1、:.-, .-., : -”,l .+ . .ADVISORY COMMITTEE FOR AERONAUTICS igq *”T.No a71 708-A SIMPLIFIED METtiOD FOR THE CALCULATION OFAIRFOIL PRESSURE DISTRIBUTIONBy H. Julian AllenLangley Memorial Aeronautical Laboratory- -wahigtonMay 1939.Provided by IHSNot for ResaleNo reproduction or networking permitted with
2、out license from IHS-,-,-.,31176014165352.uNATIONAL ADVISORY COMti.ITTEZl.-TECHNICAL NOTE NO,- -A SIMPLIFIED METHOD FOR THE-FOR AERONAUTICS*708CALCULATION OFAIRFOIL PRESSURE DISTRIBUTIONBy H. Julian AllenSUMMARYoA method is presented for the rapid calculation ofthe pressuredistribution over an airfo
3、il section whenthe normal-force distribution and the pressure distribu-tion over the lbase profile” (i.e., the profile of thesame airfoil were the camber line straight and the re-sulting airfoil at zero angle of attack) are known. Thisnote is intended as a supplement to N,A.C.A. Reports NOS.631 and
4、634 wherein methods re presented for the calcu-lation of the normal-force distribution over plain andflapped airfoils, respectively, but not of the pressureson the individual surfaces.Base-profile pressure-coefficient distributions forthe usual N.A.C.A. family of airfoils, which are alsosuitable for
5、 several other commonly employed airfoils, areincluded in ta%ular form. With these tabulated base-profile pressures and the Computed normal-force distribu-.tions, pressure d,istri%utions adequate for most engineer-ing purposes can %e o%tained.INTRODUCTIONA method is given in reference 1 for computin
6、g thechprdwise pressure distribution over both the upper andthe lower surfaces of an airfoil. In this method, a per-=feet nonviscous fluid was assumed and, consequently, theagreement %etween the integrated forces and moments andthose obtained from experimental observations was in ,manyF cases inadeq
7、uate. In the work reported in reference 2,*,the effect of viscosity was accounted for by an adjustment of the mean camber line of the airfoil and the agreementd“ was improved.for practicalereii adequatoBoth methods, however, are tool aborioususe even though the results might he consid-for design pur
8、poses.iProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.2 N.A.C.A. Technic%l Note No. 70!3A subsequent analysis of theory and experimental data(references % and 4) resulted in a series of charts where-by the normal-force distri,lmtions, %ut not the p
9、ressures Ion the individual surfaces, could be obtained for ordinaryairfoils and airfoils with flaps. In this method, themagnitudes of the various component distributions that areadded to obtin the normal-force distribution are deter-mined from experimental force and moment coefficients.When the cal
10、culated normal-force distribution is inte-grated, it then yields normal-force and moment coeffi-cients that must agree in magnitude with the correspondingexperimental coefficients.The present paper, which is.a supplement to refer-ences 3 and 4, gives a method of utilizing the calculatednorml-force d
11、istribution to obtain the pressures on theindividual surfaces of an airfoil. Again, the resultingpressure distributions when integrated must yield normal-force and moment coefficients that agree with those ob-tained by experiment.This method requires, in addition to a knowledge ofthe chordwise norma
12、l-force distribution over the airfoilsection (as may he obtained from references 3 and 4), thepressure distribution over the *base profile! of the air-foil section (i.e., the profile of the same airfoil werethe camber line straight and the resulting airfoil at zeroangle of attack). The method is app
13、licable, to date, tonormal airfoils and to airfoils with plain trailing-edgeflaps . :The base-profile pressure distributions for theN.A.C.A. famiy of airfoils (as well as for the Clark YAnd the Gttingen 398) calculated by the method of refer-ence 1 are given in this report.THEORY OF THE METHODLet it
14、 be assumed that the chordwise distribution ofthe filaments of the bound vortices within an airfoil sec-tion are located along the mean camber line and that thecurvature of the mean camber line Ys slight so that theinduced velocities on the upper and the lower surfaces atany given distance, x, behin
15、d the leading edge of theairfoil are equal in magnitude but opposite in sign.The velocities on the upper and the lower surfaces ofthe airfoil at any point, x, behind the leading edge are,respectively,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-/*
