NATIONALADVISORYCOMMITTEE FORAERONAUTICS · nationaladvisorycommittee foraeronautics technical note...
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NATIONALADVISORYCOMMITTEEFORAERONAUTICS
TECHNICAL NOTE 3172
EFFECTSOF LEADING-EDGERADIUSANDMAXIMUMTHICKNESS-
CHORDRATIOONTHEVARIATIONWITHMACHNUMBER
oF YHEf3J3R0D~A.MIcc-cTERISTIcS oF
SEVERALTHINNACAAIRFOILSECTIONS
ByRobertE. BerggrenandDonaldJ. Graham
AmesAeronauticalMoffettField,
Laboratorycam.
WashingtonApril 14,1954
AFM2CTECHNICALK“xx!ay
https://ntrs.nasa.gov/search.jsp?R=19930083890 2018-10-11T16:42:38+00:00Z
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TECHLIBRARYKAFB,NM
NATIONALADVISORYCOMMITTEETOR
.
TECHNICALNOTE3172
EFFECTS(X?LEADING+3X+ERADIUSANDMAXIMUMTEICKNESS-
cmozmmmo oNTHEVA31AIHONmm mm mm
OF TSXAERODYNAMIC
SEVXRALTEIl?NAC!A
By RobertE.Berggren
CHARACTERISTICS07?
AIRFOILSECTIONS=
andDonaldJ.Graham
SUMMARY
A wind-tunnelInvestigationhasbeenJu3deto &etemlinetheeffects-- —of leading-edgeradiusandmaximumthickness-chordratioonthevariationwithMachnunheroftheaerodynamiccharacteristicsof severalthinsymmetricalNAcA&Ligit-seriesairfoilsections.T@ Machnumberrangeoftheinvestigationwasfrom0.3toa~proximatelyO.9andthecorre-spondingReynoldsnumberrangefromapproximately1 x lCF to 2 x l&.
ThevariationswithMachnumberofthelift,drag,andTitchingmommt fora &percent-chord-thickairfoilsectionarenotsignificantlyaffectedby a changeof leading-edgeradiusfrom0.18to 0.53percentofthechord.A s3milarconclusioncanYe drawnfora leadi~dge-radiusvariationfrom0.10-toO.4Qercent chordona &percent+herd-thicksection.
Wogressive@rovementofthevariationofllft-curveslopewithMachnunber,theliftanddrag4ivergencecharacteristics,andthemx-imumsectionliftcharacteristicsat Machnuuibersa%ove0.6resultsfromreductionofthbmimum thicknes~hordratiofrom10to 4 percent.Sectionpitchiexmnt characteristicsarenotgreatlyaffected%y vari–ationofthemaximumthiclmess+hordratfo.
INI’RODU3TION
To investigatetheinfluenceofairfoilleading-edgeradiusonthevariationwithMachnumberoftheaerodynamiccharacteristicsofthin
&
‘SupersedesNACARMA50EQ4,“EffectsofLeading+dgeRadiusandMaximP ThicknesHhordRatioontheVsriationWithMachNumberoftheAerc-● dynamicCharacteristicsofSeveralThfnNACAAirfoilSections”by
RobertE.BerggrenandDonaldJ.Graham,1950.
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2
airfoilsections,a seriesofairfoilby 3-1/2-foothigh-speedwindtunnel.
-..NACATN 317’2
test8wasconductedintheAmes1-Theresulteof theinvestigation
fora thicbess-chordratioof10 percenthavebeenreportedinrefer-ence1. Theresultsforthickness-chordratiosof 6 and4 percentarereportedinthepresentpaxm. ThebasicthicknessformoftheairfoilsinvestigatedwastheNACAtiigibseries(seereference2)withmaximumthfclmessat 40 percentoftheairfoilchord.
InadditiontotheI.eading+dge-radiusstudy,theInvestigationpez+mfttedfurtheranalyslsoftheeffects,ofthfcknes~hord-ratiovariationonthecharacteristicsofairfoilsectionsathighsubsonicMachnumt)ers.Thisanalysisisalsocontainedinthepresentreport.
a. section
c airfoil
cd section
c? section
c2- maximum
c%4seotion
NUIM!I!ION
lift-curveslope,~r ~~ee
chord,feet
dragcoefficient
liftcoefficient
sectionliftcoefficient
pitching~mentcoefficient
M free-stream
M= Machnumber
aboutthequarter-chordpoint
Machnumber
fordragdivergezme,definedas theMachnuniberatu
()dcdwhich — = 0.1mao = constant
‘2 Machnumberforliftdivergence,definedas the&oh nuuiberat
(J
d2c~which — =0
dM2 o = constant
T free-streamvelocity,feetpersecond
.
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NACATN 3172 3
9
v localvelocity,feetpersecond
uAva incrementinlocalvelooitycorrespondingtoadditionaltypeof
loaddistribution,feetpersecoti
x distancealongchordfromleadingedge,fractionofchord
Y distancePerpendic- to chord,fractionofchord
a. sectionangleofattack,degrees
DESCRIPTIONOFAIRFOILS
Theairfoilsectionsofthepresentstudyare:
9
Leadiqdge radiusNACAairfoildesignation (percentchoti)
0004-1.10 40/1.~~ 0.180004– 3.30 40/1.5~ .530006– 1.10 40/1.575 .400006- .70 40/1.373 .250006– .27 40/1.’575 .100008– 1.20 40/1.575 .700010– 1.10 40/1.575 1.10
Thefirstdigitof theairfofldesignationindicatesthecaniberinper-centofthechord;thesecond,thepositionof thecamberintenthsofthechordfromtheleadingedge;andthethirdandfourth,themaximumthiclmessinpercentofthechord.Thedecimalnumberfollowi~thedashistheleading+dge-radiusindex;theleading+dgeradiusas a fractionoftheairfoilchordisgivenby theproductoftheradiusindexatithesq,usreof thethiclmes~hordratio.A radiusindexof 1.10isstandardfortheNACA44igit-seriesairfoilsections.Thetwodigitsinmdiatelyprecetingtheslantrepresentthepositionofmaximumthicknessinper-centofthechordfromtheleadingedge. Thelastdecimalnuniberisthetralli~dge+ngle index,theanglebeingtwicethearctangentoftheproiuctof theangleindexandthethichess+hordratio.
