as the square of the velocity. This applies not 
 only to the separate parts* but also to an airplane as a whole. 
 Thus, if a certain airplane has a parasite resistance of 64 
 pounds when flying at 40 miles per hour, it will have a 
 resistance of 256 pounds at 80 miles per hour. In this case 
 the parasite resistance is o.o^V 2 . 
 
 The curves in Fig. 33 show the values for parasite resistance 
 at different velocities for three cases, R = 0.02V 2 , R = 
 
 "There is an appreciable departure from the square law when the 
 skin resistance of a body is large compared with the direct impact or 
 dynamic resistance the more so when the surface is rough and the f ore- 
 atid-aft dimension of the body is large in proportion to the diameter 
 but practically it is simplest to neglect this and to assume the square law 
 as strictly true. For only a small range in velocity, any error in this is 
 inappreciable; for a large range, it may be necessary to take different 
 values of tHb coefficient at different velocities. 
 
52 
 
 AIRPLANE CHARACTERISTICS 
 
 and R = o.o6V 2 , these illustrating the variation for a certain 
 range of moderate size machines. 
 
 Distribution of parasite resistance. 
 
 Parasite resistance is roughly distributed about as follows : 
 body, one-third; wires and struts, one-third; tail and 
 
 600, 
 
 40 60 80 100 1-20 
 
 VELOCITY - - MILES PER HOUR 
 
 Fig. 33. Variation of parasite resistance with velocity; the three 
 curves show R = 0.02 V 2 , R - 0.04 V 2 and R = 0.06 F 2 . 
 
 landing gear, one-third (about one-sixth for tail and one-sixth 
 for landing gear). 
 
 Increase of parasite resistance due to propeller slip stream. 
 
 Back of the propeller the air is driven backward in what 
 is called the slip stream or propeller race; in this slip stream 
 
RESISTANCE 53 
 
 the velocity of the air relative to the airplane is increased, 
 say, 20 or 2 5 per cent. V 2 is thus increased about 50 per cent. 
 The parasite resistance of the tail and all parts of the structure 
 in the slip stream is accordingly increased, let us say, 50 per 
 cent, when the propeller is running. Approximate cal- 
 culations may be made on this basis. Another approxim- 
 ate method is to consider that the increase of the total 
 parasite resistance due to the propeller slip stream is 10 per 
 cent. To get accurate results, careful computation would be 
 necessary. 
 
 SOME CONCLUSIONS 
 
 Three lines for improvement are suggested by the forego- 
 i ng discusions : 
 
 (1) Reduce parasite resistance. 
 
 (2 ) Reduce weight. 
 
 (3) Improve wing-section, so as to get a greater L/D ratio. 
 
 Wing-resistance, which is equal to weight -i- L/D, is 
 reduced by (2) and (3). Most important are (i) and (2), as 
 the improvement that can be made in L /D ratio is probably 
 rather small. 
 
 In design every effort should be made to reduce weight 
 and to cut down parasite resistance. 
 
 The chief weight is in the engine and the reduction of 
 weight is largely a problem for the engine designer. Re- 
 duction in parasite resistance is to be looked for in improved 
 design of structure. 
 
 Thrust and power characteristics. 
 
 The reader is referred to Appendix II and Appendix III 
 for curves showing the variation of thrust and power required 
 at different velocities. 
 
54 AIRPLANE CHARACTERISTICS 
 
 s 
 
 For horizontal flight, thrust is equal to the total resistance, 
 i. e. y is equal to the sum of wing-resistance and parasite re- 
 sistance. 
 
 Horse power is equal to the product of thrust (in pounds) 
 and velocity (in miles per hour) divided by 375. 
 
 NOTE. The following chapters are in preparation and 
 logically should follow Chapter III. Thrust. Power. 
 Climbing. Gliding. Altitude. Single and Mutliple Planes. 
 Stability in General. Longitudinal Stability. 
 
CHAPTER IV 
 
 LATERAL STABILITY 
 
 Lateral stability of an airplane is stability about a fore-and- 
 aft axis, called the "rolling" axis, which passes through the 
 center of gravity and either coincides with the line of flight 
 or is slightly displaced therefrom. 
 
 Rolling axis. 
 
 The rolling axis lies in the plane of symmetry of the 
 machine and, as shown in Fig. i, it may be either: 
 
 A neutral axis, when it coincides exactly with the line of 
 
 flight; 
 A raised axis, when its forward end is raised above the line 
 
 of flight (the common case) ; or, 
 
 A lowered axis, when its forward end is lowered below the 
 line of flight, which is not a common case. 
 
 'FLIGHT PATH 
 
 Fig. I . Three positions of rolling axis. 
 
 The line of flight is always understood to be the path of the 
 center of gravity. 
 
 Stability requires that a restoring moment be set up 
 whenever the machine is displaced from its normal position. 
 If the machine is rolled over to one side, with one wing 
 raised and the other lowered, there must be a rolling moment 
 tending to roll the machine back until the two wings are 
 again on the same level. Although for steadiness in normal 
 
 55 
 
56 AIRPLANE CHARACTERISTICS 
 
 flight a certain positive lateral stability is desirable, for quick 
 manceuvers a less positive or even an indifferent stability 
 becomes advantageous. But in no case is it desirable to have 
 a negative stability, which would tend to overturn the 
 machine when once displaced from its normal position. 
 
 Neutral axis. 
 
 A machine with a neutral axis has, from symmetry, a neutral 
 or indifferent stability, inasmuch as the angle of incidence at 
 which the air strikes the various surfaces (including keel and 
 other surfaces as well as wings) and hence also the pressure, 
 remain unchanged, irrespective of any displacement of the 
 machine about its rolling axis. The displacement, therefore, 
 causes neither a resorting nor an upsetting moment. Such a 
 machine needs no further study. By "incidence" is always 
 meant the angle between a surface and the stream of air it 
 encounters ; in case of a curved or cambered wing, the angle 
 between the chord and the air-stream. 
 
 Inclined axis. 
 
 The conditions for stability in a machine in which the 
 rolling axis is inclined depend upon whether the axis is raised 
 or lowered and upon the disposition of keel surfaces and upon 
 the shape of the wings. 
 
 Keel surface as affecting lateral stability. 
 
 An important element in lateral stability is the keel 
 surface which includes all surfaces that can be seen in a 
 "side view" of the machine, that is, when the machine is 
 viewed in a direction perpendicular to the plane of symmetry. 
 The keel surface of body, struts and other structure may in 
 itself be sufficient, but it is frequently supplemented by a 
 vertical stabilizer or keel so as to give a keel surface of desired 
 
LATERAL STABILITY 
 
 57 
 
 size and location, i. e., either a high keel above the rolling 
 axis or (rarely) a low keel below the rolling axis, as may be 
 required for stability. 
 
 Small keel surfaces are sometimes placed on top of the 
 wings, when this position suits the design of the machine, or 
 between the wings of a biplane. The keel or vertical stabilizer 
 is, however, more commonly in the rear of the machine, with 
 the rudder hinged to its back edge, as shown in Fig. 12 of the 
 next chapter. 
 
 Raised axis; high keel gives stability, low keel gives insta- 
 bility. Place a card on a stick or wire, so as to make a flag- 
 shaped model as in Fig. 2, and view it from in front along the 
 
 Fig. 2. Stable. 
 
