SECURITY INFORMATION copy26~

I

RESEARCHMEMORANDUM.

THEEFFECTSOFREYNOLDSNUMBERAT MACHNUMBERS

UPTO 0.94 ONTHELOADINGONA 35° SWEPT-

BACKWINGHAVINGNACA651A012

STREAMWISESECTIONS

By Bruce E. Tiding andArmandoE. Lopez

Ames AeronauticalLaboratoryMoffettField, Calif.

i

NATIONAL ADVISORY COMMITTEEFOR AERONAUTICS

1

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WASHINGTONJune16, 1952

*.*.

‘31?.57Y/3f _.._.....— .-

.—

..:‘.-x

IN NACARMA~2B20

-.NATIONALADVISORYCOMMITPEEFORAERONAUTICS

b

RESEARCHMEMORANDUM

TEEEFFECTSOFREYNOLDSNUMBERAT MA@ NUMWW

UPTO0.94

BACK

ONTHELOADINGONA 35° SWEPT-

wmG HAvmG ~CA 651Ao=

STREWWISESECTIONS

ByBruceE.TinlingandArmando* -.-, ,,.=.-:...:..

.:+% SUMMARY,------’-....,.-” ..

E. Lopez

,...*

An investigat~hasbeenmadeof theeffectsof a variationofReynoldsnuniberon~hef~&s, moments,andsurfacepressuresona semi-spanmodelofa winghavid@.35°“of sweepback,an aspectratioof 5, ataperratio ofO.Y$+andtl@lACA65~AO12sectioninplanesparalleltotheplaneof symmetfi.Dataare-presentedfora rangeofReynoldsnum-bersfrom2,000,000‘to10,QQO,OOOat a Machnmiberof0.25,andfrom2,000,000toapproximately-k,500,~00atMachnmibersfrom0.60to0.94.b..= >,

Theresultsi~cated thatj in general,theeffectsofReynoldsnumberweregreatertows@ $hetipof thewingthanneartheroot. At

h

a MachnumberofO. ~,the-maxlm~normal-forcecoefficientsforwingsectionsinboardo otii@Qpercentofthesemispanweregreaterthanpredictedby appl s$mple”sweeptheorytotwo-dimensionalsectiondata.A lowervaluebf ms@mumsectionnormal-forcecoefficientthanpredictedfromsectiondatawasobtainedforsectionsat 90 and95~er-cent ofthesemispan.AtMachnumbersgreaterthanthatfordragdiver-gence,a changei;Reynoldsnumberfrom-2,000,(X)0to 4,500,000c&sedchangeinloadingat smallliftcoefficientswhich,at a Machnuiberof0.94,wassufficientto shiftthecenterofpressurerearwardby150percentofthemeanaerodynamicchord.Thischangein loadingisbelievedtohaveresultedfroma changeh thetypeofboundarylayertheregionof theshock.

3

a

in

2 NACARM A72B20

INTRODUCTION.

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An investigationof theeffectsofMachnumberandReynoldsnumberontheaerodynamiccharacteristicsof several12-percent-thickwingshaving35°of sweepbackandvariousamountsof camberhasbeenreportedinreference1. Theresultsof thisinvestigationindicatethatanabruptdecreaseoflift-curveslopeaccompaniedby a largereductionofstaticlongitudinalstabilityoccurredat thedesignliftcoefficientata Reynoldsnumberof 2,000,000whentheMachnumberfordragdivergence

—

wasexceeded.Similarphenomenahavebeenreportedinreference2 whichpresentsresultsoftestsata Reynoldsnumberofabout6w,000of sev-eralwingshaving45°of sweepbackandtheNACA631A012sectioninplanesparalleltotheplaneof symmetry.Thisreductionof staticlongitudinalstabilityiscontrarytopreviousresultsfromtestsof swept-backwingshavingsectionslessthan12percentthick.(See,forexsmple,refer-ences3 and4.) Theresultsofreference1 alsoindicatetheeffectsofReynoldsnuniberon theaeroi@amiccharacteristicsofthewingsat low

w—-

Machnumberstobe large. P-Inorderto determinethenatureofthechangesinloadingwhich

restitedintheabovephenomena,a duplicateofoneof thesemispanmodelsofreference1 wasconstructed.Thismodelwasequippedwithflushorificesforthemeasurementof surfacepressures.High-speedtestswereconductedintheAmes12-footpressurewindtunnelandintheAmes16-foothigh-speedwindtunnelinorderthattheeffectof a vari-ationofReynoldsnumberfrom2,000,000toabout4,500,000couldbeassessedathighMachnumbers.Low-speedtestswereconductedinthe12-footwindtunneloverthesamerangeofReynoldsnumbersas reportedinreference1.

NOTATION

b wingsemispanperpendicularto the?!!

CD dragcoefficient()9@

planeof symmetry,feet

c% pressure-dragcoefficienttressuredr

@ 9

CL liftcoefficient()liftT

.

f

NACARMA52B20 3

. Cm

-

c

Cav

?!

Cm

c~

M

P

pcrA=c&

pitching-momentcoefficientaboutthequarterpuintofthe

meanaerodynamicchord(

pitching)

momentqsE

span-loadpitching-momentcoefficientaboutthequarterpointof themeanaerodynamicchordcomputedfromthespanloadingassumingthesectioncentersofpressureat 26.2percentchord

normal-forcecoefficient

localwingchordparallel

( )normalforce@

to theplaneof symmetry,feet

averagewingchordparalleltotheplane

/’J’b’2a--( !J

meanaerodynamicchord 1.

of symmetry,feet

,feet

{~b”cdY--sectionpitching-momentcoefficientaboutthequsrterpointofthesectionchord

(sectionpitchingmoment

qc~ )

sectionnormal-forcecoefficient( )sectionnorml force\ qc

free-streamMachnumber

(

localstaticpressure-pressurecoefficient

)

free-streamstaticpressure$1

criticalpressurecoefficient,correspondingto a localnumberof1.0quarter-chord

[ -u2 2z’ —7+1

ina directionperpendicularto thewtngline

(1 +tiM2 COS2 35°2 )1+-1}1

(SeereferenceA forderivationofthisexpression.)

free-stre=-c=’)$ ~~~pers~urefoot

4--

R Reynoldsnumber,basedonthemean

s areaof semispanwing,squarefeet

NACARMA52B20

aerodynamicchord

v free-streamvelocity,feetpersecond

Y lateraldistancefromtheplaneof symmetry,feet

a angleof

Y ratioof

~ fraction

attack,degrees

specificheats(1.11-00]

of

P free-stream

semispan()Y’~

massdensityofair,slugspercubicfoot

MODEL

.

.

.

P

Thesemispan”modelrepresenteda winghavinganaspectratioof ~andhad350of sweepbackofthequarter-chordline,a taperratioof0.7,andtheNACA6~AO12airfoilsectionparalleltotheplaneof symmetry.Theplanformandsectionof thismodelareidenticaltooneof thosetestedduringtheinvestigationreportedinreference1.

Thesurfaceofthemodelwasan alloyoftinandbismuthwhichwasbondedtoa steelspar. Inordertomeasuresurfacepressures,themodelwasequippedwithflushorificesinrowsorientedparallelto theplane

—

of symmetryat 10,20,~, 60,80,90,and95 percentofthesemispan.Thedimensionsofthemodelareshownin figure1,andthecoordinates

..

oftheNACA6~1A012airfoilsectionaregivenintableI. Shnilarsemi-spanmountingswereusedinboththeAmes12-footpressurewindtunnelandtheAmes16-foothigh-speedwindtunnelas showninthephotographsoffigure2. Ineachcase,themodelwasmountedwiththerootchordintheplaneofthek-foot-diameterturntable,andthejuncturebetweenthemodelandtheturntablewassealed.Thel/8-inchgaparoundtheedgeoftheturntablewasnotsealed.

TESTS ..

Ames12-FootPressureWindTunnel’.

