1、NATIONAL ADVISORY COMMITTEEFOR AERONAUTICSREPORT No. 824_/imon use was started in 1929 with a systenmtic investigationof a family of airfoils in the Langley variable-density tmmel.Airfoils of this family were designated by numbers havingfore“ digits, such as the NACA 4412 airfoil. All airfoils ofthi
2、s family had the same basic thickness distribution (refer-ence 1), and the amount and type of camber was systemati-cally varied to produce the family of related airfoils. Thisinvestigation of the NACA airfoils of the four-digit seriesproduced airfoil se(,tions having higher maximum liftcoefficients
3、and lower minimum drag co(,flieients than thoseof sections developed before that time. The investigationalso provided infornmtion on the changes in aerodynamiccharacteristics resulting from wtriations of geometry of themean line and thickness ratio (reference 1).Provided by IHSNot for ResaleNo repro
4、duction or networking permitted without license from IHS-,-,-SU_/IMARY OF AIRFOIL DATA 3The investigation was extended in references 2 and 3 toinclude airfoils with the same thickness distribution butwith positions of the maximum camber far forward on theairfoil. These airfoils were designated by nu
5、mbers havingfive digits, such as the NACA 23012 airfoil. Some airfoilsof this family showed favorable aerodynamic characteristicsexcept for a large sudden loss in lift at the stall.Although these investigations were extended to include alimited number of airfoils with varied thickness distribu-tions
6、 (references 1 and 3 to 6), no extensive investigations ofthickness distribution were made. Comparison of experi-mental drag data at low lift coefficients with the skin-friction coefficients for fiat plates indicated that nearly allof the profile drag under such conditions was attributableto skin fr
7、iction. It was therefore apparent that any pro-nounced reduction of the profile drag must be obtained by areduction of the skin friction through increasing the relativeextent of the laminar boundary layer.Decreasing pressures in the direction of flow and low air-stream turbulence were known to be fa
8、vorable for laminarflow. An attempt was accordingly made to increase therelative extent of laminar flow by the development of ah-foils having favorable pressure gradients over a greaterproportion of the chord than the airfoils developed in refer-ences 1, 2, 3, and 6. The actual attainment of extensi
9、velaminar boundary layers at large Reynolds numbers was apreviously unsolved experimental problem requiring thedevelopment of new test equipment with very low air-stream turbulence. This work was greatly encouraged bythe experiments of Jones (reference 7), who demonstratedthe possibility of obtainin
10、g extensive laminar layers in flightat relatively_ large R_l,_u_l_ ,_u,_,s.l“_ TT,_._._.;_,._._._jwithregard to factors affecting separation of the turbulentboundary layer required experiments to determine thepossibility of making the rather sharp pressure recoveriesrequired over the rear portion of
11、 the new type of airfoil.New wind tunnels were designed specifically for testingairfoils under conditions closely approaching flight condi-tions of air-stream turbulence and Reynolds number. Theresulting wind tunnels, the Langley two-dimensional low-turbulence tunnel (LTT) and the Langley two-dimens
12、ionallow-turbulence pressure tunnel (TDT), and the methodsused for obtaining and correcting data are briefly describedin the appendix. In these tunnels the models completelyspan the comparatively narrow test sections; two-dimensional flow is thus provided, which obviates difficultiespreviously encou
13、ntered in obtaining section data fromtests of finite-span wings and in correcting adequately forsupport interference (reference 8).Difficulty was encountered in attempting to design air-foils having desired pressure distributions because of the lackof adequate theory. The Theodorsen method (referenc
14、e 9),as ordinarily used for calculating the pressure distributionsabout airfoils, was not sufficiently accurate near the leadingedge for prediction of the local pressure gradients. In theabsence of a suitable theoretical method, the 9-percent-thick symmetrical airfoil of the NACA 16-series (referenc
15、e 10)was obtained by empirical modification of the previouslyused thickness distributions (reference 4). These NACA16-series sections represented the first family of the low-draghigh-critical-speed sections.Successive attempts to design airfoils by approximatetheoretical methods led to families of a
16、irfoils designatedNACA 2- to 5-series sections (reference 11). Experience withthese sections showed that none of the approximate methodstried was sufficiently accurate to show correctly the effectof changes in profile near the leading edge. Wind-tunneland flight tests of these airfoils showed that e
