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NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
REPORT No. 824
SUMMARY OF AIRFOIL DATA
.._vll#11_! H. ABBOTT, ALBERT E. YONDOENHOFF
"_ ; and LOUIS S. STIYERS, Jr.
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1945
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REPORT No. 824
SUMMARY OF AIRFOIL DATA
By IRA H. ABBOTT, ALBERT E. VON DOENHOFF
and LOUIS S. STIVERS, Jr.
Langley Memorial Aeronautical Laboratory
Langley Field, Va.
I
National Advisory Comnfittee for Aeronautics
tteadquarter_', 1500 New Hampshire Avenue NW., WashiT_gton, 25, D. ('.
Created by act of Congress approved March 3, 1915, for tile supervision and direction of the scientific study
of the problems of flight (U. S. Code, title 49, sec. 241). Its membership was increased to 15 by act approved
March 2, 1929. Tile members are appointed by the President, and serve as such without compensation.
JEROME C. HUNSA_,'ER, Sc. D., Cambridge, Mass., Chairman
L)'MAN _]. BRII:;GS, Ph. D., Vice Chairman, Director, National AUBREY W. FITCH, Vice Admiral, United States Navy, Deputy
Bureau of Standards. Chief of Naval Operations (Air), Navy Department.
CH._RLES G. ABBOT, So. D., Vice Chairnmn, Executive Committee, WILL1AM LITTLEWOOI), M. E., Jackson Heights, Long Island,
Secretary, Smithsonian Institution. N.Y.
]tENR'¢ H. ARNOLD, General, United States Army, Comnianding
FRANCIS W. REICHFLDERFER, So. D., Chief, United States
General, Army Air Forces, War Department. Weather Bureau.
_rlI,I,IAM A. M. BURI)EN, Assistant Secretary of Commerce for
P LAWRENCE B. RICHARDSON, Rear Admiral, Untied States Navy,
Aerolmutics.
Assistant Chief, Bureau of Aeronautics, Navy Departmdnt.
VANNEVAR BUSH, Sc. 1)., Director, Office of Scientific Research
and Devclot)ment, Washington, D. C. EDWARD WARNER, So. D., Civil Aeronautics Boar(t, Washington,
D.C.
WILLIAM F. I)URAND, Ph.D., Stanford Ulfiversity, California.
ORVILLE WRI(;HT, So. D., Dayton, Ohio.
OLIVER 1). E(:HOLS, Major General, United Status Army, Chief
of Mat6rM, Maintenance, and l)istribmion, Army Air Forces, THEODORE P. _Valt;wr, So. D., Ad,ninistrator of Civil Aero-
War Depart nlent. nautics, I)epartment of Commerce.
(_EOR(;E _V. I,EWIS, Sc. D., Director of Aeronautical Research
,loIIi F. VII'TORY, EL. _I., Secretary
HENRY J. E. I{EID, So. D., Engineer-in-('harge, Langley Memorial Aerona/ltical Laboratory, Langley Field, Va.
SMITII J. I)EFRAN('E, B. S., Engineer-in-(_harge, Ames Aeronautical Laboratory, Moffett FMd, Calif.
EDWARD R. SHARP, LL. B., Manager, Aircraft Engine Research Laboratory, Cleveland Airport, Cleveland, Ohio
CARLTON KEMPEIt, B. S., Execmivc Engineer, Aircraft Engine Research Lai)oratory, ('leveland Airport, Cleveland, Ohio
TECHNICAL COMMITTEES
AERODYNAMIC,_ OPERATING PROBLEM,'-;
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LANGI,Ey .'_IEMoRIAL AERONAUTICAL LARORATORY AMES AERONA'FI'I('AI. LABORATORY
Langlt,y Field, Va. Moffe_t Field, Calif.
AIRCRAFT ENGINE RESFAR('H LABORATORY, Cleveland Airport, Cleveland, Ohio
('o_*d**ct, *_nder unified control, for all agencies, of _'cicnlific research on the f**ndamental problems of flight
OFFICE OF AERONAUTICA|, INTELLIGENCE, Washinglon, I). C.
