THEORY OF WING SECTIONS Including a SummaryofAirfoil DataBy IRA H. ABBOTTDIRECTOR OF AERONAUTICAL AND SPACE RESEARCH NATIONAL AERONAUTICS AND SPACE ADMINISTRATION and ALBERT E. VON DOENHOFF RESEARCH ENGINEER. NASA DOVER PUBLICATIONS, INC. NEW YORK Copyright ' ~ 9 91959 by Ira H. Abbott andAlbertE.von Doenhoff.AllrightsreservedunderPanAmericanandInter-nationalCopyrightConventions.PublishedinCanadaby General PublishingCom-pany, Ltd., 30 Lesmill Road, Don Mills, Toronto,Ontario.This Dover edition, first published in1959. is anunabridged and corrected republication of the firstedition fint published in 1949bythe McGraw-HillBook Company, Inc. This Dover edition includes anew Prefacebythe authors.Stand4,-dBook.Number: 486-60586-8 Library01 CongressCatalogCardNumber:60-1601 ManufacturedintheUnitedStatesofAmerica Dover Publications, Inc. ISOVarlekStreet New York, N.Y. 10014 PREFACETODOVEREDITION The newedition ofthis book originallypublishedin1949results fromthe continuingdemandforaconcisecompilationof 'thesub-sonicaerodynamic characteristics ofmodernNACAwingsections togetherwithadescriptionoftheirgeometryandassociated theory.Thesewingsections,ortheirderivatives,continuetobe themostcommonlyusedonesforairplanesdesignedforboth subsonicandsupersonicspeeds,andforapplicationtohelicopter rotorblades,propellerblades,andhighperformancefans. Anumber oferrorsinthe originalversionhavebeencorrected in the present publication.Theauthors are pleased toacknowledge their debt to the many readers who calledattention tothese errors. Sinceoriginalpublicationmanynewcontributionshavebeen madetotheunderstanding ofthe boundarylayer,themethodsof boundary-layer control, and the effectsof compressibility at super-criticalspeeds.Propertreatmentofeachofthesesubjectswould requireabookinitself.Inasmuchasthesesubjectsareonly peripherallyinvolvedwiththemainmaterialofthisbook,and couldnot,inany ease,be treated adequatelyinthis volume,it was consideredbesttoexpediterepublicationbyforegoingextensive revision. IRAH.ABBOTT CHEVYCHASE,MD.ALBERTE.VONDOENHOFF June,1958 v PREFACE In preparing thisbook an attempt hasbeenmadetopresent concisely the most important and usefulresultsofresearchonthe aerodynamics of wingsectionsatsuberiticalspeeds.Thetheoreticalandexperimental resultsincludedarethosefoundbytheauthorstobethemostuseful. Alternative theoretical approaches tothe problem and many experimental datahavebeenrigorouslyexcludedtokeepthebookatareasonable length.Thisexclusionofmanyinterestingapproachestotheproblem prevents any claim tocomplete coverageofthe subject but should permit easier useofthe remaining material. The book is intended to serve as areference for engineers,but it should alsobeusefultostudentsasasupplementarytext.Toalargeextent, thesetwousesarenot compatibleinthat they requiredifferentarrange-mentsanddevelopmentsofthematerial.Considerationhas' beengiven totheneedsofstudentsandengineerswithalimitedbackgroundin theoreticalaerodynamicsandmathematics.Aknowledgeofdifferential andintegralcalculus and ofelementarymechanicsispresupposed.Care hasbeentaken inthetheoreticaldevelopmentstostatetheassumptions and toreview briefly the elementary principles involved.Anattempt has beenmadetokeepthemathematicsassimpleasisconsistentwiththe difficulties ofthe problems treated. Thematerial, presentedislargelytheresultofresearchconductedby theNationalAdvisoryCommitteeforAeronauticsoverthelastseveral years.Althoughtheauthorshavebeenprivilegedtoparticipateinthis research,theircontributionshavebeennogreaterthanthoseofother membersoftheresearchteam.Theauthorswishtoacknowledgees-pecially the contributions of Eastman N.Jacobs, who inspired and directed muchoftheresearch.Theauthorsarepleasedtoacknowledgetheim-portantcontributionsofTheodoreTheodorsen,I.E.Garrick,H.Julian Allen,Robert M.Pinkerton,John Stack,Robert 1'.Jones,and the many otherswhosenamesappearinthelistofreferences.Theauthorsalso wishtoacknowledge the contributions tothe attainment of low-turbulence air streams made byDr. Hugh L.Dryden and his former coworkers at the National Bureau of Standards, and toexpresstheir appreciation forthe in-spiration and support of the late Dr.GeorgeW.Lewis. IRAH.ABBOTT ALBERTE.VONDOENHOFF CHEVYCHASE,~ { July,1949 vii CONTENTSPREFACE TO DOVER EDITION . . . . . . . . . . . . v PREFACE. . . . . . . . . . . . . . . . . . . . . . . vii 1. THE SIGNIFICANCE OF WING-SECTION CHARACTERISTICS .. 1Symbols. The Forces on Wings. Effect of Aspect Ratio. Application ofSection DatatoMonoplaneWings: a.BasicConceptsofLifting-lineb.SolutionsforLinearLiftCurves. c. GeneralizedSolution. ApplicabilityofSection Data.2. SIMPLE TWO-DIMENSIONAL FLOWS31Symbols. Introduction. ConceptofaPerfectFluid. Equationsof Motion.DescriptionofFlow Patterns. SimpleTwo-dimensional Flows: a.UniformStream. b.Sources and Sinks. c.Doublets. d. Circular Cylinder in aUniformStream. e. Vortex. f.CircularCylinderwith Circulation.3. THEORY OF WING SECTIONS OF FINITE THICI{NESS . 46Symbols.Introduetiou. Complex Variables. ConformalTransformations.Transformationofa Circle into&WmgSection. FlowaboutArbitraryWingSeetiODS. EmpiricalModificationoftheTheory. Design ofWing Sections.4. THEORY OF TJIIN WING SECTIONS . . . . . . . . . . . . 64 Symbols. BasicConcepts. AngleofZeroLiftand PitchingMoment. De-sign of Mean Lines. EngineeringApplicatioD8ofSection Theory.5. THE EFFECTS OF VISCOSITY . . . . . . . . . . . . . . 80 Symbols. Concept of Reynolds Number and Boundary Layer. Flowaround Wmg Sections. Characteristics of the Laminar Layer. LaminarSkinFrietion. Momentum Relation. Laminar Separation. TurbulentFlow inPipes. TurbulentSkin Friction. Calculation of Thickness of theTurbulent Layer. Turbulent Separation. Transition from Laminar toTurbulentFlow. Calculationof Profile Drag. Effect of MachNumberonSkin Friction.6. FAMILIES OF WING SECTIONS III Symbols. IDtroduction. MethodofCombiningMean Linesand ThicknessDistributions. NACAWingSections:a.ThicknessDistributions.b.Mean Lines. c. Numbering System. d.Approximate TheoreticalCharacteristics. NACA Five-digit Wing Sections: a.Thickness Distribu-tions. b.MeanLines. c.NumberingSystem. d. ApproximateTheoreticalCharacteristics. ModifiedNACAFour- andFive-digitSeriesWingSections.NACA l-SeriesWing Sections:Q.Thickness Distributions. b. MeanLines.ixCONTENTSx c.NumberingSystem.d.ApproximateTheoreticalCharacteristics. NACA6-SeriesWingSections: G.Thickness Distributions.b.Mean Lines. c.NumberingSystem.d.ApproximateTheoreticalCharacteristics. NACA7-8eriesWingSections.SpecialCombinationsofThicknessand Camber. 7.EXPERIMENTALCHARACTERISTICSOFWINGSECTIONS.124 Symbols.Introduction.StandardAerodynamicCharacteristics.Lift Characteristics:4.AngleofZeroLift.b.Lift-curveSlope.c.Lift.d.Effect of Surface Condition onLift Characteristics.Drag Charac-teristics:G.MinimumDragofSmoothWingSections.b.Variationof ProfileDrag withLift Coefficient.c.EffectofSurfaceIrregularitieson DragCharacteristics.d.UnconservativeWingSections.Pitching-moment Charncteristics. 8.HIGH-LIFTDEVICES.188 Symbols.Introduction.Plain Flaps.Split Flaps.SlottedFlaps: 4.De-scription of Slotted Flaps.b.Single-slotted Flaps.c.Extemal-airfoil Flaps. d.Double-slotted Flaps.Leading-edge High-lift Devices:a.Slats.b.Slots. c.Leading-edgeFlape.Boundary-layerControl.TheChordwiseLoad Distribution ovcr Flapped 'Ving Sections. 9.EFFECTSOFCOMPRESSIBILITYATSUBSONICSPEEDS....247 Symbols..Introduction.Steady Flowthrough a Stream Tube: 4.Adiabatic Law.b.Velocity of Sound.c.Bernoulli's Equation forCompressible Flow. d.Cross-sectional Areas and Pressures inaStream Tube.e.Relationsfor aNormalShook.First-order CompressibilityEffects:G.Glauert-Prandtl Rule.b.Effect ofMach Number onthe Pressure Coefficient.Flow' about WingSectionsatIIighSpeed:4.FlowatSubcriticalMachNumbers. b.Flowat SupercritiealNumbers..ExperimentalWingCharacteris-ticsatHighSpeeds:4.LiftCharacteristics.b.DragCharacteristics. c.Moment Characteristics.WmgsforHigh-speed Applications. REFERENCES300 I.Basic Thickness Forms.309 II.Mean Lines...382 I II.Airfoil Ordinates 406 IV.AerodynamicChnracteristies of\Ying Sections449 . CHAPTER 1THE SIGNIFICANCE O:F WING-SECTION CHARACTERISTICS1.1. Symbols.AaspectratioAn coefficients of theFourierseries for thespan-loaddistributionCDdragcoefficientCo, induceddra.g'"coefficientCLliftcoefficientCLmaxmaximumlift coefficientCAlpitching-momentcoefficient CJIoe pitching-momentcoefficient abouttheaerodynamic center D dragEJonesi' edge-velocity factor, equals ratio of the semi perimeter of the planformof thewing underconsiderationto thespanof thewing Ea factor (see Fig. 13) G a factor (see Fig. 14) Ha factor (seeFig. 15) J a factor (see Fig. 9) Llift L."additional"loadingcoefficient L, U basic"loadingcoefficient M pitchingmoment 8 wing areaVspeedX," longitudinaldistancebetween the aerodynamic centerof therootsection andtheaerodynamiccenterof thewing, positiveto the rearawing lift-curveslopea. effectivesectionlift-curveslope, 40/E Go sectionlift-curveslope acaerodynamiccenter b wingspan C wing chord c meangeometricchord,8/b c' meanaerodynamicchordCd sectiondrag coefficientCd, sectioninduced-dragcoefficientc, sectionliftcoefficientClel localU additional"sectionliftcoefficientforawinglift coefficientequaltounityCI.localU basic"sectionliftcoefficientsectionmaximumliftcoefficient Clmaxc. section-momentcoefficient c.... section-momentcoefficient abouttheaerodynamic center C. rootchord Cc tipchord 12THEORYOFWINGSECTIONS d. sectiondrag fa factor (seeFig. 8) ka spanwisestation lsectionliftZ. "additional"sectionlift It ",basic"sectionlift m seetionmoment ran even number of stations used in the Fourier analysis of the span-loaddistributionu a factor (seeFig. 10)va factor (seeFig. 11)tD a factor(seeFig. projected distance inthe plane of symmetry fromthewing reference pointto theaerodynamic centerofthewing section, measuredparallelto thechordof therootsection, positivetotherear71 distancealangthespanprojected distance in the plane of symmetry from the wing reference pointto theaerodynamic centerof thewing sectionmeasured perpendicu1U' to therootchord, positiveupwardex angleofattackact sectionangleofattacka. effectiveangle.ofattack eliangleofdownwash a,.sectionangleofattackfor zero lift a ...angleof zero liftofthe rootsection a. wing ang1e ofattack measuredfrom thechordof the rootsection0.:VV VV '/I 1\