 Fig. 3. Unstable. 
 
 line of flight ; let the stick represent the rolling axis and the 
 surface of the card represent the keel surface. When the 
 model is thus viewed from the front (from the left in the 
 illustration), it will be seen that with a raised axis a high keel 
 surface is stable, for when displaced by rolling, one side of the 
 keel plane is exposed to the wind (in the model, is exposed to 
 view) and the pressure on this side is in a direction to restore 
 the plane to its normal position. Likewise, as shown in Fig. 
 3 , it will be seen that with a raised axis a low keel is unstable. 
 
 The restoring moment is seen to depend upon the position 
 of the keel surface with respect to the rolling axis, and to be 
 independent of its position with respect to the center of 
 gravity, that is, it may be above or below the center of 
 
58 AIRPLANE CHARACTERISTICS 
 
 gravity, in front of or behind it, without affecting lateral 
 stability. (The location of the keel surface with respect to 
 the center of gravity has, however, a direct effect, on direc- 
 tional stability discussed later, and on stability in gusts.) 
 
 Lowered axis; low keel gives stability, high keel gives insta- 
 bility. In a like manner, it may be seen that, with a lowered 
 rolling axis as shown in Figs. 4 and 5, a low keel gives sta- 
 bility and a high keel gives instability. 
 
 As the center of pressure on the keel surface is never very 
 far from the rolling axis, the restoring moment is correspond- 
 
 Fig. 4. Stable. 
 
 ingly small. A longer lever arm and hence a larger moment 
 would be obtained if the keel surface were located well out 
 on the wings, and some machines have keel surfaces so 
 placed. The same effect, however, is practically obtained by 
 turning the wings up so as to form a dihedral angle, as 
 discussed below. 
 
 Wing shape, as affecting lateral stability. 
 
 Lateral stability is materially affected if the two wings, 
 instead of lying in a straight line, when viewed from in front, 
 are turned up so as to form a dihedral angle (or V) as in Figs. 
 6 and 7, or are made to retreat as in Fig. 8, or are given a 
 raked end as shown in the same figure. 
 
 The dihedral angle (called "lateral" or "transverse" 
 dihedral to distinguish it from the "longitudinal" dihedral 
 
LATERAL STABILITY 
 
 59 
 
 angle between the main plane and tail) may be caused or 
 noticably increased by flexure of the wings in flight. The 
 dihedral angle often amounts to several degrees and is dis- 
 tinctly noticeable, but it may be so small (perhaps one degree 
 or less) as to be scarcely noticeable to the eye. 
 
 DIHEDRAL ANGLE o 
 .V 
 
 Figs. 6 and 7. Dihedral angle for monoplane 
 and biplane; front view. 
 
 Model to show effect of wing shape. 
 
 The effect of wing shape upon lateral stability depends 
 upon the position of the rolling axis and this is best seen by 
 inspection of a model, readily made from a small rectangular 
 board, as in Fig. 9. 
 
 Different types of wings, made of card board or tin, can 
 
 SWEEP BACK 
 / OR RETREAT 
 
 - RAKED END 
 
 Fig. 8. Showing retreating or swept-back wings; showing 
 also raked ends to wings. Top view. 
 
 be inserted in the slits i , 2 or 3 to obtain different angles of 
 incidence. The board can be rotated about the pegs NN for 
 a neutral axis, about RR for a raised axis and about LL for a 
 
60 
 
 AIRPLANE CHARACTERISTICS 
 
 lowered axis. (Other pegs may be used to give other angles 
 to these axes.) 
 
 Lateral Stability as affected by dihedral angle. 
 
 By such a model the following conclusions can be readily 
 verified. 
 
 (i) Dihedral angle (V) and raised axis, gives stability, 
 because, when the machine is displaced by rolling: 
 
 Raised wing has a smaller angle of incidence and hence less 
 lift; 
 
 N 
 
 N 
 
 < FLIGHT PATH 
 
 Fig. 9. Model. Wings of different forms are inserted in 
 the slits i, 2 and 3 and viewed from the front (from 
 the left in the illustration) the line sight being in the 
 direction of the air stream. 
 
 Lowered wing has a greater angle of incidence and hence 
 more lift. 
 
 This makes a restoring moment and it can be shown that 
 this moment is greater as the angle of incidence at which the 
 machine is flying is greater. 
 
 Case (i) is the method actually employed for obtaining 
 lateral stability. 
 
 (2) Dihedral angle (V) and lowered axis, gives instability, 
 because, when machine is displaced by rolling: 
 
LATERAL STABILITY 61 
 
 Raised wing has a larger angle of incidence and hence more 
 
 lift; 
 Lowered wing has smaller angle of incidence and hence 
 
 less lift. 
 
 This makes an upsetting moment, which can be shown to 
 be greater as the incidence* is greater. 
 In a like manner, it may be seen that : 
 
 (3) Inverted dihedral (A) and raised axis, gives instability. 
 
 (4) Inverted dihedral (A) and lowered axis, gives stability. 
 With the inverted dihedral, the upsetting or restoring 
 
 moment is less as incidence is greater. The inverted dihedral 
 is practically never used, although machines have been so 
 made and flown. It may be noted that a gull, when it lowers 
 its head as it flies near the water in search of fish, also droops 
 its wings so as to make an inverted dihedral; in this way 
 stability is secured with what is now a lowered axis. As the 
 head is raised again for normal flight and the rolling axis 
 changes from a lowered axis to a neutral and then to a raised 
 axis, the inverted dihedral (A) may be seen to disappear and 
 an upright dihedral (V) to take its place. 
 
 A dihedral angle, or an inverted dihedral angle, makes a 
 tendency for a machine to roll when struck by a side gust. 
 Too large a dihedral angle is, accordingly, undesirable; but 
 other means may be used for increasing lateral stability. 
 
 Straight wings. 
 
 With straight wings, that is when there is no dihedral, the 
 incidence on both wings is always the same. Irrespective of 
 
 "This is true for small angles of incidence only , *. e., for the range 
 employed in flight in which the lift increases with incidence. Were the 
 incidence increased beyond, say, 14 or 15, the lift and the restoring 
 moment would decrease. 
 
62 AIRPLANE CHARACTERISTICS 
 
 whether the axis is raised or lowered, there is no difference 
 in the incidence of the two wings when the machine rolls and 
 hence no restoring or upsetting moment due to this cause. 
 
 A raised axis, however, has a small tendency toward sta- 
 bility, because when the machine rolls the lowered wing 
 moves forward and its center of pressure (which is always 
 ahead of the middle of a plane) now moves toward the wing- 
 tip, thus increasing the lever arm of the lift on this wing; the 
 raised wing on the other hand moves backward and its center 
 of pressure moves towards the body of the machine, thus 
 decreasing its lever arm. There is thus a restoring moment, 
 obtained with straight wings and a raised axis; it is 
 much less, however, than the restoring moment obtained by 
 using a dihedral angle. 
 
 In a similar way, a lowered axis with straight wings tends 
 toward instability. 
 
 Retreating wings and wings with raked ends. 
 
 Retreating or swept back wings, with a raised rolling axis, 
 give lateral stability, for (as may be seen by inserting such 
 wings in the model, Fig. 9), when the machine rolls, the 
 descending wing moves forward and enters the air more 
 squarely so as to attack more air and get more lift, thus 
 restoring the machine to its position of equilibrium. 
 
 In a like manner it can be shown by the model that, with 
 a raised axis, lateral stability is increased if the ends of the 
 wings are raked, i. e., if the trailing edge is longer than the 
 entering edge. 
 
 With a lowered axis, retreating wings and wings with 
 raked ends would be unstable. 
 