('olleetion, classification, compilation, and d|'ssemimltion of scientific and technical information on ae,'onauties
II
CONTENTS
Page Page
SUMMARY .............................. 1 EXPERIMENTAL CHARACTERISTICS--Continued
INTRODUCTION ................... 1 Drag Characteristics of Smooth Airfoils--Continued
SYMBOLS ................................... 1 Effects of type of section on drag characteristics ..... 18
HISTORICAL DEVELOPMENT ..................... 2 Effective aspect ratio ..................... 21
DESCRIPTION OF AIRFOILS ........................ 3 Effect of surface irregularities on drag ................. 22
Method of Combining Mean Lines and Thickness Permissible roughness .......................... 22
Distributions ............................. 3 Permissible waviness ......................... 22
NACA Four-Digit Series Airfoils ............ 4 Drag with fixed transition ............... 24
Numbering system ................. 4 Drag with practical construction methods ...... 24
Thickness distributions ............... 5 Effects of propeller slipstream and airplane vibration_ 29
Mean lines_ : ................... 5 Lift Characteristics of Smooth Airfoils .............. 30
NACA Five-Digit Series Airfoils ......... 5 Two-dimensional data .................. 30
Numbering systeni ................. 5 Three-dimensional data ............... 37
Thickness distributions ............... 5 Lift Characteristics of Rough Airfoils ........... 37
Mean lines ..................... 5 Two-dimensional data ........... 37
NACA 1-Series Airfoils .............. 5 Three-dimensional data ................. 38
Numbering system ............... 5 Unconservative Airfoils ..... : ....... 39
Thickness distributions .............. 5 Pitching Moment ................... 40
Mean lines ................... 5 Position of Aerodynamic Center ................ 43
NACA 6-Series Airfoils .............. 5 High-Lift Devices ................. 43
Nunabering system ................. 5 Lateral-Control Devices ..................... 43
Thickness distributions ............ 6 Leading-Edge Air Intakes .................. 49
Mean lines ................ 6 Interference ............................ 50
NACA 7-Series Airfoils ..................... 7 APPLICATION TO WING DESIGN ............... 51
Numbering system ........... 7 Application of Section Data ............... 51
Thickness distributions ............. 7 Selection of Root Section .................. 51
THEORETICAL CONSIDERATIONS ............... 8 Selection of Tip Section ................. 52
Pressure Distributions ................... 8 CONCLUSIONS ................................. 52
Methods of derivation of thickness distributions __ 8 APPENDIX--_IETHODS OF OBTAINING DATA IN THE LANGLEY
Rapid estimation of pressure distributions ..... 10 Two-DIMENSIONAL Low-TuRBULENCE TUNNELS ......... 54
Numerical examples ................... 12 Description of Tunnels .................. 54
Effect of camber on pressure distribution ...... 13 Symbols ..................... __ .... 54
Critical Mach Number .................. 13 Measurement of Lift ..................... 55
Moment Coefficients ................ 14 Measurement of Drag .................. 56
Methods of calculation ......... 14 Tunnel-Wall Corrections ............... 57
Numerical examples ............. 14 Correction for Blocking at High Lifts ........ 59
Angle of Zero Lift ................. 14 Comparison with Experiment ............ 59
Methods of calculation .............. 14 REFERENCES ......................... 60
TABLES ......................... 64
Numerical examples ............... 14
SUPPLEMENTARY DATA :
Description of Flow around Airfoils ....... 15
I--Basic Thickness Forms .............. 69
EXPERIMENTAL CHARACTERISTICS ............... 16
II--Data for Mean Lines ................ 89
Sources of Data .................... 16 III--Airfoil Ordinates .................... 99
Drag Characteristics of Smooth Airfoils .......... 16 IV--Predicted Critical Mach Numbers ............... 113
Drag characteristics in low-drag range ........... 16 V--Aerodynamic Characteristics of Various Airfoil
Drag characteristics outside low-drag range ........ 18 Sections ........................... 129
iil
REPORT No. 824
SUMMARY OF AIRFOIL DATA
By IRA H. ABBOTT, ALBERT E. VON DOENHOFF, and Lovls S. STIVERS, JR.
SUMMARY
Recent information on the aerodynamic characteristics of
ReceT_t airfoil data for both flight and wind-tunnel tests have NACA airfoils is presented. The historical development of
been collected and correlated insofar as possible. The flight NACA airfoils is briefly reviewed. New data are presented
data consist largely of drag measurements made by the wake- that permit the rapid calculation of the approximate pressure
distributions for the older NACA four-digit and five-digit
survey method. Most of the data on airfoil section characteris-
tics were obtained in the Langley two-dimensional low-turbulence airfoils by the same methods used for the NACA 6-series
airfoils. The general methods used to derive the basic tki_k-
pressure tunnel. Detail data necessary for the application o]
ness forms for NACA 6- and 7-series airfoils together with
NACA 6-series airfoils to wing design are presented in sup-
their corresponding pressure distributions are presented.