ThecoordinatesoftheairfoilsinvestigatedaregivenintablesIto VII. Theprofilesareillustratedinfigure1 andthetheoretical
* low-speedpressuredistributions,determinedby themethodofreference3,infigure2.
*
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4 NACATN 3172
Thetestsweremadetunnel,a low-turbulence
Theairfoilmodels,
.APPARATUSANDTESTS .—
wintheAUBS1-by 3-1/2-foothfgh-speedwindtwtiimensional-flowwindtunnel.
constructedofaluminumalloy,wereof &inchchordandcompletely@ned thel-footdimensionofthewind-tunneltestsection.Endleakgewaspreventadby mans ofcontouredsponge-rubbergaslmtscompressedbetweenthemodelendsandthetunnelwalls.
Measurementsoflift,drag,andpitchingmomentweremadeat Machnumbersfrom0.3toas highas 0.9foreachoftheairfoilsatanglesofattackincreasingby 1°or 20 incremmtsfrom42°toa maximumof 12°.Thisrangeofanglesofattackwassufficien.tto encompasstheliftstallup toMachnumbersoftheorderof 0.8. TheReynoldsnumberofthetestsrangedfromapproximtel.y1 X 106at theminimumMachnumbertoapprox—imately2 x 106at thehighestMachnumbers.
Liftandpitchingmommtswereevaluatedby a mthod similartothatdescribedInreference4 fromintegrationsofthepressurereactionsonthe tunnelwallsude bymeansof
producedby theairfoilmodels.Drag?masurementswerewalmsurveysusinga rakeoftotal-headtubes.
~—
?
8“HHJIITSANDDISCUSSION
Ssctionlift,drag,andquarte~hordpitching+no~ntcoefficientsfortheairfoilsectionsinvestigatedarep~sentedas functionsofMachnumberat constantanglesofattackinfigures3, 4,ad 5, respectively.ThecharacteristicsfortheM+ercenbthfclmess+hord ratioaretakenfromreference2. Theanglesofattackindicatedinthefiguresrepre-sentbutnominalvalues,beingsubjecttoa maximumexperimmtalerrorin settingofO.l~O.Thecharacterlsticshavebeencorrectedfortunnel-wallinterferenceby themthodsofreference5. wshed lineshavebeenusedinthefiguresto ~ndicatetheregion@ possibleinfluenceofwi.nd-tunnelchokingeffectsontheresults.
Leadtng4dgeRadius
Withinthelimitsof thepresentinvestigation,theleading+dgeradiusdoesnotsignificantlyinfluencethevariationwithMachnumberof theaerodynamiccharacteristIcsof ~ and&percentihord-thickair-foilsections.A smallsuperiorityimthemximumsectionliftcoeffi-
●
clentat Machnumbersfrom0.4to0.75isindicatedinfigures6 and7forthe&percent-thickairfoilwiththeverylargenoseradiw. Forthe *
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NACATN 3172 5
.
,
.
&percent-thicksectionsho importantdifferencesexist.No importanteffectofnoseradiuschangeonthelift+mrve-lopevariationwithMachnuniberisindicatedinfigure8 foreitherthichess-chordratio.Theminimumdragcoefficientisnotedfroma studyoffigure9 (illustratingthevariationof sectiondragcoefficientwithsectionliftcoefficientat constantMachnuniber)tobe lowerat allMachnmibersforthe~ercent-thicksectionwiththestandardleading-edgeradius;but,atnmderatetolargeliftcoefficientsforMachnumbersupto 0.7, thedragcoefficientsareloverfortheprofilewiththelargernoseradius.Thelattertrendcanalsobe notedfromthisfigureforthe6-percent-thicknesHhordratio.No realdifferencesareobservedinthevariationsof sectionpitching-momentcoefficientwithsectionliftcoefficientat constantMachnmiber(fig.10)forthesectionswiththevariousleading+dgeradii.
MaximumThicknestihordRatio
A progressiveimprovementinairfoil+ectionliftcharacteristicsresultsfromreductionoftheairfoilmaximumthickness-chordratiofrom10to 4 percent.FromfigureU, thelift+livergenceMachnuriberisobservedto increasenearlyMnearlywiththicbessreduction.2 TigureU illustratesthegaininmaximumsectionliftcoefficientwithdecreaseinHimum thicknessatMachnunibersabove0.6. ThevaluesatMachnum+hersbelowabout0.6arestijectto questionbecauseofthelowscale.However.,theresults01theinvestigationofreference6 indicatethatatthehigherMachnunibersthevaluesarenotmuchinfluencedby therela-tivelylowtestReynoldsnmibers(approximately2X106).Theeffectsofmaximumthi.ckness-chord+atiovariationonthesectionli=urve slope}illustratedinfigure13,arewhatshouldbe expectedinthateachsucces-sivereductionofthicknessincreasestheMachnuniberatwhichthelift-curveslopebreaks.
Theeffectofreductionofthickness-chordratioontheMachnuniberfordragdivergence(fig.14)isto increasemarkedlythevalueofthisparameterat zerolift. Withincreasingliftcoefficientthisfavorableeffectdiminishesbecomingverysmallat a liftcoefficientof0.5.
At Machnunibersbelow0.7,thevariationof sectiondragcoefficientwithsecti?nliftcoefficient(fig.9) isadverselyaffectedby reductionofthemaximumthickness;forMachnumbersgreaterthanOn, theconverseistrue. Theminimumdragcoefficientisprogressivelydecreasedwithmaximuuthicknessreductionat allMachnunibers.
