CHARACTERISTICS OF THE N. A. C. A. 23012 AIRFOIL FROM ...

●

REPORT No. 530

CHARACTERISTICS OF THE N. A. C. A. 23012 AIRFOIL FROM TESTSFULL-SCALE AND VAEL4BLEDENSITY TUNNELS

. By EASTMAIJN. JACOBSand WILLIAM C. CLAY

SUMMARY

This report giaes the results of tests in the N. A. C. A.f+scale and variable-dendy tunnei% of a new wingsection, the N. A. 0. A. %9019,which is m of the morepromising of an em%nded8erk8 of rel&d airj%ik re-cently developed. Th4 hwts were mude ai wveral vakes

of theReyn.o?.dxNumber between1,000,000 and 8,000,000.2!h.enew a?kfoit?deve-hp8a remmndy high maximum

lift and a low prom drag, which reswilsin an unueuallyhigh value of the speed-range index. In ad.dii?ion,tlwpitching-momeni coejickni h vw small. The supe+O&y Of the W 88Cti07t0V8r &k710wTL a7Ut CO?M’10?@

used sectitma of & camber and moderaie thickm?ssisindiazted by making a direct annparison with wmiaMe-dendy tests of the N. A. 0. A. %??19,tlw well-knownN. A. (7. A. family airfoil thd nw8tnearly rewnbles it.Th4.superiority 1%further indixzted by comparing thecharacteriatimwith those obtainedfrom f&caLe-tunnelteds of the Clark Y airfoiL.

A compation h made betweenthe resu.1.%forilu newlyo%vel~ed airfoil from tests in the N. A. C. A. UZriuble-d-eneityand fuLL8caLewind Wm.eL3. When the T88ui%efrom the two te8t8 are inierprded on the hawk of an“e$ective Rwlds Number” “to allawfor th e$ect8 ofturbulence,reamnu.bly8ati8fac40ryagreem.eniis obtaiwd.

INTRODUCTION

As a continuation of the invediigation recently com-pleted of a large family of related airfoils (reference 1),two new series of related airfoils have been built andtested in the vmiabldmsity tunnel. The originalinvestigation indioated that the effects of camber inrelation to maximum lift coeilicients are more pro-nounced when the maximum camber of the mean lineof an airfoil section ooours either forward or aft of theusual positions. The after positions, however, are

IN THE

of lesser interest, owing to adverse effeck on thepitching-moment coeficienti, and the forward positionscould not be satisfactory investigated with the meanlines avsilabIe in the original family.

One series of the new airfoils hav@ the forwardcamber position appears to be of particuk interest.The mean-Iine shapes for this series are designated bynumbers thus: 10, 20, 30, 40, and 50, where the seconddigit (0) represents the numerioal designation for theentire series and the first refers to the position of themaximum camber. These positions behind the lead-ing edge are 0.05c, O.1OC,0.15c, 0.20c, and 0.25c,respectively.

The mean line having the shape designation 30 anda camber of approximately 0.02c (designated 230)when combined with the usual family thiclmess dis-tribution of 0.12c maximum thickness produoes theN. A. C. A. 23012 section. This airfoil seotion ap-peared h be one of the most promising invcdigated inthe variabh+density tunnel. A preliminary announcement of this section, then referred to as the ‘(N. A;C. A. A–312”, was made at the Ninth Annual AircraftEngineering Research Conference in M~y 1934.

At the subsequent request of the Bureau of Aero-nautic, Navy Department, a 6- by 36-foot model ofthe N. A. C. A. 23012 airfoil was tested in the N. A.C. A. full-scale tunnel to verify the aerodynamicoharaotaristics found’ for this airfoil in the variable-demitg tunnel. This test was made possible throughthe cooperation of the Chance Vought Corporation,who constructed the wing and supplied it to the Com-mittee for the purpose. The present report has beenprepared to present and compare the results of thetm”tsof the N. A. C. A. 23012 motion made in theN. A. C. A. variable-density and fulkcale tunnels andto compare the results with those for well-knownsections.

435

cohmmrrm FoR tiONATJTTCS436 REPORT NATIONAL ADVISORY.

.CbOrct

.44

2.0 .40

18 .36

1.6 .32Q

L4 28;2 I I i I I I Ic.pl I 1/IIlfkt I I I I .? -5 , , , l\l 1 I

-..-- I I I I I I I I I I I I I i I { wn

I I 1. I 1, I I I ! II I I I I I I I I I r O?

