1、NATIONAL ADVISORY COMMITTEEFOR AERONAUTICSREPORT No. 634CALCULATION OF THE CHORDWISE LOADDISTRIBUTION OVER AIRFOIL SECTIONS WITH PLAIN,SPLIT, OR SERIALLY HINGED TRAILING-EDGE FLAPSBy H. JULIA_ ALLEN1938For sale by the Superintendent of Documents, Washington, D. C. o . . _ . Price 10 centsSubscriptio
2、n price, $3 per yearProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-W,g,m,I,-Sw,G.b,_g,b_v,q,L,D,Do,DoDr,c,R,AERONAUTIC SYMBOLS1. FUNDAMENTAL AND DERIVED UNITSLength Time Force_ .lSymboltF /Power : _Speed_ PvMetricUnitmeter second : weight of 1 kilog
3、ram .Abbrevia-tionmskg/!horsepower (metric) . r)kilometers per hour k.p.h.meters per second . _ m.p.s., EnglishUnitfoot (or mile) .second (or hour) .weight of 1 pound_ _“_horsepower .miles per hour _feet per,second IIAbbrevia-tionft. (or mi.)sec. (or hr.)lb.hp.m.p.h.f.p.s.2. GENERAL SYMBOLSWeight-ra
4、gStandard acceleration of gravity-9.80665m/s 2 Or 32.1740 ft./see. 2WMass =gMoment of inertia-ink 2. (Indicate axis ofradius of gyration k by proper subscript.)Coefficient of Viscosity3. AERODYNAMIC SYMBOLSv, Kinematic viscosity0, Density (mass per unit volume)Standard density of dry air, 0.12497 kg
5、-m_-s 2 at15 C. and 760 mm; or 0.002378 lb:-ft. -4 sec. 2Specific weight of “standard“ air, 1.2255 kg/m s or0.07651 lb./cu, ft.AreaArea of wingGapSpanChordAspect ratioTrue air speed_ . 1 T?- 2Dynamic pressure-_p_absolute coefficient CL_Lift,J_DDrag, absolute coefficient CD-_-_-SDoProfile drag, absol
6、ute coefficient CD0=_GInduced drag, absolute coefficient _-qSParasite drag, absolute coefficient CD_-_Cross-wind force, absolute coefficient Cc,-_SResultant forceiw,it,O,V1I.tCP_0,Olo,Angle Of setting of wings (relative to thrustline)Angle of stabilizer setting (relative to thrustline)Resultant mome
7、ntResultant angular velocityReynolds Number, where l is a linear dimension(e.g., for a model airfoil 3 in. chord, 100m.p.h, normal pressure at t5 C., the cor-responding number is.234,000; or for a modelof 10 cm chord, 40 m.p.s., the correspondingnamber is 274,000)Center-of-pressure coefficient (rati
8、o of distanceof c.p. from leading edge to chord length)Angle of attackAngle of downwashAngle of attack, infinite aspect ratioAngle of attack, inducedAngle of attack, absolute (measured from zero-lift position)Flight-path angleProvided by IHSNot for ResaleNo reproduction or networking permitted witho
9、ut license from IHS-,-,-REPORT No. 634CALCULATION OF THE CHORDWISE LOADDISTRIBUTION OVER AIRFOIL SECTIONS WITH PLAIN,SPLIT, OR SERIALLY HINGED TRAILING-EDGE FLAPSBy H. JULIAN ALLENLangley Memorial Aeronautical Laboratory74938-38-1Provided by IHSNot for ResaleNo reproduction or networking permitted w
10、ithout 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 scientificstudy of the problems of flight (U. S. Code, Titl
11、e 50, Sec. 151). Its membership 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, Sc. D., Chairm
12、an, Executive Committee,Chief, 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
13、 States Navy,Chief, Bureau of Aeronautics, Navy Department.HARRY F. GUGGENHEIM, M. A.,Port Washington, Long Island, N. Y.SYDNEY M. KIAUS, 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, D
14、epartment of Commerce.AUGUSTINE W. ROBINS, Brigadier General, United StatesArmy,Chief Matdriel Division, Air Corps, Wright Field,Dayton, Ohio.EDWARD P. WARNER, So. D.,Greenwich, Conn.OSCAR WESTOVER, Major General, United States Army,Chief of Air Corps, War Department.ORVILLE WRIGHT, Se. D.,Dayton, O
15、hio.GEORGE W. LEWIS, 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
16、FOR AIRCRAFT AIRCRAFT ACCIDENTSAIRCRAFT MATERIALS INVENTIONS AND DESIGNSCoordi_mtion of Research Needs of Military arm Civil A i_iationPreparation of Research Progrant,_Allocation of ProblemsPrevention of DuplicationConsideration of InventionsLANGLEY MEMORIAL AERONAUTICAL LABORATORYLANGLEY FIELD, VA
17、.Unified conduct, for all agencies, efscientific research on the fundamentalproblems of flight.11OFFICE OF AERONAUTICAL INTELLIGENCEWASHINGTON, D. C.Collection, classification, compilation,and dissemination of scientific and tech-nical information on aeronautics.Provided by IHSNot for ResaleNo repro
18、duction or networking permitted without license from IHS-,-,-ERRATATECHNICAL REPORT _10. 684CALCULATI0hT OF THE CHORDWISE LOADDISTRIBUTI0)T OVER AIRFOIL SECTIONS WITII PLAIN,SPLIT, OR SERIALLY HINGED TRAILING-EDGE FLAPS.Page 3, legend for figure 5:Change the flap deflection from “30 o“ to “50 .Page