./0.20 Drog'coefficiert,Co FIG.3.Polar diagrams forseven wings with aspect ratios of7to 1. ratio,whichisalsoplottedinFig.1.Thisratioincreasesfromzeroat zerolifttoamaximum value at amoderate lift coefficient,after whichit decreases relatively slowlyasthe angle ofattack is further increased. It isdesirableforthewingtohavethe smallestpossibledrag.Inas-muchasthehigh-speedlift coefficientisusuallysubstantiallylessthan thatcorrespondingto-thebestlift-dragratio,oneofthebestwaysof reducing the wingdrag is to reduce the wingarea.This reduction of area isusuallylimitedby considerationsofstalling speedormaneuverability. Theseconsiderationsaredirectlyinfluencedbythemaximumliftcoeffi-cientobtainable.Thewingshouldthereforehaveahighmaximumlift 6THEORYOFWING8ECTION8 coefficient.combined with low drag coefficients forhigh-speed and cruising flight.Thiscombination ofdesirable qualities can beobtainedonlyto a limited extentby asinglewingconfiguration.It isthereforecustomary to usesomeretractable devicesuchasflapstoimprove the maximum lift characteristics of the wing. 1.3.Effect ofAspect Ratio.Aspectratio is definedasthe ratio ofthe spansquaredtothewingarea(IJI/S),whichreducesto theratioofthe 1.4 1.2 1.0 .8 .. .. 0 -6 0 o ."\ c lA+ i"II' A -I--

oII 8tf,.,.a +=2 -I----lUd' 0=4 61 J:5 to e:6 ,,'" til:T-cl tI + G p9 o -.2 01020-Angleofoltock,a,(degteeS) FIG. 4.Lift coe8iciente asfunction ofaqle of attack, reduced toaspect ratio of 5. spantothe chordinthe caseof&rectangularwing.Earlywind-tunnel investigationsofwingcharacteristics showedthattheratesofchangeof the lift and drag coefficients with angleofattack werestronglyaffected bytheaspectratioofthemodel.Wingsofhighaspectratiowereob-served tohave higherlift-curve slopes and lowerdrag coefficients at high lift coefficients than wings oflow aspect ratio.The effect9aspect ratio onthe lift curve is showninFig.2.88 The wingsofvarious aspect ratios areshowntohaveaboutthesameangleofattackat zerolift,butthe slopeoftheliftcurveincreasesprograNivelywithincreaseofaspect 7THESIGNIFICANCBOFWING-8ECTIONCHARACTERI8TICS ratio.Theeffectofaspectratioonthedragcoefficientisshownin Fig.3.88 Although the drag coefficients for all the models of various aspect ratiosaresubstantially equalat zerolift,markedreductionsinthedrag 1.4 1.2 1.0 .8 0 -0 ~ A 0of 6... 0 D + A :C- I~ ~ 411+-20 a ~ -~ t A-3 o-4 c o -5 at I--til e-6 b e-7 ~ -J, 11 ~ '1) ft-A 0 0 .2 o -.2 .I.2 Drag coefficienfl Cd FIG. S.Polar diagramsreducedtoaspect ratio of S. coefficientoccurat thehigherliftcoefficients asthe8Bpectratioisin-creased. As aresultofsuchobservations,theLanchester-Prandtlwingtheory wasdeveloped.This theory shows that, forwings having ellipticalspan-wisedistributionsoflift,the following simpleexpressions relatethe drag 8 THEORYOFWINGSECTIONS coefficientsandanglesofattackasfunctionsofaspectratioatconstant lift coefficients ,CL2 (11)CD=CD+- ---(1.4)1["A'A = a+CL (-!.._!) a'(1.5)1["A'A whereCDanda'correspond,respectively,tothedragcoefficientand angle of attack (radians)ofawing of aspect ratio A'. Application of Eqs.(1.4)and(1.5)to reduce the data ofFigs.2and 3 to an aspect ratio of five results in the data of Figs.4 and 5.88 These figures showthatthecharacteristicsofawingofoneaspectratiomaybepre-dicted with considerable accuracy from data obtained fromtests of awing ofwidely different aspect ratio. Equations(1.4)and(1.5)may besimplified by the concept ofinfinite aspect ratio.If Cdand aoindicate the drag coefficientand angle ofattack ofawingofinfiniteaspectratio,the characteristicsofanellipticalwing ofaspect ratio Amay beexpressed as (1.6) (1.7) Awing ofinfinite aspect ratio wouldhave the same flow pattern inall planesperpendiculartothespan.Inotherwords,therewouldbeno componentsofflowalongthespan,andtheflowoverthewingsection wouldbetwo-dimensional,Infiniteaspectratiocharacteristicsareac-cordinglycommonlycalled"sectioncharacteristics.IIThesectionchar-acteristics are intrinsicallyassociatedwith the shape ofthe wingsections ascontrastedwith'lingcharacteristics,whicharestronglyaffectedby thewing plan form.The detailed study of wingsisgreatly simplifiedby tileconceptofwing-sectioncharacteristicsbecausewingtheoryoffersa method forobtaining the properties ofwingsofarbitrary plan formfrom asummation ofthe characteristics ofthe component sections. 1.4.ApplicationofSection nata toMonoplane Vmgs.a.Basic Con-ceptsofLifting-lineTheory.The simplestthree-dimensionalwingtheory is that based onthe concept of the lifting line. 88,In this theory the wing isreplacedbyastraight line.The circulationabout the wingassociated withtheliftisreplacedby vortexfilament.Thisvortexfilamentlies alongthe straight line;and,at each spanwise station,the strength ofthe vortex is proportional to the local intensity of the lift.According to Helm-holtz'stheorem,avortexfilamentcannotterminateinthefluid.The variation of vortex strength along the straight lineis therefore assumed to 9THESIGNIFICANCEOFWING-BECTIONCHARACTERISTICS resultfromsuperpositionofanumberofhorseshoe-shapedvortices,as shownin Fig.6.Theportionsofthevorticeslyingalongthespanare called the" bound vortices."The portions of the vortices extending down-stream indefinitely arecalledthe" trailing vortices." The effect of trailing vortices corresponding to a positive lift is toinduce adownwardcomponentofvelocity at and behind the wing.This down-ward component is calledthe Udownwash."The magnitude of the down-washat any section alongthe span is equaltothe sumof the effectsof all thetrailingvorticesalongtheentirespan.Theeffectofthedownwash FIG.6.Vortex pattern representing alifting wing. istochange the relative direction of the airstream overthe section.The sectionisassumedtohavethe sameaerodynamiccharacteristics with re-specttothe rotatedair stream asithasinnormaltwo-dimensionalflow, The rotation of the flow effectivelyreducesthe angle of attack.Inasmuch asthedownwashisproportionaltotheliftcoefficient,theeffectofthe trailingvorticesistoreducetileslopeoftheliftcurve.Therotationof the flow alsocausesacorrespondingrotationof the liftvector to produce adragcomponentinthedirectionofmotion.Thisinduced-dragcoeffi-cientvariesasthesquareoftheliftcoefficientbecausetheamountof rotation and the magnitude ofthe liftvector increasesimultaneously. The problem of evaluating the downwashat eachpoint is difficultbe-cause of the interrelation of the downwash,liftdistribution, and plan form. A comparatively simple solution was obtained byPrandtl'" foranelliptical lift distribution.Inthis casethe downwashis constant between the wing tips andthe induceddragislessthanthat foranyother type ofliftdis-tribution.Equations(1.6)and(1.7) give the relation between the section and wingcharacteristics foranelliptical lift distribution. b.SolutionsforLinearLift Curves.Glauert"appliedaFourierseries analysis tothe problemand developedmethods forobtaining solutions for wingsofany plan formand twist.Anderson 10appliedGlauert's methods 10 THEORYOFWINGSECTIONS to the determination ofthe characteristics ofwingswith awiderangeof aspectratioandstraighttaperandwithalinearspanwisevariationof twist.Andersonconsideredthe spanwiselift distribution forany typical wingto consistoftwoparts.Onepart,calledtheUbasicdistribution", isthe distribution that dependsprincipallyonthetwistofthe wingand occurs when the total lift ofthe wing iszero; it does not change with the angleof attack of the wing.The second part of the lift distribution, called theI( additionaldistribution,"is the lift due tochange ofthe wing angle ~r--..

