THE LIBRARY 
 
 OF 
 
 THE UNIVERSITY 
 OF CALIFORNIA 
 
 LOS ANGELES 
 
 GIFT OF 
 
 BALDWIN M. WOODS
 
 MILITARY ALROPLANL5 
 
 AN EXPLANATORY CONSIDERATION OF THEIR CHARAC- 
 TERISTICS, PERFORMANCES, CONSTRUCTION, 
 MAINTENANCE AND OPERATION, FOR 
 THE USE OF AVIATORS 
 
 GROVER CjLOENING, B. Sc., A. M., C. E. 
 
 Author of "Monoplanes and Biplanes" 
 
 Formerly Aeronautical Engineer U S. Army, Chairman Technical Committee Aero Club 
 of America and Engineer with the Wright Co. 
 
 Since 1915 Vice-Pres. and Chief Engineer, Sturtevant Aeroplane Co. 
 
 FOURTH EDITION
 
 COPYRIGHT BY G. C. LOENING 
 ALL RIGHTS RESERVED 
 
 Printed by 
 
 W. S. Best Printing Company 
 
 Boston, Mass. 
 
 1917
 
 Engineering 
 Ubrary 
 
 TL 
 
 17 
 
 TABLE OF CONTENTS 
 
 CHAPTER I Introduction : 9 
 
 CHAPTER II Types of Aeroplanes 13 
 
 CHAPTER III Primarily for Reference 25 
 
 CHAPTER IV Air Resistances 41 
 
 CHAPTER V Inclined Surfaces 57 
 
 CHAPTER VI Aerodynamic Theory 69 
 
 CHAPTER VII Characteristics of Aerofoils 73 
 
 CHAPTER VIII Characteristics of the Aeroplane 89 
 
 CHAPTER I X Stresses and Safety Factors 105 
 
 CHAPTER X Assembly and Construction 121 
 
 CHAPTER XI Marine Aeroplanes 139 
 
 CHAPTER XII Flying, Stability and Airworthiness 147 
 
 CHAPTER XIII The Eyes of the Army and Navy 171 
 
 CHAPTER XIV Conclusion.. 175
 
 PREFACE TO SECOND, THIRD AND FOURTH EDITIONS 
 
 Although great strides have been made in the application of military 
 aeroplanes to problems of strategy and tactics, actual war lessons show 
 that the principles of design, construction, and flying remain the same. 
 Many important improvements in details, however, are given great im- 
 petus by the exacting and inspiring rivalry of war. 
 
 The object of this book, in assisting military aviators to acquire a 
 more intimate knowledge of their machines, appears to be attained, in 
 that at the military and naval aviation schools of several nations it has 
 been adopted. 
 
 These new editions are corrected, more conveniently re-arranged and 
 somewhat enlarged. 
 
 Boston, June, 1917.
 
 PREFACE 
 
 That military or naval aviators should desire to acquire a sound 
 knowledge and just appreciation of the machines to which, day after 
 day, they entrust their lives, is but natural. And at the suggestion 
 of the officers of the Signal Corps Aviation Section, the writer has 
 gathered together some information acquired in practical experience, 
 into the form of a text-book for flyers. 
 
 Based, in its composition, on questions asked and information 
 sought by military aviators, and written practically on the field, at 
 the largest aviation center in this country, with unusual facilities for 
 inspection, test, flying and discussion of aeroplanes every effort 
 has been made in this work to permit this practical atmosphere to 
 permeate its pages. 
 
 It is to be noted that enlargement on or repetition of any matter 
 contained in the author's previous work, "Monoplanes and Biplanes," 
 has been avoided. There is presented here a new text-book, limited 
 to the practical consideration of Military Aeroplanes in a manner 
 particularly applicable on an aviation field, and containing knowledge 
 that every aviator should have. 
 
 Occasion is taken to point out that the considerations of flying, 
 stability, airworthiness and performances, are based on experiences 
 of the author himself, in acting as observer, noting aeroplane move- 
 ments, reading instruments and taking observations, in flight (a specialty 
 to which the writer has devoted scores of hours in the air), particularly 
 in the extensive experimental flying on the Signal Corps aeroplanes 
 designed by him and piloted by Lieut. T. DeWitt Milling. To the 
 latter, the author wishes to express appreciation of much valuable 
 co-operation and assistance; and he is also indebted to Capt. Town- 
 send F. Dodd, Lieut. Walter R. Taliaferro, George Hallett, and Oscar 
 A. Brindley, expert aviator, for many valuable suggestions and assist- 
 ance in proof reading, and to Capt. Arthur S. Cowan, in command, for 
 every encouragement in this work. 
 
 Opportunity cannot too often be taken by aeronautical engineers 
 to recognize and pay tribute to the great work of the Aerodynamical 
 Laboratories, and in particular to the labors of the eminent French 
 engineer, Gustav Eiffel, whose exhaustive tests and their splendid 
 presentation form a basis for accurately predicting performances that 
 one cannot help but marvel at. This work, and the reports of the 
 British Advisory Committee, have been freely consulted, and refer- 
 ence frequently made to information they contain. 
 
 Coronado, Cal., May, 1915.
 
 MILITARY AEROPLANES 
 
 CHAPTER I. 
 
 INTRODUCTION 
 
 Although Aviation is a new field of human endeavor, its appli- 
 cation to the art of warfare is already becoming a specialty. Only 
 recently has it been appreciated, that military requirements have a 
 most vital and important influence on many features of aeroplanes 
 not only in the art of using them in military operations, but in their 
 fundamental design and construction. 
 
 It is planned, therefore, to give particular attention here to the 
 military aeroplane, as we find it today emerged from a crude state 
 of invention and development into a more or less finished product, 
 which, in the greatest war of history, has gloriously demonstrated its 
 strategical and tactical importance. 
 
 It is no longer necessary to speculate on the uses of aeroplanes in 
 warfare. What has actually been accomplished in directing artillery 
 fire, in reconnaissance, in dispatch-carrying, and in offensive work 
 has opened a new phase of warfare, as significant as it is surprising. 
 
 The technique of the use of aeroplanes in strategy and tactics, is 
 decidedly a subject for the military expert, but the general design 
 and construction of aeroplanes to accomplish certain definite purposes, 
 and their operation and maintenance in the field, are subjects that may 
 properly be considered here. 
 
 In addition to expert ability in their operation, it is found that 
 a sound and practical knowledge of the design and construction of 
 aeroplanes is exceedingly helpful to the military aviator. 
 
 A full consideration, therefore, is given to elementary theory and 
 practice applied in aviation, and the information used is primarily 
 designed to be of definite service, in the field, where many unforeseen 
 difficulties constantly arise. 
 
 Before taking up the determination of its elements, it is neces- 
 sary, clearly, to distinguish the aeroplane from other craft designed 
 to navigate the air. 
 
 Aircraft may be divided into the following classes :
 
 10 
 I. AIRSHIPS OR DIRIGIBLE BALLOONS. 
 
 The "airship," is distinctly a lighter-than-air machine, con- 
 sisting of a balloon or gasbag, containing a gas hydrogen for 
 example lighter than air, which by displacement of an equal 
 volume of air, gives a notation, the magnitude of which is de- 
 termined by the kind of gas, the size of gas container, and atmos- 
 pheric conditions. The ordinary free balloon is, in short, nothing 
 more than a harnessed "bubble," and the dirigible, or airship, 
 is a balloon of elongated shape, fitted with steering apparatus 
 and propelling mechanism. 
 
 Airships are constructed mainly in three different types, 
 the "Rigid," the "Semi-Rigid" and the "Flexible or Non-Rigid." 
 These designations refer, entirely, to the manner of combina- 
 tion of gas container and framework carrying the weights of en- 
 gines, etc. A flexible gas container, held in shape only by the 
 pressure of gas within and to which the load is hung, character- 
 izes the "Non-Rigid" system. A gas container, held in shape by 
 gas pressure, with an additional stiffening keel to which the weights 
 are attached, is descriptive of the "Semi-Rigid." Whereas, in the 
 "Rigid" system, a stiff, braced frame-work or hull, carrying di- 
 rectly the motors and loads, is formed to contain within it numer- 
 ous separate, drum-shaped gas containers instead of balloons. 
 The stiff frame provides, in itself, that necessary rigidity of hull, 
 which interior gas pressure on the envelope provides in the other 
 types. 
 
 The Zeppelin airship was the first successful development of 
 the rigid system. 
 
 A Zeppelin "Rigid" airship and above it an aeroplane. The airship can float at rest 
 but an aeroplane must acquire speed in order to fly.
 
 11 
 
 2. FLYING MACHINES. 
 
 The Aeroplane In distinction to the airship, supported in the air 
 by a buoyant gas, the aeroplane is supported by an upward wind 
 pressure, generated by its own speed through the air. This lift- 
 ing pressure is obtained on specially formed wing surfaces, which 
 are set at an inclined angle, and forced through the air at the re- 
 quired speed by an air propeller. Suitable auxiliary surfaces 
 and rudders are used to preserve the equilibrium of the craft and 
 to enable the pilot to steer it. 
 
 The Helicopter Air propellers are similar in character to marine 
 screw propellers, and not only are they made use of to push or 
 pull an aeroplane, but it has been proposed, in operating them 
 on a vertical axis, to use their thrust directly, in lifting loads. 
 This type of flying machine is called the "Helicopter" or "direct 
 lift" machine, and does not involve the principle of lift from the 
 inclined arched plane, used in the aeroplane. 
 
 The Ornithopter Nature's flying machines the birds are neither 
 screw propelled aeroplanes nor helicopters. They derive their 
 support from the wind pressure on their outstretched wings pre- 
 cisely as does the aeroplane, but for propulsion, the bird flaps 
 its wings in a rowing, weaving motion, which gives a forward 
 push. When an aeroplane glides, it resembles in character the 
 soaring of a bird, with wings outstretched, but attempts to de- 
 rive propulsion from a reciprocating movement of wings, have 
 not been successful, as yet. Machines of this type are called 
 "Ornithopters" or "Flapping-wing" Machines. 
 
 Although little has been accomplished with them, the possibil- 
 ities of the helicopter and ornithopter have by no means been fully 
 investigated, and whether or not a combination of "direct lift" and 
 aeroplane, often called the "gyroplane," has any future, is still a sub- 
 ject for study. 
 
 Airships, on the other hand, are very highly developed, and al- 
 though they are difficult to handle and very expensive, they are looked 
 upon as "battleships" of the air. Their design and construction are 
 full of interesting, and difficult, engineering problems, and it is planned 
 to give them consideration elsewhere. 
 
 In this connection it is important to point out, that the oft-stated 
 "principle," that aeroplanes are limited in size, due to a proportionally 
 greater increase in weight as the size is increased, is a fallacy, and, as 
 a matter of fact, recent work on large-sized machines, appears to demon-
 
 12 
 
 strata, that in proportion to the weight of the machine, as the size 
 increases, a greater excess load can be carried. (In later chapters this 
 feature will be further investigated.) Aeroplane "battleships" are, by 
 no means, an impossibility. The consideration of large-size aircraft, 
 therefore, becomes merely an efficiency comparison of the lift by gas 
 bag and the lift by air pressure on planes. If the dirigible balloon lifts 
 more "live load," per pound head resistance, at the same speed than does 
 an aeroplane, the dirigible is apt to survive. 
 
 Of the various kinds of aircraft, only one type of flying machine 
 is to be considered here, primarily, because we find the aeroplane, at 
 present, the most successful, the most economical and the best developed 
 means of navigating the air.
 
 CHAPTER II. 
 TYPES OF AEROPLANES 
 
 At the present time the early inventive stage in the development 
 of the aeroplane is gradually but perceptibly giving way to a state of 
 more precise engineering. And, in this step in its progress, aviation 
 is but following the course taken by almost every other art and sci- 
 ence. Any classification of aeroplanes, therefore, is subject to modi- 
 fication as newer craft are developed, and old ones rendered obsolete. 
 But the general principles of the machines do not change as rapidly as 
 do their concrete interpretations. 
 
 The principle of sustentation of an aeroplane from the upward 
 push of air flowing past it, has been stated, and, in the following chap- 
 ters, will be analyzed. The support being derived from the free air, 
 an aeroplane is readily subject to loss of balance, due to air disturb- 
 ances, gusts, convection currents, etc. It follows, therefore, that 
 many features designed to overcome loss of balance, are used on aero- 
 planes. Organs are also introduced to give the pilot control over the 
 craft within definite limits. 
 
 An aeroplane consists, therefore, of lift-generating surfaces at- 
 tached to a frame carrying motor, fuel, pilot and equipment, and in 
 combination with devices to balance and steer the craft. 
 
 Flying freely, in the air, an aeroplane has three axes of rotation. 
 
 1. It may ascend or descend, by virtue of changes in its longi- 
 tudinal path. The nosing up and nosing down of an aeroplane is termed 
 "pitching," as in boats. 
 
 2. An aeroplane, in flight, may change its direction of travel. 
 This is termed "yawing," as in boats. 
 
 3. In addition to these, an aeroplane can tip over to either side, 
 on a transverse axis, and this movement is termed "banking" or "roll- 
 ing." In making turns, it is necessary to "bank" up an aeroplane, 
 side wise, sufficiently to overcome the centrifugal force, and prevent 
 skidding. This "banking" is obtained by manipulating the lateral 
 control. 
 
 The locomotive driver, is steered by the tracks, and has to give 
 his attention, only to the control of the speed of his engine; an auto- 
 mobile driver, controls his motor, also, but in addition must steer his 
 machine; whereas the aeroplane pilot both steers and operates his 
 engine, and in addition must give his best attention, continually, to 
 balancing the machine, fore and aft and side to side.
 
 14 
 
 Like every science, Aviation has a language of its own, and a 
 method is used here of expressing this language in photographs. Study 
 of the explanatory caption and of the photographs themselves, there- 
 fore, is equal in importance to the reading of the text. 
 
 The types of aeroplanes considered here are typical ones of dis- 
 tinct features, and a more detailed discussion of their merits will be 
 found in later chapters. 
 
 THE "TRACTOR" AND THE "PUSHER" 
 
 An aeroplane, that is pulled through the air by a propeller situ- 
 ated at the front of the machine, is called a "tractor." 
 
 On the other hand if the propeller is back of the main lifting planes, 
 the machine is called a "pusher." These terms are very expressive 
 and very widely used. 
 
 The single propeller "tractor" is the most widely used type now, 
 but the "pusher" type, particularly for gun-carrying, has still a "raison- 
 d'etre." 
 
 The term "biplane" refers to an aeroplane with wings, super- 
 imposed, and "monoplane" to a single deck type of plane. 
 
 THE CONTROLS. 
 
 Since there are three axes about which an aeroplane may rotate, 
 it follows that three controlling organs are required : 
 
 1. The "elevator," for pitching; 
 
 2. The "rudder," for steering or "yawing;" 
 
 3. The "lateral" or "rolling" control. 
 
 The principle of the air force derived from an inclined plane, is 
 used in all of these controls. The "elevator" is inclined up or down, 
 to lift or depress the tail of the machine. The rudder is turned so 
 as to permit the wind to blow on it, to one side or the other, whereas 
 the lateral control consists, merely, in giving a difference in angle to 
 the two sides of the wings, causing one side to lift more than the other. 
 
 There are three general means of lateral control : 
 
 1. "Ailerons," or separate small planes, on either side independ- 
 ent of the main lifting surface; 
 
 2. "Wing flaps," or portions cut out of the main surface and 
 hinged thereto; 
 
 3. "Warping," which consists in twisting the main lifting sur- 
 face, so as to get a greater angle of inclination to the wind on one side 
 and less on the other. 
 
 In the construction of rudders and elevators, the necessary change 
 in angle to alter the wind pressure, is accomplished either by pivoting 
 the entire surface, or by turning a flap hinged to a fixed surface in front 
 of it.
 
 15 
 
 Above Rear view of tractor, with overhang wings, and wing flaps for lateral control. 
 Center Front view of tractor with ailerons. 
 
 Below Rear view of tractor with equal planes, and lateral control flaps on both upper 
 and lower planes. 
 
 The combination of fixed tail plane and movable flap is often termed a "flap and fin" 
 elevator.
 
 16 
 THE TRACTOR BIPLANE. 
 
 The form of aeroplane that at present approaches the nearest 
 to a standardized type is the Tractor Biplane. 
 
 The main lifting surface, as may be seen from the photographs, 
 consists of two super-imposed planes, with their widest dimension 
 across the flight path. 
 
 The main planes are attached to a long, fish-shaped body, termed 
 the "fuselage," which, in effect, is the backbone of the machine, since 
 it carries the motor and propeller at the front and the seats near the 
 center, while at the extreme rear are mounted the rudder and elevator. 
 
 The use of an enclosed fuselage in a tractor type is almost uni- 
 versal, and greatly increases the efficiency of a machine, by reduction 
 of head resistance in the wind. The disposition of the seats in the 
 body gives excellent protection to the aviators. It will be noticed 
 that two seating arrangements are shown "tandem," one ahead of 
 the other, and "side by side." The former is good for military scouting, 
 and the latter possibly for training. 
 
 In the types of tractor biplanes shown, the chassis is mounted 
 to the body, as is also the center section of the wings. By taking the 
 outer wings off, this type is readily made transportable by road. 
 
 The distinction between a double flap and single flap elevator is 
 shown in the illustrations, and there is also shown the difference between 
 ailerons and flaps for lateral control. 
 
 In the photograph of the biplane tractors in flight, several de- 
 tails show up clearly, ' particularly, angles of view of the pilot, whose 
 vision is interfered with by the lower plane. 
 
 PUSHER BIPLANES. 
 
 The older types of machines, particularly the early Wright and 
 Curtiss, were pusher types the Wright, however, had two propellers 
 and the Curtiss only one. These types were open-bodied, entirely 
 unprotected, and with the motor to the side of or behind the aviator. 
 
 A few years of development, led to the adoption of either a na- 
 celle short fuselage, protecting seats and motor only, or a fuselage. 
 In using a fuselage on a "pusher" machine, it becomes necessary either 
 to mount a propeller at the extreme rear "torpedo" fashion, to mount 
 a propeller on either side, or to have a propeller running on a large bear- 
 ing around the fuselage. In "pusher" flying boats the propeller tips 
 just clear the boat. 
 
 The earliest Wright machine had the elevator in front, so that 
 to ascend the elevator was turned up, thus lifting up the nose, and 
 vice versa; whereas, when it was later changed to the rear, for reasons 
 of stability, to ascend it became necessary to turn the elevator the 
 opposite way, thereby pressing down the tail. This distinguishes "front 
 elevator" and "rear elevator."
 
 17 
 
 MILITARY TRACTORS 
 
 Above Tractor with stagger, overhang, wing flaps and flat span. 
 
 Center Tractor with ailerons and dihedral span. The rudder has no fixed surface 
 
 in front of it, and being hinged so as to balance the air pressures, it is called a 
 
 "balanced" rudder. 
 Below Tractor with double flaps, high rudder and fins for directional stability.
 
 IS
 
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 MM 
 
 "PUSHER" BIPLANES 
 
 Above Left Wilbur Wright, the inventor, and the early type of Wright double pusher 
 biplane, with elevator out in front. Right Double screw pusher Wright biplane, 
 of later pattern, elevator in rear. 
 
 Center Twin screw, pusher fuselage biplane, with engine in front. 
 
 Bottom Left Early Curtiss open body, pusher one screw, three wheel chassis, 
 rudders in rear. Right Farman pusher biplane with nacelle or enclosed body. 
 
 A "fuselage" encloses motor seats, etc., but in addition serves as the main structural 
 unit of a machine, whereas a "nacelle" serves merely for wind protection, since a 
 separate frame carries the rudders. 
 
 The term "empennages" refers to the tail surfaces of a machine, whether they be "bal- 
 anced" or "flap and fin." 
 
 The term "fin" largely replaces the term "keel." It will be noted that the early Wright 
 machines have no fins or keels in the empennages. 
 
 The side surfaces of an enclosed fuselage are virtually keels.
 
 20
 
 21 
 MONOPLANES. 
 
 It has often been the custom, distinctly to separate biplanes 
 and monoplanes, as different types. This is hardly justified, since the 
 only distinguishing feature is the use of a single deck, "king post" 
 type of truss to carry the air pressure lifting load, in the monoplane, 
 and a double deck, "Pratt" type truss, in the biplane. Biplane sur- 
 faces, do interfere slightly with each other, but in tractors the disposi- 
 tion of motor, wings, body, rudders and even chassis, is identical, whether 
 biplane or monoplane. 
 
 A further misconception, in this connection, is that the monoplane 
 is faster than the biplane. The more recent speed scout biplanes have 
 proved the fallacy of this, and, in later chapters, it will be found that 
 biplane and monoplane are both similar aeroplanes, differing primarily 
 in wing surface bracing. 
 
 Several monoplane photographs are given on the opposite page. 
 
 Monoplanes, like biplanes, may be tractors, pushers, open-bodied, 
 or have two propellers. Several European firms construct a body 
 and chassis, complete with rudders, to which either monoplane or bi- 
 plane wings may be mounted. 
 
 In general, the biplane carries more load, and the monoplane is 
 simpler in construction. But even these differences are fast disap- 
 pearing. 
 
 A distinct advantage of the tractor monoplane over the tractor 
 biplane, is found when the wings of the monoplane are raised slightly 
 above the body, thereby enabling the pilot to look under them and 
 to have a free and unobstructed view. 
 
 AEROBOATS OR FLYING BOATS. 
 
 For the purpose of starting from and alighting on water, aero- 
 planes of tractor, pusher, or any type are readily modified. 
 
 Merely adding pontoons to a tractor, in place of wheels, gives 
 the hydro-aeroplane; and the construction of aeroplanes, fitted to 
 receive either wheels or pontoons, as circumstances require, has de- 
 veloped considerably. Craft of this kind are called "convertibles." 
 
 But in order to obtain greater sea- worthiness and better co-ordi- 
 nation in design, a special type of aeroplane has been developed, suit- 
 able only for over-water work. The keynote in its design is found 
 in its treatment as a boat with wings, rather than an aeroplane with 
 floats. The aeroboat, or flying boat, therefore, is primarily charac- 
 terized by a staunch, boat-like body, around which the rest of the 
 aeroplane is built. The photographs show several different types. 
 
 For further discussion of aeroboats and hydro-aeroplanes refer- 
 ence is made to the chapter specially devoted thereto.
 
 22 
 
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 23 
 THE "DUNNE" AEROPLANE. 
 
 In the preceding types, the auxiliary organs for pitching and yaw- 
 ing are separated from the main planes and are distinct. In the Dunne 
 aeroplane, there is only one set of controlling organs, and due to the 
 peculiar shape and construction of the machine, the control of yaw- 
 ing, pitching and rolling is combined and governed, only, by the double 
 wing flaps. As may be seen from the illustrations, the main planes 
 are set in a "retreating" position. Their position in plan, and their 
 angle setting, give inherent stability characteristics, which will be taken 
 up irf a later chapter. 
 
 The "Dunne" principle of a retreating plane is used, though in 
 a modified way, in the German aeroplanes, called "Pfeilfliegers" or 
 "Arrowplanes," but the customary fuselage and rudders are retained. 
 The German "Taubes" are monoplanes with pigeon-like retreating 
 wings. (See p. 170.) 
 
 It may be stated here, that the "retreating" planes have much 
 the same effect as a dihedral angle, on lateral stability, but are not 
 so sensitive to side puffs. The effect on pitching stability, obtained 
 on the Dunne, by the negative incidence at the tips, can be had, though 
 in a lesser degree, on the more ordinary types of aeroplanes, by a nega- 
 tive setting of the tail planes. While "inherent" stability is descrip- 
 tive of that obtained by the construction of the aeroplane itself, in shape, 
 
 THE U. S. ARMY DUNNE TYPE BIPLANE 
 
 The changing wing section and reducing angle of incidence are clearly seen. 
 
 The bustle is used to deflect the air sideways. The wing flaps on upper and lower 
 planes, are the only means of control. To ascend all flaps are turned up, and to de- 
 scend they are all turned down. Inverse movement rolls the machine laterally, causing 
 it to turn.
 
 24 
 
 wing setting, balance and fin disposition, a clear distinction is drawn 
 between stability of this type and that obtained by adding to any aero- 
 plane an auxiliary mechanism, designed to be actuated by movements 
 of the aeroplane, and automatically operating the controls, for proper 
 corrective effect. Such a mechanism is virtually an automatic pilot, 
 and is often termed, a stabilizer. "Automatic" stability may be ob- 
 tained, by use of a mechanism of this nature, on an aeroplane that is 
 inherently lacking in stability. 
 
 There are many other types of aeroplanes, but their general features 
 resemble those described, and the art moves too quickly to give 'them 
 all consideration. A general idea, of the various types, having been 
 given, a more detailed study of the aeroplane may be taken up. 
 
 STURTEVANT MILITARY TRACTOR 
 A load-lifting type, built almost entirely of steel construction.
 
 CHAPTER III. 
 PRIMARILY FOR REFERENCE 
 
 As much as possible, mathematics are avoided in the technical 
 parts of this work. Where formulae are of real help, however, in stat- 
 ing clearly the relation between quantities, they are used and fully 
 explained. 
 
 In a field like this one, so eminently practical in its nature, com- 
 mon-sense is of much greater benefit than abstruse scientific knowl- 
 edge. There is justification for decrying the vast amount of com- 
 plicated mathematics that have been built up on fundamental assump- 
 tions which the practical air pilot knows are wholly erroneous, but 
 in doing so, let us not forget that scientists and the laboratories have 
 contributed a great and valuable share, in advancing the aeroplane's 
 efficiency. 
 
 It is praiseworthy in presenting a subject, to simplify it, and to 
 avoid a too technical impression, but where this is at the expense of 
 a clear and full understanding, it is inadvisable. 
 
 Aeroplanes, as machines, naturally involve many scientific ele- 
 ments, and it is certainly best, at the outset, to realize this and to ac- 
 quire a working conception of what they are. 
 
 1 . It is necessary to know the simpler types of equations and why 
 they are so handy. 
 
 2. The elements used in solving triangles, such as sines and cosines 
 of angles, should be familiarized, and a logarithm table is sometimes 
 very convenient. 
 
 3. Mechanics dealing with momentum, inertia, accelerations, 
 centrifugal force, and gyroscopic force, should, at least, be understood, 
 and a comprehensive review should be made of Elasticity, Stress and 
 Strain, and Fluid Motion. 
 
 4. A clear conception of Work, Energy, Power and Power Ef- 
 ficiency, is of fundamental importance. 
 
 5. Graphical representations, composition and resolution of forces, 
 are constantly of use. 
 
 6. Various modes of representing variations of quantities on 
 charts, serve as the basis of recording air pressure results, and should 
 be fully appreciated. 
 
 7. The relative values and conversion factors of different sys- 
 tems of units, are most useful, and areas, volumes, etc., are frequently 
 called for. 
 
 Recalling these elements is made simpler, if a brief summary of 
 the features particularly applicable to this study be given.
 
 26 
 FORMULAE. 
 
 To attempt to present a study of flight without any formulae 
 would make it necessary to express relations between quantities in 
 long paragraphs of words, that could more readily be stated in simple 
 equations. 
 
 There is nothing mysterious about an equation. 
 
 It is merely a sentence tersely expressed. 
 
 Thus, if it was desired to state the rule that the quantity A mul- 
 tiplied by twice the quantity B is equal to C, the formula represent- 
 ing this would be, 
 
 Ax 2B = C 
 
 Each letter or symbol in a formula represents some factor that 
 is substituted when its value is known. If A = 16 and B = 4, then 
 C = 128, since, the rule interpreted, reads, 
 
 16 x 8 = 128 
 
 Besides equations, other relations may be represented by formu- 
 lae. Thus, the sign " c ," signifying "varies as," would permit the 
 statement that "wind pressure varies as the square of the velocity 
 of the wind," to be expressed 
 
 P oc V 2 
 
 Equations are of two kinds, derived and empirical. A derived 
 equation is susceptible of proof, by use of mathematical processes 
 based on proven assumptions. 
 
 An empirical equation is neither derived nor proven. It is merely 
 a statement of the results of experiment, regardless of mathematical 
 proof. 
 
 In many branches of engineering, empirical formulae are con- 
 stantly used, and in Aviation, the lack of a satisfactory basic theory 
 of air flow makes empirical formulae based on experiment, most neces- 
 sary. 
 
 Empirical formulae are really experimental averages. As an 
 example: The theory of long columns, has not as yet permitted of the 
 mathematical derivation of a satisfactory set of formulae for the stresses. 
 Very extensive experiments have been conducted therefore, on the 
 loads necessary to deflect and break such columns. Grouping these 
 experimental results together it is found that if 1/d denotes the length 
 ratio of a certain column, and p, the stress per square inch of cross 
 section, the average of the experiments, may be expressed as 
 p = 32,000 - 277 1/d 
 
 This is strictly an empirical formula. The engineer is interested 
 in its practical application, not in its derivation, and when a column 
 of this type is to be designed, for any value or 1/d he can find the value 
 of p. 
 
 Formulae of empirical nature are fundamental in a study of Aviation.
 
 27 
 
 It is often found necessary, particularly in an experimental field, 
 to introduce numerical constants, to balance the two sides of an equa- 
 tion. It may be known, for example, that the horse-power of a pro- 
 peller varies as the cube of the revolutions and the fifth power of the 
 diameter, but we could not express this relation as an equation, capable 
 of solution, until a numerical factor is found which gives a value to the 
 h. p. (horse-power) for any r. p. m. (revolution per minute) or diameter, 
 that agrees with the experimental results. 
 
 Thus the relation could be written, 
 
 H. P. = kN 3 D 5 
 
 but unless k = 1, the equation cannot be solved until a value of k is 
 found. Since the equation is empirical, it becomes necessary, actu- 
 ally to try many propellers, until an average is found. As a matter 
 of fact, k, in the above formulae, has been determined by experiment 
 to be 0.54 when certain units are used. The formula becomes, 
 H. P. = 0.54 N 3 D 5 , 
 
 and is capable of simple arithmetical solution by substituting values 
 for the letters. A term like k is called a "constant." 
 
 The majority of formulae for air pressures involve "constants," 
 and the great advance in designing during the past two years may be 
 traced directly to the determinations by the aerodynamic laboratories, 
 of better values of these constants, for use in empirical formulae. 
 
 SOLVING TRIANGLES. 
 
 Every triangle has six parts, three sides and three angles, and if 
 we know any three (including a side) the triangle may be solved 
 that is the other sides and angles may be determined. 
 
 Triangles may be solved in two ways : 
 
 1. By trigonometry. 
 
 2. By graphical methods. 
 
 In aviation work only the simplest trigonometry is used, and 
 about the only functions of angles used are the sine, the cosine and 
 the tangent. It is well to recall, here, that "sine" and "cosine" are 
 merely numerical ratios, representing the fractions that certain sides 
 of a triangle are to the hypothenuse. 
 
 The accompanying chart shows what these functions are, and 
 also gives formulae for solving the triangles. 
 
 In later chapters it will be found that in the representation and 
 solution of forces, in the determination of angles of incidence, glides 
 and climbs, and in stress determinations, many occasions arise for 
 solution of simple triangles. 
 
 But in aeroplane work great accuracy of computation is not ne- 
 cessary, so that a simpler way of solving triangles may, at times, be 
 used, i. e., the graphical method. This consists merely in a mechani- 
 cal process of laying off on a sheet of paper the known angles, by a
 
 fcvn ANC,(I 
 
 < /> *, 
 
 O(_ Yart^s o* 
 :; equals in fmfcrtm 
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 fnint/lf fcbefcd ' 
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 7T fa) -3, 14 1 1 
 A- Angle 
 
 V~ n* rwr 
 
 fan - 
 
 CCS - 
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 (ptyiai) ScliiK/i tfa triauq/f 
 
 4/HW7, OIX)>? ~ 7C* Jxtr - ^"^/?//3 4-Yt.JL 
 
 J t any* T, nntl jdn a arul b 
 
 Pint eeotlTufl tint Af, -t A AJf, <7/iy Av ///i y 
 tfl^olfl, lay cff asx)* "/ 7' "'") prvlroclcr. Rvjrrl lint BY 
 
 HV<r BY, mltrsrds M - **>' "- .- 
 I? cfarv^t-/* founil,. 
 
 Jrj de*ertrjin/ry tfr jjyn oj fvftetKrv t -> or 
 it ti irmrty necrnory to imit t >fy>+ 
 
 I. - /III datOrres fsfur^lxi </i>arf, l,tr AB, 
 Off wflrt Onti ctutonns fft,ir,alfct 
 
 /III ctislamn estimated -k>nnt *4e right , <7> CA 
 pevt-^ and Jatomfj rrtirrfrd -h Ht 
 
 I.- The 3**} cfafihxe tr 
 SiQes cf tyeir ctecxtt a 
 
 fine ^ots e*1 n/t thc/udcd orxjlr arf 
 /<*> /r './< meal /i e Ae tyf>f 
 
 s-ts' : t^f :: t-c':s-s 
 
 fesC* - o-W (^ = ^?_' 
 
 VARIOUS MATHEMATICAL SIGNS - FORMULAE FOR AND GRAPHICAL 
 SOLUTION OF TRIANGLES -AND FUNCTIONS OF ARCS
 
 29 
 
 protractor, and the sides to some convenient measurement scale. By 
 closing the triangle, all that is necessary in order to determine the 
 other sides or angles, is to measure them off. At first sight, this seems 
 to lack the value of preciseness, but if a large enough scale is used, 
 it is surprising how quickly and correctly, triangles may be solved in 
 this way. 
 
 In aeroplane studies the use of logarithms is rarely justified ex- 
 cepting possibly in propeller determinations, where formulae involv- 
 ing, for example, the fifth power of the diameter, D 5 , are used. 
 
 It may be recalled that a logarithm is merely the exponent, like 
 five in the above, to which it is necessary to raise 10, in order to pro- 
 duce the given number. 
 
 It will suffice to give here, the method of determining powers of 
 numbers. For example, in determining D 5 , a laborious calculation 
 is avoided by looking up the log of D, multiplying it by five, and find- 
 ing the number corresponding to the log represented by this quotient. 
 
 The occasion will rarely arise where logs have to be used, or even 
 trigonometry, if graphical methods are pursued. 
 
 MECHANICS. 
 
 Mechanics is the most logical of sciences the causes and effects 
 are so evident. It is often defined as the science that treats of the ac- 
 tion of forces upon bodies. And anything that concerns the action of 
 air forces on aeroplane wings and bodies, is of vital importance here. 
 It is almost needless to recall, that as long as the propeller is pulling 
 or pushing, or the aeroplane gliding, it is storing up momentum, which 
 is defined as the product of the mass m by the velocity v at any instant ; 
 whereas, inertia is that property of a body by virtue of which it tends 
 to continue in whatever state it happens to be, until acted upon by 
 some other force. 
 
 Velocity and Acceleration. 
 
 Acceleration of a particle is the amount of increase or decrease 
 of its velocity in a unit of time. In other words, while the velocity 
 is rate of motion, acceleration is rate of change by velocity. 
 
 A force is equal to a mass multiplied by its acceleration, because 
 it is universally agreed that a force be measured by its effect in chang- 
 ing the velocity of a particle. When we measure weights in pounds, 
 we actually measure the force of the earth's attraction, which is equal 
 to the mass of the body times the acceleration of gravity, g, which 
 increases the velocity of a particle 32 feet per second every second. 
 
 Therefore w = m x g. So that when the mass of a particle is 
 considered, it must be recalled that it is equal to what we call the "weight" 
 divided by acceleration of gravity or
 
 A body falling freely under the action of the constant pull of the 
 earth, disregarding the retarding effects of air resistance, is an example 
 of uniformly accelerated motion. It must not be forgotten that in a 
 vacuum all bodies, whether a feather or a piece of lead, fall at the same 
 speed. Air resistance, alone affects rate of fall, in free air. 
 
 It is useful to recall, that a falling body attains a velocity v in 
 feet per second, falling a distance h feet, represented by 
 
 v = \/2gh 
 where g = 32 feet per second per second. 
 
 Rotary Motion and Centrifugal Force 
 
 In a circular orbit of radius r a particle making in revolutions per 
 second, covers in each revolution the circumference, 2 TT r, so that its 
 velocity in feet per second 
 
 v = 2 TT r n 
 
 The numerical value of this velocity is solved by the above equa- 
 tion, easily enough, but the particle swingng in a circle is constantly 
 changing the direction of its velocity. This change in v, involves an 
 acceleration, and since the particle has mass, it follows that a force 
 is introduced, which is constantly making or trying to make the particle 
 hold its circular path. This is the centripetal force. 
 
 The force acting from without and tending to make a particle 
 take a curved path is called centripetal force, and is the opposite to 
 centrifugal force. 
 
 Since this acceleration towards the center of the circle is equal 
 to v 2 /r, it follows that 
 
 V 2 W V 2 
 
 Centrifugal force F = m x = 
 r gr 
 
 where w is the weight in pounds, v is speed in feet per second, r is the 
 radius of the orbit in feet and F is the force. 
 
 The Pendulum 
 
 What applies to the speed with which weights fall, applies also 
 to the simple pendulum. No matter what the weight of the pendu- 
 lum, it is the length of arm 1 alone, that governs the period of oscillation. 
 This period, 
 
 P = 2 7T V~T7g~ 
 
 Moment of Inertia. 
 
 Inertia has been defined, but "Moment of Inertia" must be con- 
 sidered when we come to rotary motion. 
 
 Moment of inertia is the quantity obtained by multiplying the 
 mass of each particle of a body by the square of its distance from the 
 axis. Whether a propeller, a flywheel, or a wing spar, every object 
 has a "moment of inertia" I, about any axis. It would be a laborious
 
 31 
 
 computation to find I for various shaped bodies. Fortunately it has 
 been done for us, and values are given later in a table. I is expressed 
 in pounds x feet squared (Ibs. ft. 2 ). 
 
 Angular Velocity 
 
 The "radian" is often used as the measure of a distance along 
 the circumference of a circle. There are 2 TT or 6.28 radians, covered 
 in one revolution of a circle. So that one revolution per second, r. p. s., 
 equals 2 TT radians per second. 
 
 If w is called the rotational or angular velocity of a particle, and 
 n the r.p.m., then, 
 
 w = 2 Trn 
 
 It has been indicated that acceleration of a rotating particle, due 
 to change in direction, gives rise to centrifugal force. 
 
 But the rotational velocity of a particle, may increase or decrease. 
 This is called angular acceleration and is a rate of change of angular 
 velocity, called s. 
 
 Torque. 
 
 In linear accelerations, we have Forces, while in rotational accel- 
 eration, forces are also to be considered, but instead they are called 
 Torques. 
 
 Torque, T, also equals mass X acceleration, but in its case mass 
 is the moment of inertia and acceleration is angular. 
 
 1 
 
 .'. T = I x s x - 
 32 
 
 where T is in pounds weight x feet and s in radians per second per 
 second. 
 
 The Gyroscope 
 
 Linear motion and rotating motion have been considered. The 
 axis upon which a body is rotating can be moved in a linear motion. 
 
 In addition the axis of a rotating body may change its direction 
 continually. This brings us to the gyroscope. 
 
 An unbalanced force is of course necessary to change the direc- 
 tion of linear motion of a particle. 
 
 In the same way an unbalanced force is necessary to change the 
 direction of the axis of a rotating body. When a wheel is set rotat- 
 ing, the direction of the axle tends to remain unaltered, as long as no 
 unbalanced external force acts upon it. But when an unbalanced 
 force is applied suddenly enough the axle's fixed position in space gives 
 rise to a curious phenomenon, not only resisting movement by this 
 force, but actually causing the axle to move in a direction at right 
 angles to the applied force. It is unnecessary here to take up the 
 relation of this phenomenon to the earth's rotation or the derived formu- 
 lae, representing it.
 
 32 
 
 An example of gyroscopic force, however, may be given. If a 
 bicycle wheel is held out in front of one, by one end of its axle, and 
 set rotating clockwise as viewed by the holder, when the axle is pointed 
 down the tendency is for it to swing around and point to the left, and 
 any effort to point the axle upward, meets a pronounced resistance, 
 the axle at the same time turning sharply to the right. 
 
 The effect of this phenomenon on the aeroplane's stability is taken 
 up later. In steadying ships or monorail cars, or in stability devices 
 for aeroplanes, the movement at right angles to the direction of the 
 applied force of a sensitive "gyro" is made use of. 
 
 Elasticity Stress and Strain. 
 
 The phenomena which are associated with the distortion of bodies 
 due to stresses are excessively complicated, and one has but to think 
 of the many familiar properties of brittle substances, like glass or chalk, 
 elastic ones like spring steel or rubber, and plastic ones like clay or 
 wax, to realize that this is in itself a formidable study, much too ex- 
 tensive to be given anything but a meagre consideration here. The 
 importance of the study of Resistance of Materials, to aviation, can- 
 not be overestimated, since in the design of the aeroplane proper, this 
 is the branch of engineering that solves the fundamental problem 
 to build light and yet strong. 
 
 This necessary combination is one that truly represents a cri- 
 terion of the excellence of an aeroplane, as a structural engineering 
 unit, and although it often does not, nevertheless, the aeroplane should 
 involve the most refined, advanced and expert, structural features 
 that engineering development has made possible. It has been a great 
 detriment to aviation that so many of its devotees have failed to realize 
 that the very best material obtainable, and the most ingenious and 
 perfect construction, is still hardly good enough to bear the strains 
 properly. 
 
 Of all the great variety of solid substances, having almost every 
 imaginable degree of elasticity, softness, hardness and brittleness, 
 we are concerned in later chapters, only with the behavior under stress 
 of those which are used as materials of construction, such as steel, 
 aluminum, brass, linen, spruce, ash, glues, paints and rubber. 
 
 Of the three classes of substances, solids, fluids and gases, let it 
 be recalled, that an "elastic" solid, like spring-steel, can withstand 
 a stress which tends to change its shape for an indefinite length of 
 time, whereas a "plastic" solid, like wax, does not recover from strain 
 when the stress ceases to act. One must qualify the above, however, 
 since the best spring steel never completely recovers from distortion, 
 and even wax is slightly elastic. A fluid is a substance which at rest 
 has no power definitely to resist a stress, and when at rest it is always 
 pressing, normally, on the sides of the vessel containing it. A gas is a
 
 matter with no independent shape, adjusting itself to take the form 
 of the vessel in which it is confined, and tending to diffuse and expand 
 indefinitely. 
 
 Substances are of two kinds grained and ungrained. Glass 
 and water are examples of ungrained substances, while wood, steel, 
 and practically all materials of construction, have a grained struc- 
 ture. The grain in steel is well marked, and though often lost sight 
 of, it is most necessary in aeroplane work, that care be taken not to 
 put too great a stress across the grain of a steel plate. 
 
 Elasticity may properly be defined as the resisting property of a 
 body to motion of its molecules. 
 
 Strain is the distortion of a body measured at a given point. 
 
 Stress is the force by which the molecules resist a strain at any 
 point. Stresses are developed, and strains caused, by the application 
 of external forces. Each stress is accompanied by its own character- 
 istic strain. 
 
 Stresses are of five kinds Tension, Compression, Flexure, Tor- 
 sion and those induced by Fluid pressure. They are illustrated on an 
 accompanying cut. 
 
 It is a fact of fundamental importance in the theory of elasticity, 
 that however irregularly a body may be distorted, any small portion 
 of the body suffers that simple kind of distortion which changes a circle 
 into an ellipse, the change of shape consisting essentially of an increase 
 or decrease of linear dimensions in three mutually perpendicular direc- 
 tions, sometimes accompanied by a slight rotation of the small parts 
 of a body. 
 
 The stress on a body is usually represented as pounds per square 
 inch, or the force in pounds acting on a one-inch square part of the 
 body. The total force P on a body, divided by area A, of its cross- 
 section gives this unit stress which is called "intensity of stress." The 
 strain 1 accompanying this is not represented in actual inches or units 
 of total deflection d, but is given as a fraction of the span L of the piece, 
 such that strain 1 equals d/L. 
 
 The basic law of Resistance of Materials is that intensity of stress 
 p is proportional to strain 1. And to balance the proportion into an 
 equation, a constant is introduced, called E, giving the simple rule, 
 
 that 
 
 p = P/A = d/L x E = 1 x E 
 
 This constant E, is called the "Modulus of Elasticity," and is of 
 the greatest convenience in indicating what the proportion of stress 
 in a given material is to strain. Thus, it is readily seen that steel is 
 stronger than aluminum, when it is learned that E for steel is 28,000,- 
 000 and for aluminum 1,700,000.
 
 l/bnous hinds of Stresses 
 
 faflical SoMicv offerers 
 
 _^ / Iff** A. 4* 
 
 /, -Hen, 0' ><>*> 
 
 Y C **tC* t<t> 
 
 yiren faint - frrtf K trrrr arm , 
 
 / m JL dsfarrc? from hne of octto 
 
 fffanr tc fwnt of momfriK. 
 