 Retreating wings and wings with raked ends are thus seen 
 to have the same effect as a dihedral angle upon lateral 
 
LATERAL STABILITY 63 
 
 stability, but with the advantage that in a side gust they 
 create no tendency for a machine to roll. It will be shown 
 later that all three devices dihedral angle, retreating wings 
 and raked ends give directional stability. But they all 
 have the disadvantage of reducing the so-called lifting 
 efficiency, or L/D ratio, i. e., there is a decrease in the amount 
 of lift for a given wing-resistance. 
 
 Effect of velocity on lateral stability. 
 
 All stability, depending upon the pressure of relative air 
 upon surfaces, increases as the velocity increases. 
 
 Control. 
 
 Lateral control might well be obtained by shifting the 
 center of gravity, but this is not done. It has been obtained 
 
 Fig. 10. Aileron independent 
 of main wings. 
 
 by warping (i. e., distorting) the planes, but lateral control 
 is now generally obtained by means of auxiliary planes or 
 ailerons which may be independent of the main planes (i. e., 
 between the two planes of a biplane as in Fig. 10) or attached 
 to the wings as wing flaps, as in Fig. 1 1 . To roll the machine 
 the pilot, simultaneously, turns the aileron on one wing down 
 and the other aileron up, thus giving more lift to one wing so 
 that it rises and less left to the other so that it descends. 
 This movement of the ailerons is commonly effected by 
 pushing the control stick, or by turning the control wheel, to 
 
64 AIRPLANE CHARACTERISTICS 
 
 left or to right, as illustrated in Appendix IV. The term 
 "warping" is frequently used to include this control by 
 ailerons. 
 
 Banking may or may not produce turning. 
 
 A machine is said to be banked when it is keeled over on 
 a turn, as a bicycle rider leans inward on a curve. 
 
 A machine is banked on a turn by elevating one wing and 
 depressing the other, this being accomplished by manipulat- 
 
 Fig. ii. Section of wing with wing-flap or aileron. 
 In (a) the wing-tip and aileron normally have 
 positive incidence; in (b) they are up-turned and 
 have negative incidence. 
 
 ing the ailerons in the manner described ; but this manipula- 
 tion of the ailerons will itself tend to turn the machine to one 
 side, if the wing-resistance is thereby increased on that side 
 and decreased on the other side. 
 
 If the raised wing has its resistance increased when its 
 aileron is turned down, and the lowered wing has its resistance 
 decreased when its aileron is turned up (as will occur with 
 many wing sections, as a in Fig. n), the raised wing will be 
 retarded and the machine will turn toward the higher (outer) 
 wing. Such a turn is not desirable but, under these condi- 
 tions, will occur unless prevented by the rudder. 
 
 A turn toward the lower (inner) wing is more desirable 
 and this may be accomplished by having the wing tips 
 (including ailerons) somewhat upturned so as to have a 
 negative incidence in normal flight; see b in Fig. n. The 
 
LATERAL STABILITY 65 
 
 resistance of the raised wing is then decreased when its 
 aileron is swung down, and the resistance of the lowered wing 
 is increased as its aileron is swung up, so that the lower wing 
 is retarded and a turn is made toward the lower (inner) wing. 
 Indeed some machines are made so as to depend entirely 
 upon banking as a means for turning, no rudder being pro- 
 vided. (Conversely, as discussed in the next chapter, turning 
 produces banking and in some machines the rudder has been 
 the only means for banking, no ailerons or similar devices 
 being provided.) 
 
 Although it is in many ways desirable to have a machine 
 thus turn in automatically when it is banked, some prefer to 
 have the control left entirely to the pilot, the machine having 
 no tendency to turn either in or out. This condition may be 
 approached by a nicety in design of section of wing and 
 aileron. The negative wing-tip and aileron, although 
 advantageous for the reasons just described, mean a sacrifice 
 for they give less lift and greater wing-resistance. 
 
 There is room for difference of opinion as to how great an 
 extent banking and turning should be automatically depend- 
 ent upon each other and to what extent their control should 
 depend upon the pilot. 
 
 Propeller Torque. 
 
 In a machine with one propeller, as the propeller rotates in 
 one direction there is a tendency (when the power is on) for 
 the whole machine to rotate in the opposite direction. This 
 may be easily corrected for in the control by the pilot, or 
 automatically by a difference in the lift of the two wings, as 
 described below. When flying, any correction is made by 
 the pilot unconsciously. When starting, however, the cor- 
 rection may be noticeable, for the amount of correction 
 
66 AIRPLANE CHARACTERISTICS 
 
 changes as the engine accelerates ; furthermore it is particu- 
 larly important while near the ground to keep both wings 
 even. When two propellers are used, rotating in opposite 
 directions, the effects of propeller torque are neutralized. 
 
 Automatic correction for propeller torque. 
 
 The correction for the torque of the propeller when power 
 is on is often made automatically by a lack of symmetry in 
 the two wings so that one wing has more lift than the other. 
 This is sometimes done by a droop and rise (a droop near the 
 end of one wing and a rise near the end of the other) and 
 sometimes by a wash out on one wing (a progressive decrease 
 in incidence from body to wing-tip) and a wash in on the 
 other wing (a progressive increase of incidence from body to 
 wing-tip.) 
 
 Any such lack of symmetry, however, gives a tendency for 
 the machine to rotate when power is off. In horizontal 
 flight this may be corrected for by the controls, but in diving 
 it may make a spin that can not be controlled; for this 
 reason lack of symmetry is very undesirable and should be 
 avoided. 
 
CHAPTER V 
 
 DIRECTIONAL STABILITY 
 
 When an airplane swings off from its course, to left or right, 
 it is said to yaw. Directional stability is the stability that 
 keeps a machine on its course, that is it restores the machine 
 to its course whenever it yaws. The vertical or yawing axis 
 passes through the center of gravity of the machine, lies in the 
 plane of symmetry and is more or less perpendicular to the 
 flight path. 
 
 This stability is similar to that of a weathercock and 
 depends upon having the center of the keel surface back of the 
 yawing axis, thus insuring a restoring moment whenever the 
 machine departs from its course. It is to be remembered 
 that the keel surface is all the surface seen from the side, 
 including structure as well as auxiliary keels or fins. In 
 some machines enough directional stability is obtained by the 
 keel surf ace of the body itself, but this is usually supplemented 
 by the addition of a small keel or vertical stabilizer in the 
 rear. If the keel center is too far aft, side gusts will cause the 
 machine to yaw too much. 
 
 A machine should fly straight on its flight path ; but it will 
 fail to do so and will proceed crab-fashion if there is unequal 
 resistance on the two sides . This might be caused by unequal 
 incidence of the two wings, distorted surface or cambre, lack 
 of symmetry in the tail, wrong alignment of body or fin or 
 anything that might act as a rudder, for example the setting 
 of struts or stream-line wires not in the line of flight, points 
 to be looked at in "tuning up" a machine. 
 
 Dihedral angle and retreating wings. 
 
 Although the keel surface is the chief element in directional 
 
 67 
 
68 
 
 AIRPLANE CHARACTERISTICS 
 
 stability, the wings may contribute. Directional stability is 
 in all cases aided by retreating wings and by wings with a 
 transverse dihedral angle, on account of the greater resistance 
 of the wing which advances when the machine swings off from 
 its course; this is independent of the location of the rolling 
 axis. The same is true of wings with raked ends (i. e. with 
 trailing edge longer than entering edge). As pointed out in 
 the preceding chapter (see Figs. 6, 7 and 8) these forms of 
 wings likewise tend toward lateral stability, provided there is 
 a raised rolling axis. 
 