.........,;~r--..-l10-----la r---~ c-~ ~ .... ~ ~ ~ r-,r-..... "--r-; &5 -0.272 -0.265 -0.272 -0.265 -0.272 -00264 \-00262 -0.272-0.2i0 Spanwise station y/(b/2)==0.4 2 3 -0.006 -0.002 -0.011 -0.010 -0.013 -0.012 -0.015 -0.015 -0.016 -0.016 -0.016 -0.018 -0.018 -0.016 -0.016 -0.016 -0.018 -0.017 -00016\-0.0111-0.018-0.018 40-0.006-0.011-0.012-0.016-0.016-0.018-0.019-0.020-0.020-0.021 5O.OM-0.004-0.010-0.012-0.016-0.018-0.020-0.021-0.021-0.022-O.O'J3 60.009-0.002-0.008-0.012-0.018-0.018-0.020-0.021-O.o-?l-0.024. -0.026 70.012-0.001-0.010-0.013-0.017-0.018-0.020-0.022-0.025-0.027-0.029 80.0140-0.008-0.012-0.017-0.019-0.021-0.025-O.O".19-0.030-0.030 100.0210.007-0.002-0.010-0.017-0.020-0.022-0.027-0.030-0.032-0.032 120.0280.009-0.001-0.010-0.017-0.021-0.025-0.029-0.032-0.036-0.038 140.0360.0130-0.010-0.017-0.021-0.028-0.031-0.035-0.040-0.00 180.0430.0190.002-0.008-0.016-0.022-0.029-0.034:-0.038 -000'11-0.00 18 20 0.049 0.050 0.022 0.023 0.004 0.006 -0.008 -0.006 -0.015 -0.014 -0.022 -0.022 -0.031 -0.031 -0.038 -0.038 -0.041 -0.041 -0.043-o./ax)dx + (o(j)loll)dy] +i+ (iJ1/I/iJy)dyJ dz=d.x+ idy In order fordw/dz tohave adefinite meaning, itis necessary that the value of du: 'dz beindependent ofthe manner withwhich dzapproaches zero.If dyisassumedtobezero,thevalueofthedifferentialquotientdw/dzis oA..I'to..... V-- -EXPERIMENTALCHARACTERISTICSOFWINGSECTIONS127-6-- /\. A.(o....0" -.- -Cl1a 0-2 a 0.1o 0.2A 0.L...s:::o" 0.6o ().,"0t)20 1& 8 12 16 20 :I .Alrtoll thickness. percent of chord (c) NACA serIes.eo't:J II. 8 12 16 20 Alrtoil thickne.s. percent orchord :I(d) IIACA 65- eeriea.airfoilsectionsof variousthicknessesandcambers. R,6X 10'..-6";'-4-4rot0-4s.."'"0-2....1105c00 ....p0--JI A At.

-. A.v V04-)-."vEXPERIMENTALCHARACTERISTICSOFWINGSECTIONS127-6f ~It~A.. ~A.~(>"..0_.-- -CII ....oQ0.!f -2 a 0.1taOo 0.2 ctI6 O.L.C" 0.6...o.., oe ..., ~20 1& 8 12 16 20 I.Airtoll thlckaess. percent of chord (cJ NACA 6 ~ serles.i~2 0 Ja. 8 12 16 20 24i A1rfoil tblckn percent or chord(d) BACA 65- eerieairfoileectiooaorvariousthickneseesandcambers. R,6 X lOS.eo-6 ....,......ro40-4s...~ 0-2...1105c00 ...p0--.ll I;. A...:tt.. ~ ~ 4 ~...... A...,;,. Vn0- '" 128 THEORYOFWINGSECTIONS thoseobtainedinflight.Applicationofthesewing-sectiondatatothe predictionofthecharacteristicsofwingsoffinitespandependsonthe adequacy of three-dimensionaltheory.These data are not applicable at high speeds where compressibility effects become important. 7.3.Standard AerodynamicCharacteristics.The resultantforceona "ringsectioncanbespecifiedbyt"90componentsofforceperpendicular andparallelto theairstream(theliftanddrag,respectively)andbya momentinthe planeoftheset\VOforces(thepitching moment).These forcesarefunctionsofthe angleofattack ofthe section.The standard methodofpresenting thecharacteristicsof'ling Sectionsisby meansof plots ofthe lift,drag,and moment coefficients against angleof attack or, alternately, plots of angle of attack, drag, and moment coefficients against lift coefficient. Plots of wing-section characteristics are presented in Appendix IV fora wide range of shape parameters.On the left-hand side of each plot, the lift coefficientandthe momentcoefficientaboutthequarter-chordpointare plottedagainstthe angleofattack.Onthe right-handsideofeach plot the drag coefficient and moment coefficient about the aerodynamic center areplottedagainstthe liftcoefficient.In most cases,the data indicated inthe followingtable are presented. Charneteristie Surface condition Split flap deflection degrees Reynolds number, millions Left-hand side Lift.Smooth03,6,9 tift.Rough- 06 Lift.Smooth606 I4Iift...........Rough- 606 Moment.Smooth03,6,9 .Smooth606 Right-hand side Drag.Smooth03,6,9 Drag.Rough"06 Moment.Smooth03,6,9 *O.011-inehamincarborundumlipreadtbinJytocover5to10percentoftheareafromthe leadincedeto 0.0& alungboUa surfaces ofaIleCtion wit.h achOldof24inchee. 7.4:.Lift Characteristics.4.Angle of Zero lift.As indicated inChap. 4,theangleofzeroliftofawingsectionislargelydeterminedbythe camber.The theory ofwingsections provides ameans forcomputing the angle ofzerolift fromthe mean-line data presented inAppendix II.The agreement between the calculated and the experimental angles ofzerolift EXPERIMENTALCHARACTERISTICSOFWINGSECTIONS129depends on the type of mean line used. Comparison of the theoreticaldata given in Appendix II'lith the experimental data of Appendix IVshowsthattheagreementis goodexceptfor theuniform-loadtype(a =1)ofmeanline. Theanglesofzeroliftforthistypeofmeanlinearegenerallycloser to0degrees thanpredicted.Theexperimentalvaluesoftheanglesofzeroliftfor anumberofNACAfour.. and five-digit and NACA C)-series wing sections are presented inFig. 56. The thickness ratio of the wing section appears to have littleeffecton theangleof zero lift regardless of thetypeof thicknessdistribu-tID-3_ -6-ol(.)A.. o6vQ-. -.euC)v '-t..c....o; -4II'-'4o8 12 16 20Alrton thicknes.. percent or chord(e) MACA 66- .eries.FIG. 56. (Cond1ldal) tionor camber. FortheNACAfour-digit serieswing sections, theanglesof zero liftareapproximately0.93 ofthevaluegiven bythetheoryof thinwing sections. For the NACA 23o-serics wing sections, this factor isapproximately1.08; andfor theX.\Cl\r iessectionswith theuniform-loadtypeof meanline, thisfactor isapproximately0.74.b. Slope.Lift-curveslopes fOI" a numberof NACAfour- andfive-digitseriesandKACAwing areplottedagainstthick-ness ratioin Fig. 57. These values of the lift-curveslope were measuredfor a Reynoldsnumberof 6million atvuluesof theliftcoefficientapproxi-mately equal to thedesign lift coefficient of the wing sections. This liftcoefficient is approximately in the center of the low-drag range for theNACAf>-Series wingsections.In therangeof thickness-ratiosfrom (i to 10percent,theNACAfour-and five-digit seriesand theXAC.-\ 64-series wing sectionshavevaluesofthelift-curveslopeveryclose to thevaluegivenbythetheoryof thinwingsections (2...perradian,or 0.110 per degree). Variationof ReynoldsDum-130THEORYOFWINGSECTIONS roUSb.., .12

