1

Curiosity Number 21. Comparison of some key airfoil geometric characteristics W.H. Mason, August 8, 2017

This one came about due to some surprising results from a recent panel method code calculation. It led me to review some characteristics of airfoils. Specifically, I’ve collected typical values of the airfoil trailing edge thicknesses and included angles. For completeness I’ve included the leading edge radius values for some airfoils.

The root of this study arises because airfoils don’t have zero thickness at the trailing edge, a razor blade is not a practical geometry. For inviscid calculations this causes a problem. Jameson extended the classical conformal transformation methods to include the trailing edge thickness.1 Sometimes panel methods model thick trailing edge as a source. Drela wrote a paper describing an extension to the integral boundary layer method to handle thick trailing edges.2 I thought that for a low order panel method you could just leave a hole at the trailing edge and nothing terrible happened. In most bases this is true. However, studying flap deflections for Curiosity 7 I revised this opinion somewhat. Nevertheless, it is worth looking at typical real airfoils.

Trailing edge thickness. Figure 1 shows the trailing edge ordinate for several classes of airfoils as they change with the maximum thickness to chord ratio, t/c (the half thickness ay the trailing edge). I’ve included the NACA 4-digit airfoils, the NACA 6A-series airfoils, the NASA supercritical SC(2) airfoils from Harris, NASA TP 2969, the GAW(1) and GA(W)-2 airfoils that were also part of Whitcomb’s work.NotethattheoriginalNACA6-seriesairfoilsspecifiedacuspedzerothicknesstrailingedge,andtheairframerspointedoutthedifficulty!TheNACA4-digitairfoilsaretheonlyairfoilsshownherethathaveananalyticdefinitionforthetrailingedgethickness.Lookingatthefigure,weseethattheNACA6AseriesairfoiltrailingedgesareafractionofthethicknessoftheNACA4-digitseries.Incontrast,thesupercriticalandGA(W)airfoilsaremorethantwiceasthickatthetrailingedgeastheNACA4-digitseries.Aswe’llseeinFig.2,youcanhaveathickertrailingedgewithoutadragpenalty.Thetrickbeingtoreducetheincludedanglebetweenthetopupperandlowersurfaces.ThetrailingedgethicknessfortheNASASC(2)airfoilsgetsasectioninNASATP2969.Harrissaysthatinthetunneltheyfoundthata0.7-percent-thicktrailingedgecouldbeusedattransonicspeedswithoutasignificantsubcriticaldragpenalty.LateronusingCFDtheyfoundtheycoulduse“somewhatlessthan0.7percent”forthetrailingedgethickness.Healsostatesthatitappearedthatthisvaluewasconnectedtotheboundarylayerdisplacementthickness.Hedoesn’tcitetheworkofHoerner,3whoconnectedbasedragtothestateoftheboundarylayeratthetrailingedge,thatwouldofcoursedependontheReynoldsnumber.Hispapershouldbeaddedtoanycollectionofpapersonthicktrailingedges.1AntonyJameson,“TransonicFlowCalculations,”VKILectureSeries#87,1976,publishedin1978.SeeSection5.2.2MarkDrela,“IntegralBoundaryLayerFormulationforBluntTrailingEdges,”AIAAPaper1989-2166,1989.3SighardF.Hoerner,“BaseDragandThickTrailingEdges,”JournaloftheAeronauticalSciences,Oct.1950,pp.622-628.

2

Figure1.Airfoiltrailingedgethicknessesforavarietyofairfoils.

Includedangleatthetrailingedge.

Figure2showstheanglebetweentheupperandlowersurfacesforthesameairfoilsshowninFig.1.Inthiscasethestoryisreversed.ThesupercriticalairfoilshaveamuchsmallerincludedtrailingedgeanglethantheclassicalNACAairfoils.Themessageisclear:allowthetrailingedgethicknesstobelargerthattheNACA4-digitseries,butmaketheupperandlowersurfacesnearlyparallel.There’salittlemoretoitthanthis,butthisisastartingpointforputtinganairfoiltogether.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

5 10 15 20

Trailing edge ordinate (half thickness)

y/cTE

%

max t/c %

NACA 4-Digit Airfoils

NACA 6A-series Airfoils

GA(W) 1 and 213 and 17% thick

SC(2)-Series C

Ldesign = 0.4

Note: NACA 6-series airfoilshave zero TE thickness

3

Figure2.Trailingedgeincludedangleforavarietyofairfoils

Leadingedgeradius

TocompletethissurveyI’mincludingtheleadingedgeradiusvaluesofsomeairfoils.ThisshowsthatyoucanhavealeadingedgeradiusgreaterthentheoldNACAairfoils.Curiosity20presentedsomeresultsshowingthatincreasingtheleadingedgeradiusdidn’tresultinanincreaseinbasicparasitedrag.Thereareseveralbenefitsoftheincreasesradius.Theyincludeareducedsensitivitytoangleofattackandtheyalso“fillout”thepressuredistributionovertheforwardpartoftheairfoil.Figure3isachartIputtogethermanyyearsagoprovidingacomparisonofairfoilcharacteristicssimilartotheresultspresentedinFigures1and2.Thefigureconcentratesontypicalsupersonicfightervaluesofthicknesses.Figure4isfromtheHarrisreportandshowstheleadingedgeradiusvaluesfortheSC(2)seriesofsupercriticalairfoils.Inthiscuriositywe’vefocusedonsubsonicflow.It’sworthnotingthataroundleadingedgeisnormallyusedatsupersonicspeedstoo.Generallya6A-seriesairfoilisusedbecausetheleadingedgeradiusislow.Thisisespeciallytruewhentheleadingedgeissupersonic.Iftheleadingedgeissubsonictheuseofalargerleadingedgeradiusdoesnotleadtoasignificantdragpenalty.Ihavedonesometests(intheAEDC16Tnoless)andcomparedCFDwithDATCOM.IfIrunacrosstheresultsI’lladdanewcuriosity.

0.0

5.0

10.0

15.0

20.0

25.0

0 5 10 15 20

Trailing edge included angle

te anglete 6A anglete angle SC uncamte angle sc(2) cam)te angle GAW

trailing edgeincluded angle

- deg.

t/c max %

GA(W) 1 and 2

NACA 4-digit Airfoils

NACA 6A-series Airfoils

SC(2) Series CL des = 0.7

4

Figure3.Leadingedgeradiusvalues(assembledcircaearly1980s).

5

Figure4.LeadingedgeradiusvaluesofSC(2)airfoils(fromHarris,NASATP2969)

Takeaways:

Somebasicsubsonicairfoilguidelineshaveemergedfromthiscomparison.•Theairfoilcanhavesometrailingedgethickness(asitmust!)andtheincludedanglebetweentheupperandlowersurfaceshouldbesmall(fortransonicairfoilsGreggandHennefoundthedivergenttrailingedgeairfoilprovidedfurtherbenefits).•TheleadingedgeradiuscanbelargerthantheclassicNACA4-digitseriesairfoils.

Somethingfurtherthatcouldbestudied:

•Lookatthesurfacecurvatureoftheaftportionofairfoils.