Twoseriesof testswereconducted:oneto evaluatetheeffectsofReynoldsnumberat--aMachri-er of 0.25,andoneto evaluatetheeffects

NACARMA52B20

ofMachnumberata Reynoldsnumberof 2,000,000.(Seefig.3.) Surfacepressures,lift,drag,andpitchingmomentweremeasuredoveran angle-of-attackrangesufficienttoobtaindataforliftcoefficientsfromzeroto thatforthestall,limitedby wind-tunneleterwhichwasusedto

Ames

Surfacepressures

exceptwherethemaximumangleofattackwaspowerorby theheightofthemultipletubemanom-measuresurfacepressures.

16-FootHigh-SpeedWindTumnel

weretheonlymeasurementsmadeduringthetestsconductedintheAmes16-foothigh-speedwindtunnel.As showninfigure3,theReynoldsnumberofthesetestsvsriedfrom3,900,000at a~ch nwiberof0.62”to4,600,000ata Machnuniberof0.94.

CORRECTIONSTO DA!I!A

~c Pressure

Thedynsmicpressuremeasuredineachwindtunnelwascorrectedforconstrictioneffectsdueto thepresenceofthetunnelwallsby themethodofreference5. Thesecorrectionshavenotbeenmodifiedto allowfortheeffectsof sweep.Thiscorrectionandthecorrespondingcorrec-tionto theMachnumberarelistedinthefollowingtable:

12-footpressurewindtunnel16-foothigh-speedwindtunnelCorrectedMachnumber Uncorrected qcorrected Uncorrected qcorrected

Machnumber uncorrected Machnuniber quncorrected

0.60 0.60 1.000.80

0.60 1.000●799 1.002 .799 1.001

.85 .84g 1.002 .849

.8731.001

.873 1.003 .874 1●002.90 987 l.oo~+ .898 1.002.92 .915 1.005 .918 1.003.94 .934 1.006 .936 1.004

6

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@@!Eim-tiia3b

ForceMeasurements

NACARMA52B20

ThedataobtainedintheAmes12-footpressurewindtunnelwerecorrectedfortheeffectsoftunnel-wallinterferenceoriginatingfromliftonthemodelby themethodofreference6 usingthetheoreticalspanloaddistributionforincompressibleflowcalculatedby themethodofreference7. Thecorrectionsaddedtothedragandtotheangleofattackwere:

lb= 0.263cL

Sincetheturntableuponwhichthemodelwasmountedwasdirectlyconnectedtothebalancesystem,a tarecorrectionto thedragwasneces-sary.Thiscorrectionwasdeterminedfromtestswiththemodelremovedfromthewindtunnel.Thefollowingcorrectionsweresubtractedfromthemeasureddragcoefficients:

R XIO-e M CD*er

10 0.25 0.00666 ●25 .00674 .25 .00692 .25 .00762 .60 .00852 .00 .00942 .85 ●00972 .875 ●01002 .90 .01022 .92 ●01032 .94 .0105

No attempthasbeenmadeto evaluatetaresdueto interferencebetweenthemodelandtheturntableorto compensateforthetunnel-floorbouqdarylayerwhich,attheturntable,hada displacementthick-nessof

-:

1/2inch.

IntegrationofSurfacePressures

orderto evaluatetheeffectsofReynoldsnumberontheaero-characteristicsofthewingathighsubsonicspeeds,itwas

C--

._—

?

t

NACARM A52B20 7

necessaryto integratethesurfacepressuresmeasuredinthe16-foothigh-speedwindtunnelto obtainnormalforce,pitchingmoment,andpressuredrag. Inperformingtheintegrations,theloadingwasextrapo-latedfrom10percentofthesemispantowardthewingroot. ItW’S-S foundthatpitchingmomentsobtainedby integrationofthesurfacepressuresmeasuredinthe12-footwindtunnelagreedwiththepitchingmomentsobtainedfromforcemeasurementsiftheloadingcurvewasterminated1/2inchfromthewingroot,a distanceequalto thetunnelboundary-layerdisplac”aentthickness.Thisprocedtiewasfollowedwhenextrapo-latingtheloadingobtainedfromthe16-footwind-tunneltestssincetheresultsof theintegrationsweretobe comparedwithforcemeasurementsmadeinthe12-footwindtunnel.

Theangleofattackmeasuredduringthetestsinthe16-foothigh-speedwindtunnelwascorrectedfortheeffectsof tunnel-wallinter-ferenceduetoliftonthemodelby themethodofreference8. Thefollowingcorrectionwasaddedtotheangleofattack:

k= 0.135cL% 0.135 CN

where CN wasobtainedby integrationof surface

RESULTSANDDISCUSSION

Theaerodynamiccharacteristicsofthemodel

pressures.

testedduringthepresentinvestigationweresimilaratmoderateliftcoefficientsto thosereportedinreference1 fora modelhavingthessmesectionandplanform. However,atliftcoefficientsnesrthatforthestall,differencesintheaerodynamiccharacteristicsoccurredatReynoldsnumbersof2,0C0,CK)0ad 10,OOO,OOOat a Machnumiberof 0.25,whicharebelievedtobe attributableto smalldifferencesinboththesurfacecontourneartheleadingedgeandtheconditionofthesurfacesof thetwomodels.

Thefollowingdiscussionof theresultsofthepresentinvestigationhasbeendividedintotwoparts:tineeffectofReynoldsnuniberat a Machnumberof 0.25,andtheeffectofReynoldsnumberat highsubsonicMachnumbers. Thesurfacepressuresmeasuredduringthetestshavebeenintegratedtoyieldsectionnormal-forceandpitching-momentcoefficientsforstresmwisesectionsat10,20,~, 60,80,90,and95percentofsemispan.Onlya limitedamountofthechordwisepressure-distributiondatahasbeenpresentedinplottedform. Howeverjallthepressuredatahavebeentabulatedintables11,111,andIV.

.

cO&mWii~ NACARMA52W0

EffectsofReynoldsNumberatMachNumberof0.25.

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Thelift,drag,andpitching-momentcharacteristicsandthecorre-spondingsectionnormal-forceandsectionpitching-momentcharacteristicsfora Reynoldsnumberof10,000,000arepresentedinfigure4. Similardataarepresentedinfigures5,6, and7 forReynoldsnumbersof6,000,000,4,000,000,and2,000,000,respectively.Thedataobtainedata Reynoldsnumberof10,OOO,OOOareincludedineachOfthelatterftguresto showmoreclearlytheeffectsofReynoldsnumber.Althoughdatawerenotobtainedbeyondthestallata Reynoldsnumberof10,000,000,thesectionnormal-forcedatafortheoutersectionsofthewing(fig.h(b))indicatethatthestallwasimminentatanangleofattackof19°. Thelift,drag,andpitching-momentdataof figures5(a),6(a),and7(a)showthattheeffectsofReynoldsnumberwerelarge,

—

particularlyintheupperlift-coefficientrange.Thesectionnormal-forceandsectionpitching-momentdatashowninparts(b)and(c)of .figures7 through7 indicatethattheeffectsofReynoldsnumberweregreatertowardthetipthanneartherootofthewing.