 Fig. 12. Vertical stabilizer (v) and rudder (r). 
 
 On the other hand an inverted dihedral or advancing wing 
 tips, forms of wings which are not used, would in all cases 
 tend toward directional instability; with a lowered axis, 
 these forms would, however, give lateral stability, as already 
 explained. 
 
 Turning. 
 
 Turning is the deflection of the flight path to left or right. 
 Rotation of the machine about its vertical axis, although it 
 usually accompanies turning, is not in itself sufficient. 
 Although turning might be effected by other means, as by 
 shifting the center of gravity, extending a panel on one wing 
 
DIRECTIONAL STABILITY 69 
 
 to increase its resistance, etc. it is usually effected by a 
 rudder at the rear of the machine. This is often hinged on a 
 vertical fin or stabilizer, already referred to in connection 
 with lateral stability, which forms part of the keel surface; 
 such a rudder is shown in Fig. 12. A balanced rudder, as in 
 Fig. 13, reduces the force necessary for control and for this 
 reason is commonly used on large machines. The rudder is 
 usually operated by the pilot's feet, as illustrated in 
 Appendix IV. 
 
 Fig. 13. Balanced rudder (r). 
 
 Turning by rudder. 
 
 A rudder alone without a keel would be ineffective, for 
 the machine when rotated by the rudder would tend to 
 skid along its original flight path, as does a toboggan on 
 smooth ice. Turning control like all control depends also 
 on a certain speed, as in watercraft which require "steerage 
 way" in order to answer the helm. 
 
 The relation between keel and rudder in turning is shown 
 in Fig. 14. When the rudder is turned to one side, the pres- 
 sure on the rudder causes the whole machine to rotate about 
 its vertical axis until the rudder moment (p times its lever 
 arm) is balanced by the keel moment (the keel pressure P 
 times its lever arm) ; the lever arm in each case is the dis- 
 tance measured from the center of gravity G, to the force 
 p or P, measured on a line perpendicular to the force. 
 
70 AIRPLANE CHARACTERISTICS 
 
 It is clear that, when the two moments are equal, the force 
 P, with the shorter lever arm, is greater than p. The result- 
 ant of the forces P and p is a force R* deflecting the machine 
 from its original flight path. 
 
 This deflecting force : 
 
 Increases as P increases (increasing, for a given keel 
 moment, as the keel surface is greater and its distance 
 from G is less) ; 
 
 Increases as p decreases (increasing, for a given 
 rudder moment, as the rudder surface is smaller and 
 further back.) 
 
 A rudder is most effective, therefore, when it is placed far 
 back, and the keel surface is placed near the center of gravity. 
 
 Secondary effects. 
 
 There are important secondary effects on turning, the 
 principal ones (see Fig. 14) being: 
 
 (a) Turning causes banking, for two reasons: (i) The 
 outer wing having the higher velocity and greater lift tends 
 to rise and the inner wing tends to descend on a turn; (2) 
 The pressure on the keel surface on a turn tends to keel the 
 machine over in the same direction as in (i), provided (as is 
 usually the case) the keel center is above the rolling axis. 
 (In some machines, as mentioned in the preceding chapter, 
 
 *Strictly speaking, R is not the resultant of P and p, although for the 
 present purpose it may be so called. More correctly, P and p may each 
 be replaced by a couple and by a force acting at G, these two forces 
 being shown in the figure by light dotted lines. The two couples thus 
 formed are equal and opposite and so cancel each other. This leaves the 
 two forces acting at G with the resultant R. 
 
 The two couples thus cancelled do not affect the motion of the air- 
 plane as a whole; they do, however, enter into strength computations. 
 
DIRECTIONAL STABILITY 
 
 71 
 
 the rudder has been the only means for banking, no ailerons 
 or similar devices being provided.) 
 
 (b) Turning causes increase of resistance and loss of speed 
 due to the fact that the pressures P and p on keel and rudder 
 each have a backward component. 
 
 COURSE: 
 
 XAKCN 
 
 \ 
 
 \ 
 
 ORIGINAL. 
 
 COURSE: 
 
 ^-^ 
 
 RVDDETR 
 
 Fig. 14. Action of keel in turning. 
 
 (c) Turning causes a decrease in lift and a tendency to 
 descend, i. e., a tendency to stall, for two reasons: (i) On 
 account of loss of speed described in b, the pressure on the 
 wings, and hence the lift, is decreased; (2) On account of 
 banking described in a, the vertical component of the lift is 
 decreased, see Fig. 1 5 ; this component becoming zero when a 
 machine is banked ninety degrees. 
 
72 
 
 AIRPLANE CHARACTERISTICS 
 
 (d) Machine may nose up on a turn and thus have a further 
 tendency to stall, if the pressures P and p on keel and rudder 
 are higher than G, on account of the backward component of 
 these pressures. Stalling may end in a tail slide. 
 
 The tendency to stall on a turn may be overcome, if neces- 
 sary, by maintaining speed either by putting on more power 
 or by nosing down a little by means of the elevator. Loss 
 of speed is to be avoided. Obviously, to attempt to climb on 
 a turn is dangerous. 
 
 Fig. 15. Horizontal and vertical components 
 
 lift when banking note that lift is 
 
 not vertical. 
 
 Side slipping and skidding. 
 
 If a machine is banked too much for a particular turn, it 
 will slip in and down, on account of the horizontal component* 
 there is to the lift (see Fig. 15) and the decrease in the vertical 
 component. This may result in a nose dive. 
 
 If a machine is not banked enough, it will skid out and (in 
 some cases, due to the inertia of the machine) up, this being 
 likely to happen on sharp turns and at high speeds. This 
 may end in a stall, as the relative wind strikes the machine 
 
 *It is to be kept in mind that lift, as the term is used, lies in the plane 
 of symmetry of a machine and becomes inclined when a machine rolls. 
 
DIRECTIONAL STABILITY 73 
 
 less from the front and more from the side and so gives less 
 support to the machine on account of its decreased forward 
 velocity. 
 
 Banking on a turn. 
 
 With the proper banking, the centripetal force towards the 
 center of the turn due to the banking must just equal the 
 centrifugal force away from the center. There being no 
 skidding or side slipping, the pilot will feel no side wind on 
 either cheek. He will feel a pressure holding him to his seat 
 with no pressure to left or right. Strings tied to guy- wires, 
 blow straight back and not at an angle. If rolling is indi- 
 cated by an inclinometer like a level (arched upward), placed 
 across the machine, the bubble remains central. In skidding 
 or side slipping, the machine leaves the bubble behind; the 
 pilot ought to keep in mind that the control should follow 
 the bubble. It is a good plan to start banking just before 
 beginning a turn. 
 
 The pilot instinctively gets the proper "feel" of a turn, as 
 does the rider of a bicycle, without a study of moments and 
 couples. The bicycle rider, however, usually learns by taking 
 a few spills, but this the air pilot can not afford to do. 
 
 Turning by banking. 
 
 When the wings are inclined, whatever the cause, the lift 
 on the wings has not only a vertical component but also a 
 horizontal sideways component, as shown in Fig. 15, which 
 tends to move the machine horizontally toward the side of 
 the machine that is down. The flight path is thus deflected. 
 This becomes more pronounced in machines with large keel 
 surface. By placing large keel surfaces, both forward and 
 aft, certain machines are turned entirely by banking and are 
 provided with no rudder. 
 
74 AIRPLANE CHARACTERISTICS 
 
 Gryoscopic action. 
 