Maximumthickness-chordratio,withinthelimitsofthepresentinvestigation,hasno importantinfluenceonairfoil-sectionpitching-momentcharacteristics.%l?heportionsofthecurvesshownforthelift-coefficientrangefromapproximately-0.2to0.2representestimatedvaluesofthelift-divergenceMachnuniber,therebeinginsufficientdatato permitpo~itivedeterminationofthisparameternearzerolift. Thelift+iiivergenceMachnuniber,of course,hasno significanceat zerolift.
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6 NACATN 3172
CONCLUSIONS“
“
Fromtheresultsofa h@h-syeedwind-tunnelinvestigationof theeffectsof leadin&edgeradiusandmximumthickness+hordratioonthevariationwithMachnumberoftheaerodynamiccharacteristicsof severalthinsymmetricalNACA~igit-seriesairfoileections,itisconcluded:
1. ThevariationswithWch numberofthelfft,drag,andpitchingmo~nt fora &percent-chord-thickairfoilsectionarenotsignificantlyaffectedby a changeoftheleading~dgeradiysfrom0.18to 0.53percentofthechord.Theu is trw fora leading+dge-radiusvariationfromO.l& to O.-percentchordona 6-percent+chord-thicksection.
2. Reductionofthemaxfmumthickness-dordratiofrom10to 4percentprogressivelyimprovesthevariationoflift-curveslopewithM%chnumber,theliftanddrag-divergencecharacteristics,andthemax-im sectionliftcharacteristicsatMachnunibersabove0.6.
39 Sectionpitchi~nmmntcharacteristicsarenotgreatlyaffectedby variationofthemaximumthlckness+hofiratio.
&s AeronauticalLaboratory,N3tionalAdvisoryCotitteeforAeronautics,
MoffettTield,Calif.,May4, lg50
REFERENCES
1. Smmws, JamesL.,andGraham,DonaldJ.: EffectsofElystematicChangesofTrailing~dgeAngle- Ieadh@ldgeRadiusontheVbriationwithMachNumleroftheAerodynamicCharacteristicsofa 10-Percen=hord-I’hickNAcAAirfoilSection.NACARMA918, lgkg.
2. Stack,John,andvonDoenhoff,AlbertE.: Teetsof16RelatedAirfoilsatHighSpeeds.NAcARep.4$72,1934.
3. Theodorsen,Theodore:TheoryofWingSectionsofArbitraryShape.NACARep.411,1931.
4. Abbott,_ E.,vonDcmhoff,AlbertE.,andE%ivers,LouisS.,Jr.:SummaryofAirfoilIhta. NACARep.824,1943.
—
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NACATN 3172 7
.
5. Allen,H. Julian,andVincenti,WalterG.: WalllnterferenoeinaTwQtinslonal+lowWindTunnel,WithConsiderationof theEffect* ofCompressibility.NACARep.782,1944.
6. Spreiter,JohnR.,andSteffen,PaulJ.: Effectof&h andRemoldsNumbersonMaximumLiftCoefficient.IIACATN1044,1946.
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8 NACATN 3172
TAKCEI. – COCIRDINAZESANDTHEORETICALIRESSUREDISI!RIBUTIOMSFCE?TEENACA000L1.1040/1.775AIRFOIL
(per~entc) (per~entc) (v/v)= V/v Ava/V
o 0 0 0 5.3651.23 .603 l.lq 1.061 1.4272;5 .8U3 1.130 z.063 1.010y.o l.o~ 1.123 1.060 ●7057*5 1.270 1.115 1.056 .56610 1.413 1.108 1.053 .48315 1.620 1.099 1.048 .382
1.765 1.097 1.048 .320; 1.940 1.093 1.046 .243
2.000 1.088 1.043 .lg550 1.940 1.085 1.042 .15660 1.773 1.082 1.040 .12570 1.493 I..061 1.030 .09680 1.106 1.032 I.016 .069
.622 ;;3 .997 .037~~.. .342 ●970 .013
.040 0 0 0
L.E. radius:0.18percentc.
.
.
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NACATN 3172 9
.
. TABLE11.– COORDINATESANDTEEOIUZTICALI?KEESUREDISITUWTIONSFORTHENA.CA0004-3.3040/1.575AIRFOIL
(perc~ntc) (perc~ntc) (v/v)z VP Ava/V
o 0 0 0 3.5151.25 .g31 1.328 1.153 1.1992.5 1.196 1.317 1.148 .9945.0 1.468 1.214 1.102 .6857=5 1.611 1.182 1.087 .34910 1.717 1.153 1.074 .46615 1.799 1.112 1.054 .36620 L 862 1.091 1.045 .30630 1.955 1.078 1.038 .23440 2.000 1.082 1.040 .18950 1.940 1.(X3 1.041 .154‘60 1*773 1.079 1.039 .v6
1.493 1.059 1.b29 .099U I.106 1.033 1.016 .07590 .6222 .994 .%7 .04993 .342 .935 ●967 .033100 .040 0 0 0
L.E. radius:0.53P9rcentc.
.
.
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10 NACATN 3172
.
.
!lXBLllIII.– coommATEsAm THEORETICALmxsm DISTRIBUTIONSFmTHENACAOOO&l.10 40/1.575AIRFOIL
(per~entc) (perc~ntc) (v/V)’ Vp Ava/V
o 0 0 0 3.7811.25 ●!307 1.149 2.072 1.3612.5 1.228 1.174 1.054 ●9745.0 1.633 1.174 1.084 .6847*5 1.908 I.164 1.080 .55110 2.120 1.158 1.076 .47015 2.433 1.145 1.070 .37220 2.643 1.141 1.068 .31230 2.915 1.143 1.069 .23940 3.000 1.141 1.06a .189.50 2.915 1.u8 I.062 .15460 2.660 1.115 1.056 .12570 2.240 1.038 1.043 .0$)880 1.660 1.053 1.026 .07290 .934 1.002 1.001 .04595 .514 .915 =957 .027100 .060 0 0 0
L.E. radiua:0.40~rcentc.