uIthasbeendemonstratedby theresultsofan investigationreported

inreference9 thattheaerodynamiccharacteristicsofan infinitewinginobliqueflowaredetemd.nedby theaerodynamiccharacteristicsofthesectionsnormaltothequarter-chordlineinaccordsmcewiththeconceptsof simplesweeptheory.Thesectionof thesweptwingof thisinvesti-gationwasapproximately14percentthickinplanesnormaltothequarter-chordline.Applicationofthesimplesweeptheoryto sectiondataofreference10 indicatesthatthevalueofthemaximumnormal-forcecoef-ficientfora sectionof thiswingshouldbeabout0.91and0.84 foreffectiveReynoldsnunbers,basedonthevelocityandchordperpendiculartathequarter-chordline,of6,700,000and4,000,000.TheseReynoldsntierscorrespondto streamwiseReynoldsnumbers,basedonthemeanaerodynamicchord,of10,OOO,OOOand6,000,000,respectively.Inspectionof thedatapresentedinfigure5(b)revealsthatthesevaluesofmaximumsectionnormal-forcecoefficientcorrespondto thosefora sectionatabout80percentofthesemispan;a highervalueexistingforsectionsnearertherootof thewing,anda lowervalueexistingforsectionsnearerthetip. Itmustbe notedthatthiscorrelationisnotexactsincetheMachnumbersatwhichthesectiondataofreference10wereobtainedareprobablylowerthanthecomponentof theMachnuniberperpen-diculartothequarter-chordlineofthewing. A correctiontothetwo-dimensionalsectiondataforthedecreaseofmaximumsectionnormal-forcecoefficientwithincreasingMachnumber(referenceId.)wouldresultinthepointof correlationbeingmovedfsrthertowardthetipof thewing.Thereductioninthevalueof-themaximumsectionat&)percentofthesemispanwitha reductionofto2,000,000isofthesamemagnitudeaswouldbe

normal-forcecoefficientReynoldsnumberanticipatedfromthe

NACARM A52B20 9

resultspresentedinreference12whichshownumberonNACA6-seriesairfoilsections.

.

theeffectsofReynolds

Thechordwisedistributionofstaticpressureat 20,60,and90per-centofthesemispanforReynoldsnunibersof10,000,000and2,000,000ispresentedinfigure8. Thesedataindicatethatthestalloftheoutersectionsata Reynoldsnumberof2,000,000wasprecededby a smallamountoftrailing-edgeseparation,as indicatedby a decreaseof thetrailing-edgepressures,priorto completeseparationfromtheleadingedge.Ata Reynoldsnuniberof10,000,000andanangleofattackof16°,a definitelossofpressurerecoveryat 90percentofthesemispanoccurredwithlittlelossofleading-edgesuction,indicatingthatthestallat thisReynoldsnuriberwaspredominantlyof’theturbulentortrailing-edgetype.An analysisofthecharacteristicsofa swept-backwingwhichstalledfromthetrailingedgehasbeenpresentedinreference13. Thedataofthisreferenceshow,as do thoseofthepresentinvesti~tion,thatthemaximumliftcoefficientsoftheoutersectionswere approxbately.equaltothosewhichcanbe predictedfromsectiondata. Inreference13,theincreaseinthevalueofthemaximumsectionliftcoefficientofthe

4 innersectionsoverthatpredictedfromsectiondatawasattributedtoa boundary-layer-controleffectaffordedby thedrainageoftheboundary-layerairawayfromtheinnersectionsof thewing. Thisoffersa par-tialexplanationforthesmalleffectsofReynoldsnuniberontheinnersectionsofthewingofthisinvestigation.in contrastto thatwhichoccurredat theoutersections.(See,forexample,fig.7(b).) ThesmallereffectofReynoldsnumberontheinnersectionsmayalsobe dueinpartto thelargerlocalReynoldsnumbersofthesesectionsas com-paredtothelocalReynoldsnumibersoftheoutersections.

At a Reynoldsnumberof2,000,000,a reductioninthelift-curveslopeoccurredatan angleofattackofabout3°,accompaniedby apositiveincreaseintheTZtchingmoment.(Seefig.7.) C!arefulmeas-urementoftheslopesoftheltitandpitching-mmnentcurvesoffigures5 and6 indicatesthata similarchangein slopeoccurredatReynoldsnumbersof4,000,000and6,000,000,buttoa lesserextentthanat a Reynoldsnumberof2,000,000.As reportedinreference1, thisincreaseinpitchingmomentandreductioninlift-curveslopeoccurredat theliftcoefficientatwhichthelow-dragrangeterminated.Thelow-dragrangeata Reynoldsnuniberof2,000,000extendedbeyondthean@e ofattackatwhichanadversegradientfirstexistednearthelead-

. ingedgeas shownbythepressuredataoffi~ure8(a). Suchan extensionofthelow-dragrangeat lowReynoldsnumbershasbeenpreviouslyreportedinreference12.

‘*Ona sweptwd.ng,thechangesinstaticlongitudinalstabilitycan

be separatedintothatcausedby changesinthedistributionofloadingalongthesectionchordsandthatcausedby changesinthedistributionofloadingalongthespan.Theportionof thechangeinpitchingmoment

.

NACARMA52B20

.

withliftattributableto changesinthedistributionofloadingalong-—

thespanis showninfigure9. Inthisfigure,thepitching-momentcoef-ficientscomputedfromforcemeasurementsarecomparedwiththosecom-putedsolely”fromthespanwisepositionofthecenterofpressure.In

.

makingthiscomputation,thechordwisepositionofthecenterofpressurewasassumedtobe onthelinejoiningthequarter-chordpointsofthesectionsperpendiculartothequarter-chordline. Thepitching-momentcoefficientaboutthequarterpointofthemeanaerodynamicchordcalcu-latedinthismannerhasbeentermedthespan-loadpitching-momentcoef-ficientC%. Fromtheagreementoftheslopes-ofthepitching-momentcurvesshownin figure9, itmaybe seenthatthespanwisecenterofpressurelocatedontheline~oiningthequarterchordsoftheairfoilsectionsperpendicularto thequarter-chordline(26.2percentlocalchord)provedtobe thelocationofthewingcenterofpressurenearzerolift. Thesmallerdepartureof Cms thanof Cm froma linear —

variationwithliftcoefficientatliftcoefficientsbelowthestallsignifiesthatmuchofthechangein Cm wascausedby movementofthe ‘“ .-sectioncentersofpressureratherthanby a changeinthespanwisedis-tributionofloading.Ofparticularinterestistheabruptincreaseinthepitchingmomentbetween3° and4°an@e_._ofattackat a Reynolds inumberof2,000,000whichis indicatedtobe causedby a changeinthesectionpitchingmomentsandnotby a changeinthesxmnwisedistribution ~~ofloading.At liftcoefficientsnearthestall,a largepositiveincreasein C% occurredwhichistraceabletoa reductionofthelift-curveslopesoftheoutersectionsofthewing. Thisincreasein s_pan-loadpitching-momentcoefficientCms wasmuchgreaterthantheincreaseinthepitching-momentcoefficientCm therebyindicatingthatrearwardmovementofthesectioncentersofpressureoccurredat theseliftcoefficients.

EffectsofReynoldsNumberatHighSubsonicMachNumbers

ThedataafhighsubsonicMachnumbersanda Reynoldsnumberof 2,000,000were obtainedintheAmes12-footpressurewindtunnel.AtMachnumbersgreaterthan0.875,measurementsof thestaticpressureonthetunnelwall.oppositetheuppersurfaceof themodelindicateda localMachnumbergreaterthan1.0at somepositiveanglesof attack.Sincechokingofthetunnelrendersquestionablethevalidityofdataobtained ●

underthiscondition,thesedatahavebeenfairedwitha dottedline.

ThedataatthehigherReynoldsnumberswereobtainedfromtestsin iitheAmes16-foothigh-speedwindtunnel.TheReynoldsnumberof thesetestsvariedfrom3,900,000at a Machnumberof 0.62 to 4,600,000ataMachnumberof0.94. (Seefig.3.) TheMachnumbersofthesetestsweredeterminedfroma tunnelcalibrationwhichwasconductedafterthedata

co@JglQ$LL*

NACARM A52B20 32

forthisreportwereobtained.Consequently,thevaluesofMachnuniberformostofthedataat thehigherReynoldsnumberdonotcorrespondexactlyto theMachnmibersof thedstaobtainedat a Reynoldsnumber “d of 2,000,000.Forthisreason,actualdatapointsat thehigherReynoldsnumberssrepresentedforcomparisonwiththosefora Reynoldsnuniberof2,000,000onlyat a I&chntier of 0.94,wheretheMachnumbersforthetwotestswereidentical,andata Machnumberof0.62,wherethediffer-enceof 0.02inMachnumberisnotconsideredtobe important.Theremainderof thedatapresentedfromthetestsconductedinthe16-foot“windtunnelwereobtainedfromfairedcurvesoftheaerodynamiccoef-ficientsasa functionofMachnuniber.Nomeasurementsto determineatwhatliftcoefficientandMachnumberthelocalMachnuniberat thetunnelwallexceededunityweremadeduringthetestsinthe16-footwindtunnel.Dueto itslargertest-sectionarea,however,chokingconditionscanbe expectedtooccurat liftcoefficientssomewhatgreaterthaninthe12-foottunnelfora givenMachnuniber.