plementary figures, together with recent data for the NACA 00-,
Detail data necessary for the application of the airfoils to
1_-, 2_-, _-, and 230-series airfoils. The general methods
wing design are presented in supplementary figures placed at
used to derive the basic thickness forms for NACA 6- and
the end of the paper. The report includes an analysis of
7-series airfoils and their corresponding pressure distributions
the lift, drag, pitching-moment, and critical-speed charac-
are presented. Data and methods are given for rapidly obtain-
teristics of the airfoils, together with a discussion of the
ing the approximate pressure distributions .for NACA four-
effects of surface conditions. Available data on high-lift
digit, five-digit, 6-, and 7-series airfoils.
devices are presented. Problems associated with lateral-
The report includes an analysis of the lift, drag, pitching-
control devices, leading-edge air intakes, and interference
moment, and critical-speed characteristics of the airfoils, to-
are briefly discussed, together with aerodynamic problems
gether with a discussion of the effects of surface conditions.
Data on high-lift devices are presented. Problems associated of application.
with lateral-control devices, leading-edge air intakes, and inter- Numbered figuces are used to illustrate the text and to
ference are briefly discussed. The data indicate that the effects present miscellaneous data. Supplementary figures and
of sub:face condition on the lift and drag characteristics are at tables are not numbered but are conveniently arranged at
least as large as the effects of the airfoil shape and must be the end of the report according to the numerical designation
considered in airfoil selection and the prediction of wing charac- of the airfoil section within the follo_'ing headings:
I--Basic Thickness Forms
teristics. Airfoils permitting extensive laminar flow, such as
II--Data for Mean Lines
the NACA 6-series airfoils, have much lower drag coe_icients
III--Airfoil Ordinates
at high speed and cruising lift coeficients than earlier types of
IV--Predicted Critical Mach Numbers
airfoils if, and only if, the wing surfaces are suy_ciently smooth
V--Aerodynamic Characteristics of Various Airfoil
and fair. The NACA 6-series airfoils also have favorable
Sections
critical-speed characteristics and do not appear to present
unusual problems associated with the application of high-lift These supplementary figures and tables present the basic
data for the airfoils.
and lateral-control devices.
SYMBOLS
INTRODUCTION
A aspect ratio
•A considerable amount of airfoil data has been accumulated An, B, Fourier series coefficients
from tests in the Langley two-dimensional low-turbulence a mean-line designation, fraction of chord from lead-
tunnels. Data have also been obtained from tests both in ing edge over which design load is uniform; in
other wind tunnels and in flight and include the effects of derivation of thickness distributions, basic length
high-lift devices, surface irregularities, and interference. usually considered unity
Some data are also available on the effects of airfoil section b wing span
on aileron characteristics. Although a large amount of these b_ flap span, inboard
data has been published, the scattered nature of the data bIo flap span, outboard
and the limited objectives of the reports have prevented C, drag coefficient
adequate analysis and interpretation of the results. The drag coefficient at zero lift
CDL 0
purpose of this report is to summarize these data and to lift coefficient
correlate and interpret them insofar as possible. _5¥ 1 increment of maximum lift caused by flap deflection
1
REPORT N'O. 824--NATIONAL ADVISORY COMMITTEE, FOR AERONAUTICS
¢ chord XL abscissa of lower surface
Ca aileron chord Xu abscissa of upper surface
(x),,
Ca section drag coefficient
chordwise position of transition
minimum section drag coefficient
Cdmi n flap chord, inboard Y distance perpendicular to chord
cf_
¢fo flap chord, outboard Yc mean-line ordinate
yL ordinate of lower surface
cf
flap-chord ratio yt ordinate of symmetrical thickness distribution
c
Yv ordinate of upper surface
CH section aileron hinge-moment coefficient (q_c_) z complex variable in circle plane
_eu increment of aileron hinge-moment coefficient at zp complex variable in near-circle plane
constant lift angle of attack
Ol
ACH_ hinge-moment parameter A(_o
section aileron effectiveness parameter, ratio of
section lift coefficient A5
V_
change in section angle of attack to increment of
design section lift coefficient
el l aileron deflection at a constant value of lift
moment coefficient about aerodynamic center
Cma. c, coefficient
moment coefficient about quarter-chord point
Cmc/4 angle of zero lift
section normal-force coefficient Ollo
Cn
section angle of attack
D drag Olo
Aoto increment of section angle of attack
AH loss of total pressure
section angle of attack corresponding to design
Ho free-stream total pressure Oti
lift coefficient
h section aileron hinge moment
flap or aileron deflection; down deflection is positive
h, exit height
flap deflection, inboard
k constant
flap deflection, outboard
L lift
airfoil parameter (6--0)
M Mach number
value of e at trailing edge
M. critical Mach number _.TE
complex variable in airfoil plane
typical points on upper and lower surfaces of airfoil