.
.
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NACATN 3172 11
TABLEIv. - COORDINATESANDTHEORl?TICALPRESSUREDISTRIBUI’101’TSFORTHENACAOboti.70ho/1.575AIRFOIL
(perc~ntc) (perc&tc) (v/’v)2 v/T Av3/v
o 0 0 0 4.5201.25 .766 I.083 1.041 1.3652=5 1.067 1.123 1.060 .9775.0 1.473 1.138 1.067 .6877*5 1.767 1.142 I.069 -55510 1.989 1.144 1.069 .47415 2.354 1.148 1.072 ●37720 2.607 1.152 1.073 .317{: 2.908 1.148 1.072 .241
3.000 1.145 1.070 .193;; 2●915 1.136 1.066 .156
2.660 1.117 1.057 .1262.240 1.095 1.046 .0S9
X 1.660 1.056 1.028 .07490 .934 ●997 *999 .04795 .514 .924 .961 .030100 .060 0 0 0
L.E. radius:0.25percentc.
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12 NACATN 3172
.
TABLEV.– COORDINATESANDTHEORETICALPRESSUREDISTRIBUTIONSFC!RTHENACAOO06A3.2740/1.575AIRFOIL
(perc~ntc) (perc&tc) (v/v)2 T/v Ava/V
o 0 0 0 6.8931.25 .566 .962 *g81 1.3492.3 .8ko 1.029 1.015 .9745.0 1.247 1.077 1.038 .6897*5 1.567 1.0$?7 1.047 ●5%
10 1.826 1.119 1.058 .48015 2.246 1.140 1.068 .38320 2.546 1.154 1.074 .32230 2*WQ 1.16040
1.077 .2453.000 1.148 1.071 .194
50 2●914 1.134 1.065 .15760 2.660 1.120 1.O% .127P 2.240 1.097 1.047 .09980 1.660 1.058 1.029 ●073w .934 ●999 ●999 .04693 .514 .g20 ●959 .028100 .060 0 0 0
L.E..radius:0.10percentc.
.
.
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NACATN 3172 13
.
TABLEVT. - cOORDINXLESANDTHEORETICALIRESSUREDISTRIBUTIONSFQRTEElWICA0008-1.10kO/1.5~ AIIU?OIL
,
(perc~ntc) (perc;ntc) (v/v)2 v/7 Ava/V
o 0 o“ o 2.%31.25 1.210 1.138 1.067 1.3292.5 1.636 1.228 1.108 .9745.0 2.179 1.236 1.3X2 .6867.5 2.540 1.223 1.106 .55210 2.825 1.217 1.103 .47115 3.240 1.206 1.098 .37420 39530 1.199 1.095 .31430 3.889 1.194 1.093 .23940 4.CQO 1.191 1.0$.?2 .19150 3.889 L 182 1.087 .15560 3.545 1.160 1.077 .12570 2=985 1.123 1.06Q .O*80 2.212 l.o~ 1.037 .0729 1.243 .994 ●997 .04595 .684 .919 .958 .029lW .080 0 0 0
&
L.E. radius:0.70percentc.
.
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14 NACATN 3172
.
w
TABLEVII.- COOIU2WITESANDTHEORETICALTRESSUREDISTRIBUTIONSFORTEENACA0010-1.1040/1.575AIRTOIL
(perc~ntc)
o1.252.5~.o7~5
1015203040w6070809095100
(perc~ntc)
o1.5112.0442.7223.1783.5334.@64.4114.8P65.0004.8564.4333-7332.7672.556.856.100
(v/v)2
o1.1081.245I.2861.2771.2691.2611.2481.2441.2421.2311.2111.1551.089.980.912
0
L.E, radius:1.10percentc.
o1.0531,1161.1341.1301.1271.1231.1171.1161.1151.1101.1011.0741.043
● 990● 955
0
2.3241.286.966.690.556.475.377.316.241.193.155.126.og8.072.045.0300
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NACATN 3172 15
L
NAGA 0004-UU 40/L575
cNACA 0004-330 40/’.575
NAGA 0006 -LIO 40/L575
u
NACA 0006-0.70 40/L575
NACA 0006-0.27 40//.575
NACA 0008 –LIO 40//!575
.
NAGA 0010- UU 40/4575
=S=’FigureL- NACA airfoil profiles invesfiguted.
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L4
M
Id
.8
(9e
v
.6
.4
2
n
\
4
\— ~ _ / . . — . _
~ _
-
NAGA 0004-3.30 40/1.5?5 \__ NACA 0004-1.10 40/L5R5
1 1 1-o ./ .2 .3 d .5 .6 .7 .8 .9 LO 5
x(0) Maximumthixness-cbad mtio of 0.04.
GEl
Figun?2.- Theoreticalpressm distributions showhg Me effect ofthichess-chotd mtb and leading-edge mdius. ~, Oj M, O.
.
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IL4
I!2
h
aNACA 0006-1.10 40/1.575
V2(+
— —_ /VACA 0006-0.70 40/1575v ______ AJACA 0006-0.27 40/L575
.6
.4’
.2
o ‘o .f .2 ●3 .4 .5 .6 .7 .8 .9 LO
(b) Moximum thkks - chtvd tznlo of 0.06.Figure 2.- confihtteo!
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.- 171 I I
IL- I-7---I--+ -+-—I-+--I---I---L--L-T 1A
lo
.8
(+YNACA 0010-1.10 40/L5?5
;
.6 _– _ NACA 0004-1.10 40/1.575
#
.2
0 1 I 1
0 J 2 9.3 4 5 .6 .7 .8 .9 M
(c) Variation of m;imum thickness-chord rohb.Figure 2.- Conchded
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NACATN 3172 19
.