,.2 04

ti-

00

-.2

-.4

t~! &dO1/:/i!A.C.,i23012 I ,.--3 —m.‘$ I I t?.IM?3J090,CX?0(Eff R.IVV8,160O(M) “c5-.4 -1 .Dafe: 9-7-34 Tes+: 1}67-8 --,64 I Correcfed io in finlfe aspect roiio

76 74 72 0 .2 .4 .6 .8 LO 12 44 L6Lift coefficie~ C=

d-8 Y/l W&e fesfed-LJL.U. Test: KD.ZIA57-8

Correc+ed fir +unnekwalJ effecf. -

-404 8 /2 16 20 2.4 28 32Angle of offuck, a (degrees)

FMumL–TIMN.A. O.A. !Z?412s&IML Vaiabkiemitywindhnmd:standardt.A

Q 2C ‘ % n7 I I ! I I I I I I I I i I I I I 1

20

40

.60

80

100 i

.2

0

72

-.4

.04

0

.-

.:.- I

o-45

G-.2o

-8 %4

i-.3-/2

$-.4 -16

Y6Y4:Z 0.24 .6 .8 LO [2 L4 M

c) “’ Ml I I I I II I 1“-1qL: ‘1 I I

1‘$’’”-404 8121620242832

Angle of attack, U (degrees) Liff coefficim~CL - - ‘“ . “’-

FI13URE2—TheN. A. O.L !Z3MZ8h’fOil. VsriabkimsltyWndhnnel: mimed EeYMIdsNumtw.

CHARA~RISTICS OF THJ3N. A. C. A. 23012 AIRFOIL 437

DESCRIPTION OF THE AIRFOIL SECTION

The mean-line shape for the series to which theN. A. G. A. 23012 belongs was derived empirically tohave a progressively decreasing curvature from theleading edge aft. Somewhat behind the mm”mum-camber position, the curvature of the mean line de-creases to zero and remains zero from this point aft;thrttis, the mean line is stiaight from this point to thetrailing edge. The 230 mean line has its maximumcamber at a position 0.15c behind the leading edge.The camber is not exactly 2 percent but was deter-mined by the condition that the ideal angle of attackfor the mean line shouId correspond to a lift coefficientof 0.3, a value corresponding approximately to theusual conditions of high-speed or cruising flight. TheN. A. C. A. 23012 airfoil results born the combinationof the 230 mean line with the usual N. A. C. A. thick-ness distribution of 0.12c maximum thickness by themethod described in reference 1. The airfoil profile anda table of ordinates at standard stations are presentedin figure 1. In order to give a basis for the develop-ment of related airfoilE of diflerent thiclmwsw, theordirmtesy of the N. A. C. A. 230 mean line we givenas follows:

Nose, from z=O to x=m

!/=; W-3mo?+m2(3–m)3]

Tail, from x=m to x=1

where, for the 230 mean line, m= O.2025and k= 16.957.

VARL4ELE-DENSITY-TUNNEL TESTS AND RESULTS

Routine measurements of lift, drag, and pitchingmoment were originally made at n Reynolds Numberof approximately 3,000,000 to compare the vtiousairfoils of the forward-camber series under the con-ditions of a standard 20-atmosphere test in thevmiabledensi~ tunnel. Later the N. A. C. A. 23012airfoil was reheatedm a pfut of a general invcdigationof scale effect. The data presented in this report weretaken from the latter twts which were made at severalvalues of the Reynolds Number between 42,400 and3,090,000.

The test results obtained in connection with theforward-camber airfoil investigation, as well as thecomplete remits of the scale-effect investigation, areomitted from this report but both sets of results willappear subsequently in reports on the respective sub-jects. Complete results are given, however, &m testsat two values of the Reynolds Number (figs. 1 and 2).

Some additional data taken from the available tests at

other values of the Reynolds Number are also pre-sented with the discussionto indicate the scale effect forsome of the important characteristics.

Descriptions of the variabl~density tunnel, methodsof testing, standard airfoil models, and the accuracy ofthe tests are given in references 1 and 2. The sys-tematic errorsmentioned in reference 1 have since beenlargely eliminated by allowing for the deflection of themodel supports and correcting for the errora involvedin the measurement of the air velocity. As an aid inevaluating differences between results from the twotunnels, the estimated errors from reference 1 axereproduced as follows:

Quantitymwsard Acdderdal

G.-. --.....-—----------------- #. 16”CL-“--------------------- { _;g

c.a ~----------------------------CDO(CL=O)------------------.... { :g

C%(CL-l)-------------- . ----- { _:~

hors dnc)Zup IiIntern%.

mm

+aCtJ

maL m

.Mma

.m+. 0310

FIJLIACALE-TUNNEL TESTS AND RESULTS

A description of the full-scale m“ndtunnel and equip-ment is given in reference 3. The N. A. C. A. 23012airfoil was mounted in the tunnel on two supports

FIGURE3.-The N. L O. A. !a312a.!rfoilmountedin the fnIlaale wind tunnel.

that attached to the one-quarter-chord point (fig. 3).

The genemil arrangement was similar to that used in

testing a seriw of Clark Y airfoils (reference 4).The airfoil had a chord of 6 feet and a span of 36

feet. The frame was constructed of wood and cov-ered with sheet aluminum. The surface was smoothand the section throughout was not in error by morethsn +0.06 of an inch from the speciiied ordinates.