OU, OL 0 angular coordinate of z' ;also, angle of which tangent
P pressure coefficient (_L_oP°) is slope of mean line
q
Per critical pressure coetficient { Tip chord "_
taper ratio \Root chord/
P. resultant pressure coefficient; difference between
local ul)per- and lower-surface pressure coefficients {Effective Reynohls number'_
T turbulence factor \ Test Reyimldsnumber ]
P local static pressure; also, angular velocity in roll in
pb/2V angular coordinate of z
free-stream static pressure ¢ airfoil parameter determining radial coordinate of z
PO
pb/2V helix angle of wing tip _o
average value of _b (21r£2_ ¢ d_)
qo free-stream dynamic pressure
R Reynolds number
Re, critical Reynolds mmfl)er HISTORICAL DEVELOPMENT
S
pressure coefficient (_) The development of types of NACA airfoils now in con>
tl first airfoil thickn(.ss ratio mon use was started in 1929 with a systenmtic investigation
t: second airfoil thickness ratio of a family of airfoils in the Langley variable-density tmmel.
V free-stream velocity Airfoils of this family were designated by numbers having
inlet velocity fore" digits, such as the NACA 4412 airfoil. All airfoils of
local velocity this family had the same basic thickness distribution (refer-
At" increment of local vdocity ence 1), and the amount and type of camber was systemati-
AVa increment of local velocity caused 1)y additional cally varied to produce the family of related airfoils. This
type of load distribution investigation of the NACA airfoils of the four-digit series
produced airfoil se(,tions having higher maximum lift
(")
velocity ratio correspon(ling to thi('kness t,
qV coefficients and lower minimum drag co(,flieients than those
of sections developed before that time. The investigation
velocity ratio corresponding to thi(,l_ness t2
also provided infornmtion on the changes in aerodynamic
x distance along chord characteristics resulting from wtriations of geometry of the
xc mean-line abscissa mean line and thickness ratio (reference 1).
SU_/IMARY OF AIRFOIL DATA 3
The investigation was extended in references 2 and 3 to was obtained by empirical modification of the previously
include airfoils with the same thickness distribution but used thickness distributions (reference 4). These NACA
with positions of the maximum camber far forward on the 16-series sections represented the first family of the low-drag
airfoil. These airfoils were designated by numbers having high-critical-speed sections.
five digits, such as the NACA 23012 airfoil. Some airfoils Successive attempts to design airfoils by approximate
of this family showed favorable aerodynamic characteristics theoretical methods led to families of airfoils designated
except for a large sudden loss in lift at the stall. NACA 2- to 5-series sections (reference 11). Experience with
Although these investigations were extended to include a these sections showed that none of the approximate methods
limited number of airfoils with varied thickness distribu- tried was sufficiently accurate to show correctly the effect
tions (references 1 and 3 to 6), no extensive investigations of of changes in profile near the leading edge. Wind-tunnel
thickness distribution were made. Comparison of experi- and flight tests of these airfoils showed that extensive laminar
mental drag data at low lift coefficients with the skin- boundary layers could be maintained at comparatively large
friction coefficients for fiat plates indicated that nearly all values of the Reynolds number if the airfoil surfaces were
of the profile drag under such conditions was attributable smfficiently fair and smooth. These tests also provided
to skin friction. It was therefore apparent that any pro- qualitative information on the effects of the magnitude of
nounced reduction of the profile drag must be obtained by a the favorable pressure gradient, leading-edge radius, and other
reduction of the skin friction through increasing the relative shape variables. The data also showed that separation of
extent of the laminar boundary layer. the turbulent boundary layer over the rear of the section,
Decreasing pressures in the direction of flow and low air- especially with rough surfaces, limited the extent of laminar
stream turbulence were known to be favorable for laminar layer for which the airfoils should be designed. The air-
flow. An attempt was accordingly made to increase the foils of these early families generally showed relatively low
relative extent of laminar flow by the development of ah'- maximum lift coefficients and, in many cases, were designed
foils having favorable pressure gradients over a greater for a greater extent of laminar flow than is practical. It was
proportion of the chord than the airfoils developed in refer- learned that, although sections designed for an excessive
ences 1, 2, 3, and 6. The actual attainment of extensive extent of laminar flow gave extremely low drag coefficients
laminar boundary layers at large Reynolds numbers was a near the design lift coefficient when smooth, the drag of such
previously unsolved experimental problem requiring the sections became unduly large when rough, particularly at lift
development of new test equipment with very low air- coefficients higher than the design lift. These families of
stream turbulence. This work was greatly encouraged by airfoils are accordingly considered obsolete.