19、3, legend for figure 6:Change the flap deflection from “50 “ to “_0 .Page 4, column 2, line 58:Change “figures 5 and“ to “figures 6 and“.Page 13, table II, third line of heading of last column:Insert “100“ before r,Zc/C,.Provided by IHSNot for ResaleNo reproduction or networking permitted without li
20、cense from IHS-,-,-REPORT No. 634CALCULATION OF THE CHORDWISE LOAD DISTRIBUTION OVER AIRFOIL SECTIONSWITH PLAIN, SPLIT, OR SERIALLY HINGED TRAILING-EDGE FLAPSBy H. JULIAN“ALLEN-SUMMARYA method is presented for the rapid calculation of theincremental chordwise normal-force distribution over anairfoil
21、 section due to the deflection of a plain flap or tab,a split flap, or a serially hinged flap. This report is in-tended as a supplement to N. A. C. A. _leport No. 63I,wherein a method is presented for the calculation of thechordwise normalzforce distribution over an airfoil withouta flap or, as it m
22、ay be considered, an airfoil with flap (orflaps) neutral.The calculations are made possible through the corre-lation, by means of thin-airfoil theo_y, o numerous exper-imental normal-force distributions. The method enablesthe determination of the form and magnitude of the incre-mental normal-force d
23、istribution to be made for an airfoil-flap combination for which the section characteristics havebeen determined.A method is included for the calculation of the flapnormal-force and hinge-moment coefficients without neces-sitating a determination of the normal-force distribution.INTRODUCTIONThe gene
24、ral importance of airfoils equipped withtrailing-edge flaps has promoted both experimentaland theoretical determinations of the chordwise dis-tribution of normal force over such surfaces in an effortto increase the structural efficiency of their design.The theoretical investigations have been made m
25、_derthe assumption that the fluid viscosity is negligiblysmall. This assumption must be made, for the presentat least, in order that the problem may be analytic:fllyhandled. Unfortunately, as experiments have shown,viscosity clearly is not a negligible factor in this problemand, consequently, the th
26、eory is not able to predictadequately either the magnitude of the incrementalnormal force brought about by the deflection of theflaps or the nature of the chordwise distribution of thisincremental normal force.On the other hand, the large number of variablesinvolved in the problem makes it too diffi
27、cult to developan adequate method, applicable in the general clse, forthe calculation of the incremental normal force andthe incremental normal-force distribution from theexperimental pressure-distribution measurements thathave been made.In this report a method is developed for the calcula-tion of t
28、he incremental normal-force distribution dueto the deflection of the flap based upon the results ofexperimental investigations; the theoretical relation-ships are used as a basis for the coordination of theexperimental observations. Employment of exper-imentally- determined airfoil section character
29、isticsmakes it possible, moreover, to obtain a distributio_consistent in magnitude with that obtained by exper-iment. The method has been made applicable to anairfoil section equipped with a plain flap or tab, a splitflap, or a serially hinged flap. This report is intendedas a supplement to referenc
30、e 1, wherein a method,similar in its details of development, is presented forthe calculation of the chordwise normal-force distribu-tion over an airfoil section without a flap or, as it maybe considered, an airfoil section with flap (or flaps)neutral.In order to facilitate the employment of this met
31、hod,the report has been divided into two sections:I. The Derivation of the Method.II. The Application of the Method.In the derivation, Glauerts theoretical chordwise liftdistribution is discussed and the empirical alteration ofthe theory is treated. In addition, the developmentof the requisite equat
32、ions for the determination of themagnitude of the distribution from force-test results isgiven. In the application, the general procedure to befollowed in using this method either for airfoil sectionswith plain or split flaps or for airfoil sections withserially hinged flaps is given in concise form
33、 along withan illustrative example. The mathematical derivationof the theory is given in the appendix.I. THE DERIVATION OF THE METHODGlauert (references 2 and 3) has treated analyticallythe problem of the symmetrical airfoil with a plainflap, assuming the airfoil to be of infinitesimal thickness.The
34、 thin-airfoil theory is treated in the appendix ofthis paper. It is shown that the incremental lift dis-tribution or, as it will be regarded, the incrementalnormal-force distribution due to the deflection of aflap may be considered, for convenience, to be com-posed of two component distributions: (a