..ca.t.10...E:s...o:J.06, 8 10 12 14 161820 22Alrtoll thickneas. percent orchorehal NaCAtour- andf'lve-d1s1taerie"'8aIootb.-r--'. - ... -.iii ----:t t-- c -. 1--.. ---- -

Berl '\e 00' --.-.:EI at(4 41g1t)Bogp-eAI "230 (54181t)"I0.lIa.-33.12

.0820 22 r 8lllooth_ III II -.Iw-- --.!t- - --

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1'f---r- ----,r-1\ - T ., RouP 1.1e 0 e0.1e

A o.'9 o.III .., .12.a.. I. .10t... C .08 1 5, 8 10 12 1416 18 20Alrtoll.thicknesa. percerat or chord(0) lACA 6l,- .eriea.FrG.51. Variationoflift-eurveslope1Ifith arfoilthicknessratioandcamberfor a22EXPERIMENTALCHARACTERISTICSOFWINGSECTIONS131na...d -Jllbo11 indicate rouF condition"1.. 0 31;; -I2t .;s.De 8'...I ... :I 4 22 20 12 10 8, 14I --r.ootb.... J.....J.,

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- po-- 1'--1tt-- 1---.,I-I" .,101"-_

'1\Roup E> 0 080

6o.V o.06II1AlrtoU tb1c1cne percent orchord(d J MACA65-n i.1211..A.108'rf6 8 10 122022'r 8IIIooth/, -...t-_.s e to)I -=i. r'\ --' I cll, ....t0r--RoupE)e 0.2

A0.4II Alrtoll thiem.... percent or chord"t:>: .7 J pr 1ML1. .... Li..",,: -....RACA ).\ JlACA65.,-8J.8-W Sectlon coefficient.CI FIG.71.Drag characteristics ofsome NACA. 65-seriea airfoil sections of18per cent thickness with various amounts ofcamber.R,G X10'. This scale effectis too largetobe accounted forbythenormalvariation of skinfrictionandappearstobeassociatedwiththeeffectofReynolds numberontheonsetofturbulentflow followinglaminarseparationnear the leading edge.1M AcomparisonofthedragcharacteristicsoftheXACA23012andof three NACA 6-serieswingsections ispresentedinFig.73.The drag for the6-series sections is substantially lower than for the NACA 23012 sectionin the rangeofliftcoefficientscorresponding tohigh-speedflight, andthismarginmayusuallybemaintainedthroughtherangeoflift EXPERIl.{ENTALCHARACTERISTICSOFrVINGSECTIONS157 coefficientsusefulforcruisingbysuitablechoiceofcamber.The NACA 6-seriessectionsshowthehighermaximumvaluesofthelift-dragratio. At highvaluesofthe lift coefficient,however,theearlierNACA sections .generally have lower drag coefficients than the N ACA6-seriessections. c.Effect ojSurfaceIrregularitiesOilDrag Characteristics.Numerous measurementsofthe effectsofsurface irregularities onthe characteristics ofwingshave shownthat theconditionofthe surfaceisoneofthe most important variables affecting the drag.Although alarge part ofthe drag increment associated with surface roughness results fromaforwardmove-ment of transition,substantial drag increments result fromsurface rough-nessintheregionofturbulentflow."Itisaccordinglyimportantto maintainsmoothsurfacesevenwhenextensivelaminarflowcannotbe expected.The possiblegainsresulting fromsmooth surfacesaregreater, however,forwingsectionssuchastheX ~ G-seriesthanforsections wherethe extent oflaminar flowislimitedby aforwardpositionofmini-mum pressure, Noaccuratemethodofspecifyingthesurfaceconditionnecessaryfor extensivelaminarflowathighReynoldsnumbershasbeendeveloped, although some general conclusions havebeen reached,It may be presumed that,forngivenReynolds number andchordwise location,the sizeofthe permissible roughness will vary direct lywiththe chord ofthe lying section. It is known,at oneextreme,that the surfacesdonot have tobepolished oroptically smooth.Such polishing or waxing husshown noimprovement intesu,.3intheKf\CAtwo-dimensionallow-turbulencetunnelswhenap-pliedtosatisfactorily sanded surfaces.Polishing or waxing asurface that is not aerodynamically smooth ,,;U,of course,result inimprovement, and such finishesmay beofconsiderable practical value because deterioration ofthefinishmaybeeasilyseenandpossiblypostponed.Largemodels having chordlengths of5to8feettestedintheNACAtwo-dimensional low-turbulencetunnelsareusuallyfinishedbysandingintheehordwise directionwithXo,320carborundumpaperwhenanaerodynamically smooth surface is desired,"Experience has shown the resulting finish tobe satisfactory' at flight values of the Reynolds number.Any rougher surfuee textureshouldbeconsideredasapossiblesourceoftransition,although slightlyrougher surfaces have appearedto produce satisfactoryresultsin some cases..l.;oftin6S 8ho\\'00 that smallprotuberancesextending abovethe general surface levelofanotherwise satisfactory surfaceare more likely tocause transitionUlanaresmalldepressions.Dustparticles,forexample,are moreeffective than small scratches inproducing transition ifthe material at the edgesofthe scratches is not forced above the general surface level. Dust particles adhering tothe oillefton wing surfaces by fingerprintsmay beexpectedtocause transition at highReynolds numbers. 158 I I I eDCA ---..r-. DDCA65,-418,a=0.5- t---- r--- .......... rJ) 'rI r:' II r ; I -rwlr 7 --

- -" 1 (.;1 J THEORYOFWINGSECTIONS Transitionspreadsfromanindividualdisturbancewithanincluded angle of about 15 degrees.H 42Afew scattered specks,especially near the 2.8 2.0.. o 1.2 .8 o o --4 s a-.2 - .8.. o... '-t So I -.4=--16 -80a24 aDS1.orattack.(10.deg FIo.72.Comparison of the aerodynamiccharacteristicsof theNACA65,-418and66,-418, CI==.0.5airfoils.B, 9X10'. leading edge,willcause the flow to belargely turbulent.This fact makes necessary an extremely thorough inspection if low drags are toberealized. Specks sufficiently large to cause premature transition can be felt by hand. The inspection procedureused in the NACA two-dimensional low-turbulence 1.0 o .2.....'r---.....-_.8or-......._ .._+---t-_t---t-......._+---IIEXPERIMENTALCHARACTERISTICSOFWINGSECTIONS159 tunnelsisto.feel theentiresurfacebyhand,after whichthesurfaceis thoroughly wiped with adry cloth. 0J2 028tdG24 0- .1i... 020 ... o '-4 '-4rI ::0.012 0 aIf008 /J AftL "T.0 0.-o - ....4 ..1 8ou:0..ba ..1;a.o.positionzlo7/00..-..Q .2'5 -.060-.2"" 8 0-IIIIICA 653-418, =0.5.267-Qq1 011I-.,I I I-1.6-1.2- -.8-.J..0.k J1.21.6z.0 "etlon 11ftcoeff1cient. c& FIG.72.(Ccmcluded) Ithasbeennoticedthattransitioncausedbyindividualsharppro-tuberances,incontrasttowaves,tendstooccurattheprotuberance. Transitioncausedbysurfacewavinessappearstomovegraduallyup-stream toward thewave asthe Reynolds number or wave size increased. Theheightofasmallcylindricalprotuberancenecessarytocause 160 THEORYOFWINGSECTIONS transitionwhenlocatedat5percentofthechordwithitsaxisnormal to the surface" is shown inFig. 74.These data were obtained at rather low 2.8 ... o .... .: e:...u....I,1. o .p "-....... g .... .p o a o -1 e!-.4.-1. -2J,.-16-808 l'24 seotion ofattack."0' dec I1IIII eDCA!012 TIII I II Jl 9x106 """"- EIlIACA 9 .1IACA8taJdaiidroupn...6 6lIACA 9 I-- 9DCA"215 9 I . FnJ.L. 6 IhJ 2 ) " II ro 4"1 , ".-IJ' .Art t --.'9 \,.I -.......Ul.Y rv,[) "'"'" ,1--