The lift, drag, and pitching moments were measuredthroughout a range of augles of attack from – 8°

438 REPORT NATIONAL ADVISORY COMMI!IWDE FOR AERONAUTICS

to 25°. These tests were made at 5 d.itlerent airspeeds between 30 and 75 miles per hour correspondingto values of the Reynolds Number between 1,600,000and 4,500,000. The maximum lift was not measuredat speeds above 75 miles per hour as the wing was notdesigned for the loads under these conditions. Addi-tional tests to determine the scale effect on minimumdrag were made at several speeds up to 120 miksper hour corresponding to a Reynolds Number of6,600,000.

The interference of the airfoil supports upon the air-foil was determined by adding a duplicate supporting

are given for the airfoil of infinite aspect ratio. Values

of the pitching-moment coefficient about the aero-

dynamic center, C.=.O.,are considered independent ofaspect ratio and are tabulatwd against 0.. The loca-tion of the aerodynamic center (z, y) is given as afraction of the chord ahead and above the quarter-chord point. A typical plot of the dnta from table VIis given in figure 4.

Curves summarizing variations of these principalcharacteristics that change with Reynolds Number aregiven in figures 5 I%9. Curves obtainod from similarfull-scale-tunnel tests on the Clark Y airfoil are

ord .13 52

.12 48

.// 44

48 .10 40

44 .09T.%?Q

y& !!

40 ~.oo F

-i? c ~

oQ

. .36 :5.07 L?

Om

.60

80

109

40

.4d.08

.2 .04

‘:{=-’-R-es. (s findofm+ I Oofe:/O-24-34

Correcfed >or fun;ebwall ef;ect. ‘.4

o

-8-404 8 12 16 20 24 28 32

I , , I t , , , I I 1 , N IRiiili (

~j-.2 -o~o 4

:-.3 -12

E-.4$

-16

:6+:20 .2 .4 .6 .8 LO L2 14 16Angle of offock, ct [degrees) Lift coefficient CL

~QTJIIE 4.—TheN. A. 0. A. T301!2ahtoil. Rdl+walewindtunnel.

strut at the center of the wing. This “dummy” sup-port was not connected to the airfoil or to the balanceand all change-sin the measured forces with the strutin place could be attributed to its interference. Dou-bling the effect of this single dummy support wasconsidered to account for the total interference of thetwo airfoil supports. All the data are corrected forwind-tunnel eflects and tares. The corrections arethe same as those used for the corresponding Clark Yairfoil (reference 4).

The results of the full-tale-tunnel tesb of theN. A. C. A. 23012 airfoil are given in tables IV to VIII.The values of C., a, C!=,LID, and c. p. me tabulated

for the airfoil of aspect ratio 6 and values of ~ and Cw

presented in these figures for purposes of comparison.These curves are presented in semilogaritlugic form toassistin extrapolation to higher valuea of the ReynoldsNumber. Figure 5 shows the variation of the maxi-mum lift coefficient for the two airfoils; the scale effecton the angle of attack at zero lift for the airfoil sectionis show in figure 6; figure 7 gives the effect of Rey-

- nolds Numb: on he ‘slo~e of the profile-lift curve;rmd figures 8 and 9 show, &pectivel~, the scale-effec~variation of the drag cceflicient at zero lift and theminimum-profile-drag coefficient.

A detailed discussion of the prtilon of airfoil testsin the full-scale tunnel is given in reference 4. Inbrief, it may be mentioned that a consideration of cdJ

CHAE4~RISTICS OF THE N. A. C. A. 23012 AIRFOIL 439

the contributing errors ihvolved in these tests givesthe following es-tinted precision:

a= +O.1°

c.mG=&o.03

dC.~= +0.0015 per degree

o

C.. (c.= o)=+0.0004

CL).(C.=1.o)= +0.0015

c~a.c.=&o.oo3

x= +0.005 chord

y= &o.03 chord

t7eynoJcfs Number

FumrmS,–hfaxfmnrnIIftax.llldents. VarfafIonwltb ReynoldsNmnkr fromtestsfnthefulkxde wfndtunneL

DISCUSSION

Comparison with the Clark Y.—The comparison be-tween the new section and the Clark Y section is en-tirely based on the test results from the full-scaletunnel, The curves in figure 5 show that the maximumlift coefficients for the two airfoils difler by little morethan the e.sperimentalerror. The scale effect on themaximum lift coefficient for the new airfoil is, however,slightly greater than that for the Clark Y within therrmgoof Reynolds Numbers tested. The results indi-cate that the coefficient for the N. A. C. A. 23012 issomewhat greater than that for the Clark Y at Rey-nolds Numbers above 3,000,000. A compmison 01the shape of the lift curve of the 23012 (@. 4) with

bhat of the Clark Y (reference 4) shows that the new&oil has a sharper break at maximum lift than doesthe Clark Y.