 7fa t rrwmt of 'P ">ok~, <*** o .- J* on 
 
 ana " "C' ' " " " CrOm 
 
 7J?f immirrt- rj' P a arrti. cjcdtwist 
 
 Cembosrftcn of ' /tares 
 
 Xteral m1o a. rauHanT, 
 
 orftl if on? fatt 
 rf<xi J c ayitrr, kntfb e/talff. 
 
 ,!>> telgr ift.h 
 
 ,,*, 3 *, t 9 *, f- ><"". ol 
 
 ourr fy am * 
 ntl'i'i at* Jmwii ./w/", ?A,i are /** S ijotn, as *? 
 ** ar y y of Or* /. Ay mmwv^t O/.HJ Ibnt 
 h vckmt x/r on OUVTr /. 
 
 KINDS OF STRESSES - GRAPHICAL FORCE DIAGRAMS - CHARTS AND 
 
 GRAPHS
 
 35 
 
 For all materials, however, there is a limit beyond which the ratio 
 of stress to strain or coefficient of elasticity E = p/1, does not hold. 
 This region is called the "elastic limit" of the material, and while con- 
 siderable stress can be added beyond this, the material begins to stretch 
 out of all proportion and rapidly reaches the breaking away point, 
 which is called the "ultimate resistance." 
 
 When relieved of stress, before reaching its elastic limit, a ma- 
 terial will return more or less to -its former state, but when the stress 
 has exceeded the elastic limit the material takes a permanent set. 
 The forces necessary to bring any material to the elastic limit, and 
 the value of the ultimate resistance, are entirely matters of experi- 
 ment, from which are derived empirical values. 
 
 Fluids and Gases. 
 
 In liquids the phenomena of surface tension, capillary action, 
 cohesion, etc., are of but minor interest excepting in hydro-aeroplane 
 studies. It is important to recall of liquids, however, that the pres- 
 sure exerted on any part of an enclosed liquid, is transmitted undi~ 
 minished in all directions (air-pressure fuel tanks). When a fluid 
 is in motion it is being acted upon by an unbalanced force, giving it 
 velocity and by a pressure, or in other words, it has the energy of a 
 "velocity head" and a "pressure head." Any increase in one is at 
 the expense of the other. 
 
 A device very widely used for the measurement of velocities of 
 both water and air is the Pitot tube, which measures the velocity head 
 v = v / 2gh. It consists, merely of a bent tube with a nozzle, point- 
 ing into the relative flow and measuring by means of the length of a 
 column of liquid, the head h, which substituted in the above, gives the 
 velocity v. 
 
 In considering liquids the losses in head in long pipe lines and 
 the effects of expansion and contraction and of nozzles, are of inter- 
 est with reference to the gasoline and radiator connections. 
 
 Buoyancy and Specific Gravity should be considered. 
 
 A body immersed in a liquid or a lighter gas immersed in air, is 
 acted upon by a lifting force which equals the weight of the liquid or 
 air displaced. In other words, the law of Floating Bodies is to the 
 effect that a floating body will displace a volume of liquid of gas whose 
 weight equals its own. A body immersed in pure water has a flota- 
 tion of 62.4 Ibs. per ft. 3 
 
 The density of a substance is its mass per unit volume, while Spe- 
 cific Gravity of a substance is its weight as compared with the weight 
 of an equal "bulk" of pure water. So that, given the specific gravity 
 of a substance, it is necessary to multiply by 62.4 to obtain its actual 
 weight in pounds per cubic foot, since water weighs 62.4 Ibs. per ft. 3 
 Specific gravity is sometimes referred to other substances air for
 
 36 
 
 example. The specific gravity of gold is 19.26. Its weight per cubic 
 foot is consequently 1,200 Ibs. A table of weights and specific gravi- 
 ties is given later. 
 
 Gases are highly compressible, in distinction to water and solids, 
 and are perfectly elastic, though in distinction to solids their elasticity 
 is one of volume and not of form. 
 
 It must be borne in mind, with reference to gases, that the tem- 
 perature remaining the same, the volume of a gas is increased exactly 
 in the same proportion as the pressure is decreased. Or, the product 
 of volume X pressure equals a constant quantity. 
 
 The study of Aerodynamics which constitutes the major part of 
 this worJc, takes up the mechanics of gases, making it unnecessary to 
 give them further consideration here. 
 
 WORK, ENERGY, POWER. 
 
 Work is said to be done when a resistance is overcome, so that 
 movement takes place through a certain distance. The air propeller 
 which pulls against a resistance of 200 pounds, causing the machine 
 to which it is fixed to move 80 feet, is doing work, inasmuch as it is 
 continually overcoming this resistance. 
 
 The unit of work is the foot-pound, which is equivalent to the 
 work performed in moving one pound of weight through one foot of 
 space. 
 
 Work may be done in several ways pushing or pulling weights, 
 or working against pressures, such as the work performed by a piston 
 in driving a fluid of gas before it, which is equal to the intensity of 
 pressure X area of piston x distance traversed or stroke. 
 
 In the above example, the propeller is doing 16,000 foot pounds 
 work by overcoming a resistance of 200 pounds and moving against 
 it 80 feet. 
 
 Work, in whatever units it is expressed, is always "resistance 
 overcome" multiplied by "distance traversed." 
 
 Energy is distinct from work, in that it represents capacity to 
 do work, but not the actual work done. It is expressed in the same 
 units as work. 
 
 There are two kinds of energy Potential and Kinetic since a 
 body when at rest may have stored up "potential energy" due to its 
 peculiar position or condition, and when in motion, a body is capable 
 of performing work against a retarding resistance, due to its "kinetic 
 energy." 
 
 A reservoir full of water, capable of turning a water wheel, if re- 
 leased, is an example of potential energy, and another is the stored 
 energy in storage batteries or gunpowder. The weight of the stored 
 body x the distance through which it is capable of acting is the meas- 
 ure of potential energy.
 
 37 
 
 Kinetic energy or K. E. of a body, is equal to the work which must 
 have been done upon it to have brought it to its actual velocity from 
 a state of rest. While potential energy is due to the acquirement 
 of "strategical position," kinetic energy is due to the acquirement 
 of "tactical impetus" or velocity. 
 
 Kinetic Energy = wv 2 /2 g and is derived from the familiar rela- 
 tion v = V 2 g h since K. E. equals the weight of the body x height 
 from which it would have had to fall to acquire its velocity. 
 
 Finally, it becomes obvious that Energy exerted = Work done. 
 
 In referring to the amount of work done in a unit of time, it is 
 necessary to consider Power, which may be denned as the rate of doing 
 work. Whether the propeller in the above example traverses the 
 80 feet of distance in one second, or in one hour, the actual work done 
 in foot pounds is the same, since time is not a dimension of work. Ob- 
 viously, it would take more "power" to overcome any resistance in 
 one second than in one hour, and to measure power it is necessary 
 not only to consider the resistance and the distance traversed, but also 
 the time it takes to do it. 
 
 Power, then, is the number of foot pounds per second or per minute 
 or the number of mile-tons per year, if we choose to use such units. 
 
 The customary unit of power is the Horse-Power. 
 
 One horse-power equals 33,000 foot pounds per minute, or, 
 1 h.p. = 550 foot pounds per second. 
 
 Thus, when a weight of 5.5 pounds is moved 100 feet per second, 
 one horse-power is exerted. 
 
 An aeroplane,, with a resistance in the air of 200 Ibs., requires 29 
 h.p. when travelling at 80 feet per second, since 
 200 x 80 H- 550 = 29 h.p. 
 
 It is interesting to note here, with reference to the possibility of 
 man- power flight, that, for a few minutes a man can exert at the limit 
 200 ft. Ibs. per second, and for an hour about 100 ft. Ibs. per second, 
 less than l/5th of one horse-power. 
 
 Although much energy is generated and expended, the fact re- 
 mains that the sum total of all the energy in the universe remains the 
 same. Mechanical energy and heat are converted one into the other, 
 the heat of the boiler, taken from fuel coming from the earth, passes 
 into the engine and into parts which do work against various kinds 
 of friction, until finally the sum total of the mechanical energy has 
 returned to the earth, from whence it originally came, as heat. 
 
 The law of the Conservation of Energy is the most firmly estab- 
 lished of the laws of mechanics, and only by the creation of an addi- 
 tional amount of energy in the universe, which is impossible by any 
 known human agency, could perpetual motion be achieved, although 
 some magnetic and atmospheric phenomena may be used very nearly 
 to approach it.
 
 38 
 POWER EFFICIENCY. 
 
 Any machine, in order to accomplish an amount of work in a given 
 time, must have work put into it in proportion. Due to friction and 
 other losses, it is always true that the power obtained from a machine 
 is not as great as the power put into it. 
 
 Now, call P, the power delivered by a machine, and P' the power 
 necessary to put into it, then the ratio P/P' will be less than unity, ordi- 
 narily; it might be equal to 1, if the machine were a perfect one with 
 no losses but never can it exceed one. 
 
 The ratio of the power delivered by a machine and the power it 
 used in doing so is called the Power Efficiency of the machine. 
 
 We have used above an example of an aeroplane, with a flying 
 resistance of 200 Ibs., which, when it was travelling at 80 feet per second, 
 required 29 h.p. 
 
 If the h.p. of the engine were 50 h.p. then the efficiency would be 
 29/50 or 58%. 
 
 It is most important in this study clearly to understand the sig- 
 nificance of Power Efficiency. 
 
 FORCES REPRESENTED GRAPHICALLY. 
 
 The development of a simple notion into an extensive science is 
 well illustrated in Graphic Statics. 
 
 Based upon the elementary fact that a force can be represented 
 by a line, long enough to measure its magnitude to some convenient 
 scale, and placed so as to indicate the direction in which the force acts 
 with reference to some fixed point there has been built up a com- 
 plete science of the action of every kind of force, and in many cases 
 simple solutions are obtained for problems that would require com- 
 plicated mathematics. 
 
 For all ordinary engineering the numerical computation of the 
 characteristics of forces has almost entirely given way to their determi- 
 nation by machine-like graphical methods. In later chapters the 
 particular application of graphical methods to determine the stresses 
 in aeroplanes will be taken up. 
 
 It will suffice here to give a general idea of how the combined 
 effect of several forces can be determined, composition of forces : 
 and how a single force can be split up into an equivalent set of forces 
 resolution of forces. 
 
 The single force, that would have the same effect at a point as 
 a set of several forces, is called the Resultant. 
 
 Referring to the diagrams, illustrating the action of forces, it is 
 indicated that two forces of 4 and 9 Ibs. are acting at a point o. It 
 is desired to know what their combined effect is, so that a single force 
 could be placed at o that would resist their combined action. 
 
 The mechanical process of finding their resultant consists merely 
 in applying what is often called the "parallelogram of forces," p. 34.
 
 Graphically, the mechanical process is as follows: Lay off AB parallel 
 to the 4-lb. force, and from A lay off AC parallel to the 9-lb. force. Com- 
 plete the parallelogram to E, and draw AE. Then choose some scale, 
 such that AB when actually measured on the drawing measures 4 units, 
 and AC 9 units. With this same scale measure AE. It scales about 
 10 H units. 
 
 Therefore, its value is 10^ pounds. 
 
 Its direction is given by the direction of AE so that by drawing 
 the force through o, parallel to AE, and making it 10 V^ pounds long 
 to scale, we completely determine it in direction, magnitude and point 
 of application. 
 
 Finding the resultant of any number of forces, whether co-planar 
 or not, consists in finding the resultant of two, then finding the re- 
 sultant of this resultant and one other, and so on. 
 
 Moments are defined on the diagram as merely the forces times 
 their perpendicular lever arms, from the point about which moments 
 are taken. If the force is expressed in pounds and the lever arm in 
 feet, the moment is in foot-pounds. The unit is the same as in Work, 
 but obviously, moment expresses what could be termed the Potential 
 Energy of the force. 
 
 Scaling lever arms of forces, from diagrams to scale, is by far the 
 easiest and quickest way to obtain them. 
 
 Of course, if a point is in equilibrium, all the forces pulling one 
 way are balanced by forces pulling the opposite way. In the same 
 way the sum of moments of all the forces will be zero. This is a very 
 important conception to keep in mind. 
 
 The resolution of forces into parts or complements, along given 
 directions or axes, is indicated in the diagram, and is, briefly, a reverse 
 application of finding the Resultant. 
 
 The intricate-looking but simply-made stress diagrams of braced 
 frames, like bridges, are made of an elaboration of compositions and 
 resolutions of forces. 
 
 In all this graphical work, it is best to appreciate at the outset, 
 the necessity of learning the mode of procedure of laying off the lines 
 like learning to run a machine and then merely keeping the scales used, 
 clear and unconfused. Successfully to determine stresses it is as un- 
 necessary to know the theory involved, as it is for the average taxi- 
 driver to know the theory of why certain mixtures of gasoline and air 
 are explosive.
 
 40 
 
 Charts and Graphs. 
 
 The representation of the variation of something, as a graph on 
 a chart, is merely a convenient way of tabulating results. Instead of 
 having long, cumbersome tables, giving values, at certain intervals, it 
 is far easier to represent them on a chart. 
 
 If it is but appreciated that a graph is a table with values for all 
 intervals between the limits indicated, its convenience becomes very 
 evident. 
 
 Diagrams are given, as an example, of two types of co-ordinates, 
 the Rectangular and the Polar. 
 
 Graphs are used very extensively in studying Aviation, and the 
 power curves for Aeroplanes bid fair to become as universal as the 
 power curves for electric railway cars, etc. 
 
 The combination of several curves on the same chart is illustrated 
 in the diagram, and consists merely in keeping the same cross lines, 
 but assigning to them different scales. 
 
 SEVERAL VIEWS OF STURTEVANT SEAPLANES USED IN THE U. S. 
 
 NAVY
 
 CHAPTER IV. 
 AIR RESISTANCES. 
 
 The Aeroplane, having been described in a general way, and an 
 outline having been given of the ordinary conceptions of science ap- 
 plied to it, we can proceed with a detailed study of its various elements. 
 
 In considering the Aeroplane, three distinct features are pre- 
 sented : 
 
 1. The determination of the reactions of the air on the parts of 
 the moving machine, giving rise to resistances, lifting forces and thrusts. 
 
 2. The study of the construction of the machine to withstand 
 these forces. 
 
 3. The investigation of the stability and manner of operation of 
 the aeroplane, under the many conditions met with. 
 
 The determination of air reaction requires, at the beginning, a 
 clear understanding of the nature of the air and how it may be expected 
 to act. 
 
 It is well to realize that lifting forces and thrusts are no more im- 
 portant than are the resistances, at the expense of 'which flight is ob- 
 tained. And when it is found that for every ten pounds of air resistance 
 saved there can be carried an additional load of almost one hundred 
 pounds, the significance of low air resistance becomes apparent. 
 
 The late Edouard Nieuport, builder of the famous French mono- 
 plane, made one of the greatest single advances in aeroplane construc- 
 tion, in the past few years, by his practical development of aeroplanes 
 with very low head resistance. And after the introduction of his ideas 
 such rapid strides were made by constructors in the improvement 
 of the aeroplane's efficiency, that load carrying capacity was almost 
 doubled. Another lesson in the relative importance of the resistance 
 to motion of an aeroplane, is found in the development of high-speed 
 racing machines. It had been generally assumed that speed depended 
 almost entirely on having added power, but the development of the 
 Deperdussin monocoques proved that far better results could be ob- 
 tained by systematic refinement and reduction in the resistances. It 
 is needless to speculate on the speeds attainable in aeroplanes. The 
 nature of air resistance and its increase with speed as considered in
 
 42 
 
 this chapter, will lead to the realization that a high speed record of 130 
 miles per hour is not going to stand very long. 
 
 But it is not so much in the attainment of higher speeds that we 
 are interested in air resistances, as it is in the reduction of the power 
 necessary to fly. While fuselage and nacelle resistances are the largest, 
 attention must be given to the air resistance of wires, fittings, struts, 
 wheels, etc., the cumulative effect of which is surprisingly great. These 
 resistances, however, are distinct from the resistance to motion of a 
 wing that generates a lift. 
 
 The appreciation of the resistances of different forms and shapes 
 is of great value in the field in determining their effect on the efficiency 
 of a machine, and also on the stability, since changes in resistances 
 are apt to affect the center of air resistance of the machine, and con- 
 sequently the equilibrium of the air forces. 
 
 Occasions constantly arise in mounting bomb-dropping appar- 
 atus, guns and other extra equipment, and in repair work, where in- 
 formation of this kind is of value. 
 
 The Atmosphere. 
 
 The atmosphere is an ocean, consisting of a mechanical mixture 
 of several gases with water vapor, and even on the highest mountain 
 we are still living at the bottom of this ocean. The atmospheric en- 
 velope has a definite extent, and at any point exerts a pressure which 
 is given rise to by the weight of the amount of air above it. We are 
 constantly carrying around, therefore, on our shoulders, on the roofs 
 or buildings, everywhere, the weight of the column of air directly above. 
 The higher up, however, the less is the weight of air, and, consequently, 
 the less the pressure. Air being compressible this increase in pressure 
 with decrease in altitude affects the weight of air per cubic volume. 
 We would have quite an exact measure of height in the atmosphere, 
 in noting the corresponding pressure, were it not that this pressure is also 
 affected by temperature and great wave movements of the air ocean, 
 storms and winds. 
 
 As the temperature increases the density decreases, and the volume 
 of a pound of air increases at the same pressure. 
 
 The unit of atmospheric pressure is the mean pressure of the air 
 at sea level, at 60 F. and is called one "atmosphere." It value is 
 14.7 Ibs. per sq. in., and it causes the mercury in the barometer to rise 
 30 inches. Over one sq. ft., a pressure of one atmosphere is equiva- 
 lent to a weight of 2,116 pounds.
 
 43 
 
 For every 1000 feet increase in altitude the pressure decreases 
 about H Ib. per sq. in. At a height of 18,500 feet, atmospheric pres- 
 sure is one-half of that at sea level, and at a height of 40 to 50 miles 
 the air must be practically weightless. 
 
 At atmospheric pressure and 60 F., the weight or density of air 
 is .081 Ib. per cubic foot. 
 
 It is convenient to recall that air is about 1 /800th as heavy as 
 salt water, and 14 times heavier than hydrogen. 
 
 Nature of Air. 
 
 Since air has weight, it follows that, as a substance, it has inertia 
 and momentum. The possibility of night is due to the tendency of 
 air to resist movement. 
 
 In addition to this, air is very elastic, but at aeroplane speeds, 
 it may be considered, theoretically, as almost incompressible, like water. 
 
 Air is a "continuous" medium, each particle, naturally, tending 
 to hold together with every other particle, and the tenuous manner 
 in which any air disturbance influences adjacent air filaments is beau- 
 tifully demonstrated in photographs of air flow. 
 
 Disturbances of the air cause up and down currents, complicated 
 air vortices, aerial fountains, waves and pulsations, with changes in 
 the velocity and direction of air streams; and just as water boils so 
 will air boil, when heated. The action of the sun in boiling the air 
 over a dry, open space, can be distinctly felt when flying. 
 
 In the consideration of air resistances, however, it is assumed 
 that the air is uniform in flow, and at 60 F., and atmospheric pressure. 
 
 There is another very important conception, with regard to air 
 resistance determinations. Disregarding the effects of inertia and 
 acceleration of an object, the air pressures are the same in action, 
 whether the object is moved against the wind, or the wind against 
 the object. 
 
 Motion through the air gives rise to two distinct kinds of resis- 
 tance : 
 
 1. Pressure, generated by the impact of the air on an object, and 
 
 2. Friction, generated by the flow of the air filaments past the 
 surface of the object. 
 
 Characteristics of Air Flow. 
 
 Having defined air, the manner in which it flows may be con- 
 sidered. Air either flows smoothly past an object in stream lines 
 continuous filaments or it breaks up into swirls and eddies, due to 
 too abrupt a change in flow. The accompanying photographs of air 
 flow illustrate this.
 
 44 
 
 PHOTOGRAPHS OF THE EIFFEL LABORATORY IN PARIS, SHOWING 
 THE TESTING ROOM AND THE TWO WIND TUNNELS 
 
 ASPLCJ RKTIQ = 7 
 
 THE FLOW OF AIR 
 
 UPPER LEFT, A FLAT SURFACE -UPPER RIGHT, A SPHERE -LOWER 
 LEFT AND RIGHT, STRUTS OF DIFFERENT FINENESS RATIO
 
 45 
 
 It is apparent that a spindle or fusiform shape, gently dividing 
 the air at the front, and gradually permitting the filaments to close 
 together at the rear, will give a smooth flow, which amounts to the 
 same thing as a very low resistance. It is also evident that a flat sur- 
 face creates very great disturbance, and consequently high resistance. 
 
 The curve of the stream lines, necessary to prevent disrupting 
 them, may be computed for any speed, by applying fluid dynamics. 
 But it must be kept in mind that a form of this kind gives its low re- 
 sistance, only at one particular speed, since the path of flow is affected 
 by the speed. It is unnecessary here to take up the determinations 
 of these forms. If the stream lines flow smoothly past an object, and 
 close up again without eddies, it follows that the only resistance ex- 
 perienced is frictional. 
 
 There are many ways of determining the manner in which the air 
 flows past an object, such as noting the directions in which light silk 
 threads are blown, or introducing smoke or particles into the air and 
 photographing it. Ammonium Chloride is a very convenient smoke. 
 
 Importance of Visualizing the Air. 
 
 It is of great value in aeroplane work, to become accustomed to 
 visualize the streamline flow of air, and ability to "see the air" often 
 solves many problems of stability and reduction in resistance, with- 
 out any recourse to mathematics or measurements. Besides this, 
 there is offered in the study of air flow by photography, a field of in- 
 vestigation of great promise and absorbing interest. 
 
 It is a common experience that in a wind, at the front of a flat 
 surface, there is a dead region of air, where no wind is felt. Photo- 
 graphs show this air cushion clearly, and in Chapter VI this simple 
 conception is found to hold a valuable theory. 
 
 In stability discussions, effect of following planes, interference, 
 and propeller stream action, priceless secrets would be revealed if the 
 air could be followed in its every movement. 
 
 Determination of Air Resistance. 
 
 The nature of the action of air on objects has been considered, 
 but we must know in addition with what force in pounds P, the air 
 pushes on an object when it passes it at velocity V. 
 
 Applications of Theory to determine the magnitude of air pres- 
 sures, are given consideration in Chapter VI, but merely for reference, 
 since the best measures of air resistance have been obtained by actual 
 experiment.
 
 46 
 
 Methods of measuring the resistance of the air that have been 
 widely used, are the following: 
 
 1. Dropping surfaces from a height and measuring time 
 of drop and pressure, used by Newton, and Eiffel in his earliest 
 experiments. 
 
 2. The whirling arm, used by Langley, and consisting of 
 whirling the surface at the end of a large arm around a circle of 
 large diameter and recording the resistance automatically. 
 
 3. The moving carriage, an automobile, trolley or car, as 
 used in the experiments of the Due de Guiche, Canovetti, and the 
 Zossen Electric Railway tests. 
 
 4. By blowing or drawing air through a tunnel in which 
 the object or a model of the object is placed. This method is 
 the most modern and convenient, and permits of a uniformity of 
 the air current, which cannot be obtained as easily in the open. 
 
 In wind tunnels, the best practice is to draw the air in, through 
 screens and channels, that straighten it out, past the experimental 
 chamber, and thence to the fan. Practically all the great Aerodynam- 
 ical Laboratories use the wind tunnel method of experiment. The 
 prominent ones are, the Eiffel laboratory in Paris, the National Physi- 
 cal Laboratory in England, and the tunnel at the University of Goet- 
 tingen. The speed of the wind in the Eiffel laboratory can be brought 
 up to almost 90 miles per hour (40 metres per second), and its size 
 permits of testing many objects such as struts, to full size, and complete 
 models of aeroplanes to one-tenth full size. Such a magnitude per- 
 mits of exceedingly valuable determinations, and the work of the 
 laboratories is daily being applied with entire success to full-sized aero- 
 planes. 
 
 It must be borne in mind, however, that the air in a tunnel is con- 
 fined and that all tunnel results are not perfectly adaptable to machines, 
 unless suitable corrections are applied. 
 
 Measurements made in the laboratories consist of determining 
 not only the magnitude, direction and position of the wind forces, but 
 also in determining the distribution of air pressure over an object by 
 measuring the pressures at different points. 
 
 Air Resistance varies as V 2 . 
 
 It has been found by very careful and extensive experimenting 
 that the resistance of an object in an air stream is proportional to the 
 square of the velocity of the air. 
 
 In other words, if the velocity is doubled, it follows that the re- 
 sistance will be increased four times, or if velocity is five times as great, 
 the force on the same object would be twenty-five times as great.
 
 47 
 
 There are variations from this, however, due primarily to the 
 fact that friction resistance alone, as distinct from impact resistance, 
 varies as V 1 ' 8 increasing in less proportion than V 2 . On very large 
 surfaces, and particularly on dirigible balloons, of streamline shape, 
 the frictional part of the resistance is by far the greatest, and conse- 
 quently makes the total resistance increase in a proportion less than 
 V 2 . 
 
 For our purposes, however, the total resistance, of objects, in- 
 cluding the pressures and frictions, are considered as varying with V 2 . 
 
 Air Resistance varies as S. 
 
 The size of the surface area, on which the air acts, S, gives a mag- 
 nitude of air resistance that is in direct proportion to the size. If the 
 area of the object is doubled, the air resistance is doubled, at the same 
 air speed. 
 
 This experimental fact is also subject to modification, since, as 
 the size of surface increases, the pressures are somewhat greater in 
 proportion. But we can disregard this also without serious error. 
 
 Formula for Air Resistance. 
 
 It follows, therefore, from the above, that if we call P the force 
 generated by the air movement at velocity V against an object of area 
 S in cross-section, then P varies as SV 2 . 
 
 This at once leads to an empirical formula, for the air resistance, 
 if we introduce K to represent a numerical constant, which must be 
 determined for any particular shape by experiment. 
 
 It may be stated then, that 
 
 P = K S V 2 
 This is the fundamental formula of Aerodynamics. 
 
 The units used will be S in square feet, V in miles per hour and 
 P in pounds. 
 
 Although P also depends on the density of the air, sea level and 
 60 F., conditions are considered here and included in the value of K. 
 
 In this chapter we are interested in the air resistance of various 
 objects and parts made use of in flying machines and in adding 
 to the air resistance of these parts the air force on the wings, that must 
 be overcome to obtain the lift, we obtain the value of the total resist- 
 ance to motion that is overcome by the propeller thrust. 
 
 In view of the above formula, it becomes necessary, merely, to 
 review and average up the laboratory results, so as to obtain values 
 of K for the various different objects. 
 
 The most accurate determinations of the latest experiments are 
 made use of for this purpose and it is again emphasized that the values 
 of K given, include both the impact and frictional resistances.
 
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 THE RESISTANCE OF VARIOUS SURFACES AND BODIES
 
 Definitions. 
 
 In Aerodynamical studies it has become customary in defining 
 objects to use unfamiliar terms. 
 
 Aspect Ratio is a term used to define the shape of a surface, 
 and is the long span of the surface across the wind divided by the width. 
 
 Fineness Ratio is a term used to define the general shape of 
 bodies, and is obtained by dividing the fore and aft length of the body 
 by the greatest width across the wind. 
 
 Master Diameter is the greatest width of a body across the 
 wind. 
 
 Fairing is used to denote the additional "tail" or filler used to 
 make a poorly shaped body more streamline in form, thereby reducing 
 its resistance. 
 
 Diametral plane is the plane, passed through a body, facing 
 the wind perpendicularly, and cutting through at the master-diameter. 
 
 Normal plane is another expression for diametral plane, and 
 merely refers to the maximum cross-sectional projection of the body. 
 It also refers to a flat surface held normal (perpendicular) to the air 
 current. 
 
 Equivalent Normal Plane is the size of normal flat surface, that 
 would give the same resistance as does the body referred to. 
 
 It has been customary to refer to the air resistance of all bodies, 
 as a percentage of the resistance of a flat square normal surface under 
 the same conditions. 
 
 In this study, no such conception will be used, since values of K 
 for each particular body are studied, and the flat square normal plane 
 or surface is merely considered as one of several kinds of air-resist- 
 ing bodies.* 
 
 Flat Surfaces, 
 
 Normal to the Air Stream. 
 Square Planes 
 
 In square planes, normal to the air, the value of K is .003 for sur- 
 faces up to two or three feet square, and .0033 for very large surfaces 
 like the sides of buildings. 
 
 It may be stated, therefore, for aeroplane usage, that P, the air 
 resistance in Ibs., of a square surface, S sq. ft., in area, at a velocity 
 V miles per hour, is 
 
 P = .003 S V 2 
 
 Thus, for a surface 2 feet square, at 70 miles an hour : 
 P = .003 x 4 x 4900 
 P = 58.8 pounds 
 
 * Attention is invited to the author's work "Monoplanes and Biplanes," Chapt. II, 
 where a discussion of experimental results and many values of K are given.
 
 50 
 
 In curve No. 1 p. 48, the graph gives values of P in Ibs. per sq. 
 ft. for speeds up to 120 m. p. h. In the above example, at 70 m. p. h. 
 the graph gives P = 14.7 Ibs. per sq. ft., or 14.7 x 4 = 58.8 Ibs., since 
 S = 4 sq. ft. 
 
 Rectangles 
 
 The aspect ratio of a square is one. Rectangles have aspect ratios 
 above one, when presented normally to the air. 
 
 Up to an aspect of 5 or 6, K remains about .003. 
 
 An increase in the value of K is found for rectangles as the aspect 
 ratio increases. 
 
 When the aspect ratio of the rectangles increases to 15, K becomes 
 .0035 and on further increasing the aspect ratio to 30, K = .0038. This 
 is shown on the graph, p. 48. 
 
 A flat rectangle, perpendicular to the air current, with its dimen- 
 sion across the current, thirty times as large as its width, might be 
 met with in rods, temporary struts, etc., and it is interesting to note 
 how high the resistance would be. 
 
 Discs 
 
 The shape of flat surfaces also affects their air resistance. Pass- 
 ing from a square plane to a round disc, reduces K to .0028, so that 
 the air resistance of a disc 2 feet in diameter, at 60 miles per hour, is 
 P = K S V 2 = .0028 x .7854 x 4 x 3600 
 P = 32 pounds 
 
 In general rounded edges may be expected to reduce K, for flat 
 surfaces. 
 
 Parallel Normal Surfaces 
 
 Discs or flat rectangles, placed one in front of the other, interfere 
 with each other and exhibit a most important phenomenon. When 
 the discs are separated by more than two diameters, both receive pres- 
 sure; there is a pressure on the front disc somewhat greater than on 
 a single disc, K = .0031, and a very slight pressure on the rear disc. 
 But with spacing less than this, the rear disc ceases to have any pres- 
 sure, and instead undergoes a suction effect, which action actually 
 pushes it toward the front disc. The forward push of the rear disc 
 naturally reduces the total resistance of the two discs to a smaller value 
 of K, making it much less than a single disc, when the rear one is 1 J^ 
 diameters back of the front one. This phenomenon is given rise to 
 by the nature of the air flow, which is illustrated in the diagram. A 
 familiar application of this is where the racing bicycle rider follows 
 in the wake of a motorcycle pace-maker. 
 
 Various Shaped Bodies. 
 Cylinders 
 
 Passing from the disc to the cylinder, with the circular base facing 
 the wind, the resistance is found to be less as the length of cylinder
 
 51 
 
 is increased, until the length becomes greater than 5 diameters, when 
 the resistance is found to increase again. Some values of K are given 
 on the chart. K for a cylinder 7 diameters long is .002. 
 
 When this cylinder is capped by hemispherical ends, the value of 
 K falls to .0006, an interesting result. 
 
 When the cylinders are stood upon their bases various values 
 of K are given. It is most important to point out that for the two 
 cases corresponding with high aspect ratio the cylinder with height 
 very low in comparison to the diameter, and the long cylinder with 
 diameter very small in proportion to height the values of K are high. 
 
 Wires and cables are merely very long cylinders. Extensive ex- 
 periments have been conducted on them, and values of K found. For 
 smooth wires K = .0026, whereas cables are found to have considerably 
 higher resistance with K = .003. 
 
 Thus, a machine having 200 feet of 1/8 inch cable, giving a pro- 
 jected area of 200/96 = 2.08 sq. ft., will have an air resistance due to 
 the cables at 80 miles an hour of 
 
 P = .003 x 2.08 x 6400 
 = 40 Ibs. 
 
 This high value immediately suggests the advisability of reduc- 
 tion of cable resistances. In double cables, it would prove beneficial 
 to tape them together, so as to streamline each other. A graph is 
 given showing the reduction in resistance due to inclining the wires 
 i. e., staggered planes. 
 
 Experiments indicate that the vibration of wires does not increase 
 their resistance. 
 
 Spheres 
 
 The resistance of the air on spheres presents a study of interest. 
 The sphere is the simplest geometrical form, and, as a basic one, it 
 should long ago have served as the unit form for air resistance. Lack 
 of agreement in the experimental results of different laboratories was 
 only cleared up when Eiffel discovered that an increase of speed of the 
 air above 20 miles per hour caused a change of flow, due to the flatten- 
 ing out of vortices back of the sphere, which reduced the resistance 
 considerably. And that above this speed, the nature of the air re- 
 sistance remained constant. K = .00044, for a sphere, at speeds above 
 20 miles per hour, whereas at very low speeds K becomes .001. In 
 having a smoother flow at the higher speeds, less Ibs. of air are put 
 in motion, which means that the resistance is less. This action of air, 
 in tending to smoother flow with speed increase, is important to bear in 
 mind. 
 
 For a hemisphere, convex side to the wind, K = .00083, and when 
 turned so as to present the concave side to the wind, K increases to 
 .0038.
 
 res. of o n t disc by tfatH 
 indicate direction of 
 
 The bodies are placed in 
 the order of their least resist- 
 ances. 
 
 For the top one K = .00012 
 For the lower one K = .0002 
 
 Bodies 
 
 some Masler Diameter oncf area far 
 h different fids find tenths y qs iesiect, 
 by ftffeJ, X wry/iy OS follows 
 
 \H>1h speed 
 16 Zo 36 do SO (,D 76 60 96 m fj.f) 
 
 .000* 
 
 TOP LEFT - INTERFERENCE OF FOLLOWING DISCS - TOP RIGHT, THE 
 
 BODIES TESTED AT GOETTINGEN - BELOW, BODIES TESTED 
 
 BY EIFFEL.
 
 53 
 
 Streamline Shapes 
 
 In this class may be included bodies of fusi-form or streamline 
 form, shaped for least resistance. Their application to the design of 
 tanks, fuselages, nacelles, hoods, etc., is of fundamental importance. 
 
 In a most interesting set of experiments, conducted by M. Eiffel, 
 on streamline shapes, illustrated in the diagrams and chart on p. 52, 
 the bodies consist of a nose, a cylindrical central portion, and a tail. 
 The results of the experiments show that : 
 
 1. The blunter the nose, the greater the resistance. 
 
 2. The shorter the central cylindrical portion is, for the same 
 nose and tail, the lower the resistance. 
 
 3. The effect of shortening up the tail is not very great, although 
 slightly increasing the resistance. 
 
 In each case, however, measurements made at speeds up to 90 
 miles an hour showed that the resistance does not vary as V 2 , the value 
 of K becoming constantly less with speed increase. This is a very sig- 
 nificant determination, and may be explained on the ground that, 
 in bodies of this kind, the major part of the resistance at high speeds 
 is frictional and therefore increases at much less than V 2 . In addi- 
 tion the effect of velocity increase is to flatten out the flow and suppress 
 eddies. 
 
 The values of K for these bodies are given. 
 
 The Goettingen Laboratory conducted extensive experiments on 
 the best shapes for dirigible balloons which it is important to consider. 
 The models tested measured 3.75 feet long and .62 feet in diameter, 
 giving a fineness ratio of 6. The shapes in their order of least resist- 
 ance and values of K for 25 m. p. h. are given. At higher speeds, still 
 lower Ks would be expected. 
 
 The form No. 1, having the least resistance, is, perhaps, the best 
 form that has ever been tested in a laboratory, and at high speeds 
 would give a resistance about l/25th of the normal pressure on its 
 diametral plane. It is the form used in the Parseval non-rigid diri- 
 gibles. 
 
 It is interesting to note in studying low resistance bodies, how 
 closely they resemble the shapes of fishes, and of birds, measurements 
 of a fast swimming fish showing an almost exact resemblance to this 
 Parseval shape. 
 
 As a general rule, the best streamline body is the one having a fine- 
 ness ratio of 6 and with the master diameter about 40% back of the 
 nose, both nose and tail being fairly well pointed. 
 Struts 
 
 The application of fineness ratios, and shapes of least resistance, 
 to improvement in the form of struts, has in many instances tremen- 
 dously improved the performance of aeroplanes.
 
 *l NPL 
 
 THE RESISTANCE OF SEVERAL STRUTS OF DIFFERENT SHAPE
 
 55 
 
 In addition to the form for least resistance, however, the weight 
 of the struts and their strength are factors that must be considered 
 in choosing the best shapes. We will confine ourselves here, how- 
 ever, to a study of the resistance of various shapes. 
 
 A group of strut sections are given and K for each one. It is 
 to be noted that the effect of yawing is greatly to increase these resist- 
 ances by presenting the strut sidewise to the air, and it will be neces- 
 sary later to consider the amount of this increase. 
 
 Inclining the strut to the vertical, as in staggered planes, has the 
 effect of increasing the length of section in the air stream, and, con- 
 sequently, the resistance does not decrease for streamline shapes, while 
 for blunter shapes, inclination reduces the resistance considerably. 
 
 In struts, as in bodies, an increase of velocity is accomplished 
 by a reduction in the value of K, that is more noticeable the greater 
 the fineness ratio, i. e., the longer the section of the strut. This is 
 again due, probably, to the preponderance of friction in the total re- 
 sistance. 
 
 The results obtained in studies of strut resistance indicate the 
 importance of having struts well made and of a uniform section. Just 
 as in bodies, abrupt changes in contour must be avoided and atten- 
 tion paid to a smooth curve on either side of the central portion. 
 
 It is found, in general, that a fineness ratio of 5 to 1 is best for 
 use, where a fin effect is desired, and where not, - the best fineness 
 ratio is 3 to 1. 
 
 Wheels - 
 
 The air resistance of chassis wheels is a considerable item in flight. 
 
 Experiments have been conducted on various-sized wheels, and the 
 
 results are as follows : 
 
 28^" diameter by 2^" tire, K = .0025 
 24 " " " 3 " " K = .00265 
 21 " " " 3 " " K = .0018 
 18 " " " 2 " " K = .0021 
 
 When the wheels are covered in, it is found in almost every case 
 that the resistance is halved, so that for the 24" x 3" wheel, when 
 covered in, K = .00133. An average K for wheels would be .002. 
 
 As an example, it is desired to determine the resistance of two 
 26" x 4" wheels at 80 m. p. h. 
 
 The projected surface = 1.4 sq. ft. 
 
 /. P = .002 x 1.4 x 6400 
 = 18 Ibs. 
 
 If the wheels were covered in at this high speed, about 9 Ibs. would 
 be saved in resistance; this would permit of carrying about 60 Ibs. 
 more load on an efficient machine, or would add 10 gallons more fuel.
 
 56 
 
 Fuselages and Empennages 
 
 The resistances of the bodies of aeroplanes, and of the tail pieces, 
 constitute the major part of the resistance, and their importance and 
 variations, with angles of yawing and pitching, make it necessary to 
 give them separate consideration in a later chapter. 
 
 It may, however, be pointed out that the data on streamline bodies 
 given, is readily applied to fuselages. The laboratories, however, 
 have studied complete aeroplane models and fuselages, and have ob- 
 tained valuable results. 
 
 Summary. 
 
 The data given in this chapter enables the air resistance of vari- 
 ous shaped bodies to be computed for any speed V and any size sur- 
 face S, where S is the maximum cross-sectional projection of the body, 
 perpendicular to the air stream. It is merely necessary to supply 
 the numerical values of K, S (in sq. ft.), and V (in m. p. h.), in the 
 formula 
 
 P = K S V 2 
 
 It is well, again to recall that the propeller of an aeroplane must 
 give a pull or push great enough to overcome : 
 
 I. The resistance to motion of the struts, wires, body, wheels, 
 fittings, skids, gas tanks and other attachments. 
 
 II. The dynamic resistance of the wings and rudders, called the 
 Drift and generated by the same pressure that gives the Lift. 
 
 In this chapter the first has been considered. And a study of the 
 second may now be taken up. 
 
 A TRACTOR AEROPLANE CLIMBING
 
 CHAPTER V. 
 INCLINED SURFACES. 
 
 In order to understand the mechanics of flying it is necessary 
 to have a sound conception of the nature of air pressure on inclined 
 surfaces. On a plane presented to the relative air current, at an angle 
 less than 90, the generated air pressure instead of acting straight back 
 is inclined above or below the line of flow of the air. 
 
 Before discussing this, however, a few unfamiliar terms need to 
 be defined. 
 
 Span is the dimension of a surface across the air stream. 
 
 Leading edge, is the first edge of the surface upon which the air 
 impinges, whereas, trailing edge, is the rear edge of the surface. 
 
 Chord, is the dimension between the leading edge and the trailing 
 edge of a surface. It is the depth of surface along the air stream. 
 
 Surfaces are of two kinds flat in section and curved in section. 
 
 Camber, is the rise of the curved contour of an arched surface, 
 above the chord line. 
 
 It follows from the above that for any inclined surface, 
 
 Span 
 
 Aspect Ratio 
 
 Chord 
 
 The explanatory diagrams on p. 60, are referred to, and it is seen 
 that any inclined surface, is one in which the chord is inclined to the 
 line of flow of the air. 
 
 This angle of inclination of the chord to the air stream is termed 
 angle of incidence. 
 
 If the leading edge of a surface is presented to the air, above the 
 trailing edge, the angle of incidence is said to be positive. And when 
 the surface is inclined negatively to the air flow, it is meant that the 
 air impinges on the top face of the surface, since the leading edge is 
 below the trailing edge.
 
 58 
 
 Lift and Drift. 
 
 The air acting on a surface presented to it with a positive angle 
 of incidence generates a pressure, the line of action of which is pointed 
 upwards and at the same time somewhat backwards. As the incidence 
 of the surface is varied, of course, the inclination of this force above 
 the horizontal is varied. But the important conception to grasp is, 
 that the effect of inclining the surface below 90, is to cause the total 
 air pressure to assume an inclined position, with respect to the axis 
 of flow of the air. 
 
 If the inclination is such that the total pressure points upward 
 and backward, a study of the resolution of forces teaches that the verti- 
 cal portion, or component, is equivalent to a force acting vertically 
 upwards, capable of lifting weights, whereas the horizontal compo- 
 nent of the same total air pressure is a resistance to motion. 
 
 It follows that in order to obtain this lifting component the hori- 
 zontal one must be overcome, the two together corresponding to the 
 resultant total pressure on the inclined surface. 
 
 Lift is the vertical component, called L. 
 
 Drift is the horizontal component, called D. 
 
 The resolution of the air pressure on an inclined surface into Lift 
 and Drift, is the fundamental process in the mechanics of the aeroplane. 
 
 Drift is a drag or resistance to motion which is overcome by the 
 thrust of the propeller, and at the expense of which a total inclined 
 pressure is generated on the aeroplane surfaces, the vertical compo- 
 nent of which is sufficient to support the weight. 
 
 Since Drift is a function of the pressure necessary to lift the weight, 
 it now becomes apparent why Drift was classified as distinct from the 
 head resistances of the various parts of a machine. The latter are 
 due solely to their form and the speed of travel, and they exert no effect 
 on the lifting power itself. 
 
 Consideration of this resolution into Lift and Drift, at once in- 
 dicates that the characteristics to be sought for in a surface are great 
 lift with a very small drift, so that for a minimum expenditure of power a 
 maximum load carrying capacity is obtained. 
 
 The ratio of lifting power, L, to drift D, is a function widely used 
 in considering the efficiency of surfaces, and the higher the value of 
 L/D the greater is the weight that can be carried per pound of resist- 
 ance. 
 
 It is well again to emphasize, that total resistance to motion is 
 composed of two distinct items. 
 
 1. The air resistances of the various parts of a machine, such as 
 struts, wires, wheels, bodies, etc. 
 
 2. Drift (in which is included the head resistance and frictional 
 resistance proper of the wings alone, at the particular angle at which 
 they are presented).
 
 Flat Planes. 
 
