NATIONALADVISORYCOMMITTEE FORAERONAUTICS REPORTNo. 824 SUMMARYOFAIRFOILDATA ByIRAH.ABBOTT,ALBERTE.VONDOENHOFF, andLOUISS.STIVERS,Jr. 1945 w u m I s S ~ G b c A V q L D D. o AERONAUTICSYMBOLS 1.FUNDAMENTALANDDERIVEDUNITS MetricEnglish Symbol Unit Abbrevia--Unit Abbrevia-tiontion Length ______ l meter __________________ m foot(or mile) _________ ft(orrni) Time _____ ___ t second _________________ s second(orbour) _______sec(orhr) Force ___ _____ Fweight of) kilogram _____ kgweight of1 pound _____ lb Power _______ P horsepower(metric) _____ ----------horsepower ___________ hp Speed _______ V {kilometers per hour ______kphmiles per hOuL _______mph meters per second _______ mpsfeetper second ________ fps 2.GENERALSYMBOLS Weight=mg Standardaccelerationofgravity=9.80665m/s2 or 32.1740 ft/sec2 Mass=W g Momentofinertia=mP.(Indicateaxisof radiusofgyration kby proper subscript.) Coefficient of viscosity JIKinematic viscosity pDensity(massper unit volume) Standard density ofdry air,0.12497kg_m-4_s2 at 15C and760mm;or0.002378Ib-ft-4sec2 Specificweightof"standard"air,1.2255kg/ms or 0.07651lb/cu ft 3.AERODYNAMICSYMBOLS Area Area ofwing Gap Span Chord b' Aspect ratio,S True air speed Dynamic pressure, ~ PV' Lift,absolute coefficientOL= q ~ Drag, absolute coefficientOD= q ~ Profiledrag,absolute coefficientO D O = ~ Induced drag, absolute coefficient OD= ~ ~ jqu Parasite drag,absolute coefficient ODP= ~ S Cross-wind force,absolute coefficient 00=q ~ o 11 R 'Y Angle of setting of wings(relative to thrust line) Angleofstabilizersetting(relativetothrust line) Resultant moment Resultant angular velocity Reynoldsnumber,p Vlwherelisalineardimen-fJ. sion (e.g., for an airfoil of 1.0 ft chord, 100 mph, standard pressure at 15 0, the corresponding Reynoldsnumber is935,400;or foran airfoil of1.0mchord,100mps,thecorresponding Reynoldsnumberis6,865,000) Angleofattack Angleofdownwash Angleofattack,infinite aspect ratio Angleofattack,induced Angleofattack,absolute(measuredfromzero-lift position) Flight-path angle REPORTNo.824 SUMMARYOFAIRFOILDATA ByIRAH.ABBOTT,ALBERTE.VONDOENHOFF, and LOUISS.STIVERS, Jr. Langley Memorial AeronauticalLaboratory Langley Field,Va. I NationalAdvisoryCommitteeforAeronautics Headquarters,1500NewHampshireAvenueNW.,Washington25,D.O. Created by act ofCongress approved March 3,1915, forthe supervisionanddirection ofthe scientific study oftheproblemsofflight(U.S.Code,title49,sec.241).Its membershipwasincreasedto15byactapproved March 2,1929.The membersareappointed by the President,and serve as such without compensation. JEROMEC.HUNSAKER,Sc.D.,Cambridge,Mass.,Chairman LYMANJ.BRIGGS,Ph.D.,ViceChairman,Director,National Bureau ofStandards. CHARLESG.ABBOT,Sc.D.,ViceChairman,ExecutiveCommittee, Secretary,SmithsonianInstitution. HENRYH.ARNOLD,General,"GnitedStatesArmy,Commanding General,ArmyAirForces,WarDepartment. WILLIAMA.M.Bl:RDEN,AssistantSecretaryofCommercefor Aeronautics. VANNEVARBUSH,Sc.D.,Director,OfficeofScientificResearch andDevelopment,Washington,D.C. WILLIAMF.DCRAND,Ph.D.,StanfordLniversity,California. OLIVERP.ECHOLS,!\iajorGeneral,"CnitedStatesArmy,Chief ofMateriel,Maintenance,andDistribution,ArmyAirForces, WarDepartment. AUBREYW.FITCH,ViceAdmiral,UnitedStatesNavy,Deputy ChiefofNavalOperations(Air),KavyDepartment. WILLIAMLITTLEWOOD,M.E.,JacksonHeights,LongIsland, N.Y. FRANCISW.REICHELDERFER,Sc.D.,Chief,UnitedStates WeatherBureau. LAWRENCEB.RICHARDSON,RearAdmiral,United StatesNavy, AssistantChief,BureauofAeronautics,NavyDepartment. EDWARD'VARNER,Sc.D.,CivilAeronautics Board,Washington, D.C. ORVILLEWRIGHT,Sc.D.,Dayton,Ohio. THEODOREP.WRIGHT,Sc.D.,AdministratorofCivilAero-nautics,Department ofCommerce. GEORGEW.LEWIS,Sc.D.,Directorof AeronauticalResearch JOHNF.VICTORY,LL.M.,Secretary HENRYJ.E.REID,Sc.D.,Engineer-in-Charge,LangleyMemorialAeronauticalLaboratory,LangleyField,Va. SMITHJ.DEFRANCE,B.S.,Engineer-in-Charge,Ames Aeronautical Laboratory,Moffett Field,Calif. EDWARDR.SHARP,1,1,.B.,Manager,AircraftEngineResearchLaboratory,Cleveland Airport,Cleveland,Ohio CARLTONKEMPER,R.S.,ExecutiveEngineer,AircraftEngineResearchLaboratory,ClevelandAirport,Cleveland,Ohio TECHNICALCOMMITTEES AERODYNAMICSOPERATINGPROBLEMS POWERPr,ANTSFORAIRCRAFT AIRCRAFTCONSTRUCTION MATERIALSRESEARCHCOORDINATION Coordinationof ResearchNeedsof MilitaryandCivilAviation Preparationof ResearchPrograms Allocationof Problems PrevenUonof Duplication LANGLEYMEMORIALAERONAUTICALLABORATORY LangleyField,Va. AMESAERONAUTICALLABORATORY l\IoffettField,Calif. AIRCRAFTENGINERESEARCHLABORATORY,ClevelandAirport,Cleveland,Ohio Conduct,underunifiedcontrol,forallagencies,of scientificresearchonthefundamentalproblemsof flight OFFICEOFAERONAUTICALINTELLIGENCE,Washington,D.C. Collection,classification,compilation,and of scientificand technicalinformationonaeronauticll II CONTENTS PagePage SUMMARY _______ .._- - - __ - - . __ - ____- - __ - - __.,. _ . _.._ .._____ _ EXPERIMENTALCHARACTERISTIcs-Continued 1NTRoDucTION_. ________________________ .. _"_C ___ .._______1 Dragof SmoothAirfoils-Continued SYMBOLS ________________________ ._______________________1 Effectsof. typeofsectiOIlondrag charact.eristics .._ _ _ _18 HIflTORICAL .. ________________________ .. _ _ _ _ _ _2Effective aspect ratio ________ . _________________ ..___21 DESCRIPTIONOFAIRFOILS ____________________________ .._ _ _ _3Effect of surface irregularities ondrag ____. _ _ _ _ _ _ _ _ _ _ _ _ _22 :\fethodofCombining:.\IeanLinesandThickness Permissibleroughness ________ .. _ _ _ _ _ _ _ _ _ __ _ _ _ _ ___ _ _22 Distributions ______ . ______________.________________3Permissiblewaviness ______________________ ._ _ _ _ _ _ __22 NACAFour-Digit SeriesAirfoils ________________ ..______4Drag with fixedtransition ___ . ___ .._________________24 Numbering system_ _ ______ _____ ___ _____ _ ______ _ _ _4 Drag with practical construction methods_ _ _ _ _ _ _ _ _ _ _24 Thicknessdistributions ________. _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _5 Effects of propeller slipstream and airplane 29 Meanlines ____________________________ . _________ 5 LiftCharacteristics of SmoothAirfoils_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _30 NACAFh'e-Digit SeriesAirfoils ____ .... _____________ .____5Two-dimensional dat9. __________ .._ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _30 Numberingsystem__ _ _ ___ _ _ ___ ___ ______ ___ ______ _5Three-dimensional data_ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _37 Thicknessdistributions _____________________"5- LiftCharacteristicsofRoughAirfoils. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _37 Mean lines ______________________.. _ _ _ _ _ _ _ _ _ _ _ _ _ _5Two-dimensional data_ _ _ _ _ __ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _37 N ACAI-SeriesAirfoils ____ ... ____. ______________ 5Three-dimensional data ______ .____ . ____ ..______ .. _ _ _ _38 Numbering system ___________ ___5UnconservatiyeAirfoils ________ .... __ . _____ ...____________39-Thicknessdistributions _________________ . __________5PitchingMoment ____________________ . ___________ .. _ __4() Mean lin es _______ . _ _ ___ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _5 PositionofAerodynamicCenter __ . ______________. __ .. ___43: NACA6-SeriesAirfoils________________________________5 High-LiftDevices_ _ _ __ __ ___ _ _ _ _ _ _ _ _ _ _ _ __ __ ____ __ _ ___ _43: N um beringsystem _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _5Lateral-ControlDevices ___________________ .._ _ _ _ _ _ _ _ _ _ _43 Thicknessdistribu tions _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _6Leading-EdgeAir Intltkes __________ .. _ _ _ _ _ __ ___ _ _ _ _ _ __ _49 Meanlines ___ _____________________ .._____ .. ______6In terference __ .._________________________ ..____________.50 NACA7-SeriesAirfoils _____________ :.:_= _____________7ApPI,ICATIONTOWINODESIGN __________. ___ ..______________51 NUmceringsystem_ _ _____ ___ _____ _____ ___________7ApplicationofSectionData __________________________ ..51 Thir,kness distributions_ _ _ _ ____ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ __ _7Selection ofRoot Section ___._ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _51 THEORETICALCONSIDERATIONS __________ . ______.. _________ ..8 Selection of TipSection ____ ..________________ ... _ _ _ _ _ _ _ _52 Pressure Distributions _______________ c_ ___ _ __ __ __ ___ ___8 Methodsofderivationofthicknessdistributions_ _ _ _8 CONCLUSIONS _________________ .. _________________ .._ _ _ __ _ _ _52 ApPENDIX-- METHODSOFOBTAININGDATAINTHELANGLEY Rapid estimation ofpressuredistributions ____ _ _ _ _ _ _10 Two-DIMENSIONALLow-TURBULENCETUNNELS___________54 Numerical examples_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _12 Effectof camber onpressuredistribution ___ .._____ .. _ _13 CriticalMachNumber___ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ __ _ _ __ ___ _ _ _ _13 Moment Coefficients___ _____ ___ _ _ _______ ___ _____ _____ _14 DescriptionofTunnels___ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _54 Symbols ___ .. _____________. _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _54 Measurement ofLift.. ______. ______ ... _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _55 Measurement of Drag ..______________________________. _56 Methods of calculation ____ . _______ . ______ ..__._____14 Tunnel-WallCorrections _____ .._ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _57 Numerical exapl pIes _ . _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _14 Angleof ZeroLift_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _14 Methods of calculation ______________________ .... _ _ _ _14 Numerical examples______________________________14 DescriptionofFlow around Airfoils _____-___ 15 Correction forBlocking at High Lifts ______. _ _ _ _ _ _ _ _ _ _ _ _59 Comparisonw.ithExperiment.. ____________________ .._ _ _ _59 REFERENCES _____________ ..______________________________60 TABLES ___________________ .... ___ ..________________________64 SUPPLEMENTARYDATA: I-Basic Thickness Forms _______ ..____ . _. ___. _____ . _ ___69 EXPERIMENTALCHARACTERISTICS_ _ _ __ _ _ __ _ _ __ _ _ __ _ _ ___ _ _ _ _16-SourcesofData _______ ..__________________________. _ _ _16 J.I-Data forMeanLines_____________________________89 III::""':AirfoilOrdinates_ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ ___ _ ___ _ _ _ _ _ _99 DragCharacteristics ofSmoothAirfoils ________ .._ _ _ _ _ _ _ _16IV-Predicted CriticalMachNumbers ______.__________113 Dragcharacteristics inlow-drag range __ .. ______ . _ _ _16V-AerodynamicCharacteristicsofVariousAirfoil Dragcharacteristics outside low-dragrange_ __ __ _ __ _ _18 Sections___ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ III REPORTNo.824 SUMMARYOFAIRFOILDATA /, ByIRAH.ABBOTT,ALBERTE.VONDOENHOFF,andLOUISS.STIVERS,JR. SUMMARY Recentairfoildata forbothflightand testshave beencollectedandcorrelatedinsojaraspossible.Theflight dataconsistlargelyof dragmeasurementsmade' bythe survey method.Mostdataonairjoil sectiontics were obtained in theLangleypressuretunnel.Detaildatanecessary fortheapplicationof NAOA airfoilstowingdesignarepresentedinsup-plementary figures,togetherwith recent datajor theNAOA 00-, 14-,24-,44-,and230-seriesairjoils.Thegeneralmethods usedtoderivethebasicthicknessjormsjorNAOA6- and 7 -seriesairjoilsandthe'ircorrespondingpressuredistributions arepresented.Data and methodsaregiven jor rapidlyobtain-ingtheapproximatepressuredistributionsjorN AOAfour-digit,five-digit,6-,and 7-seriesairfoils. Thereportincludesananalysisojthelift,drag,pitching-moment,andcritical-speedcharacteristicsoftheairfoils,to-getherwithadiscussionoftheeffectsofsurfaceconditions. Dataonhigh-liftdevicesarepresented.Problemsassociated with lateral-controldevices,leading-edgeair intakes,and inter-ferencearebriefly discussed.Thedataindicatethattheeffects oj surfaceconditiononthe anddragcharacteristicsareat leastaslargeastheeffectsoftheairfoilsha,peandmustbe considered in airfoil selectionand theprediction of wing charac-teristics.AirjoilspermUtingextensivelaminarflow,suchas theNAOA6-seriesairfoils,havemuchlowerdragcoefficients athighspeedandliftcoefficientsthanearliertypesof airfoils if, and only if, thewing surfacesaresmooth andfair.TheNAOA6-scriesairfoilsalsoha,1'efavorable crit?:cal-speedcharacter'isticsanddonotappeartopresent 1Lnu8ualproblemsassociatedwiththeapplicat1:onojhigh-l'i:ft and lateral-controldevices. INTRODUCTION A considerable amount of airfoil data has been accumulated fromtestsintheLangleytwo-dimensionallow-turbulence tunnels.Dataha,vealsobeenobtainedfromtestsbothin otherwindtunnelsand inflightandincludethe effectsof high-liftdevices,surfaceirregularities,andinterference. Some data arealsoavailableon the effectsofai.rfoilsection on aileron characteristics.Although a large amount of these datahasbeenpublished,thescatterednatureofthedata andthelimitedobjectivesofthereportshaveprevented adequateanalysisandinterpretationoftheresults.The purposeofthisreportistosummarizethesedataandto correlateandinterpret t,heminsofar aspossible. Recentinformationontheaerodynamiccharacteristics of NACAairfoilsispresented.Thehistoricaldevelopmentof NACA airfoilsisbrieflyreviewed.Newdataare presented that permit the rapid calculation of the approximate pressure distributionsfortheolderNACAfour-digitandfive-digit airfoilsbythesamemethodsusedfortheN ACA6-series airfoils.The general methods used to derive the basic thick-nessformsforN ACA6- and7-seriesairfoilstogetherwith theircorrespondingpressuredistributionsarepresented. Detaildatanecessaryfortheapplicationoftheairfoilsto wing design are presented in supplementary figuresplaced at theendofthepaper.Thereportincludesananalysisof thelift,drag, andcritical-speedcharac:' teristicsoftheairfoils,togetherwithadiscussionofthe effectsofsurfaceconditions.Availabledataonhigh-lift devicesarepresented.Problemsassociatedwithlateral-controldevices,leading-edgeairintakes,andinterference arebrieflydiscussed,togetherwithaerodynamic.problems of application. Numberedfiguresareusedtoillustratethetextandto presentmiscellaneousdata.Supplementaryfiguresand tablesarenotnumberedbutareconvenientlyarrangedat the endofthe report accordingtothe numerical designation oftheairfoilsection withinthe followingheadings: I-Basic Thickness Forms II-Data. forMean Lines III-Airfoil Ordinates IV--Predicted Critical Mach Numbers V-AerodynamicCharactel'is ticsofVariousAirfoil Sections Thesesupplementaryfiguresandtablespresentthebasic data fortheairfoils. SYMBOLS aspect ratio Fourier seriescoefficients mean-linedesignation,fractionofchordfromlead-ingedgeoverwhichdesignloadisuniform;in derivation ofthickness distributions,ba,siclength usuallyconsidered unity wingspan flapspan,inboard flapspan,outboard drag coefficient dragcoefficientat zerolift liftcoefficient increment of maximum lift cuused by flapdeflection 2 C Ca Cd Cfi CfO 91 C !lCHO Cl Cli Cma.e. Cme/4 Cn D !lH Ho h he k L M Mer OU,OL p P Po pb/2V f}o R Rer s REPORTNO.824-NATIONALADVISORYCOMMITTEEFORAERONAUTiC;:, chord aileron chord sectiondrag coefficient minimum section drag coefficient flapchord,inboard flapchord,outboard flap-chordratio section aileron hinge-momentcoefficientgoc incrementofaileronhinge-momentcoefficientat constantlift hinge-momentparameter section liftcoefficient designsection lift coefficient moment coefficientabout aerodynamiccenter momentcoefficientaboutquarter-chordpoint section normal-forcecoefficient drag . lossof total pressure free-streamtotalpressure sectionaileron hingemoment exitheight constant lift Mach number critical Mach number typical points onupper and lower surfaces ofairfoil pressure coefficient (P-Po) go critical pressurecoefficient resultantpressurecoefficient;differencebetween local upper- and lower-surface pressure coefficients localstatic pressure; also,angular velocity inroll in pb/2V free-streamstatic pressure helixangleof wingtip free-streamdynamic pressure Reynoldsnumber criticalReynolds number pressurecoefficientP) firstairfoilthicknessratio secondairfoilthicknessratio free-streamvelocity inletvelocity localvelocity increment of localvelocity incrementoflocalvelocitycausedbyadditional type of loaddistribution velocity ratiocorrespondingtothicknessi1 velocity rat.iocorrespondingtothickness t2 distancealongchord mean-lineabscissa XL Xu G},. Y Ya YL YI Yu Z z' a !lao .10 s-O T abscissaof lower surface absciss!'\.ofupper surface chordwise position oftransition distanceperpendiculartochord mean-line ordinate ordinate oflower surface ordinateofsymmetricalthicknessdistrihution ordinate ofupper surface complexvariableincircle plane complexvariable in near-cireIeplane angleof attack sectionaileroneffectivenessparameter,ratioof change in sectionangleofattack toincrement of ailerondeflect,ionataconstantvalueoflift coefficient angleof zerolift sectionangleofattack increment of sectionangleof attack sectionangleofattackcorrespondingtodesign liftcoefficient flap01'aileron deflection;down deflection ispositi,-e flapdeflection,inboard flapdeflection,outboard i\,irfoilparameter(IP-() value ofEat trailingedge complexvariable inairfoilplane angular coordinate ofz'; also, angle of which tangent isslopeof mean line .(TiP chord) taper ratIORoot chord tbIft (EffectiveReynolds number) uruenceacorTest Reynolds number angular coordinate ofz airfoilparameter determining radialco.)rdinato ofz averagevalue of1ft502 ..1ftdIP) HISTORICALDEVELOPMENT ThedevelopmentoftypesofNACAairfoilsnowincom-mon usewasstarted in1929with asystematic investigation of a family of airfoilsin the Langley variable-density tunnel. Airfoilsofthisfamilyweredesignatedbynumbershaving fourdigits,suchastheNACA4412airfoil.Allairfoilsof this familyhadthesame basicthicknessdistribution(refer-ence1),andthe amount andtype of camber wassystemati-callyvariedtoproducethefamilyofrelatedairfoils.This investigationoftheNACAairfoilsofthefour-digitseries producedairfoilsectionshavinghighermaximumlift coefficientsandlowerminimumdragcoefficientsthanthose ofsectionsdevelopedbeforethattime.Theinvestigation alsoprovidedinformationonthechangesinaerodynamic characteristicsresultingfromvariationsofgeometryofthe mean lineandthickness ratio(reference1). SUMMARYOFAIRFOIJ"DATA 3 Theinvestigationwasextendedinreferences2and3to includeairfoilswiththesamethicknessdistributionbut withpositionsofthemaximumcamberfarforwardonthe airfoil.Theseairfoilsweredesignatedbynumbershaving fivedigits,suchastheNACA23012airfoil.Someairfoils ofthisfamilyshowedfavorableaerodynamiccharacteristics except foralarge sudden lossin lift at the stall. .Althoughtheseinvestigationswereextendedtoincludea limitednumberofairfoilswithvariedthicknessdistribu-tions(references1 and 3 to 6),noextensive investigations of thicknessdistributionweremade.Comparisonofexperi-mentaldragdataatlowliftcoefficientswiththe,skin-frictioncoefficientsforflatplatesindicatedthatnearlyall oftheprofiledragundersuchconditionswasattributable toskinfriction.It wasthereforeapparentthatanypro-nounced reduction ofthe profiledrag must be obtained by a reductionofthe skin frictionthrough increasingthe relative extent of the laminar boundary layer. Decreasingpressuresinthedirectionofflowandlowair-streamturbulencewereknowntobefavorableforlaminar flow.Anattemptwasaccordinglymadetoincreasethe relativeextentoflaminarflowbythedevelopmentofair-foilshavingfavorablepressuregradientsoveragreater proportionofthechordthantheairfoilsdevelopedin refer-ences1,2,3,and6.Theactualattainmentofextensive laminarboundarylayersatlargeReynoldsnumberswasa previouslyunsolvedexperimentalproblemrequiringthe developmentofnewt.estequipmentwithverylowair-streamturbulence.Thisworkwasgreatlyencouragedby theexperimentsofJones(reference7),whothe possibilityofobtaining extensive laminar layers in flight atrelativelylargeReynoldsnumbers.Uncert.aintywith regardtofactorsaffectingseparationoftheturbulent boundarylayerrequiredexperimentstodeterminethe possibilityofmakingtherathersharppressurerecoveries required over the rear portion of the new type ofairfoil. Newwindtunnelsweredesignedspecificallyfortesting airfoilsunderconditionscloselyapproachingflightcondi-tionsofair-streamturbulenceandReynoldsnumber.The resultingwindtunnels,theLangleytwo-dimensionallow-turbulencetunnel(LTT)andtheLangleytwo-dimensional low-turbulencepressuretunnel(TDT),andthemethods usedforobtainingandcorrectingdataarebrieflydescribed intheappendix.Inthesetunnelsthemodelscompletely spanthecomparativelynarrowtestsections;two-dimensional flowisthus provided,which obviates difficulties previouslyencounteredinobtainingsectiondatafrom testsoffinite-spanwingsandincorrectingadequatelyfor support interference(reference 8). Difficultywasencounteredinattemptingtodesignair-foilshaving desired pressure distributions because of the lack of adeql.latetheory.The Theodorsen method(reference9), asordinarilyusedforcalculatingthepressuredistributions aboutairfoils,wasnot sufficientlyaccurate nearthe leading edgeforpredictionofthelocalpressuregradients.Inthe absenceofasuitabletheoreticalmethod,the9-percent-thick symmetrical airfoil of the N ACA16-series (reference 10) wasobtainedbyempiricalmodificationofthepreviously usedthicknessdistributions(reference4).TheseNACA 16-series sections represented the first familyofthelow-drag high-critical-speed sections. Successiveattemptstodesignairfoilsbyapproximate theoreticalmethodsledtofamiliesofairfoilsdesignated N ACA 2- to 5-series sections (reference 11).Experience with these sections showedthat none of the approximate methods triedwassufficien tlyaccuratetoshowcorrectlytheeffect ofchangesinprofileneartheleadingedge.Wind-tunnel and flight tests of these airfoils showed that extensive laminar boundary layers could be maintained at cOplparatively large valuesoftheReynoldsnumberiftheairfoilsurfaceswere sufficientlyfairandsmooth.Thesetestsalsoprovided qualitativeinformationontheeffectsofthemagnitudeof the favorable pressure gradient, leading-edge radius, and other shapevariables.Thedataalsoshowedthatseparationof theturbulentboundarylayerovertherearofthesection, especially with rough surfaces,limitedthe extent of laminar layerforwhichtheairfoilsshouldbedesigned.Theair-foilsoftheseearlyfamiliesgenerallyshowedrelativelylow maximum liftcoefficientsand,in manycases,weredesigned for a greater extent of laminar flowthan ispractical.It was learnedthat,althoughsectionsdesignedforanexcessive extentoflaminarflowgaveextremelylowdragcoefficients near the designJift coefficient when sm09th,the drag of such sections became unduly large whenrough, particularlyat lift coefficientshigherthanthedesignlift.Thesefamiliesof airfoilsare accordinglyconsidered obsolete. The NACA 6-seriesbasicthicknessformswerederived by newandimprovedmethodsdescribedhereininthesection "Methods of Derivation ofThick.9.essDistributions,"inac-cordance with design criterions established with theobjective ofobtainingdesirabledrag,criticalMachnumber,and maximum-lift characteristics.The present-report deals largely withthecharacteristicsofthesesections.Thedevelop-mentoftheNACA7-seriesfamilyhasalsobeenstarted. This familyofairfoilsischaracterized by agreater extent of laminar flowon the lower than onthe upper surface.These slilctionspermit lowpitching-momentcoefficientswith mod-eratelyhighdesignliftcoefficientsattheexpenseofsome reductionin maximumliftandcriticalMach number. Acknowledgementisgratefullyexpressedfortheexpert guidanceandmanyoriginalcontributionsofMr.Eastman N.Jacobs,whoinitiated and supervisedthiswork. DESCRIPTIONOFAIRFOILS METHODOFCOMBININGMEANLINESANDTHICKNESSDISTRIBUTIONS ThecamberedairfoilsectionsofallN ACAfamiliescon-sidered hereinareobtained by combiningamean lineanda thicknessdistribution.The, necessarygeometricdataand sometheoreticalaerodynamicdataforthemeanlinesand thicknessdistributionsmaybeobtainedfromthesupple-mentary figuresby the methods describedforeach familyof airfoils. 