... f\ j3 -- Witlrgrp_Vr..,

., (temrNi7g flop C1'.-

Ieodilgedge)i'o"' ..... ..........to-- ............. 4i AtJfJop/ "--- ::::::-::- r-- t::-o--. ....... . IIoo w ReduclialofchotrJ,percenlflcp chadFIo.109.(Conduded)(b)Effect onCLmasandonCDat CLmazofreducing the chord ofa 0.2Oc aplit flap.a.. 60dep'8e8. other two configurations should beattributed to the difference inlipposi-tion.Envelope polars forthese flapsare presented- inFig.113. Whenthelipislocatedat or nearthenormaltrailing-edgeposition, the thicknessofthe flapisnecessarilylessthanthat foramoreforward location of the lip20(Fig.114a).In the case of thin wing sections, especially of the NACA 6-series type, the flapthickness may become too small with a rearward location of the liptopermit favorable slot configurations.Under suchconditions,thefavorableeffectonthemaximumliftcoefficientof movingtheliptowardthenormaltrailing-edgepositionmaynotbe realized.CahillJOshows(Fig.. 114b) that the maximum liftcoefficients for 207HIGH-LIFTDEVICES c FIo. 110. Contoursof eL..... for variouspositionsof trailingedgeof 20 percentflap.c:::: SlDTTEDFLAPWITH LONGLIPc c Ell1RNAL-AIAfllILFLAP ,1"'10. Ill. Several typesof slottedflaps.O.30cFOWLER FLAP;GAP-O.0I5c 00 I

"'< C 1 i

-s Ci

7 \ / " "II.\ I , / ,I "","--. ---'" " /" 1-0------ V.... ...... lV ,,"," )J4 ,I /,"J7 I I " 11 , j J

I /I VI I( /I " I ---- Q2!J66c..sldled1/q'J 2-h (ref.153) / I_.- Q3Oc.....Fowler l/(pj gcrJ01Jl5c 10-j--Q3Oc...slolled1/q)"!11 ex/ended I--V , IlPIgq:J-O.02c/7 ,, I I,.2 1.8 1.6 1.4 1"2 1.0 .8 .6 .4 Flopdeflection, 4, deg. Flo.112.ComparisonofincrementsofseetlonmaximumliltforthreeflapsonaNACA23012 airfoil. ----209 HIGH-LIFTDEl"ICEB the NACA 65-210 section are essentially the same forlippositions of O.84c, 0.9Oc,and 0.975c.The structural difficultiespresentedby alongthinlip extensionand themechanismnecessaryforthecorrespondinglargerear-wardmovementofthe flapare suchastodiscouragethe useofrearward locations of the lip unless such configurations result in substantial improve-ment ofthe maximum lift coefficient. -- _ :>I \ I 3.2 'VII 2.8 2.4 t I Q30c sIoIfed llop with extendedlip;-w---+--+-t--+---+----f gop=O.02c asocFowler Ilop;gop'O.o15c o.2566c s/oltedflop 2-h (referenceJ53) Plainairfoil .8 .41.21.62.0 $lion liftcoefIJc/enl1cz FIG.113.EnvelopepolarcurvesforthreeslottedflapsonaNACA23012wingsection, Theeffectofflapchordontheincrementofmaximum U3isin-dicatedbyFig.115.The datapresented .fortheO.. 25(j(ic andO.4Ocflaps arereasonablycomparableinthattheshapesoftheslotsaregenerally similar.Figure115 showsthat largerincrementsofmaximumliftcoeffi-cient are obtained with the larger chord flap, but theincreased effectiveness issmallcomparedwiththeincreaseofflapchord,Theslightlyhigher maximum lift coefficientsobtainable withlargechord flapsdonot appear tojustifythe structuraldifficulties encounteredwithsuchflaps,and flap chords inexcess of O.25cto 0.3Ocare seldomused. ThemaximumliftcoefficientsobtaineiP" 96.1&3withvariousarrange-ments ofslotted 8ap on NACA23012,23021,and 23030 wing sections are plotted inFig.116.The flapchord was25.60 per cent of the section chord inallcases.These data indicate little variation of the maximum liftcoeffi-cientwiththicknessratiofrom12to30percentforthistypeofwing section.Afewdata3,.are alsoshowninFig.116forcomparable slotted flapsonNACA 6-series wing sections,Inthis case,the flapchords are25 or30per cent ofthe sectionchord.These limited data indicatethat,for the NAC.A.6-8eries sections,the maximum lift coefficientsobtainable with ---O.84c~ Reynoldstrr!1Iw,R (0)CONFIGURATICWS (b)M X I ~LFTOlTA ,8 ,4 ~ :;;;...00"""-~~ ~ ~ ~ ~2. 2. --'.6 l---'.--~ >----1.2 ~ .8c1(degJ oPh/no/rfoI1.~ .4 e SbHfd fkJ1__45 ASIdled/Iff' 2 __41.3 '1SIdled IlqJ 3.__35 0 I -- _.-:..-s .6 :fi J J(.) I Slotledflap I 5/0111flop2 Sio/ledflop 3 -- O.90c FlO.114.Variationofmaximumeect.ion liftcooflicjent. with.RM)Onoldi'numberCorseveralslottedflapsontheNACA 66-210whig 8(wtion. ~ o""'"~ ~ ~ "'< ~ ~ ~ gj es ~ ~ 211 HIGH-LIFTDEVICBS 1.4 D.2566cflap c--------c -........... ./, .-' ------/ -,' I'V I I flap /i. f li"" O.2566cflop I 'I I ,, I I JI' " l' If 00D 20.JO40!JO Flop (0)CONFIGURATIONS(b)INCREMENTSOFMAXIMUMUFTCOEFFICIENT FIG.115.Effect of flap chord onincrements ofsection maximum lift coefficient forthe N ACA 23012wing section. 3.2 I + 1 ------..............., 4 -SymbolKfng section seriesFlop chord ratio- -0N.A&.A.230- O.2566c-xN.AC.A.6- o.ese --...N.A.CA6- O.JOc -I , 1i1I, E 2.0