16、.i.N a71A a71“C.A .,N9,$e, ”No.?, 3,., “,where Au is the inbe the velocity thatthe point x %ehindconditions. ,.If pf be desion, the base profile,Uu =:“!.,:” ;UL =.,“duce dthethe.,gnatethen,u + Aq, :. .,.:1.,.t - Au, velocitybass profleading ed as the9 by Bern1k,.Ji?:dgetsurOul.,(“”(1is assumed texpe
17、rience athe same str)otearn.:(I Urwouldunderfhce plils e%.ressure atquation,xPf:,pua-2: P(u)a.-. -2“r, :/.:d+.;.,.:-L. .Lfitrea.-orHence()Ut pf=q-q” -.,-u? =uJi- Pfstream, velocity, and/q, where q is thquations (1) and (2).:,!-$2):.essurec presu-=-uwhere U iscoefficient,r!sthePfng e1?esJ%sur”e.co,mb
18、ini gi vesUu wx-:-.u/-i - Pf-t- +(z)TJ- Au!l?hepressureq on the upper and, the lowerairfoil at x are then, respectively,surfac ofpuu 2-2,P“z AU2 the resultingpressure dietrihutions are shown in figures 3 to 6. The*Provided by IHSNot for ResaleNo reproduction or networking permitted without license f
19、rom IHS-,-,-m. N.A. C,A, Technicml Note I?oti-.708, 5.N.A.C.A. 6512 airfoi,l is representative of the more highlycam%ered airfoils;. tiheN and the N.A.C.A. 4412, of the more commonly em-ployed airfoils. The agreement Q.etween the. theoreticaldistributions and those clculate”d by equations (6) forthe
20、 seeal airfoils investigated is,good, as shown by thedistributions in figures 1 to 6. ,a71 ,“Therithis method is applied to the calculation ofairfql p“ressure distributions, the accuracy of the calcu-lation tiill depend principally on:,(1) The accuracy of the calclation of the chord-,wise normal-fo”
21、rce distribution over the air-.,foil.,(2) The accuracy of the base: profile pressure dis-tribution,(3) !I%e thickness of the boundary layer over theairfoil.The close agreement hetee the theoretical pressuredistributions of figures 1 to 6 shows that, “for airfoilsof normal profile, thickness, and ca”
22、mber, equations (6) are sufficiently accur,ate. For an airfoil with a plain Iflap deflected through a larg, angle, the basic assumptionthat the ourvature of the mean Camber line is small is dis-regarded so that the accurac,y ofequations (6) is accord-ingly less. The same statement is, of course, tru
23、 forhighly cambered airfoils. Again, the assumption that thebound vorticity may be considerd as distributed along themean camber line, although it has been shown to be per-missible for airfoils of normal thickness, will probablybe less accurate for the thicker profiles. ,For plain airoils, the accur
24、acy of the method forthe calgulati.on of the normal.force distribution given inreference 3 is, as a rule, well itin 5 percent; for. air-fois tii:h flaps, the accuracy of the method given inreference 4 is, as a ru.e$ within 1“0percent of the truenormalforce distribution.The base-profile pressure d.is
25、trilxition calculated bythe method of reference 1 will probably be sufficientlyaccurate for design purposes for all base profiles in com-mnn use. The base-proflq pressure distributions for.theN.A.C.A. family of airfoils, as well as for the Clark Y “, ,.Provided by IHSNot for ResaleNo reproduction or
26、 networking permitted without license from IHS-,-,-.6 N. A. C.A. TechnicalNote No. 708and the !lttingen 398, were calculated by the method ofreference 1 and are given in table I.That the thickness of the %oundary layer is a factorconcerning the accuracy of this method is apparent whenit is sen that
27、not only is the base profile effectivelychanged. when the boundary layer is thickened hut also thatthe effective shape of the mean ce,mbr line and thereforethe effective position of the bound vortices are alteredwhen the boundary layer is thicker on one surface of theairfoil than the other (as for e
28、xample when the angle ofmaximum lift is approached). This inaccuracy, which af-fects the distribution of pressure between the upper andthe lower surfaces of the.airfoil, exists in spite of thefact that the effe of the %oundary layer on the normal-force distribution is partly taken care of by the met
29、hodsof references 3 and 4.A consideration of the several factors would lead oneto expect that the method would be very accurate for thinairfoils with small amounts of camber and would be lessaccurate for thick highly cambered airfoils and particu-larly for airfoils with ordinary trailing-edge flaps.