.
(o) NACA 0004- 1./0 40/1.575 Airfoi~
Fi~n9 3.- Vuriutionof sectionlift coefficimt with Mach numberof constontffnglesof ottuck.
-— — —-
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NACATN 3172
Figure3.-
M7ch number,Mv
(b) NACA 0004-330 40/1.575 Airfoile
Continued.
,
Y
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NACATN 3172 21
.
ae v /
o 0:
: &A4
—
/t‘. — - — —
4.3 $ .5 .6 .7 .8 .9 Lo
Moth number,M
(C} NACA 0006- LIO 40/L575 Airfoila
Figure3.- Continued.
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22 NACATN 3172
Mach number, M
(d) NACA 0006-0.70 40/1.575 AirfoiL
F@#i93- cwim?a!
-=25=
.—
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NACATN3172 23
.
8
.
.
.
me
1
.W.2 .3 ,4 .5 .6 .7 .8 .9 40Moth number,M
(e) NACA 0006-0.27 40/1.575 Airfoil
Figure3,- Confizked.
![Page 25: NATIONALADVISORYCOMMITTEE FORAERONAUTICS · nationaladvisorycommittee foraeronautics technical note 3172 effectsofleading-edgeradiusandmaximumthickness-chordratioonthevariationwithmachnumber](https://reader035.fdocuments.in/reader035/viewer/2022081521/5bbf7d5f09d3f22e7d8c3c35/html5/thumbnails/25.jpg)
NACATN 3172
au
o:;0’ 6’ A
—
A 4°V GoD 8°a IOU<*v /2°
*W
●2 .3 ,4 .5 ,6 .7 .8 .9 koMachnumber,M
(f) NACAOm8-LIO 40/[575 Airfoil,
Figure 3.- Cmfkwed..
.
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NACATN 3172
.
.
f.i
/.c
-.2
-.4
-4s
o &
•1 /0
A 4°V 6°D go
v /p q . .-.
—
-:2 .3 4 .5 .6 .7 & .9 LoMuch numbe~M
(g) A!ACA 00/0-[/0 40//575 Arfoil,
Figure 3.- &cl.uu’ed.
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26 NACATN 3172
I I . ..-A I I I A I I I
,02
?2 .3 !4 .5 .6 .7Mach?lUmbef, M
(d NACA 0004 -1./0 40/1.575F’igure 4.- Variationof sectiondmgcoeffickntwith
constuntanglesof attack.
.8 .9 mT
AirfoihMuchnumberat
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NACATN 3172 27
0
*
*
.
.
Mach number,ttf(~) NACA 0004-3.30 40A!575 Airfoil.
Figure4.- Continued
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> Section drug coefficient,cdmm.-.
R 1 , ,- ,, u , 1 1 1 1 1 1 1 1 1 1
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NACATN 3172
d
\
\
\ rg
I$$; .f “
/ 2.1“
o 0:I
; ;:/
V 6°D 8°4/0”
.3 .4 .5 .6 .7 .8 .9 ltMachwmber,M
ii?’) NACA 0006-0.70 40/L575 Airfoil,4.- continued
29
?
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30 NACATN 3172 .—
.
.02
0 0°
‘o z“A 4°
kk’”
L!..Ll)bl I I IV 6°e: /%
.4 .5 .6 .7 .8 .9 40Machnumbe~M
(e) NACA 0006-0.27 40/1575 A)rfoil,w
Figure 4.- Gontinueal
■
.
.
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IfACATN 3172 31
.221
.20
./8
.16
.06
.04
.02
:2 .3 .4 .5 .6 .7 .8 10
~UCh #W?b8f8 M 6(f) NACA 0008-HO 40/[575 Airfm7+
Figure 4.- Confi’ued.
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32 NACATN 3172
(g) NACA00/O-LIO 40//.575 AirfoiLFigure4.- Concluded.
.
.
●
.
.
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Sectionp!tching-momenlcoefficient,Cm.1 .1 .1 c?
?‘k b h Q “< “h L “h
b
v
. .“.
I /-[f
![Page 35: NATIONALADVISORYCOMMITTEE FORAERONAUTICS · nationaladvisorycommittee foraeronautics technical note 3172 effectsofleading-edgeradiusandmaximumthickness-chordratioonthevariationwithmachnumber](https://reader035.fdocuments.in/reader035/viewer/2022081521/5bbf7d5f09d3f22e7d8c3c35/html5/thumbnails/35.jpg)
34 NACATN 3172
.4
me.3 6 .=”
N d+ 0$ ~ &
o
$’ .2 ;~ A‘-Q“+ A 4ek V 6*8 ./ : ,;”$ v /2°g . . .yo
.$* ~.3 -./Q /~“-%Q -.2w
–,3
-.42●3 .4 .5 .6 .7 .8 .9 10
Mach numbertA+
(b) NACA 0004-3.30 40/i.575 Airfoi/.
Figure 5.- Continued.
.
.
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NACATN 3172 35
. . .
[
\
+
73
y-,4.2 .3 & .5 .6 .7 ,8 .9’ [0
Much number,M
{c) IVACA 0006-110 40/1.575
Figure5.- Continued.
Airfoii”
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.
.
d
.7.2 .3 $ .5 .6 .7 ,8 .9 40/$ft#Chnumber,M
(i+) NACA 00(X -0.70 40/1.575 Airfoil.
.
4
Figure5.- CWlnueo!.
.
