naca tn 42 the determination of downwash

7/27/2019 NACA TN 42 the Determination of Downwash

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TECHNICALIOTE~0. 42.THEDETERMINATIONFDOWW!7ASH,

ByLt.WalterS.Diehl,2hmeauofConstructionRepair,U.S.N.

?ntoduc% ion.=Itis obviousthat2in accordanceiihl?etontssec-

tmdlaw,thelifton.m aerofoilustbe equalto thever-%icalmomentumcomrmnicatetiersecondtotheaixmassaffeoted,c~rlse~uenti~liftin~aerofoilin.flightis%railedby a washwhichasa definiteticiinator.corres-pondingto thefactorsproducinghelift. lt is thOUghtthat sufficientata,iheoretcalandexperimental,renowavailableora completedeterrzinatonoi tiiswashwith respectto t-heariation of itsangleof inciination


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terVIII,Br.A.C.A.R. & M. No.261),Munk(Teclinischeer-ichte111-1)seemsto havebeenthefirstto proposea quan-titativesolution,He asse-tisha.%c mustbe rejrssentedas thsproductof scnueonstantandtheangleofattackasexpressedy theformula(BeizjT.13.I-4),

where b isthespan,~c istheliftcoefficientndS is%heareaof theaerofoi.1.heformulafordownwWhthenbeccmffies

E 5?.3C=C , a= ~ . 2LC(:2)thevalueof theconstantc 3eingdeterminedy experi-ment. Theformulaas givenappliesto zonoplqnesutzay.be appliedto nultiplaneg,ccordingo Munk,by the introductionfanotherconstantk whichreducesthespan bto thespanof theequivalentonoplane. .

Thevaluesof c w.redeterminedarseveralmodels


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ally constantoverabouteigbz-tenthsf thespan,withsuddenchangesnearthetips.N, P. L. Formula.

Themostcomprehensiveeriesof testson downmsh,whichhavebeenpublished,rethoseby Sandison,lauertandJones(Br.A.C.A.R. & M. No.426).Ipthisinvestigationthevariationof downwashwasdeterminedn spaceforarnnzberfpointsbehind,above,andbelowthetrailingedge.of theaerofoil.It wasfoundthat,in accordanceithhydrodynamicheory,theangleof down~shdecreasesxponential.lyiththedistancefromtheaerofoil(ab.i-Flaneinthiscase,)ndmightbe expressedy theempiri-calformula

c = ccllo=-008cwhere.

is thedistancebehindthe wingin chordlengths,.c is thedistancebelowthe-chordf theupperwingintermsof thegap>


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- 4-empiricalormlae. It is kno?mefinitelyhatdownwashvariesexponentiallyithdistancefxornhetrailingedge,Theplotiedresultsof N,P.L. investigations,hichshowtilisariatiop.Figs.land 2,replotzedn aticaldistance

verti~ailyndhorizontally,regiveninrespectively.hedatainFig.1 havebeenloga ri ih rd .c sca le in Fig.3, %bh thever-fromthetrailingdgeexpressedn~i~~rd. .lengthsplusonechordlength*as abscis~aandanglesof

do~~~s~asordinates.It iSfoundthatfora given?-nglf2of attack,the anglesof do:m~shat variousverticaldis-tancesfromthetrailingedgelieon a straightine.Thelinescorrespondingo thevarims anglesof attackare a l l. parallelandhavea slopeof -i3* 0.50.Thisindi.cazeshatticaldistanceby anequation

thevariationf angleof downwzLshithver-fxomthetrailingedgecanbe representedoftheform:

C=c ~ (y .+1%wherec1 = a constant, .


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,,t.. -5-q of dovinwashithvariationofhorizontalistancefrom

thetrailingedgeisof theformE =C2 -..(x+ I)n

where~ = a constantx = theho~izontalistance,f thepointundercon-siderationnchordlengths,fromthetrailingedge,and

.n = tan (-210+ 0.5)= -0.38+ 0.01.Inorderto elii.ninatehecalculationsnvolvingrac-.tionalexponentshefunctions,

z = (y+ ~)-ozs. 7J = (x + JO3*

beenevaluatedndplottedinig.5.Datafromfiveseriesof downz=shdeterminationsaveplottedin Fig.6, withnglesof downwashas ordi-

andhave

beennatesandliftcoefficientss abscissae.Theslopeofi thestraightine,whichpassesthroughthepointsrepre-

L sentinga seriesoftests,determineshevalueofAC/ALc


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:. --6-. equation Indicateshatc variesinverselys theaspsct

ratio, II. Thereforehe angleof downwaskshouldbe givenby

whereK isa cGnStarit,umericallyqualto&/ALc atthe:railingedgeof a wingof aspectratiounit~y,

ThevalueofK isdeterminedoreachofthefiveser-iesof tegts.Xfiichreplottedin Fig.5>by substituting.thepropervaluesforthefunctionsf x and y andfor, theaspectratio n. Theprocedures indicatedy theheadingsof columnsinTableI.

It isfoundthatK is substantiallyonstant,aryingfrom164to 176;a singleexceptionf 158correspondsoa seriesof testsona biplanearrange~eni,hewingsofwhichwereequi~pedwithflapsandrepresentbnormalcon-ditions. It thereforeppearsthattheangleofdown-washcanbe represented-togoodapproximationy

t .~a


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Applicationf theDownwashFormla.

.,

Thechiefuseof a domiwashformulaisthecalculationof theaerodynamicngleof attackof thehorizontalailsurfaces.Forthispurposea referenceointis takenontheleadingedgeof thehorizontalailsurfaoesndtthevaluesof s obtainedromtheformula.Theaerodynamic ~angleofattackofthetailsurfaceswillthenbe

% =a- B-cwhereQ istheangleofattackofthe wingand~ istheacuteanglezontaltailifthetail

betweenthechordlinesof thewingsandhdri-surfaces,onsideredositive(intheequation)is setat a lessapparentanglethanthewings.

Thedatafromtestsseem to indicatehatin caseof a biplanethemximum angleof downwashoccursinthe\horizontallanemidwaybetmen thetwo wings.Theeffectis so slight,however,thattheabovemethodmaybe used,L referringhecoordinatesftherefe~enceointto thenear-


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DETERKINATIONF K INTHEEQUATION

Sourceof:Aspect: : : : : ~*cK~.G(+) .~(Fx.FY~.nData :Ratio:~~ :x: Y:Fx:Fy:ALcFx-Y-. :~~c::::: .., ,. n: . . . .. . . . . .NC-1 : : : : : : : .. Curtiss : 9.5 :11.20:2.5: :.625:1.00:17.9 ; 1 7 0Tests : : : : : : : ... R&M#196: 6 :15.2:2.3:0.55:64: .90: 26.4 : 158R&M#426: 6 :14.70:3,0:0.61:.595:89: 27.8 : 167R&X#426: 6 :16.00:3.0:0.43:.595:.915:9.3 : 176RN #515: 7.73:11.8:2.6:0.6:.62:.895: 21.3 : 164

NOTE: Therewillbe a slightdecreaseinthevalueofAC/ALcwithincreasenliftcoefficientfthereferencepointisnotfixedin space.Thisis causedby thechangein thecoordinatesfthepoint~th,cha~ein a~~leandtheeffectmayeasilybe aocountedor.LetD = distancefromtrailingxe, T,to~f-


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naca tn 42 the determination of downwash

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