AEROPLANE DESIGN 
 
 By F. S. BARNWELL 
 AND 
 
 A SIMPLE EXPLANATION 
 of INHERENT STABILITY 
 
 By W. H. SAYERS 
 
 Third Impression , . . 
 
 LONDON 
 McBRIDE, NAST & CO. 
 
 1917 
 
ru 7/ 
 
 PRINTED IN ENGLAND BY 
 THB WESTMINSTER PRESS, LONDON, W. 
 
A FOREWORD 
 BY C. G. GREY, EDITOR OF " THE AEROPLANE " 
 
 SO many new firms are now entering the Aero- 
 plane Industry, and in consequence so many 
 trained engineers are for the first time taking 
 a serious interest In aeronautical engineering that 
 the time seems opportune to publish a general 
 review of the general principles of aeroplane 
 design. 
 
 The disquisition on the subject, which follows 
 this preface, was originally written by Mr. F. S. 
 Barnwell to be read as a paper before the Engineer- 
 ing Society of Glasgow University. It was 
 subsequently published in serial form in " THE 
 AEROPLANE " early in 1915, and so great and so 
 constant was the demand for the numbers con- 
 taining the treatise that it has seemed worth while 
 to republish the whole in the form of a small book, 
 and to append to it a short article by Mr. W. H. 
 Sayers on the subject of The Stability of Aero- 
 planes, which also appeared in " THE AEROPLANE/' 
 Mr. BarnwelFs remarks on design as such will 
 be easily understood by any constructional en- 
 gineer, and his references to questions of stability 
 will doubtless be made more understandable to 
 those engineers who have not hitherto studied 
 aerodynamics by Mr. Sayers' simple explanation 
 of the why, wherefore, and how of stable aero- 
 planes. 
 
 3 
 
 365085 
 
A FOREWORD 
 
 It seems well to make clear why these two 
 writers should be taken seriously by trained and 
 experienced engineers, especially in these days 
 when aeronautical science is in its infancy, and 
 when much harm has been done both to the 
 development of aeroplanes and to the good repute 
 of genuine aeroplane designers by people who 
 pose as " aeronautical experts " on the strength of 
 being able to turn out strings of incomprehensible 
 calculations resulting from empirical formulae 
 based on debatable figures acquired from in- 
 conclusive experiments carried out by persons of 
 doubtful reliability on instruments of problematic 
 accuracy. 
 
 Certain British manufacturers of sufficient 
 independence of character have proceeded 
 along their own lines and have produced 
 aeroplanes which remain unbeaten, power for 
 power, by any in the world on the score of sheer 
 efficiency. These machines notably Avro two- > 
 seater " tractor " biplanes, Bristol single seater 
 biplane Scouts, Martinsyde Scouts, and Vicker's 
 " pusher " gun-carrier biplanes have done more 
 than anything else to assure to the Royal Flying 
 Corps during 1915 that ascendancy in the air over 
 German aircraft which has been such a notable 
 feature of the war. 
 
 Among these machines the speediest of all up 
 to the end of 1915 was the Bristol Scout, a tiny 
 tractor biplane designed in 1914 by Mr. F. S. 
 Barnwell (now a Captain, R.F.C.), with the 
 practical help of Mr. Harry Busteed, an Australian 
 aviator, now an officer of the Royal Naval Air 
 
A FOREWORD 
 
 Service, and at that time in the employ of the 
 Bristol Co. 
 
 The fact that the writing was done before the 
 war acquits Mr. Barnwell of any charge of dabb- 
 ling with the pen contrary to military custom, 
 and his consent to read the proofs of this reprint 
 was only prompted by the instinct of self-defence. 
 
 It is to be noted that his general method of 
 design is approved by other aeroplane designers 
 who have been successful in producing efficient 
 and effective aeroplanes. Consequently the new 
 arrival in the aircraft industry may take it that he 
 is fairly safe in following that method. 
 
 Mr. W. H. Sayers, erstwhile an electrical and 
 mechanical engineer of ability and experience, 
 was one of the first properly trained engineers to 
 take an active interest in aviation. He has been 
 intimately connected with the aircraft industry 
 since the earliest days of aeroplanes, and has 
 worked indefatigably both at construction and 
 design. He made a special study of stability in 
 aeroplanes in the days when most of the pilots of 
 to-day had never seen an aeroplane, and when not 
 more than a couple of dozen people in this country 
 could fly. The theories he then evolved by rule 
 of thumb have since been proved mathematically 
 correct. 
 
 For a considerable period he was on the staff 
 of " THE AEROPLANE," and his ability to put 
 abstruse theoretical ideas into easily understand- 
 able language proved of high value to many 
 students of aviation. At the beginning of the war 
 he joined the Royal Naval Air Service, and, 
 
A FOREWORD 
 
 much as his absence from the paper is regretted, 
 there is considerable consolation in knowing that 
 his practical knowledge of design and construction 
 has proved useful. He has since been promoted 
 to Lieutenant, R.N.V.R., and appointed for 
 technical duty with R.N.A.S., so one can only 
 hope that in the future his ability may be turned 
 to still better account in the King's Service. 
 
 C. G. G. 
 
PREFACE 
 Written November, 1915. 
 
 THE contents of this small book originated 
 as a paper which was read to the Glasgow 
 University Engineering Society in the 
 winter of 1914. 
 
 They were published during January and 
 February by my friend, Mr. C. G. Grey, in his 
 paper " THE AEROPLANE/' without any alter- 
 ations or amendments. 
 
 Since Mr. Grey has considered it worth re- 
 publishing in boo! form, I have, at his request, 
 gone over the proofs and made sundry alterations 
 and deletions, most of small moment. 
 
 The reader must bear in mind, therefore, that 
 the figures and constants quoted remain those 
 which seemed reasonable at the time of first 
 writing the Paper. 
 
 One or two clerical errors have been corrected, 
 a fair amount of unnecessary verbiage cut out, 
 the empirical formula for Rudder Area (on page 
 58) altered, and the figures for Dihedral angle 
 (on page 62) slightly amplified. 
 
 I regret that it has not been possible for me to 
 re-write entirely the sections on Lateral and 
 Directional Stability, for these are treated all too 
 scantily and inaccurately even in comparison 
 with the rest of work. 
 
 The original " Preliminary Remarks " and 
 
PREFACE 
 
 11 Conclusion " are left in, practically unaltered, 
 for the excuses and apologies contained therein 
 are still more necessary now than when the Paper 
 was first written. 
 
 F. S. BARNWELL. 
 Bristol, 9 Nov., 1915. 
 
 ERROR. In Fig. 12, p. 54, the Reaction on the 
 Tail is shown as a downward force ; this is, 
 of course, a mistake, as it would be an 
 upward one for the flight path shown. It has 
 not been altered as this would incur making 
 a new block, and it does not affect the ex- 
 planation of the method. 
 
PART I 
 PRELIMINARY REMARKS 
 
 BEFORE starting on my subject matter, I 
 wish to make some excuses and apologies 
 which I trust the reader will accept. Aero- 
 plane engineering is a young science about which 
 most people know very little ; whilst those of us 
 who do think we know something about it do not 
 know nearly as much as we should like to. So to 
 take a small sub-division of aeroplane design and 
 attempt to deal with it accurately and fully would 
 probably be of less interest to the majority than 
 to attempt a sort of precis of the whole subject. 
 
 Hence in this brief work I try to deal with a 
 very large subject in a manner necessarily dis- 
 tinctly sketchy. Now it is hard, when one must be 
 brief, to touch on all essential points, to be lucid 
 and to be academically accurate. It takes as much 
 time trying to work out how to express oneself 
 sufficiently fully, accurately, and yet briefly as to 
 plod straight on saying everything one knows, or 
 thinks one knows, about a subject, and, unfortu- 
 nately, I have not been able to give nearly as much 
 time as I should have liked to the working out, 
 altering and correcting of this paper. Asking 
 your indulgence therefore for what may be 
 obscure, for what may be incorrect, and for what 
 may be tedious, I shall commence on my subject. 
 
 B 
 
AEROPLANE DESIGN 
 
 I shall start by briefly describing of what wa 
 shall consider an aeroplane to consist, limiting 
 my description to 3 types (see Figs, (la), (aa), 
 and (sa) ). 
 
 An aeroplane we shall consider therefore as a 
 machine consisting of a closed-in body in which 
 is a seat for the pilot and (in machines other than 
 single-seaters) a seat or seats for a passenger or 
 passengers. In this body are also the control 
 mechanisms for the motor and for the movable 
 surfaces of the machine. Mounted in or on this 
 body are the tanks for fuel and lubricant. Mounted 
 on either the fore or aft end of this body is the 
 motor, the only type presently worth considering 
 being the petrol internal combustion. Directly 
 coupled to the motor is an air propeller. Attached 
 to the body are the main lifting surfaces, or, as I 
 shall henceforth call them, " Aerofoils/' Attached 
 to the underside of the body is the landing gear. 
 Attached to the rear end of the body is the tail, 
 consisting of a fixed part called the tail plane, and 
 a movable portion (or portions) called the elevator 
 (or elevators) ; also attached to the rear end of 
 the body are the movable vertical rudder and (if 
 any) a fixed vertical surface or rear fin. 
 
 This applies, of course, to the case in which 
 the engine and propeller are fixed to the fore end 
 of the fuselage (as in Figs. la and 2a). If (as in 
 Fig. 3a) the engine and propeller are at the rear 
 end of the fuselage, then the tail rudder and fin 
 must be attached to suitable outriggers, which are 
 clear of the propeller disc. 
 
 You will note that I have described only the 
 
 10 
 
AEROPLANE DESIGN 
 
 II 
 
AEROPLANE DESIGN 
 
 ^ 
 
 Bl PL ANSI, 
 
 Pbo o^rDxinoafeV sanje 
 as for TracW Moco^boe. 
 
AEROPLANE DESIGN 
 
 SEAT, 
 
AEROPLANE DESIGN 
 
 direct-driven " tractor " monoplane and biplane, 
 and the direct-driven " pusher " biplane. I think 
 that at present these three types contain the 
 greatest number of desirable features, and it is 
 not advisable in the scope of this paper to discuss 
 further types, however tempting their points for 
 future development may appear. 
 
 It is necessary to consider now the functioning 
 of an aeroplane in the simplest conditions and to 
 arrive at the primary necessities for the machine's 
 fulfilling these conditions. Let us consider an 
 aeroplane of total weight, WT, travelling at some 
 uniform velocity Vi, in a straight line and horizon- 
 tally (Fig. i). 
 
 The forces acting on this machine are (i) its 
 weight vertically downwards, (2) total " lift " of 
 whole machine vertically upwards (note here that 
 I say advisedly of " whole " machine), (3) thrust 
 of air propeller in and along direction of flight, (4) 
 total head-resistance of whole machine in and 
 opposite tq direction of flight. 
 
 For the maintenance of this condition of straight 
 horizontal flight it is obvious that at this speed Vi, 
 total " lift " of machine must be equal to total 
 weight, and propeller thrust must be equal to total 
 head resistance. Further, if, as is most probable, 
 the line of action of total head resistance does not 
 coincide with that of thrust, then the C.G. (centre 
 of gravity) of the whole machine must be such a 
 distance in front of the line of action of total lift if 
 thrust be below head resistance, or behind if thrust 
 be above head resistance, that the weight-lift 
 couple is equal to, and of opposite sign to, the 
 
AEROPLANE DESIGN 
 
AEROPLANE DESIGN 
 
 thrust-head-resistance couple. In an ideal design, 
 thrust, head-resistance, and lift should all pass 
 through the C.G. and they generally do so ap- 
 proximately. But if it be impossible to attain 
 this, it is preferable that thrust should be kept 
 as nearly as possible through the C.G., or slightly 
 below it, and head-resistance kept above thrust ; 
 but in neither case should the divergence be 
 great. 
 
 It is necessary now to consider these four forces 
 in more detail. The total weight, WT, for any par- 
 ticular machine is a constant at least, we may 
 consider it so, since in preliminary design one 
 always considers the machine as fully loaded. 
 The total lift, LT, is the sum of several forces which 
 all vary according to the attitude of the machine 
 to its flight-path, and which also all vary approx- 
 imately as the square of the speed. We shall con- 
 sider it as made up of lift of aerofoils LA, vertical 
 reaction on body of machine IB, and vertical 
 reaction on tail of machine IT. I call it " lift," for 
 aerofoils only, for it may be a downward force on 
 one or other, or both, of the other members. 
 
 The thrust of the air propeller, T, depends 
 upon the power given to it, upon its efficiency E, 
 upon its revolutions per second r, and upon the 
 speed along the flight-path v. It is matter for 
 discussion later. 
 
 The total head-resistance, RT, we shall consider 
 as the sum of the horizontal reactions upon the 
 aerofoils (which we shall call henceforth " dyna- 
 mic resistance " or " drift," and denote by RA), 
 upon the body rB, upon the landing gear ro, and 
 
 16 
 
AEROPLANE DESIGN 
 
 upon the tail IT. We shall henceforth call total 
 head-resistance minus " dynamic head-resistance/' 
 " residual head-resistance," and denote it by Rr. 
 Having noted what kind of machine we have 
 to design and the elementary conditions necessary 
 for it to fly in a straight line ; I had better turn 
 next to the consideration of our sources of data, 
 for designing the various members of the machine. 
 
AEROPLANE DESIGN 
 
 MOTORS. 
 
 The motor is the most expensive, the most 
 important, and the heaviest single item, and it 
 must be properly mounted, cooled and fed. 
 
 It is useful and convenient to prepare a table 
 of motors, as shown in Fig. 2. In the first column 
 we have name and type of motor ; in the second 
 normal full b.h.p. ; in the third, r.p.s. of motor at 
 this power ; in the fourth, weight of motor in 
 Ibs. complete with carburetter, magneto, piping, 
 etc., also radiator and water (if water cooled) ; 
 in the fifth, petrol consumption in galls ./hour at 
 full normal power ; in the sixth, the same for 
 lubricant ; in the seventh, weight of suitable 
 mounting and suitable shields or " cowling " ; 
 in the eighth, weight of suitable air propeller 
 with coupling ; in the ninth, tenth, eleventh, 
 twelfth and thirteenth columns we have total 
 weight of motor (complete as in col. 4) with 
 mounting, cowling, propeller, petrol, lubricant 
 and tanks, for 2, 4, 6, 8 and 10 hours running 
 respectively, at full normal power. 
 