![Page 38: NATIONALADVISORYCOMMITTEE FORAERONAUTICS · nationaladvisorycommittee foraeronautics technical note 3172 effectsofleading-edgeradiusandmaximumthickness-chordratioonthevariationwithmachnumber](https://reader035.fdocuments.in/reader035/viewer/2022081521/5bbf7d5f09d3f22e7d8c3c35/html5/thumbnails/38.jpg)
NACATN 3172 37
ae
o 0:
: !?OA 4°V 6“D 8°4 /0:v /g
v v
,3 ,4 .5 ,6 .7 .8 ,9 iOMuch number,M
(e) A(ACA0006-0.27 40/L575 AirfoiL
Figure5.- Continued.
![Page 39: NATIONALADVISORYCOMMITTEE FORAERONAUTICS · nationaladvisorycommittee foraeronautics technical note 3172 effectsofleading-edgeradiusandmaximumthickness-chordratioonthevariationwithmachnumber](https://reader035.fdocuments.in/reader035/viewer/2022081521/5bbf7d5f09d3f22e7d8c3c35/html5/thumbnails/39.jpg)
ylI
Sectionpitching-mamentcoefficient~Cmw4
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NACATN 3172 39
6-:0cf-/”o 0°: ;;
A 4°V 6°b 8“Q /0°v [2°
.-.2 .3 .4 .5 .6 .7 .8 .9 10
Much number,M
(9) ~ACA0010-110 40/L575 AirfoZ
Figwe 5.- Concluded
![Page 41: NATIONALADVISORYCOMMITTEE FORAERONAUTICS · nationaladvisorycommittee foraeronautics technical note 3172 effectsofleading-edgeradiusandmaximumthickness-chordratioonthevariationwithmachnumber](https://reader035.fdocuments.in/reader035/viewer/2022081521/5bbf7d5f09d3f22e7d8c3c35/html5/thumbnails/41.jpg)
.“
..%2 40 .W .56 .60 9625 .65 .675 .70 .725 .??5 .725 .60 .825 .85 .875 .90
4 8 L?Mach numbur W ae = O“ds
Sedk4 a)g~ d *ck, a., deg (f~ M“SO)
(a) A!ACA 0(W4-LIO 4CW575 AfrW.
F@tw 6.- Vmbtim of sectkm lift ooefftcient wifh o?@ of affock at constant Mach numbers.
, # .
![Page 42: NATIONALADVISORYCOMMITTEE FORAERONAUTICS · nationaladvisorycommittee foraeronautics technical note 3172 effectsofleading-edgeradiusandmaximumthickness-chordratioonthevariationwithmachnumber](https://reader035.fdocuments.in/reader035/viewer/2022081521/5bbf7d5f09d3f22e7d8c3c35/html5/thumbnails/42.jpg)
9 *
/.0
Q- .8
j’ #j
a%Q .4
g% .28$*go
72
-.4
Y6.30 L40 .50 .55 .60 .625 .65 575 ,70 .7P5 .75 ,775 .80 .825 .85 .875 .W
-4 0 4 8 12Mach twmber for me= O” axis
Section ongle of attock, ae, deg f for M= .30)
Figure 6.- Continued
(b) NACA mo4-3.30 40/1.575 Afrfbfl.
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.8 IJ. \
& i/
1 r 1 u I 1 I I I #
-.4I 1 /
/ I .90– ~
;6 -3.40 .50 ,55 ,60 .625 .65 .6Z5 .70 .?25 .75 .?= ,80 .825 .85 .875 .90
-4048Section angle of atfock,
Figure 6.- Continued
Mach number for UO-W arls1? v
ao, &g (for M=.30)
(c) NACA OOC6-HO 4GZ575 Airbif.
, . . . . .
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t , . ,
.8 I I I I I I II 1 II I II I II Ill Ill Ill Ill I II Ill I 1/ I v I I
u’ ~!, , , I , - I .
b lY1-YIYljI
/ v vI
t / /I I I
I / /I i IK;8751“ I r
+1 I t . 7(/
I 1
%6.30 .40 .50 .55 .60 .(X5 .65 .6Z5 ,~ .?25 75 .775 &30 .825 ,85 BZ5 ,90
Mach ntier fir q-00 axfs-4 0 4 8 L?
Section angle of attock, an, o’@ @r ME.30)
(d) NAC4 LW06-O.?V 4W5Z5 Ai&i!
F@w 6- Confi~ed&
![Page 45: NATIONALADVISORYCOMMITTEE FORAERONAUTICS · nationaladvisorycommittee foraeronautics technical note 3172 effectsofleading-edgeradiusandmaximumthickness-chordratioonthevariationwithmachnumber](https://reader035.fdocuments.in/reader035/viewer/2022081521/5bbf7d5f09d3f22e7d8c3c35/html5/thumbnails/45.jpg)
.
L? I I I 1 I I I I I I 1 1 I I I I I I I I I I I I I I
10 - . . —— .—
r r f I It I I l\f
-.4I I \
d I f.w– J
+5.30 .40 so .55 .60 &5 .65 .673 .~ .?25 25 .m .80 .m .65 &75 .90
Mad amber for u. =00 &-404812 w
Section *e of ottack, aO, &g (* IW=.30)
* *
[e) IU4G4 0226-0.27 40.45% AtrtivZ..
i
, .
F@R? 6.- GmWJed.
![Page 46: NATIONALADVISORYCOMMITTEE FORAERONAUTICS · nationaladvisorycommittee foraeronautics technical note 3172 effectsofleading-edgeradiusandmaximumthickness-chordratioonthevariationwithmachnumber](https://reader035.fdocuments.in/reader035/viewer/2022081521/5bbf7d5f09d3f22e7d8c3c35/html5/thumbnails/46.jpg)
-. I. . .
-4 0 4 8Section angle of attack,
Figure 6.- Continued.
ffacb munberfor ~ =0° axis/2
6
![Page 47: NATIONALADVISORYCOMMITTEE FORAERONAUTICS · nationaladvisorycommittee foraeronautics technical note 3172 effectsofleading-edgeradiusandmaximumthickness-chordratioonthevariationwithmachnumber](https://reader035.fdocuments.in/reader035/viewer/2022081521/5bbf7d5f09d3f22e7d8c3c35/html5/thumbnails/47.jpg)
@*.