The curves of the angle of attack of zero lift for thehvo airfoils are shown in figure 6. The Clark Y has a

G -----~-6 I 11111111 -- _

.

h

aL

:-

$-

t

8 /0 20 xIOSReynolds Number

Fmums O.-Angle of atWk far z.ero-lfftvmfatlon. Variationwith Rnynold6Numberfmmtqts fn theftdkale windtunnel.

considerable scale effect; whereas the N. A. C. A. 23012isunaffected by cha~~es in Reynolds Number. At zerolift a huge adverse gradient of pressure exists at theforward portion of the lower surface of the Clark Ythat probably results in an early disturbance of the

I 1 I I I 1 I 1 I 1 1 1 I I 1 I I I 1 I I

oI 2 4 6 8 10 20 xI06

Reynolds Number

FIGVES7.-uftQmv0 .dofk3.vdn~ titbmOm ~UMknomkm fUmfulkalo wfndtemd.

flow at the leading edge (reference 4). This conditionof flow has a critical effect on the angle of zero lift andvaries considerably with Reynolds Number. TheN. A. C. A. 23012 airfoil has much less oamber thanthe Clark Y and the general profile, which is morenearly symmetrical, sets up a flow about the leading

—... .._ _

440 REPOILT NATIONAL ADVISORY COMMIT13EE FOR AJ?IRONAUTK!$3

edge that is not critical; hence, the effects of male 01

the angle of zero lift should be small. This view %

supported by the tests in the full-scale and variabledenti~ tunneIs.

Figure 7 shows that the slope of the lift curve for thfN. A. C. A. 23012 airfoil is slightly higher than thalfor the Clark Y. Both sets of results indicate thalthe lift-curve slope increases slightly with ReynokbNumber.

The curves of drag coefficient at zero lift (fig. 8)and minimum profihdrag coefficient (fig. 9) show thatthe drag of the N. A. C. A. 23012 airfoil is deii.niklylower than that of the Clark Y. These @ures &cindicate that the drag decreasesmore rapidly with aDincrease of Reynolds Number for the new airfoil thanfor the Clark Y. It should be mentioned that theminimum-proille-drag re9uhk are relatively inaccurateas compared with the drag at zero lift so that cautionwill be used in extrapolating them to higher vahsof the Reynolds Number.

The remaining important characteristics for onewdue of the Reynolds Number are presented for com-

h I f I I f I f f; .012

N

“1 2 46 8 10 20 XIOSRe yriolds Number

FIGmE &—Dragemtlldmt at zeroUft. Vmiationwith ReynoldsNnmkmrfromtam fntheftdfsmlewfndtnnnal.

pa&on in the following table. The method of obtain-

ing the ratios of CzJC~Omfm~ he ~ble & somewhat

fallacious as both the lift and drag dues were takenat the same Reynolds Number; wherea!sin fLight thetwo conditions occur at different air speeds. Thecomparative ratios indicate, however, that the speedrange of the new airfoil is much better than that ofthe Clark Y. As the result of the smaller mmber ofthe N. A. C. A. 23012 as compared with the Clark Y,C.On,,the lift coefficient cmm.spendingto the minimum-proiih+d.rag coefficient, might be expected to be con-

siderably less. Airfoils such as the N. A. C. A. 23012having the camber well forward tend, however, to havehigher optimum lift coefficients than airfoils with usualmean-line shapes. Actually, table I indicates that theoptimum lift coefficiemk for the two sections are nearlyequal.

TABLE IFULL-SCALE WIND-TUNNEL TESTS COMPARING

N. A. C. A. 23012AND CLARK Y AIRFOILS

At R. N. = 4,6W@YJ

cbamet81i9uo N. #.~ A

cL-”--------------------------------aJ+(d )------------------------- –::

dy, @mrdegea)_... . . . . . . . . . . . .a- .101

.%.{.-.. ...-. ..-- ..—.-...- .. -. ..-. ~ .MmCLWe-------------------------------- 1.19cq*,.--i...-i ----------------------- -1. m

I-....................-.1.016Aerdynmrf ;center ----------------------n.@J

c

OlerkY

1.47-5. b

.Q33

.Wa1.20

-1.0761.0-26

cf..~ IA, .1----------------------------‘m” 161Cn.b --------------------- .. . . . . . . . . . .W9tiDmu -----------------------------!250CL at(~~.u_---__--..--..--..--

:g:~:doP&e)E::?::::::;~: ;;:

1No m&$tant verfetion with cbangm in Regnolda Number.

Following a recently adopbd standard procedure,

pitching-moment coefficients are referred to the aero-

$G’.~?

g

“!’1.9J<.9&w.4 t~~~ 0/ 2 4 6 8 10 20 XIO0?“ Reynolds Number

FIGURE 9.—Mlnhmm profde-drag mftkient. VerMkm with ReynoldsNumberfrom@s@InthefuH@e windttmnol.

dynamic center rather than to the quarter-chord

point. This procedure is considered preferable be-

cause, by definition, a constant pitching-moment co-

efficient is obtained throughout the flight range. Theaverage values of the pitching-moment coefficients

thus found for the two airfoils together with the merm

location of the aerodpamic center are given in the

table. The coefficient for the N. A. C. A. 23012 airfoilis very small and is only about 9 percent of the valuefound for the Clark Y.