 As to how the figures in this table are obtained. 
 Weight of motor complete is given us by the 
 makers, likewise the power, revs., and petrol and 
 oil consumption. The weight of a suitable mount- 
 ing is a matter of deduction from the actual 
 weights of satisfactory mountings for known 
 cases. I have assumed that weight of mounting 
 varies directly as weight of motor, and have taken 
 it as i-yth weight of motor for a rotary, and i-ioth 
 weight of motor for a stationary engine. 
 
 18 
 
AEROPLANE DESIGN 
 
 g" 
 
 F* 
 
 
 cr 
 
 f 
 
 cr 
 v> 
 
 8 
 
 cr 
 sra 
 
 R 
 
 00 
 CO 
 
 vo 
 
 tu cf 
 * 
 
 3i 
 
 tfi 
 
 CO 
 
 
 CO 
 
 
 00 
 
 
 XO 
 
 00 
 
 00 
 
 CvJ 
 
 CO 
 
 ui 
 AC. 
 
 3- 
 
 CQ 
 
 i/) 
 
 8 
 
 \s 
 
 esf 
 
 jr 
 
 xjB 
 
 
 
 oo 
 
 too 
 h'oo 
 
 K 
 o 
 
 -18 
 
 | 
 
 ? 
 
 I! 
 
 
 > 
 
 HJ 
 
 ^ 
 
 I 
 
 C7 
 
 (K 
 
 }2 
 
 tt 
 
AEROPLANE DESIGN 
 
 The weight of " cowling " I have taken as 
 varying as the square root of the weight of the 
 motor, and as equal to twice square root of weight 
 of motor for a rotary, and one-half this weight 
 for a stationary motor. 
 
 The weight of tanks I have taken as varying 
 directly as the capacity, and as i-5th of the 
 weight of the contents (when full, of course), 
 taking petrol as 7.2 Ibs. per gallon, and lubrica- 
 ting oil at 10 Ibs. per gallon. 
 
 The weight of propeller I have taken as varying 
 as the square root of the horse-power and as 
 numerically equal to three times square root 
 horse-power in Ibs. 
 
 All these weights are fair ones from such data 
 as I have come across. You will understand that 
 they are only approximate, but they are accurate 
 enough for first estimate of weights, and probably 
 err on the safe, that is, the heavy, side. 
 
 From this table, then, we can obtain the total 
 weight of power plant for a considerable number 
 of different powers and for any length of maxi- 
 mum power running between the extreme limits 
 of present requirements. 
 
 ao 
 
AEROPLANE DESIGN 
 
 AEROFOILS. 
 
 We must now consider what results we can get 
 from aerofoils and how to estimate the weights of 
 the other members of the machine before we can 
 decide upon what motor to employ and commence 
 the actual design. 
 
 Data for aerofoils are founded entirely upon 
 experimental work. I do not think it is possible to 
 calculate from first principles the re-actions upon 
 a body, of any but the simplest forms, in an air 
 current, though, of course, we can obtain by inter- 
 polation and analysis many further figures from 
 experimentally determined bases. The method 
 almost universally employed is that of suspending 
 a model in a steady air current of known direction 
 and velocity, and measuring the re-actions and 
 moments upon it by means of a suitable balance. 
 
 Let us, then, consider an aerofoil moving at a 
 uniform velocity in still air, or, what is equivalent 
 as regards the air reactions upon it, stationary|in 
 a steady air current. (Fig. 3) Let us denote the 
 area in square feet by A^the^angle in degrees of the 
 
 Vfefocty IT 
 
 : A $ 
 
 21 
 
AEROPLANE DESIGN 
 
 chord of the wing section to the relative air current 
 by i, and the relative air velocity in feet per sec, by 
 v. There is, of course, a total resultant re-action 
 RT upon this aerofoil, which it is most convenient 
 to measure, and consider as the sum of two re- 
 actions, one LA vertical to the direction of the air 
 current, our " lift," the other RA along the air 
 current, our " dynamic resistance " or " drift." 
 For convenience in varying A and v these forces 
 are usually tabulated for different values of i in 
 the form of coefficients. We can write : 
 
 Lift, L A *= Ky Av 2 in Ibs. weight. 
 Drift, R A Kx Av 2 in Ibs. weight, 
 for these coefficients of lift and drift, Ky and Kx, 
 are approximately constant for similar aerofoils 
 and for the same value of i for all values of A and 
 of v. 
 
 Our data for aerofoils, then, is based upon ex- 
 perimentally determined values at different values 
 of i, for the coefficients Ky and Kx, and for the 
 position of " centre of pressure," or intersection 
 of line of total resultant re-action with the chord, 
 for model size aerofoils. 
 
 It is useful to tabulate the dynamic properties 
 of aerofoils in the following manner : For every 
 model for which we can get reliable data we should 
 make on tracing cloth a standard sheet. (Fig. 4). 
 On each of these sheets, and in the same position, 
 we draw an accurate scale section of its aerofoil 
 with a standard chord length of, say, 10". On each 
 sheet, and in the same position, we also draw a 
 standard squared table for its respective curves of 
 Ky, Kx and of locus of centre of pressure, with a 
 
 22 
 
AEROPLANE DESIGN 
 
 * " 
 
 V 
 
 J 
 IL 
 
 ; 
 
 \ 
 
 
 i ' 
 j 
 
 i 
 i 
 
 $ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 * 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 __ ?) 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ - 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 7 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 w 
 
 i 
 
 s 
 V 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 V 
 
 
 
 
 
 
 
 s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 /" 
 
 
 \ 
 
 
 
 7 
 
 
 
 
 
 
 
 
 
 v> 
 
 
 
 
 
 
 j 
 
 
 
 \ 
 
 
 y 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s 
 
 
 
 
 ^ 
 
 
 
 
 
 
 fo 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 1 
 
 
 
 
 
 
 
 1 
 
 5 
 
 I i 
 
 
 
 
 
 
 \ 
 
 
 
 ? 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 .v 
 
 
 
 
 
 
 \ 
 
 
 / 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 y 
 
 
 
 
 
 
 
 k 
 
 
 
 
 
 
 
 
 
 
 
 
 > 
 
 s 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 1 
 
 \ 
 
 
 
 
 
 t 
 
 
 
 
 
 i 
 
 
 
 
 \ 
 
 
 
 
 
 f 
 
 
 N^ 
 
 
 
 
 ~ 
 
 
 
 
 
 
 
 
 
 
 N^ 
 
 
 
 c 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 N 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 N j 
 
 
 
 
 
 
 \ 
 
 
 , 
 
 
 
 
 
 V 
 
 
 
 
 
 
 
 
 \/ 
 
 " 
 
 
 
 
 A 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 / " 
 
 
 
 
 
 
 
 
 
 
 
 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 \ 
 
 
 
 
 
 
 
 s 
 
 N 
 
 
 
 
 / 
 
 
 
 N 
 
 
 
 
 
 , 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ^ 
 
 ^ 
 
 
 
 
 l - 
 
 ^ 
 
 
 
 
 
 [ 
 
 u 
 5 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 \ 
 
 
 
 v 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 s 
 
 / 
 
 
 
 
 
 
 - 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 T 
 
 1 
 
 f 
 
 uJdO-o 
 
 
 -^y 
 
 i . 
 
 4 
 
 r 
 
 "^tfeoJ 
 
 s- 
 
 'oiooi' 
 
 "aooo^ 1 
 
 -J 
 
 w 
 
 -*K 
 
 x>l. 
 
 u^ 
 
 -*, 
 
 **kbod. *+$><> J W*; ^b>s"T if* 1 
 
AEROPLANE DESIGN 
 
 base of value for i (say, \" representing i of i), 
 and with ordinate values for both Ky and KJC 
 (say, representing .0001 of Ky value, and 2* 
 representing .0001 of Kx value). The abscissae 
 values should range from 6 to + 30 for i, and 
 the ordinate values from o to .002 of Ky value. 
 That is to say, our standard table will be 18* 
 long and 10" high. 
 
 On this table i" of ordinate value will represent 
 a distance of centre of pressure from leading edge 
 of aerofoil of .1 of chord. 
 
 On this same table we draw a fourth curve 
 
 of t^-- i.e. fjpvfi value on a base of Ky value ; 
 
 Y of ordinate value representing unity for * f 
 
 value, and i" of abscissa value representing .0001 
 of Ky value. 
 
 We can now, by superimposing the sheets, 
 compare any of our aerofoil forms. The sections 
 and tables will lie one over the other, and we can 
 see which form gives us the best Ky (or Lift Co- 
 efficient) vajue at any value of i, the lowest Kx 
 (or Drift Coefficient) vdue at any value of i, the 
 least travel of centre of pressure, and the highest 
 
 value for ^ for any value of lift coefficient. 
 Drift 
 
 We must note here that these tables should all 
 be for models of the same plan form, i.e., of the 
 same ratio of Span over Chord (or " Aspect Ratio") 
 and of the same form of ends. The National 
 Physical Laboratory generally employs a standard 
 
 24 
 
AEROPLANE DESIGN 
 
 rectangular plan form of 18" span and 3" chord, 
 i.e., of Aspect Ratio 6. The coefficient values should 
 also (for absolutely safe comparison) be for the 
 same size of model at the same air speed. 
 
 I remarked before that these coefficients were 
 constants (for the same value of i) for varying 
 values of both A and V. I must now, in somewhat 
 Hibernian vein, remark that these "constants " 
 are not quite constant. The Ky, or lift coefficient, 
 has been found by experiment to be fairly con- 
 stant for widely varying values of A and V. We 
 shall consider it as such, and directly use model 
 Ky values for our calculations for full-sized 
 machines, noting that any error will probably be 
 to the good. But the Kx, or drift coefficient, de- 
 creases slightly as A increases, and also decreases 
 considerably as V increases. This has the meaning 
 that the drift coefficient of our full-size aerofoil 
 will be less than that of the model, but it also 
 means that we cannot determine quite so accur- 
 ately as we should like to, what it will be for our 
 full-size aerofoil, especially if it be for a fast ma- 
 chine. 
 
 It is most probable that this difference is due 
 to that part of the total re-action caused by skin- 
 friction, the component of which is small in the 
 direction of lift but large in the direction of drift ; 
 and skin-friction coefficient we know to increase 
 both with increase of A and with increase of V 2 . 
 The best thing that we can do is to use the results 
 which the N.P.L. gives us in the latest report of 
 the Advisory Committee. (See Fig. 5). 
 
AEROPLANE DESIGN 
 
 \ 
 PlQ.fi 
 
 /ARlA-noM or UrT /bRirr WITH LV. ft 
 
 r^NFLT^of^ 
 
 Lr Icwtb of Chord ID Jtxh 
 
 V' Velodhy in fee)- bev sex: . 
 
 
 
 / 
 
 
 
 
 
 %%^ 
 
 
 
 
 * & " 
 
 
 
 
 
 ^ 
 
 m 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Sr 
 
 o ( 
 
 B J 
 
 S c 
 
 Sr 3* 
 
 (Fig. 5.) Here we have, for several different i 
 values, curves of lift/drift on a base of log LV, 
 where L = length of chord in feet, and V = velo- 
 city in feet per second. By using this we can from 
 model figures obtain fairly accurately those for a 
 full size aerofoil at any speed . 
 
 It is necessary now to consider the effect of plan 
 form. (Fig. 6.) Assuming first that the plan form 
 of our aerofoils is rectangular and that we vary 
 the Aspect Ratio only : 
 
 The National Physical Laboratory gives us this 
 table of Lift Coefficient values, and Lift to Drift 
 values for an aerofoil of constant section and of 
 Aspect Ratio varying from 3 to i to 8 to i at 
 values of i from 2 to + 2- I suggest using 
 this table comparatively ; i.e., suppose we have 
 
 26 
 
AEROPLANE DESIGN 
 
 - sr AW- 
 
 1 
 ' 
 
 Q.6. 
 
 POR VARlATKONf Of ASPECT f?AT>0. (N pC) 
 
 A* PCT RAT 1 
 
 Vl 
 
 Ky lyb 
 
 L /b 
 
 Ky Vp 
 
 Ky 
 
 on 
 
 044 
 
 i-s 
 
 OSS' 
 
 2-4 
 
 2-3 
 
 117 
 
 loq 
 
 S-2 
 
 6-7 
 
 10-7 
 
 214- 
 
 173 
 
 300 
 
 2.^3 
 
 n-4- 
 
 246 
 
 366 
 
 ^ 
 
 13-4 
 
 346- 
 
 32.0 
 
 lo-i 
 
 4S7 
 
 4A7 
 
 12-7 
 
 430 
 
 423 
 
 10-4- 
 
 q-3 
 
 SI6 
 
 11-5- 
 
 fo-s 
 
 44!^ 
 
 q-0 
 
 12-2 
 
 11-6 
 
 10-7 
 
 ^q 
 
 $16 
 
 1 
 
 670 
 
 10-3 
 
 6^0 
 
 8-5 
 
 8-3 
 
 685" 
 
 673 
 
 7-1 
 
 S-7 
 
 3-q 
 
 662. 3-q 
 
 643 3*7 
 
 4-4 
 
 Ky yqlo<g.s i 
 
 blg. ore >Q Abso(/ufe j 
 
 fe 
 
 tb., foot; sec., upi'te nouHfa/y 
 
 VQlocs bv '00236 
 
 figures for a model of 6 to i Aspect Ratio and wish 
 to calculate its properties for some other Aspect 
 Ratio, say, 4 to i. We shall take it that its values 
 at 4 to i will be to its relative values at 6 to i as 
 are the corresponding values in this table for 6 
 to i to those for 4 to i . 
 
 27 
 
AEROPLANE DESIGN 
 
 It appears, from such few experiments as 
 have been made, that it slightly increases an 
 aerof oil's efficiency to rake the ends somewhat, 
 making the trailing edge longer than the leading 
 edge. This is because such a formation of ends 
 decreases the end losses. And probably the lower 
 the Aspect Ratio the more should the ends rake. 
 In practice, however, it is better not to rake the 
 ends too much, as we cannot then get the best 
 distribution of stay attachments along both front 
 and rear spars. 
 
 I suggest about 30 Rake for 4 to i Aspect 
 Ratio, 25 for 5 to i, and 20 for 6 to i, but these 
 are quite arbitrary values. 
 
 From a strength point of view it is advant- 
 ageous to taper the aerofoils from root to tip. But 
 as this means a structure considerably more 
 difficult and costly to make, I do not think it is 
 quife justified. 
 