.$
Mach number for ~ = OOaxls-4 0 4 8 12
Section angle of attack, ~, deg (for M 8.30)
(g)NACA 0010-IJO 40/1.575 airfoil section
F@n’e 6.- Conchded.
, . , .
Lu
ElN
![Page 48: NATIONALADVISORYCOMMITTEE FORAERONAUTICS · nationaladvisorycommittee foraeronautics technical note 3172 effectsofleading-edgeradiusandmaximumthickness-chordratioonthevariationwithmachnumber](https://reader035.fdocuments.in/reader035/viewer/2022081521/5bbf7d5f09d3f22e7d8c3c35/html5/thumbnails/48.jpg)
NACATN 33.72 47
/,2
(0
— NAGA0004-3.30 40/4575——— NAGA0004-1% 40/1575
/
\ ~ f\ * . ~ ./-
} .3 .4 .5 .6 .7 .8 .9Moth number,M
(a) Maximumfhidness- chordratio of 0.044
m’
.8 “~ ‘-— -’. .-/~ < --”.-
.6 -fVACA0006-1.10 40/L575NACA0006-0.70 4CVZ575—=G==’–
‘— NACA 0006-0.27 40/1575.42 ●3 I
.4 .5 .6 .7 .8 .9Much number, Al
(b) Moxlmumfhickness- chordratio of 0.06.
FigureZ- Effect of changeof leading-edgeradiuson the variationof maximum section hft coefficient with Mach number.
![Page 49: NATIONALADVISORYCOMMITTEE FORAERONAUTICS · nationaladvisorycommittee foraeronautics technical note 3172 effectsofleading-edgeradiusandmaximumthickness-chordratioonthevariationwithmachnumber](https://reader035.fdocuments.in/reader035/viewer/2022081521/5bbf7d5f09d3f22e7d8c3c35/html5/thumbnails/49.jpg)
4a NACATN 3172
.7-
— NACA0004-330 40/[5?5——— NACA0004-410 40/1575
.3 I
.2 “ tA/
,/
‘2 .3 .4 .5 .6 .7 .8 .9Moth num&er,M
(u) Moxlmumthkbess-dord fofioof 0.04.
.4’NACA0006-HO 40//375
.— NAGA00(26-Q7040//575
.—.. —NAGA0006-02740/L575.3
.2
,/
.4 .5 .6 .7 .8 .9Mach number, M
(b) Moximumf~kness- chordrotioof 0.06.
Fi&ure& Ef&cf of ckmgeof [eudng-edgerodusw th vur~ti ofsecfhn[ft-curve dopewfihMuchnwnkr.
![Page 50: NATIONALADVISORYCOMMITTEE FORAERONAUTICS · nationaladvisorycommittee foraeronautics technical note 3172 effectsofleading-edgeradiusandmaximumthickness-chordratioonthevariationwithmachnumber](https://reader035.fdocuments.in/reader035/viewer/2022081521/5bbf7d5f09d3f22e7d8c3c35/html5/thumbnails/50.jpg)
NACATN 3172 49.
.
.875
,85,
.
.
.
●
,/8
,/6
./4
,/2
./0
.08
,06
.04
.02
0
,
a
,
,
.80
.775*s ,75QII.725@
,70
,675
,65
4
.60
.55
.50
.40
.30
i
;
1
I A I/1 1 1 I I I I
:8 ;6 -# ;2 O .2 .4 .6 ●8 /’.042Sect/onlift coefficient,c1
(o) NACA 0004 -1.!0 40/L575 AMbil.Figure9.- Vuriotlonof sectiondrugcoefficientwifh secfion
coefficientd consfcmfMachnumbers.Rff
![Page 51: NATIONALADVISORYCOMMITTEE FORAERONAUTICS · nationaladvisorycommittee foraeronautics technical note 3172 effectsofleading-edgeradiusandmaximumthickness-chordratioonthevariationwithmachnumber](https://reader035.fdocuments.in/reader035/viewer/2022081521/5bbf7d5f09d3f22e7d8c3c35/html5/thumbnails/51.jpg)
.-. -. —.- --—.
.MWA TN
./8
./6
,/4
./2
./0
.08
.06
,04
.02
n
I ,-- - , I r 1 1 1 — v 81
/t
/ ~ 1/Ill I* I 11~1
.85 H+H+H+H[L__ I I I
.825 ~ \- I
.80 .80 I I\ f
.775
.75
.725
● 70
.675
.65
.625
1rt
//
I 1 I 1 1 I 1 1 ! -l I I I II
1 1AA I II
.60 .Ou ,f / Al)
!/1
RR > - - /.55 I I I.-Q I I 1
I II I 1 I I I 1/ If II I I
I I I1= .
.50 .50 / I I/ ‘ I I7.
.40 .40I TTwR+b4-+!?ii=’
I I I I I I
30{ I I.
‘“W-8 =6 74 :2 0 .2 $ .6 .8 LO k2Section/if/ coeff/c/ent,c,
(b) NACA 0004-3.30 40//.575 A/ifoiL
Figure 9.- Continued.
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NACATN 317P
.18
.!6
./4
./2
./0
.08
.06
.04
.02
0
.875
.85
.825
.80*a .775
T .75J
.725$& .70*~ .675cs .6582 .6S
.60
●55
.50
.40 I I I 1 I I 1/ AM=.30 1
% _ / -
●3%8 -96 + -.2 0I I I I I I
.2 4 .6 .8 !S USection lift coefficient,
(C) NACA 0006-/./0 40/M75
c,
AirfoiLFigure9.- Continued.