30、 Thatthese expectations are fulfilled is shown in figures 7 to14, where the computed. and the experimental pressure dis-tributions for several airfoils (one with a flap) aregiven. In every case, the normal-force distributions weredetermined by the methods of references 3 and 4 and thebase-profile pr
31、essure d.istribution given in table I wereused. The experimental pressure distributions over theN.A.C.A. 4412 airfoil (figs. 7 to 10) were obtained fromreference 2 and those over the N.A.C,A. 23012 (figs. 11 to14) were obtained from reference 5.One limitation should be noted although it is of neg-li
32、gible importance. Equations (6) cannot be used to pre-dict the pressure at the most forward point of the airfoilbecause at this point the slope of the airfoil profile isinfinite and, even though the normal force approaches zero,the solution must, of course, be indeterminate at thispoiht. The nose po
33、int should therefore be omitted frompractical calculations.CONCLUSIONSWhen the base-profile pressure-coefficient distribu-tions given in table I and the normal-force distributionscomputed by the methods of references 3 and 4 are used,. .,.a71a15bProvided by IHSNot for ResaleNo reproduction or networ
34、king permitted without license from IHS-,-,-N.A.C.A. Technical Note No. 708 7the pressure distributions calculated by the method of thisnote are adequate for most engineering purposes. The com-puted pressure distributions not onlY agree in form withexperiment but the integrated normal forces and mom
35、entsagree in magnitude with experiment. “Langley Memorial Aeronautical Laboratory.National Advisory Committee for Aeonautics,Langley Field, Va. ,.April 3, 19X9,.REFERENCES.,*.Theodorsen, Theodore: Theory of Wing Sections of Arbi-trary Shape. T.R, No. 411, N.A,C.A., 1931.Pinkerton, Robert M. : Calcul
36、ated and Measured Pres-sure Distributions over the Midspan Section ofthe N.A.C,A.,4412 Airfoil. ToR. No. 563, N.A.C.A. ,1936.Jacobs, Eastman N., and Rhode, R. V.: Airfoil Sec-tion Characteristics as Applied to the Predictionof.Air Forces and Their Distribution on Wings,T.R. 0, 631, N.A,(l.A. , 19384
37、. Allen, H. Julian: Calculation of the Chordwise LoadDi-stri%ution over Airfoil Sections with Plain, Split,or Serially Hinged Trailing-Edge Flaps. T.R. T,o.634, N.A,C.A. , 193s.5. Wenzinger, Carl Je, and Delano, James B.: PressureDistribution over an N.A.C.A. 23012 Airfoil witha Slotted and a Plain
38、Flap. T.R. No. 633, N.A,C.A. ,1938.4-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-“,./,-4./*.a1*“a71 -N, A. C.A. Technical Note No. 708.-, ALE IVALUES OF (1 - p) FOR N,A,C.A. YAMILY OY AIRFOIL SECTIONS- -Station(pe;ent-,1,252.557.51015202530354945
39、50556065707580859095- -6.-.1,1181.1901.2191.2221.2%1.2091.1921,1801.1651.1501.1371.1221.1091.0941.0811.0701,0561.0411.0211.002.981.949.-,-.91.0751.2321.3131.3J01.3301,3761.2981.2771.2561,2331.2101.1891.1671.1461.1251.1041.0821.0591.0321.002.970.922-,Thi . .A *-4-s0“o .2 .4 .6 .8 1.0XlaFigure 7.- Prm
40、rwm distribution. E.A.O.A. 4423 sirfniU,a,-tto.-110 .a .4 .6 .8 1.0x/oPigure 8.- p tfibuion. X.A.O.A. 441a airfoil;.X/OTiglm$.- Prca4y u,-.0 .9 .4 . .6 .8 1.6XIcFigure 3,0.-Promd,. .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-M ,. a71-11)- O- % A._- - - - -L -. k 2 d0 .2 .4 .6 .8 1.0ignre14.- Promure diatribution?.A.O.A.2S012 tirfoil tith20-percent-ohordP3.eAnflaw d , 0; 5 , “.s,IProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