In brief, it may be concluded from the results thatthe N. A. C. A. 23012 airfoil with the exception of oAmper break in the lift curve is superior in all respectsto the Clark Y airfoil.

Comparison with the N. A, C,A. 2212,—&other com-mrison betwean the new section and a well-known sec-~on is atlorded by table H, in which are compared themportant charactetitics of the N. A. C. A. 23012 and

CHARACTERISTICS OF THEJ N. A. C. A. 23012 AIRFOIL 441

the N. A.C. A ‘2212sections. For this pyrpose ordystandard 20-atmosphere test results from the variable-

density tunnel corresponding tom “effective Reynokk

Number” (discussed lm%) of approximately 8,000,000

are employed. These are the usual test results from

the standard plot in iigure 2 except that the drag co-

efficients have been reduced, as indicated in this figure

and discussed later, to allow for the reduction in the

skin-friction drag to be expected in passing horn the

test Reynolds Number to the higher effective Reynolds

Number. The Reynolds Number of 8,000,000 atwhich the comparison is made, corresponds approxi-

mdely to that for a modern two-engine transport air-

plane flying near its minimum speed. ,

TABLE IICOMPARISON OF N. A. C. A. 23012 AND 2212 AIRFOIL8

Cbaracierwo N.A. C.A. N. &l~ A,mu

—. ——Efl@lve ILN--------------------- $$la, mTest R. N-------------------------- &craQm

S,mxl,m

CLamwo

. ...............................U%(d_)---. ................... -LL? -LL?

ao=~~d~).--.........----. . KM .103

u~hi.-. -.--- . . . . . . . ..--- . .. . . . . . . . . (074 .mmc’et............................... .M .17c...#--------------.................. –.m –.Gm

{

z..........----- .012Aerodynandc(xrdtwe

m

g-------- .07 .Mc

CLmWICD,,_-----------m-----_--. 217 210

CD ................................. .CO& .M177(AD) -._.. ___. _......__.._ !a-9CLat (L@) . ..... ......... ..... .W .40c, p. forward pmitfon (permnt c)---G p. at H CLm= -t c) —-...-. 2: Fi~

All the important characteristics of the two sectionsme compared in a form that requires practically nodiscwion. It will be noted that the characteristics ofthe N. A. C. A. 23012 are approximately the same as, orslightly superior to, those of the N. A. C. A. 2212 exceptthat the pitching-moment characteristics of the newairfoil are markedly superior. The N. A. C. A. 23012

airfoil shouId therefore be used in preference to theN. A. C. A. 2212 for airplanes requiring this generaltype of airfoil section.

Comparison of variable-density-tunnel and full-scale-tunnel results.-l%e comparkon of the resultsfrom thetwo tunnels is made fist at one value of the “effectiveReynolds Number” by means of table III, which listsall the important characteristics at one value of theReynolds Number, and later by a more detailed ccm-pmison of the characteristics that show marked varia-tions with Reynolds Number within the full-scalerange. In the table, the results from the variable-dmsity tunnel were taken diredly from figure 2. Therewdts from the full-scale tunnel were taken fromcurves representing variations of the different char-acteristics with Reynolds Number.

TABLE IIICOMPARISON OF RESULTS FROM TWO TUNNEL$I

N. A. C. A. 23012 AIRFOILS

Ftdkcale ~m-&ble-ctmra.3twktIo

Qmnalztmn

EfkmtlveFLN---------------------- 3,4c9),lWJW R. N-------------------------- $Wl,llxl

&4a3,1MlL%@m

CL-------------------------------L40 L43ah (d~)----------------------- –L 2 –L 2

%=j~~d~).-.-.-.---..---. .Q3g .102cD0.{.---------.— ----------------cL*,t---=..-=--------------------.m .Cw4c.

.19 .16.4 ---------------------- -------

[

–. m –. W7r------ . . . . . . . . . .015

Amxiymunio canterC.013

?---------- .Ce .0s

.am;$;+~::z::=;::::::::::::: ~d “:

-— ------------------

The method of comparison employed utilizes theconcept of an efkctive Reynolds Number in order toallow for the effects of the turbulence present in thewind tunnels. This method, which was first proposedin reference 5 and is discussed in the succeeding para-graphs, appears to be the best at present available forthe interpretation of wind-tunnel rwults as applied toflight.

Marked scale effects, such as the ropid decrease ofdrag coe.tlicientwith Reynolds Number for the sphere,the rapid increase of the maximum lift coefficient forsome airfoils, and the increase of drag coefficient for&in-friction plate9, are associated with a transition ofthe boundary-layer flow from laminar to turbulent.Numerous experinmnts including Reynolds’ originalclassic experiments have indicated that the transitionoccurs at progressively lower values of the ReynoldsNumber as the “unsteadiness”, or initial turbulence,}f the general air stream is increased. Hence, whenturbulence is introduced into the air stream of a windmnnel, these marked scale effects appear at a progres-sively lower value of the Reynolds Number as thesir-stream turbulence is increaaed. In a wind tunnelhaving turbulence, the flow that is observed at a givenReynolds Number therefore corresponds approximatelyto the flow that would be observed in a turbuhmcdreestream at a higher value of the Reynolds Number.The observed coefficients and scale effects likewisemrespond more nearly to a higher value of theReynolds Number in free air than to the actual testReynolds Number in the turbulent stream. It is then~dvisable to refer 40 this higher value of the ReynoldsNumber at which corresponding flows would be ob-)erved in free air as the ‘WIective Reynolds Number”)f the test and to make comparisons and applyhe tunnel data to flight at that value of the Reynokk$umber.