. Thenormal-forceandpitching-momentdataforthehigherReynoldsnwnbertestswereevaluatedby integratingthemeasuredsurfacepressures.

\ Theadequacyofthisprocedureis illustratedin figure10. Inthisfigurearepresenteddatafromthe12-footpressurewindtunnelwhichwerecalculatedfrombothforcemeasurementsandsurfacepressures.Thesedatashowthattheindicatedlocationof thecenterofpressureisthesameinbothinstancessincetheslopesof thepitching-momentcurvesarenearlyidentical.However,integrationof thesurfacepressuresyieldeda valueofnormal-forcecoefficientwhichatanglesofattackgreaterthanabouthowasseveralpercentlowerthanthatcalculatedfromforcemeasurements.Itisnotknownwhetherthisisa resultof consist-enterrorsinextrapolationandintegrationof surfacepressures,oraresultofunevaluatedinterferencetares.

Dataobtainedineachwindtunnelat approximatelythesameMachnumberandReynoldsnumberarepresentedin figureI-1.Thedifferencesbetweenthetwosetsof dataareshowntobe smallexceptnearthestall..Therefore,comparisonsof thedataobtainedin eachwindtunnelathigherMachnumbers,butat differentReynoldsnumbers,shouldindicatetheeffectsofReynoldsnuniberformoderateliftcoefficients.Thesearepresentedin figures12through17.

EffectofReynoldsnumberfornormal-forcecoefficientsnearzero.-Thenormal-force-curveslopes,thepitching-moment-curveslopes,andthepressure-dragcoefficientsfora normal-forcecoefficientof zeroarepresentedas functionsofMachnumberinfigure18. Thesedataindicate

. thatthechangeinReynoldsnumberdidnotaltertheMachnumberfordragdivergence.TheMachnumberforliftdivergence,however,wasgreaterby about0.05atthehigherReynoldsnumber.A largeeffectofReynoldsnumberonthestaticlongitudinalstability,as indicatedby thevalueof &!#&!Njisevident.At a Reynoldsnuniberof 2,000,000,no change

NACARMA52B20

in stabilityoccurredup totheMachnumberfordragdivergence,where-upona largedecreaseof stabilityoccurredtithfurtherincreaseofMachnuniber.At thehigherReynoldsnumberthestabilityincreasedwith

-.

increasingMachnumber.At a Machnuniber‘of0.94,thedifferenceinthe.

valuesof aC#C!N indicate-thecenterofpressureat a Reynoldsnumberof 2,000,000tobe roughly1-2/2meanaerodynamicchordlengthsforwsrdof itspositionat a Reynoldsnumberof 4,600,000.

An estimateoftheproportionofthechangein stabilitycausedby—

changeinthespanwisedistributionofloadingmaybemadefrominspec-tionofthedataof figure19. Inthisfigure,pitching-momentcoeffi-cientsC% whichhavebeencomputedfromthespatiselocationofthecenterofpressure(chordwisecenterofpressureassumedtobe at26.2percentofthelocalchord)arepresentedforcomparisonwiththepitching-momentcoefficients~ calculatedfromforcemeasurements. .—

At a Reynoldsnumberof2,000,000anda no&l-forcecoefficientof zero(fig.19(a)),thevariationofthespanwiselocationofthecenterof , ..pressurewithMachnumberwasthepredominantcauseofthedecreaseinstatic longitudinalstability.At thehi@er Reynoldsnumber(fig.19(b)),spanwisemovementofthecenterofpressureaccountedforroughlyhalfof ?theincreasein staticlongitudinalstabilitywithincreasingMachnumber;theremainderoftheincreaseresultedfroma rearward movementofthecentersofpressureof thewingsections.ThechangesinthespanwisedistributionofloadingwithReynoldsnumber,whicharetheprincipalcauseof thechangesin staticlongitudinalstability,areevidentfromthedataof figure20.

A tentativeexplanationcanbe offeredforthelargeeffectsof .ReynoldsnumberonthiswingatMachnumbersgreaterthanthatfordragdivergence.Thesurfacepressuresontheuppersurfaceofthewingata Machnumberof0.94anda normal-forcecoefficientofaboutzeroare —presentedinfigure21. At 20percentofthesemispan,thecompressionimmediatelybehindthepositionofminimumpressurewssmoreabruptat_a Reynoldsntier of4,600,000thanat a Reynoldsrumiberof 2,000,000.A similsrdifferenceis showninreference14betweentheinteractionofa shockwavewitha turbulentboundarylayer,andtheinteractionofashockwavewitha laminarboundarylayerwhichdoesnotseparatefromthesurface.At theoutersections,60and&)percentofthesemispanforexample,theminimumpressureislessandthepressurerecoveryis. -morenearlycompleteat a Reynoldsnumberof 4,600,000thanat 2,000,000.Thesedifferencessreagainsimilartothoseshowninreference14betweeninteractionof shockwaveswithturbulentandwithlsminar

.

boundarylayers,exceptthatatthesesectionsthepressuredistributionsat thelowerReynoldsnuniberaresimilartothosewhichresultwhen kseparationofthelaminarboundarylayeroccuysaheadofthemainshockwave.Additionalevidencethattheboundary”layerhasseparated some-wherebetween20and60percentof thesemispanata Reynoldsnumberof2,000,000isthemorenearlycompletepressurerecovery at the

.

NACARMA52B20 13

trailingedgeat theinnersectionas comparedtothatat 60 and90per-centofthesemispan.Fromtheforegoing,it isbelievedthatataReynoldsnumberof 4,600,000theboundarylayernearthelocationoftheshockwavewasturbulent.At a Reynoldsnumberof 2,000,000theboundarylayerwaslaminarandseparatedsheadof theshockwaveat sectionsout-boardof 20percentofthesemispan.

Theeffectofa smallangleofattackon thesurfacepressuresmaybe seenfromfigures22and23wherethechordwisepressuredistributionsat 20,60,and90percentofthesemispanae presented.At a Reynoldsnumberof 2,000,~0,andMachnumbersof0.90and0.94,thepointofminimumpressureontheuppersurfaceoutboardof about20percentofthesemispanwasaheadofthatonthelowersurfaceatan angleofattackof1°. Thisisbelievedtohavebeencausedbytherelativemovementofthepointof laminsrseparationontheupperandlowersurfaceswiththeincreaseinangleofattackfromOO. Thisrelativemovementofthepointsofminimumpressureontheupperandlowersurfacesresultedinapositivenormalforceontheforwardpartof thesections,anda negativenormalforceontherearofthesections.Thisresultedinlpw,andsometimesnegative,sectionnormal-force-curveslopesandlargepositive.sectionpitchingmomentsat smallanglesofattackfortheoutersectionsata Reynoldsnumberof 2,000,000.At a Reynoldsnuniberofabout4,600,000,themovementofthepointofminimumpressurecausedbyasmallsingleofattackwasslightand,ingeneral,positivenormalforcesexistedovertheentirechordforallsectionsofthewing.

EffectsofReynoldsnumberatmoderatenormal-forcecoefficients.-AtMachnumbersof0.60and0.80theincreaseinReynoldsnumberhadverylittleeffectonthechangesin stabilityandinnormal-force-curveslopewithincreasesinangleofattackup to6°. (See$igs.n(a)and12(a).)Thereductioninlongitudinalstabilityandthedecreaseinnormal-force-curveslopewhichoccurredbetween3°and4°sngleofattackattheseMachnunibersaresimilartothosepreviouslynotedfora MachnurfiberofO.=.