the experiments of Jones (reference 7), who demonstrated The NACA 6-series basic _hickness forms were derived by
the possibility of obtaining extensive laminar layers in flight new and improved methods described herein in the section
at relatively_ large R_l,,,_u_l_ ,_u,,,_,s.l"_ TT,_..._._.;_,._._._jwith "Methods of Derivatinn of Thick-noss Distributions," in ac-
regard to factors affecting separation of the turbulent cordance with design criterions established with the objective
boundary layer required experiments to determine the of obtaining desirable drag, critical Mach number, and
possibility of making the rather sharp pressure recoveries maximum-lift characteristics. The present report deals largely
required over the rear portion of the new type of airfoil. with the characteristics of these sections. The develop-
New wind tunnels were designed specifically for testing ment of the NACA 7-series family has also been started.
airfoils under conditions closely approaching flight condi- This family of airfoils is characterized by a greater extent of
tions of air-stream turbulence and Reynolds number. The laminar flow on the lower than on the upper surface. These
resulting wind tunnels, the Langley two-dimensional low- sections permit low pitching-moment coefficients with mod-
turbulence tunnel (LTT) and the Langley two-dimensional erately high design lift coefficients at the expense of some
low-turbulence pressure tunnel (TDT), and the methods reduction in maximum lift and critical Mach number.
used for obtaining and correcting data are briefly described Acknowledgement is gratefully expressed for the expert
in the appendix. In these tunnels the models completely guidance and many original contributions of Mr. Eastman
span the comparatively narrow test sections; two- N. Jacobs, who initiated and supervised this work.
dimensional flow is thus provided, which obviates difficulties
previously encountered in obtaining section data from
DESCRIPTION OF AIRFOILS
tests of finite-span wings and in correcting adequately for
support interference (reference 8). METHOD OF COMBINING MEAN LINES AND THICKNESS DISTRIBUTIONS
Difficulty was encountered in attempting to design air-
foils having desired pressure distributions because of the lack The cambered airfoil sections of all NACA families con-
of adequate theory. The Theodorsen method (reference 9), sidered herein are obtained by combining a mean line and a
as ordinarily used for calculating the pressure distributions thickness distribution. The necessary geometric data and
about airfoils, was not sufficiently accurate near the leading some theoretical aerodynamic data for the mean lines and
edge for prediction of the local pressure gradients. In the thickness distributions may be obtained from the supple-
absence of a suitable theoretical method, the 9-percent- mentary figures by the methods described for each family of
thick symmetrical airfoil of the NACA 16-series (reference 10) airfoils.
4
REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Y
•10 t Ou(a'_
0 _'_. ' 1;I Chord hne
/
zu=x-y _s_n 8 yu=yc.yt cos 8
', "uc(_L, VL) _ - xc=z+y r s/n 0 YL=YO-Yt COS 8
I ',, Rodius t,hrocgh end o£ chord 1.00
Ioli "(meon-h'me 5/ope Of" _5 percent c,boFd)
SAMPLE CALCULATIONS FOR DERIVATION OF THE NACA 65,3-818, a=l.O AIRFOIL
y(_J) (yb¢) tan 8 sin 0 cos 0 yt sin 0 Ytcos 0 _u yu XL yL
O1•••.•.5000270005555 00...•.00000138483804523_594l]f3i 00••...000C03431545028182£0200;04 --0.••001668997994664 -.00...10308016499927372929 O1..•••0999904899072770685505866 0--00.0...0000003047152016365 00..-•-0000013848270455674955353 01.•••••500027004045002043079031074051 O0•••••0011015138406O05252059355 01.•••.•050027000554009756002068003659 0----------0.....0000012440054185098651315
•Thickness distribution obtained from ordinates of the NACA 65,3-018 airfoil.
bOrdinates ofthe mean line, 0.8 ofthe ordinate for cq=l.0.