1.6 1.2 61014B..222630 section Ihickness rolio, Pc,percent FIG.116.Maximum lift coefIiciente forvarious arrangements of slotted flaps. 60 212 THEORYOFWINGSECTIONS slotted flapson10percent thick sectionsare appreciably lessthan those obtainable with thicker sections. The effectsonthe maximum lift coefficient of somevariations of shape of the slot are illustrated'" inFig.117.In configurationsl-a and l-e,the slot is only slowly converging,if at all,at the end of the lip,and these COD-[ l Skilled flop 1-0 SIdled f/cfJe- 'ir.. 2.81 SbItJ fltJp2- i Czm... 2.674 SItJIIt1d fltJp3-1 Czm.. [l SIoIIedflop I-b 6,6SOdtlg.4,60dtlg. clmax. 2.76 [l SJolltJd flop t-c 6,.:55 de9. "1mcr.2.75'"'-w. .:2 'X. [I SIrJIIedfkJp '-ee6i 645t!tJ9. 'f"...2.il9c'--..60 SItJIItIdfltJp 3-g FIG.117.l\laximumlift coefficientsattainablewithvariousammgements ofslottedflaps onthe NACA 23012wing section. figurationshavethelowestmaximumliftcoefficientsoftheI-series configurations.Ashort extension of the lipasinconfigurationI-b,which makes the slot definitely convergent and directs the airdownward toward the flapsurface,is effectiveinincreasing the maximum liftcoefficient.It maybeconcludedfromtheseandotherdatathattheslotshouldbe definitely convergent in the vicinity of the lipand shaped to direct theair downward toward the flap.The effects of changing the radius of curvature at the entry tothe slotfromthe lower surface arc shown byconfigurations I-bandl-c ofFig.117 foraflaphaving acomparatively smallrearward displacementwhendeflected.Decreasingtheradiusofcurvaturefrom about 0.0& to O.04c did not produce a significant difference in the maximum 213 HIGH-LIFTDEV"ICES liftcoefficient.Other data indicate that thisradius of curvature is of little importance whenthe flapis displacedrearward enoughto produce 8.large area forthe entry of air into the slot. It isdifficulttodraw generalconclusionsaboutthe proper shape ofa slotted flap.Figure117showsthat the highest maximumlift coefficients wereobtained with flap2,whichis shapedmorelikeagoodwingsection thanflaps1or3.The differencebetweenthemaximumliftcoefficients produced by flaps1 and 2 is small and may becausedby the difference in slotshapeandlipextensionratherthanbythedifferenceinflapshape. FlO.118.Contours offlaplocationforQ lllar Slottedflap2-11.,&, =60degree.onNACA 23012wing eeetion. Flap 3,however,appears to betooblunt with atoosmall radius of curva-ture onthe upper surface aft of the lipinthe deflected position. Typicalcont.ourst61 ofthemaximumliftobtainablewithvariousflap positionsatoneflapdeflectionareshowninFig,118.In' general,the optimum flapposition forgood flaps at largedeflections appears to hethat whichproducesaslotopeningofthe orderofO.. Olcorslightly more and which locates the foremostpoint of the flap about O.Olcforwardof the lip. The maximumliftcoefficient,however,is frequentlysensitivetothe flap position,and the optimum position isbestdeterminedby test. Acompletesetofsectioneharacterisrics'Pforatypicalsingle-slotted flapconfiguration is shown inFig.119.This figureillustrates the charac-teristicabilityofslottedflapstoproducehighliftcoefficientswithcom-paratively smallprofiledrag coefficients. The increment ofmoment coefficient associated withthe useof single-slotted flaps" is illustrated by Fig.120.This figureshowsthe ratio of the incrementofthe sectionpitching-momentcoefficient" totheincrementof the section lift coefficientat anangleofattack of 0degree forthree wing sections and several flaps.The momentcoefficientsusedinthis caseare o .20o/6 t9

-0,d6g.o--b.

2O--v30--0,50--1>d60--6I.- - - /[I:lJ"

_noseI'Vfor deflecfed flop II rr ....

-'l--"""10- lD'" "-ID- l-===

-

I

"'C1/ ...... .... ;/..". "J" .....N'''' lJW--

IP" 108.9_"--238.:-'.lXJ8 A"5.9Standard rouf/hness I o 2, --.2 o ./JIU .024 10 .020 -5 -1.6-1.2-.8-.40.4.8 1.2 S:fion11ft coefficient,c, 2:>021 "-i:J';3cnion(Conlinued) 506 THEORYOFWING8ECTION8 3.6 2.8 2.4 2.0 1.6 o0 ,ttl-. I.4 ...... .i c -.2-.8 }-.3-LZ A j:' ) IlJrJU :..... la'

J, i/J ..)k 1111 I' Jr I J' If J' cK...... 1!J::!........ A If) .I' 4 IQ r'A T J. .......-a:.., -.4-1.6 -.5-2.Q-32.24 -16.-808/8 2432SecflOl7 angle of o1lJr,it deg NACA 23024 Wmg Section 507 APPENDIXIV 8 \oJ.....I 1.26-.80.4.8-1.2 .2 ---- -V """'iiiiiioI;r---...... ....t"----. .11:: """--- .20 .2.4.8.8 life 02_ 0 \J I , I I .0/6 c , v t1 Ij IIVlA.\,VJ ..,., -c r\ f"""ooolil\. 100"r/.J'"V.0/2 i'""'"'I:r 1'\10" V Ir"i f' r\. b l/ t1 '1"\ ./ J)(J8 ......... c-;,..Jr"I -- ..VV5# --".,. w... ....'" v "'t -./c; J . -.2 a.c.PQSlllon R 03.0-/0-- - .2/Z.102 -.305.9.223065 08.923/048 65.9Sfondord _.4 .... Secfion /ilf coefficient,C, NACA 23024 Winlt Section(Continued) 508 THEORYOFWINGSECTIOJ.VS 24-/6 -808 1& Secfi:m angle01"o/facle, .,cMJg NACA63-006WingSection-i- l ?'3" r IN r A 8rA fjf j Itl 4 " J'lj II Ih fT:0 ,I c rc:; ,, ''ll , , g I P-l.4 4t Ii 8Iln. n;K ru , 1\ 2

, I \ j 6 -323.61.2 1.6 20 2.8 -.e .........i e" :.::::J .6 CI)0 -./I J .!! -..;: i f..J-.3 -I. -.4 -I. -:5-2--24509APPENDIX IV .ONi.ooo""""" .fJJ2i""""lllo.. \I " 1 , I" I III .tJN.2.4.6.8LO * I J> I 1I, 1\ a ['\. 0 lJar\... r""'!)P-'Ip;I k lrf'lZ' "'rvJl'.

It -.... 1-- -j I if tl; a.C, pcsit,'on.... R tI* o3.0UO- --lJ 258 E-.48 I Q6.0 -.029e9.0II258-.033 ! 46.0 "StondardrouqlY1essI al'Oc simulafedsplit flap 61r vea ,,--v 6.0 StandardIIt, f I t a -.5 -./ .2 .004".020 i1-1.6 -:8-.if.0 .81.21.6 Sectionlift coefficient,c,NACA63-006'YingSection(Continued)510 THEORY OFWINGSECTIONS . j 11 v

j'II jJJ IIIJ!). p1IIIIf\ 11II' Q 10Id c: Vdl IAI , IT LLI-Sf IJI ,.r9 " I' y r-; ... , I.- it 1.1,. L L6 o -.8 -.4 32 2.8 2.0 2.4 o , 4-./ -.4J.6 24 M 808 2432' SecfionongIeof DlfDdr, ... de9 NACA 63-009WmgSection 511 APPENDIXIV _. .D36 .. 4..,. r---.'-----" I\ /,,... \ 'ti'.Me-'0 .2A.6.81.0... .01: It.. IA " 1\ ,., , /(\ B l. ......J Il\.. 1/ ./JOIJ c.. ... D. r,s-rv .". "'- J--- ...... -.l...- -...... r- r---,...,.. -./, I ..... ' .i-.2 R r-1: :3.0JtIOL... -...,a6!' I.258.(}()1... 09.0. /8I Af1.0514 Q__s .. UI;'.,gp di 'lticfet. I'II.-.4 rQf9;7n,SS -.s -1.2-.8-.40 .. .4.81.21 StK:tion liff coeffICitN7f,C, N ACA63-009'VingSection(Continued) 512THEORYOFWINGSECTIONS cr 10... ... ::::., a

J .6 (J '" 0 -.1 l-I ""='c: -.2 'I...:" 'to- 1-.4 -.5 -/6-808/6-Z4 -32 2.., 3.c 8 .4- .2. II ... v ." 11 r J,.2 J, .A ) ....8 IiP JII 1/5 lei .4 II( l1ft jr\. I 1. III I!\-rr u; J " j t .r'\ It .4 v IJlih. I ..J , C w

.6J, 1., r j" I l ;J c1.IS l , IId9 \JIl \1\IJ J)' r\.... , III, I"' '1J 'J'\.f'- I R "' / "- /'/J '/ " 't1 ...... J_ "'--n. 1:",- i,J;ru- ........... 'Al-Lt"\ -.- ..-.. - -- '" '" ,--"-,,iW'.... -

-I a.c. position R*1 '/;.c o 3.0Jtltr'_.256.'29 3 o6.0 .259.017"0 9.0 -.OOc 66.0 Standard rOUlJhnessa20csimulated split flopdeflecfed so: v6.01 V6.0-t ".IfI tI 5 II o .004 -1.6-1.2-.8-.40.4.8 1.2l6 Section lift coefficient,c, NACA641-012Wing (Continued) 568.1 THEORYOFWINGSECTIONS J' \(d , \A\ 7l'