 As regards choice of Aspect Ratio : For the 
 same surface, the lower the Aspect Ratio the 
 stronger is the aerofoil, or the lighter for the same 
 strength, but the lower will be the maximum 
 Lift to Drift value and the maximum value for 
 Lift. The efficiency at very small and very large 
 values for i is not much affected, and, in fact, 
 appears from this table to be rather better for the 
 lower Aspect Ratios. We must bear in mind that 
 a low Aspect Ratio is worse for both lateral and 
 directional stability than a high one. Taking 
 everything into consideration, I would suggest 5 
 to i Aspect Ratio for monoplanes and small 
 biplanes, and 6 to i to 7 to i for large biplanes. 
 
 28 
 
AEROPLANE DESIGN 
 
 lor 
 
 boll) Lifr Coefficient- 
 UFf/onf^ voluc. I'r 
 byaboul- 
 
AEROPLANE DESIGN 
 
 Next, for biplanes only of course, to consider 
 the effect of gap and stagger. Fig. 7. From model 
 experiments, we find that the greater the gap the 
 higher the efficiency, whilst stagger also increases 
 the efficiency somewhat. The gap amount, how- 
 ever, introduces the question of weight and head 
 resistance of struts and stays, the greater the gap 
 the greater these become. So we must com- 
 promise, and I should suggest a gap of .8 of Chord 
 up to equal to Chord, the smaller value for fast 
 and relatively high-powered machines, the larger 
 for slower and less highly powered ones. 
 
 The increase in efficiency is not very great in a 
 staggered disposition, and it increases structural 
 difficulties, especially if the means for obtaining 
 lateral control is by warping the aerofoils. Stagger 
 may, however, be of considerable value for im- 
 proving the view obtainable downwards from the 
 machine. Hence, I should suggest that the ques- 
 tion of stagger should mainly depend upon the 
 disposition of the pilot and passenger in the 
 machine, noting that if we use a heavy stagger 
 we should use ailerons and not warp. 
 
 We have then data for the dynamic properties 
 of model aerofoils and know how we can use 
 them for calculations on full-size ones. 
 
 Let us turn to the consideration of the weight 
 of aerofoils as a structure, for, unfortunately, 
 they have got to lift their own weight first and 
 then supply their surplus energy to lifting the 
 rest of the machine. 
 
AEROPLANE DESIGN 
 
 for Sirpilar Aerofoils'. 
 
 Cot UT* 
 A - 
 
 Wr. 
 
 So ^E-ur* a^u^gggd^ (^ ttyd? ^jpad 
 
 k, QC 
 
 k t - - 
 
 T U, -OlA* 
 
 ^Fig. 8.) Similar structures will bear the same 
 ultimate load per unit area, which means in our 
 case that similar aerofoils will have the same 
 " factor of safety " for the same value of useful 
 loading in Ibs. per square foot. 
 
 Taking basic figures from actual satisfactory 
 aerofoils, we shall assume that we can construct 
 an aerofoil of 100 sq. ft. surface, to weigh 70 Ibs., 
 
AEROPLANE DESIGN 
 
 and to stand 5.7 Ibs. per sq. ft. total loading with 
 the margin of strength necessary. This figure for 
 weight, i.e., .7 Ibs. per sq. ft., includes the weights 
 of stays for a monoplane and of stays and struts for 
 a biplane. Now we consider the aerofoil as stressed 
 only by the useful loading, i.e., total load, WT, 
 minus aerofoil weight, since in flight it is stressed 
 only by the lift it exerts over and above its own 
 weight. We shall take it then that since the weight 
 of similar aerofoils varies as the cube of the linear 
 dimension and the surface as the square, the 
 weight per sq. ft., w, will vary as the square root 
 of the total surface, A, for the same unital useful 
 
 WT 
 loading, or value of w. 
 
 Further, we shall take it that for aerofoils of the 
 same total area, within the limits of useful loading 
 desirable to employ, the weight per sq.ft. ,w, varies 
 
 WT 
 
 directly as the unital useful loading -r- - w, for 
 
 A 
 
 the same strength. 
 
 We see that on these assumptions for a total 
 surface of 100 sq. ft. the weight per sq. foot will 
 be .7 Ibs. for 5 Ibs. per sq. ft. useful loading, but 
 for a total surface of 400 sq. ft. it will be 1.4 Ibs. 
 for the same useful -loading. This is one of the 
 basic facts against the building of large sized 
 machines ; for unless we can improve our structure 
 (and of course the larger the machine the better 
 chance we have of so doing) the greater must the 
 proportion of aerofoil weight to useful load become. 
 
 32 
 
AEROPLANE DESIGN 
 
 We have then, that since 
 w = k 1/x / ATlbs. per sq. ft., and 
 
 k x = .oywhen-^- w = 5.olbs.per sq.ft.,and 
 k oc^F - w (useful loading) 
 
 /"Wx A 
 
 therefore k x = .014 ( - w J 
 
 V A / 
 
 and therefore 
 
 /WT \ 
 w - .014^7 A f -- - w J in Ibs. per sq. ft. , 
 
 an equation for the weight per sq. ft. of our 
 aerofoils, in terms of total aerofoil area and total 
 weight of aeroplane. 
 
 33 
 
AEROPLANE DESIGN 
 
 wejqHTS ., FIQ 9 
 0) VYfexMroTcuJZ. u/nUr, < c of 
 
 WO VY^xuoAi: oR SodLw . 
 3 WV 13 * 
 
 dU^til 
 
 - 45O 
 
 of b- 
 
 ITEM WEIGHTS. 
 We must now get figures for our other weights. 
 
 (% 9-) 
 
 Generally speaking, the size of the Tail, Rud- 
 der, and Vertical Fin (if used) will vary directly 
 as the size of the Wings (this assumes, of course, 
 approximately constant proportions for the 
 machine). I suggest, then, taking the necessary 
 weight of Tail and Rudder and Fin as a pro- 
 
 Eortion of the aerofoil total weight, and a fair 
 gure to take is one-fifth. 
 
 34 
 
AEROPLANE DESIGN 
 
 The weight of the body introduces the question 
 of the number of people the machine is to carry. 
 A sufficiently strong body of the timber and wire, 
 fabric covered, girder type can be made, of about 
 20 ft. length and 2 ft. mean breadth and depth, 
 to weigh about 90 Ibs., i.e. if 1 20 feet, b and 
 d = 2 feet then W B = 90 Ibs. 
 
 Since in such a structure the struts are (gener- 
 ally speaking), very strong compared to the fore 
 and aft members, for the kind of stresses to which 
 it is subjected, we shall assume that the weight 
 will vary directly as the breadth and depth, but 
 as the square of the length. Hence, we get an 
 equation for weight of Body W B = .057 I 3 b d in 
 Ibs. 
 
 As for the contents of this body. We can seat 
 each person properly for about 10 Ibs., and the 
 weight of control mechanism will be from 30 Ibs. 
 to 50 Ibs., dependent upon the type employed. 
 
 It remains only to consider the weight of suit- 
 able landing gear. I think it fair to consider the 
 weight of the Landing Gear, W , as varying 
 directly as the total loaded weight, W T , of the 
 machine, and I think a suitable one can be de- 
 signed at one-fourteenth of the total loaded weight 
 This weight we shall take as including the weight, 
 of the Tail Skid. For an average landing gear and 
 tail skid we may consider weight of Tail Skid 
 alone as - 1/20 of total weight of Landing Gear. 
 
 35 
 
AEROPLANE DESIGN 
 
 FIRST ESTIMATES. 
 
 We are now in a position, having been given 
 certain requirements, to make a first estimate of 
 weights, deciding in so doing upon the motor to 
 employ. 
 
 The designer is generally required to produce a 
 machine to carry a certain number of people, 
 petrol and oil for so many hours' flight at full 
 power, a certain weight of observing instruments, 
 perhaps some weapons of offence, fully loaded to 
 be able to fly at not less than a certain maximum, 
 and not more than a certain minimum speed, and 
 to climb at not less than a certain minimum rate. 
 
 Probably the simplest course to take in this 
 brief outline of designing methods is to assume 
 a certain set of conditions has been given and 
 see how we should set about trying to fulfil it. 
 We shall assume, therefore, that we are asked to 
 design a machine to carry two people, pilot and 
 passenger, to fly at 80 m.p.h. maximum and 40 
 m.p.h. minimum, to climb at 7 feet per second 
 fully loaded, to carry petrol and oil for 4 hours, 
 to have a good range of view downwards for the 
 passenger, to carry a full outfit of instruments, 
 i.e., barograph, compass, map case, watches, 
 engines, revolution counter, air speed indicator, 
 inclinometers, etc. 
 
 We must, of course, keep everything as small, 
 compact and simple as possible to maintain 
 strength and avoid weight. 
 
 To keep the fuselage weight and head resist- 
 ance as low as possible we shall make it a tandem- 
 seated machine. 
 
 36 
 
AEROPLANE DESIGN 
 
 As a good downward view is required for the 
 observer, we shall seat him in front of the pilot 
 as far forward as possible. 
 
 As the machine must necessarily be of a fair 
 total weight and of fairly light loading to fly at the 
 necessary minimum speed, we shall make it a 
 biplane. 
 
 Further, we shall give it sufficient stagger for 
 the observer to be able to see vertically, or nearly 
 vertically, down over the leading edge of the lower 
 aerofoils. 
 
 This will probably mean a rather large stagger, 
 so we shall decide on ailerons for lateral control, 
 these havi,ng the further advantage over warping 
 that they give much better control power at low 
 speeds (which entails, of course, large values of i). 
 Warping is equivalent to increasing the i value 
 of one aerofoil tip ; at slow speeds this may mean 
 no increased lift, as the machine may already be 
 flying with its aerofoils at their attitude for maxi- 
 mum lift, but it will mean increased drift with 
 tendency to spin in the wrong direction. But 
 pulling down an aileron is equivalent to increasing 
 the camber of part of the aerofoil, and, hence, 
 will give increased lift at any value for i. 
 
 We shall make the Body 20 feet long by 2 feet 
 mean depth and breadth, and, therefore, of 90 
 Ibs. weight, the weight decided on before for this 
 particular size. 
 
 We must allow 350 Ibs. for pilot and passenger 
 in their flying kit, and 20 Ibs, for seating them. 
 
 The controls, being not dual and being for 
 ailerons, we shall take at the lightest weight, 30 Ibs. 
 
 37 
 
AEROPLANE DESIGN 
 
 For the full kit of instruments called for we 
 must allow 30 Ibs. 
 
 This gives us a total weight of Body and con- 
 tents of 510 Ibs. 
 
 We now come to rather an impasse, as we cannot 
 get weights of Aerofoils, Tail Unit and Landing 
 Gear until we have fixed on the engine, and we 
 should like to know the total weight in order to 
 fix on the engine. So we must make a first choice 
 of an engine, judging from some previous machine. 
 
 We know that with the 80 Gnome one can 
 make a tractor biplane to fly at 40 to 78 m.p.h. 
 with 4 hours' fuel and oil, pilot and passenger, 
 and climb at about the rate we require. We shall, 
 therefore, need more power than the 80 Gnome 
 for our machine ; but, of course, we want to use 
 as low a power as possible. 
 
 Let us try the 8o-p.h. Le Rhone. From our 
 weight table for engines we find that total weight 
 for this motor with 4 hours' petrol and oil, tanks, 
 mounting, cowling and propeller will be 726 Ibs. 
 
 We now have total weight less Aerofoils, Tail 
 Unit and Landing Gear = 1,246 Ibs. There re- 
 mains to fix on wing form and loading, and thence 
 Wing, Tail Unit, and Landing Gear weights. 
 
 The total weight WT will be equal to 1,246 
 Ibs. + WG -(- (w x A) + (1/5 w x A) (Fig. 10), 
 where WG = weight of Landing Gear, including 
 Tail Skid, w = weight of Aerofoils in Ibs, per 
 square foot, and A = total surface of Aerofoils 
 in square feet. The 1/5 wA is, of course, the Tail 
 unit weight. 
 
 Further we have that WG = 1/14 WT 
 
 38 
 
AEROPLANE DESIGN 
 Hence, 13/14 Wx 1246 -f 1.2 wA. (i) 
 
 -ST/f\flATTL fQR TOTAL WEIGHT E.TC j^q./Q 
 
 To\- Q \ WKcg^f VVr l46 +u% -*LtfA -- ^A (Ibs) 
 - J|- WT = 124-6-1- I 2 UTA (lbs)(o 
 
 WE . 4 |^/0 K/( ^ 0ig * ooi.q 
 
 K y ^ _ 
 
 Ky por b^F^S '2-0* 
 
 Gq/o -K> Pborc* 
 
 -?5 Ky 
 
 Hg.QCg !>ece33qry Model 
 
 Ky of- 58 R>s- -ooi^-o 
 
 176 
 q3 
 
 K y for (0 
 
 ue* 
 
 If K y ftxax * -0015- loadio<^ 4-3 Ib 
 If W T iqOO tbo ^ V!4..3!b*/if .H)O A 
 UT- - 
 
 rroro 
 
 UT 
 
 on, 
 froro(0 $00 
 
 Of W T - iqoolbs 
 
 39 
 
AEROPLANE DESIGN 
 
 CHOICE OF AEROFOIL 
 
 We must now fix upon what form of aerofoil 
 to employ and what loading. 
 
 The first thing to note is that the machine has 
 to be able to fly at 40 m.p.h., or about 59 f.p.s. 
 So the maximum Ky value for the aerofoils must 
 be such as to give us lift per square foot at 58 feet 
 per second equal to the total loading per square 
 foot that we shall choose. 
 
 This may seem a small margin to allow for 
 obtaining the slow speed, but it must be remem- 
 bered, that at the slow speed, and consequent 
 cabre, or tail-down, attitude of the machine, there 
 will be a certain amount of added lift from the 
 tail and body of the machine, and a slight upward 
 component of propeller pull. 
 
 Also we must cut the slow speed as fine as 
 possible to get the greatest possible high speed. 
 
 Now, for 4 Ibs. per square foot, total loading at 
 58 feet per second maximum Ky must be = .00119 
 
 For 4! Ibs. max. Ky must be = .00134. 
 For 5 Ibs. max. Ky must be = .00149. 
 For 5 1 Ibs. max. Ky must be = .00164. 
 All these being values for a biplane, of course. 
 
 40 
 
AEROPLANE DESIGN 
 
 We must now consider our high-speed : 
 The high speed is to be 80 m.p.h., or 117 feet 
 per second. Considering it as 120 feet per second 
 we see, of course, that the Ky values for this speed 
 
 -02 
 
 must be -j 2 of the Ky values for 58 feet per 
 
 second, as loading is constant. That is to say : 
 Ky at 120 f.p.s. must = .233 Ky at 58 f.p.s. 
 
