NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS - NASA

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NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
REPORT No. 824
SUMMARY OF AIRFOIL DATA
By IRA H. ABBOTT, ALBERT E. VON DOENHOFF,
and LOUIS S. STIVERS, Jr.
1945
AERONAUTIC SYMBOLS
1. FUNDAMENTAL AND DERIVED UNITS
Metric English
Symbol
Abbrevia-- Abbrevia-
Unit Unit
tion tion
Length ______ l meter __________________ m foot (or mile) _________ ft (or rni)
Time ________ t second _________________ s second (or bour) _______ sec (or hr)
Force ________ F weight of) kilogram _____ kg weight of 1 pound _____ lb
Power _______ P horsepower (metric) _____ ---------- horsepower ___________ hp
Speed _______ V {mkielotemres tpeersr pseecro hnodu _r_ ___________ mkpphs fmeielte sp epre rs ehcOonudL _ ______________ fmpsp h
2. GENERAL SYMBOLS
w
Weight=mg Kinematic viscosity
JI
u Standard acceleration of gravity=9.80665 m/s2 p Density (mass per unit volume)
or 32.1740 ft/sec2 Standard density of dry air, 0.12497 kg_m-4_s2 at 15° C
and 760 mm; or 0.002378 Ib-ft-4 sec2
m Mass=Wg Specific weight of "standard" air, 1.2255 kg/ms or
I Moment of inertia=mP. (Indicate axis of 0.07651 lb/cu ft
radius of gyration k by proper subscript.)
Coefficient of viscosity
3. AERODYNAMIC SYMBOLS
s
Area Angle of setting of wings (relative to thrust line)
S~ Area of wing Angle of stabilizer setting (relative to thrust
G Gap line)
o
b Span Resultant moment
c Chord 11 Resultant angular velocity
b'
A Aspect ratio, S R Reynolds number, p Vl wherelisalineardimen-
fJ.
V True air speed sion (e.g., for an airfoil of 1.0 ft chord, 100 mph,
standard pressure at 15° 0, the corresponding
q Dynamic pressure, ~P V'
Reynolds number is 935,400; or for an airfoil
L Lift, absolute coefficient OL= q~ of 1.0 m chord, 100 mps, the corresponding
Reynolds number is 6,865,000)
D Drag, absolute coefficient OD= q~ Angle of attack
Angle of downwash
Profile drag, absolute coefficient ODO=~ Angle of attack, infinite aspect ratio
Angle of attack, induced
Induced drag, absolute coefficient OD = ~~ Angle of attack, absolute (measured from zero
qu lift position)
j
Flight-path angle
D. Parasite drag, absolute coefficient ODP= ~S 'Y
o Cross-wind force, absolute coefficient 0 = q~
0
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 Committee for Aeronautics
Headquarters, 1500 New Hampshire Avenue NW., Washington 25, D. O.
Created by act of Congress approved March 3, 1915, for the 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. The members are appointed by the President, and serve as such without compensation.
JEROME C. HUNSAKER, Sc. D., Cambridge, Mass., Chairman
LYMAN J. BRIGGS, Ph. D., Vice Chairman, Director, National AUBREY W. FITCH, Vice Admiral, United States Navy, Deputy
Bureau of Standards. Chief of Naval Operations (Air), Kavy Department.
CHARLES G. ABBOT, Sc. D., Vice Chairman, Executive Committee, WILLIAM LITTLEWOOD, M. E., Jackson Heights, Long Island,
Secretary, Smithsonian Institution. N. Y.
HENRY H. ARNOLD, General, "Gnited States Army, Commanding
FRANCIS W. REICHELDERFER, Sc. D., Chief, United States
General, Army Air Forces, War Department.
Weather Bureau.
WILLIAM A. M. Bl:RDEN, Assistant Secretary of Commerce for
LAWRENCE B. RICHARDSON, Rear Admiral, United States Navy,
Aeronautics.
Assistant Chief, Bureau of Aeronautics, Navy Department.
