1、NATIONAL ADVISORY COMMITTEEFOR AERONAUTICSREPORT No. 665CALCULATION OF THE AERODYNAMICCHARACTERISTICS OF TAPERED WINGS WITHPARTIAL-SPAN FLAPSBy HENRY A. PEARSON and RAYMOND F. ANDERSON1939REPRODUCEDBYNATIONALTECHNICALINFORMATIONSERVICE ,_bU.S. DEPARTMENTOF COMMERCESPRINGFIELD,VA, 22161Provided by IH
2、SNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-AERONAUTIC SYMBOLS1. FUNDAMENTAL AND DERIVED UNITSMetr!e EnglishSymbolUnit Abbrevia- Abbrevia-tion Unit tionLength l meter m foot (or mile) . ft. (or mi.)Time t second . s second (or hour) . see. (or hr.)Force F weig
3、ht of 1 kilogram . kg weight of 1 pound . lb.Power . P horsepower (metric) horsepower . I hp.kilometers per hour k.p.h, miles per hour I m.p.h.Speed . V meters per second . m.p.s, feet per second f.p.s./2. GENERAL SYMBOLSW, Weight-=mg _, Kinematic viscosityg, Standard acceleration of gravity-9.80665
4、 p, Density (mass per unit volume)m/s2or 32.1740 ft./sec. 2 Standard density of dry air, 0.12497 kg-m*-s2 atWMass=- 15 C. and 760 mm; or 0.002378 lb.-ft. -* see.2m, g Specific weight of “standard“ air, 1.2255 kg/m 3 or/, Moment of inertia=ink 2. (Indicate axis of 0.076511b./cu. ft.radius of gyration
5、 k by proper subscript.)t_, Coefficient of viscosity3. AERODYNAMIC SYMBOLSS, Area iw, Angle of setting of wings (relative to thrustS., Area of wing line)G, Gap it, Angle of stabilizer setting (relative to thrustb, Span line)c, Chord Q, Resultant momentb2 It, Resultant angular velocity_, Aspect ratio
6、 V1V, True air speed p-, Reynolds Number, where 1 is a linear dimensiontt1 _z_ (e.g., for a model airfoil 3 in. chord, 100q, Dynamic pressure_p, m.p.h, normal pressure at 15 C., the cor-responding number is 234,000; or for a modelrL, Lift, absolute coefficient C_=_ of 10 cm chord, 40 m.p.s., the cor
7、respondingnumber is 274,000)YD, Drag, absolute coefficient CD-=_.q C_, Center-of-pressure coefficient (ratio of distanceof c.p. from leading edge to chord length)r)_Do, Profile drag, absolute coefficient CD0-_ Angle of attackC_,e, Angle of downwashD.D_, Induced drag, absolute coefficient CD_-_,_ co,
8、 Angle of attack, ild_nite aspect ratioa_, Angle of attack, induced/9_D_: Parasitedrag, absolute CO e_cien _ CDp=_tt_ Ca, Angle of attack, absolute (measured from zero-_S lift position)C, Cross-wind force, absolute coefficient Ca- % Flight-path angleR, Resultant force| ,-/Provided by IHSNot for Resa
9、leNo reproduction or networking permitted without license from IHS-,-,-REPORT No. 665CALCULATION OF THE AERODYNAMICCHARACTERISTICS OF TAPERED WINGS WITHPARTIAL-SPAN FLAPSBy HENRY A. PEARSON and RAYMOND F. ANDERSONLangley Memorial Aeronautical Laboratory161569-39Provided by IHSNot for ResaleNo reprod
10、uction or networking permitted without license from IHS-,-,-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSHEADQUARTERS. NAVY BUILDING, WASHINGTON. D. C. _LABORATORIES. LANGLEY FIELD. VA.Created by act of Congress approved March 3, 1915, for the supervision and direction of the scientific study of the p
11、roblems offlight (U. S. Code, Title 50, Sec. 151). Its membership was increased to 15 by act approved March 2, 1929. The members areappointed by the President, and serve as such without compensation.JOSEPH S. AMES, Ph. D., Chairman, ROBERT H. HINCKLEY, A. B.,Baltimore, Md. Chairman, Civil Aeronautic