AEROPLANE DESIGN 
 
 CORRESPONDING MONOPLANE VALUES 
 
 We must next, as our machine is a biplane, and 
 our figures for model aerofoils are for single or 
 monoplane form, obtain from our tables for effects 
 of gap and stagger the necessary corresponding 
 monoplane Ky values. We shall assume that we 
 shall make gap = chord and stagger = about .4 
 of chord. We shall, therefore, as sufficiently accur- 
 ate for the present, take that Ky biplane = .85 
 Ky monoplane, as it would be about .82 for this 
 gap and no stagger, and we obtain about 4 per cent, 
 increase of efficiency due to the stagger. 
 
 That is to say, the necessary biplane Kys we 
 have found for different loadings, must be multi- 
 plied by 1. 1 8 for monoplane tests. We get then : 
 
 For 
 
 4.0 Ibs. per sq. ft. loading Ky max. must be .00140 
 4-5 .00158 
 5-o .00176 
 
 5-5 - OOI 93 
 and Ky high-speed = .233 of these values as we 
 
 saw before. 
 
 We turn now to our data sheets for Model 
 Monoplane Aerofoils and fix upon the best form 
 for our case. 
 
 We have to pick out that Aerofoil which, having 
 a maximum Ky of .00140 or over, will give us the 
 highest value for Lift to Drift for a Ky value = 
 .233 of its maximum value ; that is, we must con- 
 sult the curve of Ky value, and the curve of Lift 
 to Drift on a base of Ky value, for all our data 
 sheets, and pick out the best Aerofoil for this case. 
 
 42 
 
AEROPLANE DESIGN 
 
 We shall assume that we have done this, and 
 have found the best Aerofoil form for us to be 
 one which for a maximum Ky of .0015 gives us, 
 at Ky = .233 of .0015 (or .00035), a Lift to Drift 
 of 10/1, 
 
 With this Aerofoil we must have a loading of 
 4.3 Ibs. per square foot. 
 
 We must now make a shot at the total weight 
 WT, as we shall then be able to get a figure for 
 total Aerofoil Area, thence for Aerofoil weight, 
 thence a figure for total weight, which must be 
 very nearly the same as our guessed weight, or we 
 must guess again with increased wisdom. 
 
 We shall guess, then, that the machine is going 
 to weigh, fully loaded, i ,900 Ibs,, and it will, there- 
 
 1900 
 fore, need -- , or 440 square feet of Aerofoil 
 
 4-3 
 surface at the 4.3 Ibs. per square foot total load- 
 
 ing. 
 
 From our previously determined equation : 
 
 We get that w = .014^/440 (4.3 - - w) 
 whence w = .98 Ibs. per sq. ft. 
 This, then, gives us Aerofoil weight = 430 Ibs., 
 
 13 
 and we get that WT = 1762, or WT = 1900 Ibs.; 
 
 *4 
 
 of this, Tail unit weight is 86 Ibs., Landing Gear 
 
 weight =136 Ibs., and of this, again, 7 Ibs. is 
 Tail Skid. 
 
 43 
 
AEROPLANE DESIGN 
 
 This is our guessed weight (I admit that I 
 guessed once or twice in getting out these figures, 
 but have spared you the tedium by quoting the 
 right guess at once) ; so we can take the figures 
 for total weight and wing surface as found. 
 
 44 
 
AEROPLANE DESIGN 
 
 DEFINITE DESIGN. 
 
 We have now fixed weights, surface, aerofoil 
 form and motor, and can proceed with the 
 design. 
 
 We shall, as this is a largish machine, choose an 
 aspect ratio of 6 to i , which gives us 4 aerofoils of 
 6.15 feet chord by 17.5 feet * mean " span, which 
 with the top centre plane of 2 feet span, gives us a 
 total " mean " span of 37.0 feet, and our total 
 surface (which is surface of 4 aerofoils + top 
 centre plane), of 440 square feet. I talk of ".mean " 
 span, as we shall employ ends raking at 20 for 
 our aerofoils. 
 
 We must now draw out a side elevation of the 
 body of the machine with seats, tanks, motor, and 
 tail skid, keeping all the weights as close together 
 as possible. (Fig. n, page 46). We shall employ 
 a " non-lifting " Tail plane, that is to say, a form 
 symmetrical about its central horizontal plane and 
 with this plane parallel to the axis of the pro- 
 peller. 
 
 This form is perhaps the safest to employ, as it 
 will give no difference in lift or depression, 
 whether in the propeller slip stream (when the 
 motor is running) or not (when the motor is 
 stopped). We shall set the chord of the aerofoils 
 at 3 to the propeller axis. 
 
 We now require to place our Aerofoils and 
 Landing Gear, less Tail Skid, of course, on the 
 body in such a manner that the total reaction on 
 the Aerofoils, at 3 value for i, passes through the 
 CG of the whole machine (of this more anon), and 
 
 45 
 
AEROPLANE DESIGN 
 
 Fic-.f/. 
 
 JpS* 4 * 
 
 fitaev&t. nerr 
 
 .TABLE fDR HORIZONTAL ^ VERTICAL CQ 
 
 ITEM 
 
 W 
 
 V2-0 
 
 Motor 
 
 25-0 
 
 4-7 
 
 17 b~ 
 
 13 
 
 IS 
 
 -.2 
 
 Oil 
 
 2. 
 
 n-o 
 
 3qo 
 
 10 
 
 2S 
 
 ffetrol STaoK 
 
 fl-4 
 
 IS30 
 
 Body 
 
 -S 
 
 213 
 
 3o 
 
 IS20 
 
 Piiohs Scqh 
 
 10 
 
 1430 
 
 toil SKd 
 
 138 
 
 2IO7 
 
 IC.08 
 
 -3-c) 
 
 85L2L 
 
 Goaded) 
 
 4-ss^qi 
 
 2234 
 
 w- w^rf-of Itertjfo Ibs 
 
 1 - Noftx^ d.&h*-of 0| of ifenj /Vfi5 hoe Y-r . 
 
 X - > '"> X">- 
 
 46 
 
AEROPLANE DESIGN 
 
 that the centre of the wheel axle of the Landing 
 Gear is about 12" ahead of it. 
 
 This, of course, is another trial and error pro- 
 cess, and had best be arrived at as follows : Draw 
 on a piece of tracing paper the side elevation of 
 the Aerofoils (to same scale as Body, of course), 
 with correct gap and stagger, also a base line AB 
 inclined at 3 to the chords. From model figures 
 for the Aerofoil form mark on chord of each 
 Aerofoil the position of Centre of Pressure with 
 1 ^ 3 ; ji n these two points by a straight line, 
 and on this line mark a point P, 4/7 of its length 
 from the chord of the lower Aerofoil ; through 
 this point P draw a line perpendicular to the afore- 
 mentioned base line AB. This line we can take as 
 representing accurately enough the line of Lift 
 reaction on our biplane, for i = 3. Through this 
 same point P draw a line parallel to the Base 
 line AB, which will represent the line of Dyna- 
 mic Resistance of our biplane for 1=3. 
 
 From the figures for our Aerofoil form, we shall 
 measure off, to some suitable scale, a distance 
 from P on the Lift re-action line to represent our 
 biplane's Ky value i at = 3 and a distance from P 
 on the Dynamic Resistance line to represent our 
 biplane's Kx value at i = 3 . By drawing a parallel- 
 ogram and its diagonal through our chosen point P, 
 we now get a line (this diagonal), which represents 
 the line of Total Re-action on our Biplane at i = 3 
 
 Note that we take 4/yths of the inter Aerofoil 
 distance, not f, for the top aerofoil does more 
 work than the lower, in about the proportion of 
 4 to 3, at small values for i. 
 
 47 
 
AEROPLANE DESIGN 
 
 To same scale we must draw on another piece 
 of tracing paper a side elevation of the Landing 
 Gear. 
 
 We must now place these over our body draw- 
 ing in guessed positions, keeping the base line AB 
 on the Aerofoil drawing parallel to the axis of 
 motor, and proceed to make a first calculation for 
 position of CG. For this calculation we shall take 
 horizontal Moments about the fore end of the 
 body, and vertical Moments about the axis of the 
 motor, as convenient datum lines, taking the 
 weights of the various items multiplied by the 
 normal distances of their CGs from these datum 
 lines. We can fix pretty accurately the CGs of the 
 items. I suggest taking the CG of the Aerofoils as 
 slightly above the centre of a line joining the 
 centre points of the lines which join the centre 
 points of the spars of top and of bottom Aerofoils ; 
 slightly above (say n/2oths above bottom), be- 
 cause the centre plane and its struts are at the top 
 of the whole structure. The CG of the body alone 
 may be taken as about 1/3 of its length from its 
 fore end ; the CG of the Tail unit as about i foot 
 ahead of the rear end of the body ; the CG of the 
 Landing Gear, assuming a form as shown, as 
 lying 12" ahead of, and 2" above, the wheel 
 centres ; the CG of a man sitting as about 12" 
 ahead of the seat back and 12" above the seat 
 bottom. 
 
 The CGs of the other items, tanks with petrol 
 and oil, engine, engine mounting, engine cow- 
 ling, seats, controls, instruments, Tail Skid, etc., 
 are easy to fix accurate! v enough by inspection. 
 
 48 
 
AEROPLANE DESIGN 
 
 If our first shot for Aerofoil and Landing Gear 
 position be out we must slide them to new posi- 
 tions, and try again, till we get the positions which 
 answer our requirements. 
 
 We have now fixed up our outline design, and 
 it remains to consider strength and stability, and 
 then to finally check whether we have sufficient 
 power for the high-speed and for the climb. 
 
 But before passing on let us note that the tank 
 positions must be such that the CG alters little in 
 horizontal position, whether they be full or empty, 
 and they must also, of course, be of the required 
 capacity. As it is almost impossible to keep the 
 CG of both petrol and oil over the CG of the 
 whole machine, and since for our motor the weight 
 of petrol consumed per unit time is about six 
 times the weight of oil consumed per unit time, 
 we should keep the CG of the oil about six times 
 as far (horizontally) from the total CG as is the 
 CG of the petrol, and, of course, the tanks on 
 opposite sides of the total CG. 
 
 Bearing this in mind, we get in the tanks as 
 best we can. 
 
 49 
 
AEROPLANE DESIGN 
 
 v/ 
 
 WING STRENGTH. 
 
 For the strength of the wings, considered as an 
 ordinary framed structure, we now have the over- 
 all sizes, the position of main aerofoil spars and 
 of struts and ties. Considering each spar as a con- 
 tinuous beam and each aerofoil as uniformly 
 loaded (its own weight being of course now not 
 taken) for 5/6ths of its mean length, we must find 
 the curve of bending moments and the reactions 
 at the supports of each spar, firstly with the centre 
 of pressure at its position nearest to the leading 
 edge, and secondly at its position for full speed, 
 which will be much further from the leading edge. 
 The sections and materials of the spars must be 
 chosen such that under neither of these conditions 
 do the maximum calculated fibre stresses exceed 
 i /6th of the ultimate compressive strength of the 
 material employed. This is the so-called " factor 
 of safety " generally called for. 
 
 Similarly the cross sections and material for 
 each strut must be so chosen that (for a form of 
 low head resistance), the maximum applied load 
 does not exceed i/6th of the ultimate strength, 
 calculated by Euler's formula for a pillar pin 
 jointed at both ends. 
 
 Similarly each stay cable should have an ulti- 
 mate strength, taking into account any weakening 
 due to splicing, etc., of at least 6 times the maxi- 
 mum pull we shall, from the before-mentioned 
 calculations, find it subjected to. 
 
 I suggest considering the aerofoils as uniformly 
 loaded for 5/6ths only of their total lengths, 
 
 50 
 
AEROPLANE DESIGN 
 
 because, owing to end losses, the loading decreases 
 towards the outer ends, and this assumption 
 therefore gives a fairly accurate and a simple 
 method of accounting for the actual distribution 
 of loading over the aerofoil surfaces. Of course 
 the uniform loading used for the calculation must 
 be adjusted so that total loading remains equal to 
 the total weight for stress. 
 
 I shall not touch further on strength except to 
 say that the same requirements hold throughout 
 the machine, and the unfortunate designer is 
 expected to be able to produce reasonable figures 
 showing that his detail design is such that no part 
 of the machine has a " factor of safety " of less 
 than 6 under such condition, between slowest 
 and fastest flying speeds, as imposes the greatest 
 strain on such part. 
 
AEROPLANE DESIGN 
 
 STABILITY. 
 
 Now to consider stability and controllability, 
 which resolves itself for us into determining the 
 size of Tail Plane, Elevator, Fin, and Rudder and 
 amount of dihedral angle of the Aerofoils for our 
 design. 
 
 The full investigation of the stability of an aero- 
 plane is necessarily an extremely long and difficult 
 process, involving mathematics of a high order. I 
 do not propose, however, to consider anything 
 other than a few very simple methods in which 
 by using data from model experiments and quite 
 elementary mathematics we should arrive at 
 decently satisfactory results. Thus, though they 
 are all more or less interdependent, I propose to 
 consider longitudinal or " pitching stability,'* 
 lateral or " rolling stability," and directional or 
 " yawing stability " separately. Further, I shall 
 take no account of the moment of inertia of the 
 machine, though this has effects on the stability > 
 except to state that the moment of inertia about 
 all three axes should be kept as low as possible, 
 as much from strength as from stability consider- 
 ations. A machine of large moment of inertia 
 may perhaps be made as stable as one of small, 
 but, inasmuch it will rotate more slowly about any 
 axis, it is highly probable that it will be subjected 
 to greater local stress in a fluctuating wind, and it 
 will answer more slowly to, and is therefore more 
 likely to be locally stressed by, its controls. 
 
AEROPLANE DESIGN 
 
 LONGITUDINAL STABILITY. 
 
 First, then, for " longitudinal stability," and by 
 this I mean an innate tendency of the machine to 
 preserve a constant attitude to its flight path 
 that is, to preserve a constant value of i for the 
 aerofoils. For us this resolves itself into a deter- 
 mination of the size of the tail plane and elevators. 
 
 As you will have noted from our preceding 
 curves for aerofoils, all along the range of i values 
 useful for flight a curved aerofoil is unstable 
 that is, as i increases the CP moves forward, as i 
 decreases the CP moves backwards ; in both 
 cases, therefore, the shift of CP tends to aggravate 
 and not to stop the alteration of i value. 
 
 Similarly, the body, which for low head resist- 
 ance generally approaches a torpedo form, is 
 instable for small angles to its flight path. It is 
 left to the tail, therefore, to counteract the in* 
 herent instability of aerofoils and of body. 
 