 It is necessary to draw a distinction between planes that have 
 a flat cross-section, and surfaces that have a curved cross-section, be- 
 cause the variations of the air pressures in magnitude, position, and 
 dirction are quite distinct. 
 
 Let P 90 represent the normal pressure on a surface set at 90 to 
 the air stream and determined as explained in Chapter IV, pp. 49-50. 
 And let P a represent the total pressure on the surface when it is set 
 at an angle of incidence A to the air stream. 
 
 It would be possible to express the variation of P a , with changes 
 in the angle of incidence a, as a percentage of P 90 = K S V 2 . This 
 would necessitate determining the ratio Pa/Pgo, which is called the 
 "ratio of inclined to normal pressure." Then 
 
 P a = P a /P 90 KSV 2 
 
 where K is chosen for the particular aspect ratio used (see p. 50). This 
 is the system ordinarily employed, but for our purposes it is consider- 
 ably more convenient to return to the conception of having values of 
 K tabulated for each separate item. So that we may call K a the value 
 of the constant in the expression 
 
 Pa = K a S V 2 
 
 and proceed to investigate the values of K a for different angles of in- 
 cidence, on the various surfaces. Thus, if we desire to determine the 
 total pressure on a surface set at an angle of incidence, a = 6, our 
 system of notation becomes quite clear, in stating 
 
 P 6 = K 6 S V 2 
 Lift and Drift. 
 
 It is a fundamental fact of aerodynamics, capable of proof, that, 
 in flat planes, P a is always perpendicular to the chord. This sim- 
 plifies the consideration of inclined pressures on flat planes, since at 
 any angle of incidence we know the direction in which the air pres- 
 sure acts. Thus, a flat plane, set at an incidence of 10, is acted upon 
 by an air force, the line of action of which is pointed 80 above the 
 direction that would be taken by the normal pressure. 
 
 This uniformity in the direction of P a , with reference to flat planes, 
 enables us to obtain very simple rules for finding the Lift and Drift 
 of flat sections. 
 
 Obviously from the resolution of forces. 
 
 Lift = P a cosine a, = K a S V 2 cos a 
 
 Drift = P a sine a, = K a S V 2 sin a 
 In addition, the Lift-Drift ratio, L/D = cotangent a. 
 
 To determine the magnitude of the forces on flat planes, there- 
 fore, it is merely necessary to know the appropriate value of K a , as 
 determined by mathematics or experiment. * 
 
 * In the author's work "Monoplanes and Biplanes," many relations for Pa are 
 considered, in Chapter III.
 
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 The definitions for flat and curved sections, given on p. 57, are shown at the top 
 of the page. 
 
 Curve 2 shows the variation of Ka, for aspects of 1/3. 1. 3, and 6. 
 Curve 3 shows the c. p. movement for the various aspect ratios.
 
 61 
 
 The variations of P a are affected by Aspect Ratio, and a very 
 remarkable distinction between squares and rectangles in the man- 
 ner in which P a varies as the incidence is changed was discovered by 
 Eiffel. At angles in the neighborhood of 40, on square planes, P a 
 was found to have values very much greater than P 90 . 
 
 Values of K a for several different aspect ratios are given in Curve 
 No. 2, p. 60. 
 
 It will be seen from this graph, that an increase of aspect ratio 
 above 1 is accompanied by increases of P a , at low angles. But there 
 is a general falling off of this at 15 to 20, as the aspect ratio is in- 
 creased. For efficiency, at low angles, on flat planes it is advisable 
 therefore, to use the higher aspect ratios. 
 
 In all cases, S is the plan area of the surface. 
 
 Center of Pressure. 
 
 Although the direction and magnitude of forces on flat surfaces 
 have been considered, these forces are not fully defined until determi- 
 nations are obtained of their point of application. 
 
 The nature of the air reactions on a surface consists of a series 
 of small impact pressures and friction rubs all over the surface; but 
 their total effect can be represented graphically by a single force, in 
 the resultant direction, and applied at a point about which all pres- 
 sures balance. 
 
 This center of balance of air reactions is termed the "center of 
 pressure," and if we draw thru it a force proportional to P a , and in 
 direction normal to the surface, we have completely defined the air 
 reaction on that particular flat plane. 
 
 On flat surfaces it is indicated by Curve 3 that, as the incidence 
 is decreased, the center of pressure moves forward until at 0, it is 
 very near the front edge, and at 90 it is at the center of surface. 
 
 The representation of position of center of pressure, c. p., as a 
 percentage of the chord, is a convenient one that has become quite 
 standard. 
 
 Example. 
 
 A typical example of the use of the data given for flat planes may 
 prove of interest. 
 
 An aileron, flat in section, measuring 2 ft. chord by 12 ft. span 
 (aspect 12 -5- 2 = 6), is pivoted 4 inches back of the leading edge. 
 The aileron is moved to an incidence of 10 and the air speed is 60 miles 
 per hour. 
 
 It is desired to find the corrective force on the balance of the ma- 
 chine represented by the lifting force of the aileron, at 10 incidence.
 
 62 
 
 Lift, L = K a S V 2 cos a. 
 From the chart we find that for a plane with aspect ratio of 6, 
 
 K a = .00175, 
 
 and Cos 10 = .985, S = 24 sq. ft., V 2 = 3600, so that 
 L = .00175 x 24 x 3600 x .985 
 
 = 149 Ibs. 
 
 In addition it is desired to know the moment of the total pres- 
 sure P a , about the pivot, at 10 incidence. 
 From the graph it is found that 
 
 c. p. position = .33 chord = .33 x 24 
 
 = 8 inches from leading edge. 
 
 It follows, therefore, that the lever arm of the total pressure P a 
 about the pivot is 4 inches. 
 
 P a = K a S V 2 = .00175 x 24 x 3600 = 151 Ibs. 
 Therefore, the moment about the pivot is, 
 = 151 x 1/3 
 = 50 foot Ibs., 
 
 which would enable the pounds pull on a control mechanism to be 
 determined, and leverages suitably arranged. 
 
 Curved Surfaces. 
 
 Although the general characteristics of the action of air on flat 
 planes had been known more or less accurately for some time, the nature 
 of air reaction on curved surfaces was not well appreciated until the 
 pioneer work of Lilienthal and the Wrights disclosed it. 
 
 Lilienthal discovered that, at low angles, surfaces slightly cam- 
 bered gave very much more lift and less drift, than did flat planes, 
 at the same incidence, and that the resultant total pressure was not 
 necessarily perpendicular to the chord, as on flat surfaces. In fact, 
 he found that at certain low angles of incidence the total pressure on 
 a curved surface was leaning considerably in front of the normal to 
 the chord line, which meant that a smaller proportion of this total 
 pressure was drift, and a greater portion was lift. 
 
 It is upon this discovery that the first practical demonstration 
 of the possibility of flight may be said to have originated, and suc- 
 ceeding generations are justified in hailing Otto Lilienthal, in view of 
 his classic experiments, as the discoverer of modern flight. 
 
 The Wrights, in their gliding experiments, discovered that the 
 center of pressure on an arched surface of Lilienthal type, did not change 
 its position, in the same way as the c. p. on a flat plane, but that in- 
 stead of moving steadily forward as the incidence was diminished the 
 c. p. on the curved plane ceased to move forward at about 10-15, 
 and retrograded, moving rapidly past the center of surface, towards 
 the trailing edge as the angle grew smaller. This feature rendered 
 Lilienthal's measurements somewhat inaccurate, but the corrections, 
 readily applied, were used to make the old results applicable to the 
 modern aeroplane.
 
 K L and K D 
 
 Since the total pressure on the curved surface, which we will call 
 Pi, is not necessarily perpendicular to the chord line its resolution 
 by trigonometry into Lift and Drift is not possible unless we know 
 its inclination with respect to the chord line. But, since this neces- 
 sitates knowing its components, it becomes, at once, more convenient 
 to study curved surfaces directly from measurements and data on 
 Lift and Drift. 
 
 This is done throughout the study of curved surfaces and aero- 
 foils (aeroplane sections), and in the laboratories it is customary to 
 measure the vertical and horizontal forces on curved surfaces. The 
 resultant of these determines PI, in magnitude and direction. But 
 since we are rarely concerned with Pi, where data is already available 
 on L and D, its consideration is not so important. 
 
 To define L and D, it is most convenient to consider that 
 
 L = K L SV' 
 
 D = K D S V 2 
 
 and* information on curved surfaces resolves itself into a study of the 
 values of KL and KD for the various angles and shapes. 
 
 In this chapter, the simplest geometrical curved sections only 
 are considered, as it is desired merely to bring out the main distinctions 
 between flat and cambered sections. 
 
 The standard practice is adopted of referring to the camber of 
 curved sections, as a fraction or percentage of the chord. 
 
 Forces on Cambered Planes. 
 
 The resolution of P into L and D is fully indicated in the diagrams 
 on p. 64. The angle of incidence of the chord with the air stream 
 is called i. But, since in cambered planes Pi is not necessarily normal 
 to the chord, it follows that the angle between Pi and L is not neces- 
 sarily equal to the angle of incidence i, as it is on flat sections. This 
 angle of the resultant with the vertical is called r, and from the con- 
 struction of the triangle of forces it is apparent that tan r = drift/lift, 
 and the ratio of L/D = cotangent r. 
 
 The nature and determination of "LilienthaPs Tangential" is not 
 considered necessary in this study, although it is frequently dwelt 
 upon in elementary aerodynamic treatises. * 
 
 Influence of Aspect Ratio. 
 
 The manner in which a change in Aspect Ratio affects the forces 
 on circular arcs is shown in the charts on p. 64. It is found that not 
 only the magnitude of L and D, but the movements of the center of 
 pressure are influenced very much as on flat sections. For a circu- 
 
 * See "Monoplanes and Biplanes" Chapt. IV, p. 47.
 
 (14 
 
 To find D at any angle, divide values of L by corresponding values of L/D. 
 
 .001 
 
 \L 
 
 n 
 
 
 TA 
 
 \ 
 
 z 
 
 
 sV 
 
 
 
 \ 
 
 CVKVE 
 
 NC,I OF INOPBNCE j. 
 
 O fO 20 30 40' JW 
 
 Of 7rtC/PrtC. 
 
 *C 
 
 15 
 
 10 
 
 90' 
 
 C. P fbstnor* f/-/?4crw oe CHOW) 
 
 Curve 4 shows coefficients Lift and Ratios of L/D for changes in aspect ratio, 
 of a circular arc. 
 
 Curve 5 shows the c. p. movements for the same surfaces.
 
 65 
 
 lar arc in which the camber is 1/13.5 of the chord (an average camber 
 for good efficiency), the values of L and L/D steadily increase as the 
 aspect ratio is increased from 1/3 to 6. The difference between aspects 
 of 6 and 9, however, is not very marked, and it is indicated from these 
 results that there is not much gained by increasing the aspect of an 
 aeroplane wing above 6. With reference to the total pressure Pi, 
 it is found for cambered planes as it was for flat ones, that when the 
 aspect ratio is 1 (a square), Pi rises to a value more than once and a 
 half times the normal pressure P 90 at an angle of about 40. 
 
 The center of pressure chart shows that as the aspect is increased 
 the reversal of movement at low angles becomes sharper, and the angle 
 at which this reversal takes place falls from 45 for aspect 1/3 to 13 
 for aspect 6. 
 
 Effect of Depth of Curvature. 
 
 Alterations in the camber, i. e., in the depth of curvature of cir- 
 cular arcs, greatly affect the magnitude of L and L/D, and the move- 
 ment of the c. p. In the charts, on p. 66 there are plotted, the curves, 
 showing the values of KL and L/D for arcs of 1/27 and 1/7 camber, with 
 an aspect of 6, which are to be compared with the curve for a 1/13.5 
 camber, aspect 6. 
 
 It will be noted that the magnitude of L increases with the in- 
 crease of camber, but the ratio of L/D is decreased by camber increase 
 and the point of maximum L/D varied. This indicates that deeply 
 cambered sections would prove to be inefficient wings for aeroplanes. 
 
 For the smaller camber, the c. p. movement is sharper, and the 
 reversal point further forward. 
 
 The Reverse Curve. 
 
 Sections of cambered surfaces may, of course, be other than cir- 
 cular. Combinations of straight lines and circular arcs, parabolic 
 curves, spirals, and the like, have characteric pressures that differ 
 from each other, but in so small an amount that it is hardly necessary 
 to give them separate consideration excepting in so far as they are 
 taken up later in studies of aeroplane wing sections. 
 
 The reversed curve, however, is a distinctive geometrical section, 
 to which attention should be given. These sections, as illustrated in 
 the diagram, have the important property that the center of pressure 
 continues to move forward as the angle is decreased, the character- 
 istic retrograde movement, as found on circular arcs, being apparently 
 absent. As will be explained later, this retrograde movement tends 
 towards instability, and although the ratio of L/D and L are very 
 greatly reduced by a reverse curve, it becomes necessary to bear in 
 mind that for aeroplane wing sections the loss in efficiency may be 
 worth while, in order to gain in stability.
 
 .005 
 
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 jOOl 
 
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 III 
 
 A 
 
 \ 
 
 fa 
 
 L IF7S - fun //VF3 
 l /p -fftfOJTfH UME2 
 
 W 
 
 ' 4" C 6 
 
 * t* /4' / /S" 
 
 /t/V<f/.fS OF 
 
 .3 4- 
 
 C. P. POSITION 
 
 Curve 6, shows the coefficients for Lift, and the values of L/D, for arcs of 1/7, 
 1/13.5 and 1/27 camber, and the reverse curve section. 
 
 Curve 7, shows the c. p. movement for the same sections.
 
 67 
 Aerofoils. 
 
 Only flat and the simplest geometrical sections have been con- 
 sidered here. In aeroplane wings, it is necessary to have spars and 
 ribs of considerable depth, in order to obtain suitable strength and 
 rigidity of wing. This leads to sections of surfaces in which two cur- 
 vatures must be considered the top face and the bottom face. 
 
 An aeroplane wing section is, therefore, distinct from geometri- 
 cal sections, and it is customary to refer to aeroplane types of sur- 
 faces as Aerofoils. They are treated of fully in Chapter VII, since 
 a knowledge of their characteristics, advantages and disadvantages 
 enables the first essential step in the design of an aeroplane to be taken 
 the choice of a wing section that will give the weight-lifting, strength 
 and speed combination desired. 
 
 Examples of the application of curved section pressures are taken 
 up in several instances in the consideration of aerofoils, and many of 
 them are deduced from actual practice as applied in well known types 
 of aeroplanes. 
 
 Summary. 
 
 I. In flat surfaces. 
 
 The total pressure P a is always normal to the section, and 
 can be resolved into, 
 
 Lift = P a Cos a 
 Drift = P a Sin a 
 
 The center of pressure moves forward as the incidence is 
 decreased. 
 
 II. In cambered surfaces. 
 
 The total pressure Pi is not always normal to chord, and 
 the pressures on a cambered plane are, therefore, more easily ex- 
 pressed as 
 
 Lift = K L S V 2 
 Drift = K D S V 2 ' 
 
 The center of pressure, on curved surfaces, moves forward up to 
 a certain low angle where it reverses and moves rapidly to the rear 
 (except for reverse curved surfaces).
 
 Photographs of air flow, showing air deflections, obtained at the author's labor- 
 atory, by introducing chemical smoke into the air stream. 
 
 Normal Surface Inclined Surface 
 
 DIAGRAMS OF AIR FLOW 
 
 Photographs of air flowing from left to right, on flat surfaces, made at the Kout- 
 chino laboratory. Note the general deflection of the air stream, in the lower right 
 hand photo, where the plane is at a low angle of incidence. 

 
 CHAPTER VI. 
 AERODYNAMIC THEORY. 
 
 Although it is not so essential to consider the theoretical deriva- 
 tion of formulae for air resistances in a work of this kind, a certain 
 interest is attached to the application of the more recent experiments 
 on the flow of air streams to the older conception of the mechanics of 
 the air. 
 
 An outstanding experimental fact in air stream photographic 
 studies, that vitiates many established aerodynamic derivations, is 
 that the air stream, when it impinges against a normal surface, divides 
 to pass around the edges, and in doing so actually imprisons a cushion 
 of dead air against the surface, a phenomenon constantly met with 
 in wind effects on moving vehicles, etc. Furthermore, in dividing, 
 the air stream acts as if separated by two physical surfaces and takes 
 a deflection of about 45, instead of being turned thru an angle of 90, 
 as assumed in older hypotheses. Many photographs of air flow, in- 
 cluding several taken in the writer's laboratory in New York, confirm 
 this. 
 
 The mechanics of air flow on normal surfaces, if the air is con- 
 sidered as deflected at 90, may be stated as follows: 
 
 Moving air develops a pressure equal to its momentum, expend- 
 ing its entire energy by impact. Momentum = mass X velocity. The 
 mass of air = W/g, where W is its total weight, and equal to the unit 
 weight or density of air w, X the volume of air moved, which is equal 
 to S V, where S is the surface in sq. ft. and V the velocity in ft. per 
 sec. 
 
 Supplying appropriate values we get for the total resistance, 
 
 P 90 = w/gSV 2 
 = .0054 S V 2 
 
 which is a formula of the form P = K S V 2 in which K = .0054. 
 
 This value of K we know by experiment is quite incorrect, and 
 it follows that we must consider the derived result worthless. 
 
 If, however, we start with the more correct hypothesis, that the 
 air is deflected at about 45 (depending possibly on friction effects) 
 instead of 90, a derivation of this form would result.
 
 70 
 
 Let A B, in diagram p. 68, represent the surface of area S, in an 
 air stream of velocity V. Let ABC represent the imprisoned cushion 
 of air, and A C and C B the surfaces of air along which the deflected 
 stream flows. 
 
 Let s' and s" represent the normal projections of A C and B C. 
 
 The total energy of the air stream, before deflection, is represented 
 by N' + N", where N' = w/g s' V 2 and N" = w/g s" V 2 . 
 
 The resolution of N' into D' and F', indicates the probable state 
 of affairs along the "deflection" plane A C. The force D' is parallel 
 to and vanishes with the deflected air stream, and in fact represents 
 the stream's energy. The force F', however, is perpendicular to the 
 plane A C, and since its action is directed towards the surface it can 
 be resolved into a force P', normal to the surface, and in the same di- 
 rection as P 90 and a force R', equal and opposite to R", which is entirely 
 used up in compressing the air cushion. While a greater part of the 
 energy of the stream D', D", goes away with it, a portion P', P", of the 
 stream's force is "deposited" on the surface, 
 
 P 90 = P' + P". 
 Analysis shows that 
 
 N' = w/g S' V 2 and N" = w/g S" V 2 . 
 
 AC = BC = S sin 45 and s' = AC sin 45 = S sin 2 45 = S/2 = s' 
 F' = N' sin 45, F" = N" sin 45, and P' = F' sin 45, P" = F" sin 45 C 
 
 Recalling that sin 2 45 = 0.5 
 
 P' = w/g S 0.5 V 2 sin 2 45 and P" = w/g S 0.5 V 2 sin 2 45 
 Hence using sea level and mean temperature, conditions, for w/g, 
 P 90 = w /g S V 2 sin 2 45 
 = .0054 S V 2 0.5 
 = .0027 S V 2 
 
 which is so nearly in accord with experimental results, K = .003 as 
 at once to lead to an appreciation of the value of considering the "air 
 cushion, 45 deflection" characteristics of air flow, in any study of air 
 pressures. 
 
 The experimental results on the pressures experienced by inclined 
 planes show that at angles above 45 the change in inclination does- 
 not greatly affect the pressures. The division of the air in front of 
 a plane inclined at angles greater than 45 is of the same character! 
 as in normal surfaces, and a similar theory when applied shows that' 
 the pressure remains constant from 90 to 45. 

 
 71 
 
 Inclined Surfaces 
 
 Referring to the diagram, p. 68, the mathematics of this develops as 
 follows : 
 
 AC = S Sin (a - 45) and BC = S Cos (a - 45) 
 
 .'. S' = S Sin (a - 45) Sin 45 and S" = S Cos (a - 45) Sin 45. 
 
 The normal pressures on the projected areas, S' and S'', may be 
 considered as the energy of the air stream, a proportion of which is ex- 
 pended on surface AB as P. 
 
 Calling N' and N" these pressures, we have N' = w/g S' V 2 and 
 N" = w/g S" V 2 . 
 
 The force triangles show that, P = P' + P" and that P' = N' Sin 
 (a - 45) Sin 45 and P" = N" Cos (a - 45) Sin 45. 
 
 Supplying the values of S', S" and of the resulting N' and N", we 
 get P = w/g SV 2 Sin 2 45 Sin 2 (a - 45) + w/g SV 2 Sin 2 45 Cos 2 (a - 45). 
 
 Since Sin 2 + Cos 2 = 1, and Sin 2 45 = 0.5, and supplying values 
 of w and g there is obtained, 
 
 P = .0027 SV 2 
 
 From 35 to 45, the inclined flat surfaces there is a region of un- 
 steady flow, in which for squares the pressures become much greater 
 than the normal. 
 
 Below these angles the air flow ceases to divide along deflection 
 planes in front of the surface, and all of the air passes under the sur- 
 face. In this case the pressure would be proportional to the sine of 
 the angle of incidence, as outlined above, in forces F' F" and the 
 formula 
 
 P a = K S V 2 sin a 
 is found closely to agree with practice. 
 
 This theory, first proposed by the writer some time ago, is as rigid 
 as any resolution into Lift and Drift. The hypotheses may be briefly 
 summarized as the consideration of the division of the air along two 
 deflection planes, which act like a surface on the air, and cause the 
 energy of the air to be divided up into a force parallel to the deflected 
 stream, which goes along with it, and a force normal to the layer of air, 
 along which deflection takes place, which in turn is composed of a force 
 compressing the air cushion and a force actually causing the resistance 
 of the surface. 
 
 Proper consideration of air deflection is capable of determining 
 c. p. position (by intersection of the deflection planes) and when ap- 
 plied to curved surfaces, should give most interesting results. And, 
 it would seem, that additional measurements by the laboratories, on 
 the angles of the deflected currents, would make the data on surfaces 
 more complete. 
 
 It is seen, therefore, that derivations based on a more accurate 
 hypothesis of air flow, give much more satisfactory results. In a work 
 dealing so largely with practice it is important to point out that unless 
 the hypothesis of the physical air flow used in any theory is correct it
 
 72 
 
 is far more practical to rely on observations and abandon formulae. 
 The theory of propellers, and its lack of agreement with practice, is a 
 field in which there is a most pressing need of a satisfactory basis for 
 theoretical determinations. 
 
 The "Absolute" System of Units. 
 
 It has been indicated that K, in the formula P = K S V 2 is a func- 
 tion of w/g of air. For any body, if we introduce another constant 
 C, we may write the air resistance formula in terms of density of air w, 
 and acceleration of gravity g, as 
 
 P = C w/g S V 2 
 
 Since the units in which P is expressed depend on the units used 
 for w and g, S and V, it follows that C is a number independent of the 
 system of units employed. For this reason it is called the absolute 
 coefficient, and its value is the same whether P is expressed in Ibs. or 
 grams, providing the expression of w/g is made in the proper units. 
 
 The absolute system is used by the Goettingen and the N. P. L. 
 (British) Laboratories. It is an inconvenient system for practical 
 field use, but for the international comparison of scientific results it 
 is admirably adapted. 
 
 The system used in this work is 
 
 P (pounds) = K S (sq. ft.) V 2 (miles per hour). 
 
 Therefore, to translate results in the absolute system to these 
 units the "absolute" values must be divided by 196. 
 
 "Absolute" values x .0051 = "m. p. h., sq. ft." units 
 
 The Metric System. 
 
 The Eiffel results are expressed in metric units, 
 
 P (kilograms) = K S (sq. meter) V 2 (met. per sec.) 
 so that Metric values x 8 = "absolute" values, and 
 
 Metric values x .041 = "m. p. h., sq. ft." units. 
 Thus for K = .0033, we would have in "absolute" units 
 
 P = .64 w/g S V 2 
 and in metric units, P = .08 S V 2 . 
 
 In the consideration of these conversion factors, atmospheric 
 pressure at sea level and ordinary temperature conditions are assumed. 
 
 Summary. 
 
 The greater part of this chapter is presented for- reference, but the 
 different systems of units and the conversion factors are of import- 
 ance, and should be understood, and borne in mind. 
 
 The theory of air pressure presented, is purposely not expressed 
 in terms of the usual theorems and laws of fluid dynamics, since it is 
 iesired to emphasize, merely, the importance of continually bearing 
 in mind, that the resolution of air pressures, along the directions in 
 which they act, is the correct fundamental conception of aerodynamics.
 
 CHAPTER VII. 
 CHARACTERISTICS OF AEROFOILS. 
 
 The manner in which air pressures vary on flat and cambered 
 surfaces has been considered fully enough to enable us to proceed with 
 the study of aeroplane wings themselves. As already indicated, the 
 necessity of having spars and ribs of considerable depth for the rigidity 
 of an aeroplane surface, makes it necessary to use a section of a cer- 
 tain thickness, and consequently two curvatures the top face and the 
 bottom face must be taken into consideration. 
 
 Aeroplane wing sections are ordinarily referred to as aerofoils, 
 and the study of the various aerofoils and their characteristics is of 
 very real importance. While a good deal of the data on air pressures 
 has been given by way of explanation and general information, the 
 wing characteristics referred to here are of the greatest . practical sig- 
 nificance, and are every day being put to use and verified, on the avia- 
 tion fields of the military world. The connection between the character- 
 istics of a wing section and the operation of a great war would seem 
 remote, but when it is appreciated that superior speed and climbing 
 ability enables a hostile aeroplane to gather information quickly and 
 escape from attack and pursuit, primarily because of the greater effi- 
 ciency of its wing section, the importance of this study becomes ap- 
 parent. 
 
 The development of wing sections has been along several lines. 
 Originally geometrical sections were made thick enough to give room 
 for spars and then rounded at the edges. Other pioneers, after de- 
 ciding on the size of spar and thickness required, adopted a certain 
 camber for the mean center line, and then proceeded to fill out a sec- 
 tion that would streamline the spars. Still other investigators adopted 
 parabolic and circular curve combinations, crescent shapes, etc., and 
 finally the great laboratories took up the matter and systematized its 
 study. The Eiffel, N. P. L., and Goettingen results are complete 
 enough now to give a very firm basis for aeroplane design, and to en- 
 able the effects of any changes in aerofoils to be quite accurately an- 
 ticipated. 
 
 In general the features of an aeroplane wing that may be varied 
 are: 
 
 1. Shape of Section, curvature, thickness, etc. . 
 
 2. Shape in Plan, contour, aspect ratio.
 
 74 
 
 In addition, the manipulations of the wing by warping or moving 
 flap sections that are connected to it, modify the pressures, and there 
 are further modifications of the air forces when the proximity of some 
 other wing or body affects the air flow and interferes with the paths 
 of the streamlines. Mutual interference of surfaces with each other 
 is a formidable study, and is given special consideration. 
 
 The nature of air pressure on aerofoils is revealed by air-stream 
 photographs, the most striking feature being the manner in which 
 the rounded nose of the aerofoil in deflecting the air stream, causes 
 the air some distance ahead to take a curvilinear path up to the aero- 
 foil. This influence, frequently called the "phenomenon of the dip- 
 ping front edge," is very pronounced for some aerofoils, and when 
 generating an upward stream of this kind an aerofoil is virtually rid- 
 ing on the crest of a wave. An explanation is found here for the greater 
 lift and less drift of aerofoils, and the section that generates the most 
 pronounced wave with the least break in the flow is naturally the most 
 efficient. 
 
 Another feature that it becomes more necessary to consider now, 
 in view of the separate nature of the top face, and the bottom face, 
 is that the total air reaction, resulting in the forces on the aerofoil, 
 consists of pressure, both positive and negative. Positive pressure 
 is a compressive action, while negative pressure is a suction. In pre- 
 vious considerations of air resistances, it has been unnecessary to draw 
 this distinction, since we were interested, merely, in the total effect 
 of the air reaction. 
 
 Lift by Suction on Top Face. 
 
 Careful studies of the distribution of pressure over the surface 
 of typical aerofoils made by the great laboratories, have shown that 
 the actual effect of the air flow at the usual flying angles is not only 
 to generate a pressure (compression of air) on the lower face of the 
 inclined surface, but also to cause a great suction on the upper face. 
 Furthermore, measurements show that the value of this suction in 
 pounds force is about three-quarters of the total air force on the aero- 
 foil. In other words, the action of the air flowing past an aeroplane 
 wing, primarily causes a partial vacuum on the top face, which tends 
 to draw the surface up by suction. As long as this wave form suction 
 type of flow continues, the surface is in its most favorable attitude for 
 efficiency, but at higher angles than ordinarily employed in flying this 
 type of flow breaks down, and a disruption of the streamlines follows, 
 evidenced on the surface, by a great increase in resistance and fall 
 in lift. The angle at which this change of flow occurs is called the 
 critical angle. 
 
 While the distribution of pressure across the wing's chord is of 
 the form indicated on p. 78, there is also good reason for investigat- 
 ing the manner in which the pressures on a wing vary from the center
 
 7,5 
 
 across the span to the tips. As the tip is approached the pressures 
 reduce and the point of highest suction passes from the leading edge 
 towards the trailing edge. The drift of the wing tips is found to in- 
 crease and to be accompanied by a fall in L/D, as the tip is approached. 
 The type of flow that produces the best L/D is found at the center of 
 the wing, where the streamlines pass directly from front to rear. As 
 the tips are approached, however, the streams of air begin to flow off 
 sideways, endeavoring to escape out at the sides. Obviously, the 
 higher the aspect ratio, the less in proportion is this sideways escape 
 of air, and therefore the better the L/D. 
 
 General Characteristics. 
 
 Although the pressures, on the various sections differ consider- 
 ably from each other, there are certain characteristic features that are 
 common to the majority of the aerofoils. 
 
 At incidence there is usually a certain lift A, and at a negative 
 angle, anywhere from -2 to 9, there is a point of no lift, H (see p. 
 78). The manner in which the Lift and L/D curves are plotted, on 
 a basis of angles, is the same as in Chapter V, the Lifts being defined 
 by values of KL in the formula, Lift = KL S V 2 . From A to C, on 
 the Lift curve, is more or less of a straight line, the curve bending over 
 at C, which point is called the point of maximum lift. From C to D, 
 instead of continuing to increase, a critical state of flow has been reached, 
 where further incidence increase is accompanied by a drop in the Lift. 
 This is an interesting portion of the curve, and we will again have to 
 refer to it when we take up the control of the aeroplane in this reversed 
 pressure region. Where lift decreases in this way, it may be stated 
 briefly, that the controls on an aeroplane would have to be reversed 
 for flying in this region. To go up, it would be necessary to reduce 
 the angle of incidence, and to descend, the elevator would have to be 
 pulled back so as to increase the angle. 
 
 On the L/D curve from the point of F at 0, the value of L/D 
 increases to a maximum E, corresponding to a Lift of value B. From 
 E to G, the L/D ratio again falls off. The ordinary regions of flight 
 are limited to the peak region of the L/D curve. 
 
 In the study of the aeroplane, as a unit, taken up later, consid- 
 eration will be given to the important relations that the maximum 
 and minimum points of the L and L/D curves bear to each other. 
 
 Having, in a general way, considered the nature of air reaction on 
 aerofoils, we may proceed with a study of the effect of alterations in 
 shape and plan form and interference. The values of KL and L/D 
 in the curves, refer to the combined action of whatever compression 
 or suction is generated, unless otherwise noted. It is also well to re- 
 call that L/D represents the ratio of the Lift force obtained from an 
 aerofoil at the expense of the Drift D, a resistance that must be over-
 
 76 
 
 come. "Efficiency" refers to L/D, and is higher, the greater the Lift 
 obtained for resistance overcome. 
 
 ALTERATION IN SHAPE OF SECTION. 
 
 1. Camber of Upper Face. 
 
 Increasing the camber of the top face from 1/40 to 1/6, on a form 
 with a flat under face, shows that the maximum lift increases up to 
 a camber 1/15 and then decreases. The ratio of L/D steadily im- 
 proves up to a camber of 1/20. This camber appears the most efficient, 
 as deeper cambers show a steady decrease in values of L/D. 
 
 On an aerofoil, having the under face arched considerably, when 
 the camber of the upper surface is increased above 1/15, the Lift hardly 
 varies, while the drift steadily increases with camber increase. For 
 very thick sections, however, just as in spheres and cylinders, there 
 is a critical flow, which, due to increases in speed, tends to smooth out 
 and reduce resistance. 
 
 2. Camber of Lower Face. 
 
 Increasing the camber of the lower face, for a fixed upper face, 
 shows that L/D does not vary very much, and that L increases ap- 
 preciably with camber increase. Since the depth of spar is very greatly 
 enhanced by keeping a flat underside, there is every reason for con- 
 sidering rather flat under surfaces as advantageous. The increased 
 depth of spar reduces the weight of framework in the wing necessary 
 for a given strength, and would about compensate for the lift increase 
 obtained by camber of the lower face. 
 
 The upper face, furnishes most of the lift and variations of lower 
 face have very little effect on the upper side. 
 
 3. Thickness and Depth at Rear. 
 
 By keeping the same mean curve of a section, and adding to the 
 top and bottom faces at the same time, the drifts are found to remain 
 about the same, and a decrease in lift is found as the section becomes 
 more and more a streamline body due to the progressive bulging out 
 of the section, both top and bottom. 
 
 For any particular curve a thickening of the rear alone to permit 
 of a deeper rear spar, shows a decrease in L/D with increase in thick- 
 ness and a slight decrease in Lift, but this is not so very marked, and 
 sections can be deepened at the rear with ease, thus permitting of hav- 
 ing the front and rear spars of the same depth. 
 
 4. Bluntness and Streamlining of Nose. 
 
 Substituting a blunt for a sharp leading edge, causes the ratio of 
 L/D to fall off, but since L remains about the same there is indicated 
 a pronounced increase in D. Bluntness of the nose may, therefore,
 
 77 
 
 be considered a disadvantage. Pointing the nose of an aerofoil, to a 
 streamline shape, designed to divide the air easier, often called a "Phillip's 
 Entry," is frequently used. It is advantageous in decreasing the 
 drift slightly at high speeds and low angles, but otherwise has little 
 effect. 
 
 5. Changing Position of Maximum Ordinate. 
 
 The fraction of the chord at which the camber is the greatest is 
 termed the position of maximum ordinate. It can readily be varied 
 on aerofoils, and it is found that L/D increases as it is moved from the 
 center of the surface, or .5 chord, towards the leading edge until it 
 reaches the position of 1/3 chord, when further movement forward 
 greatly reduces the efficiency of the section. The Lift is not affected 
 very much at low angles by changes in the position of the maximum 
 ordinate, but at high angles the lift of the section falls off when the 
 greatest camber is at a point in front of 1/3 chord. 
 
 6. Reverse Curvature. 
 
 Reversing the curve of either face of an aerofoil, has a pronounced 
 effect on the c. p. movement. The lower face of a deeply cambered 
 aerofoil is readily made to reverse at the rear and meet the upper face. 
 This is often done, and is distinctly beneficial. 
 
 More pronounced reverse curves in which both faces, at the rear, 
 are turned up, have a very great influence on the air pressures. The 
 advantageous feature of having a stationary center of pressure posi- 
 tion for the various angles, is obtained by raising the trailing edge 
 about .037 of chord the curve starting from a point about .2 of chord 
 from the trailing edge. But in doing this the maximum lift is reduced, 
 and the range of lift restricted. There is also a speedy decrease in L/D, 
 and, in general, this change leads to inefficiency, reducing lift by about 
 25% and max. L/D by about 15%. 
 
 7. Warping the Aerofoil. 
 
 "Warping" an aerofoil consists in twisting it in such a way as 
 to have the various sections presented to the air at uniformly vary- 
 ing angles of incidence. The section of wing remains constant, and 
 since its characteristics for varying angles are known, the amount of 
 pressure at the different sections could be found. In the ordinary 
 range of warp in practice, on aeroplane wings where one side is moved 
 up and the other down equally at the same time, the Lift remains the 
 same, as does also the position of the mean center of pressure, and 
 tests show that computations on a basis of applying the ordinary data 
 for the section to the different regions at their various angles 
 gives correct results.
 
 78 
 
 ASPECT RATIO TABLE 
 
 Values tabulated are the ratios of L and L/D at given aspect to values for an 
 aspect of 6. 
 
 ANGLES 
 
 ASPECTS 
 
 3 
 
 6 
 
 9 
 
 L 
 
 L/D 
 
 L 
 
 L/D 
 
 L 
 
 L/D 
 
 
 2 
 
 .60 
 
 .47 
 
 .62 
 
 .54 
 
 
 .60 
 
 .55 
 
 
 3 
 
 .70 
 
 .58 
 
 .73 
 
 .64 
 
 
 .78 
 
 .72 
 
 
 4 
 
 .84 
 
 .73 
 
 .85 
 
 .77 
 
 
 .90 
 
 .83 
 
 
 5 
 
 .94 
 
 .86 
 
 .95 
 
 .90 
 
 
 .96 
 
 .92 
 
 
 6 
 
 1.00 
 
 1.00 
 
 1.00 
 
 1.00 
 
 
 1.00 
 
 1.00 
 
 
 7 
 
 1.05 
 
 1.06 
 
 1.04 
 
 1.10 
 
 
 1.04 
 
 1.09 
 
 
 8 
 
 1.08 
 
 1.09 
 
 1.08 
 
 1.16 
 
 
 1.08 
 
 1.15 
 
 1 
 
 ^- 3^ fflf <-(/^i/f /Vf/fSUffJ THf 
 
 /. ! >v AMouffr of Arec,/Tire 
 
 
 > 
 
 - "T* \ ""' i /^ 
 
 f . **J\^ 
 
 f 
 
 x ~ * ^/ 
 
 
 ^ 
 
 0' 4Mt,lS 
 
 A*C,LC5 
 
 Vt3TRI9UTlOH t on ^^^ai -, 
 
 -.**;/ ^^^Egfa* 
 
 !^22 
 
 ^SqUWC f"D P*AH S- 
 
 J founding of ^^* ': /^ 
 
 i"o-?fro ^ ^'* / 
 
 Pl~ANe 
 
 ILJ^' ^ 
 
 0SPJLAHE ^SJAWfR 
 
 Retreat * 
 PRESSURE DISTRIBUTION - TYPICAL CURVES - AND DEFINITIONS
 
 79 
 
 ALTERATION IN PLAN FORM. 
 Shape of Plane. 
 
 Cutting away the trailing edge at the tips, and rounding off the 
 ends of the plane, is often resorted to for reasons of construction and 
 appearance. It is found that this does not appreciably affect the 
 pressures, and cutting away the tips slightly reduces the weight of 
 wing. On the other hand, it is found that raking the ends of a plane or 
 that the trailing edge is of greater span than the leading edge, does 
 appreciably affect the pressures, the Drift being considerably reduced 
 and the ratio of L/D improved. The gain in efficiency is due undoubt- 
 edly to a better utilization of the sideways flow of air, in escaping past 
 the edges. For the best results, where consideration is given to the 
 strength of the wing, the ends should be raked at angles of 20 to 30. 
 
 Aspect Ratio. 
 
 The influence of aspect ratio, on the pressures experienced by 
 aerofoils is, of course, quite similar to its effect upon geometrical sec- 
 tions. It becomes quite important for us to consider this, with refer- 
 ence to aerofoils, in greater detail, since aeroplanes vary considerably 
 in aspect. The "aspect" of an aeroplane is always considered as its 
 total span -f- by the chord of wings, the wings not being considered 
 separately from their attachment to the body. 
 
 Although P a on flat planes is affected by aspect, the ratio of L/D 
 is not so affected, since it is always a function of angle of incidence a, 
 as outlined in Chapter V. But on aerofoils, not only does D vary, but 
 there is a very pronounced change in L/D. 
 
 As the aspect ratio is increased from 2 to 8, the usual limits used 
 in practice, the maximum lift coefficient remains at about the same 
 value, but it occurs at smaller angles of incidence as the aspect ratio is 
 increased. 
 
 The most marked change, due to aspect ratio variation, is in the 
 value of L/D. This is found to be due mainly to an increase in the 
 Drift, for the smaller aspects. 
 
 The average aeroplane, has an aspect of 6, which it is found is a 
 good value, but an increase up to 8 and 9, is justifiable, since the limit 
 in improvement of efficiency becomes pronounced only for these higher 
 aspects. For very flat sections of camber 1/30, or thereabouts, the 
 ratio of L/D is found to decrease at very low angles, when the aspect 
 is increased above 5. At higher angles, higher aspects give better 
 efficiency as in deeper cambered planes, but it would appear that for 
 the flatter sections, used at low angles and very high speed, on the 
 small fast scouting aeroplanes, there is justification for limiting the 
 aspect ratio to about 5 a feature that is structurally very advan- 
 tageous.
 
 The most convenient way to present* data on aspect ratio has been 
 a matter of question, and a system is adopted here which, it would seem, 
 is the most practical for the use of the engineer and the aeroplane user. 
 The data for wing sections given, is in every case, excepting where 
 otherwise noted, reduced and corrected to correspond to an aspect 
 ratio of 6. In addition, accompanying this, is a table which gives 
 the factor by which to multiply values for any other aspect ratios from 
 2 to 8, the aspect ratio of 6, being considered as unity (see p. 78). 
 
 For example, at 3, the L/D of N 36 Eiffel surface is found from 
 the graph to be 14.7 for an aspect of 6, and the corresponding lift co- 
 efficient, KL is .0014. It is desired to know what the values would be 
 for an aspect of 4. From the table, we find that L/D will be 73% 
 of the value of 14.7, which is 10.7, and the value of KL will be 84% of 
 .0014, which is .00118. If it is desired to know the values for angles 
 between 3 and 6, it is easiest to plot the values of 3, 6, 9 on the 
 chart, and draw thru them curves entirely symmetrical and of the 
 same character as the ones for the aspect of 6. 
 
 For field use, the table is put in a novel form, but one which it is 
 thought is far handier than any hitherto published. The combined re- 
 sults of all the laboratories were given consideration in deriving the 
 values given. ' 
 
 Effects of Speed and Scale. 
 
 In stepping from model tests to full-sized machines, the best ap- 
 proximation at present made appears to work out quite well in practice. 
 
 Lift values, of coefficient KL, are applied directly without any cor- 
 rection. 
 
 Friction effects on Drift cause it to decrease with increase of speed, 
 and, therefore, at speeds higher than the wind tunnel speeds, the value 
 of L/D will be greater. The Eiffel results, however, were obtained in 
 winds of 50 to 70 miles per hour and require no correction, and in or- 
 der to bring the other results presented in accord, correction for speed 
 has been made wherever necessary. The values given, therefore, may 
 be applied without further correction to full-sized machines, at ordinary 
 speeds, by supplying the values of S and V 2 . 
 
 Pressures are, of course, functions of V 2 of the aeroplane, and the 
 corrections mentioned apply only to the values of KL and L/D tabu- 
 lated. Pressures are also functions of areas, and therefore vary as the 
 scale of the model squared. In the wind tunnels pressures are meas- 
 ured in pounds, let us say, and a particular pressure on an aeroplane 
 model to 1/10 scale is found to be 1 pound, in a wind of 30 miles per 
 hour. It is desired to know what the force on the aeroplane will be at 
 60 miles per hour. The observed value must be multiplied by 
 60 2 3600 
 
 - X 10 2 ,or x 100 = 400 pounds. 
 
 30 2 900
 
 81 
 
 Typical Sections of Aerofoils. 
 
 > 
 
 Twelve aerofoil sections that represent a wide variety of actual 
 practice are tabulated. The sections are drawn out all to .the same 
 scale, and the center of pressure graph is drawn for a distance of chord 
 equal to that used in the drawings of the sections. This enables a 
 rather more graphic conception to be obtained than has been possible 
 heretofore. The values of KL and L/D are given in groups of four 
 sections. The graphs look complicated, but they are merely con- 
 venient methods of tabulating the results, and the curves can readily 
 be distinguished with a little practice in reading off the values. 
 
 Among the 'sections, given the Eiffel No. 13 bis, the one used on 
 the Bleriot monoplanes, is a very widely adopted one, and because 
 of its high lift and good efficiency it is one of the few of the older types 
 of sections remaining in use. Many of the Royal Aircraft Factory 
 biplanes, the Bristol biplane, several German and Italian aeroplanes, 
 and the Martin biplane in this country, use a section of this type, t Its 
 most serious disadvantage is the lack of spar room, necessitating either 
 a wide shallow and, therefore, heavy spar, or a lesser factor of safety 
 on a well loaded wing. The efficiency at very low angles is not as good 
 as in some of the newer types of sections, which permit of a greater 
 range of speed though not possessing quite as good a maximum effi- 
 ciency. 
 
