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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
.
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.
●
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
.
@@!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.
.
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.$5
I
I
. . .
TAKLEIv.- coI?rmlEo
(C)R, 2,000,000;M, 0.85
!2
. .. r
t
, . * *
TABLEIv. - COI?I?INUED
(c) concluded
.
TABLE Iv. - co14TmoED
(d)R, 2,000,000;M, O.&(~
E
w. ,
, ,
.-
V . 8
TABLEIv.-cOmnvuED
(d)Concluded
Tw IV.- CONTINUED
(e) R, 2,000,009; M, 0.90
%&w
.
,, I
... 11, h .,, t,l
.&
1 .,, ,!1 d,,
is
* ,,
TABLErv. - ccwlmuEo
(e) concludedt. O.m
.. O.in
TABLEIv.- co~
(f) R, z,o~,m; M, 0.92
* O.M
.
,,I ,,
r
,,
. .I ,,, ,!’
*
k?o
. < .
TABIX IV.- CONTINUED
(f)Concludedm w
1
&
l!o
UP
-. .
TKBLE IV.. CONTINUED
(id R, 2,003,030; M, 0.94
----
ulN
, 4, ,
TABLE Iv. - comJJDED
(g) concludedruCbjm
,
.. O.*
1
UIw
.
.
.
.
, , i
Aspect ratio 5./4Taper ratio O.7!3Area 3.389 f~
z /./66 ftSection /VACA 6~A0/2
&reumwisej
Shamwke tvws of orifices
located d 1~ 2~4~60,8Q90uno’95percent of semispan
.—. .—. —o.25-chod
~--- l62+-+LWensions shownin inches
unless otherwke nofed
Figure L- G&t2t@ryof the &i
—
v
7
56
(a)AIMS woot pressurewindtunnel.
NACARMA52B20
.
(b)AmesI&oot high-speedwiridtmel.”
Figure2.-Photographsofthesemispanmodelwingmountedwindtunnels.
,-.-* ,
intheAmes.
6Ioxfo t.
0 12-foot pressure wind tunnel
El 16-foot hfgh-speed windtunnel‘% 8k
~
1
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$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
. .
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f.2
1.0
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$
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0
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0 .04 .08 .12 ,16 .20 *W
Ang/e d ottock, a, deg l?tchh~t ~, Cm
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/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-
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/.t
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.8
.6
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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 \. #
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.6
.4
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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$000 ~xl WImI I I Id[ I l—–—/nmom
~c . -,--”,---
J P
1 J1 I 1 I L I4 0 4 8 12 16 20 .08 .04
0 .04 .08 ./2 .16 .20 w
At@? of attack, a, deg Pitchi~-nnMni txaefflch?d, ~
Dmg COeffkk?nt,CD
(0) Liff,a@3,d@Mwnmed Chm’dwisfks
(2
Angle of ottock, a, o!eg
(1?)Sec#m rknmd-t%e chffnmferrktks
EgWe z– Con?iiuedM,O.25
. ,. .I
,
, *
/.2
/.0
.8
.6
,4
.2
0
t
I n I 1! I K I I I I I
1L i I I I I 1 I 1 I 1 I I I 1 I I I I
.04 0 -.04 T08 -.f2 for q*,fO
Section pitching-moment coefficient, cm
(c) Sectiiaopi~hg-momnt cham~ks
Figure Z- CtmciudsdM, 0.25
,
i.
-.4
0
.4
EB.
o
15.-
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.8
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.(x o -.04 ‘.~ for R=JqOOQO&UPitchkg-nwnentcoeff&nts, ~ and~~
F&urv9.- Gonparim of the pitctihg-mamentcoefficient,~ , with #he spon+oatfpkhi~-moment coefficient,C%. M, 0.25.
, ,
.
,
L?
0
,
-4 0 4 8 /2 /620 #O@#
At?gkof oftock, a,obg H--mamwIt Wfklem’, Cm
figure n - com@Atm of nomwl-tinm Omi pwhhg-nnYmw?id7fo Ob@16d h AmL?
~men?s with thos8 abtih$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
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