1、NATIONAL ADVISORY COMMITTEEFOR AERONAUTICSREPORT No. 631AIRFOIL SECTION CHARACTERISTICS AS APPLIED TOTHE PREDICTION OF AIR FORCES AND THEIRDISTRIBUTION ON WINGSBy EASTMAN N. JACOBS and R. V. RHODF1938EEPRoD_/CEDBYNATIONAL TECHNICALINFORMATION SERVICEU. S. DEPARTMENTOFCOMMERCESPRINGFIELD,VA. 22161Pro
2、vided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-AERONAUTIC SYMBOLS1. FUNDAMENTAL AND DERIVED UNITSLength Time Force Power_ .Speed .SymbolMetricUnitmeter_ :second2 weight of i kilogram .EnglishAbbrevia- Unittionm foot (or mile) .s Second (or hour)= kg we
3、ight of 1 pound .horsepower .k.p.h, miles per hour m.p.s, feet per second PVhorsepower (metric) .fkilometers per hour meters per second .Abbrevia-tionft. (or mi.)see. (or hr.)lb.hp.m.p.h.f.p.s.w,g,m,I,s,o,b,C,b2v,q,L,D,Do,A_)v,_0,.R,Weight=ragStandard accelerationm/s 2 or 32.1740 ft./sec?WMass =- gM
4、oment of inertia-mkLof gravity=9.80665(Indicate axis of2. GENERAL SYMBOLSv, Kinematic viscosityp, Density (mass per unit volume)Standard density of dry air, 0.12497 kg-m_-s 2 at15 C. and 760 mm; or 0.002378 lb.-ft. -_ sec. 2Specific weight of “standard“ air, 1.2255 kg/m 3 or0.07651 lb./eu, ft.radius
5、 of gyration k by proper subscript.)Coefficient of viscosity3. AERODYNAMIC SYMBOLSAreaArea of wingGapSpanChordAspect ratioTrue air speed1 T72Dynamic pressure=_p_absolute coefficient C_=_Lift,DDrag, absolute coefficient CD=_- SProfile drag, absolute coefficient CD0_D,Induced drag, absolute coefficien
6、t Cm-_- _Parasite drag, absolute coefficient CDp=o_Cross-wind force, absolute coefficient Cc=-_SResultant forcei_, Angle of setting of wings (relative to thrustline)is, Angle of stabilizer setting (relative to thrustline)Q, Resultant moment_, Resultant angular velocityVlo _, Reynolds Number, where I
7、 is a linear dimension(e.g., for _ model airfoil 3 in. chord, 100m,p.h, normal pressure at 15 C., the cor-responding number is 234,000; or for a modelof 10 cm chord, 40 m.p.s., the correspondingnumber is 274,000)C_, Center-of-pressure coefficient (ratio of distanceof c.p. from leading edge to chord
8、length)a, Angle of attacke, Angle of downwasha0, Angle of attack, infinite aspect ratioa_, Angle of attack, induceda_, Angle of attack, absolute (measured from zero-lift position)7, Flight-path angleProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-REP
9、ORT No. 631AIRFOIL SECTION CHARACTERISTICS AS APPLIED TOTHE PREDICTION OF AIR FORCES AND THEIRDISTRIBUTION ON WINGSBy EASTMAN N. JACOBS and R. V. RHODELangley Memorial Aeronautical Laboratory73067.- 38-1 IProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,
10、-,-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 scientificstudy of the problems of flight (U. S. Code, Title 50, Sec. 151). Its memb
11、ership was increased to 15 byact approved March 2, 1929. The members are appointed by the President, and serve as such withoutcompensation.JOSEPH S. AMES, Ph. D., Chairman,Baltimore, Md.DAVID W. TAYLOR, D. Eng., Vice Chairman,Washington, D. C.WILLIS RAY GREGG, Se. D., Chairman, Executive Committee,C
12、hief, United States Weather Bureau.WILLIAM P. MACCRACKEN, J. D., Vice Chairman, ExecutiveCommittee,Washington, D. C.CHARLES G. ABBOT, Sc. D.,Secretary, Smithsonian Institution.LYMAN J. BRIGGS, Ph. D.,Director, National Bureau of Standards.ARTHUR B. COOK, Rear Admiral, United States Navy,Chief, Burea
13、u of Aeronautics, Navy Department.HARRY F. GUGGENHEIM, M. A.,Port Washington, Long Island, N. Y.SYDNEY M. KRAUS, Captain, United States Navy,Bureau of Aeronautics, Navy Department.CHARLES A. LINDBERGH, LL.D.,New York City.DENIS MULLIGAN, J. S. D.,Director of Air Commerce, Department of Commerce.AUGU
14、STINE W. ROBINS, Brigadier General, United StatesArmy,Chief Mat6riel Division, Air Corps, Wright Field,Dayton, Ohio.EDWARD P. WARNER, Sc. D.,Greenwich, Conn.OSCAR WESTOVER, Major General, United States Army,Chief of Air Corps, War Department.ORVILLE WRIGHT, Sc. D.,Dayton, Ohio.GEORGE W. LEWIS, Direc
15、tor 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 AIRCRAFT ACCI
16、DENTSAIRCRAFT MATERIALS INVENTIONS AND DESIGNSCoordination of Research Needs of Military and Civil AviationPreparation of Research ProgramsAllocation of ProblemsPrevention of DuplicationConsideration of InventionsLANGLEY MEMORIAL AERONAUTICAL LABORATORYLANGLEY FIELD, VA.Unified conduct, for all agen
17、cies, ofscientific research on the fundamentalproblems of flight.(ii)OFFICE OF AERONAUTICAL INTELIJGENCEWASHINGTON, D. C.Collection, classification, compilation,and dissemination of scientific and tech-nical information on aeronautics.Provided by IHSNot for ResaleNo reproduction or networking permit