17、xtensive laminarboundary layers could be maintained at comparatively largevalues of the Reynolds number if the airfoil surfaces weresmfficiently fair and smooth. These tests also providedqualitative information on the effects of the magnitude ofthe favorable pressure gradient, leading-edge radius, a
18、nd othershape variables. The data also showed that separation ofthe turbulent boundary layer over the rear of the section,especially with rough surfaces, limited the extent of laminarlayer for which the airfoils should be designed. The air-foils of these early families generally showed relatively lo
19、wmaximum lift coefficients and, in many cases, were designedfor a greater extent of laminar flow than is practical. It waslearned that, although sections designed for an excessiveextent of laminar flow gave extremely low drag coefficientsnear the design lift coefficient when smooth, the drag of such
20、sections became unduly large when rough, particularly at liftcoefficients higher than the design lift. These families ofairfoils are accordingly considered obsolete.The NACA 6-series basic _hickness forms were derived bynew and improved methods described herein in the section“Methods of Derivatinn o
21、f Thick-noss Distributions,“ in ac-cordance with design criterions established with the objectiveof obtaining desirable drag, critical Mach number, andmaximum-lift characteristics. The present report deals largelywith the characteristics of these sections. The develop-ment of the NACA 7-series famil
22、y has also been started.This family of airfoils is characterized by a greater extent oflaminar flow on the lower than on the upper surface. Thesesections permit low pitching-moment coefficients with mod-erately high design lift coefficients at the expense of somereduction in maximum lift and critica
23、l Mach number.Acknowledgement is gratefully expressed for the expertguidance and many original contributions of Mr. EastmanN. Jacobs, who initiated and supervised this work.DESCRIPTION OF AIRFOILSMETHOD OF COMBINING MEAN LINES AND THICKNESS DISTRIBUTIONSThe cambered airfoil sections of all NACA fami
24、lies con-sidered herein are obtained by combining a mean line and athickness distribution. The necessary geometric data andsome theoretical aerodynamic data for the mean lines andthickness distributions may be obtained from the supple-mentary figures by the methods described for each family ofairfoi
25、ls.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSY 10 t Ou(a_0 _. 1;I Chord hne, “uc(_L, VL) _ -I , Rodius t,hrocgh end o chordIoli “(meon-hme 5/ope Of“ _5 percent c,boFd)/zu=x-y _ s_n 8 y
26、u=yc.yt cos 8xc=z+y r s/n 0 YL=YO-Yt COS 8SAMPLE CALCULATIONS FOR DERIVATION OF THE NACA 65,3-818, a=l.O AIRFOIL1.00O 005 05 25.50 751.00yJ(_)0.01324.0383l.080_08593.0445fi0y(b)0 C0200 012;4.03580.04412.035800tan 8 18744069960-. 06996sin 00. 31932.18422.009790-. 06979cos 0O. 9476598288997561.0000099
27、756yt sin 00.00423.00706.005650-.003110Yt cos 00.01255.03765-0807308593-044450_u00007704294 2443550000 753111. 00000yuO 01455 05029 11653 13O05 080250XL0 00923 05706 25565.50000 746891.00000yL0-.01055-.02501-.04493-.04181-.008650 Thickness distribution obtained from ordinates of the NACA 65,3-018 ai
28、rfoil.b Ordinates of the mean line, 0.8 of the ordinate for cq=l.0. Slope of radius through end of chord.FIOURE 1.-Method of combining mean lines and basic thickness formsThe process for combining a mean line and a thicknessdistribution to obtain the desired cambered airfoil section isillustrated in
29、 figure 1. The leading and trailing edges aredefined as the forward and rearward extremities, respectively,of the mean line. The chord line is defined as the straiglltline connecting the leading and trailing edges. Ordinates oftim canibered airfoil are obtained by laying off the thicknessdistributio
30、n perpendicular to tile mean line Tile abscissas,ordinates, and slopes of the mean line are designated as x_,y_, and tan 6, respectively. If xv and yv represent, respec-tively, the abscissa and ordinate of a typical point of theupper surface of the airfoil and y_ is the ordinate of tllesymmetrical t
31、llickness distribution at chordx_:ise position x,the upper-surface coordinates are given by the followingrelations:Xv=X-yt sin 0 (1)yv:Y_+yt cos 0 (2)Tlle corresponding expressions for tlle lower-surface coordi-nates arex,.=x+y_ sin 0 (3)YE=-Y_-yt cos 0 (4)The center for the leading-edge radius is f
32、ound by drawinga line through tlle end of tlle chord at tlie leading edge withthe slope equal to the slope of the mean line at tllat pointand laying off a distance from the leading edge along tllis lineequal to the leading-edge radius. Tliis method of construc-tion causes tile cambered airfoils to p
33、roject sliglitly forwardof the leading-edge point. Because tim slope at the leadingedge is theoretically infinite for the mean lines having atheoretically finite load at the leading edge, the slope of theradius througli tlle end of tlle chord for such mean lines isusually taken as tlle slope of the