As regards the relation of the effective Reynolds~umber b the test Reynolds Number, it appears thatLfactor, which will be referred to as the “turbulence

REPORT NATIONAL ADVISORY

factor”, may be applied to the test Reynolds Ntiberto obtain the effective Reynolds Number. The valueof the turbulence factor for a given wind tunnel maybe determined by a comparison of sphere drag tests orairfoil masimum-lift tests in the wind tunnel and inflight. Because the factors determined by the twomethods might not agree, the airfoil method is con-sidered preferable; but adequate data on mtium liftcoefficients arenot a,vaihtblefor making the comparisonbetween both the full-scale tunnel and the variable-density tunnel and flight by this method. A value ofthe factor of 2.4 was tentatively established betweenthe variable-density tunnel and the full-scale tunnelby a comparison of tests of Clark Y airfoils in bothtunnels. This value was employed im reference 5,assuming the factor for the full-scale tunnel to beunity (no turbulence).

The assumption that the factor is unity for the fuU-scale tunnel is approximately correct because dif-ferences in the turbulence between the full-scaletunnel and flight produce only small chaqges in the

a~:..

2.-0.~N~.

]

8,&,

Effective Reynolds Number

FIGURE 10.—Dragmeflldmt at ZMOIUt. Comp.dsonof res’nlbfromvariabledenskyandMLswJewindtnnnel%

mrmimum lift coefficient, probably within the experi-mental accuracy for most airfoils. Recent comparativesphere tests in the full-scale tunnel and in flight have,however, indicated that the factor for the full-scaletunnel may be taken as approximately 1.1 instead of1.0 in deriving the factor for the varhbledensitytunnel. The corresponding value for the variable-density tunnel then becomw 2.4X1.1 or 2.64. Theseturbulence factors are used throughout this report toderive values of the eifective Reynolds Number.Incidentally, it maybe noted that sphere tests in thevariable-density tunnel and in flight indicate values forthe turbulence factor in approximate agreement withthe values given; the actual values derived from spheretests are, however, dependent on the size of the spheresemployed.

The results of the test at a given Reynolds Numbermight be directly applied at the higher effectiveReynolds Number; however, one change for which ap-proximate allowance may be made is to be expectid inpassing to the higher Reynolds Number. The part of

COMMITTEE FOR AERONAUTICS

the drag associated with skin friction is known to de-creasewith the Reynolds Number. Therefore, althoughthe conditions as applying to the trrmsitionfrom lam-inar to turbulent flow may be considered as reproduc-ing those at the higher effective Reynolds Number, thevalue of the drag coefficient should be reduced in prlss-ing to the effective Reynolds Number. The actut-dvalue of this increment that should be subtracted issomewhat uncertain, but a value determined as sug-gested in reference 5 is used in this report for correctingthe variabledensity-tunnel results. The evaluation ofthe increment is based on the assumption that at thehigher values of the Reynolds Number encountered inflight, when the profle-drag coefficient is of importance,most of the profile drhg is due to skin friction from theturbulent boundary layer. The increment may thenredetermined from Prandtl’s analysis of the completelyturbulent skin-friction layer (reference 6) aa theamount by which the skin-frictiondrag coefficientdecreases in the Reynolds Number range from thetest Reynolds Number to the effective ReynoldsNumber. Thus, when the standard airfoil test remdtafrom the variable-density tunnel at a test ReynoldsNumber of approximately 3,000,000 me applied toflight at the effective Reynolds Number of approxi-mately 8,000,000, the measured profile-drag coefficientsshould be corrected by deducting the increment 0.0011,

It should be emphasized that the values employedin this report for both the turbulence factor and thedrag increment should be considered as only tentativeapproximation. The values may be revised as theresult of further twts now on the program at theCommittee’s laboratory. In particular, the fact thatthe skin-friction coefficient for airfoils tends to behigher than for flat plates (upon which the presentvalue of drag increment is based) agrees with thepresent results in indicating that the drag incrementmay be too low.

The comparison between the profile-drag resultsfrom the two tunnels may be made on the abovo-described basis by comparing the dotted curve infigure 2 with the profile-drag curve from the full-scale tunnel in iigure 4, although the values of theeffective Reynolds Number differ slightly. A bettercomparison is afforded by the curves in figures 10 and11 representing variations of certain characteristicswith the effective Reynolds Number. It will be notedthat the results from the full-scale tunnel indicatesomewhat lower profledrag coefficients but that thediilerences are smaller at zero lift where the resultsare more reliable owing to the absence of severnl moreor less uncertain corrections involved in deducing theprofile-drag coefficient when the airfoil is developinglift.