At higherMachnumbers,thepressurecoefficientcorrespondingto aMachnumberof1 normaltothequarter-chordline(PmA=~~o)wasexceededat an angleofattackof 1°orless. (Seefigs.22 and23.) Whenthisconditionoccurs,theexistenceof shockwavescanbe expectedtohavean influenceontheeffectsofReynoldsnuiberontheforcessmdpres-suresactingonthewing. Thepitching-momentdataforMachnunibersof0.90,0.92,ad 0.94(figs.15(a),16(a),and17(a))showthatalthoughan increaseinReynoldsnumbereliminatedthestaticlongitudi-nalinstabilityat a normal-forcecoefficientof zero,am equallydrasticreductionof stabilityoccurredata positivenormal-forcecoefficientatthehigherReynoldsnumber.Thisreductionin stabilityoccurredneara normal-forcecoefficientof0.3atMachnumbersofO.~ and0.92(figs.15(a)and16(a)),andbetween0.1and0.2at a Machnumberof 0.94

14 NACARMA52B20

(fig.17(a)). Thesechsmgesin stabilitywere’causedmostlyby a change .inthespanwisedistributionofloading.(Seefig.19(b).)A reductionof thesectionnormal-force-curveslopesofthesectionscomprisingtheouter60percentofthesemispancausedthischangeinthespanwisedis- k

tributionofloadingasmaybe seenfromthedataoffigures14(b),l~(b),16(b),and17(b). ,

Thepressuredataforanglesofattackfrom2°to 5° ata Mchnumberor 0.90anda Reynoldsnumberof2,000,000arepresentedinfigures24(a)and24(b).Similardatacoveringapproximatelythesamerangeofangleofattackat a Machnumberof0.91anda Reynoldsnumberof 4,500,000arepresentedinfigures24(c)and24(d).Theabruptreduc-tionof sectionnormal-force-curveslopeat 60percentofthesemispanatMachnumbersofhozh0.90and0.92atthehigherReynoldsnumber(figs.15(b)and16(b))isaccompaniedby”thelossofpressurerecovery

—

indicatedinfigure24(d).However,at 90percentofthesemispanvery—

littlelossofpressurerecoveryisindicated.At thissection,thelowsectionnormal-force-curveslopesareassociatedwitha regionofnega-

e

tivenormalforceovertherea~halfofthesection.

CONCLUDINGREMARKS

Theresultsofteststo evaluatetheeffectsoftheloadingona 12-percent-thickwinghaving35°of

Reynoldsnuniberonsweepbackhavebeen

.—

presented.-Ingener~l,theresults~dicazedthatataK-Machnumberstheeffectofa changeinReynoldsnumberwas@eateron theoutersec-tionsthanontheinnersectionsofthewing.At a Machnumberof0.25,

—

themaximumnormal-forcecoefficientsforwingsectionsinboardofabout80percentofthesemispanweregreaterthanpredictedby applyingsimplesweeptheorytotwo-dimensionalsectiondata.A lowervalue ofmaximumsectionnormal-forcecoefficientthanpredictedfromsectiondatawasobtainedforsectionsat 90and95~ercentofthesemispan.At Machnumbersgreaterthanthatfordragdivergence,an increaseinReynoldsnumberfrom2,000,000to 4,500,000causeda changeinloadingwhichat a Machnumberof0.94wassufficientto shiftthecenterofpressurerearwardby about150percentofthemeanaerodynamicchord.Thischangeinloadingisbelievedtohaveresultedfroma changeinthetypeofboundarylayerintheregionoftheshockwavefromlsminarattnelowerReynoldsnumberto turbulentat thehigherReynoldsnumber. .

AmesAeronauticalLaboratoryNationalAdvisoryCommitteeforAeronautics

MoffettField,Calif.

NACARMA52B2f3

lm?ERENcEs

15

1. Tinling,BruceE.,andKolk,W. Richsrd:TheEffectsofMachNumberandReynoldsNuniberontheAerodynamicCharacteristicsofSeveral12-Percent-ThickWingsHaving35°ofSweepbackandVariousAmountsof Caniber.NACARMA50K27,1951.

2. Polhamus,EdwardC.,andKing,ThomasJ.,Jr.: AerodynamicCharacteristicsofTaperedWingsHavingAspectRatiosof 4,6,and8,Quarter-ChordLinesSweptBack45°,andNACA631A012AirfoilSections.Transonic-BumpMethod.NACARM L51C26,1951.

3. Tinling,BruceE.,andDickson,JeraldK.: Testsofa ModelHorizontalkailofAspectRatio4.5intheAmes12-FootPressureWindTunnel.I - Quarter-ChordLineSweptBack35°.NACARMA9G13,1949.

4. Edwards,GeorgeG.,andBoltz,FrederickW.: An AnalysisoftheForcesandPressureDistributionona WingWiththeLead$ngEdgeSweptBack37.25°.NAcARMA9ml, 1950.

5. Herriot,JohnG.: Blockage“CorrectionsforThree-Dimensional-FlowClosed-ThroatWindTunnels,withConsiderationoftheEffectofCompressibility.NACARep.995,1950. (Formerl.yNAGARMA7B28)

6. StvelJ_s,JsmesC.,andDeters,OwenJ.: Jet-BoundaryandPlan-FormCorrectionsforPartial-SpanModelswithReflectionPlane,EndPlate,orNo EndPlateina ClosedCircularWindTunnel.NACARep.843,1946. (FormerlyNACA

7. DeYoung,John,andHarper,ChsrlesW.:Loadingat SubsonicSpeedsforWfngsNACARep.921, 1948.

TN1077)

TheoreticalSymmetricSpanHavingArbitraryPlanForm.

8. Swanson,RobertS.,andToll,ThomasA.: Jet-BoundaryCorrectionsforReflection-PlaneModelsinRectangulsmWindTunnels.NACARep.770,1943. (FormerlyNACAARR3E22)

9. Dannenberg,RobertE.: Measurementsof SectionCharacteristicsofa 45°SweptWingSpanninga RectangularLow-SpeedWindTunnelasAffectedlytheTunnelWalls.NACATN2160,1~0.

10. Abbott,IraE.,vonDoenhoff,AlbertE.,andStivers,LouisS.Jr.:SunmaryofAirfoilData. NACARep.824,1945.(FormerlyNACAACRL5C05)

NACARM A52B20

11. Furlong,G. Chester,andFitzpatrick,JamesE.: EffectsofMachNumberup to0.34andReynoldsNumberup to 8x@ ontheMsximumLiftCoefficientofa WingofNACA66-SeriesAirfoilSections.NACATN 22’51,1950. —

12. Loftin,LaurenceK.,Jr.,andSmith,HamiltonA.: AerodynamicCharacteristicsof15NACAAirfoilSectionsat SevenReynoldsNumbersfromfl.7x 108to 9.0x 106. NACATN 1945,1949.

13. Eunton,LynnW.,andDew,JosephK.: TheEffectsofCamberand—

TwistontheAerodynamicLoadingandStallingCharacteristicsofa LargeScale4.5°Swept-BackWing. NACARM A50J24,1951.

14. Liepmann>HansWolfgang:InvestigationsoftheInteractionBetweenBoundaryLayerandShockwavesinTransonicFlow. Jour.Aero.SCi.L.Vol.3,no.12,Dec.1946,pp.623-639.

.

.

“--—

—

.

.

3N.

NACARMA52B20

TABLEI.-coommms OFTJ3EmcA 651A0MAIRFOILSECTION

17

[Alldimensionsgiveninpercentchord]

Upperandlowersurfaces

Wation

o95=75

1.252.5

?;101520253035404550“556065

E80859095

100

Ordinate

o.913

1.1061.4141.9422.6143.1763.6k7k.3924.956;.;;;

5:8975*9955●9975.8285.5445.1434.6544.0913.4672.7982.1061.413.719.025

L.E.radius:0.922percentchordT.E.radius:0.029percentchord

.