'ljill/)if"I'4'CV.II '" IJ , .I I(J1J-' 1"""""'1;:1UIJ, aII:tI ns " r A1m.IIr rust...J. -tltj:'1AIIS I AI. -if" II.... I l i'QI. dfy q (I l l c{ It;1 0 o -.8 -.41.6 -l2 -t 3.620 2.8 24.3.24...... -2--32o ../ } J-.2 ,-.5-/6-808/6 24 3c Sec-f,on angleof otrocn,".,deg NACA 641-112 Wing Section569APPENDIXIV -1.2-.8-40.4.8 .oN - r----r---r---_. r'---. ------ -, ,I 'N .IN. .2.4.6.8LO '* I n I 1 'IJ fiI vJ D s Q , IJIJ , " 1/ 1/If/ \ JdV , \ , l/:afJ r \ ., , I0 t 8 I ", ,JI j IIII 4 ] III .1JI [ , \ } D 0 /I,, r Jf ........jII.'-A I 1 :I 8 rr 1'\ ---.." t2. InlH y Ij.-IV ... -. -. l6 ..J6 2.4 28 2.0 .3.2 -1.2 -/.8 o -J ,,:5-2.0 -JZ-16-808 24.32 Section onqle of attock, "" deg NACA 642-415 Wmg Section 579 APPENDIXIV -.8-.40.4.8 -/.2 o .(1M l---"'""" -r---r r---r--- .(I,Jz""---100.- \ .. \ .RtJ.2.4.6.81.0 11\ J19 ,. 1\ II "I J b\ JliP \ illI,...1. 1\ " VII , 1/1/ r\.r\ r\ r-, /'j. ........ lIJ V r-, ,...po- "0'

.......f'.. H: ..... T v-.eI{.l' '""""'!!ILrV.-\J ,- - -.. .-.--L..Llo- l.--" I Cl.C.position. Jl* t !lie.6 I .264-.010 3 a 265-.051 o9.0r- 264-:040 A8.0to- standard rouqhness Q20c simulated split "0f deflected 6 96.0IIrII:t 4176.0Sraoaard rouq"'ness S 21 024 .004 l26 S6etion lift coefficient, NACA 64J-415Wing Section (Continued) 580 THEORYOFWINGSECTIONS .t o -./ !-6 2 8 '} 7 4 12 117 Y 0 1 I\ Jb J , 2 6 f A -- , IJ"".1:1 :l:J:h'"' 2 Iff J,.J , A--"""") ioo--U "' , .8 IIlrI ",V III A IN if .4 U ] I, I AI 0 "IT II rJ A III IIrQl;ll:l J'Ah 4 I...... IU bII b4J, -\(8 ... J'tI V"o. IQIo...IliDt j' 1""....b -. 2 !Oc'fj').I-IJ hJr ......6 -I. 0 -I. I. -z -JZ -:5 -24-/6-808/6 24 Sec170n anqJeof oItock,'t deg NACA 64a-018WingSection 581 APPENDIXIV .0'" ---.. ----r ----r---_ .(J.JZ IJrI"" ....... "-") '{/ fd,. 'g.c=: -.... ;0 J. I'1/1 jrl r IJ1I1 " J lr " IJII ,. 0J/ ')' II III t. 1"'41; 'a:LrJ117 --'.r III gQD... U -c. I J'r1 I" IJ.. it1"'1: II 1\ It\. tr "--'I r-r Jr- rv ....,dJ> [U ..... oo -J-.4 -.8 -1.6 -2.0 -:-32-24-/6-80B 1& .seetin 0T1fJIeof"ofIQc/(.fIC deg NACA 64r221 Wing Section APPENDIXIV591 .OJS . V ,.",.,--r----.r----. -........-. ----r-, .,. ............-.-- '"I\1i .tIlB .2.4.6.81.0 qe 6 1 ' cI 1i'tJ i\\. I \ J cI\., JI'r> r\..ltJ ,.I;' J Q I" jAf '" A .... -, l If!-"'RA IffdY t4"" II4r r:1 U (r ,.. r If Jf IW'i\. ,. . I-I:I I r I"""" tt d :'tl Q 4il1' 1-Y"o ""'1lQ y l '" \ -/6-808 Sectionengleof attach,Of deq NACA65-410 Wing Section /62432 615APPENDIXIV ---,......--r---:--- -

, I, , . ill .8 .6 .2.4.61.0 ,qe 0 I rJ tlI tI \J\ 0 \III \ I J7 /..I ';Jj) " f\vJ/r:> "'\ VV1..1 '/ .A"A0:/P'" -,J IQ.-"-. """r-{ rv-o

..._A.. ,..,...,. - I -"'-.A. .- A.- .- ..-.""\........0lIla.c.poSifiOl1 R"*i Jfc o.l01=F- .258-.025 c6.0.259-.024-c9.0 .262-.035 A6.0,IStandard rotJCjhness 1- D.2Oc simulated Sf'11Flap deflected 6 v6.0I :IIII V6.0o .004 .024 -:5 -1.6-/.2-.8-.40..4.81.2l6 Secfion liff coefficient,c, NACA 65-410WingSection (Continued) 616 THEORYOFWINGSECTIONS ./ o -.I -.5 -24-/6-80 B/62432 R J h., r'I< II J.1/ loat? II , ; :t1 ,. /I \ ! AJ' I{I)' II J' UI h...J" IJ tI8 \]1r \ f} II 'Crll. 4r. A> .... I2" rc , \..'-I U i'1rv...1 \ )'WloKJ- -II "'V'vv II g I r I I I j I I 0i o -.8 -.4 2.0 1.6 -1.2 -1.6 2.4 e.o 3.Z 3.6 -2 -32 Secfionangleof attacit.Q'oJdeg NACA 651-012Wing Section 617APPENDI",y'IV l,...--- -r--"

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-V Standard6roUS=0f l" : ... tn' 71 .......:...;. . .. . .:..J' ........, . 0.200 .sa1i1ate4 8@tflap 4en.eo'M .. : , JS.l0'tIC--16-8 o816APPENDIXIV 619 0.032 0.028 0.024 u Ie.! .!:l0.020 l0.016 c: sM 0.01% 0.008 0.004 -1.6-1.2-0.8-0.400.4 1.6 1.2 0.8 =-------"----......--r------ ,,, i-. .\.I 4) ...1 ", . 14> ,- i-o B )(106 rEI.0 0 G'.0" t IfA Standard ..a '\ iJ1 \-,6.0X10 NJ1 ti:\ \ / \ K1'If I \.c , / ... -N v' ----

'1 1 b_ ...r "V rv-" . .. -....lthAll.. - ---.-A...1*,_ - ,..... ---:--- .. 'r' 1-v J'

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4 l >"'" .t.1. 8 I'" J \ V!t'7 10 fct 6J r I\I'-n.......'" -. -. 6 0 -1.2 2.4 36 3.2 2.8 2.0 l6 -2 -l -.JZ Section angleof attock,"0, deg NACA 653418 Wing Section 637APPENDIXIV .1)16 "....-- r----.V r----. r--.....

--- -

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r !J 6 ,v A):J"}A .3- "'\-0 U""1qtr: .. .nnc

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7 \7 J" J.I

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! 0.016.& 0.012;11111111111111111111 . m -1.6-1.2-0.8-0.4o0.40.81.21.6 Sectionlift coefficient, c, NACA747A315'Ving Section(Continued) 686

2.42.0 1.61.2

.i-Iii

0.8S....0.1 c0.4 !.200 IS

..Ie -0.1 -0.4 .!