12、s Authority.VANNEVAR BUSH, Sc. D., Vice Chairman, JEROME C. HUNSAKER, So. D.,Washington, D. (_. Cambridge, Mass.CHARLES G. ABBOT, SC. D., SYDNEY M. KRAUS, Captain, United States Navy,Secretary, Smithsonian Institution. Bureau of Aeronautics, Navy Department.CHARLES A. LINDBERGH, LL.D.,HENRY H. ARNOL
13、D, Major General, United States Army, New York City.Chief of Air Corps, War Department. FRANCIS W. REICHELDERFER, A. B.,GEORGE H. BRETT, Brigadier General, United States Army, Chief, United States Weather Bureau.Chief Materiel Division, Air Corps, Wright Field, Dayton, JOHN H. TOWERS_ Rear Admiral,
14、United States Navy,Ohio. Chief, Bureau of Aeronautics, Navy Department.LYMAN J. BRIGGS, Ph.D., EDWARD WARNER, So. D.,Director, National Bureau of Standards. Greenwich, Conn.CLINTON M. HESTER, A. B., LL.B., ORVILLE WRIGHT, So. D.,Administrator, Civil Aeronautics Authority. Dayton, Ohio.GEORGE W. LEWI
15、S, Director of Aeronautical ResearchJOHN F. VICTORY, SecretaryHENRY J. E. REID, Engineer-in-Charge, Langley Memorial Aeronautical Laboratory, Langley Field, Va.JOHN J. IDE, Technical Assistant in Europe, Paris, FranceTECHNICAL COMMITTEESAERODYNAMICS AIRCRAFT STRUCTURESPOWER PLANTS FOR AIRCRAFT AIRCR
16、AFT ACCIDENTSAIRCRAFT MATERIALS INVENTIONS AND DESIGNSCoordination of Research Needs of Military and Civil AviationPreparation of Research ProgramsAllocation of ProblemsPrevention of DuplicationConsideration of InventionsLANGLEY MEMORIAL AERONAUTICAL LABORATORY OFFICE OF AERONAUTICAL INTELLIGENCELAN
17、GLEY FIELD. VA. WASHINGTON. D. C.Unified conduct, for all agencies, of scientific research on the Collection, classification, compilation, and dissemination offundamental problems of flight, scientific and technical information on aeronautics.5-24-39Provided by IHSNot for ResaleNo reproduction or ne
18、tworking permitted without license from IHS-,-,-REPORT No. 665CALCULATION OF THE AERODYNAMIC CHARACTERISTICS OF TAPEREDWINGS WITH PARTIAL-SPAN FLAPSBy HENRY A. PEARSON and RAYI_IOND F. ANDERSONSUMMARY _-_ : _-_L-_:-_-._Factors derived from wing theory are presented. By ._-_=-._-=:e_=_-_:of these fac
19、tors, the angle of zero lift, the lift-curve rd /nemean8slope, the pitching moment, the aerodynamic-center posi- Quorfer-cho J/tion,andtheinduceddragoftaperewingswithpartial-span flaps may be calculated. The factors are given .for A =S _-J-“J _z/“_-“_/“J_-_ :5with sweepback (A positive), the sign of
20、 the pitching- “_ “_ tr _ _“moment coefficient due to the basic lift is positive if “the flap deflection introduces an effective washout _ _ .I _- _toward the tip (e. g., flaps at the center deflected down- -_ “_ -“ward or flaps at the tip deflected upward). For a ._wing with sweepforward, the sign
21、of Cmtbis negativefor the same flap deflections. F/apz at tip _ _ i,.0Flop o - 2.5.05 I / _ _, -A :_-“_.-_“_-_.04 1.00_-_ _i .75 0 .2 .4 .6 .8 1.0_._ “.50 Taper rat/o, A_; FIGURE7.-Factors of section pitching moment, E and E.03 “:_ “_ “_ C_s=Ec“bEAc“*“_ _“ -_ “_ N_ _ For wings with flaps; however, t
22、he value of the sectiona / / .25 N.50 pitching-moment coefficient c_a._, may be assumed to.o_ /,/_ /:7o .i_:. consist of two parts: One denoted by c,.o,the scctio,(/i / ,t _;Rx_ coefficient with tlaps neutral; and the other denoted byAc, the increase in the section coefficient above c_o.o/ / _ due t
