Full report

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3RIIF REVIIW OF TU USOl.ts OBTAIUD 1N TU nft~~ LIM At:APLARS - l. , JIODDlf TBIORETXOJl, ABRODYNAJaOS AS j.pPLI• .,. LIGHT AIRPLUE DISJU- 11« Reprinted from "The Slipstream Kotlthly, It D~ce1l;1'be:r, 1924, and January, 1925. REPROOUCED BY NATIONAL TECHNICAL INFORMATION SERVICE u. S. OEPARTMENT OF COMMERCE SPRINGFIELD, VA. 22161 April. 1925.

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NOT ICE THIS J;>OCUMENT HAS BEEN REPRODUCED FROM THE BEST COpy FURNISHED US BY THE SPONSORING .t AGENCY. ALTHOUGH IT IS RECOGNIZED THAT CER- I TAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RE- LEASED IN THE INTEREST OF MAKING AVAILABLE AS MUCH INFORMATION AS POSSIBLE. , ,i i'

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.. :ATIOi:A1 Al) TISOR CO:.0ITTEE FOR AERO AUT I CS . TEE ':' A I R P L A _ E . L I G H :aRIEF vIZW OF TEE R3:S LTS OBTAI:!ED IT T5E Dr;VEOP lE:JT OF L I GET AJ:RPLA::ZS. PAm I. In every country interested in aeronautical development there is no question tl:.a.t is attracting more attention today than hat of the small lig:lt c.irplane . It seems to be of great interest to nearly everyone , whether connected directl Y vii th aviation or not . Some wri ters have very great hopes . Others rese r ve their opinions , while some view tLe li ght airulane as an interesting but impraaticel toy . Tnether or not the enthusiasts are cor- • r roct it is the "",)elief of a. great many that these li ttle airplanes, if roperly developed, can o nothing but good in furthering the use ar science of aviation . Such men as 1r . OrvL.lc Wrie;ht , Brig . General !Vm . Mitchell , and ,for . C. F . Kettering lave publicly stated that in their opinion the light airplanes were the rr:ost int"e.resting and important a.eronautical developnent sllCvm during the l'ecent 2.ir Races held at Da:iton. The little airplanes also seem to have captivated the mind • of te general public . The press has broadcasted articles describing the II Aerial Flivel's , II and suggesting the wonderful experience in store for all in te development of a cheap little * Reprinted. frotl liThe Slipstr eam lJo thly , II December , 1924, and January , 1925 •

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.. II, L. c. A. Techni cal Memorandum No 0 3il 2 • ai rplane using but a gallon of fuel to fly forty miles. However these popular conceptions may work out, the feeling seems to pervade the aeronautical profession that the light airplne may be the ent ering wedge, as it were, to commercial aviation. Due to their small size and relatively low horsepower light airplanes can be produced, even in small quantities, at a cost comparable to that of some of the snller motor cars. The uses to which these airplanes can be put are naturally somewhat limited, Those limits, however, are ~nly those imposed by the small size and_ lack of overloading capacity_ As far as general control ~, ability, and performance under design load is concerned a light I si.ngle seater can be constructed with a 22 horsepower engine that-will equal if not surpass the performance of several airplanes used commercially tOday. , The same degree of comfort and , safety in bad air way also be accomplished. The records of British and American races seem to show that forced landings with this type are much less,dangerous either to ITan or machine, than with the larger and heavier 'airplanes_ Very great maneuverabilityand sturdiness of construction may somewhat explain this intll eresting fact. In liThe Aeroplane of November 19, 1924, the views of an experienced pilot are given, in which he states that he would rather fly cross country in a light airplane than in a faster, pigh-powered airplane, because he has no fear of flying low. Traveling by airplane becomes very monotonous if done at 4000 to 6000 feet. Low flying on the other hand is very inter-

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~ .. N.A.O.A. Technicai Memorandum Nd~ 311 3 esting when the traveler may watch everything going on around himo 'i":lis man feels tl3.t low flying with a light airplane is perfectly safe due to its extreme maneuverabili ty and abili ty to be "put down" in small areas of nearly any kind of ground. This thought . is extremely interesting and is probably true except over mountain- .ous country. However the above idea may work out, undoubtedly the light airplane will find great usefulness for sport and for cheap rapid transportation over sections otherise poorly accommodated. There is also the possibility of their use for training. A great ar,lount of money might be diverted to the construction of combat airplanes if such were found feasible by the Government. The British are already trying out this idea. It would seem that the· United States should also experiment with light airplanes. in some part of our training program. Possibly the Air Servic8 Reserve officers might find them very satisfactory for practice during tlieir yearly return for service. We, in the United States, may also follow the lead of the Bri tll:3h in the establishment of Light Airplane clubs among the ex-service pilots and. red-blooded young men of the country. Light airplanes a7e so recent a development in this country, however, that it is very difficult to predict just what the year 1925 may have in store. The experience gained during 1924 may be the foundation for the development during 1925 of types that will meet the needs for training and practice f1ying as well as for sport. c Before proceeding with a technical discussion of the prirtci-