 The Eiffel No. 31 section, of crescent shape, is Eiffel's most ef- 
 ficient all-around wing, although its maximum L/D is exceeded by 
 many other sections. The Lift at low angles is very high, and the wing 
 is well adapted for load-carrying aeroplanes. 
 
 No. 32 Eiffel is essentially a speed range wing, for fast speed scouts, 
 lightly loaded and with high-powered engines. The high value of 
 L/D at low angles is particularly favorable to high speed. 
 
 No. 36, Eiffel is used on several military machines, and is a partic- 
 ularly good wing for a meduim speed, military scout. The Lift is 
 not run up very high, but the range of angles thru which a high L/D 
 is maintained is favorable, not only to high speed, but also to climb, 
 as will later be explained, when consideration is given to the complete 
 aeroplane as a unit. 
 
 The Dorand wing, Eiffel No. 35, is similar to the Wright wing, 
 and gives a very high lift, with a high L/D at angles from 3 to 6. 
 The small thickness of the section, however, does not make this wing 
 very favorable from the standpoint of construction. In general, thinner 
 wings are the more efficient, but spar room is a very necessary element, 
 and efficiency and strength must be compromised.
 
 82 
 
 /far/0 
 
 \ 
 

 
 \ 
 
 \ 
 
 \\ 
 
 \\ 
 
 
 O 
 
 * u " 
 
 Ss 
 
 1
 
 /f4T/o 
 
 

 
 85 
 
 The Howard Wright wing, in which the contour is stepped, has 
 been used on the White seaplanes, but its characteristics are not very 
 advantageous, excepting in that the c. p. movement is practically 
 stationary. 
 
 The Nieuport and Deperdussin are two standard wings, the lat- 
 ter designed particularly for racing aeroplanes. 
 
 R. A. F. 6 is one of the more modern sections that has become 
 standard on British Army aeroplanes, and also used on the huge fly- 
 ing-boat "America." The effect of a reversal of the trailing edge on 
 this section is shown also, and is of interest in connection with flaps 
 on the trailing edge. 
 
 The N. P. L., No. 4 wing is a particularly deep one, in which the 
 high Lift and fairly good L/D at angles of 3 to 6, are advantageous 
 for aeroplanes having a slow mean speed. 
 
 A new type of section, with a movable rear piece, is also shown, 
 as a suggestion of improvement by the writer. The combination of 
 low Lift and good L/D of a flatter section, at low angle, with facilities 
 for changing to a deeply cambered surface, which would have a high 
 Lift and also a high L/D at larger angles, could be made very greatly 
 to extend the speed range of aeroplanes. Suggested curves of a pre- 
 diction of the characteristics of a surface of this kind are indicated. 
 It should be emphasized here, that several years ago the extent to which 
 Lift and L/D could be varied on sections was not well known, and 
 many investigators looked for an extension of speed range, by varying 
 the size of the surface. The latest experiments indicate, however, 
 that since a change in section can be made to vary the Lift and L/D, 
 100 per cent, or more, at different angles, much more is to be expected 
 from a variable curvature section in extending speed range. 
 
 The Tail Planes. 
 
 The main wing surfaces determine in large measure the general 
 characteristics of an aeroplane, but the Lift and Drift of the tail pieces 
 or "empennages" are by no means negligible. The characteristic 
 variations and values of L and L/D, that have been given, are sufficiently 
 complete to enable us to determine their magnitude for these aux- 
 iliary surfaces, when it is realized that the effect of the propeller stream, 
 on the empennages is a powerful but more or less indeterminate factor. 
 
 Where balanced rudders are used, consisting of a flat surface of 
 a certain aspect ratio, it is merely necessary to apply the data given 
 on p. 60. And, as is often the case, where a pivoted balanced rudder 
 is of a more streamlined section, as illustrated on p. 78, it is proper 
 to consider the drift slightly reduced. Elevators or ailerons, con- 
 sisting of a balanced surface of constant chord, span and section, pivoted
 
 to take various angles of incidence, may be solved by the data given 
 for their particular section. 
 
 On some aeroplanes, notably the early Wright biplanes, the ele- 
 vator consisted of a normally flat plane that was quite flexible. This 
 surface was fixed, at the leading edge, and so connected at the trail- 
 ing edge that movement for control consisted of bending the ribs by 
 moving the trailing edge up or down, thus causing the section to take 
 various curvatures and angles. A surface of this kind is readily solved 
 by applying the data given on p. 66, for sections of varying camber. 
 
 The more usual type of elevator, however, is the "flap and fin" 
 type, in which movable flaps are hinged to the rear .of a fixed surface. 
 It has often been customary to consider these surfaces separately, 
 but a moment's thought on the continuity of the air flow, shows that 
 the proper conception is to consider a surface of this kind altogether 
 as a single unit, which, when the flaps are in line with the fixed por- 
 tion gives a flat surface of a certain aspect ratio. When the flaps are 
 moved, there is obtained a section that is arched (though not circular), 
 and in which the chord is a line from the trailing edge of the flaps to 
 the leading edge of the fixed plane, with a camber depending on the 
 amount the flap is turned. The data on curved sections given on p. 64 
 and 66, is then applicable, with the modification that the section being 
 a pointed arch, instead of circular, will have a somewhat greater Drift, 
 though the Lift may be taken as about the same. 
 
 INTERFERENCE OF AEROFOILS. 
 
 
 A study of the flow of the air stream about an aerofoil gives a 
 clear indication that the streamlines are influenced and deflected quite 
 a distance away from the surface, the rising streamline caused by the 
 "dipping" front edge of an aerofoil being an example. In addition, 
 the flow causes differences in pressure on an aerofoil, which, if affected, 
 would modify the total forces on the aerofoil. 
 
 It follows that placing bodies or other aerofoils in proximity to 
 any aerofoil will greatly affect its pressures. Interferences in flow 
 are very interesting, and of most practical value, in their application 
 to the aeroplane. 
 
 Biplane Effect. 
 
 When aerofoils are placed over one another, as in a biplane, there 
 results an interference and modification of their air forces. It is cus- 1 
 ternary to refer to the distance apart of the two superposed surfaces, 
 as the gap, and the ratio of gap to chord, is used as a measure thereof. 
 
 Since the suction on the upper face, is about three times as great 
 as the compression on the lower face, of an aerofoil, the effect of plac- 
 ing one over the other is greatly to reduce the Lift and efficiency of 
 
 '
 
 87 
 
 the lower plane, but only slightly to affect the upper plane. This 
 is evident when it is borne in mind that the compression on the bot- 
 tom face of the upper aerofoil and the suction on the top face of the 
 lower aerofoil merge into and mutually reduce each other, whereas 
 the suction on the top face of the upper aerofoil and compression on 
 the bottom of the lower aerofoil remain unaltered. The suction be- 
 ing so much more important, it follows that the upper aerofoil must 
 be much less affected. This is verified by the laboratories, and prac- 
 tically the entire loss due to biplane effect is found in reduction of L 
 and L/D of the lower surface. A deduction to be drawn from this 
 is, that flaps on the upper plane are much more effective than flaps 
 on the lower. Also, flatter planes,, in which the suction is not so great, 
 would be less interfered with when superposed. If the combination 
 of high camber upper plane and a very much flatter lower plane, were 
 used, it is evident that the interference would be reduced consider- 
 ably. A table of biplane reduction coefficients for an average aerofoil 
 is given. 
 
 N. P. L. BIPLANE TABLE. 
 To obtain values for a biplane, multiply values for single aerofoil by factors given. 
 
 BIPLANE 
 
 LIFT 
 
 LIFT/DRIFT 
 
 SPACING 
 
 
 
 GAP CHORD 
 
 6 
 
 8 
 
 10 
 
 6 
 
 8 
 
 10 
 
 0.4 
 
 .61 
 
 .63 
 
 .62 
 
 .75 
 
 .81 
 
 .84 
 
 0.8 
 
 .76 .78 
 
 .77 
 
 .79 
 
 .82 
 
 .86 
 
 10 
 
 .81 .82 
 
 .82 
 
 .81 
 
 .84 
 
 .87 
 
 1.2 
 
 .86 .87 
 
 .86 
 
 .84 
 
 .85 
 
 .88 
 
 1.6 
 
 .89 
 
 .90 
 
 .89 
 
 .88 
 
 .89 
 
 .91 
 
 Staggering. 
 
 The position of biplane surfaces over each other is subject to vari- 
 ation, and the term stagger is used to describe the relative position 
 referred to the vertical. For reasons of visibility, and minor consid- 
 erations of construction and balance, it is sometimes convenient to 
 stagger the upper plane ahead of the lower plane, as indicated in the 
 sketch on p. 78. The effect of staggering, on the efficiency of the aero- 
 foils, is again an illustration of the mutual reaction of the regions 
 of suction and compression. When the upper plane is staggered for- 
 ward, its Lift and L/D are improved, but at the same time the L/D 
 on the lower plane is reduced. When the stagger is .44 of the chord
 
 88 
 
 (a practical limit), the total effect is to cause the Lift, on the biplane 
 as a unit at angles of 5 to 10, to be improved by about 7% to 9% 
 with practically no effect on the L/D. 
 
 Interference of Following Planes. 
 
 The air stream deflected from the main aerofoils of an aeroplane, 
 takes a downward course, which causes the air flow past the empen- 
 nages, or any surfaces in the rear, to be affected, and causing the angles 
 of incidence of the rear surfaces (which are always the angles of the 
 chord with the air stream) to be less than the angles of their chords 
 with the horizontal flight axis. This is an exceedingly important ele- 
 ment in the balance and stability of a machine, and is taken up, more 
 fully, in considering the entire aeroplane as a unit further on. 
 
 Dihedral and Retreat. 
 
 Attention is called to the definitions of Dihedral angle and Re- 
 treat, given graphically on p. 78. The effect of these features is con- 
 sidered later with reference to stability. Within the limits used in 
 practice their effect on Lift and Drift is negligible. 
 
 Summary 
 
 From a combined consideration of Aspect Ratio, Biplane effect 
 and staggering, a biplane at 6 of aspect 6, stagger of .44 chord and 
 gap equal to chord, would have about 89% of the lift of a single aero- 
 foil (81% due to biplane effect and 8% increase due to stagger) and 
 its L/D would be 81% of that of a single aeroplane of the same as- 
 pect ratio. If this is compared with a single aerofoil of aspect 4.5, 
 however, it is found that the Lift is practically the same, and only 
 a slight difference is found in the efficiency. Likewise, a staggered 
 biplane of aspect 8 and a large gap, is practically the same as a mono- 
 plane of aspect 6. 
 
 When a comparison, like the above, is made, the reference to single 
 aerofoil means an equivalent monoplane of the same surface area as 
 the biplane. To get the same lift with the same section and aspect, 
 a monoplane would require less area than a biplane, by the amount of 
 the biplane coefficient. 
 
 The data given on surfaces enables the lifting capacity and cor- 
 responding wing resistance to be determined for the various sections. 
 Examples indicating the manner in which this data is used, and a con- 
 sideration of the aeroplane as a unit, may now be taken up.
 
 CHAPTER VIII. 
 CHARACTERISTICS OF THE AEROPLANE. 
 
 The surprising accuracy with which the performances of an aero- 
 plane may be predicted from data on the lifts and resistances of its 
 component parts, is, perhaps, the most striking indication of the great 
 progress that has been made in Aeronautical Engineering, the past 
 year or two. Constructors, fliers and the laboratories, have co-op- 
 erated to advantage, and although many important features of the 
 aeroplane remain to be explored, information that already has been 
 obtained and verified, by the great work of the Laboratories, readily 
 permits of establishing a working basis for the presentation of data 
 of importance, relative to the aeroplane, in a manner not only use- 
 ful and intelligible to the aeroplane user, but at the same time capable 
 of expansion as new conceptions develop. 
 
 It is proposed in this chapter to consider the aeroplane as a unit, 
 with a view to determination of its total lifting capacity and resist- 
 ances and the power necessary to fly. In a treatise on aeroplane de- 
 sign, the matter considered here in a few pages would of itself consti- 
 tute a text book, so that the limiting scope of this work makes it neces- 
 sary to confine our attention to the military "field use" features capable 
 of leading to an intelligent solution of problems in the modification 
 of aeroplanes and their performances, as dictated by military neces- 
 sity. Flying various types of machines, with greatly varying load 
 conditions, radius of action, atmospheric conditions, and power varia- 
 tions, presents a vast quantity of problems that often are solved best 
 by the fliers themselves. That new kind of resourcefulness, in adapt- 
 ing themselves to many changing requirements, that is demanded 
 of a Flying Corps, is a criterion of efficiency and may be gauged not 
 only by skill in maintenance, but also by the knowledge that the avia- 
 tors and mechanicians have of the performances that may be expected 
 of their machines. 
 
 It must be borne in mind that a manufacturer is required to fur- 
 nish data on his machine in detail, and although a few examples are 
 given here, information on the resistances, lifts, power available, and 
 power required to fly, under definite conditions, of particular types, 
 should come with each machine the manufacturer in other words, 
 interpreting the laboratory results applied to his type, for the benefit 
 of the user. It is clear, therefore, that the military or naval user of an 
 aeroplane must know how to read this data and how to apply it in a 
 practical way.
 
 90 
 
 In previous chapters, consideration has been given to the resist- 
 ances of bodies, and the lifting efficiency of surfaces and aerofoils 
 completely enough, to explain the significance of the forces generated 
 by an air stream, and with sufficient laboratory data to make the sub- 
 ject matter of direct value for reference. We are now at liberty to 
 combine these conceptions, and to give the definition of an aeroplane, 
 (p. 11) a more technical wording in that, an aeroplane consists of a 
 combination of sustaining and balancing aerofoils, with a Lift deter- 
 mined by the values of K L ,V and S, and with power suitably proportioned 
 to overcome the head resistance of the structure, and the Drift of the 
 wings, at the expense of which the Lift is obtained. 
 
 Types of Aeroplanes. 
 
 Reference to Chap. II, gives a renewed significance to the photo- 
 graphs of the various types of aeroplanes, and could profitably be re- 
 considered with a view 'to fixing the relation of theory and practice. 
 Thus, the wing section of the Curtiss Tractor, on p. 17, is none other 
 than Aerofoil No. 36, of Eiffel, given on p. 82, and the wings of the 
 monocoque on p. 20, have a section identical with Aerofoil No. 54, 
 defined on p. 83. The several machines differ widely in values of the 
 resistances of their various structural parts. Thus, the struts on the 
 old-type Wright Aeroplanes, shown on p. 19, have something like five 
 times the resistance of the struts on the Sturtevant tractor, p. 24, and 
 the wheels on the Curtiss Tractor, p. 17, may be expected to have 
 about half the resistance of the wheels on the Signal Corps tractor, 
 shown below it, due to covering. The maze of wires and struts on 
 the old types of pusher biplanes, are obviously more resisting than 
 the simplified bracing and covered bodies of the later types. The dif- 
 ference in aspect ratio of the Bleriot, on p. 20, and the upper plane of 
 the Farman, on p. 19, is most noticeable. And, whereas, the Curtiss 
 Model N has two staggered planes and a dihedral angle, the Deper- 
 dussin, on p. 20, has a single surface with no dihedral. And yet if the 
 surface section were the same, as is the case with the Bleriot, p. 20, 
 and the Martin, p. 15, we would apply the same aerofoil data to both of 
 them, with suitable corrections for Aspect Ratio, biplane interference 
 and stagger. In addition, it may be noticed that the shapes of the fusel- 
 ages, differ considerably, some tapering to an edge horizontally and 
 others vertically, some square, others round, etc. 
 
 Each aeroplane, therefore, is bound to have particular character- 
 istics of its own, for each of which the designer, if competent, had some 
 particular object in view, towards either efficiency, stability, strength 
 or convenience. To investigate them all would be a trespass on the 
 domain of the aeronautical engineer. But not to appreciate what 
 performances may be expected of any machine, is due to a lack of infor- 
 mation, that it is the object of this work to supply.
 
 91 
 
 From the standpoint of lifts, resistances and power required, the 
 many different types all resemble each other in having a set of main 
 supporting surfaces, auxiliary balancing surfaces, which may or may 
 not exert lifting pressure, and certain structural resistances. In power 
 available, there are differences of importance due to gearing of the 
 propellers. Whereas, in characteristics of stability and operation, 
 distinctions are most pronounced, and necessitate a full consideration 
 later. 
 
 But whether tractors, pushers, staggered biplanes, monoplane 
 aeroboats, etc., all aeroplanes have these characteristics in common: 
 
 I. A Lifting Capacity, determined by the surface characteristics, 
 
 and varying with speed and inclination of the machine. 
 
 II. A total resistance to motion, composed of 
 
 (a) The combined resistances of the various necessary 
 structural parts, called the Structural Resistance, 
 and varying with speed and inclination. 
 
 (b) The Drift, which is determined solely by the Lift char- 
 acteristics and is, of itself, independent of speed. 
 
 III. A certain Power Required to fly, varying with the speeds 
 
 of the machine and its total resistances. 
 
 IV. A certain Power Available, due entirely to the horse-power 
 
 given out by the propeller, which, in turn, for various speeds 
 is a certain proportion of the power of the engine, and there- 
 fore must correspond to a certain fuel consumption. 
 Flight is impossible unless the Lifting capacity exceeds the total 
 weight, and the Power Available is greater than the Power Required. 
 A study of these features enables the speed range, the glide, the 
 climbing rate, the load-lifting capacity and the fuel consumption, to 
 be determined in a most practical manner. 
 
 A STURTEVANT AEROPLANE RISING OFF THE GROUND
 
 92 
 Inclination of the Aeroplane. 
 
 The variations of the pressures on surfaces has been considered 
 for changes in the angle of incidence. It is customary in aeroplanes 
 likewise to refer to "angle of incidence," of the supporting surfaces, 
 in defining the attitude of the .machine. And the inclination of the 
 body to the line of flight, and the line of the propeller axis, is referred 
 to as the angle of incidence. If the wing is set at 5 to the axis of the 
 body, and the angle of incidence of the machine is 5, it follows that 
 the body lies parallel to the air-flow. Whereas, if this same machine 
 were presented to the air at 10 incidence, the body axis would make 
 an angle of 5 with the air-flow. It is of importance, now, to realize 
 that the entire aeroplane as a unit may be presented to the air at various 
 inclinations. 
 
 On p. 13 the three motions an aeroplane is subject to pitching, 
 yawing and rolling are defined. On practically all aeroplanes the 
 lifting planes are fixed to the body, so that a variation in angle of in- 
 cidence means pitching of the machine and is considered more fully 
 here than either yawing or rolling, because of the effect change of in- 
 cidence has on the surface characteristics. Yawing slightly affects 
 the resistances, and rolling may affect the Lift, but both are more pro- 
 perly considered under Stability. 
 
 The auxiliary surfaces, particularly the tail-planes, are in turn 
 affected by the pitching of the machine, or, as we have defined it, by 
 changes in the angle of incidence of the aeroplane. Where the ma- 
 chine is so balanced that the tail lifts, then as the incidence of the aero- 
 plane is increased the lift of the tail surfaces increases. And if the 
 tail is set to receive a downward pressure, an increase of incidence causes 
 this to be relieved. 
 
 As will be seen later, the variation in inclination of the structure, 
 at the different angles of incidence, gives rise to alterations in the struc- 
 tural air resistance, particularly of the fuselage, and in a staggered 
 biplane an increase in the angle of incidence, increases the resistance 
 of the struts and wires. 
 
 The Aeroplane as a combination, then, must be studied at various 
 attitudes, and changes of inclination are expressed as changes in angle 
 of incidence of the supporting planes. Where the special feature is 
 involved of varying the angle of incidence as on some recent machines, 
 inclination could be referred to the propeller axis. But it is more 
 convenient in determining Resistances, and Lifts, to consider the chord 
 of the wing as the base line. 
 
 Before proceeding with the study of Resistance and Power charac- 
 teristics of an aeroplane, attention must be given to important features 
 occasioned by combinations of lifting and auxiliary aerofoils, on the 
 aeroplane frame.
 
 93 
 Decalage, Wash-out, and Tail Interference. 
 
 The term "decalage" is used to define the difference in the angle 
 of incidence between any two distinct aerofoils on an aeroplane. It 
 is most often used to describe the difference between the setting of 
 the main planes and the tail piece, and in a biplane the term is also 
 used to denote a difference in angle of incidence between the upper 
 surface and the lower one. Thus, on an aeroplane in which the body 
 axis is in the line of flight with an angle of incidence of 5, and with 
 the chord of the elevator, inclined +2 above the body axis, the deca- 
 lage of the elevator would be 3. And in a biplane where, in order to 
 gain slightly in efficiency, the upper surface is set at an incidence of 
 3, when the lower one is at 5, the decalage would be equal to 2. 
 
 With reference to the decalage of the surfaces of a staggered bi- 
 plane, laboratory experiments indicate that the effect of setting the 
 upper surface at about 2 less incidence than the lower surface gives 
 a pronounced increase in Lift and a slight gain in L/D over any other 
 setting. This, however, is subject to modification where different 
 wing sections are used, and a field of importance remains to be explored 
 in the determination of the best combination of stagger, surface sec- 
 tions and decalage, to minimize the effect of biplane interference and 
 improve the Lift range of the biplane as a unit. 
 
 "Wash-out" is a term used to describe the progressive reduction 
 in the angle of incidence, from body to tip, used on some aeroplanes 
 for reasons of stability. Thus, on an aeroplane, in which the wings 
 are set at an angle of incidence of 7 at the body, and then steadily 
 reduced until the angle at the tip is only 3, there is said to be a "wash- 
 out" of 4. With reference to the aerodynamic characteristics of this 
 feature, laboratory results show that the approximation of considering 
 the entire wing, as set at an incidence, equal to the mean of the angles 
 at the body and the tip, is quite close enough. The stability features 
 will be given consideration later. 
 
 The air that is thrown back from the front main surfaces of an 
 aeroplane, onto the tail, is given a most pronounced downward trend, 
 governed by the particular angle of incidence and surface section com- 
 bination used. ' The tail pieces, consequently, are riding in air waves 
 generated by the sustaining surfaces, and therefore are interfered with. 
 "Tail interference" has only recently been given proper considera- 
 tion, and its importance on the functioning of a machine requires parti- 
 cular attention. Eiffel's experiments on this feature are particularly 
 complete, and from them there can be drawn the general conclusion 
 that the air, passing back from the sustaining surfaces, acquires a down- 
 ward trend, dependent on their angle of incidence, which persists for 
 some time, so that by the time this air region passes by the tail sur- 
 faces it has straightened out to only a half to one degree less than the
 
 94 
 
 actual angle of incidence of the sustaining planes. It becomes nec- 
 essary, then, to distinguish between the apparent angle of incidence 
 of the tail surfaces and their real angle with the direction of the air- 
 flow past them. The apparent angle is the incidence referred to the 
 line of flight, just as for the sustaining planes, whereas the real 
 angle at which the air attacks the sustaining planes is the one for which 
 all calculations of pressures on the tail surfaces must be made. A 
 few examples will aid in making this clear. Let us consider an aero- 
 plane, at an angle of incidence of 4, in which the body axis is parallel 
 to the line of flight, and the tail surfaces of which have a decalage of 4, 
 with the sustaining surfaces. From our definition of decalage, the 
 apparent angle of incidence of the tail surfaces would be 0, i.e., they 
 lie parallel to the body axis. But the air acquiring a downward trend 
 from the main surfaces, of 4, which gradually straightens out to 3, 
 as it passes the tail causes the real angle of attack of the air on the tail 
 surfaces to be 3. For the same case, if the tail surfaces are acted upon 
 by the air stream, so that their real angle of incidence is 0, it follows 
 that the sustaining surfaces are at an angle of incidence of +7 and the 
 body is inclined to the air flow at +3. For any particular machine, 
 it is necessary to have special data on these features furnished by the 
 designer. 
 
 Although other features causing modification of pressures on the 
 various aerofoils may be met with, their importance would not re- 
 quire special consideration here. The type of sustaining surface char- 
 acterized by the "Dunne" class of aeroplanes, see p. 23, is readily solved 
 when the laboratory data on this surface as a unit is furnished, since 
 the changing camber, and angle of incidence, would in no way alter 
 the method of considering the values of L and L/D at different angles 
 of inclination, precisely as for any other surface section. The sta- 
 bility features of this type, however, require special consideration. 
 
 Having acquired a working conception of the aeroplane as a unit, 
 we may proceed with a study of its probable performances, as out- 
 lined on p. 91, and predicted from the laboratory measurements. 
 
 I. THE LIFTING CAPACITY. 
 
 The data on surface sections furnished for any machine, together 
 with suitable corrections for biplane effect, aspect ratio, stagger, deca- 
 lage, etc., is the first essential and perhaps the most convenient 
 way to represent this is to have curves showing the corrected values 
 of L and L/D as applied to the particular machine, on the same chart 
 with the data on the wing section alone, examples of which are given 
 on pp. 82-84. The corrected curves, then, give us direct informa- 
 tion on the actual values of KL and L/D, to apply to the lifting sur- 
 faces as a unit, corresponding to angles of incidence of the chord of 
 the wings to the line of flight. Since the value of the surface area
 
 95 
 
 S is given for a definite machine, and also information on the weight 
 W to be carried, we can at once supply suitable values for solving 
 
 W = L = K L S V 2 
 
 so that we may learn at what angles the machine must be flown, for 
 given speeds, or, conversely, how fast and how slow we could go, with 
 a definite range of angle of incidence. Since features of stability de- 
 termine a safe limit of angles, the latter problem is the one most often 
 met with. 
 
 Thus, for an aeroplane with 335 sq. ft. of surface area, in the form 
 of a staggered biplane, of aspect 7, and gap equal to chord, and with 
 a wing section corresponding to Eiffel No. 53, the values of KL and 
 L/D corrected, would be shown, as indicated on p. 96. For this ex- 
 ample, let us find the speed range corresponding to a range in the angle 
 of incidence from 1 to 12. 
 
 At the low angle 1, we find by referring to the first chart that 
 KL = .00085. Supplying values of S and L, equal to the weight, we 
 obtain 
 
 W = K L S V 2 = 1800 = .00085 x 335 x V 2 
 from which it develops that, 
 
 V 2 = 6320, and V = 79.5 miles per hour. 
 
 In the same way, reference to the chart of aerofoil characteristics 
 shows that at 12, K L = .0027, so that 
 
 L = 1800 = .0027 x 335 x V 2 
 from which we obtain, 
 
 V = 44.6 miles per hour. 
 
 Since the required lifting power and area of the wing surfaces 
 are fixed, it is hardly necessary to emphasize that, for any inclination, 
 there is only one speed at which horizontal flight is attained with the 
 given load. Each angle 'has its particular corresponding speed, and 
 in the above example the angle range of 1 to 12, corresponds to a 
 speed range of 44.6 to 79.5 miles per hour, and to none other unless 
 the load is changed or the surface characteristics altered. 
 
 A simple way to record this process is to write the speeds cor- 
 responding to the various angles on the curve for KL, as has been done 
 in the example given. 
 
 This, then, is the first step in determining the aeroplane's char- 
 acteristics, i. e. : finding the speeds required in order to lift the weight, 
 at various angles of incidence.
 
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 98 
 II. TOTAL RESISTANCE TO MOTION. 
 
 As already indicated several times, the resistance overcome by 
 the propeller consists of two distinct items: Structural Resistance and 
 Drift. 
 
 Structural Resistance. 
 
 The air resistance of the structural parts of an aeroplane, such 
 as the wheels, struts, wires, body, tanks, etc., all total up to a formid- 
 able value, and are conveniently and properly classed together in one 
 item, called the "Structural Air Resistance." This term, altho a new 
 one, is deemed so much more expressive than the older terms, "body 
 resistance," "parasite resistance," etc., that its introduction is cer- 
 tainly justified. The term "parasite" is misleading, since a high drift 
 is as much a "parasite" as an uncovered wheel. 
 
 In Chapter IV the determinations of the resistances of various 
 shaped bodies were given consideration. For any aeroplane it is neces- 
 sary to know the details of construction before a working total of the 
 structural air resistances can be determined. 
 
 There are hardly any two types of aeroplanes with the same shape 
 of body, so that this item, above all others, can be considered but from 
 data given by the manufacturer. It may be of interest to note, how- 
 ever, that the values of K, for the nacelle of the Farman (illustrated 
 on p. 19), has been found by Eiffel to be .0014, and K for the Deper- 
 dussin monocoque (p. 20), is .001. It has also been determined that 
 in yawing and pitching the flat-sided fuselage has an appreciably greater 
 resistance than a rounded one. 
 
 The resistance of the tail surfaces ordinarily should include some 
 allowance for the drift of the tail, as determined by the particular shape 
 and incidence used. Altho this should, perhaps, be considered in 
 company with the wing resistances, its value is small for a well-bal- 
 anced machine, and it is more convenient to include it in the struc- 
 tural resistance until it assumes a greater value. 
 
 Altho the process of determining the Structural Resistance con- 
 sists essentially of applying information on the values of K, for the 
 various structural items, in the formula, P = K S V 2 , and adding 
 up the result, we have found that a change in V for horizontal flight 
 involves a change in the angle of incidence. This, in turn, means 
 that at the various speeds the entire aeroplane assumes a "tail high 
 nose down," or "tail low nose high" attitude. For the wheels, wires, 
 etc., these incidence variations have but a slight effect, but the bodies, 
 fuselages or nacelles are formed so as to give a least resistance in only 
 one position when the axis is in line with the wind. Any depart- 
 ure from this due to a change in the angle of incidence, causes an in- 
 crease in their resistance. So that at angles both above and below
 
 the normal angle of incidence, the resistance of the body is higher, 
 due to higher values of KL. 
 
 On p. 96 a typical resistance chart is given, and on it is shown a 
 typical curve of structural resistance. The range of incidence of 1 
 to 12, used as an example already, is, as indicated, accompanied by 
 a rise in structural resistance from 60 Ibs. at 12, to 195 Ibs. at 1, since 
 the speeds corresponding to these angles are 44.6 and 79.5 m. p. h. 
 
 Drift. 
 
 If we refer to the first chart showing KL and L/D, and recall that 
 for any value of the angle of incidence the value of KL was read, to 
 determine speed, it is seen that we can also read at the same time the 
 value of L/D for that particular KL. Knowing the weight, this ratio 
 at once gives us the Drift, since for horizontal flight, 
 
 Drift = Weight + L/D. 
 
 It becomes clear, now, why reasons of convenience lead to plot- 
 ting the values of L/D in preference to the values of KD, to supply 
 in D = KD S V 2 . Drift is always a fraction of Lift and, therefore, of 
 the weight, but is in no other way concerned with the speed, V. 
 
 Thus, when the chart is referred to, to obtain the value of KL for 
 1, the value of L/D = 13.6 could be read at the same time, and know- 
 ing that the weight is 1800 Ibs. the Drift at that angle is immediately 
 determined as, 1800 -f- 13.6 = 132 Ibs. In the same way the Drift at 
 12 is found to be, 1800 - 8 = 225 Ibs., and the least drift at about 4 
 is 1800 -=- 15 = 120 Ibs. Since these determinations are made in com- 
 pany with the determinations of the air speeds corresponding to the 
 various angles of incidence, we at once have obtained the values of 
 the Drift for the various speeds and, consequently, have solved for 
 the second part of the Total Air Resistance. We proceed, then, to 
 plot a curve showing the Wing Resistance, on the same chart, on which 
 we have already plotted Structural Resistance, for different speeds. 
 
 The Total Air Resistance is the sum of these two. On a chart, 
 curves drawn to the same cross lines are easily added graphically, by 
 merely surmounting one value on top of the other. Thus, for 60 miles 
 an hour speed, the value of the Wing Resistance, 120 Ibs. is added 
 by means of dividers (in actual measurement) above the point on the 
 Structural Resistance curve, which reads 105 Ibs., and this gives the 
 total 225 Ibs., graphically. The same process is followed with other 
 points, sufficient to establish the curve of Total Resistance to motion, 
 which is the second characteristic to be determined.
 
 100 
 
 III. POWER REQUIRED. 
 
 In Chapter III it was recalled that power expended corresponded 
 to the exertion of foot pounds work at a certain rate, and that one 
 horse-power = 550 foot pounds per second. 
 
 At any speed, therefore, the Ibs. Resistance X the speed in feet 
 pen second, gives the number of foot pounds per second used up by 
 the* aeroplane. Dividing this quantity by 550, will give us the Horse 
 Power Required for horizontal flight at that particular speed. 
 
 If we call R the resistance and V the speed in miles per hour, then 
 
 R X V X 1.47 
 H.P. = - 
 
 550 
 
 since V in m. p. h. must be multiplied by 1.47, in order to express it 
 in feet per second. Combining 1.47 -r- 550, we get the handier rela- 
 tion that, 
 
 Rx V 
 Required H. P. = - 
 
 375 
 
 where R is the total Resistance in pounds read for any speed from the 
 Resistance Chart, and V is the velocity in miles per hour. 
 
 A curve may then be plotted of Power Required to fly at the vari- 
 ous speeds. This is done in the third chart, p. 96. It is to be recalled 
 that in plotting the Drift on the resistance chart, the corresponding 
 angles of incidence were marked on the curve. 
 
 This is also done on the Power Required Curve, the correspond- 
 ence between Speeds and Angles of incidence being precisely the same 
 as originally determined, when considering the first chart of KL and 
 L/D. 
 
 As examples of the manner in which to determine Power Required, 
 let us take the machine at incidences of 12, 6 and 1. 
 
 From the Resistance Chart we find that at 12, corresponding 
 to a speed of 44 ^ m. p. h., the Total Resistance is 285 Ibs. Therefore, 
 
 285 x 44.5 
 
 Required H. P. at 12 = - - = 33.8 h. p. 
 
 375 
 
 The same values read for 6, give 
 
 215 x 54 
 
 Required H. P. at 6 = - - = 31 h. p. 
 
 375 
 
 And likewise for 1, there is obtained 
 
 327 x 79.5 
 
 Required H. P. at 1 = - - = 69 h. p. 
 
 375
 
 101 
 
 It is most important to note the general form of this curve, and 
 as a "Characteristic" of the aeroplane, it is decidedly the most im- 
 portant one. At angles below 10 there is a noticeable rise in Power 
 Required, because the increase in Drift is so much greater than the 
 decrease in Structural Resistance, corresponding to a slower speed. 
 And the pronounced increase in Power Required, at angles below 6, 
 is due primarily to the greater preponderance of the increase in the 
 Structural Resistance, as the speed increases. 
 
 At angles of 10 to 6, corresponding to speeds of about 45 to 55 
 m. p. h., the Power required is at its lowest value and remains very 
 nearly the same for this particular machine. Power required curves 
 vary greatly for different aeroplanes, both in their contour and in the 
 angles at which the low points are located. But the rise both above 
 and below a certain speed where the power is least, is noticeable on 
 all power curves, and leads to the general conclusion, that high drift 
 at low speeds, and high structural resistance at high speeds, are the 
 wasteful elements. 
 
 The establishment of all the points on the Power Required Curve, 
 is made in the manner indicated, and we then obtain the third char- 
 acteristic of the Aeroplane which is the determination of the horse 
 power, required for horizontal flight, at various speeds. 
 
 IV. POWER AVAILABLE FROM THE PROPELLER. 
 
 A certain horse power is given by the engine at various revolu- 
 tions per minute, and a curve of this "Brake Horse Power," for cor- 
 responding "r. p. m.," is as necessary and as easily furnished as in- 
 formation on the size and weight of the engine. On p. 97, a curve 
 for the particular motor taken as an example here is given. 
 
 But this power is not directly available, since its exertion on the 
 air to move the aeroplane is thru the medium of an air propeller, which, 
 unfortunately, is more or less wasteful of the power the engine gives 
 to it. 
 
 The efficiency of the propeller, therefore, must be considered. 
 Of all features of the aeroplane, propeller determinations from both 
 theory and practice are exceedingly unsatisfactory. But laboratory 
 experiments, notably Eiffel's, lately have given valuable informa- 
 tion on a few good blades, in which the shape and section are left un- 
 altered, and only the r. p. m. and diameter adjusted for different aero- 
 planes. The theory of the "similitude of propellers," which permits 
 of passing from one machine to another with the same type of blade, 
 is at present the only really valuable basis for propeller determina- 
 tions. 
 
 Experiment shows that the old notion of "pitch," etc., on a basis 
 of screw propeller theory is poorly founded. Whereas, the more mod-
 
 102 
 
 ern notion of a propeller, consists simply in a consideration of the blade 
 as an aerofoil at a certain angle of incidence, moved against the air 
 in a rotating path, and in which KL S V 2 , would represent the Thrust, 
 and K D S V 2 , the Torque. 
 
 For purposes of aeroplane design, considerations of the propeller, 
 its loading, deflections and strength, and its Thrust and Torque char- 
 acteristics, are most important. For field use the strength question 
 requires merely that a propeller never be run at a greater r. p. m. than 
 has been proven safe, without information from the manufacturer as 
 to the strength of that particular propeller; and that alterations, such 
 as metal tipping, be done by the propeller maker, unless the propeller 
 has already been designed therefor. But, we are very vitally inter- 
 ested here in the suitability of various propellers, for different aeroplane 
 performances, so as to enable us to pick out the propeller desired. 
 
 Since on any engine the power is determined from the r. p. m., by 
 merely mounting any propeller in question on the engine and reading 
 the r. p. m. for a given throttle, there is at once established the power 
 used by the propeller. This is so readily and conveniently done in 
 the field that for the present it is unnecessary to compute by extensive 
 mathematics the power necessary to drive this propeller at a certain 
 r. p. m. In the determination of the Power given out by the propeller 
 in the air, however, no such convenient measurements can be made. 
 We have recourse, therefore, to laboratory data furnished with the 
 propeller. 
 
 This data is most conveniently given as -a curve showing the Effi- 
 ciency of the propeller, corresponding to values of the quantity v/nd. 
 
 The Efficiency of the propeller is merely the % of the power put 
 into it, that is given out in Thrust Power by the propeller. 
 
 The quantity v/nd, is a convenient numerical relation, used by 
 the laboratories to express the Efficiency of a propeller of definite shape 
 and section for any combination of values of 
 
 (1) The velocity of the aeroplane in feet per second, v, 
 
 (2) The revolutions per second of the engine, n, 
 
 (3) The diameter of the propeller in feet, d. 
 
 The speed thru the air of the tip of the blade is determined in 
 feet per second by the circumference = xd, and the number of times 
 a second it covers this distance = n. The quantity v/7rnd is the actual 
 relation between the "tip speed" of the propeller and the speed thru 
 the air of the entire aeroplane. Let us say, briefly, that it has been 
 "discovered" that this relation definitely determines the efficiency of 
 any particular blade.
 
 103 
 
 Our data on the engine gives us n, which is taken in this example 
 as normally 1200 r. p. m. = 20 r. p. s. The diameter, d, in this example 
 is 8 feet. For any speed of the aeroplane, v, therefore, we can com- 
 pute v/nd, and on the Efficiency chart, p. 97, read % efficiency of 
 the propeller. Knowing the horse power of the engine for the given 
 value of n, we readily determine the actual horse power available from 
 the propeller. As an example, at 60 m. p. h. speed, v = 60 x 1.47 = 
 88 feet per second, n = 20, and d = 8, whence v/nd = .55. Reading on 
 the first chart p. 97, we find that for v/nd = .55, propeller efficiency = 
 76 %. On the second chart, p. 97, it is seen that at 20 revolutions 
 per second, or rather 20 x 60 = 1200 r. p. m., the engine may be ex- 
 pected to give 88 h. p. Our propeller Power Available, therefore, is 
 76 % of 88 = 67 h. p., and is so plotted on the Power chart for 1200 
 r. p. m., on p. 96. 
 
 In the same way all the other points, not only for this same curve 
 but for values of r. p. m. = 800, 1000, etc., are plotted, and we thus 
 obtain the fourth characteristic the thrust Power Available for any 
 r. p. m., at the various speeds of the aeroplane. 
 
 PERFORMANCES OF THE AEROPLANE. 
 
 The characteristics of the aeroplane having been determined we 
 may proceed with determinations of the performances that may be 
 expected of it. 
 
 The Glide or Volplane 
 
 In horizontal flight the thrust of the propeller in pounds is just 
 slightly in excess of the total Resistance of the Aeroplane. When 
 the motor is shut off, however, this balance between power required 
 and power exerted ceases, and a distinctly different condition of flight 
 results. If some other force were not introduced to overcome the 
 total resistance, which is still about the same as in the conditions of 
 power flight,* the aeroplane would slow down and finally fall in some 
 dangerously unbalanced condition. Such a force can at any moment 
 be introduced, by merely inclining the path of the machine down- 
 wards, enough to cause the gravity force, equal to the weight, to be- 
 come the resultant of two forces a Lift on the planes, less than the 
 weight W, and a forward component of this gravity force, equal to the 
 Total Resistance. The machine then descends, on a downward path, 
 in which the power spent in descending the machine's weight at an 
 inclined rate corresponding to a fall of a certain number of feet per 
 second is equal to the power used up in overcoming the total Resist- 
 ance, at the particular speed, on this downward path. The determi- 
 nation of the slope of this path, becomes very easy. It is merely the 
 ratio of the Weight of the machine to the Total Resistance, at the 
 particular angle of incidence and speed assumed on the glide. This 
 
 * It is to be noted that in a tractor, the air propeller throws back a stream of air 
 on the body that has a speed greater than the aeroplane's speed, so that shutting off the 
 engine slightly reduces the Total Resistance.
 
 104 
 
 feature is considered again in connection with the Stability and Opera- 
 tion of the aeroplane. 
 
 A curve of "gliding angles" is readily plotted on the Resistance 
 Chart, by dividing the weight by the Total Resistance at any point. 
 Thus, at 55 m. p. h., the Total Resistance is 215 Ibs. Therefore the 
 gliding slope is 8.4 to 1. In other words, the aeroplane will travel 
 8.4 times as far as its vertical descent. 
 
 High Speed and Low Speed 
 
 It is apparent from a study of the Power Chart, p. 96, that the 
 speed range is determined by the crossing points of the Power Re- 
 quired and Power Available curve. Thus, at 1200 r. p. m., horizontal 
 flight is impossible due to lack of power, above 82 m. p. h., and below 
 41 m. p. h. The speed ranges for other r. p. m. are also indicated. 
 
 Climbing Rate 
 
 Although atmospheric conditions vitally affect the rate of climb 
 and height attainable of any aeroplane, it is possible to determine the 
 initial climbing rate. The climbing of a machine is due to the exer- 
 tion of an extra amount of power, which raises the Ibs. weight of the 
 machine a certain number of feet per second, thereby using up a cer- 
 tain horse power. This excess power is directly available, if the Power 
 Available is greater than the Power Required. And a measure of this 
 excess power is the difference between these two curves. Thus, at 56 
 m. p. h., the Power Required is 32 h. p., and the corresponding Power 
 Available at 1200 r. p. m. in actual thrust, at that speed, is 63 h.p. 
 Therefore, we have a reserve power of 31 h. p., which can be entirely 
 made use of in climbing the machine. Since the weight is W = 1800 
 Ibs.. the equation for climb becomes, 
 
 H. P. for climb = 1800 x climbing rate in feet per second, whence, 
 Climbing Rate = H. P. in foot Ibs. per second -4- 1800 Ibs. weight. 
 Therefore, for this example, 
 
 31 x 550 
 
 Climb in feet per minute = x 60 = 570 f. p. m., rate. 
 
 1800 
 
 Summary 
 
 Other curves giving the economy in fuel consumption and cor- 
 responding engine speeds and aeroplane speeds, are explained on p. 
 97, and are of very practical value. 
 
 By the processes outlined in this chapter, the performances of 
 an aeroplane may be predicted and recorded, with an accuracy and 
 value that is, indeed, not only of great interest, but of real benefit to 
 the aeroplane user. 
 
 It is seen that the characteristics of the aeroplane, from which 
 the performances may be predicted so readily, are based on the data 
 furnished by the laboratory tests on the aerodynamic features and 
 the engine, so that the significance and importance of this informa- 
 tion becomes evident.
 
 CHAPTER IX. 
 STRESSES AND SAFETY FACTORS. 
 
 The nature and magnitude of the supporting and resisting pres- 
 sures on aeroplanes, and their effect in determining characteristics 
 and performances to be expected when the thrust power available 
 and fuel consumption are known, constitute one feature of the study 
 of the aeroplane, as outlined in Chap. IV., p. 41. We may proceed, 
 therefore, with a consideration of the second feature the study of 
 the construction of the machine. And eventually, after having given 
 attention to stability and operation, we will be at liberty to discuss 
 the various military types of aeroplanes. 
 
 It is necessary to know the distributed loading on the aeroplane, 
 of the air forces generated by the movement thru the air, before pro- 
 per consideration can be given to the stresses and safety factors in its 
 structure. 
 