 As for the form of calculation, this is best set 
 out in tabular form (Fig. 12, page 54). In column I 
 we have a values, a being the angle which the axis 
 of the motor makes with the direction of flight ; 
 in column 2 the corresponding values for i, which 
 for our case will be a + 3 throughout ; in column 
 3 corresponding values for KY, the lift coefficient 
 of the aerofoils ; in column 4 corresponding 
 values for Kx, the drift coefficient of the aerofoils ; 
 in column 5 values for total reaction coefficient R, 
 
 which is, of course, \/KY* + Kx* ; in column 
 6 values for A x R, or aerofoil surface multiplied 
 
 S3 
 
AEROPLANE DESIGN 
 
 
 
 CNJ 
 
 i/7 
 
 a 
 
 F 
 
 CO 
 
 CO 
 
 1 
 
 
 CO 
 
 IT) 
 
 Si 
 
 F 
 
 
 ^ 
 
 * 
 
 O gl 
 
 b> tr: 
 
 CO 
 
 54 
 
AEROPLANE DESIGN 
 
 by total reaction coefficient ; column 7 is for L 
 values, L being the perpendicular distance from 
 CG of machine to line of action of R. 
 
 Column 8 is for A x R x L values, which is a 
 function of the moment of the reaction on the 
 aerofoils about the CG ; in column 9 we have 
 values of /3, or inclination of tail plane to line of 
 flight, in our case /3, = a throughout ; in column 
 10 corresponding values of kY for tail plane ; and 
 in column 1 1 corresponding values of kx for tail 
 plane ; in column 12 values of total reaction 
 coefficient r on tail plane, r being, of course, 
 
 = A / ky a + kx a ; column 13 is for values of 1, 
 
 perpendicular distance from CG of machine to 
 line of action of r ; column 14 for values of r x 1 ; 
 column 15 is for values in column 9 divided by 
 
 A x R x L 
 
 values in column 16 i.e., for -. and 
 
 1 x r 
 
 this gives us the required tail area necessary to just 
 counteract the moment of reaction on the aero- 
 foils, assuming the tail as in undisturbed air. 
 
 If we can get accurate model figures for the air 
 reactions on the body of our machine we should 
 get out a second table, similar to the foregoing, to 
 find the necessary area of the tail plane to counter- 
 act the instability of the body. But as we may not 
 have these figures, and as the reaction on the 
 body is comparatively small for a narrow form 
 such as we are using, we may, in the absence of 
 reliable model figures, neglect the second table, 
 and merely add a small amount to the tail surface 
 necessary for the aerofoils alone say i/ioth. 
 
 55 
 
AEROPLANE DESIGN 
 
 As to how the figures for columns 7 and 13 are 
 arrived at, in a similar manner to that in which we 
 drew the line of total reaction on our biplane for 
 i = 3, we must draw a series of lines represent- 
 ing lines of total reaction on it for each of the 
 i values in the table. We can then on our side 
 elevation drawing measure the perpendicular 
 distances from CG of machine to each of these 
 lines, these distances being values for L, to scale 
 of drawing. On the figure I have, for clearness, 
 only drawn line for R at i' value for i. 
 
 As for the tail plane, assuming we shall decide 
 to employ one of the form shown, as a good com- 
 promise between strength and efficiency, if we 
 have not figures for a model of this form it is 
 probably accurate enough to take for it figures 
 for a rectangular plane of aspect ratio 2 to i . 
 
 As we do not know until after the calculation 
 the size for our tail plane, we do not know exactly 
 the position of its line of reaction. But the chord 
 of the tail plane is fairly small compared to the 
 distance from CG of machine to centre of pressure 
 or tail plane, and smaller still is the shift of CP on 
 tail plane compared to this distance. Hence we 
 shall assume a point, say, 2 ins. above the top of 
 the body and 2 ft. from the rear end of the body 
 as the position of C of P on tail plane, and shall 
 neglect the shift of CP. Of course, if on finishing 
 the calculation we find that, for the tail plane size 
 which we shall need, our guess is obviously a lot 
 out, we must alter up and correct our table. 
 
 We shall take the required area of tail for our 
 machine that is to say, area of tail plane plus 
 
AEROPLANE DESIGN 
 
 area of elevators as twice the greatest area called 
 for in the table. This seems rather a libel on our 
 calculations, but the reason for this apparent large 
 excess of tail area is that the tail is acting both in 
 the down-draught from the aerofoils and when 
 the engine is running in the slip -stream of the 
 | propeller ; both of these factors tend to decrease 
 1 the alteration of air flow relative to the tail, when 
 the attitude of the whole machine to its flight path 
 is altered. That is to say, they both tend to decrease 
 the correcting power of the tail. 
 
 This figure of half-value for the tail on the 
 machine to Tail considered as in undisturbed air 
 is approximately that found by recent experi- 
 ments at the N.P.L. 
 
 Before leaving the question of longitudinal 
 stability I would suggest that the value of total 
 area of tail should be kept about as it would be 
 found by the foregoing calculations for any 
 machine, but the more the pow y er of control re- 
 ! quired the greater should the relative area of 
 elevators to tail plane be made. The ratio of 
 elevator area to tail plane should lie between the 
 limits of .6 to .4 and .3 to .7. Outside these limits 
 we shall get a machine either heavy on the con- 
 trols on the one hand, or slow to respond on the 
 ! other. We shall use, therefore, a total area of 75 
 j sq. ft., of which .43, or 32 sq. ft., is in the elevators, 
 and we arrive at the sizes as shown. 
 
 57 
 
AEROPLANE DESIGN 
 
 DIRECTIONAL STABILITY. 
 
 Very briefly, for " directional " or " yawing 
 stability," for us this now means size of rudder 
 and fin required. I say rudder and fin for our 
 machine, as I think it is safer to use a fin on large 
 and heavy machines. On small and light machines 
 it is perhaps not necessary. Structurally, of course, 
 the employment of a fin is of value. 
 
 We have at present few figures on which to 
 base calculations for rudder size. The rudder 
 and fin considered as a fixed surface must be large 
 enough to counteract the inherent yawing in- 
 stability of the body, also to counteract the yawing 
 effect of the side surface of those parts of the land- 
 ing gear which are ahead of the CG, and also to 
 counteract the yawing effect of the propeller 
 considered as a front fin. 
 
 We must also be sure that, when the rudder is 
 set at about 5 degrees, say, it has ample power 
 additionally to counteract the worst spinning 
 moment induced by working the warp or ailerons. 
 Unless we have model figures for yawing moments 
 on the fuselage, and for drift on an aerofoil with 
 ailerons at different attitudes, we had better deter- 
 mine our rudder area from figures for other 
 machines as nearly like ours as possible which 
 we know were satisfactory as regards their 
 directional stability and control. 
 
 I suggest, then, using an empirical formula 
 
 (Fig- 
 
AEROPLANE DESIGN 
 
 in which s = area of rudder in sq.ft., d distance 
 of centre of area of rudder from CG of machine 
 in feet, S is area of side elevation of body, aero- 
 foils, landing-gear, and propeller in sq. ft., 
 D = distance of centre of this area S behind CG, 
 A is area of aerofoils in sq. ft., and C is a constant 
 which we shall take as 1.7, from figures for other 
 machines of this type. 
 
 The value for body side area is the area in side 
 elevation of body, complete with all added top 
 superstructure, cowling round motor, etc. 
 
 The value for side area of aerofoils is that of 
 the aerofoils with their struts in side elevation, 
 thus taking account of the fin area due to dihedral. 
 
 In our^case, then, we have 
 
 1.7 x x 15 70 
 
 70 x 2.4 
 
 ~f- 440 or s 17 
 
 That is, we require a rudder + Fin area of 
 17 sq. ft. We shall dispose this in a form as shown 
 in Fig. 13. 
 
 59 
 
AEROPLANE DESIGN 
 
 LATERAL STABILITY. 
 
 Let us consider the causes for possession of, 
 or lack of, " lateral stability " in an aeroplane. 
 An aeroplane is a body immersed in a fluid air 
 and since its average density is very great com- 
 pared to that of air, we consider it as supported 
 only by the reaction of the air upon its lifting 
 surfaces. That is to say, it is supported solely by 
 reason of its speed relative to the air. 
 
 Now, for both of the stabilities we have already 
 discussed that is " pitching " stability and " yaw- 
 ing " stability the flight path is approximately 
 at right-angles to the axes of rotation. Hence a 
 small rotation immediately induces a change of 
 reaction upon the tail plane, or rudder, as the case 
 may be, which tends to counteract the rotation. 
 But when we come to consider the third form of 
 stability that is, " lateral " or " rolling " stability 
 we see that the rotation now takes place about 
 an axis which is parallel, or very nearly parallel, 
 to the flight path. 
 
 Hence rotation about the longitudinal axis, or 
 rolling, will by itself produce no change whatever 
 upon the air reactions on the machine ; that is 
 to say, if an aeroplane rotate about an axis 
 parallel to its flight path, no other motion being 
 present, no force is created to counteract the 
 rotation. 
 
 However, when an aeroplane rolls, other 
 movements do occur, and it is from these that 
 we attain " lateral stability." 
 
 Let us consider, then (Fig. 14), an aeroplane 
 
 60 
 
AEROPLANE DESIGN 
 
 XC; 
 
 CALCULATION TABLC fttR V&RTlCAL C.G.OF Af?CA . 
 
 1TG.IVI 
 
 Procter 
 
 C6WI 
 
 Chassis froo^Strul- 
 
 Jfear 
 
 SKid 
 
 Body bdorv x-* 
 
 * above 
 
 Aerofoil Struts 
 
 Tailsfcfd ' 
 
 "ToTAL. 
 
 4--0 
 
 l-o 
 
 -5-0 
 
 1-0 
 
 3-ft 
 
 4^ 
 6-c 
 
 _L. 
 
 KCflO 
 
 -f- 
 
 AxK,. 
 
 - 2-2 
 
 - lft-6 
 
 4-3 
 
 6-0 
 
 -- 8-1 
 
 4-a-a 
 
 of frknj i 
 
 of Area of tfeip abot 
 or betewr AuJtx-x 
 
 61 
 
AEROPLANE DESIGN 
 
 flying steadily and horizontally and assume that 
 some outside force, say a puff of wind, rolls it over 
 slightly. We see that, as speed and therefore total 
 reaction, RT, remain constant, and as the lift 
 reaction is now out of line with the gravitational 
 force, the vertical component of lift is now less 
 than the gravitational force, and the horizontal 
 component is unbalanced ; that is to say, the 
 machine will commence to drop and move side- 
 ways. Directly it commences to do this we get 
 motion perpendicular to the axis of rotation and, 
 if our surfaces are properly disposed, a righting 
 moment therefrom. 
 
 Briefly, then, we see that, for " lateral stability/' 
 if the machine had a sideways velocity relative 
 to the air, the resulting reactions on the whole 
 machine must tend to raise the then leading aero- 
 foil tip. This is the main reason why a dihedral 
 angle for the aerofoils tends to give lateral stability. 
 We also see that, if the outer shape of a machine 
 remain the same, the higher the CG the greater 
 the dihedral we shall need, and vice versa. 
 
 It is necessary for us, therefore, to calculate the 
 vertical position of centre of projected side area 
 of the whole machine less the aerofoils. I then 
 suggest that, if this centre of area lie at the same 
 height as the CG, give 3 per cent, dihedral angle 
 to the aerofoils. If the centre of area lie above the 
 CG, less dihedral should be given ; if below, 
 more dihedral should be given. For amount of 
 increment (or decrement), I suggest i of dihedral 
 per 15 value (in sq. feet x feet) of vertical mo- 
 ment of side area about CG. Theae figures are 
 
 62 
 
AEROPLANE DESIGN 
 
 quite arbitrary ones and I cannot vouch for their 
 suitability. They approximately represent current 
 practice for machines of this type. 
 
 As you will note, in our design the centre of 
 projected side area is considerably below the centre 
 of gravity, .55 ft. ; so we had better decide to 
 employ 5 per cent, dihedral angle. 
 
 We must note, before leaving the subject, that 
 too much inherent stability should not be given 
 to an aeroplane. " Inherent stability," as I have 
 used it, being a tendency of the machine to retain 
 the same altitude to its flight path or to its relative 
 motion to the air, it follows that the more stable is 
 a machine in this sense the more does it tend to 
 follow alterations in wind direction, and this 
 quality in excess makes for discomfort in flying 
 and danger in landing. Hence we want to ensure 
 that our machine has a slight margin of stability 
 and that ample controlling power is afforded to 
 the pilot to enable him to quickly alter at will its 
 attitude in any direction. 
 
AEROPLANE DESIGN 
 
 PROPELLER THRUST. 
 
 We have now got our design temporarily 
 completed ; it remains to calculate the head re- 
 sistance as accurately as possible and the pro- 
 peller thrust, to see if we have sufficient power 
 for the reqtiired high speed and climb and to 
 check the balance of the machine. 
 
 Firstly for the propeller thrust, I cannot attempt 
 to touch propeller design in this paper ; it is a 
 subject for many papers in itself. I must merely 
 refer to experimentally determined figures for 
 propellers. We have a good many of these and can 
 probably pick a form that will suit us. We will 
 take it, then, that we have the curve of efficiency 
 for a suitable propeller on a base of slip ratio at 
 constant revolutions (Fig. 15). 
 
 The efficiency is expressed, of course, as 
 
 Useful work Thrust x speed 
 
 Total work H.P given to propeller 
 /p x r \ y 
 
 The slip ratio is ** where p is pitch of 
 
 r p x r 
 
 propeller in feet, r revs, per sec., and V is speed , 
 i.e., speed of advance along axis in feet per sec. 
 
 Knowing the horse-power our motor gives at 
 full normal revs., we can from this efficiency 
 curve make another curve of our actual propeller 
 thrust in Ibs. on a base of speed of advance, i.e., 
 speed of aeroplane, in feet per sec. 
 
AEROPLANE DESIGN 
 
 ve<t or c 
 
 OfT, 
 
 
 ** , 
 
 ^^ ^^^ 
 
 
 
 
 
 -* 
 
 ^ 
 
 ^ 
 
 >< 
 
 ^^ 
 
 
 
 1 
 
 N 
 
 
 -350 
 
 TI> 
 
 
 
 ^ 
 
 x^ 
 
 
 
 
 1 "^. 
 