 The propeller and revolving parts of the engine form a 
 gyroscope, so that a sudden turn of the machine sideways 
 will cause it to pitch or rear. Similarly any sudden pitching 
 or rearing will cause the machine to turn to one side; for, 
 when a sudden force is applied perpendicular to the axis of a 
 gyroscope, the axis swings sideways at right angles to that 
 force. The direction of this effect will depend upon the direc- 
 tion of rotation of the revolving parts, and so may be opposite 
 in different machines. This effect will be but small when 
 controls are not jerked suddenly; indeed they should not be 
 operated suddenly on account of the severe stresses produced. 
 
APPENDICES 
 
 APPENDIX I. Glossary. 
 
 APPENDIX II. Thrust Characteristics. 
 
 APPENDIX III. Power Characteristics. 
 
 APPENDIX IV. Control and Other Diagrams. 
 
 75 
 
APPENDIX I 
 
 GLOSSARY* 
 
 AEROFOIL: A winglike structure, flat or curved, designed 
 to obtain reaction upon its surface from the air through 
 which it moves. 
 
 AEROPLANE : See Airplane. 
 
 AILERON: A movable auxiliary surface used to produce a 
 rolling moment about the fore-and-aft axis. 
 
 AIRCRAFT: Any form of craft designed for the navigation 
 of the air airplanes, balloons, dirigibles, helicopters, kites, 
 kite balloons, ornithopters, gliders, etc. 
 
 AIRPLANE: A form of aircraft heavier than air which has 
 wing surfaces for support in the air, with stabilizing sur- 
 faces, rudders for steering, and power plant for propulsion 
 through the air. This term is commonly used in a more 
 restricted sense to refer to air-planes fitted with landing 
 gear suited to operation from the land. If the landing 
 gear is suited to operation from the water, the term "sea- 
 plane" is used. (See definition.) 
 
 Pusher. A type of airplane with the propeller in the 
 
 rear of the engine. 
 Tractor. A type of airplane with the propeller in front 
 
 of the engine. 
 
 AIR-SPEED METER: An instrument designed to measure the 
 speed of an aircraft with reference to the air. 
 
 ALTIMETER : An aneroid mounted on an aircraft to indicate 
 continuously its height above the surface of the earth. 
 
 ANEMOMETER: Any instrument for measuring the velocity 
 of the wind. 
 
 *From Report No. 15, on "Nomenclature for Aeronautics," by the 
 National Advisory Committee for Aeronautics. 
 
 77 
 
78 AIRPLANE CHARACTERISTICS 
 
 ANGLE : 
 
 Of attack or of incidence of an aerofoil. The acute angle 
 between the direction of the relative wind and the 
 chord of an aerofoil; i. e., the angle between the chord 
 of an aerofoil and its motion relative to the air. 
 (This definition may be extended to any body having 
 an axis.) 
 
 Critical. The angle of attack at which the lift-curve has 
 its first maximum; sometimes referred to as the 
 "burble point." (If the "lift curve" has more than 
 one maximum, this refers to the first one.) 
 
 Gliding. The angle the flight path makes with the hori- 
 zontal when flying in still air under the influence of 
 gravity alone, i. e., without power from the engine. 
 
 APPENDIX : The hose at the bottom of a balloon used for 
 inflation. In the case of a spherical balloon it also serves 
 for equalization of pressure. 
 
 ASPECT RATIO : The ratio of span to chord of an aerofoil. 
 
 AVIATOR: The operator or pilot of heavier-than-air craft. 
 This term is applied regardless of the sex of the operator. 
 
 AXES OF AN AIRCRAFT: Three fixed lines of reference; 
 usually centroidal and mutually rectangular. 
 
 The principal longitudinal axis in the plane of symmetry, 
 usually parallel to the axis of the propeller, is called the fore 
 and aft axis (or longitudinal axis) ; the axis perpendicular 
 to this in the plane of symmetry is called the vertical axis ; 
 and the third axis, perpendicular to the other two, is called 
 the transverse axis (or lateral axis). In mathematical 
 discussions the first of these axes, drawn from front to rear, 
 is called the X axis; the second, drawn upward, the Z axis; 
 and the third, forming a "left-handed" system, the Y axis. 
 
 BALANCING FLAPS : See Aileron. 
 
 BALLONET : A small balloon within the interior of a balloon 
 or dirigible for the purpose of controlling the ascent or 
 descent, and for maintaining pressure on the outer envelope 
 so as to prevent deformation. The ballonet is kept inflated 
 
GLOSSARY 79 
 
 with air at the required pressure, under the control of a 
 blower and valves. 
 
 BALLOON: A form of aircraft comprising a gas bag and a 
 basket. The support in the air results from the buoyancy 
 of the air displaced by the gas bag, the form of which is 
 maintained by the pressure of a contained gas lighter than 
 air. 
 
 Barrage. A small spherical captive balloon, raised as a 
 
 protection against attacks by airplanes. 
 Captice. A balloon restrained from free flight by means 
 
 of a cable attaching it to the earth. 
 Kite. An elongated form of captive balloon, fitted with 
 tail appendages to keep it headed into the wind, and 
 deriving increased lift due to its axis being inclined to 
 the wind. 
 Pilot. A small spherical balloon sent up to show the 
 
 direction of the wind. 
 
 Sounding. A small spherical balloon sent aloft, without 
 passengers, but with registering meteorological instru- 
 ments. 
 
 BALLOON BED : A mooring place on the ground for a captive 
 balloon. 
 
 BALLOON CLOTH: The cloth, usually cotton, of which 
 balloon fabrics are made. 
 
 BALLOON FABRIC : The finished material, usually rubberized, 
 of which balloon envelopes are made. 
 
 BANK : To incline an airplane laterally i. e., to roll it about 
 the fore and aft axis. Right bank is to incline the airplane 
 with the right wing down Also used as a noun to describe 
 the position of an airplane when its lateral axis is inclined 
 to the horizontal. 
 
 BAROGRAPH: An instrument used to record variations in 
 barometric pressure. In aeronautics the charts on which 
 the records are made indicate altitudes directly instead of 
 barometric pressures. 
 
80 AIRPLANE CHARACTERISTICS 
 
 BASKET: The car suspended beneath a balloon, for passen- 
 gers, ballast, etc. 
 
 BIPLANE: A form of airplane in which the main supporting 
 surface is divided into two parts, one above the other. 
 
 BODY OF AN AIRPLANE: The structure which contains the 
 power plant, fuel, passengers, etc. 
 
 BONNET : The appliance, having the form of a parasol, which 
 protects the valve of a spherical balloon against rain. 
 
 BRIDLE: The system of attachment of cable to a balloon, 
 including lines to the suspension band. 
 
 BULLSEYES: Small rings of wood, metal, etc., forming part 
 of balloon rigging, used for connection or adjustment of 
 ropes. 
 
 BURBLE POINT : See Angle, critical. 
 
 CABANE : A pyramidal framework upon the wing of an air- 
 plane, to which stays, etc., are secured. 
 
 CAMBER: The convexity or rise of the curve of an aerofoil 
 from its chord, usually expressed as the ratio of the maxi- 
 mum departure of the curve from the chord to the length 
 of the chord. "Top camber' ' refers to the top surface of an 
 aerofoil, and "bottom camber" to the bottom surface; 
 "mean camber" is the mean of these two. 
 
 CAPACITY : See Load. 
 
 The cubic contents of a balloon. 
 
 CENTER : Of pressure of an aerofoil. The point in the plane 
 of the chords of an aerofoil, prolonged if necessary, through 
 which at any given attitude the line of action of the 
 resultant air force passes. (This definition may be 
 extended to any body.) 
 
