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REPORT No. 537TESTS IN THE VARIABLE-DENSITY WIND TUNNEL OF RELATED AIRFOILS HAVING

THE MAXIMUM CAMBER UNUSUALLY FAR FORWARDBy EASTMAN N. JACOBS and ROBHRT M. PINKERTON

SUMMARYAfamiJ y of relatedairjoi.hhavingtheposition OJmaxi-mumcamber unusuallyfar forward w inve&g&ed inthevariabletiy tunnel as an aziension ~f the 8tUdyrecently completed of a largenumber of relded aiqbii%.Thenew airjoils gaveimproved characttiticc over thoseprmou.slyinvedigated,especiallyin regardtothepitchingmoment. Someoj thenew sectionsaremarkedlympmorto well-known and commonly used sectw~ and shouldreptuce them in appli .cbons requiring a 81i.ght@cam-

bered 8ection oj moderate thickm?w, having a dptching-moment coe&enLINTRODUCTION

The investigation of n largefamily of related airfoils,reported in mferonce 1, indicated that the effects ofcamber in relation to maximum lift coefficients weremore pronounced with airfoils having the maximumcamber forward or aft of the usual positions (0.3c to0.5c). The scopeof theinvestigation, however, wasnotextended to include airfoils having extreme camberpositions because the mean-line shapes originally em-ployed could not be sntisfrmtorilyextended. A con-sideration of a program to include theseextremeposi-tions led to the elimination of the after yositionsbecauseof the rtdvemepitchingmomentatobeexpected-The investigation reportedherein dealswith a familyof related airfoils having mean-line forms derived toextend the camber position from normal to extremeforward positions. These airfoils are divided into twogroups, each group containing five airfoils of the samethickness (0.12c) and covering a range of maximumcamber positions from 0.05c to 0.25c. One group isbased on a simple mean line (mean line withoutrevenml of curwzture) and theother on a reflexedmeanline. Instmd of investigding each mean-line shapethrough a rrmge of camber ratios as in the previousinvestigation of related airfoils, only one camber ratiois used for each type, the value of each be~m selectedto give an optimum lift coefficient of 0.3.

DESCRIPTIONOF AIRFOILSThe airfoils described herein are designated by thefollowing numbers preceding the number 12, whi chdesignates the thiclmeas:

Z1O,220, 230, 24I3,25o,211, 221, 231, 241, 251

Following thedesignation systempreviously employedfor the N. A. C. A. family airfoils, the fl.rstdigit of theairfoil number is used to designate thereIativemagni-tude of the camber. The various mean-line shapesaredesignated by theremaining two diggtsas follows:I~\ \ RWonof~. I ,.w I ,*& I ,,& I ,a I ,= I

IShpb---.-..- . - ..-. ;! 20 I I 40RdklL____.-...- I K121 f a 61 IThe ordinates of the airfoils were obtained by themethod described in reference 1, which consistsbrieflyin disposing the desired thickness fom about a givenmean line. The thiclmess form used is the same asthat used for the U-percent thick airfoilsof the earlierinvestigation. The airfoil profilesareshownin figure1.Each mean line is defined by two equations derivedsoastoproduce ashapehavingaprogressively decreas-ing curvature from the lead@ edge aft. The curva-ture decreases to zero at a point slightly behind themaximum camber position and, for the simple meanlines, remains zero from this point to the trailing edge.The following expressionstaken to represent thesimple

mean lines arechosen to satisfy theseconditions:~=kl (zm)ose: (3=0 to z=m)tail: (z=m to z=) g=o

The mean-line equations arederived from them expres-sions. The constants of integration areby the following conditions:x=() y=l)X=m YN=l/T

determined

x=1 y=owhere the subscripts~and T refer to the fore and aftequations, respectively. The solutions of the equa-tions then become:nose: y=~kJ &-3m&+m2 (3m)z]tail: y= ~k1m3(1z)

The values of mwere determined to give five positionsof maximum camber, namely, 0.05c, O.1OC,0.15c, 0.20c,and 0.25c. Finally, values of k, were cahmlated to521

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-._ .. .

522 RDPORT NATIONAL ADVISORY COMMZFIE E FOR AERONAUTICSgive a theoretical lift coefficient of 0.3 (cLr =0.3) atthe ideal angle of attack (reference 1). Table Ipresentsthevaluesof mandkl for convenient reference.