 
 
 
 
 \ 
 
 Boo 
 
 
 ^ 
 
 x^ 
 
 
 
 
 
 
 
 
 s 
 
 \ 
 
 
 5,O 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ss so AT 40 
 St 4s 70 77 
 
 e- 
 
 ioc nfi. K| 
 
 ( _ (^x>u)~ or 
 
 ir, tb 
 
 65 
 
AEROPLANE DESIGN 
 
 HEAD RESISTANCE. 
 
 It remains to get figures for plotting a curve 
 of total head resistance (in Ibs.) of machine on 
 this same base of speed in feet per sec. 
 
 For this we turn to the front elevation of our 
 aeroplane (Fig. 16) and determine which parts 
 lie within the propeller disc and which outside it. 
 The parts which lie in the propeller disc, i.e., in 
 the slip-stream from the propeller, will be in a 
 current of fairly constant speed irrespective of 
 speed of machine. 
 
 We make our calculation, therefore, in the form 
 of two tables. The first table is for parts in the 
 slip-stream, the second for parts outside it. In 
 neither of these tables shall we include aerofoils, 
 as the total reaction on these has already been 
 dealt with in first balancing. 
 
 The coefficients for resistance for the different 
 parts of our machine we must obtain from figures 
 from model experiments, and of these we have a 
 fair armament. 
 
 In both tables we find the resistance in Ibs. for 
 each item at some chosen fixed value of v ; at the 
 same time we take, as you see, the moment of 
 resistance of each item about the axis of the motor, 
 vertically, of course, in order to obtain a figure for 
 vertical position of centre of head resistance. 
 
 We must determine the vertical position of 
 Centre of head resistance, less aerofoils of course, 
 to see if there will be a thrust head-resistance 
 couple. If we find that there is one that is to say, 
 if the line of residual resistance is above or below 
 
 66 
 
AEROPLANE DESIGN 
 
 TABLE I. ID 
 
 67 
 
AEROPLANE DESIGN 
 
 the line of thrust we must either (if practicable) 
 alter the line of thrust or, by slightly altering the 
 fore and aft position of the aerofoils, introduce an 
 equal and opposite lift-weight couple to counter- 
 act the thrust-head resistance one. 
 
 In the first of these tables, then, we shall take 
 V as slightly below (say 5 per cent, below) the 
 pitch speed of the propeller, and we shall take the 
 total resistance R x of the items in this table as of 
 the amount thereby found, and as constant for all 
 speeds of the machine. 
 
 For our case we get R x as 67.7 Ibs. acting .01 
 foot below line of thrust and as constant. 
 
 In the second table we shall take V as 100 f.p.s., 
 being a convenient figure to work with, and the 
 total resistance R 2 obtained is, of course, the re- 
 sistance of all parts, except aerofoils, outside the slip- 
 stream at 100 f.p.s. We take R 2 as varying as V 2 . 
 
 In our case, therefore, we get a second table 
 resistance R 2 of 50.3 Ibs. at 100 feet per sec. 
 that is to say, R 2 = .00503 v 2 Ibs. and acts 1.51 
 ft. above line of thrust. We see then that for the 
 design as so far got out the line of total residual 
 resistance is going to be considerably above the 
 line of thrust. At maximum speed required, 120 
 f.p.s., it is going to be 140.2 Ibs. acting .77 foot 
 above the line of thrust. So we must either raise 
 the line of thrust or shift the aerofoils aft slightly. 
 We should, however, make the necessary correc- 
 tion for balance, for that speed at which i for 
 aerofoils = 3, as then the tail is floating. 
 
 Now when i = 3, Ky = .00055, hence v must 
 be 88.5 feet per sec., thence R, = 39.5 Ibs., and 
 
 68 
 
AEROPLANE DESIGN 
 
 thence total residual resistance R 2 + &2 = 107.2 
 Ibs. and acts at .55 ft. above line of thrust. We 
 shall therefore decide to shift our line of thrust up 
 .6 foot, which will give a satisfactory balance and 
 will have the additional advantages of bringing 
 the line of thrust nearer to the CG and of slightly 
 cutting down landing gear height, and therefore 
 weight and head resistance. 
 
 We should now correct our tables for CG and 
 for residual head resistance ; this would be a 
 repetition of the previously described calculations, 
 and the figures for amount of total residual head 
 resistance which we have already obtained would 
 hardly be altered, certainly not increased, by this 
 raising of line of thrust. Hence, as we can use 
 them as they are for looking into the remaining 
 points, I omit, for the sake of brevity, correcting 
 up these tables here. 
 
 Finally, then, we turn again to our model 
 aerofoil figures to obtain the remaining part of 
 the total head resistance, the " drift " of our 
 aerofoils (Fig. 17, p. 70). From the Ky values we 
 first determine the speeds corresponding to 
 several different values for i, say for i = i, 4, 
 7, 10, 13, 16. 
 
 Taking into account the variation of lift to drift 
 with log AV before quoted, we find then the drift 
 (RD) of our machine's aerofoils at these different 
 values for v. 
 
 By our previously determined equation we find 
 the values for part R 2 of residual resistance at 
 these speeds ; whilst part R! of residual resist- 
 ance is constant and already obtained. So now we 
 
 69 
 
AEROPLANE DESIGN 
 
 can plot out our curve of total resistance, or R x -f 
 R 2 , 4- RD. 
 
 If from these curves of propeller thrust and of 
 total resistance now obtained we see that the re- 
 sistance be less than, or equal to, the thrust at 
 the maximum speed we are asked to accomplish, 
 then this speed is, presumably, attainable. 
 
 JL 
 i 
 
 4 
 
 T 
 to 
 
 13 
 
 120 
 
 60 
 
 ros 
 
 T, (Ibs) 
 
 72 
 
 40 
 
 2* 
 
 18 
 
 17 
 
 Model 
 
 J4_ 
 
 4f 
 
 roil 
 
 JO -4- 
 
 2^7 
 
 233 
 
 271 
 
 3J8 
 
 332- 
 
 'O HO 120 
 
 
 L> 
 
 -^ 
 
 
 
 \^ 
 
 
 su 
 lo 
 
 / 
 
 
 
 
 
 
 \ 
 
 
 
 
 i 
 
 
 
 \ 
 
 70 
 
AEROPLANE DESIGN 
 
 CLIMBING SPEED. 
 
 It remains to find the greatest possible climb- 
 ing speed and see if the final requirement can be 
 fulfilled. 
 
 The vertical height of the thrust curve above 
 the total resistance curve at any point along the 
 base gives us the surplus thrust at the corres- 
 ponding base line value for speed. 
 
 This surplus thrust multiplied by value for 
 speed, gives us a value for foot Ibs. per sec. 
 available for climbing. 
 
 This value we may plot as a final curve of 
 power available for climbing. 
 
 We then take the maximum Value given us 
 by the highest point on our curve), noting the 
 speed at which this optimum value is attained. 
 
 Then our optimum value of power for climb- 
 ing -7- the total weight of machine gives us best 
 climbing rate in feet per sec. 
 
 If this be decently over the requirement we can 
 consider the preliminary design as finished. 
 
 7 1 
 
AEROPLANE DESIGN 
 
 IN CONCLUSION. 
 
 In the first over-all design, methods for arriving 
 at which I have attempted to outline, no pains 
 should be spared to get the best and most compact 
 disposition of external parts, and the best sizes 
 and forms for them. In the structural design, 
 which I have not touched upon, every detail 
 should be considered most carefully to ensure 
 that each is as simple and compact, and, there- 
 fore, as light for its strength as possible, and that 
 for each is chosen the best material. 
 
 If this be done, using with due common sense 
 every source of reliable data, and doing everything 
 methodically and thoroughly, it is highly probable 
 that the results will be good, and if one goes on 
 working thus in subsequent designs, altering up 
 empirical constants as found necessary or advisable 
 from increasing experience, one will design better 
 machines, and will know why they are improved. 
 
 It is because this system of methodical im- 
 provement is, I think, the basis of all true engineer- 
 ing advance, and because little thrashing out of 
 tables and formulae has been done so far (or at any 
 rate published) from the data presently available, 
 that I have tried in this paper to outline some 
 methods for doing so. 
 
 I am painfully aware that much necessary 
 matter has perforce been left out, and that much of 
 what I have said is incorrect, but if it prove of in- 
 terest or instructive, if it help in any way the better- 
 ment of this branch of engineering science, I am 
 amply repaid for what time and effort it has cost me. 
 
 72 
 
PART II 
 
 A SIMPLE EXPLANATION OF INHERENT 
 STABILITY. 
 
 BY W. H. SAYERS. 
 
 THE question of inherent stability is one 
 that has attracted much interest and 
 caused much strife amongst all classes of 
 those interested in aviation. It has been the cause 
 of much activity on the part of transcendental 
 mathematicians to such effect that not only have 
 they in many cases bewildered their readers but 
 they are sometimes under suspicion of having 
 successfully bewildered themselves. It is unfor- 
 tunately also the case that many writers and 
 students dealing with this question in simpler 
 language than that of the mathematician have 
 been led astray by the too apparently obvious. 
 
 The mathematical treatment of such a subject 
 is of great value, but those capable of understand- 
 ing the complex mathematics of others should 
 be able to produce the required results them- 
 selves, provided they have a clear vision of the 
 actual principles involved. Hence a simple straight- 
 forward explanation of the actual known principles 
 by which inherent stability may be attained, 
 should be of value to both the mathematical and 
 the non-mathematical reader. 
 
 73 ' 
 
INHERENT STABILITY 
 
 It may here be as well to warn the reader that 
 in all probability the inventors of various inherent 
 stability machines coming into the classes which 
 will be dealt with later, will deny that they owe 
 their stability to the simple causes herein ex- 
 plained, preferring to ascribe their results to 
 much more complicated phenomena. It is frankly 
 admitted that the action of certain stabilising 
 devices is much complicated by many curious 
 and incompletely understood causes, but the 
 simple explanations herein given account in the 
 main for the general effects produced both 
 qualitatively and quantitatively which corres- 
 ponds with the eating of the pudding. 
 
 74 
 
INHERENT STABILITY 
 
 Before proceeding further it may be as well to 
 rrive at a clear understanding of what stability 
 leally is. We may take as an example the well- 
 i;nown little toy, shown in Fig. i, consisting of a 
 Hemisphere of lead surmounted by a paper cone. 
 Placed in any position it returns, immediately it 
 Is free, to the upright. As a matter of fact, it goes 
 i>ast the vertical position and oscillates slightly 
 |>efore coming to rest. This quality is stability 
 jnd the stability is complete. It is to be noticed 
 jhat this toy, in spite of its stability, requires only 
 j very small disturbing force to move it far from 
 jts original position, but it returns very quickly. 
 ] Consider Fig. 2. This shows a balance arm 
 laving on^it two equal sliding weights. These 
 weights, being at A equi-distant from the centre, 
 nd having their centre of gravity below the point 
 >f support of the balance, the system is in stable 
 quilibrium and betrays the same general charac- 
 eristics as Fig. I. 
 
 I But move the weights out to the positions B. 
 Oie system still remains stable, but it will be 
 ound that a much larger force must be applied 
 o the arm to produce a similar disturbance 
 bviously since to move the arm through the same 
 ngle the weights have to be moved through a 
 much greater distance. Not only this. After the 
 emoval of the disturbing force the return to 
 jiormal position will be much more sluggish, and 
 !or small disturbances the system will be steadier, 
 jhough not more stable. This is a point of con- 
 iderable importance. An aeroplane having its 
 teavy parts distributed over a considerable space 
 
 75 
 
INHERENT STABILITY 
 
 will, in the same way, be slower to answer to ai; 
 disturbances, and will require more to stop he: 
 movements when once started, but, owing partb 
 to the relative slowness of her movements, anc 
 partly to that slowness giving the pilot oppor 
 tunity to use his controls, will appear steadie 
 than a machine, otherwise similar, having all it 
 large weights closely concentrated, and wil 
 generally be credited usually unfairly witl 
 greater stability than the livelier machine. 
 
 Now the aeroplane depends entirely on th 
 maintenance of its correct flight speed for support 
 and, therefore, inherent stability implies that th 
 machine possessing it shall always tend to increas 
 its speed, if the speed is accidentally reduced 
 This quality can only be secured by the action o 
 gravity, and acceleration in the line of flight du 
 to gravity can only be obtained at the expense o 
 a downward acceleration. 
 
 Now it is obvious that this accompanying down 
 ward acceleration, or rather the motion due to it 
 should be as small as possible, as involuntar 
 downward motion is dangerous if the machine i 
 low. Also, as the ratio between the downwan 
 acceleration and the corresponding horizonto 
 one is the angle of descent with the motor stopped 
 or the gliding angle as it is usually called, it is 
 matter of importance, even when the machine i 
 high, as effecting the choice of landing positions 
 Hence the importance of securing, as far as pos 
 sible, that stabilising arrangements do not interfer 
 with the efficiency of the machine. 
 
 Theoretically, any machine which possesse 
 
INHERENT STABILITY 
 
 he fundamental property of diving when it has 
 
 ost its normal support from any cause is inher- 
 
 ntly stable, provided it is properly balanced fore 
 
 nd aft, for suppose such a machine to turn over 
 
 ill its wings are vertical. It will proceed to dive 
 
 11 it attains a vertical speed equal to its flying 
 
 speed and will then flatten out and proceed on a 
 
 ourse at right angles to the original. Which is to 
 
 ay that longitudinal stability alone will eventually 
 
 ring a machine back from even a lateral disturb- 
 
 nee but it will require a considerable amount of 
 
 oom in which to do so, as some, at any rate, of 
 
 le forward velocity possessed by the machine at 
 
 le moment of disturbance is wasted, owing to 
 
 ic change of course necessary, which in itself is a 
 
 urther objectionable feature. 
 
 Practically, therefore, it is desirable to correct 
 iteral disturbances independently of longitud- 
 lal ones, and in addition it is well to reduce dis- 
 turbances of all kinds as much as possible, partly 
 n the score of comfort, but mainly to reduce the 
 >pace necessary for recovery. 
 | A very large number, in fact the majority, of 
 ixisting machines probably possess actual inherent 
 lability in the sense that, placed at a sufficient 
 eight in any position, they will, if all the controls 
 re locked in normal flying position, or in many 
 ases left entirely free, eventually assume their 
 ormal position. In most cases, however, a very 
 reat height would be necessary for this re- 
 overy. 
 