34、niean line at x-0.005. Thiscprocedure is justified by the nulnner in wllicll the slopeincreases to tlle theoretically infinite vahle as x/c approaches0. Tlle slope increases slowly until vel T snmll values of x/care reached. Large vahles of tlle slope are tllus limited tovahles of x/c very close to
35、0 and may be neglected in practicalairfoil design.Tables of ordinates are included in the supplenlentary datafor all airfoils for wtlicll standard characteristics are presentedNACA FOUR-DIGIT-SERIES AIRFOILSNumbering system.-The nunlbering system for theNACA airfoils of tlle fonr-(ligit series (refe
36、rence 1) is basedon tlle airfoil geometry. Tile first integer indicates theinaxilmml value of the mean-line ordinate y_ in percent of tllecllord. Tlle second integer indicates the (listance from thelea(ling edge to the location of tim maxinuml camber intentlls of the cllord. The last two integers in
37、dicate tlleairfoil ttlickness in percent of the cllord. Thus, tlle NACA2415 airfoil has 2-percent camber at 0.4 of ttle chord from tlleleading edge and is 15 percent thick.Tim first two integers taken together define tile mean line,for example, the NACA 24 mean line. The synllnetrical air-foil secti
38、ons representing tlle thickness distribution for afamily of airfoils are designated by zeros for tile first twointegers, as in the case of tlle NACA 0015 airfoil.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-SUMMARY OF AIRFOIL DATA 5Thickness distr
39、ibutions.-Data for the NACA 0006, 0008,0009, 0010, 0012, 0015, 0018, 0021, and 0024 thicknessdistributions are presented in the supplementary figures.Ordinates for intermediate thicknesses may be obtainedcorrectly by scaling the tabulated ordinates in proportion tothe thickness ratio (reference 1).
40、The leading-edge radiusvaries as the square of the thickness ratio. Values of(v/l) 2, which is equivalent to the low-speed pressure distri-bution, and of r/I“ are also presented. These data wereobtained by Theodorsens method (reference 9). Values ofthe velocity increments Ava/I“ induced by changing
41、angle ofattack (see section “Rapid Estimation of Pressure Distribu-tions“) are also presented for an additional lift coefficient ofapproximately unity. Values of the velocity ratio v/V forintermediate thickness ratios may be obtained approxi-mately by linear scaling of the velocity increments obtain
42、edfrom the tabulated values of v/V for the nearest thicknessratio; thns,tl 1 (5)Values of the velocity-increment ratio hva/V may be obtainedfor intermediate thicknesses by interpolation.Mean lines.-Data for the NACA 62, 63, 64, 65, 66, and 67mean lines are presented in the supplementary figures.The
43、data presented include the mean-line ordinates y_, theslope dyJdx, the design lift coefficient c, and the corre-sponding design angle of attack a, the moment coefficientC,n_, the resultant pressure coefficient PR, and the velocityratio Av/V. The theoretical aerodynamic characteristicswere obtained f
44、rom thin-airfoil theory. All tabulated valuesfor each mean line, accordingly, vary linearly with the maxi-mum ordinate y_, and data for similar mean lines withdifferent amounts of camber within the usual range may beObtained simply by scaling the tabulated values. Datafor the NACA 22 mean line may t
45、hus be obtained by multi-plying the data for the NACA 62 mean line by the ratio 2:6,and for the NACA 44 mean line by multiplying the data forthe NACA 64 mean line by the ratio 4:6.NACA FIVE-DIGIT-SERIES AIRFOILSNumbering system.-The numbering system for airfoils ofthe NACA five-digit series is based
46、 on a combination oftheoretical aerodynamic characteristics and geometric char-acteristics (references 2 and 3). The first integer indicatesthe amount of camber in terms of the relative magnitude ofthe design lift coefficient; the design lift coefficient in tenthsis thus three-halves of the first in
47、teger. The second and thirdintegers together indicate the distance from the leading edgeto the location of the maximum camber; this distance inpercent of the chord is one-half the number represented bythese integers. The last two integers indicate the airfoilthickness in percent of the chord. The NA
48、CA 23012 airfoilthus has a design lift coefficient of 0.3, has its maximumcamber at 15 percent of the chord, aml has a thickness ratioof 12 percent.Thickness distributions.-The thickness distributions forairfoils of the NACA five-digit series are the same as thosefor airfoils of the NACA four-digit
49、series.Mean lines.-Data for the NACA 210, 220, 230, 240, and250 mean lines are presented in the supplementary figuresin the same form as for the mean lines given herein for thefour-digit series. All tabulated values for each mean linevary linearly with the maximum ordinate or with the designlift coefficient. Thus, data for the NACA 430 mean linemay be obtained by multiplying the data for the NACA 230mean line by the ratio 4:2 and for