 CHORD : 
 
 Of an aerofoil section. A right line tangent at the front 
 and rear to the under curve of an aerofoil section. 
 
 Length. The length of the chord is the length of the pro- 
 jection of the aerofoil section on the chord. 
 
GLOSSARY 81 
 
 CLINOMETER: See Inclinometer. 
 
 CONCENTRATION RING: A hoop to which are attached the 
 ropes suspending the basket. 
 
 CONTROLS : A general term applying to the means provided 
 for operating the devices used to control speed, direction of 
 flight, and attitude of an aircraft. 
 
 CONTROL COLUMN: The vertical lever by means of which 
 certain of the principal controls are operated, usually 
 those for pitching and rolling. 
 
 CROW'S FOOT: A system of diverging short ropes for dis- 
 tributing the pull of a single rope. 
 
 DECALAGE : The angle between the chords of the principal 
 and the tail planes of a monopolane. The same term may 
 be applied to the corresponding angle between the direction 
 of the chord or chords of a biplane and the direction of a 
 tail plane. (This angle is also sometimes known as the 
 longitudinal V of the two planes.) 
 
 DIHEDRAL IN AN AIRPLANE : The angle included at the inter- 
 section of the imaginary surfaces containing the chords of 
 the right and left wings (continued to the plane of symme- 
 try if necessary). This angle is measured in a plane per- 
 pendicular to that intersection. The measure of the 
 dihedral is taken as 90 minus one-half of this angle as 
 defined. 
 
 The dihedral of the upper wing may and frequently does 
 differ from that of the lower wing in a biplane. 
 DIRIGIBLE : A form of balloon, the outer envelope of which 
 is of elongated form, provided with a propelling system, 
 car, rudders, and stabilizing surfaces. 
 
 Nonrigid. A dirigible whose form is maintained by the 
 pressure of the contained gas assisted by the car- 
 suspension system. 
 Rigid. A dirigible whose form is maintained by a rigid 
 
 structure contained within the evnelope. 
 Semirigid. A dirigible whose form is maintained by 
 means of a rigid keel and by gas pressure. 
 
82 AIRPLANE CHARACTERISTICS 
 
 DIVING RUDDER: See Elevator. 
 
 DOPE : A general term applied to the material used in treat- 
 ing the cloth surface of airplane members and balloons to 
 increase strength, produce tautness, and act as a filler to 
 maintain air-tightness; it usually has a cellulose base. 
 
 DRAG : The component parallel to the relative wind of the 
 total force on an aircraft due to the air through which it 
 moves. 
 
 That part of the drag due to the wings is called "wing 
 resistance" (formerly called "drift"); that due to the rest 
 of the airplane is called "parasite resistance" (formerly 
 called "head resistance"). 
 
 DRIFT: See Drag. Also used as synonymous with "lee- 
 way," q. v. 
 
 DRIFT METER: An instrument for the measurement of the 
 angular deviation of an aircraft from a set course, due to 
 cross winds. 
 
 DRIP CLOTH: A Curtain around the equator of a balloon, 
 which prevents rain from dripping into the basket. 
 
 ELEVATOR : A hinged surface for controlling the longitudinal 
 attitude of an aircraft; i. e., its rotation about the trans- 
 verse axis. 
 
 EMPANNAGE : See Tail. 
 
 ENTERING EDGE: The foremost edge of an aerofoil or pro- 
 peller blade. 
 
 ENVELOPE: The portion of the balloon or dirigible which 
 contains the gas. 
 
 EQUATOR: The largest horizontal circle of a spherical 
 balloon. 
 
 FINS : Small fixed aerofoils attached to different parts of air- 
 craft, in order to promote stability; for example, tail fins, 
 skid fins, etc. Fins are often adjustable. They may be 
 either horizontal or vertical. 
 
 FLIGHT PATH : The path of the center of gravity of an air- 
 craft with reference to the earth. 
 
GLOSSARY 83 
 
 FLOAT : That portion of the landing gear of an aircraft which 
 provides buoyancy when it is resting on the surface of the 
 water. 
 
 FUSELAGE : See Body. 
 
 GAP : The shortest distance between the planes of the chords 
 of the upper and lower wings of a biplane. 
 
 GAS BAG : See Envelope. 
 
 GLIDE : To fly without engine power. 
 
 GLIDER : A form of aircraft similar to an airplane, but with- 
 out any power plant. 
 
 When utilized in variable winds it makes use of the soar- 
 ing principles of flight and is sometimes called a soaring 
 machine. 
 
 GORE : One of the segments of fabric composing the envelope. 
 
 GROUND CLOTH : Canvas placed on the ground to protect a 
 balloon. 
 
 GUIDE ROPE : The long trailing rope attached to a spherical 
 balloon or dirigible, to serve as a brake and as a variable 
 ballast. 
 
 GUY: A rope, chain, wire, or rod attached to an object to 
 guide or steady it, such as guys to wing, tail, or landing gear. 
 
 HANGAR : A shed for housing balloons or airplanes. 
 
 HELICOPTER: A form of aircraft whose support in the air is 
 derived from the vertical thrust of propellers. 
 
 HORN: A short arm fastened to a movable part of an air- 
 plane, serving as a lever-arm, e. g., aileron-horn, rudder- 
 horn, elevator-horn. 
 
 INCLINOMETER: An instrument for measuring the angle 
 made by any axis of an aircraft with the horizontal, often 
 called a clinometer. 
 
 INSPECTION WINDOW: A small transparent window in the 
 envelope of a balloon or in the wing of an airplane to allow 
 inspection of the interior. 
 
84 AIRPLANE CHARACTERISTICS 
 
 KITE: A form of aircraft without other propelling means 
 than the towline pull, whose support is derived from the 
 force of the wind moving past its surface. 
 
 LANDING GEAR : The understructure of an aircraft designed 
 to carry the load when resting on or running on the surface 
 of the land or water. 
 
 LEADING EDGE: See Entering edge. 
 
 LEEWAY : The angular deviation from a set course over the 
 earth, due to cross currents of wind, also called drift; 
 hence, "drift meter." 
 
 LIFT: The component perpendicular to the relative wind, 
 in a vertical plane, of the force on an aerofoil due to the air 
 pressure caused by motion through the air. 
 
 LIFT BRACING : See Stay. 
 
 LOAD: 
 
 Dead. The structure, power plant, and essential acces- 
 sories of an aircraft. 
 
 Full. The maximum weight which an aircraft can sup- 
 port in flight; the "gross weight." 
 
 Useful. The excess of the full load over the dead-weight 
 of the aircraft itself, i. e., over the weight of its struc- 
 ture, power plant, and essential accessories. (These 
 last must be specified.) 
 
 LOADING : See Wing, loading. 
 
 LOBES : Bags at the stern of an elongated balloon designed 
 to give it directional stability. 
 
 LONGERON : See Longitudinal. 
 
 LONGITUDINAL : A fore-and-aft member of the framing of an 
 air-plane body, or of the floats, usually continuous across a 
 number of points of support. 
 
 MONOPLANE : A form of airplane whose main supporting sur- 
 face is a single wing, extending equally on each side of the body . 
 
 MOORING BAND : The band of tape over the top of a balloon 
 to which are attached the mooring ropes. 
 
GLOSSARY 85 
 
 NACELLE: See Body. Limited to pushers. 
 
 NET: A rigging made of ropes and twine on spherical bal- 
 loons, which supports the entire load carried. 
 
 ORNITHOPTER: A form of aircraft deriving its support and 
 propelling force from flapping wings. 
 