23、o the flaps. If c,ois const_mt across the span rod_ zXcmis constant across the tlap span (i. e., the tlap-chord/ratio is constant), then the pitching-nmment coefficiento .2 .4 .6 .8 /.o due to the sections can be given byFlop spon/w/nq _pon, b t/b (flopz 0 center)FIOURE6.-Factorofbasicliftpitching m
24、oment.G. Cms= Ecmo-FE,_c, (10)C.,b=aAczd tuna Values of E and E for these conditions are given inIn case the aerodynamic centers do not lie on a figure 7 for the tapered wings. These values have beenstraight line so that the angle of sweepback is not con- determined from the relationsstant along the
25、 span, C_b may be graphically obtained _ 2b cb/2/_=_J0 cdyfrom the equation ._ 2b _/_t:,%-_3 xc_:dy (8) _, 2b _:/_:._.,y fwhere, at any point along the span,x is the moment arm measured from the aerodynamic If neither cm0nor zXc_were constant across the span,center of the root section and parallel t
26、o the root then it would be necessary to use equation (9) and tochord (positive, rearward; negative, forward), evaluate Cruz by an integration, as will be illustratedProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TAPERED WINGS WITH PARTIAL-SPAN FLAP
27、S 5later. The total wing pitching-moment coefficient is /.cogiven by Omac=Cmsq-Cmb (11) J ,_ - - . “_The coefficient Gmac is defined by the equation .98 , “ _ : . . / M= G_o q_2, (12) “ .96 - A =6 where M is the total pitching moment. - - - - A,=/o Induced drag.-For any wing with a twist that is ,sy
28、mmetrical about the wing center line, the induced- .940 Idrag coefficient may be given by the equation .z Taper4ro_io,6A .8 /.02 Flop spon/w/ng _pon, b.f/4b (flops af t/p)(7,._w_,_v,_rT.*_=v“-t-_-hczv-t-hc_2w (13) /.o .8 .6 .z o-,. -4The factors % v, and w for wings with partial-span / ,.x_x x_ie 5f
29、laps, i. e., for the case of an abrupt twist, are given infigure 8. “_ :002The first term on the right-hand side of equation (13) / - is the usual induced-drag coefficient of an untwisted wing and the other two terms result from the aerody, _ _ E/lipf/col, _ _.-_namic wing twist introduced by deflec
30、ting the flaps. _._ _ “-“- I/It can be seen from figure 8 that, for certain taper “_ratios, the v and the w factors are of opposite sign and their contributions counteract each other. In fact, under x_ _ _x(.5o,_._ _/, _certain conditions, the sum of the last two terms may .oo_ “_ i ibe slightly neg
31、ative; and, as a result, the ellipticalwing induced-drag coefficient may be approached. _7.5This tendency exists when the flaps are so placed and X x“_-“ ._“v/ / .oozdeflected that an elliptical loading is approximated. | ,_,_, “-._ /$, /EXPERIMENTAL RESULTS / / .006_.L_ o6“ _ / /APPARATUS AND TESTS
32、 A=IO X _ / /In order to provide a check on the reliability of the ,/oo /-4 . L .008theoretical factors that have been presented, two o .z .,_ .6 .e /otapered wings with partial-span flaps were tested. In Flop_pan/wingspan, bz/b If/aps af cen_eraddition, tests were made of three rectangular wings /_
33、 -_.X-_x-_=/.oowith full-span flaps to provide section data for use in _J/ “_. _x( 75calculating the characteristics of the tapered wings. .008 ,y ,X_ “ “5o -The wings were made of aluminum alloy and had an / , , _“_1: _s_area of 150 square inches. E/,or ca “A list of the tapered wings and the diffe