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i~,A.C;,A. Technical MemorandUm No. 311 4 ples of light airplane design, it will be well to review and to • analyze the vlork that has been done in developing thi s type both abroad and in this country. It is unquestionably true that the light airplane idea is an outgrowth of gliding or soaring experiments in Gernny during the last few years. After the war German aircraft activi ties were grea.tly curtailed by the condit ionq ofthe Peace Treaty. Desiring to keep p interest in aviation and to provide practice for their trained pilots the Germans offered substantial prizes for soaring flights under' various specifications. After a period spent in gaining tht"? experience necessary for the flying of these crafts flights were rmde that astona ished the world as a wholeo It is/very significant fact that in nearly every case the most successfl gliders were designed by men of some techni.cal experience and who were thoroughly .familiar with the modern theories of hydrodynamics as applied to aeronautics by Doctors Prandtl, Betz, Munk and others of Ggttinge~ University. Although the rmjori.ty of these machines were built by trade school students under the supervision of their professors, the clear understandi.ng of the abO'lTe aerodynamical principles was plainly in evidence. The application of Dr. Prandtl's theorems enabled the glider constructor to design directly for the required performance. In other words, they had been supplied • with a formula by which they might solve directly for the size and shape of their machines knowing the results to be attained. • Mr. Geo. H. Madelung has given an illustration of such proc~dure

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.. 1:J. A. C. A. 'I'echnical MemorandUm No. 311 5 by describing the design of the Hannover Sailplane in the S, A. E. Journal of January, 1933. It 'is therefore very logical that Dr. Prandtl's theories shall be ela.borated upon to a considerable extent further along in these articles. Naturally after the publication of German records the French and English were desirous of trying their hands. Consequently, the year 1922 saw some very fine flights in those countries. A group of students from the Massachusetts Institute of Technology constructed a glider for entry in one of the French competitions. This was probably the first serious American attempt at soaring since the Wright's experiments at Kitty Hawk, The greatest result of these trials was not that fine records were obtained but that they gave birth to the light airplane idea. The Europeans thought that if they could make such wonderful flights relying solely upon the wind for the power of suste:i.1tation, by installing a small auxiliary engine they might solve the problem of cheap and practical aviation. Consequently, at the Lympne competi tion in England during the fall of 1923, and at various French trials somewhat earlier we have the adjent of the so-called light airplane. Viewed in the light of our yowledge a few years ago the 1923 single seater light airplane was a revelation. Although nearly every meet was marred by incessant engine trouble ,. the results obtained exceeded the wildest expectations. The French very quickly developed small engines for their craft but the English were forced to rely upon standard motorcycle en- • gines, which proved hardly suitable for full power airplane serv-

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• No~ 311 6 N.A.C.A. Technical Memorandum ice. The displacement of the engines in the tympne competi tion .. was limited to 750 cm3 (45.8' eu.in.). Possibly the- trouble ex.:... perienced by the Bi:tish may nave been due to the fact that they " TIere trying to take too much power out of the displacement allowed. It does not appear that the size of an engine is a particularly good indication of its suitability for an airplane. If the power output of the engine could have been limited in some way, to say 16 HP., the designers might have had considerable more latitude in their choice of power plant. A slower, larger displacement engine would have worked a natural handicap by increasing the weght but would probably have kept the airplanes in the air for longer periods. Whatever the outcome of the engine problem may . ' be the use by the English of the small displacement engine has proved one worth while fact regarding the light airplane. Forced landings nay be 1M.d'g much more pafely with these airplanes than with the heavier, more sluggish and faster types. The next step was naturally to the two-seater which made its debut at Lympne in the fall of 1924. Again engine trouble was much in' evidence although motorcycle engines had been replaced' by engines designed especially for the service. The geneal perforr ances were on the whole very satisfactory, when the airplanes were permi tted to fly by their balky engines. The results were such that the conclusion may be drawn that from 30 to 35 HP. is suf~i cient to make a two-seater light airplane equal the performance of some of the standard training airplanes using from two to three times that power. These 1924 competitions further demonstrated

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N.A.C.Ai Technical Memorandum No~ '311 7 -- the safety of these airplanes in forced landings. Out of numerous cases of engine failue away from the airdrome by nearly every airplane, but one suffered any structural darrage. The two-seater competitions "also further sUbstantiate the thought that a larger displacement engine of te same power would have kept the airplanes in the air for much longer periods and have produced a more practical airplane. During ·1922 and 1923 the United states remained inactive in the development of gliders and light airplanes, except for the one case already noted. However, the N.A.A. cane to life in 1924 with light airplane races to be held in conjunction with the Interna tional Ai r Races at Dayton. We as Americans cannot point with a great deal of pride to the results obtained. Although the conditions under which these races were run were in no way conarable to the Lyrttpne competitions, the number of the ai:rplanes was very disappointing as well as the gene:ral quality. Of nine airplanes entered, but" six wer'e on the line for the start.. Or.:.1.y one of these six finished the three races on the program, one other finished tviTO races, and one finished but one -race. The remaining three either never left the ground or were forced out shortly , after the start. The direct drive Henderson four-cylinder motorcycle engine gaye very satisfactory service in Dormoy' s "Flying Bath Tub" and Johnson! s DJ-J. airplanes Although Dormoy was forced dOYffi on his second race by very bumpy air his engine was .- rUTl..ning perf ectly. J"ohnson made three forced landings in pa stures, plowed fields, etco, due to imperfect full flow, but his