 Hence, practically, other qualities than the 
 ; undamental longitudinal stability are necessary, 
 
 77 
 
INHERENT STABILITY 
 
 and it is convenient to consider the question in 
 three divisions : 
 
 I. Longitudinal stability. 
 II. Lateral stability. 
 III. Directional stability. 
 
INHERENT STABILITY 
 
 LONGITUDINAL STABILITY 
 
 This branch of the subject is probably more 
 generally understood than any other, the prin- 
 ciple of the longitudinal V, as it has been termed, 
 having been employed by experimental workers 
 in quite the dark ages. Fig. 3 shows the most 
 common form in which this principle that of 
 setting the leading surface at a greater angle of 
 incidence than those following it is employed 
 in practice. A is the actual lifting surface of the 
 aeroplane, which at its normal angle of incidence 
 X, supports the whole machine, the centre of 
 pressure of A coinciding with the centre of gravity 
 of the aeroplane. B is the stabilising surface or 
 tail, so set as.to produce no lift at the normal angle. 
 Now, suppose the machine to pitch nose upwards 
 through the angle Y. The total lift on A will not 
 increase greatly, as the extra resistance due to the 
 increased angle will slow the machine down. (Note 
 we are assuming at the moment that the machine 
 has just sufficient power for horizontal flight). 
 The centre of pressure of A wiH move forward, 
 which will tend still further to increase the pitch- 
 ing, but the tail surface B, instead of having no 
 angle of attack and no lift, has an angle Y and a 
 consequent lift, tending to swing the tail upwards, 
 and restore the normal position. 
 
 Or, to look at the matter in another way, suppose 
 a machine, having two surfaces in tandem with 
 the weights so distributed that one surface is much 
 more heavily loaded than the other, to be in still 
 air and with no forward velocity. Obviously it will 
 
 79 
 
INHERENT STABILITY 
 
 drop, and equally obviously the more heavily 
 loaded surface will drop faster. If this more heavily 
 loaded surface is the front one, the machine takes 
 up a diving position and picks up speed, and con- 
 sequently begins to lift. Any arrangement of 
 planes in which the leading plane, or even the 
 leading part of a plane, has a greater angle of in- 
 cidence than that which follows, shows this 
 tendency i.e., a plane with a double camber 
 the leading part cambered normally and the trail- 
 ing part cambered in the reverse way, may be in 
 
 80 
 
INHERENT STABILITY 
 
 itself stable, and Fig. 4 shows, by the little shaded 
 sections, how a swept-back wing with a negative 
 tip provides in itself the longitudinal V. This 
 method of securing longitudinal stability is in 
 practically universal use, and actually produces 
 the desired result. 
 
 It is obvious that if a machine in flight meets 
 an end-on gust its air speed is momentarily in- 
 creased and that it will rise till its speed is re- 
 duced, and conversely as the gust dies away that 
 the air speed falls and that the machine must dive 
 to recover speed. These disturbances are essential 
 to the stability, but their actual magnitude may 
 be diminished by improvement of the gliding 
 angle. 
 
 But an end-on gust may produce other disturb- 
 ances. If the centre of head resistance is above 
 the centre of gravity of the machine, during the 
 growth of the gust there will be a tendency to 
 throw up the nose, and during its dying away 
 to dip the nose tending to exaggerate the move- 
 ments which are due to the stabilising force. 
 If, on the contrary, the centre of head resistance 
 is below the centre of gravity, the forces will have 
 the opposite tendencies, and will oppose the 
 stabilising forces. The latter condition is obviously 
 dangerous and the first is at least objectionable. 
 Therefore it is necessary that the centre of total 
 head resistance of the machine should be as nearly 
 as possible in the same horizontal line as the 
 centre of gravity, in order that the greatest stabil- 
 ising effect should be combined with the least 
 disturbance. 
 
 81 
 
INHERENT STABILITY 
 
 LATERAL STABILITY 
 
 Pure inherent lateral stability, i.e., that form of 
 stability which ensures that, while the flight 
 speed of the machine is sustained, it shall always 
 return to an even keel on the removal of the 
 disturbing force, is quite simply attainable. 
 
 In Fig. 5 the dotted lines show a pair of planes 
 with a dihedral in a normal position, the full lines 
 show the same planes tilted laterally. As the two 
 vertical lines show, in the tilted position there is 
 a greater resistance to downward motion on the 
 low side than on the high, hence the high side will 
 drop relatively to the low, till the normal position 
 is regained. Provided that the centre of gravity 
 is not too high, there will always be a restoring 
 force with this arrangement. 
 
 Fig. 6 may be of some interest in this connec- 
 tion. Here P! and P 2 are the resultant pressures 
 on each half of the wings at right angles to the 
 planes. When the wings are tilted downwards to 
 the left, say, the vertical effect of P l and P 2 will 
 be slightly displaced towards the left, as shown 
 at L, acting through CL (the centre of lift), and 
 the vertical line through CL will intersect a central 
 plane about which the machine is symmetrical 
 and on which the centre of gravity must lie at 
 some point above the centre of lift, as MC. As 
 long as MC is above the centre of gravity the 
 machine is stable laterally and MC is equivalent 
 to the " metacentre " of a ship, the vertical dis- 
 tance between MC and CG being the equivalent 
 of metacentric height. The conditions to be 
 
 82 
 
INHERENT STABILITY 
 
 satisfied to provide simple lateral stability are 
 practically the same in the two cases, and in the 
 aeroplane the provision of a sufficiently low CG 
 satisfies them, even without the dihedral. Un- 
 fortunately, owing to the large value of the dis- 
 turbing forces (gust effects, etc.), compared with 
 the supporting forces, which are also the righting 
 forces, and to the fact that a large disturbance 
 will greatly diminish these supporting and right- 
 ing forces, we have to consider methods of re- 
 ducing disturbances in order that recovery may 
 become quick and may be completed before 
 striking the earth. 
 
 Now a machine is disturbed laterally because 
 one side gains lift, or the other loses it, the side 
 having the excess of lift rising, that having the 
 deficit falling. In a wing of rectangular plan form 
 that is with uniform chord if the pressure per 
 square foot is uniform it is fairly obvious that the 
 total pressure acts as though it were a single force 
 at the centre of the wing, i.e., the centre of pressure 
 of each wing is half-way along the span. 
 
 Fig. 7 shows a wing of triangular plan form, 
 tapering to a point. If such a wing is acted on by 
 a uniform pressure per square foot it will be seen 
 that the total pressure on any strip, say, i ft. wide, 
 will be proportional to the fore and aft length of 
 that strip, and that the pressure on longitudinal 
 strips will be proportional to the length of the 
 arrow under that strip (in the lower part of Fig. 7). 
 Hence the total resultant force will be as the large 
 arrow (R) acting closer to the body than halfway. 
 Also if one wing receives an excess pressure which 
 
 83 
 
INHERENT STABILITY 
 
 
 
 IN 
 
 1! 
 
 lin 
 
 T T 
 
 - f ' 
 
 
 t-7. 
 
 
 
 M 
 
 
 
 is uniform per square foot the resultant of that 
 excess will act as closer to the body, and from the 
 well-known principle of the lever, will produce a 
 smaller effect on the machine. 
 
 Now, obviously, any less degree of taper will 
 produce a similar, though less, effect, and so also 
 will reduction in the camber and angle of inci- 
 dence (" wash out ") from the body to the tip, 
 for any pressure due to air moving past the wings 
 with a velocity in the line of flight. That is, a 
 [< wash out " would not make any difference to 
 the effect of purely vertical gusts, if such things 
 could exist. 
 
 Now, consider a wing, tapered or washed out 
 so as to bring the Centre of Pressure close to the 
 
INHERENT STABILITY 
 
 body side, but provided with an extension set at 
 a negative angle. This extension produces a down- 
 ward pressure, which diminishes the total pressure 
 on the wings, but also moves the point of appli- 
 cation, or centre of, total pressure closer still to 
 the body, and since this negative pressure is acting 
 much further out (at a larger radius) the centre 
 of total pressure may be caused to pass beyond 
 the base of the plane without completely neutral- 
 ising the lift. 
 
 If we can thus cause the centre of total pressure 
 of such a wing to lie on the centre line of the 
 machine (and this is possible in theory at any 
 
 85 
 
INHERENT STABILITY 
 
 rate), then one wing will maintain the machine in 
 balance laterally, the other side being absent. If 
 this condition is attained, then as long as each 
 separate wing is in uniform air, however different 
 may be the conditions around each wing, no force 
 tending to overturn the machine sideways exists. 
 This condition does not occur, of course. But 
 Fig. 8 shows an aeroplane in a side gust. Since 
 the machine has a forward movement, the actual 
 movement of the air during the gust must be 
 diagonal, and, as the diagram shows, one wing is 
 practically unshielded, i.e., if the gust is uniform 
 that wing is subject to uniform conditions, and 
 on this wing the whole compensating effects of 
 negative tips would take effect, leading to at least 
 a considerable reduction in the disturbance. The 
 far wing is partly and unequally shielded, the 
 tips receiving the least shelter. The dotted lines 
 show that sweeping back the tips places the far 
 side wing in more nearly uniform shelter. The 
 figure is, of course, diagrammatic only, and 
 should not be taken as representing that a large 
 portion of the far wing is completely shielded 
 were this the case the problem would be, indeed, 
 hopeless. In fact, with swept-back wings and 
 properly proportioned negative tips the uncor- 
 rected disturbances due to uneven shielding are 
 quite small. 
 
 86 
 
INHERENT STABILITY 
 
 VERTICAL FINS. 
 
 If the wings form a dihedral angle, then in 
 addition to the extra lift caused by a side gust on 
 the near or unshielded wing, there is a tendency 
 to lift the near side and depress the far side, due 
 to the fact that at right angles to the line of flight 
 the near wing has a positive, and the far a negative, 
 angle of incidence. 
 
 This may be compensated for by enlarging the 
 negative tip surface, or by providing a vertical fin 
 below the centre of gravity, which will produce 
 an opposite tendency when struck by the gust. 
 This fin may be made sufficiently large to over- 
 come the extra lift on the unshielded wing in 
 addition, when the negative wing tips may be 
 dispensed with as was proposed in the Ding- 
 Sayers monoplane. 
 
 It may be noted that vertical fins above the 
 centre of gravity have frequently been proposed, 
 the theory being that, on a machine tilting side- 
 ways there would be a tendency to slide towards 
 the low side, and that the consequent air pressure 
 on the fin would push the machine straight. It is 
 obvious that this fin would be acted on by side 
 gusts and tend to increase the disturbance due to 
 them. It is, in fact, equivalent in most ways to a 
 simple dihedral angle, but inferior in the degree 
 of stabilitv obtainable. 
 
INHERENT STABILITY 
 
 DIRECTIONAL STABILITY 
 
 It is obviously desirable that an aeroplane shall 
 not be liable to be deflected from its course by 
 any disturbance. Now a purely end-on gust, if 
 uniform, will not have any tendency to throw the 
 machine off its course, no matter what its force. 
 In the case of a side gust the unshielded wing will 
 have an increased resistance as compared with 
 the shielded wing. But more important than this 
 is the effect of such a gust on the body, or any 
 other side surface, such as fins or side faces of a 
 wing at a dihedral angle. 
 
 To secure that no turning tendency shall be 
 produced it is necessary that the lines of action of 
 the total resultant side pressure shall act through 
 the centre of gravity of the machine. Then the 
 only effect on the machine will be bodily motion 
 sideways without any turning effect. Unfortu- 
 nately, the centre of side pressure varies in position 
 with changes in the direction and the strength of 
 the gust ; so complete balance under all con- 
 ditions is impossible. 
 
 Now if the centre of side pressure is forward of 
 the CG, the nose of the machine will turn with 
 the gust, and the machine will turn down wind, 
 which will momentarily reduce its air speed. If, 
 on the contrary, it is behind the CG, the tendency 
 is to turn up wind and increase the air speed. 
 The first case is dangerous the latter safe, there- 
 fore it is desirable to keep to such an arrangement 
 of vertical surfaces as will always keep the centre 
 of side pressure aft of the CG. 
 
INHERENT STABILITY 
 
 But the most important aspect of this question 
 arises when the machine is turning under the 
 action of the rudder. Fig. 9 shows this case. The 
 rudder of the machine is turned to the left, and a 
 pressure (R) acts on the rudder, tending to swing 
 the tail of the machine to the right. Momentarily 
 the machine moves through the air crab wise, 
 which produces a side pressure (SP) on the right- 
 hand side. Under these two pressures the machine 
 commences to turn in the curved path shown. As 
 soon as the machine starts, actual turning, a third 
 force centrifugal force (CF) commences to act 
 through the CG of the machine, and towards the 
 outside of the curve. 
 
INHERENT STABILITY 
 
 Now, if the side pressure SP acts behind the 
 centrifugal force i.e., behind the CG it will be 
 seen that centrifugal force opposes the turning, 
 and when the rate of turning has reached a certain 
 value the three forces are in balance and the 
 machine will continue turning steadily. If the 
 rudder is now put back into neutral, R disappears 
 and CF and SP tend to take the machine off the 
 turn, and both of them disappear as soon as the 
 machine has stopped turning. 
 
 But suppose SP to act in front of the CG, as at 
 the dotted arrow. Then CF and SP themselves 
 provide a tendency to turn to the left, added to 
 the tendency due to the rudder, and instead of 
 reaching a steady state of turning the machine 
 will turn faster and faster. Even when the rudder 
 is put back to neutral, SP and CF still keep 
 increasing the rate of turning. As a matter of fact, 
 as the rate of turning increases SP tends to move 
 further forward, and to increase, hence a machine 
 may start to turn with SP behind the CG, and as 
 the rate of turning increases, SP may move 
 forward till it is in front of the CG, and may 
 eventually become so large and so far forward 
 that even with the rudder hard over in the opposite 
 direction the turning continues. 
 
 This is the explanation of the spiral nose dive 
 effect. The theory of the elevator acting as rudder 
 when the machine has a large bank does not ex- 
 plain the phenomenon, as unless there are at least 
 two forces acting independently of the pressure 
 on the control surfaces the machine will cease to 
 turn when all controls are placed in the neutral 
 
 90 
 
INHERENT STABILITY 
 
 position. The late Lieut. Parke's experience at 
 Salisbury in 1912 proved that this is not the case. 
 
 Now it is obvious that if a machine slips side- 
 ways say, is stalled, rolls over to one side and 
 slides downwards that a side pressure similar 
 to SP will be produced. Also the inertia of the 
 machine will produce the equivalent of CF, or 
 rather will produce CF, as centrifugal force is 
 only an inertia effect, and the turning effect due 
 to these forces appears. Hence the spiral may 
 occur without any use of the rudder at all. If the 
 direction of a machine is changed, extra power 
 has to be supplied, to give it air speed in its new 
 path, and if the turn is so rapid that the engine 
 margin of power is not sufficient for this purpose 
 this extra work must be done by gravity the 
 machine must dive, and the faster the turn the 
 steeper the dive, until when the turning rate is 
 such that a force equal to the whole weight of the 
 machine is required to provide the air speed the 
 machine will descend vertically. Therefore this 
 increasing turning effect produces that most deadly 
 of all aeroplane accidents the spiral nose dive. 
 