TABLEI1.- TABULA!I!ETIPRESSORJZCOEFFICIEltNFROM12-FOOTA!CA MACHNOMB~OF0.25

(a)R, 10,030,000iM, 0.25

*CJ9

, :, l,’,’ ,,

I

.

@.

TABLE11.- CONT_

(8)Concluded

,

-.

TABLEII.-CO~

(b)R, 6,coo,oco;M, o.21j

s. s

,d.

I

m. 1

,, .,

s’

TAEi=II.- CONEDWED

(b)Concluded

N- II.-CO~

(c)R, 4,C00,000;M, 0.25

%&m

I

,I

1

TABLE11.-COl?l!IIWIZll

(C) Concluded

0.s3

TABLElx.- Cor?lmuml

(d)R, 2,000,(XX3;M, 0.25

ru4=

a, O.@

, I

.=*

m.

—

..

.

I,o.m

z

I

*

B.

TABLEII.-cam.mum

(d) Clmrmldea,, o&

. 1. O.?J

I

TABLEIII.-WwIm!ml ml%ssmmcmml?IcIENlsI?Roll16-Focml’Dlw-Tm’umlTESTS

(a)R. 3,900,CCO;M, O.@l,-

JY -.-,.kf.u

.1 , 0., d !-8 ,.s 3.0 Lo %9 7.9 ,%9 IL9 13.9 V.9

, 0 I , r I

q, O&

,, 1’

,, 0s

%0.63

m. ,

1. 1,

nlm

!4

, ●

TABLEIII.-C~

(a)Conclllaecl

,,. ,

.—

TAXLEIII.-CONEUWEll

(b)R,4,3(x),000;M, 0.81

m0)

I

P,

,. ., 18 I

.

,-

%O.sl

*- Wlmdmtkk.%dum..

g -9.7 al 04 0.8 1A 8.4 3.0 w 9.9 7.9 9.9 11.9 L3.B V*

0 .44q4d9j4qd-+jJj~

,., ... . -

I&J

TABLEIII.- C~

(c)R,4,700,000;M,0.86

L4Jo

,

bum

I

!, Ill

E

*

!MBLE111.-C~

(c)concluded

‘

1. O.sd

.

I

I

1

TABLEIII.-CONTINUED

(d)R, 4,7M,000;M, 0.t!8

h-l 41..-*-

- *.7 *. I 0.3 0.8 1.8 *.B 3.8 M >9 ,.9 9.9 lL9

o . . . . . .64A .& d

b..

1, 1 ,1, , t)

,

,

TABLE 111.-CONMl?WIO

(d)Clmclllaedq,Da

uu

I

!WRIXIIIo-C~

(e)R, 4,500,000;M, 0.91*0.M a.oa

.O.Ad

I

-=s=

,‘ , ‘

,!

I

. .

●

-.

c, * ,

TABKEIII.-CO~

(e)Concluded

h O.m q,&ga

.. c., 43

. .

TAMJZIII.-COIWDWED

(f)R, 4,620,000;M,0.93

)

La

i.●

um

. I ,

TABLEIII.- COIUTMTED

(f)concluded

TABLE111,- C~

(g)R,4,@0,000;M, O.!?h

1,0.40

,

I.&m

,. ,,

TA3LEIII.-CONCLUIED

(g)WJncluaea .

—

TABLEIv.-TABuLATm PRESSURECom’mcmms FRCMEIGH-sl?mD mmsWINDTUNEELNL’A REYNOLDSNUMBEROF 2,000,CKX3

(a)R, 2,000,000;M, O.&l

m THE 12--FooT ts

I1: )

,,, , .’, . ‘:, ,! I

I ,

TABIJ3 IV.-comm

(a)Concludesboa

TABLE Iv.-ccmrmuED

(b)R,2,000,C90;M, 0.80

q,mm

.

I

w

l“, ,..

K

, ,

TABLE Iv.-colmEmuED

(b)Concluded

1, O*

q,0.$5

I

I

. . .

TAKLEIv.- coI?rmlEo

(C)R, 2,000,000;M, 0.85

!2

. .. r

t

, . * *

TABLEIv. - COI?I?INUED

(c) concluded

.

TABLE Iv. - co14TmoED

(d)R, 2,000,000;M, O.&(~

E

w. ,

, ,

.-

V . 8

TABLEIv.-cOmnvuED

(d)Concluded

Tw IV.- CONTINUED

(e) R, 2,000,009; M, 0.90

%&w

.

,, I

... 11, h .,, t,l

.&

1 .,, ,!1 d,,

is

* ,,

TABLErv. - ccwlmuEo

(e) concludedt. O.m

.. O.in

TABLEIv.- co~

(f) R, z,o~,m; M, 0.92

* O.M

.

,,I ,,

r

,,

. .I ,,, ,!’

*

k?o

. < .

TABIX IV.- CONTINUED

(f)Concludedm w

1

&

l!o

UP

-. .

TKBLE IV.. CONTINUED

(id R, 2,003,030; M, 0.94

----

ulN

, 4, ,

TABLE Iv. - comJJDED

(g) concludedruCbjm

,

.. O.*

1

UIw

.

.

.

.

, , i

Aspect ratio 5./4Taper ratio O.7!3Area 3.389 f~

z /./66 ftSection /VACA 6~A0/2

&reumwisej

Shamwke tvws of orifices

located d 1~ 2~4~60,8Q90uno’95percent of semispan

.—. .—. —o.25-chod

~--- l62+-+LWensions shownin inches

unless otherwke nofed

Figure L- G&t2t@ryof the &i

—

v

7

56

(a)AIMS woot pressurewindtunnel.

NACARMA52B20

.

(b)AmesI&oot high-speedwiridtmel.”

Figure2.-Photographsofthesemispanmodelwingmountedwindtunnels.

,-.-* ,

intheAmes.

6Ioxfo t.

0 12-foot pressure wind tunnel

El 16-foot hfgh-speed windtunnel‘% 8k

~

1

C6 /,

$Q~kg

r\ El

2 - ,-5 />

0 , ,0 .1 .2 .3 .4 .5 .6 .7 .8 .9 !.0

Much number, M

F@ure3- The Reynoldsnumbers and Mach numbersof the A?sts.v

%1,2

1.0

~j .8

.4

5

,2

0

4 0 4 8 12 .16 20 .08 .04 0 +74o .04 .08 ./2 .16 .20

A@e of &act, u, &g F%+cihg—mummtCu#fwe@ cm

, , , ,

Angle of attock, a, deg

[b) Sectkw nwnwl-ti cinmc+etitiks

ffgwe 4.- Cotn’iiwed,i?,M)~,OW; M, 0.25

Section pifcting-momd Cveftk%nt,Cm

(c) Sectibn pihhing-mtwent cborock?ritiics

Hgure 4. - CbncludedR, @OOO,OOO; M,O.25

. .

. , # , ,

f.2

1.0

-J.8Q

g3 .6~k9)E .4

$

.2

0

:2-4 0 4 8 12 16 20 .08 .04

0 .04 .08 .12 ,16 .20 *W

Ang/e d ottock, a, deg l?tchh~t ~, Cm

Lhvg coefficient, CD

/7gisw6- 7h? l.~ dreg, and pthhhg-nuwnt chwaiwkths and )YnPcorres@nahg ssctkM

mrnm’- * and *h@v-nwnent chvmcAw&%s %YM seci.bs taf the bwiw M,O.25

s!

0>1-

/.4

/.t

/.0

.8

.6

-,4

2

0

,

Angle of attoc~ u, o’eg

(b)Se&W ~f-&7M chon7cW~

figure5- Cdtkwd M,0.25

I

1

. .

Im

l%’

i%!