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52 NACATN 3
./8
./6
./4
./2
./0
.08
.06
.04
.02
0
c1
F/gwe 9.-
}mmlm
.80
.775
.75
.725
.70
.65 I t I I 1/
.625 t-1
I I v
.625 &J~ / - I I 1/ i
I1A /1H
-i. / -.60 I
66 I I
(d) NACA
Continued.
Section fif t
Ocw6-o.mcoefficient, c1
4W!575 Airf&L
.
.
.
*
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53
.
.
.20
./8
./6
,/4
./2
./0.08
.06
,04
S02
o
Ill
II II 1 I III I
I I
section/ift
(e) NACA 0006-0.27~!@tr9 9.- GOJ?finU8d.
coeffibkt, ct
40/L575 AirfolL
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‘yI NACATN 317’2
./8
./6
./4
./’
./0
.04
D2
0
Figure9.-
.
.
.
e
.[{ a=L.75-—1 I IA 1/1
.Z5 m=— I 1A I /1
●W
.625
.60
Sectim lift
{f) NACA 0008-/./0
Gontihued.
coefflcieflt*cIT40//.575 Airfo//.
.
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NACATN 3172
.
.
.f6
./4
./2
./0
.08
.06
.04
.02
0
,875
,85
.825
.80
.775
1 # 1 1, b 1 1 i
----
.75
,725
.70 1 1 1 n 1 1.675H --II I I
> -~.675 I I ,,
.65 \ },65
.625
.60
.55
.50
.40 I I I I IM=.30—11
t1
I I I I I I t I 1 I I I I I I I I I I I )“30Y8 ;6 -94 ;2 O .2 ,4 .6 .8 LO 12
Section
(g) A(ACA00/O-LIO
/ift coefficient,c1
40//.575 oirfoih~
Figure9.-
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9875
.85
.825
.80
,a-Y8 ;6 -.4 T2 O .2 d .6 .8 40 42
SectionIlft coefficient,c,v
(o) NACA 0004-1.10 40/15Z5 Airfoil.
Flgu~ 10.- Vurlationof sectionpliching-momtmtcoeffidd with$Wthnlift mefflclentot consfontMwh numbers.
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NACATN 3172 57
.
*
.
A?75
.85
.825
.80
.775
.75
‘~ .725
; ,70
t?:675
.65
.625
.60
,55
.50
,40
.30
-.8 -.6 -4 -.2 0 .2 .4 .6 .8 10 42Sectionlift coefficient, c1
=s=(b) NACA0004-3.30 4CW575 Airfoil,
Figure IO.- Gontinuetl
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58 NACATN 3172
,8Z5
.85
,825
.80
C775
.75
Jz!5
.70
.2
.1
0
-./
?2
.63tii’!!fi iiiiili P{ii iit4396
.55
.50
.40--030 r ‘--
I I I 1 I I I I I -h I
t ISection//ft coeffhhnt,c1
T(C) NACA 0006-L (O 40/L575 Airfoii,
.
—
●
✎FlgurwIO.- Conffnued
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NACATN 31-72 59
./
0
-./
-.2 ;8 76 -.4 :2 0 .2 .4 .6 .8 LO MSection Iifi coeffkient, c1~
(d) AiACA 0006-0.70 40/1.575 Airfoil.
FlpureIO.- Continued
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60 NACATN 3172
o-./
Sectiontiff coefflclen~c‘-W NACA 0006-0.27 40//.575 AirfdL
Figuta10.- Continued.
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~CA TN 3172 61
.
.
.
o
.
s Flgwe10.- Conthued
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62
Am
.&5
Jw5
,80
,775
75
.725
.m
675
.63
,63
.60
35
30
.40
30
:8 ;6 -.4 :2 0 .2 4 ,6 .8 10 &Section lift coeffkient,c,
.
.
‘i
(@] NACA 0010-LIO 401L575 airfoil.
F..gure10.- Concluded.
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h
Lo
.9
.8
.7
.6
.
.5-.6 -.4 + o .2 .4 .6
section #f) Coefficient, c1
Figure 11- Effect of change of moxlmum thickness - chord ratio on the voriotion ofMach number with section lift coefficient.
B m
Iiff-diw?rgence
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64 NACATN 3172
/.2
Lo ///k“*
s 1f~~ ‘ \. 1“~ Q .8 - /
—. .- -- /$*-
\. ..> - “s -u)~ ~ /
Q .6.g> NACA 00/0 -M7 40//.575~~ — — NACA0008-/.10 40/L 575
*————— NACA 0006-LW 40//.575 --—— NACA 0004-/./0 40/1575
.42 ●3,4 .5 .6 .7 .8 .9
Much number, MFigure/’2.- Effect of changeof maxhnumthickness-chordratio on
thevariationof muximumsectionlift coef?%i~twithMuchnumbe~
NACA0010-1.[0 40/L575NAGA0008+Y0 40//. 575
~–~— NACA0006-4/0 40/L575—.— /VACAUO04-UO 40//’.575 A
—. -— -
72 .3 .4 .5 .6 .7 .8 .9Mach number, M .
Figure/3.- Effect of changeof moxlmumthk%ess- chordrofio on the Nvariationof sectiontiff-curveslopewithMothnumber.
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$’
(,0
—,9 A~ ●
//“ ---
/ ‘ / “ ‘\ \/ /’ e~ ~. \
~/,/ /
.8 //,
\~ <\ \ \~ .7g \’ \\\
s\
b — NACA 0010- /./0 40/1.575
& ,6 . —— ffACA 0cW8-i.10 40/i.575– – – — NACA 0006-410 40/1.575_ -—NACA 0W4-LIO 40/L575
,~.6-.4 -.2 0 .2 .4 .6 .8 1’
,
Section lift coeffichwt, c1
Figure 14.- Effect of chongeof maximumthkkmss- chwd ratio on the vuriotionof dreg-divergenceMoth numbw with section iiff coefficient