...I -0.2-0.8 i -0.3-1.2-1.6-0.4 THEORYOFWINGSECTIONS .g:: I:::b....gmHf;!.flap 4ef'lecte4bOO l!h 1m::::E!!:ilillli!: i :..-ill5! :::::... .. . ....." .. .... . : : :::: .... ::-= .... ;: '" i::' ':: :r:' -;--giD.. . :::::; .. ;.. ..;g'...;gUt:.,.;:!:.. . d::r.# ::::... Ii: ..gf;e' T .... :i!: .,:: " " :":' ,ifui!iL.or: : ': ... -.....; ...._........ i::,:m....... ... ...,..rJ ::::..... 1,H.: ....: ;::1 m!:Hl. .. . I. :m:::i 1;::_..._. :..:;, .... Hf:!:Iili;i::;R JI " :...._ gj!i!. 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Hli :mH!:':1;iH. ;ir:i*i .0, ill:!i:: m:-34 .. 16 -8 08 16 24Section tmgle 0/tJttGck, deg NACA747A415 Wing Section687 APPENDIX IV INDEX AAckeret,J., 268 Adiabaticlaw, 249 Aerodynamiccenter,experimental, 182 theoretical, 69 wing, 5, 19 Aerodynamic characteristics, experimen-tal,449 Airfoils (see Wingsections) Allen, H. Julian, 65, 164, 194, 202, 236 Anderson, RaymondF.,9 Angle of attack,4 effective, 22, 25 ideal, 70 induced, 20 wing, 8,11 Angle of zero lift, experimental, 128 theoretical, 66, 69 approximatemethods, 72 variationwithflap deflection, 192 wing, 16 Aspect ratio, 6 athighspeeds, 296 BBamber, MillardJ., 234 Bernoulli'sequation,35, 251 Birnbaum,Walter,Blasius,H.,87, 96 Boshar,John, 20 80 compressibilityeffects, 109 concept, 81 crossftows, 28 ht.minar,85 Blasiussolution, 87 characteristics, 85 separation, 83, 86, 93 skin friction, 87 thickness, 89, 92 transition, 105, 157 velocitydistribution, 87 Boundarylayer,momentumrelation, 90 slip, 83 thickness, displacement,89 momentum, 92 turbulent, 95 pipeflow, 95 separation,83, 103 skin friction, 97, 174 thickness, 102 velocitydistribution, 97, 100 Boundary-layercontrol,231 cCahill, JonesF.,206, 221 Camber, 65 application to thickness forms, 75, 112 design of meanlines, 73 effect of, on aerodynamiccenter, 182 on angleof zero lift, 128 on liftcurve, 132 on maximumlift,136 on minimumdrag, 148 on pitchingmoment, 179 on profiledrag, 151, 178 induced, 28 shapes andcharacteristics, 382 Chaplygin, Sergei, 258 Chord, 113 meanaerodynamic, 21 Circular cylinder in uniform stream, 41, 49 withcirculation, 44, 49 Circulation, 37 lift, 45 thinwingsections, 65 vortex, 43 Complex number, 47 Complexvariable, 47 Compressibilityeffects, 247 boundarylayer, 109 dragcharacteristics,281 first order, 256 689 6907'REORYOFlVINGSECTIONS Compressibility effects, flap effectiveness, 281 liftcharacteristics, 269 pitching-momentcharacteristics, 287 pressurecoefficient, 257 wingcharacteristics, 268 Conformal mapping, 47, 49 Conformal transformations,49 Continuity,32, 38, 249 DDesignof wing sections,62 Designationof wing sections, III German designations of NACA sec- tioDS,118 KACAfour-digitsections, 114 XACAfive-digitsections, 116 X.ACA modified four- and five-digit sections, 116 XACA L-series sections, 119 XA.CA 6-seriessections, 120 K.-\CA. 7-series sections, 122 Doublet,41, 49 Downwash, 9, 20 Dragcharacteristics, 148 calculation, 107 compressibilityetIects, 281 minimum, 148 roughnesseffects, 157, 175 sectioninduced, 25 variation withlift, 149 winginduced, 16,27 EExperimental techniques, 125 FFamilies of wing sections (seeWing sec-tions) Fischel, Jack,218 Flaps, 188 externalairfoil, 215 leading-edge,7Zl plaintrailing-edge, 190 splittrailing-edge, 197 slottedtrailing-edge,203 Flowaround wing sections, 83 athigh speeds, 261 Fluid, perfect, 32 Fullmer, Felicien F., 231 GGarrick, I.E.,63, 258 Glauert, H., 9, 65, 67, 192 Glauert-Prandtlrule, 256 Goldstein, Sidney, 63 Gruschwitz, E., 103 HHarris,ThomasA., 218, 227 High-liftdevices, 188 I Irrotationalmotion, 37 JJacobs, EastmanN., 194, 260 JQDes,RobertT.,296, 299 Jonesedge-velocitycorrection, 11, 25 Kaplan, Carl,256, 258 Kaplanrule, 257 }{&nnaDintegral relation, 90 }{arman-Tsienrelation, 258 Keenan,JosephH., 109 }\:night, Montgomery, 234 Koster, H., 230 Krueger, W., 230 Kutta-Joukowskycondition,52 LLaminarflow (seeBoundarylayer) Lanchester-Prandtlwing theory, 7 Leadingedge, 113 Lees, Lester, 109 Lemme, H. G., 230 Liepman, n.\V., 268 Liftcharacteristics,compressibilityeffects, 269 designlift,70 INDEX691Liftcharacteristics,experimental, 128 ideal lift, 70 maximumlift, 134 theoretical, 53 wing, 3, 8 maximum, 19 Lift-curveslope, effective, 11 experimental, 129 theoretical, 53, 69, 256 wing, 11 Limitingspeed, 254 Loads, chordwise, 53, 60, 73, 75 flaps, 236 plain trailing-edge, 192, 236 slotted trailing-edge, 215, 221 splittrailing-edge,202, 236 span\\?ise,9, 19, 25 Loftin, LaurenceK., Jr., 157 Lowry,John G., 227 MMach line, 248 Mach number, 81, 248 critical, 259, 261 (SeealsoCompressibilityeffects) Meanlines, 382 (SeealsoCamber) Millikan, C. B., 93 Moment (seePitching-moment charac-teristics) Motion,equationsof, 32, 85 irrotational, 37 Munk, Max ~ I 23,65,72 NNaiman, Irven, 56, 74 Navier-Stokesequations, 85 Keely, Robert II., 20 Neumann, ErnestP., 109 Xikuradse, J., 99 Normalshock, 254 Noyes, Richard W., 304 oOrdinates of cambered wing sections,406 pPankhurst, R. C., 72 Pinkerton, Robert M., 61 Pitching-momentcharacteristics, 179 compressibilityeffects, 287 theoretical, 66, 69 approximate, 72 wing, 4, 16, 27 Platt, RobertC., 215, 226 Pohlhausen, K., 93, 106 Prandtl, L., 9, 20, 85, 96 Prandtl-Glauertrule, 256 Pressurecoefficient, 42 Pressuredistribution, theoretical, 53 approximate, 75 empirically modified, 60 Propellerslipstream,effecton drag, 170 Purser, Paul E., 218 QQuinn, John H., Jr., 234, 236 RReferences, 300 Regier, Arthur, 109 Reynoldsnumber, 81 (SeealsoScaleeffect) Reynolds, 0.,95 Rogallo, Francisl\{.,202 sSanders, Robert, 225 Scale effect, 81 aerodynamiccenter, 182 lift-curveshape, 133 lift-curveslope, 129 maximumlift, 137 minimumdrag, 148 profile drag, 151 Schlichting, H., 105 Schrenk, Oskar, 233 Schubauer, G. n.,105 Sections (see \Ving sections) Sherman, Albert, 20 Shock, normal, 254 on wing sections, 263 Shortal,JosephA., 227 692THEORYOFWINGSECTIONS Sinks, 39 Sivells, JamesCo, 20 Skinfriction (BeeBoundarylayer) Skramstad,H. x.,105 Slats,leading-edge, 225 Slots,2:1.7 Sound, velocityof, 249 Source,39, 49 Speed, limiting, 254 Squire, H. s.,101, 109 Stack,John, 272 Stagnationpoints,45 Streamfunction, 36 Streamtube,compressibleflowin,249, 252 Streamlines,36 Superposition,39, 75 Surfacecondition, 143, 157 effectof, on drag, 157, 175 on lift, 143 on transition, 157 standardleading-edgeroughness, 143 SWL-ep, 296 TTaperratio, 11 Tani, Itiro,20 Techniques,experimental,125 Temple,G., 258 Tetervin, Neal A., 102, 103 Theodorsen,Theodore,54, 63, 65, 70, 109 Thicknessdistributions, 309 effect of, on aerodynamic center, 182 on angleof zero lift, 129 on lift-curveshape,133 on lift-curveslope, 132 on maximumlift, 134 on minimumdrag, 148 on pitchingmoment, 179 on profiledrag, 148, 178 Thicknessforms andtheoreticaldata;309 Thicknessratio,effectof, on aerodynamic center, 182 on angleof zero lift, 129 on lift-curveshape, 133 on lift-curveslope, 53, 132 on maximum.lift,134 on minimumdrag, 148, 178 on pitchingmoment, 179 on profiledrag, 151 (See also Wingsections) Trailingedge, angle, 117 effectof, on aerodynamic center, 182 on lift-curveslope, 132 definition, 113 Transformation of circle into wing sec-tion, 50 Transientconditions, 133, 143 Tsien, H. S., 109,258 Turbulentflow (BeeBoundarylayer) Twist, 11 ufirich, A., 105 Unconservativesections, 175 Uniformstream,39, 49 v Velocity, limiting, 254 Velocitypotential,38 Vibration, effecton drag, 173 Viscosity (see Boundarylayer) von Kdrmdn, To, 82, 90, 93, 109, 175, 258 Vortex, 42, 49 systemon wings, 9 Vorticity,37 wWeick, FredE., 225-227 Wenzinger, Carl J., 194, 202, 215 Wing sections, combinations of NACA sections, 123 concept,8 experimentalcharacteristics, 124, 449 families, 111 NACA four-digit, 113 NACAfive-digit, 115 NACA modified four- and five-digit, 116 NACA T-series,118 NACA6 s c r i ~ s119 NACA7-series, 122 ordinates,406 unconservativcsections, 175 Wings, 1 aerodynamiccenter, 5, 19 angleof attack,8, 11 angleof zero lift, 16 applicabilityof section data, 28 Wings, aspectratio, 6 drag, 3, 16, 27 induced, 8, 16,27 forces, 2 lift, maximum, 19 lift-curveslope, 11 'liftdistribution, 9, 25 pitchingmoment, 16, 27 Wragg, C. A., 215 INDEX693y Yarwood,J.,258 Young, A. 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