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N. A. C. A. Techili"ca1 Memorandum No e " ~li 8 Henderson functioned smoothly in" eV0J:Y race. It is a significant GfG-ct in comr:rtrison \7ith the English sing1c-seateJ: trials that neither of these two engines had any adjustment whatever during the' period of the races. Those designers employing the geared twin cylinder Vee engines, however, were not so fortunate. The vibration in some cases was so excessive that the very light structures were repeatedly broken. Chain crives also contributed their share of trouble. Certain conc1usion$ nayoe dral7ll from the results of the European and Arnerican raceso -- First. For a single-seater, from 18 to 25 horsepower, and for a two-seater, 35 to 40 should be sufficient for practical purposes. Second. The displacement rating of the automobile races should not apply to 2..ircraft. POYler alone si10uld determine the classifications. Th:Lrd." Gearing in any form u:;'11e ss hi.ghly developed is a definite source of trouble. Fourth. The sMOothness of four-cylinder engines is highly desirable. Fifth. Light airplanes as a class possess qualities that make them very safe -in forced landL1gs, '" "and., ':" their sturdiness on poor ground is superior to the larger airplanes. Bixth. Performance characteristics-and r.aneuveraoi1ity equal to if not better than sor,le standard training types have a1-

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lL A. C. A. Techni cal Memorandum No. 311 9 1 ready been obtained. A great deal of general discussion has been offered ort the subject but as yet no attempt has been made to define the term II Light Airplane. II That is a question that is receiving a great deal of attention both abroad and in this country today. Is a light airplane an engined glider? Is it. an under-powered airplane? In the light of what has been accomplished it is neither. Of course, as pointed out previously the original idea was the growth of glider or soaring machine development. In fact, one of the British single-seaters, the IIWrenll, could very truly b called an lI engine-glider,lI as in 1922 the same airplane without engine had been used in the soaring competitions. However, the problems of gliding and flying from place to place are vlidely separated. A glider receives its sustentation from a wind which has a strong upward· component. Such a machine is designed so that its sinking speed will be a mininmm and equal to or less than the rising speed of the wind in which it is flying. This necessitates a very high ratio of lift to drag at a very low speed. The aim in soaring is to stay off the ground as long as possible. Powered flight, on the other hand, has for its purpose the accomplishment o~ useful work, namely, the transportation of a required pay load through the n~ximum distance, in the shortest possible time and at the least cost. This is a problem of range .. of flight rather than of duration, as in the case of the glider • Winds cannot be depended upon for assistance as it may be neces-

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.. 1'1. A. C. A•. Technical Memorandum No. 311 10 sa.ry to fly in a di rection from vlhich no help but rather nindrance • can be e:>..-pected from the ai r cu:;:orents. An airplane will be the most efficient in meeting the denands of commercial work when it is least affected by the wind. This means that the cruising speed should be high in order that the percentage reduction in velocity over the ground experienced in average air conditions may be low. The practical airplane should have a rrarGin over its most efficient cruising speed at least equal to the avera~ velocity of the winds liable to be encountered. The light ai:rplane, therefore, must have a very high ratio of ift to drag at high speed in order that flight may be accor!1plished with low p0i7ero Thus the requirements of a glider and of a light airplane ~ are similar in one respect only, the necessity for a very high ratio of lift to drag, The engined glider will have a phenomenal duration but will not be a practical airplane. Lil1t airplanes are not und6rpowe::.:.'ed in the true sense of that term. The number of pounds carried. per hOl'sepower is much great er than des ::'g!lers hal' e previously deemed aclvi sabl e in the construction of military typeso This high power loao.iT.l.g is the raisond'etre of the light aiplane. For commercial work the greatest possible load must be carried by the rmnimum power. Everything else being equal, t11a.t airplane which has the highest power loading will be the cheapest both.in first cost and in operation. An airplane is underpowered only when it is unable to • properly function in the service for which it was intended

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l!. A. C~ A. Technical Memorandum No. 311 11 If that service be to transport a pilot and baggage 200 miles at a speed of 75 miles per hour and passing over a mountain range 12,000 feet high on the way, that airplane which fails in-the accomplishment of the above is underpower-cd' whether it carries 15 . or 30 pounds per horsepower. The'advocates of the light airplane believe that there are . two ways of increasing airpla,ne performance, namely, by either I inreasing----- the engine power available or by decreasing the power required for flight; and that the latter method is by far the most logical and scientific. I An increase of power necessitates an increased fuel load, and therefore a greater total weight 0 Consequently, the cost o the airplane both as to original outlay and as to maintenance increases. Everyone has heard the statement "Give us power enough and we can fly the ki tehen table. II The light airplane is diametrically opposite to a powered "kitchen table." It may be defined as a scientific attempt to obtain the greatest possible useful • I work from the least pOl'16r. Incidentally this results in an plane extremely cheap in all. respectsc / Brief mention has been made of the different stages of light airplane dev.elopment, and at tent ion has been directed to the d&pendence of the designers to a great extent upon the work of Dr. Prandtl. The engine glider idea as well as the criticism of light airplanes being underpowered have been discussed and shown to be the wrong conception~