34、rent flap 004 lengths used is given in table I, together with the Y/j A =5 _%taper ratio, the aspect ratio, and the airfoil sections _of the root and the construction tip (the extreme tip). _ oA = 1.00The tips were rounded as shown in figure 1. The I,Ili _“_ “_-“.5o-N. A. C. A. 23012 tapered wing ha
35、d a moderate sweep- .oo8 / “,:75back (line through quarter-chord points)but the N.A. /_/ %_.z5C. A. 5-10-16 tapered wing had no sweepback. In the I I ,_ _k,construction of the wings, straight-line elements were .004 / “%used between corresponding points of the root and the A=/O kconstruction tip sec
36、tions. For the N. A. C. A. 23012 ,_wing, the chords of all sections along the span were in 1one plane; whereas, for the N. A. C. A. 5-10-16 wing, o ._ .4 .6 8 /othe highest points of the upper surface of each section Flop.spon/w,ng_pan, bf/bwere in one plane. The ordinates of the N. A. C.A. F_,_ 8.-
37、Faetors of induced drag. u,g,andw.5-10-16 wing are given in reference 4. c_,=_-c_.v,_+_,-_Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-6 REPORT NO. 665-NATIONAL ADVISORY COMMITTEE FOR AEROI_AUTICSThe rectangular wings had N. A. C. A. 23009, 23012,
38、 Cmta.c._0are given about the aerodynamic-center posi-and 23015 sections and were included to provide airfoil tion with the flap neutral.section characteristics to aid in calculating the charac- The results of the tests of the tapered wings areteristics of the tapered wings, presented in the usual m
39、anner in figures 12 to 17. InPlain 0.2c flaps deflected downward 20 were built addition to the usual characteristics, the lift-curveinto all the wings and were made to simulate flaps peaks are given for two values of the effectiv.e Reyn-pivoted about the midpoint of the thickness at 0.8c. olds Numbe
40、r to indicate the scale effect on CL,a_.Fillets of small radii were used to join the flap to the The Reynolds Number is based on the mean chord S/b.wing and to seal the gap, as indicated at the top of On the right side of the figures, effective profile-dragfigure 9. coefficients are given. This coef
41、ficient is the total dragAll the wings were tested in the variable-density coefficient with the induced-drag coefficient for ellip-wind tunnel at a pressure of 20 atmospheres. The lift, tical span loading deducted, that is, CDc=CD-CL2/TrA.the drag, and the pitching moment were measured at The values
42、 of CD_have been corrected to effective-L-LI Q-_“-,_ I I O0 20 40 60 80 IOO! ! Percent of chordii,3,6 4_ O_24,2 ,. , _/ I/ _. ;_I_,16 _ _-/ _ /“ O8. , : 4 08_. o I _/ Z RoU . I _ uLateral Y Y Pitching M Z-_ X Pitch 0 v qPNormal Z Z Yawing hr X- Y Yaw . _ wAbsolute coefficients of moment Angle of set
43、 of control surface (relative to neutralC_=L-_- C M C N position), _. (Indicate surface by proper subscript.)_:-qcS _ qbS(rolling) (pitching) (yawing)4. PROPELLER SYMBOLSPD, Diameter P, Power, absolute coefficient CP=pnaD 5p, Geometric pitch _/P V_io/D, Pitch ratio C_, Speed-power coefficmnt= )_n2V,
44、 Inflow velocityV, Slipstream velocity 7, EfficiencyT n, Re_colutions per second, r.p.s.T, Thrust abslute cefficient Cr- -n-_o _ Effective helix angle = tan-l( 2r_:)Q, Torque, absolute coefficient CQ=p_D55. NUMERICAL RELATIONS1 hp.=76.04 kg-m/s-550 ft-lb./sec. 1 lb.-0.4536 kg.1 metric horsepower=l.0132 hp. 1 kg=2.2046 lb.1 m.p.h.-0.4470 m.p.s. 1 mi.-1,609.35 m=5,280 ft.t m.p.s.-2.2369 m.p.h. 1 m-3.2808 ft.i IProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