4 REPORTNO.824-NATIONAL ADVISORYCOMMITTEEFORAERONAU'fICS y Meanline --- -------Chord Ime ---I I I \ \ \ Xv =x-Yt sin 8 XL=x+Y,sin 8 Yu=Yc+y,cos8 YL=Yc -Ytcos8 \,Rodiusfhrou9hend of chord '(mean-lineslopeot 05percent chord) 1.00 SAMPLECALCULATIONSFORDERIVATIONOFTHEKACA65,3-818,a=1.0AIRFOIL X11'11, tan 0sin 0cos0 (0)(b) 000----------"6:3i932''6:94765-' -.005.-01324;"(;0200'0.33696 .05.03831.01264.18744.18422.98288 .25.08093.03580.06996.06979.99756 .50.08593.04412001.00000 .75.04456.03580-.06996-.06979.99756 1.0000 ---------- ---------- ----------oThickness distribution obtained from ordinates of the N A OA65,3--018 airfoil. bOrdinates of the mean line, 0.8 of the ordinate forc',= 1.0. , Slope ofradius through end of chord. YI sin 0y, cos0 I Xu I 1/UXL1!L 000000 .00423.01255.ooon.01455.00923-.01055 .00706.03765.04294.05029. C5706-.02501 . 00565.08073.24435.11653.25565-.04493 0.08593.50000.13005.50000-.04181 -.00311.04445.75311.08025.74689-.00865 aa1.0000001.00000a FIGUREI.-Method of combining mean lines and basicthickness forms. Theprocessforcombiningameanlineandathickness. distributiontoobtain the desiredcamberedairfoilsection is illustratedinfigure1.Theleadingandtrailingedgesare defined as the forward and rearward extremities, respectively, ofthemeanline.Thechordlineisdefinedasthestraight line connecting the leading andtrailing edges.Ordinates of the camberedairfoilare obtainedby laying offthethickness distributionperpendiculartothe meanline.The abscissas, ordinates,andslopesofthemeanlinearedesignatedas Xc, Yc,andtan(J,respectively.If XuandYurepresent,respec-tively,theabscissaandordinateofatypicalpointofthe uppersurfaceoftheairfoilandY tistheordinateofthe symmetricalthicknessdistributionatchordwisepositionX, theupper-surfacecoordinatesaregivenbythefollowing relations: xu=X-Yt sin (J(1) (2) Thecorrespondingexpressionsforthelower-surfacecoordi-nates are (3) (4) The center forthe leading-edge radius is foundby drawing alinethroughthe endof the chordat the leading edge with theslopeequaltotheslopeofthemeanlineatthatpoint and laying off adistance fromthe leading edge along this line equaltothe leading-edgeradius.Thismethodofconstruc-tioncausesthecambereda.irfoilstop.rojectslightlyforward oftheleading-edgepoint.Becausetheslopeat theleading edgeistheoreticallyinfiniteforthemeanlineshavinga theoretically finiteloadat the leading edge,theslopeofthe radiusthroughtheendofthechordforsuchmeanlinesis usually taken asthe slope of the mean line atThis c procedureisjustifiedbythemannerinwhichtheslope increasestothetheoretically infinitevalueasx/capproaches o.Theslopeincreasesslowlyuntilverysmallvaluesofx/c arereached.Largevaluesoftheslopearethuslimitedto values of x/c very close to 0 and may be neglected inpractical airfoildesign. Tables of ordinates are included in the supplementary data for all airfoils for which standard characteristics are presented. NACAFOUR-DIGIT-SERIESAIRFOILS Numberingsystem.-Thenumberingsystemforthe NACAairfoilsofthefour-digitseries(reference1)isbased ontheairfoilgeometry.Thefirstintegerindicatesthe maximum value of the mean-line ordinate Ycin percent of the chord.Thesecondintegerindicatesthedistancefromthe leadingedgetothelocationofthemaximumcamberin tenthsofthechord.Thelasttwointegersindicatethe airfoilthicknessinpercentofthechord.Thus,theNACA 2415airfoil has 2-percent camber at 0.4of the chord fromthe leadingedgeand is15percentthick. The firsttwointegerstaken together definethe mean line. forexample,the N ACA 24mean line.The symmetrical air-foilsectionsrepresentingthethicknessdistributionfora familyofairfoilsaredesignatedbyzerosforthefirsttwo integers,asinthecaseoftheN ACA0015airfoil. SUMMARYOFAIRFOILDATA 5 Thicknessdistributions.---Data fortheNACA 0006,0008, 0009,0010,0012,0015,0018,0021,and0024thickness distributionsarepresentedinthesupplementaryfigures_ Ordinatesforintermediatethicknessesmaybeobtained correctly by scalingthetabulated ordinatesinproportionto thethicknessratio(reference1).Theleading-edgeradius variesasthesquareofthethicknessratio.Valuesof (vIV)2,whichisequivalenttothelow-speedpressuredistri-bution,andofvlVarealsopresented.Thesedatawere obtainedbyTheodorsen'smethod(reference9).Valuesof thevelocityincrementst::.va/Finducedbychangingangle01 attack(seesection"Rapid Estimation ofPressureDistribu-tions")arealsopresentedforan additionalliftcoefficient of approximatelyunity.Valuesofthevelocityratiov/V for intermediatethicknessratiosmaybeobtainedapproxi-matelyby linear scalingofthevelocityincrements obtained fromthetabulatedvaluesofv/V forthenearestthickness ratio;thus, (5) Values of the velocity-increment ratio !::.Va/V may be obtained forintermediate thicknessesby interpolation. Mean lines.-Data forthe NACA 62,63,64,65,66, and 67 meanlinesarepresentedinthesupplementaryfigures. Thedatapresentedincludethemean-lineordinatesyo,the slopedYeldx,thedesignliftcoefficienteliandthecorre-spondingdesignangleofattackai,themomentcoefficient cmei4'theresultantpressurecoefficientPR,andthevelocity ratio!::.v/V.Thetheoreticalaerodynamiccharacteristics were obtained from thin-airfoiltheory.Alltabulated values foreachmeanline, accordingly, vary linearlywiththe maxi-mumordinateYe,anddataforsimilarmeanlineswith different amounts ofcamberwithintheusual range may be obtainedsimplybyscalingthetabulatedvalues.Data fortheNACA22meanline may thus be obtainedby multi-plying thedata fortheN ACA 62mean line by the ratio2: 6, and forthe NACA 44mean lineby multiplying thedata for theNACA64mean linebytheratio4:6. NACA'FIVE.DIGIT-SERIESAIRFOILS system.-The numbering system forairfoils of theNACAlive-digitseries ,isbasedonacombinationof theoreticalaerodynamiccharacteristicsandgeometricchar-acteristics(references2and3).Thefirstintegerindicates the amount ,pfcamber intermsofthe relativemagnitudeof the design Witcoefficient;thedesign liftcoefficientintenths isthus three-halves of the first integer.The second and third integerstogether indicate the distance fromthe leading edge tothelocatlonofthemaximumcamber;thisdistancein percentofthechordisone-halfthenumberrepresentedby theseintegers.Thelasttwointegersindicatetheairfoil thickness in percent ofthechord.TheNACA23012airfoil thushasa,,aesignliftcoefficientof0.3,hasitsmaximum camberatUpercentofthe chord, and has athicknessratio of12Thicknessdistributions.--Thethicknessdistributions for airfoilsoftheN ACAfive-digitseriesarethesameasthose forairfoilsoftheNACAfour-digitseries. Meanlines.-Data fortheNACA210,220,230,240,and 250meanlinesarepresentedinthesupplementaryfigures inthesameformasforthemean linesgivenhereinforthe four-digitseries.Alltabulatedvaluesforeachmeanline vary linearly with the maxImum ordinate or with thedesign liftcoefficient.Thus,datafortheNACA430meanline ma,ybe obtained by multiplying thedata fortheNACA 230 mea,nlineby theratio4:2andfortheNAOA 640mean line bymultiplyingthedatafortheNACA240meanlineby the ratio6: 2. NACAl-SERIESAIRFOILS Numberingsystern.-TheNACAI-seriesairfoilsaredes-ignatedbyafive-digit'number-as,forexample,the NACA16-212section.Thefirstintegerrepresentsthe seriesdesignation.Thesecondintegerindicatesthedis-tanceintenthsofthechordfromtheleadingedgetothe positionofminimumpressureforthesymmetricalsection atzerolift.Thefirstnumberfollowingthedashindicates theamountofcamberexpressedintermsofthedesignlift coefficientintenths,andthelasttwonumberstogether indicatethethicknessinpercentofthechord_Thecom-monlyusedsectionsofthisfamily haveminimumpressure at0.6ofthechordfromtheleadingedgeandareusually referredtoastheNACA16-seI'iessections. Thicknessdistributions.-DatafortheNACA16-006, 16-009,16-012,16-015,16-018,and16-021thickness distributions(reference10)arepresented inthesupplemen-tary figures.Thesedata aresimilar in formtothedata for thoseairfoilsoftheN ACAfour-digitseries,anddatafor intermediatethicknessratiosmaybeobtainedinthesame manner. Mean lines.-TheNACA16-seriesairfoilsascommonly usedarecamberedwithameanlineoftheuniform-load type(a=1.0),whichisdescribedunderthesectionforthe N ACA6-seriesairfoilsthatfollows.If anyothertypeof meanlineisused,thisfactshouldbestatedintheairfoil d.esignation. NACA6-SERIESAIRFOILS Numberingsystem.-TheN ACA6-set'iesairfoilsareusu-allydesignatedby asix-digitnumbertogetherwithastate-mentshowingthetypeofmeanlineused.Forexample, inthedesignationNACA65,3-218,a=O.5,the"6"is theseriesdesignation.The" 5"denotesthechordwise positionofminimumpressureintenthsofthechordbehind theleadingedgeforthebasicsymmetricalsection at zero lift.The" 3"followingthecommagivestherangeoflift coefficient in tenths above and below the design lift coefficient in which favorablepressuregradientsexist onboth surfaces. The"2"followingthedash givesthedesignlifteoefficient intenths.The lasttwodigitsindicatetheairfoilthickness inpercentofthechord.Thedesignation" a=0.5"shows thetypeofmeanlineused.Whenthemean-linedesigna-tionisnotgiven,itisunderstoodthattheuniform-load mean line(a= 1.0)has been used. 6REPORTNO.824-NA'rIONAL ADVISORYCOMMITTEEFORAERONAUTICS Whenthemeanlineusedisobt.ainedbycombiningmore t.hanonemeanline,thedesignlift.coefficientusedint.he designation isthe algebraic sum ofthe design lift coefficients ofthe mean linesused,andthemea.nlinesaredescribedin the statement followingthe number asin the following case: NACA65,3-218' {a=0.5CII=O ..3} a=l.O,Cli=-0.1 Air'foils having a thickness distribution obtained by linearly increasing or decreasing the ordinates of one of the originally derived thickness distributions are designated as in the follow-ingexample: NACA65(318)-217,a=0.5 Thesignificanceofallofthenumbersexceptthoseinthe parentheses isthe same as before.The first number and the last twonumbers enclosedin the parentheses denote, respec-tively,thelow-dragrangeandthethicknessinpercentof thechordofthe originallyderivedthicknessdistribution. ThemorerecentNACA6-soriesairfoilsarederivedas membersofthicknessfamilieshavingasimplerelationship between the conformal transformations for airfoils of different thicknessratiosbuthavingminimumpressureatthesamt;\ chord wiseposition.Theseairfoilsaredistinguishedfrom thpearlierindividuallyderivedairfoilsby writingthenum-ber indicating the low-drag ra.nge as a.subscript; for exa.mple, NACA653-218,a=0.5 ForNACA6-se1'iesairfoilshavingathicknessratioless than0.12ofthechord,the subscriptnumberindicatingthe low-drag rangeshouldbe lessthanunity.Ratherthanusc afmctionalnumber,asubscript of unitywasoriginallyem-ployedfortheseairfoils.Sincethisusa.geisnotconsistent withthe previous definitionofanumber indicatingthe low-drag range,the designations of a.irfoil sections having a thick-nessratio lessthan 0.12of thechordare nowgivenwithout suchanumber.Asanexample,anN AOA6-seriesairfoil havingathicknessratioof0.10ofthechordwouldbe designated: NAOA65-210 Ordinates forthe basic thiclniess distributions designated by asubscriptareslightlydifferentfromthoseforthecorre-spondingindividuallyderivedthicknessdistributions.As before,iftheordinatesofthebasicthicknessdistribution have been changed 1)Y a factor,the low-drag range andthick-nessratiooftheoriginalthicknessdistributionareenclosed in parentheses as follows: NAOA65(318)-217,a=O.5 If, howevPJ',the ordinates of abasic thickness distribution having athickness ratio less than 0.12ofthe chord have been changedbyafactor,'thenumberindicatingthelow-drag rangeiseliminatedandonlytheoriginalthicknessratiois enclosedin parentheses as follows: NACA65(10)-211 If the design lift coefficient in tenths or the airfoil thickness inpercentofchordarenotwholeintegers,thenumbers giving these quantities are usually enclosedin parentheses as inthe followingdesignation: NACA65(318)-(1.5) (16.5),a=O.5 Someearlyexperimentalairfoilsaredesignatedbythein-sertionoftheletter"x"immediatelyprecedingthehyphen as inthedesignation66,2x-115. Thickness distributions.-Datafor available N AOA 6-series thicknessformsarepresentedinthesupplementary figures.Thesedataarecomparablewiththesimilardata forairfoilsoftheNACAfour-digitseries,exceptthatordi-nates forintermediatethicknessesmaynotbecorrectly ob-tained by scaling the tabulated ordinates proportional tothe thicknessratio.Thismethodofchangingtheordinatesby afactorwill,however,produce shapessatisfactorily approx-imatingmembersofthefamilyifthechangeinthickness ratioissmall.Valuesofv/Vand6.v./Vforintermediate thicknessratiosmaybeapproximatedasdescribedforthe NACA four-digitseries. Meanlines.-Themeanlinescommonlyusedwiththe NACA6-seriesairfoilsproduceauniformchordwiseloading fromtheleadingedgetothepoint~ = aandalinearlyde-creasingloadfromthispointtothetrailingedge.Data forNAOAmeanlineswithvaluesofaequalto0,0.1,0.2, 0.3,0.4,0.5,0.6,0.7,0.8,0.9,and1.0arepresentedinthe supplementaryfigures.Theordinateswerecomputedby thefollowingformula,whichrepresentsasimplificationof theoriginalexpressionformean-lineordinatesgivenin reference11: xxx ~ -c logec+U-h cI(6) where 1 [1 1] h=- - (1-a)210g(l-a)-- (1-a)2+U I-a2.e4 TheidealangleofattackIXIcorrespondingtothedesign lift coefficientisgivenby Cit cx(==-h27l'(a+D ThedataarepresentedforadesignliftcoefficientCit equaltounity.Alltabulatedvaluesvarydirectlywith thedesignliftcoefficient.Oorrespondingdataforsimilar mean lines with other design lift coefficients may accordingly beobtainedsimplybymultiplyingthetabulatedvaluesby the desireddesign lift coefficient. In order tocamberNAOA6-seriesairfoils,mean linesare usuallyusedhaving valuesofa,equaltoor greaterthanthe distancefromtheleadingedgetothelocationofminimum pressurefortheselectedthicknessdistributionatzerolift. Forspecialpurposes,loaddistributionsotherthanthose correspondingtothesimplemean lines may beobtainedby combining twoor moretypes of mean line having positive or negative valuesof the design lift coefficient.The geometric SUMMARYOFAIRFOILDATA 7 and aerodynamic characteristics of such combinations may be obtained byalgebraicadditionofthevalues forthe compo-nent mean lines. NACA7-SERIESAIRFOILS Numbering system.-The NACA 7-series airfoils are desig-nated by anumber ofthe followingtype(reference12): NACA747A315 Thefirstnumber"7"indicatestheseriesnumber.The secondnumber"4"indicatestheextentover theupper sur-face,intenthsofthechordfromtheleadingedge,ofthe regionoffavorablepressure gradient at the design lift coeffi-cient.Thethirdnumber"7" indicatestheextentoverthe lowersurface,in tenthsofthechordfromtheleadingedge, ofthe region of favorablepressure gradient at the design lift coefficient.The significanceofthe last groupofthree num-bersisthesameasforthepreviousNACA6-seriesairfoils. Theletter"A"whichfollowsthefirstthreenumbersisa serial letter to distinguish different airfoils having parameters thatwouldcorrespondtothesamenumericaldesignation. Forexample,asecondairfoilhavingthesameextentof favorablepressuregradientoverthe'upperandlowersur-faces,the same design lift coefficient,and the same maximum thicknessastheoriginalairfoilbut having adifferentmean-linecombinationorthicknessdistributionwouldhavethe 20 -r-f---" -I.B V k" ,NACA747A315 V '(uppersurface) IIIII 1.6 l 1 serialletter"B."MeanlinesusedfortheNACA7-series airfoilsareobtainedbycombiningtwoormoreofthepre-viouslydescribedmeanlines.Alistofthethicknessdis-tributionsandmean linesusedtoformtheseairfoilsispre-sentedintable 1.Thebasicthickness distribution is given adesignationsimilar tothoseofthefinalcamberedairfoils. Forexample,thebasicthicknessdistributionforthe NACA 747A315and 747A415airfoils is given the designation NACA 747 A015 even though minimum pressure occurs at O.4c on both upperandlowersurfacesat zerolift.Combination ofthisthicknessdistributionwiththemeanlineslistedin tableIfortheNACA747A315airfoilchangesthepressure distribution tothedesired type as shown in figure2. Thicknessdistributions.-DataforavailableNACA7-seriesthicknessdistributionsarepresentedinthesupple-mentaryfigures.Thesethicknessdistributionsareindi-viduallyderivedanddonotformthicknessfamilies.The thicknessratiomay,however,bechangedamoderate amount-say1or ,2percent-by multiplyingthetabulated ordinates by asuitable factor without seriously altering their characteristic features.Values of (V/V2) and of v/V forthinner orthickerthicknessdistributionsmaybeapproximatedby the method ofequation (5).If the change in thickness ratio issmall,tabulatedvaluesofI1Va/Vmaybeapplied'directly with reasonablea.ccuracy. " "" "-I _I 11------, "" . NACA747AOl5basic 1.4 1.2 ! (v)'1.0 I ! I .8 .6 .4 .2 o / ---- /' . I rhicimessdistribution k r:-:JCA I(lowersurface) .3.4.5 xlc -----:----... "" "'""-'-. "-"'" .6.7.8.91.0 FIGURE2.-TheoreticalpressuredistributionfortheNACA747A315airfoilsectionatthedesignliftcoefficient and theNACA 747AOlijhusirthickness dis:l'ibuUOll. TABLEI.-ANALYSISOFAIRFOILDE.RIVATION Mellon-linecombination 1 AirfoilBasic thickness1____-;-___--;-____ ,____,_----;--------.-----;-----,------;----,---1 designationform a=Oa=O.la=0.2a=0.3 747A315 ________747A015 ____________________________ "" ______________________________ _ 747A415 ________747A015 ____________________________________________________________ _ a=0.4 0.763 .763 a=0.5a=0.6 IThe numbers in the various columnsheaded"Mean-line combination". indicate the magnitude orthe design lift coefficient used. a=0.7a=0.8a=0.9a=1.0 ::::::::::::: :::::: ::::::: ----ii:ioo----8 REPOR'l'NO.824-NATIONAL ADVISORYCOMMITTEEFORAERONAUTICS THEORETICALCONSIDERATIONS PRESSURE Aknowledgeofthe pressuredistribution overanairfoilis desimbleforstructuraldesignandforestimationofthe critical Mach number and moment coefficient if tests are not available.Thepressuredistributionalsoexertsastrong orpredominantinfluenceontheboundary-layerflowand, hence,ontheairfoilcharacteristics.It isthereforeusually advisabletorelatetheairfoilcharacteristicstothepressure distribution rather than directlytothe airfoil geometry. Methodsofderivationofthicknessdistributions.-As mentionedinthesection"HistoricalDevelopment,"the basicsymmetricalthicknessdistributionsoftheN ACA6-and7-seriesairfoils,togetherwiththeircorrespondingpres-sure distributions,arederivedby meansofconformaltrans-formations.Thetransformationsusedtorelatethe known flowaboutacircletothataboutanairfoilsectionwere developedbyTheodorseninreference.9.Figure3shows schematicallythesignificanceofthevariousphasesofthe process. The circle about Whichthe flowisoriginally calculated has its center at the origin and aradius of aiD.The equation of Z-p/one\-------jL----"---l =-.'= e fll ->;.)4-I(S-tJ) z Z-p/one f-------,fL------'L----, f=Xri y FIGURE3.-Transformations usedtoderiveairfoilsnndcalculatepressuredistributionR. thiscircleincomplexcoordinatesis z=aefo+iq, where zcomplexvariableincircleplane angular coordinateofz abasic lengthusuallyconsideredunity 1/10constant determining radius of, circle (7) Thistruecircleistransformedintoanarbitrary,almost circular curve bytherelation