# * ,

.8 I I n In I l“. I \l \. #

o B.04

.6

.4

.2

0 704 =08 :/2 for y“.lo

Section @’ctWng-momentcoefficient cm

(c) - pi’hhi~-mmmt Chumcftw?”tis

F@we5.- ConcludM M, 0.25

-.

L2

1.0

.8

0

-2

“4 O 4 8 (2 16 20 .08 .040 .04 .08 . }2 .16 20 **

Angle of Oth7c& Q, &g Pitchhg-moment coeftkkw~ Cm

Drag coefficient, co

(d Mf, 4-478andP“hhhg-momedchonmteddhs.

-6- Th lift, Q%W,imd pt”ting-momerdchmucterkkbund th aweqowthg sechbn wmlQ}-

.I

I

/.4

0

d %“,

Angleof ottock, q deg

(w S4?ch ?kwn?I-fm dmmwsfhfigure G- tifhued ~ 0.25.

I

Jl=K-

-Fi-l-tWI I PI 1 I I I I I 4

L- TI I I I I I I I 1 I I I I

Section @’chjng-momentcoefficien~ Cm

(c) Secfbn Hh@-monmt chom&iWixfigure 6.- CWciuded M,0.25

,

. * ,

1.2

t.o

.2

0

k ,., , , 1 , , , . A

2,00$000 ~xl WImI I I Id[ I l—–—/nmom

~c . -,--”,---

J P

1 J1 I 1 I L I4 0 4 8 12 16 20 .08 .04

0 .04 .08 ./2 .16 .20 w

At@? of attack, a, deg Pitchi~-nnMni txaefflch?d, ~

Dmg COeffkk?nt,CD

(0) Liff,a@3,d@Mwnmed Chm’dwisfks

(2

Angle of ottock, a, o!eg

(1?)Sec#m rknmd-t%e chffnmferrktks

EgWe z– Con?iiuedM,O.25

. ,. .I

,

, *

/.2

/.0

.8

.6

,4

.2

0

t

I n I 1! I K I I I I I

1L i I I I I 1 I 1 I 1 I I I 1 I I I I

.04 0 -.04 T08 -.f2 for q*,fO

Section pitching-moment coefficient, cm

(c) Sectiiaopi~hg-momnt cham~ks

Figure Z- CtmciudsdM, 0.25

,

i.

-.4

0

.4

EB.

o

15.-

Q.

Ii

.4

0

.4

.8

“%nn-mrm.4

-ozv40w80m

Q=.60

u

IiJ*g@q&w -

0204060612UW

AYtxri4 cm

(0) e, q’@nd3d’

om40m&7m

—

t , ,

Q.

s

/.2

.8

.4

0

.4

.8

/.6

/2

‘.2

.4

0

.4

n“020406V%OA90

q=.tw

okw40#&?aw

an%d m

(4 Q, 4.037dtlo0-4r

1.6

1.2

.8

.4

0

.4

B

1!-2.0

- M

I -1,2

- .8

- .4

0

.4

B-020406viwm

9 =Eu

/?=@xzywo

02040mmm

RmF#cfwt

(c)u, &fainili2FF@m 8- cWfhued M, 0.t?5.

-.

‘m+’/

/

a =8. f 0

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41

I I I I I I I

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0204060WW

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02040606t2Am

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-1.6

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1!-B-. .4

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R“02040 fMwfoo

po

02040 twwm

%m?nfChd

(f)a, 16P

File- Cwmww M,Q25

ozo~mmmo

-1u

/.0

.8

.6

C54

0

-2

I

.(x o -.04 ‘.~ for R=JqOOQO&UPitchkg-nwnentcoeff&nts, ~ and~~

F&urv9.- Gonparim of the pitctihg-mamentcoefficient,~ , with #he spon+oatfpkhi~-moment coefficient,C%. M, 0.25.

, ,

.

,

L?

0

,

-4 0 4 8 /2 /620 #O@#

At?gkof oftock, a,obg H--mamwIt Wfklem’, Cm

figure n - com@Atm of nomwl-tinm Omi pwhhg-nnYmw?id7fo Ob@16d h AmL?

~men?s with thos8 abtih$d jhm h@m7thn of surkme pvawes.

/7, M,00~0OO ; M, 0.25.

. ,

-.

-4 0 4 8 12 16 .08 .04 0 704

Angk of otiock, a, deg Pl~chlng-momenf coefficien~ Cm

(a)tVormoi-hmemd #nW~ -mwnent chazwfwistics.

R’ 11.- Th normol-@ce & pktuhg-numml hmctenkti and Me cormspmf~ secfion

chorach?rlsh%s fm o Mach nwnbw d oppraimat@ 0.6os ewha%ti- &sts h ths

Ames H-foaf #vessure wind tunnd and in ths Areas 16-h# high- witi twmsl.

# , . ,

, , . I

.8

-2” ?0 +4 +2? +2 hr ~s.iO

Section pitching-nxmmt coetffcfm~ cm

(c)- @iwA$&vnxmmd ~

R@#e If. - Cvncluow

.

. , ,1 I

. #

.8

, , . .

4 0 4 8 12 16 .08 .04 0 -.04

Angle of ottock, u, deg Pitching-moment coefficient, Cm

b.. AWmol-fme and p“khing-mament dwocteristks.

F@ws12.- Z& ntwnd+bmw ad p“~ng-~ chmwdaristics and the cornwponding

sWAm #kmdwistb kr WM S* d * wing. M, 0.80. P

.

. , .

.-

. . , , ,

.

.8

2.

L 1 n 1 1 I 1 1 1 1 1 I I 1 1 1 I 1 1 1 1 1 n 1 104 .0 -.04 -.08 -JP for ~=.10

Section p#ching-momant coefficient, ~

-. -. .

?O)mm?ol-hlce UM @’h+lg-mwiwf Chwdwiwks.

Figm /3- Tti nmtd-brce tm$ p“7cMg-nKwtwt chormv%visiks ond * ctxn?qww%g

swtl%n chmiwWcs b sewn sa%ihnsof the wing. M, 0.85.

P.8

t? ,6

-.2

L — — — . . . A

-4 0 4 8 /2 /6 .08 .04 0 -.04

Angle of ottoc~ a, deg Pitching-moment coefficient G*

i2

. .

w . , ,

I I I I I I I13— –o– –A– –v– –b– –4– –v

M ,_p-.lo_ .20— .40 — .60 — .80 _ .80 — .95

4/ 1 w. 1 1ii

1 -1 1 1 u I \ 1 . 1 I 1 I

. ,

-.2-4 I I I I I Io 4 8 12 16 for q*.10

Angle of attack, a, deg

{b) Sedhw normal- fdrce AwucYer&th

Figure J3,- (htinued M,O.85.

. -.

Ill.

i?+- 2m)ooo

— — +61XyhW

W+HW+H I W I Q Q v- -

I 1 1 1 I 1 1 1 1 I

-+& ‘ ~ I 1 I I I I 1 I I I I I I I I I I I I I I I I ~ I704 -,08 +? for 9=./0

Section pitching-moment coefficient’, cm 5!2

(’c) - pi&Mlg-ln9med ~ ii!Egwe E- &MckIO’edM,0.65 ~

m

I ‘ , . . ,

11

, ● , ,

.8

.6

y

.4/

—— 460QOO0

J?

o -

-4 0 4 8 /2 .08 .04 ‘ o -.04

Angle ofoffack, q deg Pitching- moment coefficlen~ ~

[0) Mmnai-ltwe #d @kMlg-mOnet# LYkmMwidti

I%Jl#l?M. - The notmal-ftmw ond pitcting-nxnnad ticttwitis and Me ctmaqxwI#~ sechbv charodwisfkx

far semw sectians of the wing.M, 0.873

9

.