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·.. No 0 31i 12 N.A.C.A •. 'rechnicai l1emo randtim • Table I ~ Weight· Weight _iling Pouer Airplane Type ~rigine light loaded loading loading Avro 558 B-S 500 cm3 294 480 2.89 26.7 1\ Avro 560 M-S 698 285 471 3.41 23.5 1\ A.N.E.C. M-S 638 289 465 3.21 23.2 1\ Wren M-S 398 232 408 1\ Gull M-S 698 402 500 3.52 II Gannet' B-S 750 283 460 4.47 II D. H. 53 M-S 750 310 490 4.08 II Viget B-S 750 395 575 2.88 26 II Poncelet M-S 750 II P eyret M-S 750 II Raynham M-S 750 1\ Pixie M-S 500 Hurricane M-S 600 "II H.P.23 M-S 500 -n.P.25 M-S II H.P.26 M-S 698 Dormoy M-S 80 C\l. in. II Mummert M-S 74 II 520 6.4 480 2.85 430. 2.75 500 8.10 Driggs M-S 80 326 511 7.3 22.7 Snyder B-S II Turner B-S .74 Heath B-S .. Brown.ie I M-T 1095 cm3 500 870 29 II 4.3 Brownie II M-T 1096 500 870 4.5 29 Cranwell B-T 1096 510 830 3.75 29.6 " 1\ Wee Bee M-T 1096 462 837 4.47 25.6 Wood Pigeon B-T 1096 439 779 5.03 26 " II Widgeon M-T 1096 4bO 790 5.5 ·26 It A.N.E.C. M-T 1100 415 730 3.94 24.3 Short M-T 1096 483 850 5.05 28.3 II" Sparrow B-T Li.OO 478 860 3.26 28.6 II Avis B-T 1096 450 810 3.20 27.0 II Blue Bird B-T 1100 495 875 3.60 29.2 Vagabond B-T 1100 527 887 3.96 29.6 " p.ixie III M-T loc:m " II pixie IlIa B-T 1096 M - Monoplane S - Single seater . B -·Biplane T - Two Seater Outline drawings of rrany of the above-mentione light airplanes are given in N.A.C.A. Techni cal Memo randums Nos. 261 and 289.

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• N.A.C.A. Technical Memorandut:1 Nd~ &11 13 Table I ( Cont.) 'h Airplane Type Engine High Rate of Ceiling Iii 1es speed climb Gallon Avro 558 B-S 500 13,850 Avro 560 M-S 698 87.5 /I M-S 698 74 14,400 II Wren M-S 398 82.5 Gull li-S 698 55.25 " Gannet B-S 750 " II De H. 53 llI-S 750 59.3 59.3 . Vi get B-S . 750 II 58.1 Ponce1et M-S 750 'II 58 II Peyret M-S 750 9,400 II Raynham M-S 750 65.7 II Pixie 1.1-S 500 76.1 II Hurricane H-S 600 58~5 II H.P.23 M-S 500 H.P.25 M-S H.P.26 M-S 698 II . Dorm.oy M-S 80 cu. in. e, Mummert M-S 74 II Driggs 1.1-8 80 11 - Snyder B-S Turner B-S 74 /I Heath B-S Brownie. I M-T 1096 cm 3 70 II Brovmie II l!L-T 1096 70 II Cramvel1 B-T 1096 Wee Bee H-T 1096 " '86 Wood Pigeon B-T 1096 " 72 II Widgeon 1.:i-T 1096 72 II A.N.E.C. liI-T 1100 85 II Short M-T 1096 73 II Sparrow B-T 1100 If Avis B-T 1096 75 II Blue Bird B-T 1100 74 II Vagabond B-T 1100 74 11 Pixie III M-T 1096 . 11 Pixie IlIa B-T 1096 ,B - Biplane 11 - LIonon1ane S - Single Seater T - Two Seater Outline drawings of nnny of the above-r;;entioned light airplanes are given in N.A.C.A. Technical Memorandums Nos. 261 and 289 • •

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14 PART II~ .iodern Theoretical Aerodynamics as Applied to Light Airplane Design.* In the first part of this series there is reviewed briefly the results obtained in the development of light airplanes, both in IDrope and in this country. Considerable stress was laid on the importance of the mathematical work of the staff of ®ttingen Universi ty, in that it was largely the foundation of European progress. Like all good things, these theorems are very simpl·e, both to derstand and to use. A strict mathematical proof of Dr. PrandtIt s theory is quite difficult and is narally impossible in a series of this charact er. Suffice' to say that he applies the methods of clas·sical hydrodynamics to fluid flow bout a lifting organ, assuming that the fluid in question (air) has no viscosity, causes no friction and is incompressible. None of these assumptions is st:r;ictly :true, but the deviations are so small and. of such character that the truth of the theoy may be demonstrated and proved by wind tunnel tests. If it were possible to visualize the air flow about an airpl'ane in fli ght the Pra:r:.dtl theory would be very easy to under- * Author's Note:- The development of Elementary Aerodynamics in the following pages is necessarily somewhat mathenatical. Those readers who do not wish to follow this work may turn to the last page for a summary expressed in a few very simple rules. However, anyone familiar with elementary algebra should easily follow the mathematics as give:q..