 In gliding, the lifting forces on the wings are slightly less, and 
 in climbing slightly greater, than in horizontal flight, but only in a 
 small degree. When attacked by sudden puffs, the air forces are in- 
 creased in various ways; banking on turns introduces extra stresses, 
 due to the centripetal force ; and in various maneuvers such as a sud- 
 den recovery from a steep dive, looping the loop, flying with full power 
 at very high angles, etc., additional loads are imposed on the structure 
 of the machine, which must be withstood. 
 
 Safety Factor 
 
 The ratio of the breaking strength of any structural part to the 
 load imposed upon it, is termed the safety factor of that part. Thus, 
 if a wire requires a tension of 3000 Ibs. in order to break it, whereas 
 the load it carries is only 300 Ibs., it is said to have a safety factor of 
 10. In ordinary engineering practice, the load that it is considered 
 necessary for any part to carry is taken as the maximum load that 
 the particular part will ever have to stand, and, in designing it, a safety 
 factor is applied to this maximum possible load. Contrary to all good 
 engineering practice, the structural parts of an aeroplane are gener- 
 ally designed to have a certain "safety factor," with reference to the 
 normal flying load, determined by the weight of the machine. The
 
 106 
 
 excess stress due to some additional maneuver is taken account of 
 in the "safety factor" itself, so that in the engineering sense it is not 
 a safety factor at all, but merely an allowance for extra stresses, in- 
 duced by conditions other than ordinary horizontal flight. It is pos- 
 sible to estimate what the maximum possible stresses are, and to deter- 
 mine whether or not the aeroplane will collapse when they are im- 
 posed. And in general an aeroplane is so designed that the strength 
 of its weakest structural part will at least be great enough to with- 
 stand a reasonable value of this maximum stress, without breakage, 
 the real safety factor being very seldom as much as two. In most 
 other branches of engineering a safety factor of at least ten is required. 
 The object of a safety factor is to provide against the increased stresses 
 of sudden impact shocks, which are difficult to estimate, and to take 
 account of defective material and workmanship, so that, at first sight, 
 it would seem odd that intelligent engineers should permit this gen- 
 eral conception of "safety factor" in aeroplanes to survive, thereby 
 apparently still further increasing the dangers of aviation. It is useless 
 to deny this element of danger, or to attempt to excuse it, on any ground, 
 excepting that it is a well considered compromise of opposing features. 
 
 An aeroplane, constructed with a high safety factor, on the maxi- 
 mum stresses to which it can be subjected, would actually prove so poor 
 and dangerous a flyer and so difficult to land, due to its enormous 
 weight, that ever-present dangers and limitations in its operation 
 would far outweigh the possible dangers of its not being quite strong 
 enough to stand some very unusual and remote maximum stress, to which 
 in the hands of a well informed aviator it would never be subjected. 
 The justification for building aeroplanes as light as possible, and cut- 
 ting down to the limit of simplicity and necessity all the structural 
 features, is exactly what makes a well-built aeroplane one of the most 
 refined of engineering structures. The fact is only too often lost sight 
 of, that increasing the strength of an aeroplane for flight, by thicker 
 spars and struts, heavier wires, cables and larger fittings, immediately 
 requires a landing gear much heavier in proportion, all of which results 
 in a very much heavier machine, which for the same flying character- 
 istics will require a more powerful engine, not only heavier in itself, 
 but requiring more fuel, larger tanks, etc., until the final result is a 
 machine in which the higher safety factor is largely lost by greater 
 stresses due to the increased weight with nothing gained. In aero- 
 plane engineering there seems to be a remarkably nice balance be- 
 tween flying capacity and limitations of strength due to allowable 
 weight of machine. And the degree in which strength has been gained 
 by lightening up a machine, thereby improving its flying capacity, is 
 a better criterion by which to judge of an aeroplane.
 
 107 
 Maximum Stresses. 
 
 The greatest source of danger in flying, due to imposing great 
 stress on the wings, is, without question, given rise to in flattening 
 out sharply after a long dive. Modern aeroplanes have compara- 
 tively low structural and drift resistance, and when pointed earth- 
 wards the gravity force of the weight is opposed only by the air re- 
 sistance of the machine, so that in diving steeply the aeroplane read- 
 ily acquires a velocity through the air very much greater than its maxi- 
 mum high speed in horizontal flight. If, after acquiring a great speed, 
 due to a steep dive, the aeroplane is turned, to flatten out and fly hori- 
 zontally, a centripetal force must be exerted on the wings in order 
 to make the turn. For any given radius of turn r, in feet, an aero- 
 plane of weight w, pounds, having acquired a speed thru the air of 
 v feet per second, will have to have exerted upon it a force equal to 
 wv 2 /32.2 r (see p. 30). in order to flatten out at this rate. As an ex- 
 ample of the magnitude of this force, let us take the case of an aeroplane, 
 weight loaded = 2000 Ibs., which dived a few hundred feet and ac- 
 quired a speed of 75 miles an hour (110 f. p. s.), and which the pilot 
 rather quickly flattens out by turning up on an arc of radius = 100 
 feet a quick recovery to be sure, but not at all unusual. The centri- 
 petal force exerted on the wings, is, 
 
 wv 2 2000 x 12,100 
 
 = 7520 Ibs. 
 
 gr 32.2x100 
 
 a stress almost four times as great as the weight of the machine. 
 
 The magnitude of this force for greater speeds and sharper turns 
 would seem enormous, but there is a definite limit, since, if this force, 
 which makes the machine take a curved path, exceeds the maximum 
 pressure corresponding to the angle with the highest K of the wing 
 surfaces for the particular aeroplane speed, the aeroplane will "slip" 
 and refuse to take this curve, since the air pressure on its wings cannot 
 be made greater than the maximum pressure. It becomes quite easy 
 then to determine the limiting stress. The maximum speed attain- 
 able on a glide is the one for which the air resistance becomes equal 
 to the weight of the machine. This limits the speed of falling. A 
 simple way to estimate it is to determine from the Resistance Chart, 
 the minimum value of the quantity KS in R = KSV 2 . Then sup- 
 plying this same K S, and R = Weight of machine, a solution is ob- 
 tained for V 2 , the maximum diving speed. Thus, it is found, p. 96, 
 that at 85 m. p. h., on the Resistance Chart, R = 365 Ibs., and V 2 = 
 7225; it follows that K S = 365/7225 = .0505. The assumed total 
 weight is 1800 Ibs., so that 
 
 1800 = .0505 V 2 , and V = V 35,600 = 189 miles per hour.
 
 108 
 
 The maximum value of K for the wing (about .003), would indicate 
 that if the machine after diving several thousand feet vertically, could 
 suddenly be turned up, the wings would "bite" the air with a force 
 KS V 2 = .003 x 335 x 189 2 = 35,650 pounds, which is almost twenty 
 times the weight of the machine. This is the limit that is approached, 
 and it is clear that the lower the head resistance of a machine and the 
 greater the surface and weight, the greater does this become. On 
 the other hand, the greater the longitudinal moment of inertia, the 
 more difficult does it become to flatten out sharply. 
 
 In turning, the additional force on the wing, caused by banking 
 the machine, and required in order to hold the machine to the turn, 
 may be determined in the same way. Other excessive stresses, such 
 as those induced by sharp upward puffs, are not as easily evaluated, 
 but careful observation indicates that the forces of sharp puffs, or 
 sudden changes in wind direction, may easily give stresses three to 
 four times the weight of the machine. 
 
 Although the stresses in the main wings are the most important 
 ones, the other parts of the aeroplane also are subjected to great pres- 
 sures. The effects of sudden maneuvers, or of gusts, in snapping the 
 tail around, not only introduce great pressures on the tail, but subject 
 the fuselage to severe twists. The proper proportioning of parts to 
 resist vibration, due to variations in the engine and propeller, is 
 almost entirely a matter of experience. And the stresses introduced 
 by landing shocks are a separate class, requiring careful considera- 
 tion and much experience, to be properly taken care of. In taxi-ing 
 on the ground on some aeroplanes with tail skids, enormous twist- 
 ing stresses are induced in the fuselage,, by sharp turns, that every 
 careful pilot avoids as much as possible, since all such stresses are un- 
 necessarily racking and fatiguing the aeroplane structure. 
 
 The maximum stresses in an aeroplane may become very large 
 but, in the hands of an expert pilot, they can be kept under control. 
 Supported in the most perfect pneumatic fashion imaginable, and 
 operated with skill and caution, an aeroplane is not likely to receive 
 impact shocks of dangerous magnitude, and at the present time a break- 
 ing strength of 8 times the stresses due the weight, appears to compro- 
 mise all opposing features properly and to give a sufficient "safety factor" 
 for military purposes. 
 
 Kinds of Stresses. 
 
 In an aeroplane, distinction can be made between six different 
 kinds of stresses: 
 
 (1) Lift stresses on the wings due to the lifting force equal to 
 the weight, and carried by the main struts and wires.
 
 109 
 
 (2) Drift stresses on the wings, taken account of by the inte- 
 rior cross-bracing of the wing. 
 
 (3) Stresses on the control surfaces, transmitted thru the frame 
 or fuselage of the aeroplane. 
 
 (4) Stresses on various small items due to their air resistance. 
 
 (5) Stresses induced by the pull or push of the propeller and 
 secondary effects of gyroscopic action or vibrations on the engine bed. 
 
 (6) Landing stresses on the entire machine, due to the shock 
 of alighting. In view of the variable nature of landing fields and of 
 air conditions near the ground, estimates of these stresses are difficult 
 to make, and are largely a matter of experience for any particular 
 machine. 
 
 The thrust of the propeller is the largest single air force acting 
 at any point on the machine, and necessitates proper distribution over 
 the frame. But it is definite in magnitude, and easily taken care of. 
 
 The consideration given stresses here, is not for the purposes of 
 design, but rather to enable the military aviator more readily to under- 
 stand the information on stresses supplied by the manufacturer. The 
 most important stresses are occasioned by the load lifted on the wing 
 structure. 
 
 Stresses in the Wings and Bracing. 
 
 Since the consideration and method of determining the lifting 
 stresses in the main supporting wings may be extended, readily, to 
 other stresses in the machine, it may prove beneficial to take up an 
 example. 
 
 The process of determining stresses consists, of 
 
 (1) Finding what proportion of the load is carried by different 
 parts of the frame ; 
 
 (2) Determining what stresses these loads induce in the mem- 
 bers of the framework. 
 
 Since a biplane involves practically every feature requiring con- 
 sideration, we may take as an example the aeroplane assumed in Chap- 
 ter VIII, in which the full load weight is 1800 Ibs., the surface area 335 
 sq. ft., chord 5 ft., gap 5 ft., and span 36 feet. Let us assume that the 
 bracing is of the familiar strut and cross-wire type usually termed a 
 "Pratt Truss."
 
 110 
 
 REAR TRUSS CFRONT 
 
 t/ trass = IJ4& * body 
 
 MOMENT DIAGRAM 
 
 HALF SPAM Of AfROPVWE * ^8 FT. 
 
 STRESS ANALYSIS FOR BIPLANE TRUSS 
 
 The loads at the connecting points U, U', U", called panel points, are indicated on the diagram, 
 and are due to the air load on the wings. The heavy line wires are the "flying wires," taking the stresses 
 due to these loads; and the dashed lines in the truss diagram are the "landing wires," taking the weight 
 of wings on landing. 
 
 In the graphical stress method, each panel point is considered in order, and for each one a closed 
 triangle or polygon of forces is drawn. The force polygons must all close, since the point is in equili- 
 brium. 
 
 First, a "sense" of rotation for the diagram is chosen and indicated by the arrow as clockwise, 
 and a scale to which to lay off the forces is chosen. Then, on the truss diagram, the regions between 
 forces are lettered A, B, C, etc., the forces considered being only the forces carrying the truss load. That 
 is why the compression in L"U" is not considered, since it is carried to U" and from there over the truss. 
 Taking the first point U", we have the force between A and B, called ab, = 205 Ibs. total, and the force 
 of compression in U"U', called be and a third force, the tension in the wire ca. Thus, there are three 
 forces at this point. The magnitude of one is known and the direction of the other two, so that a force 
 triangle, as given on the stress diagram abc, may be drawn, such that ab = 205 Ibs. to scale, be, is parallel 
 to U"U', and ac is parallel to U"L'. Their point of intersection establishes the closing point of the tri- 
 angle, thus determining ac and be in Ibs., merely by reading their lengths to the same scale to which ab 
 was laid off. 
 
 Panel point L' is now taken, the forces being taken in the same order going around the point clock- 
 wise. First, we have ac, already solved and then cd, the strut compression, the direction of which we 
 know, so we draw cd thru c, parallel to U'L'. To obtain the rest of the polygon it is now necessary to 
 consider ea, acting upwards at L', which is laid off on the vertical, and then to close the polygon the other 
 force line de, may be drawn thru e, parallel to L'L, the point d being located by the intersection of the 
 lines of action of the two unknown forces thru e and c. Thus, with d found, cd and de are readily read 
 to scale. 
 
 A similar process is employed for the rest of the truss.
 
 Ill 
 
 A moment's thought on the manner in which the air force on the 
 wings lifts the rest of the machine, will lead to the simple conception 
 that an aeroplane is virtually a swing bridge, turned upside down, 
 with a uniform static load of the simplest kind, equal in average in- 
 tensity to 1800/335 = 5.4 Ibs. per sq. ft. (a factor often termed the 
 "loading" of the wing). The complicated stress determinations for 
 steel bridges resulting from "live loads," such as moving locomotives 
 of 300,000 Ibs. weight, are happily in another realm, and as for the 
 actual consideration of the aeroplane structure itself, it is well to real- 
 ize that it is the simplest kind of a bridge. 
 
 For the purposes of this example reference is made to only one- 
 half of the machine, since the other side is symmetrical, and it fol- 
 lows that the upper and lower wings under consideration together carry 
 half the load. 
 
 The load actually carried by the structure is the total weight less 
 the weight of the wings themselves, since the latter pressing down 
 by gravity directly against the air pressure, relieve the struts and wires 
 of having to transmit any stresses due to their weight. If the weight 
 of the wings is taken at 240 Ibs. a reasonable figure the load on the 
 side of the machine we are considering equals (1800 240) -*- 2 = 780 
 Ibs. This is the distributed load over the upper and lower wings. But, 
 due to the biplane effect (Chap. VII), the upper wing may be expected 
 to carry a considerably greater proportion of this load. In general, 
 on a biplane the upper plane carries about 60 % of the load and the 
 lower plane 40 %. 
 
 From this it is indicated that the upper plane on one side, carries 
 780 x .60 = 468 Ibs., whereas the corresponding lower plane carries 
 312 Ibs. 
 
 This load is transmitted by the cloth covering to the ribs, each 
 one of which, acting as a beam, transmits the load to the spars, which 
 in turn are suitably braced to the body by struts and wires, so that 
 Ibs. weight in the body are carried by Ibs. per sq. ft., air pressure on 
 the outstretched wings. But, since this is distributed between the 
 spars, of which in this case (see p. 110) there are two, it follows that 
 separate stress determinations must be made for the front and rear 
 truss. This at once necessitates determining what portion of the 
 load each spar carries. 
 
 The position of the center pressure determines this readily, for 
 if the c. p. were midway between the two spars, obviously they would 
 each carry half the load, and if the c. p. were directly in line with a 
 spar, the entire load on the wing would be carried by it. Since the 
 c. p. moves, and we are here interested in the maximum stresses due 
 to carrying the weight, the next step is to determine the max. rear
 
 112 
 
 position of c. p. applying the greatest load to the rear spar, and max. 
 front position for the front spar. This is done (p. 110), and from what 
 information we already have on the aerofoils and the aeroplane, we 
 may recall that the former condition corresponds to a high speed and 
 low angle of incidence, and the latter to a slow speed and high angle of 
 incidence. 
 
 Since the data indicates that the rear spar carries a maximum 
 of 75 % of the load at incidence, it follows that the upper plane rear 
 spar, which spans 16.5 feet, carries (468 X .75) -^ 16.5 = 21.3 Ibs. 
 per foot run, and the lower plane rear spar, carries (312 x .75) -r-15.5 
 = 15.1 Ibs. per foot run, the spans being taken to include allow- 
 ances for the rake and reduction of pressure of the ends of the planes, 
 and for the body section. 
 
 Knowing the spans we can, as has been done on p. 110, indicate 
 the load at each panel point U, U', U", etc. This load, which is the 
 force carried thru the truss, results from the uniform loads on adja- 
 cent spans. For example, U' carries half the load on span UU' = 21.3 
 X 3.125, plus half the load on span U'U" = 21.3 x 3.625, which to- 
 gether give 144 Ibs. The other panel loads are obtained in the same 
 way, and since the slopes of wires and depth of truss are outlined to 
 scale, the graphical method explained, p. 110, is reaily made use of 
 to determine the stresses in the members of the truss. 
 
 The tension stress on any wire, as determined in the stress dia- 
 gram, may be compared directly with the breaking strength of the wire, 
 to determine the safety factor. Thus, if L U' indicated by dg, as having 
 a stress of 730 Ibs., consists of two 5/32" cables each with a breaking 
 strength of 3000 Ibs., the "safety factor" is more than 8. 
 
 The strength of struts is not as readily found, since struts usual- 
 ly fail by bending. Only in the case where a strut is very short and 
 thick is it possible to find its strength by multiplying the compres- 
 sion strength of the material in pounds per square inch by the cross- 
 sectional area. Failure from bending makes it necessary to introduce 
 standard engineering formulae*, which vary greatly among them- 
 selves and are largely based on experiment. Their object is merely 
 to determine a reduced value of the allowable compressive strength 
 of the material, to take into account the weakening due to bending. 
 As an example, spruce, ordinarily, stands 5600 Ibs. per sq. inch in direct 
 compression, whereas one of the most practical strut formulae taking 
 into account the average dimensions of aeroplane struts, reduces this 
 
 * These formulae and data are ordinarily furnished by the manufacturer, and 
 if need be are readily checked by actual breakage test on a strut. A typical formula 
 is the RAF strut formula. 
 
 FA 
 
 Crippling Strength = , in which F = allowable compression stress, 
 
 1 + 6500 P/k 
 A = area of section 1 = length of strut in inches, and k = least radius of gyration.
 
 113 
 
 to about l/5th, giving 1100 Ibs. per sq. in., as the ultimate strength 
 to be expected. If U'L' is made of spruce, with 2.3 sq. in. cross section, 
 it may be expected to have a strength of about 2.3 x 1100 = 2500 Ibs., 
 and since the stress induced is 310 Ibs., there is a safety factor of 8 (see 
 p. 110). 
 
 Spars. 
 
 The stresses on the wing spars are considerably more compli- 
 cated and frequently of greater importance, than stresses on other 
 members. In almost all aeroplanes, nowadays, the upper spars are 
 the weakest structural parts. 
 
 This is due largely to their receiving a combination of stresses 
 which, as will be seen later, causes the spar progressively to weaken as 
 the stresses increase, due to deflection. 
 
 The type of construction of wings, is now almost universally stand- 
 ardized, and consists of carrying the air pressure by means of cloth 
 covering to light ribs running fore and aft, which are formed to give 
 the aerofoil section desired. These ribs are carried by large beams 
 or spars running across the wing transversely, and these spars are braced 
 to the rest of the machine by suitable struts and wires, as already indi- 
 cated. The stresses on the spars, therefore, may be divided into two 
 items : 
 
 (1) The stresses due to the loading of the spar as a beam, carry- 
 ing the air pressure loads transmitted by the wing covering and ribs; 
 
 (2) The stresses due to their part in the general bracing of the 
 wing truss, as found by the stress diagram, p. 110 ; which indicates 
 at once that as members of the rigid truss, the lower spars are sub- 
 jected to tension and the upper spars to compression. 
 
 The result of the application of these stresses to the spar, may 
 be taken up as follows : 
 
 (a) Compression or Tension Stress in Spar. The allowable 
 breaking load in Ibs. per sq. in., for the particular material used, mul- 
 tiplied by the area of the cross section of the spar in sq. inches, gives 
 the breaking strength, which, divided by the load as determined from 
 the stress diagram, determines the factor of safety for that stress. 
 
 (b) Bending due to the pull of wires of the frame, attached un- 
 symmetrically with reference to the neutral axis of the spar. This 
 feature on some machines is of considerable magnitude, but fittings 
 are so readily made to bring the pull of wires, etc., all together at any 
 one point, symmetrical with the beam's center line, that they should
 
 114 
 
 UNIFOKH LOAV 
 (VNCfHTKAri-t LOW W Iba . per foel *vn 
 
 . '. 73 /7/v!f> r, 
 
 OF 7f SFCTION BY 
 
 Bending Moments and Sections of Beams 
 
 always be demanded, so as to enable this unnecessary load on the wing 
 to be eliminated. 
 
 (c) Bending and Compression due to the Drift Load. This is 
 an element in the rigidity of the wing, which requires that the stresses 
 be taken care of by suitable cross bracing, etc., but as a factor in de- 
 termining the strength of the spars, the drift loads are so small in pro- 
 portion to the lift loads, that they are negligible, for our purposes. 
 
 (d) Bending due to Uniform Load of air pressure on the Wing. 
 - This load is the principal one on a long span, and since the load may 
 
 be considered as spread uniformly, along the spar, the ordinary engi- 
 neering formulae for beams are directly applicable. 
 
 (e) But the bending of the spar due to the uniform air loading, 
 introduces a certain deflection of the beam, which gives any compres- 
 sive force on the spar due to the truss load a chance still further to 
 increase the bending moment. In the inner spars of the upper wing 
 of an aeroplane, this stress is by no means a negligible one. 
 
 The stresses on a beam, then, are first considered in the deter- 
 mination of the several bending moments due to the loading and these 
 are combined and charted for convenience on a "moment diagram," 
 an example of which is given on p. 110. The truss is laid off to scale 
 as indicated, and the bending moment values are given in "Ibs. ft." 
 Suitable corrections are applied for the continuity of the spars, and 
 these diagrams, furnished for each spar by the manufacturer, enable 
 the value of the total bending moment at any point to be read.
 
 115 
 
 Bending Moment. 
 
 It would prove beneficial here to consider what is meant by "bend- 
 ing moment," and how it is made use of in strength determinations. 
 
 In the tension on wires and the compression on struts or spars, 
 the load stresses are taken up by members which have areas of a cer- 
 tain number of square inches of a certain material. It is known by 
 experiments that the particular manner in which the material is used 
 permits of assigning to it a certain breaking strength, called "fibre 
 strength" or "modulus of rupture," which is most easily expressed 
 as a certain number of "Ibs. per sq. inch." The area of the member 
 times the strength of its material per unit of area, gives the total act- 
 ual force that it is reasonable to expect would break the member in 
 question. In beams, however, the loads are not applied endwise, 
 so that instead of having a direct push or pull, the beam is subjected to a 
 bending. 
 
 The loads on the beam tend to make it sag and the amount of sag 
 for any given load is determined not only by the load, but by the man- 
 ner in which the beam is supported. 
 
 1. The beam may merely be resting freely on its supports, or 
 pinned to them in which case it is termed a "simply supported" 
 beam. 
 
 2. The beam may be fixed at both ends and held firmly in its 
 supports, or may be continuous over several spans in which case it 
 is termed a "fixed end" beam. A "cantilever" is a fixed end beam, held 
 only at one end. 
 
 When loaded, the beam resists the bending tendencies of the load 
 with a force which varies from that of a light string (which has practi- 
 cally no beam strength) to the deep plate girders of a railroad bridge, and 
 which is determined by the shape, span, size, and material of the beam. 
 
 The mechanics of the action of a beam are very simple. The 
 forces, and air pressure loads, have lever arms and, therefore, moments 
 about any point of a spar that we care to consider. These can all 
 be summed up into an equivalent force, in Ibs., with a certain lever 
 arm in feet. This moment is the "bending moment" for the partic- 
 ular point under consideration. On beams that are loaded uniformly, 
 like the spars of an aeroplane, the maximum bending moment is found 
 at the center of the beam, and decreases as the points of support are 
 approached, with the exception that the continuity of spars over two 
 or three spans may slightly modify this. 
 
 This maximum bending moment for any beam, loaded uniformly, 
 is readily found by supplying values for the quantities in the accom- 
 panying simple formulae. This, then, gives us the value of the "bend-
 
 116 
 
 ing moment" due to the air loading, which is the important one for 
 the spar, but which is slightly modified by the other forces causing 
 bending, as already indicated. 
 
 The total maximum bending moment as determined by the manu- 
 facturer and read from the diagram for the beam, is equal in its effect 
 to the twist of a force in Ibs. with a leverage in ft., giving the same 
 Ibs. ft. moment, about the center of the section of the beam, at the 
 point considered. 
 
 Any "twist" or moment of this kind would naturally be taken 
 up by a tension resistance on the upper side of the beam and a com- 
 pression on the lower. The final test is what "the extreme fibre" of 
 the beam will stand, since, if the beam begins to cripple on the upper 
 or lower flange, it will progressively weaken to the breaking point. 
 
 The strength of the extreme fibre of a beam, then, expressed in 
 Ibs. per sq. inch, will give us a measure of the resisting force of the 
 beam; and the depth of the beam from the center or neutral axis to the 
 outer edge is the lever arm of this "Resisting Moment" of the beam, 
 which opposes the "Bending Moment" of the loads. 
 
 This Resisting Moment for any beam is, 
 
 M = K I/d 
 
 where, K = the strength per sq. inch of the material, I = the moment 
 of inertia of the section, and d = the distance from the neutral axis 
 to the extreme fibre = ^ depth of beam. 
 
 If it were desired to know what fibre stress was induced in a beam, 
 for which I and d were known, by a bending moment M, the value 
 of which is known, it would merely be necessary to solve for K in the 
 above formula. So that on a spar, if to this determined fibre stress 
 there is added the stress per sq. in., due to the compression, a value 
 is at once obtained for the total intensity of stress in Ibs. per sq. in., 
 on the weakest extreme fibre of the beam. Comparing this value with 
 the breaking strength of the material in Ibs. per square inch gives the 
 safety factor for the spar. 
 
 An example would serve to illustrate how the safety factor of a 
 spar may be determined. Let us suppose that the rear spar in the 
 span UU', (see p. 110) consists of a rectangular section beam of spruce 
 3 inches deep and 1 inch wide, and with a cross-sectional area of 3 sq. 
 inches. The span 1 is 6 1/4 ft. and the load per foot of spar is w = 21.3 
 Ibs. per foot. 
 
 We could read from the moment diagram furnished what the 
 maximum bending moment is, account having been taken of the nature 
 of fixing of the ends of the spar, the moments due to any unsymmetrical 
 wire pulls, etc. For the purposes of convenient analysis, in the field, how- 
 ever, it is not necessary to go into these details. A sufficiently accurate
 
 117 
 
 conception of the bending moment in the beam is obtained by con- 
 sidering the ends fixed, and finding the large moment due solely to 
 the air load on the spar per foot run. The table given shows this to be, 
 
 wl 2 21.3x6.252 
 
 B.M. = - - = 69.5 Ibs. ft. 
 
 12 12 
 
 It is desired to find what stress this bending moment induces on 
 the outer fibre of the beam. We merely substitute, then, in the equa- 
 tion, 
 
 M = K I/d 
 
 taking care, however, to express M in Ib. inches, by multiplying by 12, 
 to correspond with the units of I and d. 
 
 For any rectangular section beam, the moment of inertia I, is 
 bd 3 /12, and in this case d = 3 inches and d = 1 inch, so that I = 27/12 = 
 2.25. The distance to extreme fibre from the neutral axis equals half 
 the depth of the beam = 1 }/ inches, and solving we get 
 
 2.25 
 
 M = 69.5 x 12 = K x , whence 
 
 1.5 
 
 K = 555 Ibs. per sq. inch. 
 
 To this stress must be added that due to the compression truss 
 load also carried by these same fibres. From the diagram on p. 110, 
 this is seen to be 870 Ibs. and being distributed over the 3 sq. inches of 
 cross-section of the spar, adds a stress of 290 Ibs. per sq. in. to the spar. 
 
 The totaf fibre stress, then, is the sum = 845 Ibs. 
 
 The material of the spar being spruce, which has a fibre strength 
 of 5600 Ibs. per sq. inch, it follows that the safety factor for the spar 
 is 5600 + 845 = 6.64. 
 
 It is of interest to note that the continuity of spars over several 
 spans is apt to reduce the value of the max. bending moment, but in- 
 creases its value at the points of support. This is determined by the 
 Theorem of Three Moments, which it is not necessary to consider 
 here, but a characteristic bending moment diagram inclusive of these 
 corrections is shown, p. 110. As indicated in this example the b. m., 
 due to the air load on the span, gives an excellent and sufficiently intel- 
 ligible indication of the magnitude of the stress in the spar. 
 
 The upper rear spar of the panel, next to the body, on a tractor 
 biplane is almost always the weakest member of the entire structure, 
 and is subjected to a combination of loads that are very formidable.
 
 118 
 
 A study of a stress diagram, as to the distribution of loads, and 
 the magnitude of bending moments, should always be made by a con- 
 scientious aeroplane pilot, in order to obtain an appreciation of the 
 nature of the stresses his machine is required to withstand. 
 
 The weakening of spars by the drilling of holes, for some extra 
 kind of fitting, should never by done, until the moment diagrams have 
 been consulted and a rough calculation made of how much the reduc- 
 tion in sectional area caused by the hole, is going to weaken the spar. 
 
 The splicing and re-enforcing of spars by ferrules, etc., is taken 
 up later, and should always be considered in the light of preserving depth 
 of section and strength in extreme fibre. 
 
 Tightening of Wires. 
 
 A feature that results directly from a consideration of the aero- 
 plane structure as a truss, is, that extra stresses may be induced on 
 the members by tightening up too much on some parts, lack of proper 
 fitting, etc. The systems of wiring on aeroplanes consist of the "fly- 
 ing wires," indicated by full lines on p. 110, and the "landing wires," 
 indicated by the dashed lines. The stresses for the former are deter- 
 mined by the methods already outlined. 
 
 The stresses on landing wires are largely indeterminate, and proper 
 strength to take landing shocks is a matter of experience. Due to the 
 possibility of large negative air loads, the "landing wires" are usually 
 made of practically the same strength as the "flying wires." 
 
 In addition to these, the general rigidity of the truss and resist- 
 ance to drift loads, twists, etc., requires, cross wiring from front to 
 rear of the panels. (See photographs in Chap. II.) 
 
 The entire structure, therefore, is cross wired and completely 
 braced, although in flying only the "flying wires" should take the loads. 
 
 Nevertheless, complicated extra loads can be induced on the spars 
 and struts and flying wires by the universal mistake of having the 
 wires too tight. Thus, if L U' and U L' are both tightened up too 
 much, L U' before it ever receives its proper flying load, is carrying 
 an initial load due merely to the tightening, while the spars L L' and 
 U U' are perhaps already bent up and weakened before they ever re- 
 ceive their air load bending moments. Buckling of spars and struts 
 and initial stresses in wires, due to having the trusses tightened up 
 too much, greatly fatigue the parts, introduce entirely uncalled for 
 stresses and are apt to result in serious crippling. Wires should never 
 "sing" and need only be tight enough to avoid deflection of the truss 
 when loaded.
 
 119 
 "Follow Thru" 
 
 The characteristic wing sections, struts and wires, the stresses 
 in which have been considered here, are readily distinguishable, in 
 the photographs of aeroplanes, p. 15 and p. 17, and may conveniently 
 be referred to. Some aeroplanes have "overhangs," others more panels 
 than taken in the example p. 110, etc., but the general principles of 
 finding the air loads and solving the stresses graphically are the same. 
 
 There is one very important feature, however obvious it maybe 
 on the stress diagram, that, to the unpracticed eye, is not so easy to 
 appreciate on a full sized aeroplane, i. e., the degree in which the stresses 
 induced in the wires, struts and spars, are carried thru the truss to 
 their logical end, so as really to "complete" their strength. A wire 
 may be strong enough in itself to hold the stress induced in it, but the 
 fitting holding this wire at the base of the strut may not be properly 
 proportioned. 
 
 On monoplanes, (see p. 20), the wing spars are subjected to a 
 large compression, due to the truss load, and may be made strong enough. 
 These spars, however, on either side* of the body, press against the 
 body towards each other with an enormous compression. Lack of 
 attention in following thru these stresses so that the spars could butt 
 directly against each other with ample compressive strength, led many 
 constructors to provide therefor merely by permitting the spars to 
 rest in sockets against the body with no suitable provision across the 
 body at this point. Many accidents are attributable to the crush- 
 ing of the body by this spar compression, due solely to lack of "follow 
 thru." 
 
 A typical example is found today in more or less serious measure 
 on many tractor biplanes of reputable construction. Reasons of sim- 
 plicity and convenience in the chassis have eliminated auxiliary safety 
 wires from points like L' (see diag. p. 110) to the chassis. It follows, 
 then, that the pull of the wire L U', and the tension in the spar L L', 
 are all exerted at the point L, on the body. It is customary to draw 
 the diagrams and determine the stresses and safety factors for all the 
 struts, wires and spars, but not always is the proper attention given 
 to the cross member at the body, indicated in the diagram by O Y. 
 As a matter of fact, this member carries an enormous tension a stress 
 of 870 Ibs., from both sides of the truss and the "following thru" 
 of the tension in wire L U', denoted as dg, across under the body, con- 
 necting to the wire symmetrical to L U', on the other side of the aero- 
 plane, is of the very greatest importance. A safety factor of at least 
 ten should be demanded on this tension stress, and more attention paid 
 to it. Similar instances can be cited, but the general principle is the 
 same, and applies equally in importance to the proportioning of bolt 
 heads, plate fittings, pins and turnbuckles to develop the full strength
 
 120 
 
 of the wire or cable to which they are attached. An expert can spot 
 these flaws in construction quite readily, but the location of the "weak 
 link" in the chain is not always so apparent to the amateur, and mili- 
 tary aviators can profitably spend considerable effort in acquiring that 
 "knack" that will enable them to locate lack of "follow thru," in the 
 construction of the machines they are using. 
 
 Details of construction that bear directly on this are studied in 
 the next Chapter. 
 
 An aeroplane with a "safety factor" of 12 throughout. The Sturtevant military 
 tractor, in which provision is made for carrying two gun turrets. 
 
 Above Views in flight with and without turrets.
 
 CHAPTER X. 
 ASSEMBLY AND CONSTRUCTION. 
 
 Although it is difficult to give in written form all the practical 
 information and directions desirable relative to the assembly, align- 
 ment and verification of construction of aeroplanes, a few notes are 
 presented here, accompanied by some data on the strength of aero- 
 plane parts, that may be of use. Structural details on aeroplanes 
 differ greatly, but the ones chosen here as examples will serve to illus- 
 trate the mode of procedure in considering these details, and, at the 
 same time, will be found to give many suggestions, to help in repair 
 and maintenance work in the field where, as already stated, resource- 
 fulness in keeping the equipment in operation is of the greatest import- 
 ance. 
 
 Aeroplanes for other purposes may become elaborate in construc- 
 tion and exceedingly replete in extra fittings, but for military pur- 
 poses it is quite certain that the structural details will become as simple 
 and as easy to repair as possible, with particular attention paid to hav- 
 ing parts accessible for inspection and easy to take down or assemble. 
 And in order to reduce the amount of stores necessary to carry around 
 in the way of "spare parts," it should be an elementary policy of the 
 construction department of a Flying Corps to standardize as many parts 
 as possible, accentuating interchangeability of parts, and reducing 
 to the minimum the different grades and thicknesses of lumber, the dif- 
 ferent sizes of wire and the thickness of steel plate used in fittings, so 
 that a small stock of raw material may be found suitable for repairing 
 practically any part of the machine. 
 
 Unpacking. 
 
 An aeroplane received from the manufacturer almost always has 
 suffered from shipment or packing in one way or another, and in taking 
 the parts out of the boxes and crates, great care should be exercised not 
 to do any more damage. 
 
 Aeroplanes do not seem so fragile when they are all assembled, tight- 
 ened up and trim, but when dis-assembled they can easily be maltreated. 
 
 One of the most serious things to watch out for is the bending or 
 twisting of wires and cables, as they are coiled or uncoiled for conven- 
 ience. Cable can readily be unravelled, and hard wire, if bent up too 
 much, should under no circumstances be straightened, but the entire 
 wire must be replaced. The same holds true of turnbuckles, fittings 
 and bolts, which, in unpacking and setting up may become more or less 
 seriously bent up or knocked out of true, and the wilful straightening
 
 122 
 
 of these'parts, without bringing them to the attention of someone who is 
 competent to judge of the degree of weakness resulting from the damage 
 is most reprehensible. 
 
 Among other things, it is the universal experience that wings or 
 other surfaces may have suffered a few holes or rips. These should all 
 be repaired, first by cross-stitching and then by covering with a glued 
 patch of the same material as the wing covering and then, 
 
 Care should be taken, never to lay tools on the planes. 
 
 Caution should be exercised, not to permit bolts or turnbuckles 
 to fall on the ground or in the sand, with possibilities of unnecessary 
 damage to the threads by grit. And to prevent any chance of loss or 
 error, each part should be tagged and tied to the place to which it belongs. 
 
 Alignment, or "Trueing up." 
 
 From a consideration of the foregoing we are at once led to the 
 study of the trueing up, or lining up, of the truss of an aeroplane, so 
 as to obtain the proper alignment of the members, with respect to 
 each other and to the rest of the machine. 
 
 "Trueing up" may be defined as the process by which the wings 
 and rudders are adjusted to the body and line of thrust, so as to give 
 the proper angle of incidence, dihedral, decalage, etc., with perfect 
 symmetry. 
 
 Since slight errors in alignment cause marked changes in flying 
 qualities, this subject is a particularly important one for practical 
 field work, and it should be borne in mind that an aeroplane must be 
 properly trued up, just like any other delicate piece of machinery, 
 before the best results can be obtained from it. 
 
 Aeroplanes can, of course, be flown when more or less out of align- 
 ment, but tricky characteristics are apt to arise from this, and the ma- 
 chines will not give their best and most pleasing performances, while 
 they may actually prove dangerous. 
 
 There are four general methods of lining up an aeroplane: 
 
 1. By level and plumb bob, in a factory or shed, with a solid 
 floor. 
 
 2. By transit, projection of angles and levels. (The most ac- 
 curate method, and of great convenience in a factory in setting up.) 
 
 3. By measurements of cross distances and wire lengths, com- 
 bined with sighting. 
 
 4. By sighting alone. 
 
 Methods 1 and 2 are obviously capable of great accuracy in a 
 factory, and should be resorted to when the aeroplane is first con- 
 structed. 

 
 123 
 
 Methods 3 and 4, may be used anywhere at all, on the side of a 
 hill, if necessary, and directly concern us here in reassembling a machine 
 for use on the field. 
 
 Types of aeroplanes differ widely among themselves, and actual 
 instructions and measurements for lining up aeroplanes are required 
 to be furnished in complete detail by the manufacturer. 
 
 Certain general principles of importance are involved, however, 
 to which special attention must be given. 
 
 All bolts on fittings should be tightened before any trueing up 
 of wires is attempted. 
 
 Turnbuckles, when assembling, should first have the barrel taken 
 off and then be started even and turned up about 6 or 8 turns enough 
 to give a firm hold. 
 
 In tightening up any wires, as already indicated, the tension should 
 not exceed that required to make the wire just taut and free of sag or 
 vibration. 
 
 In placing bolts in fittings, or in spars, great care should be taken 
 to see that the threads are neither worn nor burred, and that the bolts 
 are not forced in too strongly since they have been made to fit well 
 and are driven home best by carefully directed, easy pressure. 
 
 Under no circumstances should wings and their parts be ham- 
 mered and jerked into place, since if the parts do not fit together snugly 
 and smoothly there will be some extra strain somewhere, when they 
 are finally assembled. In this connection it must be borne in mind, 
 however, that treated linen covering may tighten so much on a wing 
 frame that, if left standing for a long time, it may twist and warp the 
 wing out of shape. 
 
 Assuming a biplane of the common tractor type, with a small 
 center section and wings, each of two panels, in which the chassis and 
 body are assumed to be in proper alignment, it may prove of interest 
 to consider the assembly and trueing up by methods (3) and (4), out- 
 lined above. 
 
 Assembly and Alignment by Cross Distances. 
 
 The several steps in the assembly are indicated by referring to the 
 sketch on p. 124. To begin with, the center section of wing over the 
 body, is set over the body, on the four small struts. The first step in 
 alignment is to make this center section parallel to the body and centered 
 over it. Since the body is lined up, and the section aff'a', is a parallelo- 
 gram, it follows that the cross distances, indicated as af, may be made 
 equal, in order to center up. When this is done for both front and rear 
 trusses, the center section is bound to lie parallel to the body axis, provid- 
 ing, of course, the distances were measured between symmetrical points.
 
 124 
 
 , THE 
 
 HIKES PC, DH, DA,MUST4Ll BE LOOifNff (JP, BfFOKe 
 C CAN BE M/5&, JMCF THT HOW OJ //V PVITKIN. 
 AFTfft 7fjf AKE LOCSfNED C IS ^A/SfD Bf 
 TlC,HTHin/(, 
 
 Diagrams for Alignment. 
 
 It then remains to adjust the front and rear wires until the section has 
 been pulled forward or back, so that one measurement f"a agrees with 
 the similar one on the other side of the body and with the data on the 
 machine. But these wires should not be tightened up until the wings 
 are on, in order to give play for the spar fittings of the wing section. 
 Unless the center section is somewhat near centered, however, difficulty 
 will be found in fitting the rest of the wings. The next step is to fit the 
 lower wings on either side to the body, and to hold them up by means 
 of their landing wires, fastened to the proper fittings at aa', but not 
 tightened up. The top wings next to the body are then fastened to the 
 center section and held in place by hand until the struts de, d'e', are 
 inserted, when the landing wire ae, a'e', will hold both wings in place. 
 If the wings have no dihedral and the fittings are symmetrical, the 
 distances ae and bd, should be equal and can readily be made so, by tak- 
 ing up the landing wire on both sides, front and rear. This will then give 
 the proper setting laterally. If a dihedral is employed, there will be 
 differences in the measurements, ae being shorter than bd, but for proper 
 alignment it is merely necessary to have similar wires on the other side, 
 the same length. Of course, it is assumed that the struts and the size 
 and position of fittings on the spars are unalterably correct. The outer 
 sections may now be put on by the same method, the lower one first, held 
 by the landing wires, and then the top one, supported on the struts, 
 and the cross distances made equal similarly by taking up on the landing 
 wire. The entire wing structure is now assembled, attached to the body, 
 which is resting on the chassis. It is assumed that, laterally, the wings 
 are symmetrical to the body and properly transverse thereto. This is 
 readily checked by measuring the two distances, a h and c d, as indicated. 
 The cross wires running from front to rear between the struts are next 
 adjusted, just to tautness, and the alignment of the struts as viewed 
 from the side is checked by eye. Measurements of these cross distances 
 from top front to lower rear, and lower front to top rear, at the body, 
 are then carried out to the tips, and thus the angle of incidence is checked. 
 The "flying wires" are then all tightened up, just so as not to give the 
 landing wires more than the strain of carrying the weight. Final meas- 
 urements are then made from the rear point of the tail to panel points
 
 125 
 
 h, h', out at the ends of the wings, in order to determine if the transverse 
 wing axis is symmetrical with the longitudinal body axis. The machine 
 is then lined up correctly providing that the distances measured are all 
 taken to some points on fittings or marks on spars and struts, that are 
 absolutely symmetrical for the two sides. 
 
 Alignment by Sighting. 
 
 The process of assembly, as outlined above, would be the same. 
 After the wings are attached to the frame, the trueing up process proper 
 begins. The method consists merely in doing by eye what was done in 
 the previous example by extensive measurements. The first sight is 
 taken, from below the body, up to the center section, so as to get the 
 points a, a', over the points b, b'. Both sides, front and rear are sighted 
 and the positions averaged up by the wires. In assembling, however, 
 no lining up is done, until all the wings are on, held by the landing wires. 
 The observer then stands at s, to one side, and sighting along the top 
 plane, establishes the line across the bolt heads or fittings at a, a', and 
 proceeds first, to bring up d, d', by means of the wires a e, a'e', and then 
 g g', on either side, are brought up by taking up their landing wires until 
 they are in line with a, a', d, d', etc. In other words, the transverse line, 
 across the top of the center section, is projected to either side. The same 
 is done for the rear spar, and then the load wires for the front spar only 
 are tightened, just enough so that when the point h, for example, is al- 
 ternately raised and lowered no wires are seen to slack or sag, the 
 alignment held by the landing wires being the correct one to be held. 
 