 PANEL: The unit piece of fabric of which the enevelope is 
 made. 
 
 PARACHUTE : An apparatus, made like an umbrella, used to 
 retard the descent of a falling body. 
 
 PATCH SYSTEM : A system of construction in which patches 
 (or adhesive flaps) are used in place of the suspension band. 
 
 PERMEABILITY. The measure of the loss of gas by diffusion 
 through the intact balloon fabric. 
 
 PITOT TUBE : A tube with an end open square to the fluid 
 stream, used as a detector of an impact pressure. It is 
 usually associated with a coaxial tube surrounding it, 
 having perforations normal to the axis for indicating static 
 pressure ; or there is such a tube placed near it and parallel 
 to it, with a closed conical end and having perforations in 
 its side. The velocity of the fluid can be determined from 
 the difference between the impact pressure and the static 
 pressure, as read by a suitable gauge. This instrument is 
 often used to determine the velocity of an aircraft through 
 the air. 
 
 PONTOONS : See Float. 
 
 PUSHER : See Airplane. 
 
 PYLON : A mast or pillar serving as a marker of a course. 
 
 RACE OF A PROPELLER: See Slip stream. 
 
 RELATIVE WIND : The motion of the air with reference to a 
 moving body. Its direction and velocity, therefore, are 
 found by adding two vectors, one being the velocity of the 
 air with reference to the earth, the other being equal and 
 opposite to the velocity of the body with reference to the 
 earth. 
 
86 AIRPLANE CHARACTERISTICS 
 
 RIP CORD : The rope running from the rip panel of a balloon 
 to the basket, the pulling of which causes immediate 
 deflation. 
 
 RIP PANEL : A strip in the upper part of a balloon which is 
 torn off when immediate deflation is desired. 
 
 RUDDER : A hinged or pivoted surface, usually more or less 
 flat or stream lined, used for the purpose of controlling the 
 attitude of an aircraft about its "vertical" axis, i. e., for 
 controlling its lateral movement. 
 
 Rudder bar. The foot bar by means of which the rudder 
 is operated. 
 
 SEAPLANE : A particular form of airplane in which the land- 
 ing gear is suited to operation from the water. 
 
 SERPENT : A short, heavy guide rope. 
 
 SIDE SLIPPING : Sliding downward and inward when making 
 a turn; due to excessive banking. It is the opposite of 
 skidding. 
 
 SKIDDING: Sliding sideways away from the center of the 
 turn in flight. It is usually caused by insufficient banking 
 in a turn, and is the opposite of side slipping. 
 
 SKIDS : Long wooden or metal runners designed to prevent 
 nosing of a land machine when landing or to prevent drop- 
 ping into holes or ditches in rough ground. Generally 
 designed to function should the landing gear collapse or 
 fail to act. 
 
 SLIP STREAM OR PROPELLER RACE i The stream of air driven 
 aft by the propeller and with a velocity relative to the air- 
 plane greater than that of the surrounding body of still air. 
 
 SOARING MACHINE : See Glider. 
 
 SPAN OR SPREAD : The maximum distance laterally from tip 
 to tip of an airplane wing, or the lateral dimension of an 
 aerofoil. 
 
GLOSSARY 87 
 
 STABILITY : A quality in virtue of which an airplane in flight 
 tends to return to its previous attitude after a slight dis- 
 turbance. 
 
 Directional. Stability with reference to the vertical axis. 
 
 Dynamical. The quality of an aircraft in flight which 
 causes it to return to a condition of equilibrium after 
 its attitude has been changed by meeting some dis- 
 turbance, e. g., a gust. This return to equilibrium is 
 due to two factors; first, the inherent righting 
 moments of the structure; second, the damping of 
 the oscillations by the tail, etc. 
 
 Inherent. Stability of an aircraft due to the disposition 
 and arrangement of its fixed parts i. e., that property 
 which causes it to return to its normal attitude of 
 flight without the use of the controls. 
 
 Lateral. Stability with reference to the longitudinal (or 
 fore and aft) axis. 
 
 Longitudinal. Stability with reference to the lateral 
 axis. 
 
 Statical. In wind tunnel experiments it is found that 
 there is a definite angle of attack such that for a greater 
 angle or a less one the righting moments are in such a 
 sense as to tend to make the attitude return to this 
 angle. This holds true for a certain range of angles on 
 each side of this definite angle; and the machine is 
 said to possess "statical stability" through this range. 
 
 STABILIZER: Any device designed to steady the motion of 
 aircraft. 
 
 STAGGER: The amount of advance of the entering edge of 
 the upper wing of a biplane over that of the lower, expressed 
 as percentage of gap; it is considered positive when the 
 upper surface is forward. 
 
 STALLING: A term describing the condition of an airplane 
 which from any cause has lost the relative speed necessary 
 for control. 
 
88 AIRPLANE CHARACTERISTICS 
 
 STATOSCOPE: An instrument to detect the existence of a 
 small rate of ascent or descent, principally used in balloon- 
 ing. 
 
 STAY : A wire, rope, or the like used as a tie piece to hold 
 parts together, or to contribute stiffness; for example, the 
 stays of the wing and body trussing. 
 
 STEP : A break in the form of the bottom of a float. 
 
 STREAM-LINE FLOW : A term in hydromechanics to describe 
 the condition of continuous flow of a fluid, as distinguished 
 from eddying flow. 
 
 STREAM-LINE SHAPE: A shape intended to avoid eddying 
 and to preserve stream-line flow. 
 
 STRUT: A compression member of a truss frame; for 
 instance, the vertical members of the wing truss of a 
 biplane. 
 
 SUSPENSION BAND : The band around a balloon to which are 
 attached the basket and the main bridle suspensions. 
 
 SUSPENSION BAR: The bar used for the concentration of 
 basket suspension ropes in captive balloons. 
 
 SWEEP BACK : The horizontal angle between the lateral axis 
 of an airplane and the entering edge of the main planes. 
 
 TAIL : The rear portion of an aircraft, to which are usually 
 attached rudders, elevators, stabilizers, and fins. 
 
 TAIL CUPS: The steadying device attached at the rear of 
 certain types of elongated captive balloons. 
 
 THIMBLE: An elongated metal eye spliced in the end of a 
 rope or cable. 
 
 TRACTOR : See Airplane. 
 
 TRAILING EDGE: The rearmost edge of an aerofoil or pro- 
 peller blade. 
 
 TRIPLANE : A form of airplane whose main supporting sur- 
 face is divided into three parts, superimposed. 
 
GLOSSARY 89 
 
 TRUSS: The framing by which the wing loads are trans- 
 mitted to the body ; comprises struts, stays, and spars. 
 
 UNDERCARRIAGE : See Landing gear. 
 
 WARP : To change the form of the wing by twisting it. 
 
 WASH OUT : A permanent warp of an aerofoil such that the 
 angle of attack decreases toward the wing tips. 
 
 WEIGHT: Gross. See Load, full. 
 
 WINGS : The main supporting surfaces of an airplane. 
 
 WING FLAP: See Aileron. 
 
 WING LOADING: The weight carried per unit area of sup- 
 porting surface. 
 
 WING MAST : The mast structure projecting above the wing, 
 to which the top load wires are attached. 
 
 WING RIB: A fore-and-aft member of the wing structure 
 used to support the covering and to give the wing section 
 its form. 
 
 WING SPAR OR WING BEAM: A transverse member of the 
 wing structure. 
 
 YAW : To swing off the course about the vertical axis. 
 
 Angle of. The temporary angular deviation of the fore- 
 and-aft axis from the course. 
 