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IT.A.C.A. Tecn:i.ca1·Uomorand.i1m N·o. 311 15 stand. As a wing is drawn through the air an infinite number of air molecules impinge upon its surface. If this wing is exerting a lift it naturally must be forcing these air particles downward,· giving rise to the well-known II dm'ffiwashll observed in numerous wind tunnel and free flight tests. This phenomenon may be demonstrated by a silk cord secured to the trailing edge of an airplane wing. In flight the cord will be seen to maintain an angle with the wing chord considerably greater than the actual angle of / . attack with the relative vnnd. Tis deflection of the air stream is equivalent to the airplane fly:i,ng at. all times in a curr-ent of air directed downwardo The fact that this downward deflection is caused.by the airplane itself in no way invalidates this assumption. If an airplane is flying in such a downward current, in order o maintain level flight it nrust have a vertical velocity upward exactly equal to the vertical velocity of the air downward. In other Vlords it nI'-lst be climbingo 'I'hi s is actually w:b...a t happens. The airplane is cOlltinually climbing away from the air that it has passed over and therby forced downward. Power is expended in thus causing thc airplane to climb. This power negessitated to maintain the ai rplane in level flight in the downwash induced . by its own pas sagJ through the air is 9alled induced power. Dr. Prandtl :b...as been able to arrive at a mathematical expression for this proportion of the power required. This formula represents • the basis of the so-called Prandtl theory. It has -been extended

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N.A.C.A. Technical llemorandum No. 31.1 16 to apply to multiplanes as well as to monoplanes from which the original expression was derived. Let W = Weight of airplane in pounds = Lift. b = Span of airplane wing in feet. (Average in case of biplane with uneven wings.) v = Velocity of flight in miles per hour. P = Density of the air at any altitude rele.tive to that at the ground (always uni ty or less). . p....:rn"d. = Induced poner required as explained above. ' 2 Then W for a monoplane (1) Pind = 2 3b PV . W2 Pind - for a biplane ( approximately) (la) 2 306'0 PV Formula (1) hot-rever does not represent the total power required for flight. As pointed out previously the assumptions under which the induced power has been calculated by Dr Prandtl do not coincide absolutely with the actual facts. He was forced to ignore the friction of the 8.ir on the wings as vlell as other slight discrep:mcies. At the prE-sent time a wind-tunnel test is the only means. available for detnmining the magni tude of the power necestsary to overcome th5.s aided wing resistance. Tests on nu,.'YLerous ·airfoils have shown that the frictional resistance, or Profil Drag as it is call~d, is very nearly constant for all angles of attack in the ordinary flying range .. It increases sligctly at the lower and higher angles. Extensive wind-tunnel tests have shown that this Profil Drag does not vary exactly as the velccity • squared as ordinarily supposed but at a somewhat lower rate. This

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No. 311 17 N.P-.C.A. Technical Memorandum gives rise to the so-called Scale Eff~ct mentioned in numerous , aE;ronauti,cal wor}~s. The wing Profil Drag is entireTy parasi tical in its aotion as it contributes nothing to the usefulness of the airplane. The power expended in overcoming this form of resistance may be called the Wing Parasite Power. L,et PW. P. = Wing parasi te Power K = Coefficient depending 'upon th8 ai.l'foil used. To be determined by wing turned test. = (Profil D'rag of 1 sq. ft. of wing area at 1 mile per hour. ) Sw = Area of wings in square feet. 3 KflWV 0 (2) ThenPW.p. = 375 . In the foregoing paragraphs the pO',1er required by the wing alone has been develepedo There are alw8,Ys certain other structural parts necess:1ry for bracing or con-Gaini.ng the pewer plant and us'eful load. ''I'hese bod.i 83 also ab s07b povier rthen propell ed through the at r. ~rhi s propo:::-ti ")n of the power required may be called the Structur.e.l Paras"!.te Power to d.ifferentiate it from the Wing Parasite POW31'c The magni tu.de of the struct-..lr.al Parasite resi stance is the mo st diffi cuIt to obtai,n. PIobably the most 'accurate method is to, test a scale r:lOdel of a proposed airpla:'le in the l"lind tur..nel for resist:,nce at various angles of attacko If a wind-tunnel test is OU'c of the question the resi stance ofall items exposed to thE:) air stream may be calculated by refer- • r'ing to experimental data on similar snapes. The laboratories of

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N.- A. C; A. Technical Memoranduin NO. 311 18 various countries have tested great numbers of fuseiages, wheels., - wires, struts, etc., and have published the data on those objects in a form conveni ent for ready use. Af-ter the resi stance of each item has been found_ as above, the total resistance is the sum of all the small components. Probably the simplest way to arrive· at the magni tude of the structural Parasite resistance is to eS,,"imate it by comparison with airplanes of similar type which have had coefficients experimentally derived by flight test. This is most conveniently done by imagining all the miscellaneous structural items to be replaced by a flat plate of such area that the resi stances at any given velocity wi 11 be identi cal. A table of such flat plate areas of equivalent structural Parasite Resistance may be easily calculated from published tests on different airplanes. When this equivalent flat plate area is determined, whether by tunnel test, calculation, or by estimation, the Structural Parasite Porler may be expressed as in formula (3). Let PS. P. -- St::-uctural Parasite Power. Sp. s. = Ar'3a of flat plate of resistance equivalent to structural bodies. 3 .00327 S?, s. V p Ps. p. = 3'15 (3 ) Formulas 1 (or la), 2 and 3 r:1ay now be added to give an exthe total Power Required - PRo pression for 3 .00327 Sp. S. V P • PR = 375 • KSWV3p Wz + + ( 4) 2 375 3b VP