•Slope of radius through end ofchord.
FIOURE 1.--Method of combining mean lines and basic thickness forms•
The process for combining a mean line and a thickness of the leading-edge point. Because tim slope at the leading
distribution to obtain the desired cambered airfoil section is edge is theoretically infinite for the mean lines having a
illustrated in figure 1. The leading and trailing edges are theoretically finite load at the leading edge, the slope of the
defined as the forward and rearward extremities, respectively, radius througli tlle end of tlle chord for such mean lines is
of the mean line. The chord line is defined as the straigllt
usually taken as tlle slope of the niean line at x--0.005. This
line connecting the leading and trailing edges. Ordinates of c
tim canibered airfoil are obtained by laying off the thickness procedure is justified by the nulnner in wllicll the slope
distribution perpendicular to tile mean line• Tile abscissas, increases to tlle theoretically infinite vahle as x/c approaches
ordinates, and slopes of the mean line are designated as x_, 0. Tlle slope increases slowly until vel T snmll values of x/c
y_, and tan 6, respectively. If xv and yv represent, respec- are reached. Large vahles of tlle slope are tllus limited to
tively, the abscissa and ordinate of a typical point of the vahles of x/c very close to 0 and may be neglected in practical
upper surface of the airfoil and y_ is the ordinate of tlle airfoil design.
symmetrical tllickness distribution at chordx_:ise position x, Tables of ordinates are included in the supplenlentary data
the upper-surface coordinates are given by the following for all airfoils for wtlicll standard characteristics are presented
relations:
NACA FOUR-DIGIT-SERIES AIRFOILS
Xv=X--yt sin 0 (1)
Numbering system.--The nunlbering system for the
yv:Y_+yt cos 0 (2)
NACA airfoils of tlle fonr-(ligit series (reference 1) is based
on tlle airfoil geometry. Tile first integer indicates the
Tlle corresponding expressions for tlle lower-surface coordi- inaxilmml value of the mean-line ordinate y_ in percent of tlle
nates are
cllord. Tlle second integer indicates the (listance from the
x,.=x+y_ sin 0 (3) lea(ling edge to the location of tim maxinuml camber in
tentlls of the cllord. The last two integers indicate tlle
YE=--Y_--yt cos 0 (4) airfoil ttlickness in percent of the cllord. Thus, tlle NACA
2415 airfoil has 2-percent camber at 0.4 of ttle chord from tlle
The center for the leading-edge radius is found by drawing leading edge and is 15 percent thick.
a line through tlle end of tlle chord at tlie leading edge with Tim first two integers taken together define tile mean line,
the slope equal to the slope of the mean line at tllat point for example, the NACA 24 mean line. The synllnetrical air-
and laying off a distance from the leading edge along tllis line foil sections representing tlle thickness distribution for a
equal to the leading-edge radius. Tliis method of construc- family of airfoils are designated by zeros for tile first two
tion causes tile cambered airfoils to project sliglitly forward integers, as in the case of tlle NACA 0015 airfoil.
SUMMARY OF AIRFOIL DATA 5
Thickness distributions.--Data for the NACA 0006, 0008, Thickness distributions.--The thickness distributions for
0009, 0010, 0012, 0015, 0018, 0021, and 0024 thickness airfoils of the NACA five-digit series are the same as those
distributions are presented in the supplementary figures. for airfoils of the NACA four-digit series.
Ordinates for intermediate thicknesses may be obtained Mean lines.--Data for the NACA 210, 220, 230, 240, and
correctly by scaling the tabulated ordinates in proportion to 250 mean lines are presented in the supplementary figures
the thickness ratio (reference 1). The leading-edge radius in the same form as for the mean lines given herein for the
varies as the square of the thickness ratio. Values of four-digit series. All tabulated values for each mean line
(v/l') 2,which is equivalent to the low-speed pressure distri- vary linearly with the maximum ordinate or with the design
bution, and of r/I" are also presented. These data were lift coefficient. Thus, data for the NACA 430 mean line
obtained by Theodorsen's method (reference 9). Values of may be obtained by multiplying the data for the NACA 230
the velocity increments Ava/I" induced by changing angle of mean line by the ratio 4:2 and for the NACA 640 mean line
attack (see section "Rapid Estimation of Pressure Distribu- by multiplying the data for the NACA 240 mean line by
tions") are also presented for an additional lift coefficient of the ratio 6:2.