='_= e(f-fol+i{O-q,) z the equation of the almostcircular curveis z' =aef+iO where z'complexvariableinnear-circleplane aef radialcoordinate ofz' f}angular coordi.nateofz' (8) (9) Inorder Jorthetransformation(8)tobeconformal,itis necessarythatthequantity(f}-r/(giventhesymbol-E) be the conjugate function of (1/I-if;0);that is, if Eis represented by aFourier seriesofthe form '"'" e=L: Ansin n-L: Bncosn 11 then(if;-1/Io)isgivenbytherelation '"'" (1/1-1/10)="'22An cosnr/>+::8 Bn sin nr/> 11 This relationshipindicatesthat,ifthe functionE(r/isgiven, (1/1-1/10)canbecalculatedasafunctionofr/>.Meansof performingthiscalculationarepresentedinreference13. Thetransformationrelatingthealmostcircularcurveto tbe airfoilshape is (10) wherefisthecomplexva.'iableintheairfoilplane.The coordinatesoftheairfoilxand yare the realandimaginary parts of f, respectively.These coordinates are given hy the relations .c= 2acosh1/1cos8 y=2a sinh 1/1sin f} (11) (12) The velocity distribution interms of the airfoil parameters 1/1and is given exactly for perfect fluid flow by the expression v[sin (aO+TE)]efO V= (sinh21/1+sin28)[( 1-:;y (13) SUMMARYOFAIRFOILDATA 9 where localvelocityover surfaceofairfoil ':I. vfree-streamvelocity r aosection angle ofattack 0/0averagevalueof 0/(i1f'L21J"0/de/> ) ETEvalueofe at trailing edge Thebasicsymmetrical shapeswerederivedbyassuming suitable values of de/de/>as.a function of e/>.These values were chosen on the basis ofexperience and are subjectto the eonditions that andde/de/>at e/>isequaltodf/dcpat-cp.Theseconditions arehecessaryforobtainingclosed'symmetricalshapes. ValuesoffCe/wereobtainedsimplybyintegrating ;; de/>. Valuesofo/(cp)were foundby obtaining theconjugateofthe curveofeCe/andaddingavalue%suffieienttomakethe. ,'alueof0/equaltozeroatcp=1f'.Thisconditionassuresa sharptrailing-edgesbape. Inasmuch as small changes in the velocity distribution at any point ofthe surface are proportional to1 +J; (seerefrrence14),theinitiallyassumedvaluesof df/de/>were alteredbyaprocessofsuccessiveapproximationsuntilthe desired type of velocity distribution was obtained.After the finalvalues of 0/and e were obtained, the ordinates of thr basic thicknessdistributionwerecomputedbyequations(11) and(12). When these computations were made, it appeared that there wasan optimumvalueoftheleading-edgeradiusdependent. upontheairfoilthicknessandthepositionofminimum pressure.If theleading-edgeradiuswastoosmall,apre-maturepeakinthepressuredistributionoccurredinthe immediatev-icinityofthr leadi.ngedgeas theangle ofatt.ack wasincreasrd.If theleading-edgeradiuswastoolarge,a premature peak occurred a few prrcent of the chord behind thr lradingedge.WiththeCOrI'rctl(lading-edgeradiusj t.he pressuredistribut.ionbecamenearlyflatovertheforward portionoftheairfoilbeforethenormalleading-edgepeak formedat the higher liftcoefficients.Curvesofthe param-eters0/,f,dl/;/de/>,de/de/>plottedagainste/>fortheNACA 643-018airfoilsection aregivenin figure4. Experience has shown ,,,,henthe thickness ratio of an originallyderived basic formwasincreased merely by multi-plying all the ordinates by a constant factor,an unnecessarily largedecreaseinthecriticalspeedoftheresultingsection occurred.Reducingthethickness ratioinasimilar manner caused an unnecessarily large decrease inthe low-dragrange. For this reason, each of the earlier N ACA 6-series sections was individually derived.It was later foundthat it was possible .16 .08 o d;dE dfjJ'dfjJ. -.08 -.16 .24 .16 .08 o >I,e I -.08 -.IB o "\ '--i V V '---. / ! ... dE / V \dfjJ / \ '\ \ 1\ J --1\ i\ V \' V \ ----2 / / \- Ir dlf.-I V\ "'" h dtPJ / "j II // V/ , \ / V i V V "'/ /E II \ j V 1\ V-/ C\ I/ '" / .. -f--_ ..