I I I IEl— –o– –A– –~— –L _:_–;

Lo -9 “ .@-— —20— —.40 _ _.60_ -.80 — .90. – .95

I R

u=\ ~ goowoo

x- .8 / — — 4,60(7000

$

! nl\

6 -6QQ liii HAW’H/ #

w I I I I I\ I

r-in!!Iwrldllrl ”-”

1

I #, m 1 I I , I Y “ d1

-.4?-4 0 4 8 12 for q- .!0

I 1

Afigle of attack q deg

(W Secfh normal-we awwtt?n”titi

figure /4.- Contthued M, 0.875.

, “. 4 a

.

!l !!!!!!! JI I 1 I 1 r 1 1 1 I ,

.2 111111 litml=ll.08 ,04 0 704 +)8 -.12 for y =.10 ond.80

5@ction pitching-mommt coefficient cm

(c) Secfim PJWng-mta7mV#ckwvctitks.

F@~ 14.- &nwhdeo! M, O.875

F- 15. - h? nunW-fm3 and pikWg-mwnenl charoc&vWs & * cornwpwd.. seciion cfnwocttnkfk.s

tb siwn secttis o# tAe wing M, 090.

# . . ,

. ,, .

1.0

,8

.6

.4

2

0

72-4 0 4 8 L? 16 for q =.10

Angle of ottock, e, deg

fb) 5kc#ti mml-f- ~ti

figure t5.- Confinued. M, 0.90.

-. . .,

“708 .04 0 ?U4 ?08 712 tbr T =./0 ond.80

Section pliching-moment cosffkk+ne cm

[c) slwkm @&mmsnt dom%tiistl%s

FV Is.- GcmiwW M,090.

‘8

. i

i I

, . ,

.8

,,0/.6 ,,

,.,(

.4

./j f—— qsoqooo

.21‘

/

-.2

0.

,,./)

)

.

\

,/

/

d

--4 0 4 8 L? .08 .04

‘emAngle of attack, 4 &g Pitching-moment coefficient, Cm

(u)Normof-tine ond pitchhg-rmnenf cimrocttwWs

i7@m?16– The iwrmol-ti ornf pitchhg—mwnent ch&oc4&&tb and the Comsptnu$ng St?cilhl mti%%h

ti -n sectirms of the wing. M, (292.

.

I I I I I I IEl o A P— “

Y= ,1O .20 .40 .:0 .80 .2 95

,8 *

) ‘} 1

Ii ‘R

<1[ + gow,ooo...

,..f,,, /— — 4,500,000

.6 <

$’..’

,. ..””,,. /J

,,“ / / .

I~ ) y T // .+ “

.4 /

$ A /r “

& *=A(

/

~/

/k

i

od ‘

,f? “ w ‘“/“

1

-P.—-4 0 4 L? L? for q = Jo

Angle of attack, a, &g

, I i

I

. . . . , ,

Section pitching-moment coefM&, cm

@fe16” c%dmbd. 4Ct92.

I

. .r I

, .

Angle of Wock, a, dey

. -.

.6

.4

.2

.8

0

.8

.61 I 1 u

wr I 1 1

VIw

.4

.2

0

“’.8 .04 0 704 -08 ;12 -J6 for , -./0 and .80.9 L_uuLLu 11[1 I-lm

*

Section pitching-moment coefflcien~ cm

(c) *cMn p%hi&HmMnf cxtmvwtis.

17gum R- Gmcluw. M 0.94.

I

.,1

. . , , ,

.10

.@

.(X

.04

1

— —— — ff. 4,5~,~

-. 0 .1 2 .3 .4 .5 ,6 .7 ,8

Wch twmber, M w

F@Jre B.- T~ effwt of Ii@wolds mnnber on the w?rlotian with Moth num&er d the nwmol-tlwm -

curve S/O@?,MO pitching-moment-curveS@h9, & the premm-dmg ca?ffichwt. ~, O,

-.4

0

44

.8

/.2

. . ,

.

. . . ,

I

./2

.CJ6

.04

0— R= ~oo@OO—— t?a4#0@O0

!,...,.,./6

./2

.08

.04

0

=04O .20 .40 .60 .80 100

Fh7ciftmof

O .20 .40 .60 .80 LOO

Fgwt? 2t2- The sponwia c#3ffi- of boting Mbofed by AhQs@ws of #e stwtkm mhnmol-ti

curves ot on qgk of Om of 0?

. . , .

,

78

‘-.4

o

.4

“80 20 40 60 80 /00

. , .

!$!

R=@OO#CkW; a= 0°

.——. PQd.@

@o

ot?0406080n3

q=.sw

o 20 40 60 80 IW

Percent *d.

.

9 “.20

.00 zo40w80ioo

u—@arsu* u———Lawrb

o 204060801CU

Rment Chd

(WQ, 0: Mom tm$o@5

020406080100

FQW 22- T4ec4mTtnk? c?w?twwds@tmEssuR? ~ at ~,60md90PmaW of m smkprm !2&

!

. . ,

,

u— @w surti u

———Lalmr sunl?ce

o l?0406080iO0

9 =.90

lli-fi?iu1u... ---L

0 i?0406080iiM

R?tmnt Choni

(4) a,O~ M,(XM d 094

E@we 22.- witwed. R, ~OOQGOO.

9 ●.20 q “.60

1 1 1 1 1 1 1 1 r 1 1

--- --- -+-- - -- --- —--

/ — - .

/h’! 1 1 1 1 1 1 Y

1 r 1 1 1 I

}1 I I I I I I I II

o 204060801tM

. Percent dlofd

(c) U,P! M,two QM amflwm 22.- Gzwfhued R, 2,00@XX2

77-%1 iii I

1 1 1

I

0204060 mKJo

*

, a . 1 .

~=.60

.— ___‘&As~O

0 204060 mltx7

Percent chord

(d) a, 1? M,O.90 d 0S4

F@urw 22.- Co@udsd. R, 2jOW,0iW,

P2

1

98.4?0

78

-4

0

Q.

-4

~ :8

q s.60

u —.t@ur_ u

——— Lfwers@xw

o/?0406080fGk7

Aweenf M

(ii.)L7,-e” M,a81 & G%

y =.90

1020406080UW

.U

o 20 40 60 80 m

.——‘~A=3.#- . .

02040 tM80m

Fimwnt chord

(b) a,-C!~. M, QWond 094

I 1 I

I

02040 ~801LW

““O 20 40 60 80 1~

I --- --- .I

u —Uzpersunbce LJ———1.cwr sunbce

O 20 40 60 80 IW

EAlllll-.ill

j

E@re 2.3- Canthued. Appw.rima# ~ ~W,000,

-.Y

\

I

020406U8VKW

. ● ✎

020406080fti

9“.90

7 ,. I

020406080KM

?emunt chord

(ii) a,0.8$ M, QSY d 0.84

PPP

9-.20

““020406080/00

—-— P&A=3S”

o 2040 tw 80100

I I I I I I I r-=b0 =2.0°

a “3.0°

Penawtckrd

(da, 2.#ami 3.0?N,0.90;6 ig0@0tX2

* ,

# ,

9=.20

“-0 20 40 60 80 100 0 20 40 60 80 100

7=.90

0204060~~

a. 4.0°

a= 5.P

RmefJtdlotri

(Nu, Uoi7nd 5.I!’Afmo; & .?’,000.

F&urs 24- CaWmwd

~ =.20-12

-.8

-.4

0

.4

.8

~ =.m

——&an?f-

02+340602009

1

;U=2.LP

u 20 4ow&k2 m

(c)a, wand #!?.@M,o.9f; ~ qi50@wo.

1%1.wX- C#rheti

,4 t

;.. !,

. I , ,

!/’ 1,

‘ ,

9 =,20-12

-.8

-.4

8-12

g

1!-8

-.4

0

,4

‘0204060 &31cw

, I

t92040w 60100

Rmw#dn’d

,

g+’

s

a-

08?0406vwltxJ

4.8°

(i#Q, 3fl%d 4.8!’M, 0.91;&4,50@O0.

l?@wa24.- C~. PG