The values of the maximum lift coefficient are com-pared in figure 12 by means of curves representingvariations with the ,Reynolds Number. The agree-

CHARACTERISTICS OF THE N. A. C. A. 23012 AIRFOIL 943

ment between the results from the two tunnels, con-

sidering the diihculties of mwumrement, is reasonably

satisfactory. The small discrepancy that remains may

indicate either that the value of the turbulence factor

should be modified or possibly that an increment

corresponding to that used with the drag should be

employed.

For the remaining characteristics, tabular values

may be directly compared. The results from both

tunnels agree in indicating that within the flight

range of values of the Reynolds Number investigated

the following characteristics for the N. A. C. A. 23012

section show no variations with Reynolds Number

su5ciently marked to require their being taken into

account in engineering work: angle of zero lift, aLo;

optim~ hft coefficient, C’.O~; pi~~g.moment co-

Jc.~’

8,

~1.m

~0k.~~

$ Effecflve Reynolds Number

FmmE 11.—hflnlmum pm~edmg ccallkfent. Cemrarlmn of results fmmvarinbledcndty and kdkcrde wind tunnels

efficient about the aerodynamic center, Cm~.C,;andthe corresponding aerodynamic-center position. I?orthese characteristics, the tabular values presented intable III may therefore be directly compared. Itwill be noted that, in all cases, the values obtained fromthe t’wo tunnels show reasonably good agreement.The lift-curve slope % shows a slight in~rease withincensing Reynolds N-umber in both wind tunnels.

CONCLUSIONS

1. The N. A. C. A. 23012 airfoil section shows

characteristics that are generally superior to those of

well-known and commonly used sections of small or

medium camber md moderate thickness.

2. When airfoil test results at large values of theReynolds Number from the N. A. C. A. variable-

density and full-scale tunnels are interpreted on thebasis of an “effective Reynolds Number” to allowfor the efi%ct.sof turbulence, reasonably satisfactmy

m

11, ,111111

.- .4 .6 .8 / 2 4 6 .8x10nEffeciive Reynolds Number

l?mmm 12—MaxinmmIfft cc@llldenLCompa+wn of msolta fmm vmiabl~demfty and fnllde wfnd tunnel%

agreement may be expected, at lenst for efhcientairfoils of moderate thickness.

LANGLBY ME~ORIAL AIiIRONA~CAL LABORATORY,

NATIONAL ADVISORY COUJfI~E FOR AERONAUTICS,

LANGLEY I?IDLD, VA., March 1, 1936.

REFERENCES

1. Jacobs, Eactman N., Ward, Kenneth E., and Pinkerton,Robert M.: The Characteristics of 78 Related Airfoil Sec-tions from Teats in the Variable-Density Wind Tunnel.T. R. No. 460, N. A. C. A., 1933.

2. Jacob~, Eastman N. and Abbott, Ira H.: The N. A. C. A.Varwble-Density bind Tunnel. T. FL No. 416, N. A.C. A., 1932. -

3. DeFrance, Smith J.: The N. A. C. A. Full-scale WindTunnel. T. R No. 459, N. A. C. A., 1933.

4 Silve&eiu, Abe: Scale Effect on Clark Y Airfoil Charaoter-ktks from N. A. C. A. Full-scale VJind-Tumel Test..T. R. No. 502, N. A. C. A., 1934.

5. Jacobs, Eastman N.: Recent Progresg Concernin the Aero-%dynamica of Wing Section.. Paper prmen d before

A. S. M. E., Berkeley, California, June 19, 1934 (availablefrom the Office of Aeronautical Intelligence, N. A. C. A.,

‘m~~%$%;bulenten Str5mung in IWmen und6. PrandtlIAnge Platten. Ergb. Aero. Vera zu Gtittingen, IVLieferung, 1932, pp. 1S-29.

REPORT NATIONAL ADV18011Y COMMITIZEE FOR AERONAUTICS

TABLE IV

FULL-SCALEWTTD-TUNNEL DATA

N. A. C. A. 23012

A12Yon.CEARAcrmlsm=

RN-:ZeroUt?-L72Lm Max. IUC—I.EZWW

c’ a

.—

-a; --1o—. –26o –L 2.1 .2.2.3 ;;.4 4.5.5 E.9.6 7.1.7.8 1;:

i; %:LI 14.3L2 16.9:? 10.9

17.5L1l.; E:

.8 $%I 1111

CD WD e. P. CDO a. c-a.<.

r-o.(KKw.