45 6 tP,radians FIGURE4.-Variation of airfoilparameters,p,with", for;heXACA643-018airloil. sectionbasic thicknessform. t.oderivebasicairfoilparametersI/;andethatcouldbe multipliedbyaeonstantfaetortoobtainairfoilsofvarious thicknessratios,withoutha.vingtheaforementionedlimita-tionsintheresultingsect.ions.Eachofthemorerecent familiesofNACA6-seriesairfoils,inwhichnumericalsub-scripts are usedinthe designation,having minimum pressure at a given chordwise position was obtained by scalingupand downthebasicvaluesoftheairfoilparameters1/;,andE. Theoreticalpressuredistributions(indicatedby(V)) fora, familyofN ACA65-seriesa.irfoilscoveringnrangeof thicknessratiosaregiveninfigure.5(a).Thisfigureshows the typical increase in the magnitude of the favorable pressure gradient, increase in maximum velocity over the surface,and increase in the relative pressure recovery over the rear portion oftheairfoil'withincreaseinthicknessratio.Figure5(b) showsthe pressure distrihution foraseriesof bnsicthickness formshavingathicknessratioof0.15andhavingminimum pressureatvariouschordwisepositions.Thevalueofthe minimumpressurecoefficientisseentodecreaseandthe magnitudeofthepressurerecoveryovertherenr portionof theairfoiltoincreasewiththerearwardmovementofthe pointofminimumpressure. 10 REPOR'!'NO.824-NATIONAL ADVISORYCOMMIT'!'EEFORAERONAU'rtCS 2.828 24 ,,,,,, -_--- MACA65,-012 ------- MACA652-015 --'--- NACA65-018 ---- MACA65.-021 c::: ====-2.4 MACA65,-012 - 64 -oJs I-- ' -------- MACA65,-015 r--_--- NACA---- NACA67,1-015 NACA64,-015 2020 c::==::::::=- c::==::::::=-/.6 (V! 1.2 .8 .4