18、ted without license from IHS-,-,-REPORT No. 631AIRFOIL SECTION CHARACTERISTICS AS. APPLIED TO THE PREDICTIONFORCES AND THEIR DISTRIBUTION ON WINGSBy EASTMAN N. JACOBS and R. V. RHODEOF AIRSUMMARYThe results of previous reports dealing with airfoil sec-tion characteristics and span load distribution
19、data arecoordinated into a method for determining the air forcesand their distribution on airplane wings. Formulas aregiven from which the resultant force distribution may becombined to find the wing aerodynamic center and pitchingmoment. The force distribution may also be resolved todetermine the d
20、istribution of chord and beam components.The forces are resolved in such a manner that it is unneces-sary to take the induced drag into account.An illustration of the method is given for a monoplaneand a biplane for the conditions of steady flight and asharp-edge gust. The force determination is com
21、pleted byoutlining a procedure for finding the distribution of loadalong the chord of airfoil sections.INTRODUCTIONThis report originated in a request Of the Bureau ofAir Commerce, Department of Commerce, for a coodinated system of applying airfoil section data to thedetermin_tion of wing forces and
22、 their distribution.The system presented herein yields, within the limi-ta.tions of our present knowledge of aerodynamics, ,_general solution of the resultant wing forces and me-ments and their distribution. For the sake of complete-ness and facility in use, the report contains a table of theimporta
23、nt section parameters for many commonly usedsections and all other necessary data required to solvethe most practical design problems coming within thescope of the system.Although the usefulness of the system extends intoseveral phases of airplane design, its application tostructural design is illus
24、trated by following through awing loading condition corresponding to that specifiedin reference 1.Two basic principles underlie the system employed.First, a force coefficient is treated as the independentvariable, thus eliminating, as far as possible, the angleof attack; and second, the forces are d
25、erived throughoutin terms of certain basic parameters of the airfoil sec-tion, which are tabulated for each airfoil section. Themethod followed then builds up the forces progressivelyfrom simple combinations of certain basic forces andsimple formulas involving the basic airfoil section pa-rameters.
26、As the forces are thus built up, they are re-solved into any convenient components. This methodalso has another important advantage in that the in-duced drag, which is really only a component of the locallift at each section, may be entirely eliminated from theanalysis.In some problems it is desirab
27、le to know the locationof the aerodynamic center of the wing and the pitching-moment coefficient about this center in order to con-struct the balance diagram of the complete airplane.Methods are therefore given for determining these twoproperties. For problems in which the aerodynamiccenter and the
28、pitching moment are not required, a directsolution of the forces and force distribution can bemade.BASIC CONSIDERATIONSThe forces on a wing may be considered to be func-tions of the characteristics of the airfoil sections and ofthe spanwise distribution of lift. At a given sectionlift coefficient, t
29、he resultant air force and moment onthe section are, according to wing theory; assumed to beindependent of all geometric properties of the wingexcept the section shape; moreover, the forces andmoments acting on any individual section may beconsidered to be independent of adjacent sections or ofother
30、 characteristics of the wing, except as they affectthe lift distribution and thus the local lift coefficientat that section.The problem is thus divided into two parts: First,the determination of the spanwise lift distribution;and, second, the determination of the correspondingforces and moments at e
31、ach section and the smnmationof these quantities to obtain the corresponding forcesand moments for the entire wing. The spanwise liftdistribution is obtained in terms of values of the localsection lift coefficient cz0 for a number of sections dis-tributed along the span. The subscript zero is used t
32、odistinguish this section lift coefficient, perpendicular tothe local relative wind at the section, from the liftcoefficient c_ perpendicular to the relative wind at agreat distance from the wing. The lower-case lettersused for these coefficients have been chosen to dis-tinguish the lift coefficient
33、 for a section (c_=dL/qcdy)from the usual lift coefficient for the wing, CL.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 REPORT NO. 631-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSIn order to permit easy reference, the symbols usedin the text, th