N..CA.2!0?2. . . .

lvAcA 22012

. . . ..NJ .CA.230J 2

.. .-. NACA.24012

.. . --/?&f.GA25012

- -- . ~NALM 22112

.. -N/1.CA.23112

.. -. NA.CA24112

. ---h!ACA 25112HQUEEAIrfeilPIoflk&

TABLE IyiiMean-linedesfgnntlon m t, k~k,kg .210-------------------------- :: amm....-..------------------- 33L4 ----------.rmm-------------------------- 5L64 ----------.15 .202s 1s.9.57 --.---m-------------------------- .mm.-_ . ..._. _--. . ... .. a.on -- . . . . . .:3 .amo211---------- ------------- .0sEl-------------------------- .10ml-------------------------- .15241--------------------------BE ------------------------- % .4410,

Iedatafor tbh afrfoflarenot Includedbwansetheafrfofltakil wassak-1 fenndtodifferfromtb lntend6drdrfeflthroughen errorin derivingthela.

The equationsfor thereflmedmeanlinesarederivedfrom the following expressions again taken to giveprogressively decreasing cnrmture and to give zerocurvature where the two parts join. The tail part,however, is represented by an expression giving acurved mean linepermitting of adjustment togive zeropitching moment. d%nose: (z=O to z=m) ~=kl (zm)

titaih (z=m to Z=) ~=kz (Zm)Determining the constants of integration by the sameconditions as for the simple mean lines, the solutionsof theseequation9 are:

[k, 1ose:=+l (Zm)srl (Im)s ZmaZ+ma

[ail: v=+ k, ~ (zm)a$ (lm)aznzs1The ratio & is expressed in terms of the position ofmaximum camber p and the juncture point m.

k,_3 (m )maK+For each of five values of p (0.05c, O.1OC,0.15c, 0.20c,and 0.25c), m was determined to give G&J =O and,holly, kl wascalculated to give CLI=0. 3. Vrdues ofk,~1,m, and kl, aregiven in tnbloI .

The models, which aremade of duralumin, are rec-tangular and have a chord of 5 inches and a span of 30inches. They are constructed from the computodordinates by themethod described in reference 2.TESTSANDRESULTS

-Routine measurementsof thelift, drag, andpitchingmoment about thequarter-chord point woremadent nReynolds Number of approximately 3,000,000 (tankpressure, approximately 20 atrnosphercs). A descrip-tion of the varitibledensity tunnel; in which the testswere made, and of the method of testing is given inreference2.The discussion of precision in reference 1points outan error in thevelocity measurementsdue to a changein the apparent density of the mrmometer fluid witha change in tank pressure from atmospheric. Thissource of error has sincebeen eliminated by correctingthe manometer settings used in iking the tunnel airspeed.The data axe presented in standard graphic form(figs.2 to 10) as coefficientscorrected after themethodof reference 2 to give airfoil characteristics for infiniteaspect ratio rind aspect ratio 6. Included in thosetigures are tables of airfoil ordinatas ot standard sta-tions and n plot of the profile.

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AIRFOILSHAVING TRE M44mMuM CAMBER UNUSUALLYARFORWARD 523

2.0 .40

I I I I I I I I I I 1 I I.11 I !I l 1111 !

iii

484440

L&l)4 I I I I I ll .+WW+WWHOW 60100-ItOfcbord .10

11 II 11 I 1/( .44 .09 m& ,*.. O3 II I I I I I I I I I I I.07

.05.= &.04=141!2:.24* ~ , , , , I ,l.o~ .20$ .:.03

oI1-.12 .04 j

w I I I I I ii~~il o 0 $-.2 I I I I I I. ----- ----- . . ----- --- I I I I I I I I I I Ii iii -8 ~! I I I -K-.3 Aidoil: N.4CA. 21W2 R./i320QOO0OO -12-.4 ..Dofe: 4-24-34 Tesf: k D.Z 1126 .-/6Correcfed io in fhiie osp+f raiio74 .2 0 .2 .4 .6 .8 LO 12 L4 L6 M

1 t 1 n I L

Angl. of offack, a (degrees] L H we f7icied, C.Fmum 2.N.A. O.A. !MO12frfoil.