approximately unity. Values of the velocity ratio v/V for NACA 1-SERIES AIRFOILS
intermediate thickness ratios may be obtained approxi-
Numbering system.--The NACA 1-series airfoils are des-
mately by linear scaling of the velocity increments obtained
ignated by a five-digit number--as, for example, the
from the tabulated values of v/V for the nearest thickness
NACA 16-212 section. The first integer represents the
ratio; thns,
series designation. The second integer indicates the dis-
tance in tenths of the chord from the leading edge to the
tl 1 (5) position" of minimum pressure for the symmetrical section
at zero lift. The first number following the dash indicates
the amount of camber expressed in terms of the design lift
Values of the velocity-increment ratio hva/V may be obtained
coefficient in tenths, and the last two numbers together
for intermediate thicknesses by interpolation.
indicate the thickness in percent of the chord. The com-
Mean lines.--Data for the NACA 62, 63, 64, 65, 66, and 67 monly used sections of this family have minimum pressure
mean lines are presented in the supplementary figures. at 0.6 of the chord from the leading edge and are usually
The data presented include the mean-line ordinates y_, the referred to as the NACA 16-series sections.
slope dyJdx, the design lift coefficient c, and the corre-
Thickness distributions.--Data for the NACA 16-006,
sponding design angle of attack a,, the moment coefficient
16-009, 16-012, 16-015, 16-018, and 16-021 thickness
C,n_,,,,the resultant pressure coefficient PR, and the velocity
distributions (reference 10) are presented in the supplemen-
ratio Av/V. The theoretical aerodynamic characteristics tary figures. These data are similar in form to the data for
were obtained from thin-airfoil theory. All tabulated values
those airfoils of the NACA four-digit series, and data for
for each mean line, accordingly, vary linearly with the maxi- intermediate thickness ratios may be obtained in the same
mum ordinate y_, and data for similar mean lines with manner.
different amounts of camber within the usual range may be
Mean lines.--The NACA 16-series airfoils as commonly
Obtained simply by scaling the tabulated values. Data
used are cambered with a mean line of the uniform-load
for the NACA 22 mean line may thus be obtained by multi-
type (a=l.0), which is described under the section for the
plying the data for the NACA 62 mean line by the ratio 2:6,
NACA 6-series airfoils that follows. If any other type of
and for the NACA 44 mean line by multiplying the data for
mean line is used, this fact should be stated in the airfoil
the NACA 64 mean line by the ratio 4:6.
designation.
NACA6-S_.RIESAIRFOILS
NACA FIVE-DIGIT-SERIES AIRFOILS
Numbering system.--The NACA 6-series airfoils are usu-
Numbering system.--The numbering system for airfoils of ally designated by a six-digit number together with a state-
the NACA five-digit series is based on a combination of ment showing the type of mean line used. For example,
theoretical aerodynamic characteristics and geometric char- in the designation NACA 65,3-218, a=0.5, the "6" {s
acteristics (references 2 and 3). The first integer indicates the series designation. The "5" denotes the chordwise
the amount of camber in terms of the relative magnitude of position of minimum pressure in tenths of the chord beifind
the design lift coefficient; the design lift coefficient in tenths the leading edge for the basic symmetrical section at zero
is thus three-halves of the first integer. The second and third lift. The "3" following the comma gives the range of lift
integers together indicate the distance from the leading edge coefficient in tenths above and below the design lift coefficient
to the location of the maximum camber; this distance in in which favorable pressure gradients exist on both surfaces.
percent of the chord is one-half the number represented by The "2" following the dash gives the design lift coefficient
these integers. The last two integers indicate the airfoil in tenths. The last two digits indicate the airfoil thickness
thickness in percent of the chord. The NACA 23012 airfoil in percent of the chord. The designati0n "a=0.5" shows
thus has a design lift coefficient of 0.3, has its maximum the type of mean line used. When the mean-line designa-
camber at 15 percent of the chord, aml has a thickness ratio tion is not given, it is understood that the uniform-load
of 12 percent. mean line (a= 1.0) has been used.