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• NoA.C~A. Technical Memorandum :rJo.311 19 KSvI If = Sp.w •. = The area of a flat plate of equal ·00327 resistance to the wing profil drag. and if Sp = Sp. W,; + Sp. S'. Formula (4) may take this simplified form; .00327 Sp .~p + 2 W 2 ( 5) PR = 375 3b PV ( 5a) Equation (5) is very simple when compared with the ordinary procedure of calculating the Power Required curve .. One of the accepted methods is to start from a tunnel test on the chosen airfoil and apply to it various corroections· for aspect ratio, gap chord ratio in case of a biplane, stagger, wing tips, etc. From the chosen wing area and weight the velocity is computed at a series values of the lift coefficient corrected from tunnel test. Then from the values of LID obtained after corrections at the above lift coefficient the wing drag and then the wing power is computed. The Parasite Power is then calculated and added to that of ydng to give values of the Total required at 'various velocities. If the same quantities were used as in calculating power by equation (5) and if an extension of Dr. 1 Prandtl s theory were applied to correcting for aspect ratiO, ete., the curves of Power Required in both cases would be identical. The labor expended, however, in using (5) is infinitely less. This, however, is not the only advantage of the above applica-

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N. A. C.A. Techni cal Memorandum No. ·311 20 tion of Prandti I s theory .. In fOrrmlla (5) every quanti ty that af--: fects the power required for flight is shown in its proper re1ationship to every other. There are no coefficients to confuse and emphasize the wrong quantity. Every item but. one is accurately known, assuming that the power is required at a given velocity and air density. The value of 5p, the parasite area, is the only quantity that must be determined either experimentally, by calculation or by estimation. This difficulty, however, is expeyienced by all methods equally. A further advantage lies in the fact that the principles ·of mathematics may be applied to manipulate equation (5) into different forms and show variQus laws that have not been clearly expressed previously. This work will not be carried out here, due to the fact that an attempt is being made to keep this series as simple as possible. Suffice to say that by applying the principles of differential calculus the following may be demonstrated. I. At the speed of minim~~ power required the Induced Power is three times the Parasite Power. II. At the speed of minimum drag the Induced Power and Parasite power are equal.* Theorem I applies to questions of duration, least sinking speed for a soaring machine and to ceiling, while Theorem II is * Differentiate (5) with respect to V and place differential equal to zero for t~e speed of minimum power. Divide (5) through by V and multiply by 375 to reduce to equation of drug. Differentiate this equation with respect to V and place differential equal to zero for the speed of minimum drag.

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No. .311 21 l'J. A. C. A. Tc chn:. cal t1emo randum important for ·range of flight-and best gliding angle. These rules .. show the very marked influence of induction on airplane perfor~ ane, especially in the design of light airplanes and gliders. The induced power at any speed and air density is determined solely by the ratio of weight to span, W/b. Herein lies the most important fact relative to Light Airplane design. A span loading, Wit, of 20 pounds per foot on a 500-poundlight airplane means but a span of 25 ft. The same value of W/b on a 4000-pound airplane calls for a span of 200 ft. Such a spread is impossible without excessive wing weight and almost-impossible maintenance and hangar conditions. The limit of span for 4000-pound airplanes in practical use is approximately 50 ft. Therefore, W/b = 80 pounds per foot. Since the Induced Power :2 varies as (W/b) from formula (1), for the 500-pound light aiplane this portion of the power required will be 1/16 -as great as for the larger airplane. If the propeller efficiencies are the same in both cases the power available, and general performance of the two airplanes would vary somewhat as below; 4000-pound Airpla.ne Span, 50 feet. W/b, 80. Power Available, 400 HP~ .. Absolute ceiling, 19,000 ft. Rate of Climb, 1200 ft./min. 500-pound Light At~plane. Span, 25 feet W/b, 20. Power Available, 25 HP. Absolute Ceiling, 19,000 ft. Rate of Olimb, 600 ft./min.

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E.. A. C. A. Technical iImnorandum No _ 311 22 4000-pound Airplane • Span, 50 feet. W/'r, 10 lb. per HP. • Parasite Arca, 16 sq. ft. High Speed, 120 miles per hour. Parasite Area, .004 Weight 500pound Light Airplane . Span, 25 feet. W/p, 20 lb. per HP • Parasite Area, 1 sq.ft. High Speed, 120 miles per hour. Parasite Area, .002 Weight In the foregoing example the Parasite Power has been assumed to vary in the same ratio as the Induced Power. This assumption is not justified by the facts in the case. The wing parasite will probably vary directly as the relative weiGhts of the·tw~ airplanes. The structural parasite mayor may not vary in some such ratio, probably, .however, it wi 11 never decrease fast er than the ratio of weights. If such be the case the value of ·lp for the light airplane becones 2 sq. ft. and the high speed becomes 95 miles per hour approximately- Very little effect will be noticed in the rate of climb and ceiling, however, since the lowered propeller pitch used with the lower high speed will probably increase the Power Available at lower speeds sufficiently to compensate for an increase of Parasite Power, which has a relatively small effect at lower speeds. The simple example given brings to light another important fact. In order to obtain the maximum utility out of these airplanes the Parasite Area should be reduced to the lowest possible limit. Parasite is, of course, of prime importance in any air~ • plane 4 for a light airplane, however, its importance increases in