-""\

.-:------' f;;::- - " { " ','

MACA652-015/6 (VI . /2 MACA65.J-0I8 .8 MACA654-021.4 -:::c==-u. = -- \ f "

c:::> NACA67,/-015 NACA65.-015 c:=:::::::=-NACA6tJ,-015 (a)(b) o.2.4.6.81.0o.2.4.6.81.0 .:rIc.:ric (a)Variation with thickness.(b)Variation with position of minimum pressure. FIGURE5.-Theoretical presmre distributions for some basic symmetrical NACA6-seriesairfoils at zero lift. The pressuredistribution foroneofthebasic symmetrical thicknessdistributions at various lift coefficientsisshownin figure6.Atzeroliftthepressuredistributionsoverthe upper and lower surfaces are the same.As the lift coefficient isincreased,theslopeofthepressuredistributionoverthe forward portion of the upper surface decreases until it becomes flat at a lift coefficient of 0.22(the end ofthe low-drag range). As the lift coefficient is increasedbeyondthis value, the :usual peak inthe pressuredistributionformsattheedge. Rapidestimationofpressuredistributions.-Inthedis-cussion that follows,the term "pressure distribution" isused to signify the distribution ofthe static pressures on the upper 5.0 4.0 3.0 (v! 2.0 FIGURE6.-TheoreticalpressuredistributionfortheN ACA65.-015airfoilatseverallift .coefficients. and lowersurfacesoftheairfoilalongthe chord.Theterm "loaddistribution"isusedtosignifythedistributionalong the chord ofthe normal forceresulting fromthe difference in pressureonthe upper and lowersurfaces. Thepressuredistributionaboutanyairfoilinpotential flowmay becalculatedaccuratelyby ageneralization ofthe methodsoftheprevioussection.Althoughthismethodis notundulylaborious,thecomputationsrequiredaretoo longtopermit quickand easy calculations for large numbers of airfoils .. The need for a simple method of quickly obtaining pressmedistributionswithengineeringaccuracyhasledto thedevelopmentofamethod(reference15)combining featuresofthin- andthick-airfoiltheory.Thissimple methodmakesuseofpreviouslycalculatedcharacteristics of a limited number of mean lines and thickness distributions thatmaybecombinedtoformlargenumbersofairfoils. Thin-airfoiltheory(references16to18)showsthatthe load distribution of athin airfoil may be considered to consist of:(1)abasicdistributionat theidealangleofattackand (2)anadditionaldistributionproportionaltotheangleof attack as measured from the ideal angle of attack. The first load distribution isa function only of the shape of thethinairfoil,or(ifthethinairfoilisconsideredtobea meanline)ofthemean-linegeometry.Integrationofthis loaddistributionalongthechordresultsinanormal-force coefficientwhich,at smallanglesofattack,issubstantially equaltoaliftcoefficientCit,whichisdesignatedtheideal ordesignliftcoefficient.If,moreover,thecamberofthe mean line ischangedby multiplying the mean-lineordinates byaconstantfactor,theresultingloaddistribution,the ideal or design angle of attack at and the design lift coefficient Cli may be obtaIned simply by mUltiplying the original values by the same fnctor.The characteristics of a large number of mean linesarepresented in both graphicalandtabular form inthesupplementaryfigures.Theload-distributiondata arepresentedbothintheform oftheresultantpressure. coefficient PR and in the formofthecorresponding velocity-increment ratios !.lv/V.Forpositivedesignlift thesevelocity-incrementratiosarepositiveontheupper SUMMARYOFAIRFOILDATA 11 !'Iudaceandnegativeonthelowersurface;theoppositeis truefornegativedesignliftcoefficients. The second loaddistribution,which results fromchanging the angleofattack,isdesignated herein the" additional load distribution"andthecorrespondingliftcoefficientisdeRig-natedthe" additional liftcoefficient."Thisadditional load distribution contributes nomomentabout thequarter-chord point and,accordingtothin-airfoiltheory,isindependent of theairfoilgeometryexceptforangleofattack.Theaddi-tionalloaddistributionobtainedfromthin-airfoiltheoryis oflimited practical application, however, because this simple theory leadstoinfinitevaluesofthevelocityat the leading edge.This _difficultyisobviatedbytheexactthick-airfoil theory (reference 9)which also shows that the additional load distributionisneithercompletelyindependentoftheaidoil shapenorexactlyalinearfunctionoftheliftcoefficient. Forthisreason,theadditionalloaddistributionha,sbeen calculated by the methods of reference 9 for each of the thick-nessdistributionspresentedinthesupplementaryfigures. Thesedataarepresentedintheformof velocity-increment rat.iosAVa/V corresponding to an additional liftcoefficientof approximatelyunity.Forpositiveadditionalliftcoeffi-c:ients,these. velocity-incrementratiosarepositiveonthe uppersurfacesandnegat.iveonthelowersurfaces;the oppositeistruefornegativeadditionalliftcoefficients. In tothepressuredistributionsassociatedwith twoloaddistributions,anotherpressure' distribution existswhichisassociatedwiththebasicsymmetricalthick-nessformorthicknessdistributionoftheairfoil.This pres-suredistributionhasbeencalculatedbythemethods describedintheprevioussectionfortheconditionofzero liftandispresentedinthesupplementary figuresas('f; )2, whichisequivalentatlowMachnumberstothepressure coefficientS,andasthelocalvelocityratioVIV.This localvelocityratioisalwayspositiveandisthesamefor correspondingpoints onthe upperand lowersurfacesofthe thicknessform. The velocity distribution about the airfoil is thus considered tobecomposedofthreeseparateandindependentcom-ponentsas follows: (1)Thedistributioncorrespondingtothevelocitydis-tributionoverthebasicthicknessformatzeroangleof attack (2)Thedistributioncorrespondingtothedesignload distributionofthemeanline (3)Thedistributioncorrespondingtotheadditionalload distributionassociatedwithangleofattack The velocity-increment ratiosAviV and At'a/V correspond-ingtocomponents(2)and(3)areaddedtothevelocity ratiocorrespondingtocomponent(1)toobtainthetotal velocityatonepoint,fromwhichthepressurecoefficientS isobtained; thus, (14) When this formula is used,values of the ratios corresponding to one value ofxareaddedtogether and the resultingvalue ofthepressurecoefficientSisassignedtotheairfoilsurface It tthe same value of X. Thevaluesof.v/V andof inequation(14)should, ofcourse,correspondtotheairfoilgeometry.Methods of obtaining the proper values of these ratios from the values tabulatedinthesupplementary figuresarepresentedinthe previous section"Description of Airfoils. " WhentheratioAvalV hasthevalueofzero,theresulting distributionofthepressurecoefficientSwillcorrespond approximatelytothepressuredistributionoftheairfoil sectionat thedesign liftcoefficientCli ofthe mean line,and theliftcoefficientmaybeassignedthisvalueasafirstap-proximation.If thepressure-distributiondiagramisinte-grated,however,thevalueofClwillbefoundtobe greater than Cliby anamountdependentonthethicknessratioof thebasicthicknessform. . The pressuredistributionwillusuallybedesiredat some specifiedliftcoefficientnotcorrespondingtoCli'Forthis purposetheratiomustbeassignedsomevalue.ob-tainedby multiplyingthetabulatedvalueofthisratioby a factorj(a).Forafirstapproximationthisfactormaybe assignedthe value (15) where CIisthelift coeffici(1ntfor whichthe pressure distribu-tionisdesired.If greateraccuracyisdesired,thevalueof j(a)maybeadjustedbytrialanderrortoproducethe actualdesiredliftcoefficientasdeterminedbyintegration ofthe pressure-distribution diagram. Althoughthismethodofsuperpositionofvelocitieshas inadequatetheoreticaljustification,experiencehasshown thattheresultsobtainedareadequateforengineeringuse. Infact,theresultsofeventhefirstapproximationsagree wellwithexperimentaldataandaretl,dequateforatleast preliminaryconsiderationandselectionofairfoils.Acom-parisonofafirst-approximationtheoreticalpressuredistri-bution with an experimental distribution is shown in figure7. c ___

NACA '66(215)-2/6,a06 2.0 sJ-f'a;e: ."_0. V r-o-: r-\ /;6 II i\ I--2 surface "-;; '" 1.2

.8 .4 --Theory oExperimenf o.2.4.. 6.8/.0 :rIc FIGURE7.-Comparison of theoretical and experimental preS3ure distributions for theN ACA 66(215}-216,a=0.6 airfoil.c,=0.23. 12REPORTNO.824-NATIONAL ADVISORYCOMMITTEEFORAERONAUTICS Somediscrepancynaturallyoccursbetweentheresultsof experiment and of any theoretical method basedon potential flow'becauseofthepresenceoftheboundarylayer.These effectsaresmall,however,overtherangeofliftcoefficients for whichthe boundary layer isthin .andthe drag coefficient ifllow. Numericalexamples.-The followingnumericalexamples areincludedtoillustratethemethodofobtainingthefirst-approximationpressuredistributions: Example1:FindthepressurecoefficientSatthestation x=0.50ontheupperandlowersurfacesoftheNACA 653-418airfoilat aliftcoefficientof 0.2. FromthedescriptionoftheNACA6-seriesairfoils, itis determinedthatthisairfoilisobtainedbycombiningthe NACA653-018basicthicknessformwiththea= 1.0 .type meanlinecamberedtoadesignliftcoefficientof0.4.The followingdataareobtainedfromthesupplementaryfigures forthis thickness formand mean lineat x=0.50: v V=1.235 The desired.valueofAVa/V iscomputedasfollowsby useof equation(15):

=-0.031 ThedesiredvalueofAV/V isobtainedby multiplyingthe tabulatedvaluebythedesign liftcoefficient as stated in the descriptionoftheNACA6-seriesairfoils.Thus, AV V=(0.250)(0.4) =0.100 Substituting these values in equation (14)gives the following valuesof S: For the upper surface S= (1.235+0.100-0.031)2 =1.700 For the lower surface S= (1.235-0.100+0.031)2 =1.360 Example2:FindthepressurecoefficientSatthestation x=0.25ontheupperandlowersurfacesoftheNACA 65(215)-214,a=0.5airfoilat aliftcoefficientof 0.6. The airfoil designation shows that this airfoil was obtained by combiningathicknessformobtainedby multiplying' the ordinatesoftheNACA652-015formbythefactor14/15 withthea=0.5typemeanlinecamberedtoadesignlift coefficientof 0.2. Thesupplementaryfiguresgiveavalueof1.182forv/V atx=0.25 forthe NACA 652-015 basic thickness form.The desiredvalueofv/Visobtainedbyapplyingformula(5) asfollows: v14 V=(1.182-1)15+1 =1.170 Fromthesupplementaryfiguresthefollowingvaluesof AVa/V are obtained at x=0.25 for the following basic thickness forms: ByinterpolationthevalueofAVa/Vof0.287maybe assignedtothe14-percent-thick form.The desiredvalue of AVa/V isthencomputedasfollowsby useof equation(15): A'v Va=(0.287)(0.6-0.2) =0.115 Data presentedinthesupplementary figuresforthea=0.5 typemean linesgivethe value of0.333forAv/V at x=0.25. AsstatedinthedescriptionoftheNACA6-seriesairfoils, thedesiredvalueofAV/Visobtainedbymultiplyingthe tabulatedvalueby the design liftcoefficient.Thus, = (0,333)(0.2) =0.067 Substituting theforegoingvaluesinequation(14)givesthe valuesofSas follows: For the upper surface S= (1.170+0.067 +0.115)2 =1.828 For thelower surface S= (1.170-0.067 -0.115)2 =0.976 Example3:FindthepressurecoefficientSat the station x=0.30ontheupperandlowersurfacesoftheNACA2412 airfoil at alift coefficientof0.5. ThedescriptionofairfoilsoftheNACAfour-digitseries shows that the necessary data may be found from the NACA 0012thicknessformand64mean lineinthesupplementary figures.From these figuresthe followingdata are obtained: At x=0.30 At x=0.30 v V=1.162 SUMMARYOFAIRFOILDATA For theNACA64mean lineat x=0.30 b.1) V=0.260 For theNACA64meanline Thevaluesofb.v/Vllndelicorrespondingtotheairfoil geometryare obtainedbymultiplyingtheforegoingvalues bythefactor2/6asexplainedinthedescriptionofthese airfoils;thus,