APPENDIX II 
 
 THRUST CHARACTERISTICS 
 
 91 
 
THRUST CHARACTERISTICS 
 
 93 
 
 c/, 700 
 
 Q 
 
 600 
 
 C/3 500 
 
 400 
 
 200 
 
 100 
 
 40 60 80 100 
 
 VELOCITY - MILES PER HOUR 
 
 Fig. 34. Total resistance or thrust is the sum of wing-resistance 
 and parasite resistance. The curves represent case when 
 W = 2000 Ibs.; W/S = 6; parasite resistance = 0.04 F 2 . 
 
THRUST CHARACTERISTICS 
 
 95 
 
 500 
 
 
 300 
 
 g 
 
 100 
 
 ^0 40 $0 8p 100 
 
 VELOCITY - - MILES PER HOUR 
 
 Fig. 35- Variation of thrust with velocity. The three 
 curves show effect of changing weight (W = 1000, 2000 
 and 3000 Ibs.) when loading is kept constant( W/S 6) ; 
 parasite resistance = 0.04 F 2 . 
 
THRUST CHARACTERISTICS 
 
 97 
 
 SCO 
 
 400 
 
 o 
 
 500 
 
 CO 
 
 4* 
 
 . _ 
 VELOCITY - - MILES PER HOUR 
 
 Fig. 36. Variation of thrust with velocity. The three curves 
 show effect of changing loading (W/S = 4, 6 and 8) when 
 weight is kept constant (W = 2000 Ibs.); parasite resist- 
 ance = 0.04 F 2 . 
 
THRUST CHARACTERISTICS 
 
 99 
 
 I 
 
 i 
 
 600 
 
 500 
 
 400 
 
 360 
 
 8 
 
 200 
 
 100 
 
 4 20 40 40 SO 100 
 
 VELOCITY - - MILES PER HOUR 
 
 ig- 37- Variation of thrust with velocity. The three 
 curves show effect of changing weight (W = 1333, 
 2000 and 2666 Ibs.) and loading in proportion (W/S 
 = 4, 6 and 8), wing-area being constant; parasite 
 resistance = 0.04 F 2 . 
 
THRUST CHARACTERISTICS 
 
 101 
 
 00 
 
 600 
 
 400 
 
 CO 
 
 D 
 
 300 
 
 100 
 
 20 40 60 .60 100 
 
 VELOCITY - ~ MILES PER HOUR 
 
 Fig. 38. Variation of thrust with velocity. The three 
 curves show effect of changing parasite resistance 
 (R = 0.02 F 2 , R = 0.04 F 2 and R = 0.06 F 2 ); weight 
 and loading constant (W = 2000 Ibs.; W/S = 6). 
 
, c (> .- f ^i ,- * ^ 
 
APPENDIX III 
 POWER CHARACTERISTICS 
 
 Horse power required is equal to thrust, in pounds, 
 multiplied by velocity, in miles per hour, divided by 375. 
 The following U-shaped curves show the variation of re- 
 quired power with velocity. (The power available forms a 
 U-shaped curve, as shown on outside cover.) 
 
 103 
 
POWER CHARACTERISTICS 
 
 105 
 
 160 r 
 
 itc 
 
 100 
 
 60 
 
 o 
 
 W 60 
 
 MINIMUM VELOCITY -# 
 
 VELOCITY - 
 
 io ea iqo 
 
 - MILES PER HOUR 
 
 Fig. 39. Required power at different velocities, when 
 W = 2000 Ibs.; W/S = 6; parasite resistance = 0.04 V 2 . 
 
POWER CHARACTERISTICS 
 
 107 
 
 100 
 
 ec 
 
 tO 40 6C 80 100 
 
 VELOCITY - - MILES PER HOUR 
 
 Fig. 40. Variation of required power with velocity. 
 The three curves show effect of changing weight 
 (W = 1000, 2000 and 3000 Ibs.) when loading is kept 
 constant (W/S = 6); parasite resistance = 0.04 F 2 . 
 
POWER CHARACTERISTICS 
 
 109 
 
 ICO 
 
 8 
 ES 
 
 2 
 
 I. 
 
 20 40 60 80 109 
 
 VELOCITY - - MILES PER HOUR 
 
 Fig. 41. Variation of required power with velocity. 
 The three curves show effect of changing loading 
 (W/S = 4, 6 and 8) when weight is kept constant 
 (W = 2OOolbs.); parasite resistance = 0.04 F 2 . 
 
POWER CHARACTERISTICS 
 
 111 
 
 140 
 
 120 
 
 100 
 
 M 
 
 I 
 
 I. 
 
 20 
 
 20 40 60 80 100 
 
 VELOCITY - - MILES PER HOUR 
 
 Fig. 42. Variation of required power with velocity. 
 The three curves show effect of changing weight 
 (W = 1333, 2000 and 2666 Ibs.) and loading in propor- 
 tion (W/S = 4, 6 and 8), wing-area being constant; 
 parasite resistance = 0.04 V 2 . 
 
POWER CHARACTERISTICS 
 
 113 
 
 90 
 
 O r 
 
 
 
 I 
 
 1 
 
 40 
 
 10 
 
 80 
 
 VELOCITY - - MILES PER HOUR 
 
 Fig. 43. Variation of required power with velocity. 
 The three curves show effect of changing parasite re- 
 sistance (R = 0.02 F 2 , R = 0.04F 2 and R = 0.06 F 2 ); 
 weight and loading constant (W = 2000 Ibs.; W/S = 6). 
 
APPENDIX IV. 
 CONTROL AND OTHER DIAGRAMS. 
 
 115 
 
CONTROL 
 
 117 
 
 Fig. 44. Distribution of pressure 
 on a single wing. Negative pres- 
 sure on the upper surface pro- 
 duces more lift than the positive 
 pressure on the lower surface. 
 
 PRESSURE 
 
 PRESSURE: 
 
 Fig. 45. Distribution of pressure on a 
 biplane. Negative pressure on upper 
 surface of lower wing is much reduced 
 by interference with the uppper wing. 
 
CONTROL 
 
 119 
 
 1 
 
 Fig. 46. Biplane Construction. 
 
CONTROL 
 
 121 
 
 a 
 
 Fig. 47. Balanced Control. 
 
 BALANCED RUDDER 
 
 FOOT BAR 
 
 RODDER POST 
 
 Fig. 48. Operation of rudder. 
 
CONTROL 
 
 123 
 
 EUCVATcm RAISED 
 
 NORXAL POSITION 
 CLEVATOR LOV2F.ED 
 
 Fig. 49. Stick control for operating elevator. To nose 
 down, push stick forward thus lowering elevator. To 
 nose up, pull stick back thus raising elevator. 
 
 FLAP AILERON 
 
 WHSEL CONTROL 
 
 STICK CONTROL 
 
 Fig. 50. Operation of ailerons for lateral control. Turning 
 wheel or moving stick to one side causes wing to descend on 
 that side. 
 
THIS BOOK IS DUE ON THE LAST DATE 
 STAMPED BELOW 
 
 : 
 
 AN INITIAL FINE OF 25 CENTS 
 
 WILL BE ASSESSED FOR FAILURE TO RETURN 
 THIS BOOK ON THE DATE DUE. THE PENALTY 
 WILL INCREASE TO SO CENTS ON THE FOURTH 
 DAY AND TO $1.OO ON THE SEVENTH DAY 
 OVERDUE. 
 
 
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 DEC 26 1935 
 
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 UNIVERSITY OF CALIFORNIA LIBRARY