.44

.40

.36

.08

.040

> -.3 I I I I I I I. . . ..ii AlrJOll:A.C~. 220/2 /7;).!: 3; 1 70,bO0 cI IE -.J Dofe: 4-23-34 Test: KD.Z 1125. -,6$ Co~cf~d #q in fip!fe pspqc/ rqfrn ,-.4 .2 0 .2 .4 .6 .8 1.0 1.2 1.4 f.6 1.8Liff coeft7cient, CLngle of offack, ff (degrees)

Fmum 8.N.A. O.A. ZOll tiU.

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524. REPORT NATIONAL ADVTSORY COMMITTEE FOR &ORONATKIZCS

. f2 4844Jmll I I I I

u I , , , I , , 8 I I 1 , r k 1 1 1?-+-1>in

.02 I I I I I I I I I

. 01 I I /1 ! ! I I-hitQ.60.12q

.44.08.2 .04

O? 00.-.2

I I I I I I I I I 1++- 1 I I-8 ~I I I I I I I I I I I I I I I I I I

I , , I

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AIRFOmtsHAVING THE l MAxumJM CAMIIDR UNUSUAILY FAR FORWARD 525

Angk of offack, e (degrees)

,, I

I I I I I I I I Ii! , , 1 I.010J-.1 4

%-.2: -~0,

Liff coefi7cien~ C=Fmms &-N. A. O.A. W12 afrfdl.

Angle of affack Q (degrees) L iff coefficient. CLFmmm 7.N. A. C. A. Z212irfoil.

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.. ..-. -- -----

526 REPORT NATIONAL ADVISO13Y COMMITKEE FOR AERONAUTICS

~-zirfoil: ~A.I+A. 23112 R.h! :3, 110,000Where fesied:L.MA.L- 7ZSf: ED.Z 1129 _-4.404- 8121620242832

.44

.40

.36

./2

.08

.040

Angle of atfack w (degrees)

20

02040 ~80100

Lift coefficient C.

.44

.40

.36

.32u. 28%-5>.24 ~

.20 ~

./6 ~Q-12

.08

.040

!< I ~ , , , 1 , , , I , , , , I , ,

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AIRFOIIS HAVING TECElMAXIMUM CAMBER UNUSUALLY FAR FORWARD 527In addition to the standtird plots the importantchrmcteristica of these airfoils are presented in tableI I , including also the N. A. C. A. 0012 and the N. A.C. A. 2212 airfoils for comparison. These tabulatedcharacteristics me corrected for turbulence and tipeffects as discussed briefly in the succeeding para-

graphs. The more accurrh section chamctaristimthus obtained are designated by lower-case instead ofcnpitfd letters, e. g., c~O~~nstead of CDO~m,etc.Section clmracteristimderived from wts of airfoilshavingsquaretipsaresubject tosmall correctionsmadenecessary by tip 10SSW. hfaking the reasonableassumption that more acccrate section characteristicscan be obtained from tests on rounded-tip airfoils,corrections have been determined from comparative

.44

.40

.36

.12

.08

.040

Angle of ottack, a! (degrees)

an effective value. The data given in table H aretherefore directly applicable at the effective ReynoldsNumber and, when supplemented by additional infor-mation to be published about the character of thescale effect as indicated by the scale-effect cla&iica-tion, will enable improved predictions of maximum liftcoefficients at other values of the Reynolds Number.DISCUSSIONThe important independerit variable, asmentioned inthe introduction, is the camber -position. The varia-tion of the aerodynamic characteristics with camberposition, discussed in the following paragraphs, isshown by cross plots (iigs. 11 to 16) of the character-istics taken horn thestandard plots (figs. 2 to 10)..12 48.11 44.10 40.09 23,5:&

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... ----- .

528 RDPO13P NATIONAL ADVISORY COMMPITOB FOR AERONAUTICSsimple mean-line airfoils. This conclusion is furtherconfirmed by &u.re 13, which rdso shows a slightincrease in drng as the camber position changas from

.16

$ .12~ ---- --4: ::% FL-.fw! ?--- ----- ----- ----- ---- 1%G .08 Io bimple meon lineg x Reflexed = -Iu bum048

0 .05 .10 ./5 .20 25Comber position in fracfion of chordFmwm 11.-Var iat f0n of MftmnmSlowWfth mmber pc-sith.

0. 15ct o 0. 25c. The optimum lift (&. 14) for bothtypes is about the same but increases as the positionof the camber moves aft in the range tested. Them

i ~ $~ ; ~