=0.087 =0.253 The desiredvalueofb.va/V isobtained fromequation (15) asfollows: (0.239) (0.5-0.253) =0.059 Substituting the proper values in equation(14)givesthe valuesofSasfollows: For theuppersurface S= (1.162+0.087+0.059)2 =1.712 For the lowersurface S= (1.162-0.087 -0.059)2 =1.032 Effect of camber on pressure distribution.-At zero lift the pressuredistributionsovertheupperandlowersurfacesof abasicsymmetricalthicknessdistributionare,ofcourse, identical.The effectofcamber onthepressure distribution NACA65,-015 1--+--I---+_+--1--.,..4-'N.A CA65,-015 20,,NACA65,-215 f-+--+-=-,....,,=f--;. 81216 cO , J,/r[:... ;i/ th:ckness,percen,+or' chord (a)XACA four- and fivedigitseries. (b)XACA63series. (elXACA64-series. (d)X .'I.e A55series. (e)XAC A66-series, II eli o0r--().2 Ll.4 r---'V ,6 qi 00-'---a.I .2 " .4 r--'V,6 I cli 00- .2 ". .4 r--'V .8 C't o r--I .2 " ,4 r--Ii 28 ':> Jc. FIGFRE12.-Variationofminimumsectiondragcoefficientwithairfoilthicknessratiofor severalNACAairfoilseNionsofdifferel1', inbothsmooth androughconditions. R=6X106 Thedatapresentedinthesupplementaryfiguresforthe NACA6-seriesthicknessformsshowthattherangeoflift coefficientsforlowdragvariesmarkedlywithairfoilthick-ness.It hasbeenpossibletodesignairfoilsofthickness with a total theoretical low-drag range ofliftcoeffi-cientsof0.2.Thistheoreticalrangeincreasesbyimately0.2foreach3-percentincreaseofairfoilthickness. Figure13showsthatthetheoreticalextentofthelow-drag rangeisapproximatelyrealizedataReynoldsnumberof 9 X106.Figure13alsoshowsacharacteristictenclE'ncyfor thedragtoincreasetosomeextenttowardtheupper endof thelow-dragrangeformoderatelycamberedairfoils,pai'-ticularlyforthethickerairfoils.AlldatafortheX ACA 6-seriesairfoilsshowadecreasein the extent of the IO\'l-drag rangewithincreasingReynoldsnumber.Extrapolationof therateofdecreaseobservedatReynoldsnumbersbelow 9X 106 wouldindicat(>avanishinglysmalllow-dragrangeat flightvaluesoftheReynoldsnumber.Testsofacarefully constructedmodeloftheXACA65(421)-420airfoilshowed, however,thattherateofreductionofthelow-dragrange withincreasingReynoldsnumberdecreasedmarkedlyat Reynoldsnumbersabove9X 106 (fig.14).Thesedataindi-catethattheextentofthelow-dragrangeofthisairfoilis reducedto about olH'-half thetheoretical value ata Reynolds number of35 X 106 .032 .028 .024 J '1-.' c:

"Q)o lJ.016 {; (;:.012 .0 .;:: (; .004 f!.;.6-1.2 6 N)CA oNACAtN. -415 . 35.0 'i' If ,

(I) 00 -./-.4 >t "Q. ""-.2-.8 ..... t:

-"-12 'l:> .> o \J ..... t:-.4-/.0 -.5-2.0, -32 I,....-: -rp..:: V-IA' 1Jt' rJ I "I I t

II \ I VIIL '1/ -24-16-808162432 Section anqleof attack,0, deq .2

-.2 .2

-.2 .0/6 +.:c c.012

.0 ..::: "-III o ".008 8' {; o -.I ciEci'-'

-.2 \ o \.)-.3 ..... -.4 V 'J V r--7 -.5_ -1.6 f.--"' t--.2 f.--"' I--.2 -1.2 I .036 -r---r---t--I---.032 I--N1CA f5a-fB .028 .4.6.81.0 J:/c -.024-r------... e---.020. NACA 0=0.5 IILII .4.6.8t.O :ric / 1& r I II {I " ( .....-III ..... Iif 'Q. lsi a.c. posHion oNACA65r418 x/cy/c 0.265-0.060 0" i\fAt:::A.65.:c.11,B,-.. 04.7, -.8-.40.4.81.2 Section lift coef'fiCient,c, FIGURE16.-Comparison of the aerodynamic characteristics of the NACA 653-418 and NACA 65.-418,Q=0:5 airfoils "t aReynolds nnmber of 9 X10'.TDT tests 314,320,406,and 411. 19 IT 1.6 Y1 c:1 is:: is:: :> o "9 :> .... "'I o .... t"' t:l :> >-3:> c:o 3.6 3.2 28 2.4 2.0 1.6 1,)-.....1.2 t::

-1-\ NACA652-4159.0.268-.062 "lNACA66(215)-416' -- 9.0 .265-.105. I T StandrdrauCJhnessl----1.2-.8-.40.4.81.2/.6 Section lift coeffIcient,c1 FIGURE17.-Comparison of the characteristics oCsomeNAC.'\.airfoils fromtests intheLangley twodimensional low-turbulencepressure tUIlIlCI. o il:l trJ '"d o il:l >-3Z P 00 ... !:3 ..... o Z >-t"' >-t:::)-3trJ trJ o il:l il:l o Z >-q >-3'"'C1 W SUMMARYOFAIRFOILDATA 21 Effectiveaspect ratio.-The combinationof highdragsat highliftcoefficients,lowdragsatmoderateliftcoefficients, andthenonregularvariationofdragwithliftcoefficient shownbytheNACA6-seriesairfoilsmayleadtopara-doxical results when the span-efficiency concept (reference 29) isusedforthecalculationofairplaneperformance.Inthe usualapplicationofthisconcept,theairplanedragcharac-tc!risticsareapproximatedbyacurve of the type (17) Thiscurveisusuallymatchedtotheactualdragcharacter-isticsat arather lowandatamoderately highvalueofthe liftcoefficient(reference30). Theapplicationofthisconcepttotwohypotheticalair-planeswithN ACA230-.andsections,respectively, isillustratedinfigure18(a).Thewingdragsoftheair-planeshavebeencalculatedbyaddingtheinduceddrags corresponding to an aspect ratioof10withellipticalloading totheprofile-dragcoefficientsoftheNACA23018and 653-418airfoils.Thesesectionsareconsideredrepresenta-tiveofaveragewingsectionsforalargeairplaneofthis aspectratio.Ordinatescalesaregiveninfigure18(a)for thewingdragandforthetotalairplanedragcoefficients obtainedbyaddingarepresentativeconstantvalueof ./0 I!.1.,l!1.1II1.1 oNACA653 -418wing;aspecf ratio,/0 t--oNACA23018wing;aspecf,rotio,/0 - ---- NACA653-418wing;. effectiveaspectratio,830 - - - NACA2.3018wing; I.1. effectiveaspect rofio,929 V J .08 .O{) .07 08 .06 l'll Ii If '/ X Airplane

A V b=18.5 ma. c;,-00068+ a0343c,,' . . c;,a 0045 + a 0383lfX V "Airplane ......--: -a =19.8 ma -- V,y ,-V . 01 .02 / / .01 (a) V o o.81.0/2.4.6.2 Lifl coefficienf,c;, (a)NACA 653-418and 23018wings of aspect ratiolO. 0.0150tothewingdragcoefficients.Theresultingdrag coefficientshavebeenapproximatedbytwocurvescorre-spondingtoequation(17)and matched tothe dragcurves at liftcoefficientsof0.2and1.0.Thesetwocurvescorre-spondtoeffectiveaspect ratiosof9.29forthe airplane with NAOA23018sectionsandof8.30fortheairplanewith NACA653-418sectionsandillustratethetypicallarge reductionintheeffectiveaspectratioobtainedwithsuch sections. It should benoted,however,thatalthough equation(17) providesareasonablysatisfactoryapproximationtothe dragoftheairplanewithNACA23018sections,such isnot thecasefortheairplanewiththeNAOA653-418section. Themostimportantreasonforusinghighaspectratioson large airplane3 is to reduce the drag at cruising lift coefficients andtoobtainhighmaximumvaluesofthelift-dragratio. Forthetwowingsconsidered,themaximumvalueofthis ratioisappreciablyhigherfortheairplanewithNACA 653-418sections(19.8ascomparedwith18.5)despitethe factthat this airplane showsthe lowereffectiveaspect ratio. Figure18(b)showsasimilarcomparisonwithsimilar resultsfortwoairplanesofaspectratio8andNACA2415 and652-415airfoils.It isaccordinglyconcludedthatthe effectiveaspeCt ratio isnot asatisfactorycriterion foruse in airfoil selection . ./0 .09 .08 .08M 01 IWinb; )Otid,8 oNACA24/5 wing;aspect ratio,8 r- - --- NACA652-415winq; effectiveaspect ratio,6.97 7 - - - NACA24/5 win91 I effectiveaspect rafio,746 I III .0 .06 .07 '-SIS t- "'- .05

.IJ 'Qi.04 I I " L I/, / P: '/ oQ)II.058 \)) eQ

-K.02 .\..:- I:: :2.00. \.) i 1 ') 5':>1 ') -1.6 l' \ \\ \ "I-> \ 10,,: I'\.. ro;

"-tf jtl{' I\,.YI"", """v'[Q:t-/-..i"'-V'-LAV .... t-,., +-+ 1:--1--+, "-t:::::: P-I-- --oSmooth +ShelloconL. xo.OO?-inch-qroinroughnessonL. o.004-inch-qrain roughnessonL.. o.0/ I-inch-groin roughnessonL.. -/.2 -:40.4.8 Section lift coefficient,c, FIGURE23.-Lift and dragcharacteristicsofanNACA63(420)-422 airfoil with various degrees of roughness at the leading edge. In II x X ,-t::1::1 m o I:tI >1 o o t"l t=l "'i o I:tI >-t=l ::tI o Z >-q 1-3I-< o m SUMMARYOFAIRFOILDATA 27 .040 .036 .032 ".028 I;,) ....' c:

:t III o l).020 8' ii I::.016 .0 ..::: l) III '0.012 .008 '"'. "ci: NACA63(420)-422---+ I I V 4'l V k- f-J::::: t;7 .004 NACA65(223)-422(modified) o -1.6-/.2-.8-.40.4.81.2 Sectionliftcoefficient,0. 1.6 FIGURE25.-DragcharacteristicsoftwoNACA6seriesairfoilswithO.Ollinch-grain roughness at 0.30e.R=26XI06 Thewind-tunneltestsofpractical-constructionwingsec-tionsasdeliveredbythemanufacturershowedminimum drag coefficientsof the order of 0.0070to0.0080in nearly all casesrpgardlessoftheairfoilsectionused(figs.28to32). Suchvaluesmayberegardedastypicalforgoodcurrent constructionpractice.Finishingthesectionstoproduce smooth surfaces always produced substantial drag reductions althoughconsiderablewavinessusuallyremained.Noneof the sections tested had fair surfaces at the front spar.Unless speeial care istaken to produce fair surfaces at the front spar, the resulting wave may be expected to cause transition either atthesparlocationorashortdistancebehindit.One practical-eonstructionspecimentestedwith smooth surfaces maintainedrelativelylowdragsuptoReynoldsnumbers ofapproximately30X106 (NACA66(2x15)-116airfoilof fig. Thisspecimenhadnosparforwardofabout35 percent chord from the leading edge and no spanwise stiffeners forwardofthespars.Thistypeofconstruction resultedin unusuallyfairsurfacesandisbeingusedonsomemodern high-performanee airplanes. Acomparisonoftheeffectofairfoilsectiononthemini-mumdragwithpractical-construetionsurfacesisverydiffi-eultbecausethequalityofthesurfacehasmoreeffecton thedragthan thetypeofsection.Probablythebestcom-parisoncan be obtained frompairsof modelsconstruetedat 32X106 \ i'\.--NAd35;'215 ....... $-3,/'--.... '"

, 1. /NACANACA24(4.S: fZ t--66,2-2(14.7) t-, NAd27-212 I>- S -3, 13 'N-22 o , Rep0blic ,S-3, 13 .. N-22.-- --RepublicS-3,11 '"I.,V/'

fS-2}5 ,/ NACA24145-V V''NACA66,2-2(14.7)

,, \ " ---V f7-2(2 / 'N1 CA4, 2-(1. 4}(.13.5} ./6.32.48.64.80.96 Sectionlift coefficient,cl FIGURE 26.-ComparisonofsectiondragcoefficientsobtainedinflightonvariousairfoilS. 30 o IJ.OI2 .....' c:

.\.J c;:: 'Q;.008 o \.J 8' 004 c: .0 -i:: \.J o Tests ofN A CA27-212and 35--215 sections made on gloves. x/OS "" :---.. i'--r--r-----oFactoryfinish,camouflage,cuoped flop I---oSurfaceglozed,sanded,surfaCingI--compoundapplied,camouflage, cuspedflap ()Surfacewavinessreduced,camouflage, -flopcuspremoved,flopgopseoled_ "ViSiblewovesfilled,wa--"'""" :.-- ./.2.3.4.5.6 Liftcoe fficient,c,. FIGURE27.-ConsolidatedVultee flightmeasurements of the effect of wing surface condition on drag of an NACA 66(215)-1(14.5)wing section. thesametimebythesamemanufacturers.Dataforsuch pairs of models are presented in figures30to32.The results indicatethataslongascurrentconstructionpracticesare usedthetypeofsectionhasrelativelylittleeffectat flight valuesofthe Reynolds number formilitary airplanes.. 28 REPORTNO.824- TATIONALADVISORYCOMMITTEEFORAEROAUTICS :>-)!> ' ---6 - - -- -0 I Airfoil with splifflap Plain airfoil .4 o4812/62024 Airfoil Thickness;percentof chord (e)NACA GO-series. I 33 Airfoil with splitflop Plain oirfoil Airfoil with splitflop Plain airfoil FIGURE 39.-Variatioll of maxiwum section lift coefficientwithairfoilthicknessratioandcamberforseveralNACAairfoilsectionswithandwithoutsimulatedsplitflapsandstandard roughness.R=6X106 34 REPORTNO.824-NATIONAL ADVISOIWCOMMITTEEFORAERONAUTICS Thevariationofmaximumliftwithtypeofmeanlineis showninfigure40forone6-seriesthicknessdistribution. Nosystematic data are available formean lineswith values of a less than 0.5.It shouldbe noted,however,that airfoils suchastheN ACA230-seriessectionswiththemaximum camberfarforwardshowlargevaluesofmaximumlift. Airfoil sections with maximumcamber far forwardand with thicknessratiosof6to12percentusuallystallfromthe leadingedgewithlargesuddenlossesinlift.Amorede-sirablegradualstallisobtainedwhenthelocationofmaxi-mum camber is farther back,asforthe NACA 24-,44-,and 6-series sectionswith normaltypes of camber. 2.0 y--r-I,.---f-Reynoldsnumber o6.0x106 o9.0 o.2.4.6.81.0 Typeof camber,a FIGURE40.-VariationofmaximumliftcoefficientwithtypeofcamberforsomeNACA 65a-418airfoilsections fromtestsin theLangleytwo-dimensional low-turbulence pressure tunnel. AcomparisonofthemaximumliftcoefficientsofNACA 64-seriesairfoil sectionscambered for adesign lift coefficient of0.4withthoseoftheNACA44- and230-seriessections (fig.39)showsthatthemaximumliftcoefficientsofthe NACA64-seriesairfoilsareashighor higherthanthoseof theNACA44-seriessectionsin allcases.TheNACA230-seriesairfoilsectionshavemaximumliftcoefficientssome-what higherthan thoseof the NACA 64-seriessections. The scaleeffectonthe maximum liftcoefficientof alarge numberofNACAairfoilsectionsforReynoldsnumbers from3 X 106 to9 X 106 isshowninfigure41.Thescale effectfortheNACA24-,44-,and airfoils(figs. 41(a) and 41(bhaving thickness ratios from 12 t024 percent isfavorableand nearlyindependentoftheairfoilthickness. IIwreasingtheReynoldsnumberfrom3 X 106 to9 X 106 resultsinanincreaseinthemaximumliftcO('fficientof approximately0.15to 0.20.The scaleeffectontheNACA 00- and14-seriesairfoilshavingthicknessratioslessthan 0.12cisvery small. Thescale-effectdatafortheNACA6-seriesairfoils(figs. 41(c)tv 41(fdo not show an entirely systematic variation. Ingeneral,thescaleeffectisfavorablefortheseairfoil sections.FortheNACA63- and64-seriesairfoilswith smallcamber,theincreaseiIimaximumliftcoefficientwith increasein Reynolds number isgenerally small forthicknes.s ratiosof lessthan 12percent but issomewhat larger forthe thickersections.Thecharacterofthescaleeffectforthe NACA 65- and66-seriesairfoilsections issimilar tothat for theNACA63- and64-seriesairfoilsbutthetrendsarenot sowelldefined.InmostcasesthescaleeffectforNACA 6-seriesairfoilsectionscamberedforadesignliftcoefficient of 0.4or 0.6doesnot vary much with airfoil thickness ratio. The data of figure42showthat,the maximum lift coefficient forthe NACA 63(420)-422airfoil continues to increase with Reynoldsnumber,atleastuptoaReynoldsnumberof 26X106 The valuesofthe maximum lift coefficientpresentedwere obtainedforsteadyconditions.Themaximumliftcoeffi-cientmaybehigherwhentheangleofattack isincreasing. Suchaconditionmightoccurduringgustsandlanding maneuvers.(Seereference 41.) ThesystematicinvestigationofNACA6-seriesairfoils includedtestsoftheairfoilswithasimulatedsplitflapde-flected60.It. wasbelievedthatthesetests wouldserveas anindicationoftheeffectivenessofmorepowerfultypesof trailing-edge high-lift devices although sufficient data to verify thisassumption have not been obtained.The maximum lift coefficientsforalargenumberofNACAairfoilsections obtained from tests with the simulated split flap are presented in figure39. The data forthe NACA 00- and 14-series airfoils equipped withsplit flapforthickness ratios from6 to12percent show aconsiderableincreaseinmaximumliftcoefficientwithin-crease in thickness ratio.Corresponding data for the NACA 44-seriesairfoilswit,hthicknessratiosfrom12to24percent showverylittlevariationinmaximumliftcoefficientwith thickness.ForNACA6-sel'iesairfoilsequippedwithsplit flapsthemaximumliftcoefficientsincreaserapidlywith increasing thickness Overa range of thickness ratio, the range beginning at thickness ratios between 6 and 9 percent, depend-ing upon the camber.The upper limit of this range forthe symmetricalNACA64- and65-seriesairfoilsappearstobe greaterthan 21percent andfortheNACA 63- and 66-series airfoils, approximately 18 percent.Between thickness ratios of6 and 9percent thevaluesofmaximum lift coefficient for thesymmetricalN ACA6-seriesairfoilsareessentiallythe sameregardlessof thicknessratioandpositionofminimum pressureonthebasicthicknessform.Themaximumlift coefficientdecreaseswithrearwardmovementofminimum pressure for the airfoils having t,hickness ratios between 9 and 18percent. .02. .6 I--.21--.8 .6 I.2 .6 2 8 2. 0 6 2 6 2 8 .B !.6 1.2 1.6 1.2 1.6 1.2 (a) (e) (e) SUMMARYOl!'AIRFOILDATA R>-=-..NACA24-series (4-digit) oJ.OxIOi"--.. I'b. --;::: k o9.0 r-..... f:::: e:.6.0Standard Dr. rughness r-.. /' NACA14-series(4-digit) IA A NACADO-series(4-digit) i-' SymbolswithflagscorrespondtocuO.6 f:::;: .... ;;:: b:" r-::::-i,.-1--6::: el; =0.4and0.0 V-i'---::::::::: h,..c-1-0 ........, i'D cl;=O.c V v ........ v /'-., C'i=0 kf/' r--.... I' bI..---' .... ..... V ?--h:,. -.......::: r-. c1i=o.4and0.8 Vr- ...tc

\-0 ..4' ...... R"" k V ....... t-...... fOc1j=0.2 #..-' >-- 'F/ J...6-. t-- "0 cll=O \ lL V ..A i .b-/. - 48Ie16eOC402832 Airfoil thickness,percent of chord (a)N ACA four-digit series. (c)NACA 63-serles. (e)NACA 65-series. .02 .8 I. 2 8 J .6 .2 8(b) c: :2 /. I. I. 6 2 (5 6 8(J (\) v, 1.6 ::J. x 1.2 .8 1.6 /.2 1.8 1.2 .8 /.2 (d) (f) I ;.c:: NACA23O-series (5-diq/t)' ::::.".. t--."""" I::::-............ :.-- t--. r-..... ......... I"--.r. -0-. -- ......... f0-r-, '-...... NACA(4-dlqit) ""- !o=, r-J-o.. r--..,;; -i=OC,j=O.4and 0.6 '-"l r--.... r--; t:-"0 '" r-- e'i =0.2 t--.P-V t-i> ;l; y VII "'1=0.1 if !,-,:::1-0 t1' \'0... t--. ?--t-o CI'=O IBI--- .... C'I =0.4 0-V V)'" :>--1-0 e'l = 0.2