918392--51----2
6 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AEHONAUTICS
When the mean line used is obtained 1)y combining more NACA 65(3_s)-(1.5)(16.5), a=0.5
than one mean line, the design lift coefficient used in the
Some early experimental airfoils are designated by the in-
designation is the algebraic sum of the design lift coefficients sertion of the letter "x" immediately preceding the hyphen
of the mean lines used, and the mean lines are described in
as in the designation 66,2x-115.
the statement following the number as in the following ease: Thickness distributions.--Data for available NACA 6-series
thickness forms are presented in the supplementary
(a=0.5, cli=0.3 t
figures. These data are comparable with the sinfilar data
NACA 65,3-2181a=1.0 ' c,_=--0.11
for airfoils of the NACA four-digit series, except that ordi-
Airfoils having a thickness distribution obtained by linearly nates for intermediate thicknesses may not be correctly ob-
increasing or deereasing the ordinates of one of the originally tained by scaling the tabulated ordinates proportional to the
derived thickness distributions are designated as in the follow- thickness ratio. This method of changing the ordinates by
ing example: a factor will, however, produce shapes satisfactorily approx-
NACA 65(318)-217, a=0.5 imating members of the family if the change in thickness
ratio is small. Values of v/V and hvdV for intermediate
The significance of all of the numbers except those in the
thickness ratios may be approximated as described for the
parentheses is the same as before. The first number and the
NACA four-digit series.
last two numbers enclosed in the parentheses denote, respec-
Mean lines.--The mean lines commonly used with the
tively, the low-drag range and the thickness in percent of
NACA 6-series airfoils produce a uniform chordwise loading
the chord of the originally derived thickness distribution.
The more recent NACA 6-series airfoils are derived as from the leading edge to the point -=a and a linearly de-
c
members of thickness families having a simple relationship
creasing load from this point to the trailing edge. Data
between the conformal transformations for airfoils of different
for NACA mean lines with values of a equal to 0, 0.1, 0.2,
thickness ratios but having minimum pressure at the same
0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 are presented in the
ehordwise position. These airfoils are distinguished from
supplementary figures. The ordinates were computed by
the earlier individually derived airfoils by writing the num-
the following formula, wlfich represents a simplification of
ber indicating the low-drag range as a subscript ;for example,
the original expression for mean-line ordinates given in
NACA 653-218, a=0.5 reference 11:
For NACA 6-series airfoils having a tlfickness ratio less
Y¢--c--2r(a+l)Cq ll_la[l(a x)-"log_la_X
than 0.12 of the chord, the subscript number indicating the
low-drag range should be less than unity. Rather than use
a fractional number, a subscript of unity was originally em- 61(l--X) 2log. (1-- x)+14 (1--c/--4x'_" 1(a_;)2 _
ployed for these airfoils. Since tt, is usage is not consistent
with the previous definition of a number indicating the low- :log_ ;+g-h c} (6)
drag range, the designations of airfoil sections having a thick-
ness ratio less than 0.12 of the chord are now given without where
such a number. As an example, an NACA 6-series airfoil
g=--l--a •1 [ a2(1_log, a- 1) + 1]
having a thickness ratio of 0.10 of the chord would be
designated:
NACA 65-210
h=l_ al [ 21(l_a)2 log. (1--a) -- _1 (1--a)2] +g
Ordinates for the basic thickness distributions designated by
The ideal angle of attack a: correst)onding to the design
a subscript are slightly different from those for the corre-
sponding individually derived thickness distributions. As lift coefficient is given by
before, if the ordinates of the basic thidkness distribution
(?lt= -- ]b eli
have been changed by a factor, the low-drag range and thick- 27r(a+ 1)
ness ratio of the original thickness distribution are enclosed
The data are presented for a design lift coefficient c,
in parentheses as follows:
equal to unity. All tabulated values vary directly with
NACA 65(a_8)-217, a=0.5 the design lift coefficient. Corresponding data for similar
mean lines with other design lift coefficients may accordingly
If, however, the ordinates of a basic thickness distribution
be obtained simply by multiplying the tabulated values by
having a thickness ratio less than 0.12 of the chord have been
the desired design lift coeffieicnt.
changed by a factor, the number indicating the low-drag
hi order to camber NACA 6-series airfoils, mean lines are
range is eliminated and only the original thickness ratio is
enclosed in parentheses as follows: Usually used having vahles of a equal to or greater than the
distance from the leading edge to the location of nfinimum
NACA 65c10)-211
pressure for the selected thickness distrilmtion at. zero lift.
If the design lift coefficient in tenths or the airfoil thickness For special purposes, load distrihutions other than those
in percent of chord are not whole integers, the numbers corresponding to the simple mean lines may be obtaiz_ed 1)y
giving these quantities are usually enclosed in parentheses as combining two or more types of mean line having positive or
in the following designation: negative values of the design lift coefficient. The geometric