34、e figures, and the tables are grouped inappendix C.For many purposes, it is convenient to express theair forces in terms of components along two axes fixedwith respect to the airplane rather than as the usualcomponents, lift and drag. This resolution is con-veniently accomplished from the Cto values
35、, when theprofile drag and other fundamental characteristics ofthe airfoil section are taken into account, by means ofsimple formulas involving parameters given for eachairfoil section in a table of airfoil characteristics. Thismethod has an important advantage in that the induceddrag, which is real
36、ly only a component of the ct0 ateach section, is entirely eliminated from the analysis.For the purpose of determining the lift distributioncorresponding to the % values along the span, the liftload along the span is considered as being made up oftwo independent parts that will be referred to as the
37、“basic lift distribution“ and the “additional lift dis-tribution.“ The basic lift distribution is representedby the % distribution along the span when the totalwing lift is zero. This basic lift distribution, which isthe distribution arising by virtue of aerodynamic twist,may be considered to exist
38、unaltered as the lift and angleof attack are changed. The additional lift distribution,as the name implies, represents the distribution of addi-tional lift associated with changing the angle of attack.Wing theory indicates that, as long as the airfoil sec-tions of the wing are working within a range
39、 of normallift-curve slope, the form of the additional lift distribu-tion is the same at all lift coefficients and is independentof wing twist, of aileron or flap displacements, and ofother characteristics that affect only the basic lift dis-tribution. Experiment shows that this deduction isapproxim
40、ately correct for wings with well-roundedtips. For such wings, the additional rift distribution isgiven as a function of the plan form and _spect ratioin terms of the additional lift coefficients eZal, that is,the section additionM lift coefficients for a wing liftcoefficient of 1. The lift distribu
41、tion for any wing isthen found in terms of the wing lift coefficient Cs, thebasic lift coefficient css, and the additional lift coeffi-cient cz_,le,o=%+Q, e_,. (1)GENERAL PROCEDUREMONOPLANEIt is advisable first to choose a backward fore-and-aftreference _xis x usually parallel to the reference axis,
42、 orthrust line, of the airplane and an upward z axis per-pendicular to it. (See fig. 1.) Upward and backwardair forces and distances are thus considered positive.Air-force components along these axes are then ex-pressed at each section of the wing bydX=c_ _ c dy (2)and dZ=c_ q c dy (3)where X and Z
43、are the components of air load along theaxes, and Cx and c_ are determined from cz0 and theknown characteristics and attitude of each airfoil sec-tion. The pitching moment about the origin contrib-uted by each section isdM=c,_ q c2 dy+c_ q c z dy-c_ q c x dy (4)where x and z are distances measured f
44、rom the originto the aerodynamic center of the airfoil section (seetable I and appendix B) and the signs of the terms treso taken that stalling moments are positive.,22Sect oncenter- 12Yz_-WFIaUr_E t.-Airplane drawing and balance diagram.Thus far the origin has been arbitrarily chosen. If,with this
45、arbitrarily chosen origin, the coordinates z .and z. of the aerodynamic center of the entire wing(fig. 1) are found, the origin of coordinates may thenbe moved to this point and from equation (4) theremay be determined a value of ll/L,._./fl that has sensiblythe same value for all flight conditions.
46、Aerodynamic center and additional lift distribution.-For the purpose of finding the aerodynamic center ofthe wing, it is necessary to consider only the additionMdistribution. In fact, the aerodynamic center of thewing may be considered as the eentroid of all the addi-tional loads. For wings with lin
47、ear taper and roundedtips, values of L_, giving the load distribution for Cc= 1,may be found from table II for various sections alongthe span. The values of L_ were derived as outlined inreference 2. The corresponding values of cz,_ for varioussections along the span are found from the relationLaSc_
48、=-eb-. The corresponding values of Cao at eachProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-THE PREDICTION OF AIR FORCES AND THEIR DISTRIBUTION ON WINGSsection are calculated using the method indicated infigure 2 or, if the profile-drag polar curve
49、 for the sectionis available, they may be read from it. ThenCxal-Cdo COS Oza-Cla 1 sin 0, (5)aud%:-ct_: cos O_+c_ o sin 0_._ (6)in which 0 :-c_“i-L_ ao“ c%-._; ao, the section lift-curveslope, and a_0, the angle of attack of zero lift, are givenin table I; and i is the incidence of the chord at eachsection with respect to the x axis036.032028_ .0201.012008.004Z ./-0 .I .2 .3 .d .S .6 .7 .8 ._