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N.A.C.A. Technical Memorand1;tm lt6; 311 23 ! direct proportions to the increase of power loading. It wi1l • probably be found impossible to decrease the parasfte area beyond a limit of approximately 2 sq.ft. for a 500-pound airplane. Naturally this will lead to a reduction in the high speed over that whicli would be expected reasoning from the Induced Power reduction alone. This i"s oTI:e of the penalties that must be paid for flight with low power, and should affect the general utility of these airplanes but little when considered in the light of . their low first 'cost and upkeep. To draw a para.llel from the automobile industry the most useful and widely sold car manufactured is capable of developing but less than one-half the speed cro ss country than some of the larger and more expensive automobiles. Its utility in congested traffic, however, compensates in a great measure for such lowered high speed. Likewise the Light Airplane, due to the fact that it can get in and out of smaller areas and possibly paved roads, if necessary, closer in to the center of cities, ma.y ma17e up in the long run for some of the difference in maximum velocity. Light airplane races with high speed as the only criterion have been somewhat criticized in this country as not furthering development along the proper lines. Such a thought is absolutely . without foundations. High speed is the most important single item to be developed provided, however, that the power is not increased and that no sacrifice is made in utility. An increased'~high(:~peed (with same power) necessitates a re-

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.. IT.A.C.A,· Technical Memorandum No .. 311 24 duction in parasite. towering weight and lowering parasite are the two most important problems confronting the light airplane designer today; provided, of course, that neither is done at the sacrifice of first ·cost, upkeep, or general utility. If tho para-' site and weight be lowered sufficiently, rate of climb, ceiling, • emd time to al ti tude may be increased at will by decreasing the span loading. The design which wakes the best high speed may be revised slightly if it be lacking in any of the above particulars and made to out-perform any other design of sar.1e power and weight. Returning to formula (5) it will be seen that no mention has been made of two quantities hithetto thought to be of prime importance in airplane design, namely, wing loading (:po~nds per ,.square foot of· area) and aspect ratio (ratio of span to chord of wing). If the span be constant, wing loading (or wing area) has , but little effect upon the curve of Power Required. Its main influence lies in the fact that it controls the wing Parasite Power, formula (2), and also the minimu'm speed at which level flight may be maintained. It is naturally assumed in application of formula (5) that the wing area is sufficient to maintain level flight at any veloci ty substi tuteo. into the equation. Wing area controls the lower limit of velocity (constant span and airfoil), and to a slight degree the parasite .. Aspect Ratio, on the other hand, is ... a perfectly useless term. Span and area tell the whole story. This is true whether a monoplane OT multiplane be under considera tion. A little thought will show wherein lies the fallacy of the

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• I:? A. C. A. Techni cal Meli10randum No. 311 25 belief that rate of climb and ceiling vary as the wing area. J When these relationships were first wOTked out showing such c.epend.ence of performanc.e upon 'iving area te investigators overlooked the fact that since they were keeping the Aspect Ratio Constant in their calculations they were varying the span as well as the wing loading. The effect obtained was due to the variation in span so produced and not to the wing loading. This is an example of reasoning from an experimental rather than a theoretical basis. The effect was attributed to a cause which in reality acts just the opposite than generally f:'D..s .. 8u-;::rricsed. With cons tant span an increase of vling area wi 11 decrease cei ling, rate of climb and high speed through the increase of parasite. However, at the same time a 10Yler landing speed will also be obtained. From Theorer.1. I above defining the speed of minimum pO'ner it may be shovm that if VM. P. = Speed 0 f ITI.ininn.lm power 10.64 ~ at the ground. (6) = 4./ .2 . ./.b Sp The theoretical low speed of the airplane should not be greater than the value given by equation (6) in order that the maximum effect may be realized from the given span loading. For the 500-pound light airplane investigated above with a value of p = 1 sqft., V,, p. J:iI.•• vrorks out to be 47.7 miles.per hour. If the airplane, houever, has an Sp of 2 sq.ft., V becomes 40.1 miles per hour. The wing area should be such that in

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N.A.C.A. Technical Memorandum No. 311 26 either case flight might be maintained at the speeds given, or • preferably, slightly less. Therefore, wing area enters into consideration but entirely in a secondary manner. If Ky max= Maxinum lift coefficient of airfoil used in Ibs~ per sqft. miles per hr. units. Then" ( 7) Equation (7) deterines the wing area necessary for a required low speed. Table II lists some of the best American airfoils, giving . the value of the maximum 1 ift coeffi ci ent as well as the minimum profil drag of the sections. Since the low speed as given by formula (6) is more or less determined by this or other considerations Ky n1Ll.X should be as large as possible in order that a (' smaller area may be used with corresponding reductions in wing weight. Similarl y, . K, the profil drag coeffici ent should be as small as possible in order that the wing Parasite Power, Pw (sec formula 2) should be low. •Po Thereforc, thc ratio of Ky max to minimum profil drag coefficient, Gho~ld be a very good criterion for the choice of an airfoil, not conSidering structural requirements or stability. This ratio also enters into Table II for ready comparison.