 The final and important element in the sighting is to establish the 
 correctness and uniformity of the angle of incidence, which is the main 
 object of the alignment. To do this best, the observer stands 15 to 20 
 feet in front of the fuselage, taking care to center himself, by sighting 
 along the center struts, shaft, axle center, tail piece, etc. The observer 
 then chooses a height, or tilts the machine, so that, when sighting along 
 the top plane, he can see just a little of the under side. This permits 
 him to see a certain point of the rear strut sockets showing against the 
 lower side of the front beam. Then, by holding the head, central, and 
 just high enough to see these points, and moving only the eyes, to right 
 and left, he can note any lack of alignment of the rear spar, parallel to 
 the front spar. This is corrected by means of the rear spar landing wires, 
 if necessary, after which the rear load or flying wires are also tightened. 
 
 The fore and aft cross wires are now set, so that when standing 10 
 feet or so from either end of plane all struts will lie in line and parallel 
 with each other and with the center struts. These wires are then set no 
 tighter than necessary, for if too tight they merely tend unduly to com- 
 press and buckle the ribs. 
 
 A check on the perpendicularity of the transverse wing axis to the 
 longitudinal body axis is then made by measurement, and if necessary, 
 adjusted by the "drift" wires running from the nose of the machine to 
 the front intermediate struts.
 
 126 
 
 The tail pieces are then lined parallel to the wing axis, by merely 
 sighting and adjusting them until they are parallel. It is well to sight 
 from behind and below, so as to get the tail line just below the front edge 
 of the top plane. 
 
 The last wires to be tightened are any auxiliary wires from the chassis 
 to the wings. 
 
 This method, in the hands of one who has had some experience, is 
 the quickest, easiest, and accurate enough for field work. 
 
 A judicious combination of the sighting method and the method of 
 measuring cross distances, gives the best results in the alignment or 
 trueing up of aeroplanes. 
 
 Particular attention is called to the systematic manner of doing 
 the aligning with the landing wires, leaving the tightening of the "flying" 
 wires to the very last thing. 
 
 On the diagram, a note is given relative to the importance of loosen- 
 ing up the proper wires when a local adjustment of one panel point is 
 made, on a machine already all wired up. 
 
 I Propeller Diagram and Balancing stand. 
 
 Propeller Balance. 
 
 After the machine is assembled and lined up the propeller may be 
 mounted, but before doing so its balance should at least be checked up. 
 A propeller "out of balance" is heavier on one blade than on the other, 
 and when run on the engine will vibrate. Any vibration of this nature 
 is, really, a severe strain on the machine, and particularly on the engine. 
 A propeller may also be troublesome in vibrating if the blades are warped, 
 and lacking in symmetry. This may be checked up by measurements 
 of offsets on the blade. 
 
 The accompanying diagram shows a method of propeller balancing 
 that is effective, and also shows the manner in which the useful data on. 
 the shape, section and angles of the blade may be presented.
 
 127 
 
 If the propeller is slightly out of balance, a little more varnish on 
 the light side is the best way to equalize it. 
 
 Metal tips along the entering edge of the tip of the blades are a 
 great protection against both water and shrubbery, to prevent cracking 
 and splitting of the edge of the blade. These, however, must be very 
 firmly attached and because of the centrifugal force should be made as 
 light as possible. For water work, it is necessary to bore a few small 
 holes in this metal tipping, in order that the water, that has soaked in 
 by impinging so hard, may be freely thrown off by centrifugal force, 
 instead of tending to work in under and finally to split open the metal 
 tipping, and for land work such holes will prevent "dry rot." 
 
 Attention should also be given the propeller bolts to make sure that 
 they are properly proportioned as to thread, that the nut fits and shows 
 no sign of having been forced, and that the bolts are properly locked 
 by a wire, which is not likely to be cut by the nut of the bolt "backing 
 
 off." 
 
 Details of Construction. 
 
 Examination of the details of construction, to make sure of the 
 proper fitting of parts and "follow thru," is most important, and special 
 training in the proper inspection of machines is next in importance 
 to training in flying. No matter how well built or how reliable struc- 
 tural features appear to be, there is always the possibility of breakage. 
 Just because an aeroplane has flown very successfully is no excuse for 
 being any the less careful in inspection of its construction. 
 
 It is well, first, to go over the entire machine and make sure that 
 all the bolts are locked, and while doing so the material of the bolt, 
 whether special steel or "commercial" iron bolts, should be examined, 
 and also the thread of the bolt, and fit of the nut and its locking. If 
 iron bolts (stove bolts) are found, with deep threads, in places taking 
 any vital stress, they should be replaced. 
 
 Bolts may be locked in four ways : 
 
 1. By a lock washer, or cut washer, fitting under the nut and 
 "biting" into it when the nut turns backwards. 
 
 2. By a pin, or lock wire, passing thru a hole drilled into the bolt, 
 and fastened in such a way that vibration will not permit "backing off" 
 of the nut, to break the locking wire. 
 
 3. By riveting the head of the bolts. This is the most positive 
 lock. 
 
 4. By painting the bolt head. This is suitable only where a 
 small, relatively unimportant fitting is concerned. 
 
 The practice of "spoiling the thread" of the bolt for locking is not a 
 reliable one.
 
 128 
 
 Knowing the comparative strengths of various bolts in shear and 
 pull, as outlined in the table p. 136, the inspection will intelligently 
 reveal the uniformity of "safety factor" and "follow thru." 
 
 After attending to the bolts, the pins in the fittings and the turn- 
 buckles may be examined at each panel point, one by one the pins for 
 proper locking, unless already riveted, and the t. b.'s for the purpose of 
 making sure that enough threads are everywhere engaged in the barrel 
 and that the t. b. is, in each case, locked so that the safety wire will not 
 wear or tend to break at any point. 
 
 The general inspection of the wires, struts and remainder of the 
 machine can then be made, special attention being given to the controls, 
 so as to make sure that they are connected up to work properly, and 
 
 that all t. b.'s and pins are suitably locked, with no possibility of a cable 
 binding by running off its pulley, or of parts of the control "catching" 
 anything. 
 
 To assist in the detection of flaws in construction, improper propor- 
 tioning of parts for a uniform strength and "follow thru," and for gen- 
 eral information on the construction of aeroplanes, some tables and 
 data are presented. It is perhaps necessary to state that the strength 
 values are largely based on tests and experiences of the writer relative 
 to aeroplanes, and may be taken as at least a beginning of a handbook 
 for Aviation, to which new data of value should constantly be added. 
 
 The illustrations of details of construction, with examples of ap- 
 parently reliable and unreliable features, should receive particularly 
 close attention from military aviators. The small variety of details 
 shown must, of course, be taken as serving merely as examples, since 
 no attempt has been made to present all the structural features that 
 might be found on a various assortment of types of aeroplanes. 
 
 In order to avoid the inconveniences of cross reference, notes 
 relative to the various features have been incorporated on the illus- 
 trations themselves, and should be read and digested as carefully as any 
 emphasized text. 
 
 Steel. 
 
 Steel is obtained from iron by many processes, differing in ore treat- 
 ment, expense, etc., the most extensive ones being Bessemer, open- 
 hearth and crucible. All refer to the original method of obtaining 
 the steel, and have little bearing on the quality of the steel, excepting 
 in the amount of carbon, alloy, etc., in it. There are many instances, 
 however, of Bessemer process steel proving less reliable than the others. 
 The crucible process is used to obtain the most uniform tool steels. 
 
 The percentage of carbon in steel largely determines its hardness, 
 strength and ductility, and ranges from .05 % to .25 %. The higher the 
 carbon, the harder, more tenacious and less ductile is the steel. The
 
 129 
 
 lower the phosphorus or sulphur, the less likely is the steel to develop 
 flaws and cracks. 
 
 The word "temper" is used by manufacturers to represent the 
 amount of carbon in steel. Thus, a "high temper" steel is a "higher 
 carbon" steel, and therefore hard, tenacious, but brittle. Steels may be 
 "tempered," after manufacturing by applying various degrees of hard- 
 ening and softening that is, most uniform steels can be made as hard 
 and tenacious, or as ductile and soft as desired. 
 
 "Hardening" is done by heating the steel with particular attention 
 to uniform heating of the metal and then quickly immersing in brine, 
 oil or water; the amount or nature of this quick uniform cooling, or of 
 the heat to which the steel was brought, being determined by the kind 
 of hardening desired (all of which requires personal skill and experience). 
 
 "Softening" of steel is designed to make its texture more uniform, 
 easier to manipulate, and less brittle. This process is termed "anneal- 
 ing," and consists merely in heating steel up to a desired temperature 
 and then letting it cool very slowly, the slower the cooling the softer the 
 steel. As in any other treatment of steel, uniformity of heating or cool- 
 ing is of the utmost importance. Practically all high grades of steel 
 come from the mills in annealed condition, but if not, and if it is de- 
 sired to bend the steel sharply, great care must be exercised in heat- 
 ing it in a forge for annealing to make sure that the steel is uniformly 
 heated, otherwise its grain and texture will be uneven and weakened. 
 
 In this connection, it is important to point out that steel has as 
 marked a "grain" as wood, only not as easy to see. Steel is always weak- 
 est across the grain. 
 
 Alloy steels, by various heat treatments, can be made to give various 
 strengths, but increased hardness or elastic limit is almost always 
 obtained at the expense of ductility. In the annealed condition, which, 
 because of the reduction in brittleness, is desirable for aeroplane work, 
 steels do not show much variation. A table is -given of the strengths 
 of various grades of alloy steels, and the elongation or per cent that any 
 length will stretch before breakage is given, and 'is an indication of the 
 ductility. 
 
 In aeroplane work, it is essential to have the maximum of reliability, 
 and since local thoughtless heating may have robbed a "special" steel 
 of its special qualities, it is the best practice to proportion all parts for a 
 ductile, easily bent, mild carbon steel, with the strength given in the 
 table. Then, if any advantageous alloy like Vanadium steel is used, its 
 greater resistance to fatigue is an added and much needed safety factor. 
 
 The commercial names of "tool steel," or "drill rod" (bars of tool 
 steel), refer to a specially uniform and reliable grade of rather pure steel, 
 particularly adapted to being heat treated, tempered and hardened for
 
 1, 2, 3, 4. Various single and double pulley arrangements for control cables, 
 5. The Curtiss double U bolt fitting. 6. The Burgess clip fitting. 7. The 
 Curtiss single U bolt fitting. 8. Signal Corps, pin and plate fitting. 9. The steel 
 block and eye head strut bolt fitting used on German aeroplanes. 10. The Wright 
 hook fitting. 11-12. Hinge details.
 
 131 
 
 1. Control with cables and pulleys on ball bearings. 2. Same with friction leads. 
 3. Detail of rubber shock absorber bridge. 4. Steel Spring chassis, with central 
 skid. 5. Softer rubber chassis with no skid. Both of them are typical chassis for 
 exactly the same work. 6. Fuselage details. 7. Details of wing frames, ferrules 
 and lumber.
 
 132 
 
 special tool purposes. Tool steel and drill rod, in annealed condition, 
 are good, mild steels for bolts, pins, etc. 
 
 Bolts, pins, turnbuckles, and particularly wires and cables, may often 
 be of heat-treated special chrome nickel or vanadium steel, and care must 
 be taken not to heat unequally any of these parts, and thus reduce 
 the added safety factor they furnish. This is particularly important 
 in the case of steel wires and cables, in which the material and method 
 of drawing of the wire have been designed particularly to give a high 
 tension strength, which any local heating, for the purposes of bending 
 or attachment, may very seriously weaken. For example, a tension 
 brace of a particularly fine grade of piano wire, received undamaged 
 from the manufacturer and properly put into place, may be relied upon 
 to give its average tested breaking strength. But let this same wire 
 come into long contact with a torch flame, being used to bend, solder or 
 braze some fitting, and it may well have been reduced in strength to one- 
 third of what it is supposed to be. 
 
 Cold rolled steel (abbreviated c. r. s.), which is used so largely in 
 aeroplane work, in fittings, ferrules, clips, etc., is steel that has been 
 rolled out to the sheet or bar in question, but in doing so the grain of the 
 steel becomes more marked. This steel is harder and more tenacious 
 than mild annealed steel, but works very easily and has splendid wearing 
 qualities. Bends in c. r. s., however, should not be made too sharp, 
 and when plate more than 1-8" thick is used, care should be taken to 
 anneal before bending, or else to bend slowly in a vise in which the jaws 
 are protected by thick copper pads, to avoid nicking the plate. 
 
 Other Metals. 
 
 The table on p. 136 gives the strengths and weights of other metals, 
 but they are rarely used in the parts of an aeroplane carrying the main 
 stresses, excepting the bronze barrels of turnbuckles. 
 
 Aluminum should never be used in any important fitting, and its 
 alloys, though at times exhibiting remarkable characteristics, are almost 
 as unreliable as aluminum itself. Many of them, however, are ad- 
 vantageously of use in castings, sheet metal coverings, etc., requiring 
 a metallic construction, but carrying no great stress. Duralumin has 
 very nearly the strength of mild steel, in spots, and is somewhat more 
 weather and water-resisting than any of them. Aluminum sheeting 
 should never be used on coverings in sheeting of less than 1-1 6th inch 
 thick, as it eventually flakes and cracks. 
 
 Tin and copper are used for the ferrules of wire joints and for 
 tankage. 
 
 "Monel" metal, an alloy of about the same qualities as mild steel, 
 is extensively used on metal fittings where particular rust resisting quali- 
 ties are desired. 

 
 133 
 Crystallization and Fatigue. 
 
 The wearing down of the resisting qualities of a material by constant 
 vibration and jar, is a familiar phenomenon met in practical engineering 
 of all kinds so much so, that a certain "life" is assigned to metal parts, 
 after which their strength is considered unreliable. This should be 
 followed in relation to aeroplane metal fittings, but a great error is made 
 in attributing so much danger to "crystallization" in the failure of parts, 
 since the vibrations on aeroplanes are neither sharp nor excessive. 
 
 "Fatigue," is the destruction of the resisting qualities of a material 
 by repeated strains of bending or twisting, exceeding what the "springi- 
 ness" of the material will stand, as illustrated by the ease with which a 
 wire can be broken by repeated twisting or a steel plate by repeated 
 bending. It is of the utmost importance, then, to make sure that the 
 structural details are not such as to permit the pull or flexing of a part 
 to result in bending or twisting strains on details not suitably made for 
 them. Attention to some examples of this is given in the illustrations 
 of structural details. 
 
 In the construction of military aeroplanes it is desirable to eliminate 
 brazed and welded fittings as much as possible, not only because of the 
 added difficulty of replacement, but because a welded joint does not 
 always reveal a possible flaw to the naked eye, and, though apparently 
 satisfactory, might actually prove dangerously inadequate for its stress. 
 Practically all aeroplane fittings may be made of simple and effective 
 steel plate clips, as light and as strong as more "refined" and elaborate 
 arrangements- refined only in that they are harder to make, replace, and 
 pass on. 
 
 CABLES 
 
 WIRES 
 
 HARD WWE. 
 
 THf iTRAHDS AKt 
 !> ffiLfP WITH SCLDfR TO 
 PWC. 
 
 L[/VC,TH or fcxrrvLE 
 -?%." 
 
 8t SCMffft 
 lHf* BINT 
 
 Cable and Solid Wire Ends.
 
 134 
 Aeroplane Woods 
 
 For use in the construction of aeroplanes wood has peculiar virtues, 
 one of the best of which is the ease with which flaws can be detected. 
 In this connection, it is a great mistake to paint wooden parts on aero- 
 planes, since varnish, or "dope," will give as good preservation and yet 
 bring out clearly in evidence any defective features. 
 
 Among the woods used in aeroplane work attention may profitably 
 be given to Spruce, Ash, Maple, Hard Pine, Walnut, Mahogany, Cedar 
 and Hickory, strengths and weights of which are given in the table. 
 
 Spruce, of clear silver grain, straight, smooth and free of knotholes 
 or sap pockets, is the lightest, strongest and most generally satisfactory 
 material for aeroplane construction available. It must be properly 
 ferruled, where fittings are attached, however, to prevent splitting. 
 As a material for spars, ribs, struts, etc., it gives a splendid combination 
 of flexibility, lightness and strength. 
 
 Ash is springy, strong in tension, hard, and very tough. Its weight, 
 however, is considerably greater than spruce, which, when properly 
 ferruled, can for the same weight be made stronger than any other 
 wood. 
 
 Maple has excellent qualities, in strength and reliability, for very 
 small wood details requiring unusual resisting powers like the blocks 
 connecting rib pieces across a spar. 
 
 Hard Pine is a tough, uniform wood, particularly applicable to 
 members like the "longerons" of fuselages (longitudinal members). 
 
 Walnut and Mahogany are used extensively on propellers, their 
 uniformity in finishing and strength giving excellent results for this 
 purpose. 
 
 Cedar is often used as planking of hulls, or fuselage covering, is 
 readily obtained in the boards, and quite uniform and easily worked. 
 
 In this connection, fuselages, particularly "monocoques," are some- 
 times made of veneers, or glued layers of wood, with tr e grains crossing 
 for added strength. Tulip wood, bass wood, cedar, alder and mahogany, 
 are used for veneer covering work. There are innumerable trade makes 
 of "veneers," some of them very satisfactory in aeroplane work. 
 
 Hickory, which is tough and springy, and with a hard surface, is a 
 favorite material for skids, control levers, etc. 
 
 For the preservation of wood several coats of spar varnish, or of 
 aeroplane dope, should be used, after an original "filler" of oil or shellac. 
 
 Laminations in wooden members are designed to make splitting of 
 the member more difficult by having different layers of wood with the 
 grain running in opposite directions, glued firmly together. Weather- 
 ing, however, is apt to affect the glue and open the laminations, and it is 
 good practice to wrap the members with linen or paper, or to freshen up 
 the paint or varnish from time to time.
 
 135 
 
 The wrapping of wooden members with linen, may be made to 
 increase the strength against splitting, if the linen is wound very tight 
 and treated with "dope" or glue in such a way that it will forcibly 
 tighten up. The "dope" should be renewed from time to time. 
 
 Due to the necessity of having a certain least width to a strut, so 
 that the ratio of the length of a strut 1 to its least width r will not exceed 
 by too great a margin, the 1/r of 45, that engineering practice prescribes 
 as a limit, wooden struts, particularly of spruce, are better than steel or 
 any other material, for the saving in width and therefore head resist- 
 ance of a stronger material, would sacrifice strength against bending. 
 
 Experience in being able to pick out good lumber and detect flaws, 
 is of great benefit, and should in a measure be acquired by any aviator 
 who is interested enough in his machine to desire assurance as to its 
 strength. 
 
 Wing Covering. 
 
 The general practice in wing construction is to cover the rib and spar 
 framework with an air-tight cloth, giving a smooth finish to the surface 
 and some degree of resistance to deterioration by exposure. 
 
 Rubbered fabrics were used for several years, but it was necessary 
 to tighten them by hand in stretching on the frame, and the cloth would 
 sag in dry, sunny weather, and tighten in damp weather. 
 
 An improvement in covering was made by the adoption of fine, 
 unbleached linen, which is stretched rather loosely on the wing frame, 
 and is then treated with "dope." 
 
 "Dopes" are of several kinds, but they are almost all cellulose or 
 "collodion" compounds, some soluble in ether and some in aceton. 
 "Cellon," "Novavia," "Emaillite," "Cavaro," "Titanine," are but a 
 few of the trade names, all with some particular virtue some fireproof, 
 others lacking in bothersome chemical odors, but all designed to accom- 
 plish the same purpose, i. e., to tighten up the linen on the frame, and 
 after a few coats, applied with a brush, to give to the surface a smooth, 
 weather-resisting finish. 
 
 Skill in applying dopes and various "formulae" for the processes, 
 give varying degrees of finish, but in general four or five coats of a 
 tightening solution, followed by three coats of a thicker finishing solution, 
 will give a good finish. It is customary to varnish this covering with spar 
 varnish, after the dope has set, but, in view of the difficulty of patching 
 and "re-doping" over the varnish, the advisability of this practice is 
 questionable. To clean most doped fabrics, some soap and water will 
 be found better than anything else. 
 
 The linen fabric used for this covering is woven in the customary 
 way with "warp," the yarn running lengthwise, and "weft," the yarn 
 running across the cloth.
 
 136 
 
 Good aeroplane linen should test to a tension of at least 50 Ibs. for 
 1-inch width strip of cloth undoped, and should be difficult to tear and 
 rip. When doped it should show a strength of at least 70 Ibs. per inch. 
 
 Cloth with a fine thread is not quite as strong as cloth with a coarser 
 thread, but the latter absorbs very much more "dope" for a good finish. 
 
 Aeroplane linen, doped to a good finish, weighs approximately 
 0.10 Ibs. per sq. ft. of surface, inclusive of tape or batten rib-covering 
 and varnish, for both top and bottom faces of a surface taken together. 
 
 WEIGHTS AND STRENGTHS OF METALS 
 
 Weights Elastic Limit Ultimate 
 per cu. in. Tension Tension Compression Shear 
 Steel c. r. s 283 35,000 50,000 50,000 40,000 
 Steel, piano wire 280,000 300,000 
 Aluminum 096 10,000 15,000 12,000 10,000 
 Duralumin 103 29,000 45,000 50,000 40,000 
 Tin 265 3,000 3,500 6,000 4,000 
 Brass 310 20,000 25,000 30,000 30,000 
 Mn. Bronze 319 50,000 50,000 80,000 70,000 
 Copper 320 12,000 20,000 30,000 20,000 
 
 Modulus of 
 Elasticity 
 29,000,000 
 30,000,000 
 11,000,000 
 
 4,000,000 
 9,000,000 
 14,000,000 
 16,000.000 
 
 All strengths are in Ibs. per sq. inch and averages. 
 WEIGHTS OF SHEET METAL 
 
 B&S 
 
 Thickness 
 
 Steel 
 
 Gauge 
 
 Inches 1 
 
 bs. per sq. 
 
 2 
 
 .258 
 
 10.5 
 
 5 
 
 .182 
 
 7.4 
 
 8 
 
 .128 
 
 5.24 
 
 10 
 
 .102 
 
 4.16 
 
 12 
 
 .081 
 
 3.30 
 
 14 
 
 .064 
 
 2.62 
 
 16 
 
 .051 
 
 2.07 
 
 18 
 
 .040 
 
 1.64 
 
 20 
 
 .032 
 
 1.31 
 
 22 
 
 .025 
 
 1.03 
 
 24 
 
 .020 
 
 0.82 
 
 Aluminum Brass or Copper 
 Ibs. per sq. ft. Ibs. per sq. ft. 
 
 3.59 
 2.53 
 1.79 
 1.42 
 1.13 
 0.89 
 0.71 
 0.56 
 0.45 
 0.35 
 
 per sq. 
 11.6 
 8.2 
 5.8 
 4.6 
 3.65 
 2.90 
 2.3 
 1.83 
 1.45 
 1.14 
 0.91 
 
 Tension of c. r. s. steel plate in Ibs. per inch width = Thickness X 50,000. 
 Bearing strength of wire in plate = diam. wire X thickness plate X 50,000. 
 
 STRENGTHS OF VARIOUS 
 
 Kind of Steel 
 Softest Low Carbon Steel 
 
 GRADES OF 
 
 Elastic 
 Limit 
 25,000 
 
 STEEL 
 
 Ultimate 
 Strength 
 45,000 
 
 Elongation 
 
 28% 
 
 Commercial Mild Carbon Steel, annealed 
 Chrome Nickel Steel, annealed 
 Type "D" Vanadium Steel, annealed 
 Chrome Nickel Steel, -tempered 
 Type "D" Vanadium Steel, tempered 
 
 35,000 
 55,000 
 67,000 
 134,000 
 195,000 
 
 55^000 
 80,000 
 100,000 
 150,000 
 210,000 
 
 *O /Q 
 
 20% 
 25% 
 26% 
 15% 
 10% 
 
 STEEL BOLTS 
 
 Diam. 
 Inches 
 
 1/8 
 
 3/16 
 
 1/4 
 
 1/4 
 
 5/16 
 
 5/16 
 
 3/8 
 
 1/2 
 
 5/8 
 
 3/4 
 
 No. of Threads 
 
 to the Inch 
 40 U. S. St. 
 32 U. S. St. 
 20 U. S. St. 
 28 A. L. A. M. 
 18 U. S. St. 
 24 A. L. A. M. 
 24 A. L. A. M. 
 20 A. L. A. M. 
 18 A. L. A. M. 
 16 A. L. A. M. 
 14 A. L. A. M. 
 
 
 Single 
 
 Diam. at 
 Root 
 .092 
 
 Tension Shearing 
 @ 50,000 @ 40,000 
 320 256 
 
 .147 
 
 880 704 
 
 .185 
 
 1,350 1,080 
 
 .205 
 
 1,650 1,320 
 
 .253 
 
 2,500 2,000 
 
 .271 
 
 2,865 2,292 
 
 .321 
 
 4,050 3,240 
 
 .435 
 
 7,500 6,000 
 
 .553 
 
 11,900 9,520 
 
 .669 
 
 17,650 14,120 
 
 .907 
 
 32,500 26,000
 
 137 
 
 STRENGTH OF MILD STEEL RIVETS AND PINS 
 
 
 Diam. 
 Inches 
 
 Lbs. Strength 
 Double Shear 
 
 Diam. Lbs. Strength 
 Inches Double Shear 
 
 
 1/8 
 
 1100 
 
 3/8 
 
 9,500 
 
 
 
 3/16 
 
 2400 
 
 1/2 
 
 17,600 
 
 
 
 1/4 
 
 4400 
 
 3/4 
 
 39,000 
 
 
 
 5/16 
 
 6900 
 
 1 
 
 70,000 
 
 
 For single shear take 1/2 loads given. 
 
 
 
 CABLES 
 
 
 
 
 
 
 
 
 Breaking 
 
 
 Diameter No. of 
 
 Wt. Lbs. 
 
 Strength in 
 
 
 Inches Wires 
 
 per 100 ft. 
 
 Pounds. 
 
 
 
 1/32 R 
 
 7 
 
 0.35 
 
 200 
 
 
 
 1/16 R 
 
 19 
 
 0.96 
 
 500 
 
 
 
 1/16 R 
 
 flexible 
 
 
 400 
 
 
 
 3/32 R 
 
 19 
 
 2^6 
 
 899 
 
 
 
 .091 MS. . . . 
 
 
 
 1000 
 
 
 
 7/64 R 
 
 !!.!!!!!! 19 
 
 2.8 
 
 1400 
 
 
 
 .118 MS. . . . 
 
 
 
 2100 
 
 
 
 1/8 R 
 
 '. .' .' .' .' '. '. '. 19 
 
 '3.'6 
 
 2300 
 
 
 
 .138 MS 
 
 
 
 3000 
 
 
 
 5/32 R 
 
 19 
 
 'S.5 
 
 3000 
 
 
 
 3/16 R 
 
 19 
 
 7.2 
 
 3600 
 
 
 
 .158 MS. . . . 
 
 
 
 4000 
 
 
 
 .209 MS. . . 
 
 
 
 6000 
 
 
 
 1/4 R 
 
 ".'.'.'.'.'.'.'. 19 
 
 13.8 
 
 8300 
 
 
 R= " 
 
 Roebling" 
 
 MS = "Morane Saulnier" 
 
 SOLID WIRES 
 
 
 
 
 
 Breaking 
 
 
 
 Diameter 
 
 Gauge 
 
 Wt. Ibs. 
 
 Strength in 
 
 
 
 Inches 
 
 or descr. p 
 
 er 100 ft. 
 
 Pounds. 
 
 
 
 .032 
 
 20 R 
 
 .264 
 
 225 
 
 
 
 .040 
 
 19 R 
 
 .436 
 
 340 
 
 
 
 .051 
 
 16 R 
 
 .718 
 
 540 
 
 
 
 .055 
 
 ASW, 
 
 .78 
 
 530 
 
 
 
 .064 
 
 14 R 
 
 1.13 
 
 830 
 
 
 
 .065 
 
 ASW 
 
 1.21 
 
 680 
 
 
 
 .080 
 
 ASW 
 
 1.80 
 
 1000 
 
 
 
 .081 
 
 12 R 
 
 1.82 
 
 1300 
 
 
 
 .090 
 
 ASW 
 
 2.26 
 
 1300 
 
 
 
 .100 
 
 ASW 
 
 2.90 
 
 1500 
 
 
 
 .102 
 
 10 R 
 
 2.91 
 
 2000 
 
 
 
 .130 
 
 ASW Van. 
 
 4.50 
 
 3000 
 
 
 
 .250 
 
 ASW Van. 
 
 16.00 
 
 5000 
 
 
 R and 
 
 No = gauge 
 
 Roebling. ASW = American Steel and Wire Co. 
 
 
 
 STEEL TUBE 
 
 TABLE 
 
 
 
 Outside 
 Diam. 
 
 
 Area of Wt. per 
 Section foot 
 
 Moment of 
 
 Rad. of Lbs. Tension 
 
 Inches 
 
 1/2 
 
 1/2 
 
 3/4 
 
 Thickness 
 20 ga. 
 1/16" 
 18 ga. 
 
 sq. in. length 
 .051 .17 
 . 086 . 30 
 .108 .37 
 
 Inertia I 
 .0014 
 .0021 
 .0067 
 
 Gyr. r. 
 .165 
 .156 
 
 .248 
 
 @ 30,000 
 1,530 
 2,580 
 3,240 
 
 3/4 
 
 1/16" 
 
 .135 .46 
 
 .0080 
 
 .244 
 
 4,050 
 
 
 20 ga. 
 1/16" 
 
 1/8" 
 
 .106 .36 
 . 184 . 63 
 .344 1.17 
 
 .0124 
 .0203 
 .0336 
 
 .341 
 .332 
 .313 
 
 3,180 
 5,520 
 10,320 
 
 1/4 
 11/4 
 11/4 
 11/2 
 11/2 
 11/2 
 
 21/2 
 3 
 
 20 ga. 
 1/16" 
 1/8" 
 1/16" 
 1/8" 
 3/16" 
 3/16" 
 1/4" 
 1/4" 
 
 . 134 . 45 
 . 233 . 79 
 .442 1.50 
 . 282 . 96 
 .540 1 . 84 
 .773 2.63 
 1.07 3.63 
 1.77 6.01 
 2.16 7.34 
 
 . 0247 
 .0412 
 .0708 
 .0730 
 .1287 
 .1699 
 .4431 
 1.132 
 2.059 
 
 .430 
 .420 
 .400 
 .509 
 .488 
 .469 
 .644 
 .800 
 .976 
 
 4,020 
 6,990 
 13,260 
 8,460 
 16,200 
 23,190 
 32,100 
 53,100 
 64,800
 
 138 
 STANDARD GAUGES 
 
 No. of Gauge Birmingham Brown & Sharp United States 
 
 .380 
 .238 
 .165 
 .134 
 .109 
 .083 
 .065 
 .049 
 .035 
 .028 
 .022 
 
 .36480 
 .20431 
 .12849 
 .10189 
 .08081 
 .06408 
 .05082 
 .04030 
 .03196 
 .02535 
 .02010 
 
 .34375 
 .23437 
 .17187 
 .14062 
 .10937 
 .07812 
 .06250 
 .05000 
 .03750 
 .03125 
 .02500 
 
 Diameter of 
 Amer. Steel 
 & Wire Go's 
 
 Gauge 
 
 .3310 
 
 .2253 
 
 .1620 
 
 .1350 
 
 .1055 
 
 .0800 
 
 .0625 
 
 .0475 
 
 .0348 
 
 .0286 
 
 .0230 
 
 ^,* . \J, . \J*\JL\J . \J^^J\J\J 
 
 Birmingham, used for steel tubes; B and S for sheet metals. 
 
 TURNBUCKLE TABLE 
 
 Length of Length of Last diam. No. of Strength 
 
 Name Barrel ends of ends threads in Ibs. 
 
 Burgess 3" 1^" -2" 32 3370 
 
 Burgess 3" 1 Y 2 " . 175" 32 2470 
 
 3" iy 2 " .15" 32 1700 
 
 5" 2 1 A" -23" 26 3457 
 
 4^" 2J4" .20" 26 2492 
 
 3" 1W .15" 34 1442 
 
 National . 
 National . 
 National . 
 
 WEIGHT AND STRENGTH OF WOODS 
 
 Weight in Tension Extreme 
 
 Kind of Wood Lbs. per cu. ft. Strength Fibre Stress 
 
 Ash 50 14,000 6500 
 
 Bamboo 22 6,000 1000 
 
 Cedar 28 5,000 3000 
 
 Hickory 48 13,000 7000 
 
 Hard Pine 45 12,000 6000 
 
 Mahogany 51 11,000 7000 
 
 Maple 46 10,000 8000 
 
 Oak 52 10,000 6000 
 
 Spruce 32 10,000 5600 
 
 Walnut 42 9,000 5000 
 
 All strengths in Ibs. per sq. in. 
 
 AREAS AND VOLUMES 
 
 Triangle. Area equals one-half the product of the base and the altitude. 
 Parallelogram. Area equals the product of the base and the altitude. 
 Irregular figure bounded by straight lines. Divide the figure in triangles, and find 
 the area of each triangle separately. The sum of the areas of all the triangles equals 
 the area of the figure. 
 
 Circle. Circumference equals diameter multiplied by 3.1416. 
 Circle. Area equals diameter squared, multiplied by 0.7854. 
 
 Circular arc. Length equals the circumference of the circle, multiplied by the num- 
 ber of degrees in the arc, divided by 360. 
 
 (Useful for tanks, partly filled.) 
 
 Circular sector. Area equals the area of the whole circle multiplied by the quotient 
 of the number of degrees in the arc of the sector divided by 360. 
 
 Circular segment. Area equals area of circular sector formed by drawing radii from 
 the center of the circle to the extremities of the arc of the segment, minus area of tri- 
 angle formed by the radii and the chord of the arc of the segment. 
 Prism. Volume equals the area of the base multiplied by the altitude. 
 Cylinder. Volume equals the area of the base circle times the altitude. 
 Pyramid or Cone. Volume equals the area of the base times one-third the altitude. 
 METRIC CONVERSION TABLES 
 
 kilometer = 0.6214 mile 
 meter = 3.2808 feet 
 centimeter = 0.3937 inch 
 
 sq. meter = 10.764 sq. feet 
 sq. centimeter = 0.155 sq. inch 
 
 cub. meter = 35.314 cub. feet 
 liter = 0.0353 cubic foot 
 
 1 kilogram = 2.2046 pounds 
 
 mile 
 foot 
 inch 
 
 1.609 kilometer 
 0.3048 meter 
 2.54 centimeters 
 
 sq. foot = 0.0929 sq. meter 
 
 sq. inch = 6.452 sq. centimeters 
 
 cub. foot = 28.317 liters 
 U. S. gallon = 3.785 liters 
 
 1 pound = 0.4536 kilogram
 
 CHAPTER XI 
 MARINE AEROPLANES. 
 
 Hydro-aeroplanes and aeroboats involve all the features of aero- 
 planes that we have considered, and in flight, whether land born 01 
 water born, no distinctions can be drawn. But in the replacement oi 
 landing wheels by watertight pontoons for flotation, there' is intro- 
 duced an important feature worthy of special attention. 
 
 Because of the continuous and broad expanse for alighting, and 
 the generally smoother air conditions, large water courses offer par- 
 ticularly practical inducements for flying, whether it be for the pur- 
 poses of coast defence and naval operations, or for travel and sport. 
 And for preliminary instruction in flying there are many who hold 
 and justifiably that flying should first be taught over water, be- 
 cause of its greater safety, more uniform conditions, and continuous 
 facilities for practice in alighting. 
 
 The general care and maintenance of aeroboat hulls, or pontoons, 
 differs in no way from that of high-class boats, excepting that in be- 
 ing hauled out and in, with more or less abuse, the light structure neces- 
 sary is apt to suffer rather severe wear and tear. 
 
 The necessity of strongly braced construction, the best of lapped 
 and copper-rivetted planking, the elimination of metals liable to rust, 
 the use of the proper wood and its protection, so as to avoid water 
 soaking, protective keels and coating, all with a minimum of weight, 
 are but applications of good motorboat practice. 
 
 In the form, functioning and adaptability, of pontoons or hulls to 
 the aeroplane, however, there is found a specialty about which more 
 than one entire textbook could profitably be written. 
 
 To assist in the solution of difficulties, in the proper application 
 of pontoons or hulls to aeroplanes, a few brief notes are presented here, 
 so that the military or naval aviator may understand the mechanics 
 of water-flying machines, sufficiently to detect difficulties in balance 
 or "planing," and be able to judge of the suitability of various units 
 of flotation for any particular machine. 
 
 Air Resistance. 
 
 Attention should be given to having as little disturbance as pos- 
 sible to flying characteristics, by the addition of pontoons. Of ne- 
 cessity, the floating members must be low, and being bulky, more or 
 less additional air resistance is introduced. The addition of this weight, 
 so low, appreciably lowers the center of gravity.
 
 140 
 
 Pontoons have, generally, a considerable expanse of side surface, 
 which by being low and at the front, brings the directional center of a 
 surface forward, and also introduces large fin effect below the c. g., a 
 condition ordinarily giving serious lateral instability. Both of these 
 features must be cared for, preferably by adding a fin at the rear and 
 giving a slight extra dihedral to the wings, or by rebalancing the ma- 
 chine, unless the design was originally made for water flying. Refer- 
 ence is made to Chap. XII, on the significance of these features. 
 
 The difference in resistance of pontoons and wheels is not nearly 
 as great as commonly supposed, excepting at cabre attitudes or large 
 angles of yaw. Some values of K are given on p. 142 for several dif- 
 ferent pontoons. 
 
 When the fuselage and hull are combined,* as done in the aero- 
 boats or flying boats, efficiency in flying may actually be gained by 
 the elimination of the resistance corresponding to the chassis. Al- 
 though the seaworthiness of this type is not necessarily greater or less 
 than other types, the compactness of design and gain in efficiency 
 that may be obtained by placing the crew, motor, etc., in the hull, 
 which of itself has the proper strength and form to serve as the fusel- 
 age is considerable, and the entire craft becomes more boatlike in 
 design, passing from the "aeroplane with floats," to the "boat with 
 wings." 
 
 Flotation. 
 
 In order to support the weight of the machine on the water, the 
 pontoons or hull must displace 1 cubic foot for every 62 to 64 Ibs. of 
 weight. The number of cubic feet necessary for the total weight of 
 the aeroplane, loaded will then represent the volume of the pontoons 
 or hull "under water." The center of flotation (merely the center of 
 this volume) will be under the center of gravity. 
 
 The total available amount of flotation, for any kind of prac- 
 tical use, should be, at the very least, two and one-half times as much 
 as this, and the subdivision of the pontoons or hull into water-tight 
 compartments, is as necessary for reasons of safety in flotation as it 
 is to prevent any water that has leaked in, from acting as a shifting 
 ballast to the detriment of the flying qualities. 
 
 The distribution of the flotation used and the extra flotation pro- 
 vided must be such that there is : 
 
 1. Ample flotation at the rear of the c. g., in order to prevent 
 the craft, when at rest, from being blown over backwards by a wind 
 from the front. The amount is largely a matter of experience but 
 depends on the size and height above the water of the wing surfaces 
 and air-resisting parts. 
 
 * Several years ago the author proposed this feature, and was the first to put it 
 into actual practice in his aeroboat, publicly exhibited in 1912, after months of pioneer 
 experimenting.
 
 141 
 
 2. An excess of flotation forward, to give plenty of lift over on- 
 coming waves, and to prevent upsetting by a wind under the tail. 
 Ordinarily ample flotation is given forward, because of the necessary 
 forward position of the pontoon for hydro-planing. 
 
 3. Sufficient flotation on either side, to prevent side gusts from 
 pushing a wing into the water, the construction of the wings being 
 so fragile, ordinarily, that contact with the water may result in dam- 
 age. This side flotation is usually obtained by using either a twin- 
 float or a three-float system, the latter consisting of a large central float 
 and smaller side floats placed on the tips of the wings Even where 
 twin floats of large size are used additional floats on the wings are some- 
 times fitted. 
 
 The provision forj excesi flotation, as indicated, is of the utmost 
 importance, since high winds out on the water exert a most power- 
 ful force in tending to upset the craft when it is at rest, drifting or 
 anchored. When anchored in a severe storm, it has often happened 
 that the wind blowing on the wings has lifted the entire craft bodily 
 out of water, upsetting it. In this connection the feature of folding 
 back the wings, when on the water, is a particularly advantageous one. 
 
 Hydroplaning. 
 
 The action of a surface at an angle of incidence, moved/ in water 
 or "hydroplaning," is the same as "aeroplaning" in air, in that a Lifting 
 Force is generated at the expense of a Drift or Resistance. The {plan- 
 ing surface on pontoons or hulls is obtained by suitable conforma- 
 tion of the bottom, the sides of the hull causing this action to be very 
 similar to the action of a surface of the "wetted" area and shape of the 
 bottom on which the water is impinging when immersed. 
 
 The various shapes of the bottom of aeroboat hulls^ ojr pontoons, 
 arched, flat, or double concave "V" all appear to have very nearly 
 the same hydroplaning power in lifting force. The contours and dis- 
 position of these planing surfaces, however, differ greatly in efficiency. 
 
 In getting under way, the marine aerpplane, ploughs thru the 
 water as a displacement boat for some time, until the speed thru the 
 water becomes great enough to cause the hydroplaning action of the 
 hull to take effect, after which, as the speed increases, the "planing" 
 surface lifts more and more of the hull out of the water, at the same 
 time reducing its own surface and resistance. Meanwjiile,, the wings 
 are acquiring , speed ( enougji relative to the air to acquire their lift, 
 and, finally, the amount of surface "planing" on the water is reduced 
 to a fraction of an inch, and the speed of the wings thru the air being 
 sufficient for support, the craft leaves the water. In the .acquirement 
 of flying speed on the w,ater,|the greates powejr is required at just 
 that stage wher^ displacement travel ceases and "hydroplaning" be-
 
 142 
 
 FLAT BOTTOM FLAT BOTTOM 
 
 CfturtcK BOW PLUM- xaw BOW 
 
 Diagrams of Floats or Pontoons, and air resistance values Aeroboats and Pontoon 
 Hydro-aeroplanes, showing centers of forces and balance.
 
 143 
 
 gins, and unless enough power is available to overcome the drift on 
 the hull, necessary to obtain this lift, ''planing" will not be attained. 
 
 Any suction tending to hold the craft down, or to add to (the hull's 
 resistance, may render "planing" at speed difficult, so that everything 
 should be done to make the bottom of the hull or pontoon a good "planer." 
 
 This is secured primarily by having a high aspect ratio to the 
 planing area of the bottom as important in hydroplaning pontoons 
 as it is in aeroplanes. 
 
 So definite a factor is this in determining "planing," that it may 
 be laid down as a general rule, regardless of laboratory results, that 
 for every 500 Ibs. weight of machine there should be at least one foot 
 width of bottom. If this be obtained in two pontoons, the increased 
 side resistance would give slightly more drag than if a large central 
 float were used, with the small side pontoons lifting readily out of the 
 water. 
 
 The angle of incidence of the flat bottom that gives the best re- 
 sults is about 4 incidence; any greater angle than this gives too high 
 a resistance and is, therefore, wasteful of power. 
 
 The contour of the bottom, so as to obtain this angle on the wetted 
 surface and with the area and center of lift properly placed, is worthy 
 of extensive study. 
 
 Centers of Forces and Balance. 
 
 As indicated in the diagram, the proper balance for planing' is de- 
 termined by considering the thrust, the lift on the tail in the pro- 
 peller stream, the c. g., and the c. h., or center of the hydroplaning 
 pressure on the bottom. The thrust, being so high above the water, 
 exerts a powerful I moment about the point of support, i. e., the water 
 surface. This moment may be overcome by turning the tail up, giv- 
 ing a downward pressure and moment opposing that of the propeller. 
 This is actually used at the very start, before the planing ajction on the 
 hull is appreciable in order to prevent the propeller push from forc- 
 ing the bow in too deep. When the planing comes into effect, however, 
 it is possible to do away with this negative tail moment, which is both 
 slowing down and adding weight to what the pontoons must lift by 
 having the wetted hydroplane surface far enough forward to have the 
 c. h. in front of the c. g. 
 
 The Shape of the Bottom. 
 
 The contour of the bottom of the floats must be such that the 
 c. h. is well forward, when planing, and yet with sufficient planing 
 surface aft to feather on the water and prevent the craft from jump- 
 ing back too easily on its tail, since the latter condition, causing sud- 
 den changes in the angle of the bottom and its planing pressure, is
 
 144 
 
 what gives rise to the disagreeable effect of "porpoising" -a fore and 
 aft rocking and jumping, which is, at times, difficult to stop. 
 