l---,--I .....,

'" c11O mt....- f-" V ..... 48121820?42832 Airfoil thickness)percent of chord (b)NACA four- and five-digit series. (d)NACA 54-series. (f)NACA 66-series. FIGVI\& 41.-Variation of maximum section lift coefficientwith airfoilthickness ratio at several Reynolds numbers fora number of NACA airfoil sections of different cambers. 35 3.6 3.2 2.8 2.4-20 1.6 ...:-1.2 "-- ., .80 t.) t:'" > ......Ul o (l o ?' .... ?' ,.., ..... H H M M "'1 o > M o >-d ..., ,... (") Ul SUMMARY0]'AIRFOILDATA 37 Substantialincrementsinmaximumliftcoefficientwith increase in camber areshownfortheN ACA6-seriesairfoils ofmoderatethicknessratios(10to15percentchord)with splitflaps.Fortheairfoilshavingthicknessratiosof6 percent and forthe airfoils having thickness ratios of18or 21 percent, the maximum lift coefficient is affected very little by achangeincamber.Forthicknessratiosgreaterthan15 percent,the maximum liftcoefficientsoftheN ACA63- and 64-seriesairfoilscambered foradesignliftcoefficientof0.4 equippedwithsplitflapsare greater than thecorresponding maximum lift coefficientsoftheNACA 44-seriesairfoils. Three-dimensionaldata.-Norecentsystematicthree-dimensionalwingdataobtainedathighReynoldsnumbers areavailable,sothat it isdifficulttomakeanycomparison withthesectiondata.Whenthemaximum-liftdatafor three-dimensionalwingsarecomparedwithsectiondata, accountshouldbetakenofthespan loaddistributionover thewing.Thepredictedmaximumliftcoefficientforthe wingwillbesomewhatlowerthanthemaximumliftcoeffi-cientsofthesectionsusedbecauseofthenonuniformityof thespanwisedistributionofliftcoefficient.Thedifference amounts to about 4to 7 percent forarectangular wing with an aspect ratioof6. Maximum-liftdataobtainedfromtestsofanumberof wingsandairplanemodelsintheLangley19-footpressure tunnelarepresentedintableII.Althoughsectiondataat theReynoldsnumbersnecessarytopermitadetailedcom-parisonarenotavailable,themaximumliftcoefficientfor plain wingsgiven in tableII appearsto be in general agree-ment with valuesexpected fromsection data.The data for theairplane'modelsarepresentedtoindicatethemaximum liftcoefficientsobtainedwithvarIOUSairfoilsand eonfigurations. LIFTCHARACTERISTICSOFROUGHAIRFOILS Two-dimensionaldata.-Mostrecentairfoiltests,espe-cially of airfoils with the thicker sections, have includedtests with roughened leading edge(reference 37),and the available data are included in the supplementary figures. Theeffecton maximumliftcoefficientofvariousdegrees ofroughnessappliedtotheleadingedgeoftheNACA 63(420)-422 airfoil is shown in figure23.The maximum lift coefficientdecreasesprogressivelywithincreasing roughness (reference36).For agiven surface condition at the leading edge,themaximumliftcoefficientincreasesslowlywith increasing Reynolds number(fig.43).Figure 24showsthat roughnessstripslocatedmorethan0.20efromtheleading edgehavelittieeffectonthemaximumliftcoefficientor lift-curveslope.Theresultspresentedinfigure38show thattheeffectofstandard leadingedgeroughnessistode-creasethemt-curveslope,particularlyforthethickerair-foilshavingthepositionofminimumpressurefarback. These data are for a Reynolds number of 6X 106Maximum-20 I--~ I---...... l--.--, I .-o0.002 roughness o.004roughness o.01/roughness LISmooth o48Ie16cOe4x/O' Reynoldsnumber,R FIGURE43.-Effects of Reynolds number onmaximumsectionliftcoefficientCImaxofthe N ACA63(420)-422 airfoil with roughened and smooth leading edge. lift-coefficientdataataReynoldsnumberof6 X 106 fora large number ofNACA airfoilsections with standard rough-nessarepresentedinfigures39and41.Thevariationof m a x i ~ u mliftcoefficientwith thicknessfortheNACA four andfive-digit-seriesairfoilsectionsshowsthesametrends fortheairfoilswithroughnessasforthesmoothairfoils exceptthatthevaluesareconsiderablyreducedforallof theseairfoilsotherthantheN ACAOO-seriesairfoilsof 6 percent thickness.For a given thickness ratio greater than 15percent,thevaluesofmaximumliftcoefficientforthe four- and five-digit-seriesairfoilsare substantially the same. Much less variation in maximum lift coefficient with thick-nessratioisshownby theNACA6-seriesairfoilsectionsin theroughconditionthanwithsmoothleadingedge.The maximumliftcoefficientsofthe6-percent-thickairfoilsare essentiallythesameforboth smoothandroughconditions. The variation of maximum lift coefficient with camber, how-ever,isabout the same forthe airfoilswith standard rough-nessasforthesmoothsections.Themaximumliftcoeffi-cientofairfoilswith standard roughnessgenerallydecreases somewhatwith rearwardmovementofthepositionofmini-mumpressureexceptforairfoilshavingthicknessratios greaterthan18percent,inwhichcasesomeslightgainin maximumliftcoefficientresultsfrom3,rearward movement of theposition of minimum pressure. Except forthe NACA 44-seriesairfoilsof12to1.'5percent thickness,thepresentdataindicatethattheroughNACA 64-seriesairfoil sectionscambered foradesign lift coefficient of 0.4 have maximum lift coefficients consistently higher than theroughairfoilsoftheNACA24-,44-,and230-seriesair-foilsofcomparablethickness.Standardroughnesscauses decrementsinmaximumliftcoefficientoftheairfoilswith split flapsthat aresubstantially the sameasthoseobserved forthe plainairfoi.ls. 38 20 1.6 ~4 \.J' ~ "....'>-' o -4 '-8 1.4 1.2 !.O . ~.8 ..1 I I ~ ~ R , If-"" ~ ~ I I I , I j ~I I I II \I: II b I 1/ \I \I \ ~ I -, J II V II I oAsdelivered by shop, TOTtest 4158J oAsdelivered %shop,. TDTtest64/ oAs delivered by shop, TDTtest 494 I oFinal condition, V oFinal condition, I oFinal condition, TOTtest ':COTOTtest 498TOTtest 523 J II o J II7 (b)(e)17 81624-8o81624-8o8162432 Sectionangle of attack,a"de-:) (a)NACA2412.(b)NACA2415.(c)NACA23012. FIGURE H.-Lift characteristics of the NACA 23012,2412,and 2415airfoil sections as affectedby normal model inaccuracies.R=9X106 (approx.). r-1= CJ I....) -;-== S=-'"' lnl J ;}, tv VI J 4 W 1I JJ J . ~ / I/; V jV W 1/ r'tJ ~ 'l, The maximum lift coefficient may be lowered by failureto maintainthetrueairfoilcontournearthe leadingedge,but nosystematicdataonthis effecthavebeenobtained.Ex-amplesofthiseffectthat wereaccidentallyencounteredare presentedin figure44,in which lift characteristicsare given foraccurateandslightlyinaccuratemodels.Themodel inaccuracies were sosmall that they were not foundprevious tothetests. Three-dimensional data.-Tests of several airplanes in the Langley full-scaletunnel(reference 42)showthat many fac-torsbesidestheairfoilsectionsaffectthemaximumliftco-efficientofairplanes.Suchfactorsasroughness,leakage, leading-edgeairintakes,armamentinstallations,nacelles, and fuselagesmake it difficult to correlate the airplane maxi-mumliftwiththeairfoilsused,evenwhentheflapsare retracted.Thevariousflapconfigurationsusedmakesuch acorrelation even more difficult when the flapsare deflected. Whentheflapswereretracted,boththehighestandthe lowestmaximumliftcoefficientsobtainedinrecenttestsof airplanesand complete mock-upsofconventionalconfigura-tionsintheLangleyfull-scaletunnelwerethoseobtained with NACA6-seriesairfoils. j [;Model (Longley19-foot pressuretunnel)-AirplaneIIIIIII oSealed condition}(LanglefiII-scale jf oServiceconddlonLj t::nnel) 1I o48121152024 Angleof atfack,a,deg FIGURE45.-Theeffectsofsurfaceconditionsontheliltcharacteristicsofafighter-type 'airplane.R=2.8X106 Resultsobtainedfromtestsofamodelofanairplanein theLangley19-footpressuretunnelandoftheairplanein theLangleyfull-scaletunnelarepresentedinfigure45. Both testsweremadeat approximatelythe sameReynolds number.Theresultsshowthattheairplaneintheservice conditionhadamaximumliftcoefficientmorethan0.2 lowerthanthatofthemodel,aswljllasalowerlift-curve slope.Some improvement in the airplane lift characteristics wasobtainedby sealing leaks.These resultsshowthat air-planeliftcharacteristicsare stronglyaffectedby detailsnot reproducedon large-scale smooth models. SUMMARYOFAIRFOILDATA 39 I. 6 1.4 * ) t'o-. II "'0 1-0 I ,V" d V Ii I ! ~ V 1.0 ~ ....... ~ . ~ .8 ~ lV /1Airfoil sections f----51 Root,Davis(c2-percent) J, Tip,Dovis(9.J-percent) /1 "-~ ~ .6 .......:t::; -.J .4 jP I 0Naturalfransifion 1I 0Transi!iOI7,.fixedof.lDc .2 j II 0 I I i o4812/62024 Anqleof at tack,(x,deq FIGURE46.-The effectonthe liftcharacteristicsoffixingthetransitiononamodelinthe Lang]ey 19-foot pressure tunnel.R=2.7XI06,(Model withDavis aifroil sections.) LiftcharacteristicsobtainedintheIJangley19-footpres-suretunnel fortwoairplane modelsinthe smoothcondition andwithtransitionfixedatthefrontspararepresentedin figures 46and 47.In both cases,the Ilft-curve slope was de-creasedthroughoutmost oftheliftrangewithfixedtransi-tion.Themaximumliftcoefficientwasdecreasedinone casebut wasincreased in the other case. UNCONSERVATIVEAIRFOILS The attempt toobtain lowdrags,especially for long-range airplanes, leads to high wing loadings together with relatively lowspanloadings.Thistendencyresultsinwingsofhigh aspectratiothatrequirelargespardepthsforstructural efficiency.Thelargp- spardepthsrequiretheuseofthick root sections. Thistrend tothick rootsectionshasbeenencouragedby the relatively small increase in drag coefficient with thickness ratioofsmoothairfoils(fig.12).Unfortunately,airplane wingsarenot usually constructed with smooth surfacesand, in any case, the surfaces cannot be relied upon to stay smooth underallserviceconditions.Theeffectofrougheningthe leading edges of thick airfoils is to cause large increases in the I. 6 I. 4 m V rs-Hl..-~ f--/.2 -I. 'i' -2. 1 -32 I" -24 , -!/e

15 l/, IJ' Iff Iff Iff II II 1\V \I/! 1',- V Airfol'!:NACA165(223 Chord:36 in. -422 (modified) Test:TOT258 III IIIIII -/6-808/624 Sectiononq/@of of tack,(;(0,deg --:72 .056, , .052 .048 .044 I .0401 .036 OJ2 \l>a I ,I 'I l>.028 g> L i5 .;::.024 \:) Jl I 0201 .0/6 .012 I .008 ! .004 o -/.6-/,2 , I ... T x , \I x\ I 0 +I0 ,\I

JIII \'I\,/" f/ / -I'/,

:::0:/,l,Ij -'-'-;;/ 'c.-+ :.i"x R o6,oxI0' +- 10.0I x14.0 I 020.0 026.0 I III I IIII 0.4- .8 Sectionlift coefficient,c[ FIGURE 49.-Lift and drag characteristics of an NACA 65(223)-'422(modified)airfoil with standard roughness applied to the leading edge. --1-+- -1.21.6 o ':rJ >-...... o ......t" t::l ..... 42REPOR'fNO.824-NATIONAL ADVISORYCOMMITTEEFORAEHONAUTICS I 1 Singleflagged symbolsare for60simulatedsplitflapI 1 (a) -.';; .I o I--(c) Seri6'> 5 0 0 14(4-diqit)_ -...,

II ,6 'V230(5-digit) r------:----, ;.-.... -I--4812162024 .-:: 28 , Airfoil thickness)of chord (a)N AUAfourandflvediglt Cz 0 0'-I--0.! .2-I---l- f!..4_ I--r---. t:; -'---b. 'V.6 ..... .--"V .....: r-481216202428 Air-foil thickness)percent of chord (c)NACA 04-series. I o I F=: -...., NA (e) .................... / fb) -.1; 1 o J I I"'-"'--(d) ; ....... .. CZi-I--v 00 r-I V .2-----f!..4_ I--! """' r----. --1-0- 'V.6 I---r--.,. -0 "'""" --, 4bR Airfoil thickness)percenf ofchorrl ZR (b)NAUAf>3 selles. la=O.5 , , , , eli -,.... r--00,_ -.2 r---- f!..4_ ->---. r--'V.6 '---l:l.. ""-... ::- r-----;;---tl -... :-- 4b12/6202428 Airfoil thickness.,percent of chord (d)NACA C'i-I--00 -tr.l :tl o c:j ..., .... c m SUMMARYOFAIRFOILDATA 47

Flapretracted 1 NACA 0015 _________________________________________________ do______________________________ _ NACA 23012, __________ . ____. ___ . ______ . ____ .. ___ .. __ .___ .. do ___ ... ___ ... _._, .. _.. ____ .. __ .. NACA 66(2xI5)-OlU_Plain, straight contour ___ ... ____ ... _ NACA 66-009._ ... ____ ... ___ "' __________ .. _____ .. ___ "'_Plain __ .. _._ .... _.... _____ .... __ .. _ NACA 63,4-4(17.8)(approx.) ______ . _______ . __ ._ . _____ .Internally balanced __ .... ___ ._. __ ._. NACA 66(2xI5)-216,a=0.6. _________ . _____ .. ___ ... ___ .. _.. ,.do.... __ ..... ___ .... ___ .. ______ ._ NACA 66(2xI5)-116,a=O.6 .. __________. ____ '. __________.. ___ do _______________________________ _ NACA 64,2-(1.4)(13.5) _____ .. ___________ . ____ . __ _______Plain_.______ ____ .. ______ . _____ .. __ ._ NACA 65,2-318(approx.) ________ ._ .... ________ ... __ .. _Internally balanced ____________ .. __ _ NACA 63(420)-521(approx.) __ .. ______ .. _______________ .. __ do .. ___ .... _______________ . _____ _ NACA 66(215)-216,a=O.6 __ .. ,_ .. ______ . ___ . ___ .. ____ ._' ___ do._ .. __________ .. ______________ _ NACA 66(215)-014.. ____ 00___ " ____ .. ____ ___ _____ ,___Plain ______ .. ________________ ______ _ NACA 66(215)-216,a=O.6 ____ ._ ._. ___ .. _. _______ . ____ . _______ do _______________________ ______ _ NACA 65,-415 _______ .. ________ . ___. ______ . ________________ .do_. ____ ________________ ______ _ NACA 653-418 ___ ____. _______ .00 ____ _____ ______ _________ do ______________________________ _ NACA 65,-421. ___ . ___ ._. __ . ___________ .. ___. ______ . ________ do ______________________________ _ NACA 65(112)-213 .. ________ . _____ . _____ ._. __.. ______._. __ Internally balanced. _______ ._. _____ _ NACA 745.A317(approx.). _____________ . ___ .. ___ ... _. ____ ___ do ___ ..... _... __ .... __ .. _._ ... __ . NACA 64,3-013(approx.)_. _______ .. ____ ... ____________. ____ do __________ . ___________________ _ NACA 64,3-1(15.5)(approx.). ____ . ____ . __ . __________________ do ______________________________ _ IApproaching 1.00. .8 .... .. .. /' 1. 93 1. 60 1. 93 1. 93 (I) (I) (I) .=0.33 V Geometric washout, 1.00 ---. r. Sections: X Root: N ACA 64(215)-418 NoneNone 'v-o-. Tip: NACA 66,2x-415 v-vA=8.92 Split >'=0.33 ./.Split V Geometric washout,1.00----II d Sections: Root: NACA 64(215)-418 XI Tip: NACA 66,2x-415NoneNone -,,------\r-A=8.92Split.\. ),,=0.33 Geometric washout, 1.00 V t ExtensibleNone c:tl1t slotted I Sections: 1 Root:NACA63(420)-418, XII---:'.

a=l.O Tip:NACA65M15.a=1.0 - v A=7.77 1 V >'=0 ..10 Geometric washout, 2.80 Split -Propellers win'=0.48SlottedI50 ------- I-------I -------3.52.04 Geometric washout, 3.00 1 I 4.92.13 V I 5.92.16 I 1Split50 ------- .J.------- -------3.52.02 4.S2.12 I 5.92.17 --------,.... Sections: SlottedNone0 -------20 -------60-.-----3.4XI061. 55 Root:NACA 23015.6 1 I I I 4.81.58 Tip:NACA 23009 1 5.61.60Very abrupt stall, leftwing XVA=5.5 I stalling very rapidly, for >'=0.52 50 ------- .J.------- .J.-------3.42.46all conditions Geometric washout, 0.00 4.82.50 V 5.62.52 --- --------------p. ExtensibleNone0 -------