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No~ 311 27 N.A.C.A. Technical Memorandum Airfoil Ky max Kmin R.A.Fj 15 .0026 .000025 , Ky max Kmin 104 Thin - very -good. U. S' A. 27 ~0000345 99.8 Medium thick. .00344 G8tt. 387 .00366 .000041 G8tt. 430 .00328 .000033 89.3 Medium thick. 102.5 Medium -thick. G8tt. 436 .00307 .0000313 98 Medium thi9k. U.S.A.35 B .00333 .0000325 102.5 Medium thick. U.S.A.35 A .00376 .000044 85.5 Very thickG Clark W .00291 - ~.0000294 99 Medium thick. Clark X .0000289 99G8 Medium thick • •00289 -, Clark Y -.00318 - .0000269 118.2 Medium thick - good. Clark Z .00321 . 000030 107.4 . Medium thick - good. U.S'A. 16 0000229 11905 Thin good. .00274 Curtiss 0-62 .00233 .000022 106.0 Thin - racing secion . U.S.A. 35 .00383 . 0000334 114.5 Tapered cantilever . U. So.I.. 45 .00331 . 0000276 120.0 Taper-ed - cantilever • Sloane 105 .00238 •0000232 102.5 Very thin. Power required for flight at any velocity has been investigated wi th special reference to the light airplane. The power available from the engine-propeller group has not as yet been touched upon. The engine itself is generally determined by con- .. siderations of price, availability or race rules. The design of the propeller, however, may have a mar.ked influence upon the general performance through its control to a certain measure of the

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H.A .. CA. Techn1cai Membrandum No, 311 28 Power Available, PA· The Prand t1 theory has been extended to apply to propeller design and suggests some. very useful theorems especially pertaining to tight Airplane propellers. In the preceding discussions it has been shown that the ratio Wlb should be very small, similarly it may be demonstrated in case of the propeller that the thrust over the diameter should also be as small as possible. Mr. Max M. Munk, in N.A.C.A. Technical Note No. 94, has worked out a formula for propeller diameter, D, based upon this theory. Let PM = Power of engine at N = Revolutions per minute of propeller· shaft. = Velocity in miles per hour at which the p-rope11er efficiency is desired to be a maximum, normally the designed high speed of the airplane. D = Propel1r diameter in feet. 3 (P;;- (8) Then D =564/ In '. - If equation (8) gives a diameter such that .0524DN exceeds' 820 ft. per sec., the diameter will have to be reduced until that limit is not exceeded. This is due to the fact- that as the speed of the propeller tips appr'oaches the velocity of sound the cornpressibi1ity of the air becomes a noticeable factor and lowers , the efficiency very rapidly. Equation.(8) will give diameters ... in excess of present practice, which is based upon the assumptions that 1/2 the diameter divided by the maximum blade width .. shall be approximately 6. That is, with the diameter above corn-

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N.A.C.A. Technic(ll Memorandum No. 311 29 puted, the maximum blade width will be smaller than present pract ice would allow. Due to the fc.ct t:1U t t:1e weight and t~1rust are low, the stresses imposed upon the light airplane propeller permit this increased ratio of diameter to blade wiQth. The reasoning is similar to that which allows a larger span in proportion to weight for a light airplane than for the-larger type. The pl'opeller used on the D-J-l 1;'[as 58 inches in diameter and but 3t inches maximum ~idth. No trouble whatever was experienced. Weros, grass, etc. ,had no appreciable effect except to wear the fabric tips. The influence of increasing the diameter is two-fold. The slipstream velocity is less and therefore the energy losses are also decreased TIith a consequent increase in propeller efficiency. The velocity of the slipstream being less and distributed further away from the fuselage causes less interference between the body and propeller. Both of these considerations make for better all around performance. A numerical example will serve to show more clearly the differances between ordinary practice and diameters given by equation (8) • VD = 95 miles per hour. N = 3000 revolutions per minuteo D •

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1 H. A. C. A. Techni cal Memo ra.nduIll No. 311 30 ) D = 5.5 feet = 66 inches. A formu.la derived by H. C. Watts, for propellers of Aspect Ratio G, give D = 4.84 feet = 58 inches. If the maximum blade width in the latter case works out to be 29/6 = 4.84 in., the width, using a 66-inch diameter.propelleI', is approximately 4 inches or 1/8 of the blade radius, in- ,stead of 1/6. No attempt has been made to propose a method of performance calculation or propeller design. The main intention in mind has been to bring out a few very simple rules important in the design of light airplanes. These ideas are sUffarized below • . • Rule I. Make the ratio of span to weight as small as possible cor:1patible wi th structural and housing condi tions Rule II. Bui11 as light as possible. Rule III. Reduce Parasite to the absolute limit, even at the sacrifice of eighto Rule IV. Usc large diameter, narrow ble,de propellers, 'I< The next sections 'Will show by means of a defini te numerical example how the different performance characteristics are affected by the vQrj e,.0_n8 :L~~.h.§.!).mel1sions of a light ai!.i?.:.l<;l.le 0 * Will be issued by Comm::;.ttee as a Technical Memoranc.um in the ~. ·near future. r .•