 At the front the contour should be such that there is a large ex- 
 panse of hydroplaning surface in front of that wetted in ordinary opera- 
 tion, in order to give ample lift at the bow for proper recovery when 
 alighting on the water at a steep gliding angle otherwise the nose of 
 the float might catch in the water and upset the craft. 
 
 It is interesting in this connection to point out a feature on many 
 floats or hulls that defeats its own purpose. It is assumed by many 
 designers that a bow gradually turning up steeply, presenting a greater 
 hydroplaning angle, will be the most effective in recovery charac- 
 teristics on a "nose down" landing. As a matter of fact, the recovery 
 moment is dependent not only on the size of surface and speed of landing, 
 but also on the lever arm of this pressure at the bow, about the c. g. 
 As indicated on the diagram (the pressures being normal to the sur- 
 face) a flatter angle at the bow gives a much more powerful recovery 
 moment. This is fully verified by actual practice. 
 
 Steps. 
 
 In order to break up the contour into the various areas at dif- 
 ferent positions and angles, the practice of building the bottom in 
 "steps" is resorted to. A reduction of friction resistance and splen- 
 did effect in dividing up the surface is obtained by this feature, if the 
 steps are made from two to five inches deep, with ample ventilation, 
 i. e., large air tubes or air slots in the hull, to feed air into the corner 
 of the steps, for the relief of the suction created there by movement 
 of the water.* 
 
 In considering the contour of a float, the fact that the water will 
 acquire, and for a time hold, an acceleration downwards, produced by 
 passing under an inclined surface, is often lost sight of. And the friction 
 resistance of long surfaces is very great. 
 
 Seaworthiness. 
 
 Perhaps the most difficult incompatibility (excepting that of 
 "stability and controllability" on an aeroplane) is to make a hydro- 
 plane type of hull seaworthy. The fact that the hull, when it gets 
 up to speed, is supported by dynamic water pressure, means that any 
 increase or decrease of angle or surface wetted, caused by choppy water, 
 will result in terrific bumping and pounding, and the old saying about 
 the hardness of water, if hit hard enough, becomes uncomfortably 
 evident. If the angle at the bow, as the craft goes into a wave is very 
 
 * The surprising magnitude of this suction is illustrated by the fact, that, in the 
 early development of hydro-aeroplanes, a single J^-inch air-tube was considered suffi- 
 cient ventilation for a step, which today would be required to have at least three 2>- 
 inch tubes.
 
 145 
 
 steeply upturned, the bump is felt with unusual force, since it also 
 tends to slow down the craft. Where a hull is used in which the upturn 
 at the bow is kept as flat as possible, very little bumping is felt, in com- 
 parison, the hull riding over the waves instead of pounding into them. 
 However, in the latter case, since considerable depth to the bow is 
 necessary to avoid "tripping" on waves, a freeboard is obtained by a 
 "cruiser" bow construction quite readily, or by use of a "turtle back" 
 bow. The cruiser bow cuts thru very large waves, throwing a great 
 amount of spray to be sure, but the speed of the craft is not stopped 
 as suddenly as with an upflare bow, and spray is readily protected 
 against. 
 
 The shape of the bottom is of importance .for seaworthiness, since 
 a V bottom is found to give much less pounding, an easier entry, a 
 softer landing, and much less tendency to bounce on alighting. In 
 addition, tendency of the craft to skid outwards, when being turned 
 on the water, is somewhat provided against. Pounding on the bottom 
 causes very great strains on the seams, by spreading, and a V bottom 
 by relieving this, of necessity reduces the possibility of leakage. 
 
 The long dragging hull in the rear, on some types, greatly increases 
 the length of run necessary to get off, because of its added and un- 
 necessary resistance. The hull at the rear should be given a positive 
 action that will lift it out of the water, but this may become too great, 
 resulting at the start in digging the nose in too deeply. 
 
 All these features require careful compromise and balance. Sev- 
 eral outlines of hulls and floats are given. 
 
 Many features, such as self -bailing cockpits, and thorough water 
 protection of the motor, etc., require attention for increased sea-worthi- 
 ness. 
 
 But the most seaworthy characteristic of marine aeroplanes has 
 been, and possibly always will be, ability to rise out of the water quickly 
 and with the shortest run. 
 
 The greater excess of flotat'on of the aeroboat type is a feature 
 of considerable importance. On a marine aeroplane, consisting of a 
 land machine mounted on pontoons, a very large pontoon at the rear is 
 required, to give anywhere near the excess of flotation obtained with 
 the aeroboat. In this and in the greater ease with which the centers 
 of flotation, hydroplaning, thrust and c. g., may be brought closer 
 together there are found the only real advantages of the "boat" type 
 over the "hydro" since flying characteristics and even "planing," on 
 either one, are governed by the same limitations. Structurally, the 
 aeroboat type can be built stronger for the same weight than a "hydro," 
 or pontoon aeroplane, and when the great stresses induced by "side 
 swiping" in landing across wind are considered, the boat is decidedly 
 advantageous in being so well self-contained.
 
 146 
 
 The relative merits of the single pontoon and twin pontoon sys- 
 tems are not yet well defined. The single pontoon is handier in a 
 sea, but twin pontoons, on a large craft, give a wider expanse of bot- 
 tom, thereby improving the planing by a higher "aspect ratio," but 
 at the expense of more frictional resistance. The twin pontoon system 
 is apparently well adapted to launching devices. 
 
 Elements of seaworthiness found in the larger sized marine aero- 
 planes are distinctly advantageous, and indicate that for real work in 
 the open sea, seaplanes will become huge in size, and will have to pos- 
 sess great range of action and excess of power. 
 
 Above left The Burgess-Dunne Seaplane, pusher type with pontoons. 
 Above right Martin Tractor Seaplane, shown also at lower left. 
 
 Lower right Loening Monoplane Aeroboat, an early experimental marine 
 aeroplane, the first of the flying boat class.
 
 CHAPTER XII. 
 FLYING, STABILITY AND AIRWORTHINESS. 
 
 The characteristics of resistance, lift, speed, and power of the 
 aeroplane having been studied, and attention having been given to the 
 construction and adjustment of these machines, it is appropriate now 
 to consider the actual flying of the machine. 
 
 As already outlined, it must be borne in mind that the aeroplane 
 is supported in a perfectly free fashion on a medium that is, at times, 
 very treacherous, and the most efficient aeroplane in the world, as 
 to speed and power, and the very best and refined in construction, is 
 more or less worthless unless it embodies "controllability" and, above 
 all "airworthiness." 
 
 For the military aviator, the importance of acquiring a very sound 
 and intelligent grasp of the principles of stability and operation involved 
 in the notion "airworthy," cannot be overestimated. 
 
 Actual instruction in the manipulation of controls on the ma- 
 chines, thorough practice in acquiring the "feel" of the air, and de- 
 velopment of unerring judgment on landings, form the major part 
 of the practical work in the training of aeroplane pilots. But unless 
 this is accompanied by an intelligent understanding of the actions 
 of aeroplanes in the air, the pilot is little more than a somewhat in- 
 stinctive automaton. 
 
 No mathematics, or formulae, need be involved in the consid- 
 eration of the stability and operation of aeroplanes. But there is 
 required a continued and judicious use of "common sense." 
 
 The subject may be divided into the three broad generalities of 
 considering : 
 
 1. The flying of the machine, the assuming of different atti- 
 tudes, unsafe positions that may be taken, and proper methods of oper- 
 ation. 
 
 2. The stability of the machine, which may at once be defined 
 as the degree and manner in which the aeroplane tends of its own accord 
 to keep a certain relative "even keel" attitude to the air stream. 
 
 3. The airworthiness of the machine, or degree in which com- 
 fortable stability is obtained without too much sensitiveness to air 
 disturbances, and controllability, is obtained without making the aero- 
 plane too easy to upset.
 
 148 
 
 The absolute opposition of inherent stability to controllability is 
 always met in flying characteristics, and it is a fact that an inherently 
 stable and safe aeroplane is stiff and apt to "fight" its controls, while 
 it is sensitive to and moved by air disturbances whereas a "neutral" 
 stability aeroplane, with powerful controls and no tendency to hold 
 any position relative to the air, is handy and precise in answering its 
 helm, and is not readily upset, if equipped with a good automatic pilot 
 mechanism. 
 
 The popular notion, held by many intelligent people, that "sta- 
 bility" means "steadiness in flight" is very erroneous. The least air 
 disturbance causes a "stable" aeroplane correspondingly to adjust 
 itself to keep the same attitude relative to the air so that its position 
 relative to the ground is changed by air movements, and so percep- 
 tibly that on a rough, puffy day an inherently stable aeroplane ap- 
 pears to roll, pitch and sway in a most alarming fashion, while, as a 
 matter of fact, it is merely answering to the air billows. It is much 
 more correct to conceive of an "inherently stable" aeroplane, pri- 
 marily as "non-capsizable," and not at all steady in its flight. For 
 that reason a neutral stability aeroplane, with a delicate mechanical 
 automatic pilot, makes a much steadier gun platform. 
 
 CENTERS OF FORCES. 
 The aeroplane, in flight, is subjected to the action of four forces: 
 
 (1) The Thrust acting at the center of thrust, C. T. which is 
 merely the line of the propeller axis. 
 
 (2) The Total Resistance acting at the center of resistance, 
 C. R. which is determined by balancing the air resistances of all the 
 separate structural parts (see Chap. IV) with the drift, and finding 
 the resultant point at which a force equivalent to the total resistance 
 would be applied. 
 
 (3) The Lift acting at the center of pressure, C. P. which 
 is the center of pressure of the lifting forces for the particular angle 
 of incidence, at which flying is taking place, and found from the sur- 
 face section data and tail lift data. 
 
 (4) The Weight acting at the center of gravity, C. G. 
 
 Center of Gravity. 
 
 It is of fundamental importance, before studying this subject 
 further, to know how and where the center of gravity of any machine 
 is located. 
 
 An aeroplane is suspended in the air and rotates about its center 
 of gravity, so that it is proper to consider the path of the center of gravity, 
 in considering the trajectory of any machine. An aeroplane distinctly 
 does not rotate about any center of lift or resistance. 
 
 The center of gravity, therefore, must be known, and should be 
 measured and marked on the machine. 
 
 The manufacturer furnishes drawings and data, indicating the 
 proper position of the center of gravity. The aeroplane user, after fully
 
 149 
 
 loading the machine for flight, should determine whether or not the 
 weight of the machine is properly balanced. 
 
 There are several methods of finding the center of gravity.* 
 
 (1) The machine could be swung, by flexible suspension from 
 an overhead point, and a plumb line dropped from this point, would 
 intersect the body at the c. g., no matter what the position of the 
 machine. 
 
 (2) The machine could be supported on a large pipe, or knife 
 edge, and moved until balanced on either side. The c. g. fore and 
 aft, and side to side, may be obtained readily by this method, although 
 it is, at times, awkward to support a machine in this way. In this method 
 the height of the c. g. above the bottom of the body is not so easily 
 obtained, and the total weight is not measured. 
 
 (3) The method of moments in which the measurement of 
 weight is made at any two points, and the distance between them 
 measured. The total of the weight at any two points of support is 
 the total weight of the machine, and as indicated on the diagram, p. 152, 
 the center of gravity is very easily obtained by solving the suitable 
 lever arms. This is an exceedingly quick, simple and accurate method 
 for a combined determination of the weight and balance, and at any 
 large aviation field, where platform scales are available, this method 
 is particularly convenient. To determine the lateral correctness of 
 the c. g., it is merely necessary to see if weights measured at either 
 end strut, lifting the machine about the opposite wheel, are equal. 
 The lateral c. g., however, is rarely variable enough to require check- 
 ing. To determine the actual height of the c. g. above the wheels, 
 it would be necessary to repeat the operation for the horizontal bal- 
 ance, with the tail very low and the front as high as possible, thus es- 
 tablishing an intersection where the two c. g. lines cross each other. 
 Or, if the chassis permits, the machine may be tilted up at the rear, 
 until a balance is obtained over the axle, and by projecting a plumb 
 line above this an intersection point is also obtained. 
 
 The longitudinal position of the c. g. is the important one, and 
 consideration of the accompanying diagram shows that if the total 
 weight is reasonably well known, the single measurement of the weight 
 carried by the tail skid, and its distance from the axle, will at once 
 determine how far back of the axle the c. g. is situated. For this only 
 a 200 Ib. spring balance is necessary in the field, and data on the cor- 
 rect weight the tail skid should carry is given by the manufacturer. 
 
 * It is necessary to note that correct results in balancing are apt to be upset, if 
 a draught or wind blows on the aeroplane, when being balanced. Still air is a prere- 
 quisite.
 
 150 
 
 The Equilibrium of the Forces. 
 
 These four forces of Thrust, Resistance, Lift and Weight, acting 
 at their respective centers, must be in equilibrium when the machine 
 is in steady flight. 
 
 Generally, an aeroplane is so designed that the line of thrust passes 
 very nearly thru the center of resistance and the center of gravity is 
 made in line with the center of pressure. The aeroplane is then said 
 to be balanced on the principle of "coincident centers" (centres con- 
 fondus). But there are notable exceptions to this practice. For 
 reasons of handiness in taking proper angles, as later explained, the 
 center of thrust is often placed below the center of resistance. This 
 couple, tending to turn the machine, as indicated on the diagram, 
 is overcome by the couple obtained by having the center of lift in back 
 of the center of gravity. This can be obtained either by having the 
 center of pressure of the surface slightly back of the c. g., or by intro- 
 ducing a small lifting force on the tail. We are at once led then to 
 consider, 
 
 The Effect of Tail Lift on the Center of Lift. 
 
 Up to now we have considered that the center of the lifting forces 
 on the machine, was found at the center of pressure of the main wings. 
 This is only true if the tail surfaces are perfectly neutral, as found 
 in the majority of well balanced aeroplanes. If the tail surfaces re- 
 ceive a negative pressure a downward air force the center of lift of 
 the aeroplane will be in front of the center of pressure of the main wing, 
 and if the tail actually exerts a lift, then the center of lift will be pro- 
 portionately behind the c. p. of the wings so that the lift of the tail 
 X its lever arm back of the resultant center of lift = the lift of the wings 
 X the lever arm of the wing c. p. about the resultant center of lift. 
 This, then, is the nature of the position of the Total Lift force (tail 
 + wings) acting at the center of pressure, C. P., of the entire machine, 
 and is the point referred to, ;n considering the four forces in equilibrium. 
 
 Lateral and Directional Centers. 
 
 There are two other centers to be considered. The center of sup- 
 port, or pressure, may shift slightly laterally as the aeroplane takes 
 different positions in the air, due to differences in the lift of either wing. 
 Attention is given to this under "rolling." 
 
 The aeroplane, with fins, covered body and wheels, rudders, etc., 
 presents a sidewise expanse of surface to the air. It is necessary to 
 know the position of the center of surface of all this side area. Of 
 course, the areas can be computed and the center of area determined, 
 but it is much easier to cut out a paper pattern to scale, of the side ele- 
 vation of the aeroplane, and then by balancing this on a pin point,
 
 151 
 
 finding the center of gravity of the paper. The center of side sur- 
 face, or directional center, as it is sometimes called, may then be taken 
 as slightly in front of this point, and may be marked on the machine. 
 
 The centers having been defined, we are free to proceed with the 
 study of the relative movements of the aeroplane and the air. Their 
 classification into, Pitching, Yawing, Rolling, has already been out- 
 lined on p. 13. 
 
 The Moments of Inertia of the aeroplane about the various axes 
 must also be considered, since the inertia largely governs the rate 
 with which a machine responds to changes in attitude, with reference 
 to the ground.* 
 
 CHARACTERISTICS OF PITCHING OR LONGITUDINAL MOTION. 
 
 The longitudinal motion of an aeroplane in rising or descending, 
 corresponding to changes in the angle of incidence, is controlled by 
 the elevator, but is subject to inherent effects in the aeroplane itself, 
 due to the disposition of surfaces and the magnitude of the longitu- 
 dinal inertia. 
 
 The action of an elevator in merely steering the machine up or 
 down, in its trajectory, is remarkably powerful, and only a fraction 
 of a degree change in the angle of the flaps is sufficient in normal fly- 
 ing, to direct the machine to a different angle and path. For any one 
 speed there is only one elevator setting and balance, corresponding 
 to the one particular angle of incidence for that speed, and any change 
 in the elevator manipulated by hand, changes the incidence, and for 
 the same initial speed will cause the machine either to climb or point 
 downwards. Flight at the different angles is effected by changes in 
 speed obtained by throttling of the engine, combined with a more 
 or less unconscious setting of the elevator to give the proper balance. 
 The necessity of introducing lifts or depressions by the elevator, to 
 keep the relation of the center of lift about the c. g., in the form that 
 will balance the action of the centers of thrust and resistance, is al- 
 ways present for flight at any angle of incidence. The pitching control 
 can be varied greatly in delicacy and power by alterations of the size, 
 movement and leverage of the elevator flaps. The general charac- 
 teristics of this control, however, and the movements, positions and 
 limits of equilibrium longitudinally are common to all aeroplanes. 
 The angle ranges that have been studied in Chap. VIII now assume a 
 more particular significance. 
 
 1. There is a "normal flight" position of the aeroplane gen- 
 erally when the body axis is in the line of flight where there is the 
 desired combination of speed, power, glide and climb characteristics. 
 
 * It must be borne in mind that inertia effects tend to keep the machine in what- 
 ever state of position, motion, or rest, it happens to be. And the greater the distance 
 separating items of weight, the greater is the moment 01 inertia, and, therefore, the 
 slower the oscillations.
 
 &ALANCE. 
 
 .c.c,'. ^ 
 
 CANARD BIPLANE 
 
 'TANDEM" MONOPLANE. 
 
 TORPEDO" MONOPLANE 
 
 if/ew jtjtti*y anyJe different 
 
 
 
 
 
 
 
 
 
 
 :! 
 
 i 
 
 5 
 
 
 
 
 
 
 J7> 
 
 u 
 
 NC, 
 
 
 ' ' "V 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 "-~. 
 
 * , 
 
 
 
 
 
 
 
 
 
 
 
 ^. 
 
 x 
 
 - . MOMENT cvfrcs 
 
 \NiNVTUHNEL 
 
 STABILITY DIAGRAMS 
 In the negative and lifting tail diagrams, the total C. P. is at the C. G.
 
 153 
 
 2. There is a "low angle," or "vol pique," position, generally 
 corresponding to the attitude for highest speed and least angle of in- 
 cidence at which the machine is said to fly "tail high." 
 
 3. There is a "high angle," or "vol cabre," position, correspond- 
 ing to the attitude for slowest speed and large angle of incidence, at 
 which the machine is said to fly "tail low." 
 
 The "regime" of flight, at different speeds and angles, is all the 
 way from the "tail high" to the "tail low" position. At any of these 
 positions, governed longitudinally by the elevator and the throttle, 
 the machine has a certain climb, depending on the excess of the Power 
 Available over the Power Required, a glide governed by the total 
 resistance, and a certain fuel consumption, all as outlined in Chap. 
 VIII. But in its path through the air, if the machine does climb or 
 glide, it must always be borne in mind that the angle of incidence is 
 the angle between the chord and the flight path. Just because a ma- 
 chine is pointed up very steeply, does not mean that it will necessarily 
 climb steeply, since it might have much more excess power at a very 
 much lower angle, and actually climb more feet per minute by the 
 application of this excess power, with the machine on an apparently 
 level keel. As a corollary, a machine does not necessarily glide best 
 the more it is pointed down and speeded up. By holding a machine 
 apparently pointed up, the actual glide slope would be flattest if the 
 particular high angle of incidence, corresponding with this attitude 
 to the air flow, was actually the angle for best glide. Speeding up a 
 machine by nosing down on a glide may increase the Total Resistance 
 so much as to cause the glide to steepen, greatly. All these charac- 
 teristics may be studied from the Power and Resistance charts, and any 
 aviator can profitably acquire familiarity with them. 
 
 Although its significance is often overestimated, consideration 
 of the "reversed flight" region may be given here. Referring to p. 96, 
 it is seen that at speeds below angles of 10, increase of angle of inci- 
 dence, corresponding to slower speeds, involves a pronounced rise in 
 the Power Required, due to increased resistance. And above 17 
 the lifting power of the wings actually decreases. The effect of flying 
 at these high angles is to ause an inversion of controls. Increasing 
 the angle of incidence, whn in horizontal flight, without giving the 
 engine "more throttle," actually causes the machine to sink, and whereas 
 if flying at 14, let us say, the machine's incidence were to be reduced 
 to 10, with the same engine power, the maneuver would result in 
 a climb, due to gain in excess power. The old conception, then, of 
 pointing a machine up for climbing, and down for gliding, is not al- 
 ways correct; and the aviator at some angles may, much to his surprise 
 find himself climbing when he points the machine down, and sinking 
 when he points it up for a climb. Such phenomena are only too often 
 blamed on "puffs and uptrends," when, as a matter of fact, a glance
 
 154 
 
 at the power chart would show the reason for apparent inversions of 
 this kind. 
 
 This leads at once to the realization that higher power is often 
 of advantage in attaining slower speeds, since flying can then be done 
 at angles where the resistance would prove too much for a lower-powered 
 machine. Thus, referring to p. 96, it is seen that the slow speed attain- 
 able at 800 r. p. m. is 43 miles an hour, whereas an increase to 1400 
 r. p. m. would very likely permit of flying at 39 miles an hour. The 
 "regime lente" or "slow," at which the aeroplane is flying, in cabre atti- 
 tudes, is perhaps, the most difficult one to negotiate, and there are not 
 many pilots expert enough to get the very slowest speeds out of their 
 machines. Flying at the high speeds is merely a matter of giving the 
 engine all the power it has, and being on the alert for the uncomfortable, 
 quicker action of puffs. Flying a machine at its attitude for best 
 climb, or best glide, is, of course, a matter of systematic practice, but 
 information from the Power Chart is particularly of value for this. 
 
 Stalling and Diving. 
 
 An aeroplane's angle of incidence can be increased or decreased, 
 providing the speeds are changed in proportion. But, at any angle, 
 if the speed drops the aeroplane is subject to loss of headway, and con- 
 sequently to loss of support. This condition is called a "stall." There 
 are many ways in which an aeroplane can be stalled, either by a false 
 maneuver or a peculiar air disturbance. Immediately after a machine 
 has lost headway, however, it begins to sink, either sideways, tail first, 
 or on a level keel. The latter condition corresponds merely to a sud- 
 den rise in the angle of incidence, and recovery is possible. In the 
 other two conditions, speed for flight can be regained only after a long 
 fall, and then only if the machine has the necessary recovery charac- 
 teristics and the pilot the presence of mind to apply them. 
 
 Stalling on turns is considered later. Stalling due to pitching 
 maneuvers may be considered here. 
 
 On a steep climb, continual incidence increase and slowing down 
 may eventually result in exceeding the maximum lifting angle, and 
 the condition of lost support, due to too great an angle and lack of 
 speed, is merely a stall. Novices, when leaving the ground, often point 
 their machines up too steeply and thereby lose headway, necessary 
 for support. 
 
 Pancaking is usually taken to define the settling of a machine, 
 on landing, due to having turned up so steeply that a stall is reached, 
 and the machine robbed of speed and support sinks more or less ab- " 
 ruptly to the ground, with little if any forward speed.
 
 155 
 
 The acquirement of the proper skill in operation to feel an ap- 
 proaching stalled condition and to be in such position that, if the power 
 suddenly ceases, a tendency to stall may immediately be overcome 
 by taking a proper gliding angle, is better taught by experts in flight, 
 on any particular machine. 
 
 In taking a downward path an aeroplane may be gliding float- 
 ing down on a long slope, held at a certain incidence, and therefore 
 coming down at a constant speed or it may be diving, i. e., coming 
 down on what is practically a fall with no particular value to the inci- 
 dence, and constantly increasing speed. 
 
 Any of the foregoing kinds of stalling may be met with as easily 
 by sudden changes in wind direction, due to up or down trends, as 
 by changes in the attitude or speed of the aeroplane. 
 
 Stalling, when on the gliding path or slope, is a frequent and lit- 
 tle appreciated source of accident. The fact is lost sight of, only too 
 often, that angles of incidence are just as important on the down- 
 ward slope in a glide, as in horizontal flight, and stalling may be reached 
 by a gradual loss of headway and increase of angle. After a long dive, 
 a mistake in recovery to more level flight may result in a stall. It has 
 frequently happened that aeroplanes with a small longitudinal inertia 
 (resembling the old type "pusher" aeroplanes) have been turned up 
 too quickly after a dive or glide so that the tendency of the machine 
 to keep on going in the direction of the dive, for a moment results in 
 the wings attacking the air at a very high angle of incidence and a 
 quickly retarded speed. A characteristic of this kind is due largely 
 to so small a longitudinal moment of inertia, that the aeroplane could 
 be turned around its transverse axis, without much displacement of 
 its center of gravity, and is distinctly a dangerous one. Lack of knowl- 
 edge on this feature has cost, doubtless, many lives. 
 
 The usual pitching control of pushing forward on a post to go 
 down and pulling back to increase the angle, is very instinctive. 
 
 The general construction of the elevator surfaces on aeroplanes, 
 in the form of a large fixed area to which trailing flaps are attached, 
 gives rise to an interesting phenomenon. 
 
 In flying at very high angles of incidence, since the entire machine 
 is inclined, it follows that the fixed tail surface has a high angle 
 of incidence to the air flow past it, and therefore is subject to a Lift. 
 In the preservation of the balance, it may happen where the fixed 
 portion is large and the flap small, that the flap is turned to a con- 
 siderable angle upwards. The air flows past the inclined front fixed 
 surface, and breaks up into eddies, seriously interfering with the air 
 pressure on the flap, with the effect that a further up-turn to the flap
 
 156 
 
 would result in no appreciable change in the air forces. In other words 
 the pitching of the machine would lack any response to the elevator 
 movement, due to the masking of the air on the flaps by the fixed plane 
 in front of them. If an action like this were to take place at about 11 
 incidence, on an aeroplane that would not stall before 12 to 14 had been 
 reached, it would obviously be impossible in flying level to stall such a 
 machine by pulling the elevator control to its limit. This feature, though 
 in a sense a serious limiting factor in controllability, has actually been 
 used on many aeroplanes for training purposes, with excellent success, 
 as a "safety factor" against stalling. 
 
 Steep dives introduce other dangers than those already indicated 
 as due to the possibility of stalling on recovery. The most import- 
 ant effect of a steep dive is the acquirement of very greatly increased 
 velocity, which may prove exceedingly dangerous, due to the tail effect 
 considered below, and due to the possibilities of great strains on the 
 machine. 
 
 Different types of aeroplanes, of course, vary widely in their pitch- 
 ing characteristics, but in practically all aeroplanes with deeply cam- 
 bered surfaces, at low angles of 1 or 2 flying becomes exceedingly 
 uncomfortable. The machine apparently loses much of its handiness 
 in the control of pitching, because the surfaces at these low angles 
 are flying at low values of KL, and greatly varying values of L/D, 
 so that slight variations in the wind direction cause rather large and 
 sudden changes in the pressures, and consequent "jumping" of the 
 machine. Large surfaced, deeply cambered machines, with any con- 
 siderable excess power, always exhibit this characteristic when flown 
 with full power on the horizontal. And the angle on some sections 
 may come so perilously near to the angle of no Lift, and rear most 
 c. p. position, as to. introduce the danger of a sudden dive, which the 
 elevator may not be big or powerful enough to negotiate. Aeroplanes 
 with deeply curved wing sections and an excess of power for climb, 
 should never be flown on the horizontal, with "all power out," if this 
 low angle region is approached thereby. 
 
 Longitudinal Stability. 
 
 The attitudes assumed and limits of control reached in pitching 
 having been considered briefly, attention may be given to the natural 
 characteristics of the longitudinal equilibrium of aeroplanes quite in- 
 dependent of manually controlled pitching. 
 
 The center of pressure . on practically every type of aeroplane 
 surface extensively used at present, excepting the "Taube," moves 
 backward as the incidence is decreased, and forward as the incidence 
 is increased, within the ordinary range of flight angles of to 12 
 (see Chap. VII). This means that the main lifting force has a pro-
 
 157 
 
 nounced tendency to make a machine dive still more when the angle 
 of incidence is decreased, and to stall when the angle is increased. This 
 is, clearly, a condition of instability, i. e., any pitching is accentuated 
 by the air pressure. For stability that is, a tendency for the ma- 
 chine to right itself it would be necessary to have the center of pres- 
 sure move back on increase of angle, and move forward on decrease 
 of angle. Many attempts have been made to attain this by the use 
 of reversed curve sections of wing, but up to now they have all been 
 at a great sacrifice of efficiency. A c. p. position that is almost sta- 
 tionary, thru the range of angles, has been closely approached by some 
 of the newer flat section wings, and by use of a washout in the angle 
 or the upturned tip as in the "Taube." But for actual positive stabil- 
 izing action, it has been necessary to rely on the action- of a tail plane or 
 auxiliary surface. 
 
 This brings us to the consideration of, perhaps, the most import- 
 ant and essential inherent stability characteristic of an aeroplane 
 the powerful corrective action, on disturbances of longitudinal equi- 
 librium of the convergent tandem arrangement of surfaces. 
 
 The definitions of the convergent tandem system, often called the 
 "longitudinal dihedral," which is so desirable for longitudinal stability, 
 and sketches of several systems of tail and main surface combinations, 
 are given in the accompanying diagram. 
 
 For most practical purposes, on the average present day aero- 
 plane, the complete tail surface, situated at about three chord lengths 
 from the main surface, is made to have an area of about l/6th of the 
 main surface. This is inclusive of the flaps, which are merely a means 
 of altering the camber and pressures on the tail surface for purposes 
 of control. The error should not be made of considering the fixed tail 
 pieces as separate from the flaps, because of the continuity of the two, 
 except in the extreme case of "masking ' already considered. The 
 main and auxiliary surfaces could be of various different proportions, 
 such as the tandem disposition of equal surfaces, as in the old Langley 
 machines, or the "Canard" arrangement with the smaller surface in 
 front (see p. 152). 
 
 Whatever the relative size of the surfaces, if the angle of the front 
 one is positive and the angle of the rear one negative,* the system 
 is said to be a "convergent tandem"; and its characteristic is that 
 when the angle of incidence of the aeroplane is decreased, the air force 
 on the tail becomes more negative, acting downwards, thus tending to 
 force the nose of the machine up, while if the aeroplane assumes a cabre 
 position, the rear surface lifts more, thus pointing the nose of the ma- 
 chine down. 'This action is accentuated, in addition, by the slowing 
 
 * In all this discussion the angle of the tail surfaces with the air is meant, i. e., 
 interference of the air flow by the main surface is taken account of by the usual reduc- 
 tion of a degree or two.
 
 158 
 
 down of the machine at high angles and the speeding up at low angles. 
 Practically all Lift values on aerofoils increase at a much steeper rate 
 at low angles than at high angles. So that the rear surface, as in the 
 divergent tandem, will actually change its Lift in less proportion than 
 the front one, for changes in incidence, and this accentuates the action 
 of the pressures on the main surface alone, tending to make the machine 
 nose over still further of its own accord when it pitches forward, and 
 to make it nose up still more when the incidence increases. The ''di- 
 vergent tandem," then, is naturally an unstable system. The con- 
 vergent tandem is often spoken of as a "longitudinal dihedral," because 
 the surfaces are turned up relative to each other. 
 
 It is not always necessary to have a negative tail in order to obtain 
 the desirable pitching stability, since the main surface may be set at 
 + 3 and the tail surface at + 2, with an interference on the tail caus- 
 ing a 1 negative flow, which would give a longitudinal dihedral of 2, 
 and still leave the tail a lifting one, at an incidence to the air of 1. 
 
 This leads to the consideration of the effect on the balance of speed 
 variation of the air passing the tail surfaces. Varying the r. p. m. 
 of the propeller by the throttle varies the speed of the air thrown back 
 by the blades. In every type, excepting the "torpedo" type, the pro- 
 peller is in front of the tail surfaces, and therefore changes in the pro- 
 peller stream affect the pressures on the tail.* In machines with a 
 neutral tail, neither negative nor lifting, the effect of stopping or speed- 
 ing up the propeller is not felt. But on a lifting tail machine, sudden 
 stoppage of the propeller will relieve the lift on the tail, and give a 
 tendency to stall just at the wrong time, while sudden starting again 
 will nose the machine over. This can, of course, be offset by having 
 the center of thrust below the center of resistance. Where the tail 
 is a negative one, with a large longitudinal dihedral, sudden stoppage 
 of the propeller stream causes the negative tail pressure partly to be 
 relieved and the machine to nose over to a proper gliding angle. And, 
 when the propeller is speeded up, there is introduced an increased nega- 
 tive tail pressure, tending to make the machine climb at just the right 
 time. On overpowered machines this tendency of a negative tail 
 surface, to make the machine climb when the full power is applied, is 
 an exceedingly comfortable and air- worthy feature. 
 
 The most dangerous feature of a pronounced lifting tail is in the 
 acquirement of higher and ever-increasing speeds on a steep dive. 
 The lift of the tail is directly increased as the square of the speed, but 
 its lever arm about the center of gravity remains the same; so that, 
 as the speed increases and this tail lift moment increases, an unbalanced 
 force is introduced. The speeds attained on dives increase so greatly 
 and this tail lift action may become so powerful that the maximum 
 
 * It must be borne in mind that, due to "slip," the actual velocity of the air 
 thrown back by the propeller averages 20 to 25% faster than the velocity of the aero- " 
 plane.
 
 159 
 
 exertion on the part of the pilot on the elevator control, may not be 
 enough to overcome it. This exceedingly dangerous feature of the 
 lifting tail has resulted in some very severe accidents. 
 
 It is seen, then, that a longitudinal dihedral giving the "converg- 
 ent tandem" system, favorable to inherent stability, is far preferable 
 to a lifting tail, for safety, stability and airworthiness. Their compari- 
 son on a basis of efficiency is not favorable to the negative tail, because 
 the machine must constantly carry double the negative air load, and 
 extra resistance, whereas a large lifting tail will add just that much 
 area for the load lifting capacity and give very great improvement 
 in Climbing Rate, Speed, Range, etc. 
 
 At times it is necessary to compromise stability and safety for 
 efficiency, and for special performances in the hands of an expert a 
 powerful lift on the tail is often used. Rarely, however, does this ex- 
 ceed 50 to 60 pounds. 
 
 The effect of having the Center of Thrust below the c. r. and the 
 
 c. g., is to introduce a tendency for the machine to assume a glide angle 
 when the engine is shut off, and to cl mb when the power is applied 
 characteristics that are certainly more desirable than a high thrust, 
 which, when the power is shut off, would tend to stall the machine. 
 
 The control of longitudinal balance and the natural tendency of 
 machines to keep an even keel, fore and aft, having been considered, 
 we may proceed with a study of 
 
 ROLLING AND LATERAL BALANCE. 
 
 The lateral balance of an aeroplane is understood to refer to the 
 balance of the wings transversely across the flight path. And rolling 
 is the movement about the longitudinal axis, caused by alterations 
 in lateral balance in distinction to pitching, which is the movement 
 along the longitudinal axis. 
 
 The lateral balance of an aeroplane may be varied by air disturb- 
 ances and by the torque of the propeller (assuming that the wing setting 
 and weight are symmetrical). 
 
 The Torque of the Propeller, is an air force due to the pressure 
 of the propeller blades on the air, which on single propeller machines 
 must be resisted or else the propeller might stand still and the motor 
 turn about it. The tendency of the machine is to turn 'opposite to 
 the propeller, so that the effect of the torque is to unbalance the aero- 
 plane laterally, in so much as it is necessary to introduce a lift on 
 one side by a slight increase in the incidence, which will have a tend- 
 ency to make the machine roll in the same direction as the propeller
 
 160 
 
 turns. Of course, where two propellers are used, working in opposite 
 directions, the torque is neutralized. When the engine is suddenly 
 turned on or off, on single propeller aeroplanes of high power and small 
 surface, the torque is a very perceptible force. It is interesting to 
 note that the torque of small, high-speed propellers is very much less 
 than that of large, slow, geared-down propellers. 
 
 The effect of air disturbances on lateral balance is merely to tip 
 up one side or the other, or to throw the entire machine sideways, 
 thereby affecting its transverse attitude. 
 
 Since the actual attitude of the aeroplane to the air that is pass- 
 ing it, governs the stability characteristics, it follows that we are con- 
 cerned here with the effect on the wings of a sidewise flow of air, and 
 of a difference in the angle of attack on either side. The latter, on any 
 type of aeroplane, merely makes the air force on one side greater than 
 on the other, and for the preservation of the balance requires a correc- 
 tive effort. 
 
 Lateral Stability and Instability. 
 
 Pitching requires control for the attainment of different angles 
 of incidence and altitudes. Yawing requires control for the steering 
 of the machine. But, independent of the necessary feature of bank- 
 ing on turns, the lateral control of an aeroplane is primarily for the pre- 
 servation of lateral balance. 
 
 "Lateral stability" may be defined as a natural tendency for an 
 aeroplane to keep an even keel transversely. If a machine departs 
 from an even keel laterally, it may roll over and fall sideways, and 
 it is well for any pilot to realize, that of all conditions of instability, 
 lateral instability is the easiest to acquire and the most difficult to 
 eliminate, without sacrificing controllability. 
 
 The lateral stability characteristics of an aeroplane are consid- 
 ered before taking up the study of lateral controls, so as to acquire a 
 better understanding of their function. 
 
 The effect of side winds, or, what amounts to the same thing, a 
 sidewise movement of the machine, is not necessarily destructive of 
 lateral balance, as will be explained presently. 
 
 On the older type of open-bodied aeroplanes,, with the wings straight 
 across the span, and at constant incidence, a side wind would pass 
 thru the machine with very little effect in tipping up one side more 
 than another. But as soon as a large covered fuselage or nacelle is 
 used, it is obvious that a side wind on the body will blanket the wing 
 away from the wind, to a certain extent, so that the machine will have
 
 161 
 
 a slight tendency to lift up on the inside wing. This, however, is largely 
 overcome by the effect of the body wheels, etc., which as covered areas 
 below the c. g., catch the side wind and tend to turn the inside wing 
 down. This opposition may be balanced on a machine quite readily 
 and neutral lateral stability obtained, to the degree that the machine 
 will not tip up sideways. The entire machine, however, being acted 
 upon by a sideways flow of air of less velocity fore and aft, has less 
 lift and would tend to stall, were it not that the "weathercock" action, 
 considered later, turns it to meet the side wind. The "side wind" 
 referred to is not of "puff" nature giving an actual incidence difference 
 on the wings and tipping up the side with the greater angle. This must 
 be borne in mind. 
 
 It is well to realize, at once, that any arrangement for natural 
 corrective effort when the machine moves sideways, relative to the air, 
 makes the same machine roll when hit by a side wind. 
 
 There are three general ways of obtaining natural lateral sta- 
 bility: 
 
 1. By a Dihedral Angle to the Span. 
 
 The wings are bent up, as indicated on the diagram, and when 
 the machine, due to some disturbance, rolls over, the low wing lifts 
 more than the high wing and tends to correct the roll. When the 
 machine moves sideways the dihedral angle of the wings causes a greater 
 area and angle to be presented to the air on the leading wing, thus 
 lifting it up. At the same time, however, the higher resistance on 
 this wing tends to make the machine turn into the relative wind. A 
 side puff will lift up the inside wing that it first attacks and then throw 
 the machine sideways after which the dihedral causes a greater 
 lift on the low wing, tending to bring the machine back to an even 
 keel. This answer to a side puff, followed by the righting effect, is 
 always characteristic of a dihedral wing, and is uncomfortable. 
 
 2. By a Retreating Wing Shape. 
 
 The shape of wing in the form of a retreat, as indicated, gives 
 clearly a difference in projected entering edge, and shape of wing, which, 
 without quite as much sensitiveness to sharp side puffs, at the same 
 time gives considerable difference in lift, and strong recovery. Like 
 the dihedral, however, the difference in wing, laterally, causes a dif- 
 ference in resistance, tending to turn the machine into the side wind, 
 and the great leverage of the difference in lift and resistance about the 
 c. g. makes both systems exceedingly sensitive. 
 
 3. By the Double "High Fin" System. 
 
 As indicated (diagram p. 152), the rudder is placed high and a fin 
 above the c. g. is placed forward. The action of a side wind on this 
 system tends to roll the machine up on the inside wing, but while the
 
 162 
 
 dihedral and retreat are exceedingly sensitive to the least sideways 
 deviation of the air flow from its direction along the axis of the ma- 
 chine, fins of this class require a most pronounced sideways attack of 
 the air before any considerable effect is created. Ordinary deviations 
 of the wind direction in flight (which would cause a dihedral or retreat 
 to roll the machine) have very little effect on this fin system, and the 
 small leverage of the fin pressures about the c. g. rob them of sen- 
 sitiveness. At the same time, when the machine itself moves sideways, 
 to any great extent, the high fin action resists the movement and tends 
 to bank the machine up properly, and to overcome lateral instability. 
 
 If the fin surfaces were below the c. g., or if the angle across the 
 span is made catedral (turned down) instead of dihedral, a side puff 
 would press down the inside wing, and a side movement of the ma- 
 chine would introduce a force tending to roll the machine over, and to 
 upset it, i. e., lateral instability. 
 
 It is clear, then, that on a machine with provision for corrective 
 effort, tending to right the machine laterally when it is thrown over 
 sideways, it is actually necessary for the machine to be disturbed and 
 moved sideways before this corrective force is created. Every inherent 
 lateral stability feature, as a corollary, has more or less tendency first 
 to permit air disturbances to roll the machine high fins less so than 
 any other system. 
 
 The position of the c. g. may effect this, in so far as a low c. g. 
 does tend to give a lateral righting effect, although the machine is apt 
 to swing in increasing amplitude if too low, while a high c. g., if above 
 the center of support and displaced, would tend to roll the machine 
 over and upset it. The lateral moment of inertia is ordinarily small, 
 since the weights are practically at the same height, laterally. But 
 on the old Wright aeroplanes, and the Curtiss flying boats (with motor 
 high and hull low), there is a considerably greater inertia laterally, 
 which makes the roll slower, and the resistance to initial movement 
 by air puffs greater. However, this feature causes the machine, after 
 it has acquired a roll, to keep on rolling with considerable force, which 
 is detrimental to controllability. 
 
 Lateral Controls 
 
 For the purposes of assuming the proper banking on turns and 
 the preservation of equilibrium, laterally, aeroplanes are provided 
 with transverse controlling devices. 
 
 Practically all of these take the form of adjustable surfaces out 
 at the sides, in which changes of incidence or changes in camber (as 
 in wing flaps), are relied upon to give a greater lift on one side than on 
 the other, thereby rolling the machine.
 
 163 
 
 The several different arrangements for lateral control warping 
 of the wings, ailerons and wing flaps have been explained in Chap. 
 II. Other devices for this purpose, such as variable surface area and a 
 movable center of gravity, have been proposed and tried, but not as 
 yet with any degree of success. 
 
 Because of extensive patent litigation, great stress has too often 
 been laid on a relatively unimportant point, i. e., the difference in 
 the air resistance of either side, due to the operation of the transverse 
 control. If a wing is warped to a greater angle of incidence on -one 
 side and a lesser angle of incidence on the other, and if the Drift of 
 the higher angle is greater than the Drift of the lower angle, obviously 
 the machine will tend to turn about the wing with the greater angle. 
 The relative nature of this difference, however, depends on the L/D 
 characteristics of the particular surface section used. The old circular 
 arc sections normally, at an incidence of 5 or 6, had this characteristic. 
 But the placid assumption that all wings when warped must necessarily 
 have a higher resistance on the side with the greater incidence, needs 
 but a little intelligent investigation to be amply discredited and is 
 fully refuted by actual flying experiments. For example, referring to 
 Chap. VII, the Eiffel 13 bis section may be taken as an illustration. 
 If flying normally at an angle of incidence of 2 3^, the wings are warped 
 to incidences of at one side and 5 at the other, it is seen that K L 
 will be .0006 for and .00175 for 5, and that L/D will be 5 at and 
 15 at 5. Since the surface area and speed may be taken as the 
 same (the machine flying normal), it follows that this mean warp, 
 applied to the wing will cause the side with the lesser angle to have 
 the higher resistance. The values of KL for the two sides will deter- 
 mine the difference in Lift, that will result in rolling and the values 
 of L/D will determine the resistance. The ratio, then, of KL -* L/D, 
 will give (in the form of KD) the actual numerical proportion of the 
 resistances. For 0, K L +- L/D = .0006/5 = .000120, and for 5, 
 the same quantity = .00175/15 = .000117, which means that the wing 
 with incidence has the greater resistance. R. A. F. 6 section in 
 the form of a biplane warped 3 either way for an incidence of 3 (which 
 would be an excellent one to use), would also exhibit a higher resist- 
 ance for the lower angle. Various angle combinations, on different 
 sections, exhibit every shade of increase and decrease of the resist- 
 ance of one side over the other, and in the tuning up of a machine with 
 warping wings, it is readily possible to adjust the amount of warp and 
 washout, so as largely to eliminate this characteristic of turning, when 
 the wings are warped. 
 