35、) the incre-1Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2 REPORT NO. 634_-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSmental additional distribution Pus, and (b) the incre-mental basic distribution Pbs. The incremental addi-tional distribution is
36、, in form, independent of theflap-chord ratio and does not contribute to the quarter-chord pitching moment, whereas the incremental basicdistribution is, in form, dependent upon the flap-chordratio and is responsible for the entire incrementalquarter-chord pitching moment due to the deflectionof the
37、 flap.The theoretical additional distribution, as given bythe thin-airfoil theory (appendix, equation (A-17), isshown by the dotted curve in figure 1. Since the incre-0 .I .2 .3 .4 .5 .6 .7 .8 .,9 LOx/cFIGURE 1.-AdditionM normM-force distributions.mental additional distribution due to the deflection
38、 ofthe flap is identical in form with the additional dis-tribution for the airfoil with flaps neutral, the experi-mentally determined additional distributions given inreference 1 will be used for this method. The fourclasses of additional distribution presented in reference1 are given in table I and
39、 figure 1 (solid lines) of thepresent report. A key to the class of distribution to beemployed for 22 airfoils is given in table II of the presentreport. (The letters A, B, C, D, and E in column“Classification PD _ designate the class of distribution.)The remaining airfoil characteristics for these
40、airfoilsare given in table I of reference 1.T.he shape of the theoretical incremental basic liftdistribution (appendix, equation (3_-19) or, of whatis considered to be its equivalent, the incremental basicnormal-force distribution is shown by the dotted linesof figures 2 to 6. Proceeding rearward fr
41、om the lead-ing edge of the airfoil, the pressure difference, which iszero at the leading edge, increases rapidly at first, thenmore slowly and, as the hinge is approached, it increasesmore and more rapidly until the pressure differencebecomes unlimited at the hinge point, where the airfoilradius of
42、 curvature is zero. Rearward from the hinge,the pressure difference drops rapidly at first, then moreslowly, and finally more rapidly again to zero pressuredifference at the trailing edge. With a hinge radius ofcurvature other than zero, the basic pressure differenceat the hinge becomes finite.m17/1
43、oon-lZ-iZ _-il0 ./ .2 .3 .4 .5 .6“ .7 .8 .9 /.0z/ctTmUIIE 2,-1asie incremental normal-force distribution, R.A.F. 30 section; 0.10c1)IMu flap at _=10 .Numerous comparisons between experimental (madewith 0.10c, 0.20c, and 0.30c plain-flap airfoils with flapdeflections ranging from 10 to 60 ) and theor
44、eticalincremental basic normal-force distributions (P_dc_b_)for plain-flap airfoils generally showed good agreementahead of the hinge but poor agreement behind thebinge, particularly for large flap angles. This result isto be anticipated for ahead of the hinge favorablepressure gradients retard the
45、growth of the boundarylayer and, conversely, back of the hinge adverse gradi-ents accelerate the growth of the boundary layer. Anexamination of these comparisons, however, disclosedthat, for all three flap-chord ratios at any one given flapdeflection, the ratio of the experimental basic normalProvid
46、ed by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TtIE CHORDWISE LOAD DISTRIBUTION OVER AIRFOIL SECTIONS WITH FLAPS 3200 ./ .2 .,2 .4 .5 .6 .7 .8 .,9 /.0x/cFIGURE 3.-Basic incremental normal-force distribution. 2. A. le. 30 section; 0.20cplain flap at 5=10 .
47、0 ./ .2 .3 .4 .5 .G .7 .8 .9 /.0x/CFIGURE 4.-Basic inerementM normal-force distribution. Clark Y section; 0.3plain flap at _=_I5 ._ o, /P0 ./ .2 .3 ,4 ,5 .6 ,7 .8 .,9X/CFZGURE5.-B_sie incremental normal-force distribution.plain flap at 6=a0 .R. . ?. a0 section; 0.20cProvided by IHSNot for ResaleNo r
48、eproduction or networking permitted without license from IHS-,-,-REPORT NO. 634-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSforce to the theoretical was practically constant forcorresponding points along the airfoil. That is, if fl isdefined asCn b_/ exp.fl=(Pba_ (1) c,_J theor.it has been found that values of 5 computed from experi-mental pressure-distribution measurements made over0.10c, 0.20c, and 0.30c plain-flap airfoils with the sameflap deflection (references 4 and 5), when plotted in thecurves of fl against both _ (points ahead of the2form ofhinge) and 1- (x/c) (points back of
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