aolfa ....-..-s.ao22c

Iao a omI –3. 3 -_: ;g.0104..-.–– 120 .m –.23.m o ---=-G- .am –L 2 –. 012

lL4 .aw –.1 –.013:%% la4 3L2 ~~ –.014.0131 22; !m.o k! –.014.0173 27.9 .m4 3-0 –.014.0228 2L 9 27.0 .Cm9 40 –.014.03al ~: ~; .C#3 &o –.013.C4m .0107 –.012.M8s 10.6 25.6 .01Z3 H -.011.0m7 I&1 26.5 .0146 8.2 –.011.0723 12.8 %6 .ole8 Q3 –.011.aw 1%8 25.6 . Olsa la 4 –. 011. 102I lL8 %5 .0m3 IL7 –.o12.m lL 3 =5 .02w ~: -.012.140 8.6 .Clsm –. 021.104 w .1287 15.7 –. w. m :; 33.0 .165 –. C&2.3al 28 35.5 .276 ~~ –. 107.224 21 33.0 .248 –. 118

TABLE V

FULL-SCALE WIND-TUNNEL DATA

N. A. C. A. 23012

AIRroLcEA2A~RN: ZemUft—2,6S0.W Max. Uft-2j4WW0

1 111

CL a CD VD ~ P. CD =~ c# ----

. —

x-a OM6PaCmt o

-0.: LO aolm ------g~a ~

19.o aom—. –26 .Oalo _–i-.. 13. o .030 –::o

–. ma–L 2 .W4 -----..- .ar34 –L 2 –. m

.1 .2 .asl 124 23.5 .0375 –. m

.1 .m34 2L3 no ~g ‘i; –. m

.3 k: .0L26 &: –. m

.4 4.6 .0170 % . ml N –. 0106.9 .0240 m.7 ~: .010 41 –. 010

:: la 9 .012:; g’

&1 –. 01117.5 2s.1 .012 Ill –. 011

:: la o 10.2 2s1 .013 –. 011

.9 11.4 .aw l&2 2s.1 .014 k; –. 010

LO 128 .071 142 Ml .016 6.1 –. m

L1 141 .CR3 ~; 2&l .015 la 1 –. m

L2 L5.5 :OJ 26.1 .017 IL 1 –. 037

L32 17.8 ILO 25.1 .Cu2 12.2 –. m?.162 . 7.9 .072 12.9 –. m

:: w .210 6.2 2: .143 l&5 –. 064LO 221 .246 . 40 320 . 1s4 1s. 5 –. 076

TABLE VL—FULIA3CALE WIND-TUNNEL DATAN. A. C. A. 23012

A7FLPoncHAuACm2usncaW !ko lUt-3,362)~ bfu IIR-3,189,13XI

CL

-a;—.o

.1

.2

.3

::.6.7.8

i;

::

L 41L3

::LO

a

Lo–26–::

i;44h8

ii

lk :12413816.216.718.618.9Kl om3223

CD UD. —

0.0110 --------.Owl.--.6-...UB2.m 125.Cm4 2L 3.0125 2L0.0175 228.O!m 2L 7.m la o.am 18.4.0470 17.0.am 16.6.CD?a2 147.CEm I?L6.0a46 127.1102 IL8.124 la 5.M3 a5.IEa.212 :;.222 40

c----Ir-a o191p===aa~

–. Cm–. Cm–. m–. w–. m–. on–. m–. m?–. Cm–. m–. Cm–. m–. m–. m–. 0)5–. lx?-. am–. m4–. 055–. 072

TABLE VH.-FULI.A3CALE WIND-TUNNEL DATAN. A. C. A. 23012

AIE701LoEA2AmE6iEmC9RN Zero lUt-3,9W~ MaL llft-3,6&9@3

c=

–2 o—. 10.1.!2.3.4.6.6.7

::LOL1L2L3L4L 46L2L 1Lo

CL

-a;—.o.1.2.3.4.5.6.7.8

$;

?:L4L46L2L1

a

-LO–26–L 2

.3

H46

::a49.7

lL O12313716.1l&6l&lIQ 2la 6m.7226

+

Cn LID -l–c. p. c% =0

-“L 3–23–L 1

ig

;:4.0&o0.00.9

k:

1;;1L9lx o13,8lh 51&819.1

r=a 0147pa 058–a w-,Cu3-.W3–.W7–,m-.m-.m–.am–.Oua-.Mt3-.U19-.ara-.Mt3-.w–.m–.W3-.w–.w?-.ml-,M3-,on

TABLE VIH

FULL-SCALE WIND-TUNNEL DATA

N. A. C. A. 23012

-IL OIIAEA~

RN. 2km lUt-4456,M0; MaI. Mt+143,CBll

a

–“%Q–26–L 2

.2

::43h77.0a3

It i12313716.110.417.Q19.2

E.:.

L/D c.P.

%’rceni18.8140

......320n.8aLo25.52h22s.02s02ho26.02ho2ho251g:

2&423.23ao

@J-’o ‘c

-“L 2–22-L2-,

.:

4:3.849&9

;;a’a

I&:1L813.013.9I&417.1

c-..,.-f=a 014Ud. 6i9

-o.m–.WJ-.w-am-,m-.an-.au-.m-.Km-.w-,w-.025-.CQ7-.Mm-,m-.m–.w-.010-.037-.MT?