 In sharp turns, the difference in the higher speed of the outside 
 wing and slower speed of the inside wing, must also be considered in 
 determining which wing has the greater Drift. But even in this case 
 it is possible to have KL div. L/D low enough, on the high wing, to 
 make its resistance equal to or less than the lower wing.
 
 164 
 
 Whether or not ailerons can be made to function without show- 
 ing tendencies to turn the machine, depends so much on their shape, 
 setting and interference with the flow on the main surfaces, that it is 
 necessary to analyze particular cases. As a general rule, they always 
 exhibit turning tendencies, due to "choking" effects. 
 
 With wing flaps, however, the combination of change of camber 
 and angle at the same time, gives splendid latitude for proportioning 
 the transverse control, so as to eliminate any tendency to turn the 
 machine. Particularly is this true where very large flaps on a flat 
 section are used, which, because of their ample size, may be operated 
 thru a small range. In the consideration of modern aeroplanes any 
 very pronounced tendency to turn, when the lateral control alone is 
 operated, is considered as evidence of poor balance and careless de- 
 sign and adjustment. It is high time to explode the absurd conten- 
 tion of the necessity of always having to overcome a tendency to turn, 
 when the lateral control is operated, although this uncomfortable 
 characteristic is still found on some types of aeroplanes. 
 
 A change in Lift on either side, then, is made use of to control 
 the lateral equilibrium of the machine, in those instances where the 
 inherent features on an aeroplane do not give the required response. 
 It is important to note here, that the inherent features of lateral sta- 
 bility are steadily receiving attention and development, and it may 
 well be possible, in view of the great progress already made, that the 
 lateral balancing by manual control will give way to an automatic 
 functioning of the aeroplane itself, thus eliminating one of the con- 
 trols, and rendering flying that much easier. At any rate, the assist- 
 ance to lateral balancing given by natural stability features, at pres- 
 ent, is very great and very promising. 
 
 TURNING. 
 
 In several instances reference has been made to the necessity of 
 banking up an aeroplane, so as to obtain a centripetal force sufficient 
 to hold the aeroplane to the degree of turn dictated by the amount of 
 rudder movement given. The manner in which the added pressure on 
 the wing is resolved into this banking force, and the weight, is shown 
 on the diagram, and for very steep banks the magnitude that this 
 pressure must attain in order to have a component equal to the weight 
 is evident. 
 
 The steering by rudder is simple enough; and wide turns may be 
 made, in calm weather, without any appreciable degree of bank, but 
 for maneuvering of any consequence there is but one proper bank 
 for any particular turn, and that is the one that will give just the proper 
 centripetal force to keep the machine flying on the turn at the same 
 angle of incidence relative to the air, without any gain or loss of altitude.
 
 165 
 
 The faster the speed and the greater the weight the steeper must be the 
 bank for any turn. And fast, small-surfaced machines are limited in 
 the sharpness of turns that can be made, since the centrifugal force 
 may exceed the maximum pressure the wings can give at the aeroplane's 
 speed, with the result that the machine will slip outwards, and in doing 
 this the aeroplane may perform the odd maneuver of sliding outwards 
 uphill the path of least resistance. 
 
 Skidding. 
 
 If the bank assumed by an aeroplane is not sufficient to hold it 
 to a given turn, the centrifugal force generated by the turn will cause 
 the machine to skid outwards, and in doing so the. relative flow of air 
 past the machine changes from axial to more or less sideways. A fairly 
 sharp turn, in which the tail was whipped around by the rudder with- 
 out enough bank, would find the machine facing around after completing 
 the turn, but with its speed so greatly reduced, that a stall and a 
 bad one would be apt to follow. In riding with a pilot who skids badly 
 on his turns, the side wind created by the skidding outward of the 
 machine is readily detected, and the feeling is distinctly uncomfortable. 
 The relative side wind created will give a powerful corrective effort 
 tending to bank the machine more steeply, if a dihedral, retreat, or 
 high fin, are incorporated. Here is one of the important stability char- 
 acteristics of these features. 
 
 Even though some pilots of long experience skid their turns badly, 
 the fact that so many serious accidents have resulted directly from 
 stalling after a skidded turn can but lead to the conclusion that the 
 practice is distinctly inadvisable, excepting under some very excep- 
 tional landing conditions where the pilot desires to "kill" his speed. 
 
 Side-Slipping. 
 
 Too much bank for a given turn causes the machine to roll over 
 into the turn and to slip down sideways. This error ordinarily re- 
 sults in a nose dive, which, after a long fall may, on a well-balanced 
 machine, permit of recovery. A bad side slip, however, is as serious 
 and positive a destruction of the equilibrium of the machine, as is 
 possible in ordinary flying, and certainly a tendency on the part of 
 a pilot to skid his turns is far preferable to overbanking them. Side- 
 slipping also introduces a sidewise flow of air, and, consequently, the 
 inherent stability characteristics obtained from a dihedral, a retreat, 
 or a high fin system, tend at first to stiffen a machine against slipping 
 and then to exert a positive corrective effort. It is safe to say that 
 in their recovery power on this characteristic alone these features, 
 particularly a high fin system, are distinctly desirable and fully justified. 
 
 The proper combination of bank and rudder for any particular 
 machine, and skill in the detection of skidding or slipping, are drilled 
 into the pilot by instruction in flying on the field. But the following 
 general principles may be stated :
 
 166 
 
 Skidding is apt to result in a stall, and is overcome by decreas- 
 ing the rudder, or increasing the bank. 
 
 Side-slipping is apt to result in a nose dive, and is first overcome 
 by more rudder and less bank, and later, if too far gone, by ruddering 
 outwards. 
 
 These features, relative to turns, however, are subject to modi- 
 fication, because on steep banks and turns there is 
 
 The Inversion of the Rudder and Elevator. 
 
 The degree in which this is accentuated varies greatly for differ- 
 ent machines and steepness of banks. But, as a general rule, a turn 
 banked to over 45 has begun to make the rudder perform the func- 
 tion of the elevator, and if left, offset for the turn, the machine will 
 begin to spiral down. Whereas, on a steep bank the elevator becomes 
 the rudder, and to keep the degree of turn, whether to right or left, 
 the elevator must be pulled in. 
 
 The "Feel" of a Proper Turn. 
 
 Whether to the pilot or to the passenger who, by experience, has 
 acquired sensitiveness to the movement of the aeroplane in the air, 
 a properly made turn, should give rise to no change in the relative 
 wind, no tendency of the body to swing either out or in, but only to 
 a slight increased pressure on the seat. 
 
 Yawing and Directional Stability. 
 
 There remains to be considered the stability of direction, or "yaw- 
 ing." If the directional center were in front of the c. g., a side wind 
 would obviously tend to turn the machine away from the wind and 
 either stall or upset it laterally. Some tendency to head into the rela- 
 tive wind is necessary. This is obtained by having enough rudder 
 or fin surface aft to bring the directional center back of the c. g. and 
 is called "weathercock" stability. 
 
 However, if this feature is accentuated too much, the machine 
 tends to yaw uncomfortably, on meeting the least side wind. What 
 is called "spiral instability" may also be developed, i. e., the machine, 
 when making a spiral turn downwards, has a tendency to sharpen 
 the spiral and dive, due- to the side pressure on the body, and when 
 spiralling upwards on a climb, a tendency to stall is readily developed. 
 In this connection modern fuselage tractors should prove more dif- 
 ficult to get out of a small field by a spiral climb than the old open- 
 bodied pushers. 
 
 It is important to point out that struts of large fineness ratio, and 
 propellers, present considerable side surface and affect the directional 
 center, at different angles of yaw, by the amount indicated for any 
 machine on its yawing moment diagram.
 
 167 
 
 The Dunne. 
 
 An examination of the photographs of this type (p. 23) reveals an 
 aeroplane with a very accentuated retreat, with the angle of incidence 
 varying from positive at the nose to negative at the tips, and con- 
 trolled solely by flaps on the ends of the wings. While there is no 
 tail, there are virtually what amounts to two tails on this type, and 
 the operation of pitching consists of turning all flaps up or down for 
 rising or descending. There is the added feature of the large braced 
 panel, on either end of the wing span. The "bustle" and change in 
 camber are not considered vital. 
 
 Studying this type of machine, it becomes apparent that the change 
 in angle of incidence gives the effect of the "convergent tandem" sur- 
 face arrangement, but with an exceedingly powerful negative tail. 
 For a normal flap setting there is no question but that stalling or diving 
 are rendered practically impossible by this inherent stability feature. 
 This might lead to the conclusion that the machine was, in conse- 
 quence, a constant incidence, constant speed machine, with no range, 
 and a climb obtained solely from excess propeller push. This, how- 
 ever, is actually not the case, due to the changes in trim obtained from 
 flap adjustment in flight, and it is found that the speed range, glide and 
 climb of this type compare favorably with the more common types, 
 excepting in the loss of efficiency due to the negative pressures at the 
 tip. 
 
 The retreat, combined with the change in angle, give most re- 
 markable effects on rolling and yawing. To begin with, the least 
 deviation of the air is immediately felt, and the machine has a power- 
 ful tendency to turn into any side wind, which results in a great deal 
 of yawing in flight, although the action is slow and deliberate. Yaw- 
 ing and rolling, however, appear to be inseparably combined. Oper- 
 ation of the flaps, inversely, will lift up one side and press down the 
 other, and in doing so the machine will tend to sideslip in. This, how- 
 ever, is met by the presentation of the low inside wing, across its en- 
 tire span, to the relative side movement, which causes the low side to 
 lift and turn at the same time. In being thrown over on one of its 
 sides in this fashion the inside side-panel of the machine receives a 
 considerable pressure, which tends still more to accentuate the turn. 
 A skid is, of course, impossible, since the machine would turn into it 
 and the negative tips would keep the wing from rising. Various de- 
 grees of climbing on turns, or spiralling downwards, are obtained by 
 pulling up the flaps on the low side, or pulling down the flaps on the 
 high side, both maneuvers causing the machine to be thrown over 
 on one wing, in the first case at a high angle of incidence, and in the 
 other at a lower one. Any turn is at the expense of a roll, and any 
 roll, even when caused by a puff, results in a turn. 
 
 The inherent tendency and power of the machine to hold an even 
 keel, with respect to the air, is unmistakable. Because of its constant
 
 168 
 
 answering to air disturbances, however, the machine is not comfort- 
 able and handy in flight. 
 
 The safety features of its inherent stability when used over water, 
 where there is a great deal of room for alighting, makes the Dunne type 
 of practical use. But for land flying, where operations in more or 
 less restricted places are necessary, it is apparent that the Dunne in- 
 herent stability features hardly compensate for the dangers of catching 
 a wing or landing across wind, due to the inherent rolling and yawing 
 movements of the machine. These, however, may be capable of im- 
 provement, though they might very possibly lead to this type becoming 
 more and more like the ordinary airworthy, controllable type of "main 
 surface and tail" aeroplane, so widely and successfully used. 
 
 The Taube 
 
 The outstanding feature of this type, a German "pigeon" shape 
 monoplane, is a retreating wing shape combined with upturned wing 
 tips, of flexible construction. The upturned wing tips, when warped 
 for lateral control, give a distinctly greater resistance on the side that 
 it is desired to lower, thus helping to turn the machine properly when 
 banked. This, combined with the retreat, does give a strong, in- 
 herent stability action, tending to eliminate side-slipping and skid- 
 ding, very much as on the Dunne, but the Taube has rudders which 
 permit of powerful control, near the ground. The flexible, upturned 
 wing-tip feature, renders the c. p. movement for the wing favorable 
 to longitudinal stability, by increased negative pressure at the rear 
 of the wing when the incidence is decreased, and reduction of this 
 pressure when it is increased. In addition, the flexibility of the wing 
 causes the tip to be pressed up, thus giving a righting effect, when an 
 upward puff hits the wing tip, and vice versa. Since the inertia of the 
 machine resists movement at first, this flexibility causes the machine 
 to cede to side puffs without rolling and yet to have an inherent cor- 
 rective action. Any side wind action "washes out" the negative tip, 
 just enough to prevent the machine from swerving into it too strongly, 
 and yet without sacrifice of the inherent stability features of the re- 
 treating wing. The upturned flexible wing .tip, however, is wasteful 
 of power, but developments along this line are apparently promising. 
 
 Summary 
 
 There may be drawn from the consideration of the common ele- 
 vator rudder and laterally controlled "main and tail surface" aero- 
 plane, several interesting conclusions on airworthiness. 
 
 The most airworthy combination for longitudinal control and 
 stability would appear to be a slightly negative tail, on a convergent 
 tandem system, of which the flaps form a large percentage of the area, 
 so that ample control is obtained with minimum effort and drag.
 
 169 
 
 On the lateral equilibrium, handy control, wind-fighting qualities, 
 natural stability and comfort, seem best obtained by a combination of 
 powerful lateral controls, on an aeroplane with a high fin system and 
 a slight retreat or dihedral. In a high fin system it must be borne in 
 mind that a dihedral in side projection is virtually a fin. 
 
 The arching of the wing transversely (see p. 152), appears to give 
 excellent "fin" qualities without being too sensitive to rolling in side 
 winds. 
 
 Since the approach to the critical angle and a stall greatly affect 
 the sensitiveness of the lateral control, thus accentuating tendency to 
 side slip, a very powerful control by large flaps (variable camber) is 
 most desirable. 
 
 The degree in which many qualities of controllability and inher- 
 ent stability can be combined and accentuated are much more a mat- 
 ter for the personal taste and "feel" of the pilot than has been sup- 
 posed. Some pilots rather prefer a quick handy machine, while others 
 favor a high degree of natural tendency to a level keel, requiring less 
 attention and being less tiring to operate. 
 
 The necessity at present of considering the landing and starting 
 conditions as the real limitations for flying, need hardly be emphasized. 
 And the constant effort of designers to extend the speed range, not 
 only to higher speeds but to slower speeds for landing, and to obtain 
 greater climbing rate for rising out of confined areas, must be accom- 
 panied by an equally great effort to make the machines handy, quickly 
 controllable, and devoid of tricks or whims, in order to make operations 
 under puffy, treacherous conditions as practical as possible. It is un- 
 fortunate that, thus far, every device for inherent stability or automatic 
 mechanically controlled stability lacks the flexibility and quick power 
 of judgment of the human brain, necessary for operations in landing 
 in difficult places in a bad wind. Flying aloft is, after all, not so very 
 difficult, on a comfortable, well-balanced "inherently airworthy" ma- 
 chine, but aside from the advantage gained in relieving the pilot of 
 having constantly to operate the controls, all "inherent" or "automatic" 
 stability features fail to add in safety, unless they first render safer 
 the operation of coming back to earth. In this connection safety 
 is, perhaps, better served by a robust landing gear on a machine that is 
 perfectly controllable, and in the hands of a pilot with good judgment. 
 
 A few notes in the form of directions may prove of value : 
 
 1. If a machine is tail heavy, with a lifting tail, move the entire 
 c. g. of the machine forward. If tail heavy with a negative tail, first 
 reduce the negative tail angle, slightly. 
 
 2. If a machine is nose heavy with a lifting tail, thus tending to 
 dive, first move the c. g. back by some weight in the rear, and if the 
 characteristic is still exhibited, take the weight out, and reduce the angle 
 of the tail two or three degrees.
 
 3. If there is a pronounced tendency for the machine to yaw, at 
 the least puff, and to want to dive steeply into a spiral, there may be too 
 much "weathercock" action, in which case, either mount a small rudder, 
 or put some fin surface forward. 
 
 4. If an unbalanced (flap and fin) rudder is too hard to operate, 
 increase the lever arm. If a balanced rudder "catches" it is a sign that 
 its hinge is too far back. 
 
 5. Adjustment of flaps is capable of giving various degrees of 
 sensitiveness and ease of operation, depending on the machine. The 
 best all-around results are given by having the trailing edge of the flap 
 a little below the trailing edge of the plane. 
 
 6. Only two maneuvers need be resorted to, as tests of the im- 
 portant inherent features. When the aeroplane is flying horizontally, 
 application of excess power without any elevator change, should cause 
 the machine to climb. And in a turn with rudder alone, skidding out 
 strongly, the machine should display a natural tendency to bank. 
 
 A Taube in flight. The up- Above A modern Taube. the flexing of the wing 
 turned wing tips are evident. end is indicated. 
 
 Below A typical modern German biplane an Avi- 
 atik. Note the retreating wing.
 
 CHAPTER XIII. 
 THE EYES OF THE ARMY AND NAVY. 
 
 A proper appreciation of military aeroplanes, cannot be had with- 
 out giving consideration to the manner in which aeroplanes may be used 
 in military and naval operations. But, in doing so, let us not trespass 
 on the special studies of flying officers in the use of aeroplanes in strategy 
 and tactics, further than to state that aeroplanes are used, 
 
 1. To see with; 
 
 2. To communicate with; 
 
 3. To attack with. 
 
 Superiority in speed, facility and accuracy of observation, com- 
 bined with fighting power to run the enemy's aeroplanes "out of the 
 sky," or to do damage to important points, must be sought for in com- 
 pany with efficiency in construction, equipment, repair and operation. 
 
 The command of the sea belongs to the ship that can "overtake, 
 observe the most, hit the hardest, and run away" with the greatest 
 reliability. 
 
 And the command of the air belongs to the aeroplane that can 
 get up into the sky the quickest and observe the most, with precision 
 and ease, and with sufficient fighting power to prevent the enemy 
 from doing the same all of which also must be accomplished with re- 
 liability and efficiency. 
 
 Structural Perfection. 
 
 For military purposes, efficiency and reliability in the structural 
 features of the machines must be sought in : 
 
 1 . The utmost simplicity in construction, ease of repair and facility 
 in rapid assembly. 
 
 2. Resistance to deterioration by weathering and hard use, min- 
 imizing the requirements for parking and overhauling. 
 
 3. Standardization of parts, requiring a minimum of stores and 
 facilitating interchangeability. 
 
 There are many different types of metal fittings, wooden parts, 
 struts, controls and chassis (see Chap. X), that differ so slightly from
 
 172 
 
 TYPES OF MILITARY AEROPLANES 
 
 1. The Bleriot Monoplane used by France earlier in the war. 
 
 2. The Taube Monoplane used by Germany, at the start of the war. 
 
 3. The Aviatilc Tractor, a German high powered biplane. 
 
 4. The B. E. 2 British Reconnaissance Tractor. 
 
 5. The Twin-Motored Caudron, used by the French. This machine climbs very 
 fast but is not very speedy. 
 
 6. The Vickers Pusher with gun. 
 
 7. The French Nieuport Speed Scout a highly successful type, with excellent 
 speed and splendid climb. 
 
 8. The Martinsyde Biplane, a typical British speed scout.
 
 173 
 
 one another in the use to which they are put that a Flying Corps can 
 readily standardize many of these features for all machines. In general, 
 welded or brazed fittings, or laminated wooden members, requiring 
 special facilities for manufacture, can largely be eliminated, and aero- 
 planes for military purposes with a few rugged, easily accessible and 
 repaired parts, are far more preferable than aeroplanes with delicate 
 construction and countless small parts, clips, pins, bolts and ''gadgets," 
 all differing from each other. The "military" aeroplane is bound to be 
 trie one the construction of which is typified by the feature that only 
 one size of bolt, with the same thread and nut, is required for the entire 
 structure. 
 
 It is not at all impossible to have an aeroplane so designed, with 
 solid wire braces and simple steel plate fittings, that the crew of the 
 machine need carry on the machine in flight only a few tools, a blow 
 torch, a soldering iron, a roll of wire, and a piece of steel plate, with 
 an extra wheel or two and a few wooden members (and engine spares) 
 for the immediate repair of the machine without outside assistance. 
 
 How impossible this would be on some types of otherwise sat- 
 isfactory aeroplanes, is evident at the first glance. The more difficult 
 an aeroplane is to repair, and the more extensive the expert labor and 
 equipment required to do it, the less satisfactory is the machine for 
 military work in the field. 
 
 Observation. 
 
 Whether in actually observing the movements of troops, the effect 
 of artillery fire, or in taking sights for and noting the results obtained 
 by gun firing or bomb dropping, the most important requirement in 
 military aeroplanes is that the field of view be as unrestricted as possible. 
 Obviously, the "pusher" type offers a better view and arc of gun fire than 
 does the "tractor," but in the latter type many modifications, such as 
 openings in the planes near the body, the raising of the wing, as in the 
 "parasol" type, and special posts for the observer ("prone" below the 
 fuselage or above the wings), are certain to be incorporated. The 
 ordinary tractor monoplane is exceedingly difficult to observe from. In 
 this connection the use of suitable periscopes is well worth experiment. 
 
 The effect of speeds of aeroplanes in rendering observation more 
 difficult is not of as much consequence now, in view of the great height 
 from which observations are made. 
 
 Although it generally has not been so considered in the design 
 of the more common tractors, it is the writer's opinion that, for mili- 
 tary purposes, the "eyes" of the army and navy should be made to 
 see, and everything that is possible should be done to extend the field 
 of view.
 
 174 
 
 SEVERAL MILITARY AEROPLANES 
 
 1. The Morane-Saulnier "Parasol" Monoplane, a highly successful French speed 
 scout, later copied in the German Fokker Monoplane. 
 
 2. The Albatros a long range, heavy duty German Tractor, which has proven 
 to be an effective type. 
 
 3. The Twin Tractor German Battleplane, with gunners in center nacelle. 
 
 4. The Voisin "avion de guerre," a pusher gun carrier. 
 
 5. The Bristol Speed Scout used by the British.
 
 CHAPTER XIV. 
 CONCLUSION. 
 
 Whether monoplanes or biplanes, tractors or pushers, with rotary 
 engines or. water cooled engines, the most suitable aeroplanes for mili- 
 tary purposes will be the ones that are superior in flight to the aeroplanes 
 of the enemy. And this means that, precisely as in naval work, a 
 "race" is on between nations for superiority in aircraft! 
 
 In what, then, may we find "superiority?" 
 
 Simplicity of construction and efficiency in organization for main- 
 tenance of the machines is not all. More is required than numbers, 
 although a Flying Corps is not of much use without plenty of spare 
 machines. Thorough training and great personal skill, on the part 
 of the flying officers as important as the personal . equation in any 
 line of human endeavor may still fail to give superiority, because 
 our aeroplanes in flight must have command of the air, which can be 
 obtained only by ability to start from and alight in more difficult country, 
 higher climbing rate, greater speed and radius of action, better facilities 
 for observation and gun fire, and greater load-lifting capacity. 
 
 High speed, so desirable for operations in the air, means a re- 
 duction in load-lifting capacity, and limitations of landing and start- 
 ing, requiring special aerodromes. Facilities for observation and gun 
 fire may necessitate sacrifice of flying efficiency and simplicity of con- 
 struction. Great radius of action and climbing speed may limit the 
 load capacity, in bombs, etc. So that the ingenuity and skill of the 
 engineer officers of a Flying Corps, must be exerted to the utmost 
 in compromising properly these opposing features. 
 
 It is barely possible that there will be many types of military 
 aeroplanes, light, fast speed scouts, slower load-carrying, gun and 
 bomb machines, aeroplanes especially adapted to artillery observa- 
 tion, to naval coast defense work, to messenger service but the fact 
 remains, that from all of them the maximum possible view must be 
 obtained, with fighting quality superior to the enemy's and with the 
 greatest load-lifting capacity and climbing speed possible. Every- 
 thing must be done, therefore, to improve the aeroplane's efficiency 
 for military work, in extending the speed range, the climbing rate and 
 the load capacity.
 
 176 
 
 Instruments. 
 
 Although flying is properly taught on a basis of acquiring the 
 "feel" of the air, any instrument of assistance to flying without adding 
 considerable weight is most desirable. On the dashboard of a well- 
 equipped aeroplane there are found the usual clock, aneroid, fuel gauges, 
 and engine tachometer. But, in addition to these, other devices are 
 mounted to indicate the relation of the aeroplane to the air. For 
 this purpose pitot tube or pressure plate air speed indicators are used. 
 Angles of incidence to the air may be indicated by a vane floating in 
 the stream, operating a needle on a dial. The inclination of the aero- 
 plane to the ground may be indicated by inclinometers, such as a bubble 
 in a curved tube, or a pendulum. Various simple devices, such as 
 strings or light vanes, may be used to indicate any sidewise movement 
 or skidding of the aeroplane thru the air. In the determination of 
 the speed, climb, etc., for any position, the pilot, having at hand a 
 power chart of the machine, may read the r. p. m. of his engine, thus 
 establishing its power; by reading the air speed or the angle of inci- 
 dence (either one determines the other) he readily notes the power 
 required so that he can judge what his climbing power and rate 
 are, and what the fuel consumption is. Or, if he is flying on the hori- 
 zontal and desires to use the minimum of fuel per mile, he throttles to 
 the r. p. m. indicated, and checks the speed of greatest economy, by 
 reading his angle of incidence and referring to his power chart. A very 
 extensive use of these charts may be made in flight, the only two instru- 
 ments necessary being the engine tachometer and an angle of incidence 
 indicator. Comparison of the inclinometer and incidence dial will 
 readily reveal whether or not he is flying in up or down trends, since 
 the one reads the "air angle" and the other the "ground angle." 
 
 Stabilizers or Automatic Pilots. 
 
 In addition to giving the pilot information on his flying, there are 
 the "automatic stabilizers," instruments to relieve him of having to 
 hold the controls. Inherent features of airworthiness in the machines 
 will also do this, but only after answering to disturbances in much 
 greater measure than a delicately adjusted stabilizer. The latter, also, 
 if pendulum of gyroscope governed, holds the aeroplane to a "base line" 
 relative to the ground and not to the air. 
 
 Level flight is thus obtained, with more or less success, and with 
 pendulum and gyroscope stabilizers it is possible for the pilot to be re- 
 lieved of having to attend to the controls, in that the "stabilizer" or 
 "automatic pilot" keeps the aeroplane on a fixed and steady course. 
 This requires careful adjustment for each particular type of aeroplane, 
 however, and since flying on an airworthy machine, with inherent 
 features not too much accentuated is comfortably possible with con- 
 trols locked, reasons of safety alone do not demand "automatic 
 stabilizers," in view of their added complication.
 
 177 
 
 Stabilizers can also be made to bank an aeroplane properly on a 
 turn and hold it, with an accuracy and precision that is remarkable. 
 
 For night flying, an automatic pilot mechanism has very great 
 advantages. And for bomb dropping, etc., in improving the steadiness 
 of the aeroplane as a platform, it is a valuable auxiliary. 
 
 Performances and Operation. 
 
 It is of the utmost importance in military operations to have in- 
 formation on the radius of action, the load-lifting capacity and the 
 speeds of the aeroplanes to be used. For the purpose of assisting in 
 these matters, particular attention has been given to the prediction of 
 the performances of aeroplanes. 
 
 In choosing machines to lift a great load of bombs here, or to travel 
 a great distance at high speed on a raid there, or to climb up very quickly 
 and return with information for some other purpose, a study of the 
 Power Charts and data on fuel consumption and lifting capacity (Chap. 
 VII and VIII) is not merely helpful it is necessary. And for all 
 intelligent military aviators, a study of this kind is of great import- 
 ance. In fitting auxiliary devices, guns, bomb droppers, etc., in- 
 formation on the resistances (Chap. IV), and on proper balancing 
 of the weights (Chap. XII), as well as the strength of parts necessary 
 to do the work desired (Chap. IX and X), may be applied directly 
 to such problems in the field. 
 
 The conditions of actual operation of aeroplanes as dictated by 
 the weather are quite variable. Fog is the most serious detriment 
 to flying, next to which may be put the possible limitations of start- 
 ing and alighting. In certain winds some small fields are not difficult 
 to negotiate, but under different conditions they may prove impos- 
 sible. Here again local conditions bring up questions of suitability of 
 various aeroplanes in such a way that countless problems are pre- 
 sented requiring "heady" resourcefulness. For example, a condition 
 may readily arise where a machine of slow speed, which gets off the 
 ground in a short run but does not climb fast, may be preferable to a 
 very much faster machine of longer run, even though its climb is better. 
 
 Not only may the performances of an aeroplane be studied on 
 the field, but in their work the technical officers and engineers of a 
 Flying Corps should be able to judge of the probable performances of 
 an aeroplane from charts and drawings sufficiently to limit the ac- 
 ceptance tests to satisfactory construction and balance, and to choose 
 the aeroplanes needed for any particular purpose before delivery. It 
 is decidedly inefficient blindly to try a machine out for some special 
 performance without first going through all the simple computations 
 and determinations bearing thereon. 
 
 The operation of aeroplanes in a wind requires consideration of 
 the direction and force of the wind, in determining the radius of action. 
 The aeroplane always keeps its particular attitude and speed relative
 
 178 
 
 INTERESTING WAR LESSONS 
 
 The Caudron Twin Tractor, with centre nacelle for gunner (upper left) gained excellent climb, 
 at the sacrifice of speed, by the two-motor arrangement. This, however, obstructs the view of the pilot. 
 Below it is shown the Curtiss Seaplane, with two tractor motors of so called "America" type. This large 
 craft, due to its size shows good seaworthiness, but at the expense of flying characteristics. At lower 
 left is shown a view of the huge Sikorsky multi-motored machine, used by Russia. In general, huge 
 land aeroplanes have not yet attained the perfection or excellence in performance that will warrant their 
 adoption as Zeppelin fighters, although large gun carriers are very successfully used at night as "avions 
 de bombardement." 
 
 On the right are shown some speed scouts. The big aeroplane has still much to prove for itself, 
 although its gradual development is inevitable. The light, fast speed scout, however, is -decidedly the 
 success of all war aeroplanes. Operated by one man only, who is expert in both flying and military work, 
 these small machines outclimb and outspeed all the heavier, larger types. Their offensive value has 
 consisted merely of a light machine gun, shooting over or through the propeller. The Nieuport, as seen 
 from a companion machine in flight, is shown at the top right. Below it is a "pusher" type speed scout, 
 built in England, and at lower right is the S. E. 4, a very fast machine, constructed by the British Gov- 
 ernment. 
 
 Speed scouts are frequently equipped with an automatic pilot such as the Sperry gyroscope, to 
 relieve the pilot of having to operate the controls, and making the aeroplane a steadier platform for gun 
 fire. 
 
 Great excess of power gives these small machines a very real advantage in acquiring command 
 of the air.
 
 179 
 
 to the body of air it is passing thru, but this entire body in the form 
 of wind may be moving so that the aeroplane's travel relative to the 
 earth becomes the resultant of its velocity and the wind velocity. 
 
 In naval work, only speeds on the horizontal need be considered, 
 but in speed thru the air an aeroplane must have superior velocity up- 
 wards as well as onwards. 
 
 For tactical observation and for artillery work, it becomes of the 
 utmost importance to consider that climbing speed, after all, may prove 
 the most, vital criterion of superiority since a slower machine, superior 
 in load capacity and climbing speed, may dominate a faster machine, 
 and climb away from it so that efficiency may well be strained to the 
 limit to obtain speed upwards. 
 
 The fight between aeroplane and aeroplane is where the real test 
 of superiority is certain to be found, and both the moral ascendency 
 and actual command of the air, goes to the pilot whose aeroplane and 
 whose skill permits him to climb over and dominate or drive the enemy 
 out of the sky. 
 
 It has been assumed throughout this work that one of the most 
 vital parts of an aeroplane the motor was working smoothly and 
 without a miss. If not universally the case, at present, the day is 
 certainly not far distant when aeroplane motors may be relied upon 
 exactly as are automobile motors today. 
 
 Attention has purposely not been given to the military technique 
 of the use of aeroplanes in military or naval operations, neither has 
 any special attention been given to the art of flying, cross country 
 navigation, etc. features that are acquired by the military aviator 
 from the officers and instructors of the Flying Corps, in their routine 
 work. Consideration has been given to the military aeroplane, for the 
 particular purpose of assisting the military aviator or student to acquire 
 a better appreciation of the machine, a fuller knowledge of why it flies 
 and what he may expect of it, in performance, in strength and in flying 
 characteristics.
 
 INDEX 
 
 Absolute system of units, 72. 
 
 Acceleration, machines of, 29. 
 
 Aeroboats, 21, 142, 146. 
 
 Aerodynamics, 36, 69. 
 
 Aerofoils, 67, 73-75. 
 
 Aeroplane, definite, 11, 13, 90. 
 
 Aeroplane types, 14, 90, 152. 
 
 Aeroplane characteristics, 89. 
 
 Aeroplane linen, 136. 
 
 Ailerons, def., 14. 
 
 Air flow, diagrams, 68. 
 
 Air, nature of, 43. 
 
 Air resistances, 42, 45, 140. 
 
 Airships, def., 10. 
 
 Airworthiness, 147. 
 
 Alignment of wings, 122-125. 
 
 America, flying boat, 22. 
 
 Angle ranges, 153. 
 
 Angle of incidence, 57, 60. 
 
 Angular velocity, 31. 
 
 Areas of figures, 40. 
 
 Ash, 134, 138. 
 
 Aspect ratio, 44, 57, 60. 
 
 Aspect ratio, corrected table, 78. 
 
 Aspect ratio of aerofoils, 79, 80. 
 
 Aspect ratio of hydro surfaces, 142. 
 
 Atmosphere, 42. 
 
 Automatic stability, 24, 176. 
 
 Axes of rotation of aeroplane, 13. 
 
 Balance, directions for, 170. 
 
 Balance of hydros, 143. 
 
 Balanced rudder, 78. 
 
 Beam sections, 114. 
 
 Beam, bending moments, 114. 
 
 Bending moments, general, 115, 116. 
 
 Biplanes, tractors and pushers, 16. 
 
 Biplane effect, 86. 
 
 Biplane table, 87. 
 
 Bleriot monoplane, 20. 
 
 Blunt nose aerofoil, 76. 
 
 Boat upkeep, 140. 
 
 Bolts, locking of, 127. 
 
 Bolts, strength of, 137. 
 
 Bracing of wings, 110, 111. 
 
 Breguet Hydro, 22. 
 
 Burgess-Dunne, 23. 
 
 Burgess-Loening tractor, 146. 
 
 Bustle, 23. 
 
 Cables, 48, 51. 
 
 Cable ends, 132. 
 
 Cable strengths, 137. 
 
 Cabre attitude, 18, 152, 153. 
 
 Camber, 57. 
 
 Cambered planes, 62, 63. 
 
 Camber of upper and lower face, 76, 78. 
 
 Centers of forces, 148. 
 
 Center of pressure, 60, 61, 111. 
 
 Center of pressure total for aeroplane, 150. 
 
 Center of gravity, by moment method 
 
 148, 149. 
 
 Centers co-incident in balancing, 150. 
 Center panel, 15. 
 
 Centrifugal and Centripetal forces, 30. 
 Centripetal force, stress, 107. 
 Charts, 40. 
 Chord, 60. 
 Climbing Rate, 104. 
 Complements, forces, 39. 
 Composition of forces, 38. 
 Constants, 27. 
 
 Construction details, 127, 130, 131. 
 Controls, 14. 
 Controllability, 148. 
 Co-ordinates, 40. 
 Crystallization, 132. 
 Curtiss Flying Boat, 22. 
 Curtiss Tractor, 18. 
 Cylinders, resistances, 48, 51. 
 
 Decalage, 93. 
 Deflection of Beams, 114. 
 Deflection of air, theory, 71. 
 Density of air, 35. 
 Deperdussin monoplane, 20. 
 Depth of curvature, 65. 
 Depth of aerofoil section, 76. 
 Diametral plane, 49. 
 Dihedral angle, 17. 
 Dihedral arched, 152, 161. 
 Dihedral, longitudinal, 158. 
 Dipping front edge, 74. 
 Directional stability, 166. 
 Directional center, 151, 152. 
 Dirigible Balloons, 10. 
 Diving, def., 155. 
 Diving speed, max., 107. 
 Dopes for wing surfaces, 134. 
 Drift, 56, 58, 91, 99. 
 Dunne aeroplane, 23, 167. 
 
 Efficiency in power, 38. 
 
 Eiffel's experiments, 44, 46. 
 
 Eiffel wings, Nos. 19, 37, 38, 42 p.. 82. 
 
 Eiffel wings, Nos. 41, 45, 59, 60 p., 83. 
 
 Elastic limit, 35. 
 
 Elasticity, 32. 
 
 Elevator, def., 14. 
 
 Elevator flap, descr., 15. 
 
 Elevator, rear and front, 16. 
 
 Elevator Masking, 155. 
 
 Empennages, def., 19. 
 
 Empirical constants, 27. 
 
 Energy, kinetic and potential, 36. 
 
 Enlargement from model tests, 80. 
 
 Equilibrium of the air forces, 150. 
 
 180
 
 Fairing, 44. 
 
 Fatigue, 132. 
 
 Fiber stress, 117. 
 
 Fineness ratio, 44. 
 
 Fins, 17. 
 
 Fin system, double high fins, 152, 162. 
 
 Flap and fin rudder, 17, 78. 
 
 Flaps, def., 14. 
 
 Flat planes, 59, 60. 
 
 Flotation.. 140. 
 
 Flying machine, def., 11. 
 
 Flying in region of inverse controls, 154. 
 
 Flying at low angles, 156. 
 
 Flying Boats, 21. 
 
 Follow thru, 119. 
 
 Forces, graphics of, 34. 
 
 Formulae, derived and empirical, 26, 27. 
 
 Formulae for Aerodynamics, 47. 
 
 Friction def., 43. 
 
 Fuel Charts, 96. 
 
 Fuselages, 56, 16, 17. 
 
 Mechanics, theory of, 29. 
 
 Metals, weights and strengths, 132-138. 
 
 Metric system, 72. 
 
 Metric conversion, 40. 
 
 Modulus of Elasticity, 33. 
 
 Moment curves for models, 152. 
 
 Moments of forces, 39. 
 
 Moments of Inertia of Aeroplanes, 151. 
 
 Moments of Inertia, mechanics, 30, 31. 
 
 Monocoques, 20. 
 
 Monoplanes, 20, 21. 
 
 N 
 
 Nacelle, 19. 
 Newton, 46. 
 Nieuport, 41. 
 Normal plane, 49. 
 Normal surface, 68. 
 NPL 4 wing, 84, 85. 
 
 Gap, definition, 78. 
 
 Gases, mechanics of, 36. 
 
 Gliding, 103, 155. 
 
 Goettingen results, 52, 53. 
 
 Graphical stress methods, 34, 40, 110. 
 
 Gyroscope, 31. 
 
 H 
 
 Helicopter, definition, 11. 
 
 Horsepower, defined, 37. 
 
 Horsepower, available and required, 111. 
 
 Hydro-aeroplanes, 142. 
 
 Hydroplaning, 141, 142, 143. 
 
 I 
 
 Inclination of Aeroplane, 92. 
 Inclined surfaces, 57, 68, 71. 
 Inherent stability, 23. 
 Interference of aerofoils, 86. 
 Interference of tail plane, 88. 
 Inversion of Rudder and Elevator, 166. 
 
 Langley's experiments, 46. 
 Lateral balance, 159. 
 Lateral center, 150. 
 Lateral control, 14, 163, 164. 
 Lateral stability, 160. 
 Leading edge, 57. 
 Lifting capacity, 91, 94, 96. 
 Lift and Drift, 58. 
 Lilienthal's Tangential, 63. 
 Loening Aeroboat, 22. 
 Longitudinal stability, 156. 
 
 M 
 
 Marine aeroplanes, 22, 139. 
 Martin tractor, 18. 
 Master diameter, 49. 
 Mathematical signs, 28. 
 
 Ordinate, maximum, 77. 
 Ornithopter, definition, 11. 
 Overhang, definition, 15. 
 
 Pancaking, 155. 
 
 Parallel normal surfaces, 51. 
 
 Parseval dirigible shapes, 62. 
 
 Pendulum, mechanics of, 30. 
 
 Pfeilfliegers, 23, 170. 
 
 Phillips Entry, 77, 78. 
 
 "Pique, vol," 152, 153. 
 
 Pitching, definition, 13. 
 
 Pitching, stability. 157. 
 
 Pitot Tube, 35. 
 
 Polar Co-ordinates, 34. 
 
 Pontoon bottom, aspect ratio, 142. 
 
 Pontoon, double float system, 142. 
 
 Pontoons, sections and details, 142. 
 
 Power, definition of, 37. 
 
 Power charts, 96. 
 
 Power required and available, 91. 
 
 Pressure, definition, 43. 
 
 Propeller, general, 101, 102. 
 
 Propeller balancing, 126. 
 
 Propeller tipping, 126. 
 
 Propeller thrust, 109. 
 
 Propeller diagram and offsets, 126. 
 
 Propeller stream action in tail, 158. 
 
 Propeller Torque, 159. 
 
 Pushers, descr. and def., 14, 16, 19. 
 
 RAF 6 wing, 84, 85. 
 
 Raked end wing, 78. 
 
 Rectangles, resistances, 50. 
 
 Rectangular Co-ordinates, 34. 
 
 Regime of flight, 153. 
 
 Resistance, Total, to motion, 91, 98, 99. 
 
 Resisting Moment of a beam, 116. 
 
 Resolution of Forces on planes, 60. 
 
 Resultant, 38. 
 
 Retreat, definition, 23, 78. 
 
 Retreat, effects, 152, 161. 
 
 Reversed curve sections, 65, 77. 
 
 181
 
 Reversed curve wings, 84, 85. 
 Rolling, definition, 13. 
 Rolling control, 14. 
 Rolling and stability, 159. 
 Rotary motion, mechanics of, 30. 
 Rounded end plane, 78. 
 Rudder, definition, 14. 
 
 Safety Factors, 105. 
 
 Seaworthiness, 140. 
 
 Shapes of Pontoons, 144. 
 
 Sheet Metal table, 136. 
 
 Shoulder yoke, def., 17. 
 
 Side Slipping, 165. 
 
 Signal Corps Tractor, 18. 
 
 Similitude, Theory of, 101. 
 
 Sines and Cosines, 28. 
 
 Skidding, 165. 
 
 Span, definition, 57. 
 
 Spars, stresses in, 113. 
 
 Spar, sections, 114. 
 
 Spar weakening, 118. 
 
 Specific Gravity, 35. 
 
 Speed and Scale effect, 80. 
 
 Speed, High and Low, 104. 
 
 Spheres, Resistance of, 48, 51. 
 
 Spiral Instability, 167. 
 
 Spruce, 134, 138. 
 
 Square normal plates, 48, 49. 
 
 Stability, definition, 147. 
 
 Stagger, def., 17, 78. 
 
 Staggering, effect of, 87. 
 
 Stalling, def., 154. 
 
 Steel, general, 129. 
 
 Steel, tables, 136, 138. 
 
 Strain, def., 33. 
 
 Stream lines, 43, 45, 52, 53. 
 
 Stream photos, 68. 
 
 Stress, def., 33. 
 
 Stresses, general, 105. 
 
 Stresses, maximum, 107. 
 
 Stresses, on body joints, 119. 
 
 Structural Air Resistance, 91, 98. 
 
 Struts, 54, 55. 
 
 Strut Formula, 111. 
 
 Suction on top aerofoils, 74, 78. 
 
 Tail planes, discussion, 85. 
 Tail skid, 17. 
 
 Taube, descr., 23, 168, 170. 
 Tandem system, convergent and diver- 
 gent, 158. 
 
 Tandem seating, 16. 
 Tanks, formulae for, 40. 
 Thrust, center of, 102, 159. 
 Torque, 31, 102. 
 Tractor, def. and disc., 14, 16. 
 Trailing edge, 57. 
 Triangles, solution of, 27, 28. 
 Trueing up wings, 122. 
 
 U 
 
 Ultimate Resistance, 35. 
 Unpacking of aeroplanes, 121. 
 
 "V" bottom on pontoons or hulls, 141, 142. 
 Variable camber wing, 84, 85. 
 Velocity, mechanics of, 29. 
 Visualizing air, its importance, 44. 
 Volumes of various shapes, for tankage, 40. 
 
 W 
 
 Warping, 14, 77. 
 Washout, 93. 
 
 Weathercock stability, 166. 
 Wheels, resistance of, 55. 
 Wing, covering, 134. 
 Wing, loading, 111. 
 Wing stresses, 109. 
 Wires, 48. 
 
 Wire tightening, 118. 
 Wire ends for solid wire, 132. 
 Work, definition, 36. 
 Wright, Aeroplanes, 19. 
 
 Yawing, definition, 13. 
 Yawing, stability, 166. 
 
 Tail high attitude, 18, 152. 
 Tail interference, 94. 
 
 Zeppelin dirigible balloon, 10. 
 
 182
 
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