 The side pressure here evidently includes that 
 due to all possible causes as pressures on the body, 
 on any vertical fins, or on upturned sides of wings. 
 There will obviously be a side pressure on wings 
 with a dihedral when turning, or on flat wings 
 when banked, and this side pressure may be very 
 large, and is bound to act not far from the centre 
 of gravity, owing to the position of the wings. 
 Hence, as far as possible, this side pressure must 
 be kept small. Obviously, the wings themselves 
 
 9 1 
 
INHERENT STABILITY 
 
 cannot be reduced, but swept -back wings with 
 negative tips must always have their centre of side 
 pressure farther back relatively to their centre of 
 lift than normal wings. Also the negative tips tend 
 to reduce banking on turns to within reasonable 
 limits, reducing thereby the side area due to wings 
 on which such pressure acts. 
 
 Fins beneath the centre of gravity, when acted 
 on by the side pressure, oppose banking with the 
 same desirable effect, and may obviously be so 
 arranged as to have their own centre of side pres- 
 sure as far aft as may be desired, thus securing 
 this essential form of stability. 
 
 With fins above the CG the tendency, on the 
 contrary is to increase banking on turns, or to 
 increase the tilt due to a side gust, and therefore 
 to increase the total value of side pressure possible, 
 and particularly the most dangerous component 
 that on tilted wings and are hence objection- 
 able and even dangerous, as tending to produce 
 the very catastrophe for which they have been 
 proposed as a remedy, unless made extremely 
 large and placed very far back. 
 
 At the time at which the preceding statements 
 on spiral instability were written nothing had 
 been published on this subject (so far as is known 
 to the writer), with the exception of certain para- 
 
 fraphs in " Aerodonetics " (Lanchester, " Aerial 
 light, 5 ' Vol. z) ; but in the meantime, Mr. Bair* 
 stow has dealt with the matter in his lecture before 
 the Aeronautical Society (January 2ist, " The 
 Stability of Aeroplanes "). Both Mr. Lanchester 
 and Mr. Bairsto'w' claim that the cure for directional 
 
 92 
 
INHERENT STABILITY 
 
 93 
 
INHERENT STABILITY 
 
 instability lies in a forward centre of side pressure, 
 and apparently prove their assertions by experi- 
 ments with models, thus definitely contradicting 
 the writer's conclusions. It may be as well, there- 
 fore , to go into this question a little more completely. 
 
 In Fig. 10, 1 is a replica of Fig. 9, except that it 
 shows how the centre line of the machine deviates 
 from the tangent to its circular path, which is the 
 momentary line of flight i.e., that it " crabs " 
 slightly, thereby producing the side pressure, SP. 
 II shows the case of the machine with the forward 
 centre of side pressure. In this case, as soon as 
 the rudder is put slightly over, " crabbing " com- 
 mences, and the forward side pressure swings the 
 machine still further askew until the angle be- 
 tween AB (the momentary line of flight) and the 
 centre line of the machine is greater than that 
 between the centre line of the machine and of the 
 rudder. The force on the rudder then becomes 
 reversed and acts from the outside, so that we 
 again have SP and R acting in opposition, though 
 their respective roles are reversed. The machine, 
 as long as the rudder is held in such a position, 
 will turn steadily at a definite radius, with the 
 rudder checking the tendency to spin. 
 
 Now in a model aeroplane the rudder is actually 
 a fixed surface, hence this arrangement apparently 
 gives the required stability. But in any actual 
 aeroplane it is not fixed, and may be put into a 
 position of no resistance to turning, and will take 
 that position itself if a rudder wire breaks or the 
 pilot's foot slips from the bar, when the machine 
 becomes completely unstable and spirals violently. 
 
 94 
 
INHERENT STABILITY 
 
 AN IMPORTANT OVERSIGHT. 
 
 A rudder is not a fixed surface and must not be 
 counted on as such in a full-sized machine 
 although it usually is, and acts as such, in a model. 
 
 It may be remembered that Mr. Bairstow re- 
 ferred to marked lateral oscillations in his " stable" 
 models. What happens in this case is that the 
 model, on tilting sideways, slides down slightly 
 and produces the side pressure SP, which tends 
 to spiral it to the other side. This tendency is 
 checked by the damping of the very large fins and 
 by the reversed rudder action but with a free 
 rudder this model would spiral and nose-dive 
 towards the (original) high side after each lateral 
 disturbance ; while the machine with the side 
 area aft merely dives and swings towards the low 
 side without any tendency to spiral continuously. 
 
 Mr. Bairstow's " unstable " model produced 
 by removing the front fin was in the condition 
 already referred to in which the centre of side 
 pressure is at the commencement of a turn behind 
 the CG, but moves forward as the turn progresses. 
 This change over is extremely dangerous much 
 more so than the really unstable condition, with 
 the permanently forward centre of side pressure, 
 as this latter, on account of the permanent nega- 
 tive pressure on the rudder-bar, gives the pilot a 
 continual warning that the machine is trying to 
 spin, while the change over is sudden and dis- 
 concerting. 
 
 95 
 
INHERENT STABILITY 
 
 A WARNING AGAINST ASSUMPTIONS. 
 
 From the foregoing it would appear as if in 
 order to secure complete immunity from direct- 
 ional instability, it is only necessary to supply an 
 ample rear fin, and that it is desirable to reduce 
 the dihedral style to as small a value as is consonant 
 with the requirements of pure lateral stability so 
 as to avoid undue banking. 
 
 Unfortunately the case is somewhat more com- 
 plex. In order to be able to turn without excessive 
 : ' crabbing," or skidding sideways, it is necessary 
 that the side pressure at a small rate of movement 
 sideways shall balance the rudder force and centri- 
 fugal force. 
 
 Now if the centre of side pressure is very close 
 to the centre of gravity, and the side pressure is 
 nearly equal to the centrifugal force in magnitude, 
 there will only be required a quite small rudder 
 force to provide the required state of balance. 
 But if the centre of side pressure be very far aft 
 of the centre of gravity the rudder force required 
 to produce a state of balance will be greatly in- 
 creased. That is to say that the pilot will have to 
 make greater muscular efforts to steer the machine 
 and the machine will also respond less rapidly and 
 easily to the rudder. 
 
 Also, since centrifugal force increases as the 
 radius of turning decreases, it is necessary that on 
 sharp turns both the side pressure and the rudder 
 force should increase. The rudder force will in- 
 crease with the increase of the angle to which the 
 rudder is put over, but to increase the side pressure 
 
INHERENT STABILITY 
 
 either the rate of motion sideways, or the side 
 area, must increase. As it is desirable to keep the 
 sideways motion as small as possible it is neces- 
 sary to increase the actual side area, and that can 
 only be done by increased banking, thus making 
 the inclined faces of the wings effective for this 
 purpose. 
 
 For these two reasons a machine which shall be 
 easily steered can only be made by approaching 
 very closely to the condition in which the centre 
 of side pressure corresponds with the centre of 
 gravity and the margin between this condition and 
 one of instability is very narrow. 
 
INHERENT STABILITY 
 
 EXPERIMENTS NEEDED 
 
 In this connection it may be remarked that a 
 series of experiments are desirable on the be- 
 haviour of bodies of the form used as aeroplane 
 fuselages or nacelles, and of flat surfaces moving 
 in a curved path and at a slight angle to that path. 
 
 Very little is known on this subject, but there 
 is much evidence showing that differences in 
 body form may completely alter the behaviour 
 of a machine in this respect, and one might hazard 
 a guess that in Fig. n the centre of side pressure 
 of A would occupy a considerably more forward 
 position than that of B when acted on by a wind 
 as indicated by the arrows, and that a machine 
 with a fuselage or nacelle entry such as A might 
 be unstable, whereas an otherwise identical 
 machine with a body entry such as B might be 
 stable. 
 
 C 
 
 98 
 
INHERENT STABILITY 
 
 STABILITY IN VARIOUS TYPES. 
 
 Having now, if not briefly, at least rather 
 hastily, considered the question of inherent 
 stability in all its more important aspects, we will 
 consider one or two types of machine in order to 
 notice to what extent the various desirable features 
 may be combined, and what disadvantages from 
 other points of view sxich combinations may have. 
 
 1. Machines with planes at right angles to the 
 line of flight, with tapered and or " washed out fl 
 planes. Appreciable reduction in the disturbance 
 due to side gusts. Combined with the longitudinal 
 V, and a proper vertical position of the CG, both 
 longitudinal or lateral stability may be obtained, 
 with a fair degree of steadiness. With a correct 
 disposition of side surfaces ensuring that the centre 
 of side pressure is always aft of the centre of 
 gravity, immunity from the uncontrollable spiral 
 nose dive is secured. 
 
 2. Machines as above with negative wing tips. 
 Partial or complete neutralisation of disturbing 
 forces due to side gusts, reduction of tendency to 
 overbanking on turns, leading to further reduction 
 of risk of spiral nose dives. In combination with 
 the longitudinal V, correct position of CG, etc., 
 has the same good qualities as No. i, with an en- 
 hanced degree of lateral steadiness and immunity 
 from spiral dives. 
 
 In both the above forms the tendency is rather 
 to increase the sensitiveness of the machine to the 
 warp while longitudinal controls are normal, 
 
 3. Machines having negative tips and swept-back 
 
 99 
 
INHERENT STABILITY 
 
 wings. These give the same lateral steadiness 
 as the above, a greater and possibly a complete 
 immunity from side slip, owing to the centre of 
 side pressures on such wings being aft of the 
 centre of normal pressure, and have in the plane 
 themselves a longitudinal V which can be made to 
 provide longitudinal stability. As with previous 
 classes, lateral controls are, if anything, unusually 
 sensitive. 
 
 If, like the Dunne, the planes are relied on for 
 longitudinal stability, and tail planes and booms 
 are not used, they may be more sensitive to 
 elevator control than normal machines, owing to 
 the better concentration of weights. 
 
 As with the other forms, the stability due to 
 the wings themselves may be supplemented by 
 any of the other methods of stabilising already 
 considered. In practice, machines of this type 
 show themselves to be safe, steady and sensitive 
 to control. It must be noted that all machines 
 with negative tips must lose in efficiency some- 
 where, as the head resistance of the part of the 
 wing beyond the non-lifting line not only is 
 accompanied by no lift, but by an actual negative 
 lift. Actually owing to several causes one being 
 the large value of dead resistance, i.e., body, 
 chassis, etc. this loss in efficiency is not pro- 
 hibitive, some machines with negative tips having 
 better gliding angles than some not so provided. 
 
 4. Machines in which a dihedral angle and a 
 low centre of gravity are relied on for lateral 
 stability. In this case disturbance due to lateral 
 gusts is great ; also, when turning a corner, there 
 
 100 
 
INHERENT STABILITY .-, 
 
 is a tendency to overbank, owing to centrifugal 
 force acting below the centre of side pressure, 
 hence risk of side slip. By the adoption of vertical 
 fins below the centre of gravity both these dis- 
 advantages are overcome. By suitable proportion- 
 ing of the fin, i.e., by keeping its centre of side 
 pressure back far, immunity from spiral diving 
 can be obtained. This arrangement can, of course, 
 be combined with the longitudinal V, giving, as 
 far as can be predicted, as good results as any 
 combination yet tried. In this case no interference 
 with the elevator controls occurs. With the fins 
 some damping of the warp and rudder controls 
 is inevitable owing to the large fins necessary. 
 This damping, however, could not be greater 
 than about one-tenth of the damping due to other 
 essential parts of the machine, which in practice 
 would be inappreciable. No example of this type 
 has been completed, but the behaviour of certain 
 deep-bodied monoplanes, notably the R.E.P. and 
 Clement-Bayard, tend to confirm the value of 
 this method. 
 
 There are doubtless other forms of machine 
 claiming inherent stability, but little or nothing 
 is known as to their performance or of the ideas 
 which have prompted their designers. 
 
 It will be noted that the question of the con- 
 trollability of the various types of stable machines 
 has been referred to, and that very little dis- 
 advantage as compared with normal machines 
 has been admitted. It is assumed that the machine 
 has been arranged to be stable with all controls 
 in the normal condition* and it can be easily seen 
 
 101 
 
INHERENT STABILITY 
 
 that if sufficiently powerful controls are fitted 
 the inherent stability may be largely or com- 
 pletely destroyed. 
 
 For instance, if a sufficiently powerful rudder 
 is held hard over, any machine must spiral and 
 nose dive. But, except in the case of a jammed 
 control, this does not matter, as the pilot can at 
 once stop the effect, by leaving the rudder free, 
 provided the machine has the proper disposition 
 of side surfaces. Therefore the pilot can use his 
 controls to any extent in an emergency, at the 
 expense, of course, of a dive, with the certainty 
 that after the removal of the control force the 
 machine will return to the normal conditions. 
 This is not true of an unstable machine as 
 shown in the section on spiral dives. A large 
 amount of the prejudice on this head arises from 
 the confusion already pointed out between the 
 slow movements of the machine whose weights 
 are widely distributed, and the lively motion of 
 the one in which they are concentrated. The first 
 are usually credited with a large amount of 
 stability by those who see them in flight. They 
 are inevitably slow in answering their controls, 
 hence the myth that a stable machine does not 
 answer well to controls. Actually this quality 
 from which the steadiness arises is adverse to 
 stability and the objection is groundless. 
 
 lot 
 
THIS BOOK IS DUE ON THE LAST 
 
 RETURN CIRCULATION DEPARTMENT 
 
 202 Main Library 642-340 
 
 LOAN PERIOD T 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 LIBRARY USE 
 
 This book is due before closing time on the last date stamped below 
 
 DUE AS STAMPED BELOW 
 
 .; 
 
 fti. Uw 
 
 8 '80 
 
 --' -o? 
 
 APR 8 J9IO 
 
 SENT ON ILL 
 
 MAR 8 1995 
 
 U. C. BERKELE 
 
 UNIVERSITY OF CALIFOr 
 
 FORM NO. DD6A, 20m, 1 1 778 BERKELEY, CA 
 
YB 16060 
 
 -Mi -. 
 
 TU7/ 
 
 UNIVERSITY OF CALIFORNIA LIBRARY