VANNEVAR BUSH, Sc. D., Director, Office of Scientific Research
and Development, Washington, D. C. EDWARD 'VARNER, Sc. D., Civil Aeronautics Board, Washington,
D. C.
WILLIAM F. DCRAND, Ph. D., Stanford Lniversity, California.
ORVILLE WRIGHT, Sc. D., Dayton, Ohio.
OLIVER P. ECHOLS, !\iajor General, "Cnited States Army, Chief
of Materiel, Maintenance, and Distribution, Army Air Forces, THEODORE P. WRIGHT, Sc. D., Administrator of Civil Aero
War Department. nautics, Department of Commerce.
GEORGE W. LEWIS, Sc. D., Director of Aeronautical Research
JOHN F. VICTORY, LL. M., Secretary
HENRY J. E. REID, Sc. D., Engineer-in-Charge, Langley Memorial Aeronautical Laboratory, Langley Field, Va.
SMITH J. DEFRANCE, B. S., Engineer-in-Charge, Ames Aeronautical Laboratory, Moffett Field, Calif.
EDWARD R. SHARP, 1,1,. B., Manager, Aircraft Engine Research Laboratory, Cleveland Airport, Cleveland, Ohio
CARLTON KEMPER, R. S., Executive Engineer, Aircraft Engine Research Laboratory, Cleveland Airport, Cleveland, Ohio
TECHNICAL COMMITTEES
AERODYNAMICS OPERATING PROBLEMS
POWER Pr,ANTS FOR AIRCRAFT MATERIALS RESEARCH COORDINATION
AIRCRAFT CONSTRUCTION
Coordination of Research Needs of Military and Civil Aviation
Preparation of Research Programs
Allocation of Problems
PrevenUon of Duplication
LANGLEY MEMORIAL AERONAUTICAL LABORATORY AMES AERONAUTICAL LABORATORY
Langley Field, Va. l\Ioffett Field, Calif.
AIRCRAFT ENGINE RESEARCH LABORATORY, Cleveland Airport, Cleveland, Ohio
Conduct, under unified control, for all agencies, of scientific research on the fundamental problems of flight
OFFICE OF AERONAUTICAL INTELLIGENCE, Washington, D. C.
Collection, classification, compilation, and diss~'minatiori of scientific and technical information on aeronauticll
II
CONTENTS
Page Page
SUMMARY _______ .. _- --__ --. __ -____ --__ -- __ ., . _ . _. . _ .. _____ _ EXPERIMENTAL CHARACTERISTIcs-Continued
1NTRoDucTION_ . ________________________ .. _"_C ___ .. _______ 1 Drag Chara~teristics of Smooth Airfoils-·Continued
SYMBOLS ________________________ ._______________________ 1
Effects of. type of sectiOIl on drag charact.eristics .. _ _ _ _ 18
HIflTORICAL .. ________________________ .. _ _ _ _ _ _ 2 Effective aspect ratio ________ . _________________ .. ___ 21
DE~·ELOPMENT
DESCRIPTION OF AIRFOILS ____________________________ .. _ _ _ _ 3 Effect of surface irregularities on drag ____ . _ _ _ _ _ _ _ _ _ _ _ _ _ 22
:\fethod of Combining :.\Iean 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 Fh'e-Digit Series Airfoils ____ .... _____________ .___ _ 5 Two-dimensional dat9. __________ .. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 30
Numbering system__ _ _ __ _ _ _ __ _ __ _ ___ __ _ __ _ __ ____ _ 5 Three-dimensional data_ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 37
Thickness distributions _________________ -~_c ____ ~c-_ "5 - Lift Characteristics of Rough Airfoils. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 37
Mean lines ______________________ .. _ _ _ _ _ _ _ _ _ _ _ _ _ _ 5 Two-dimensional data_ _ _ _ _ __ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 37
N ACA I-Series Airfoils ____ ... ____ . ______________ "~_-=-=- 5 Three-dimensional data ______ ._ ___ . ____ .. ______ .. _ _ _ _ 38
Numbering system ___________ ___ 5 Unconservatiye Airfoils ________ .... __ . _____ ... ____________ 39-
~________________
Thickness distributions _________________ . __________ 5 Pitching Moment ____________________ . ___________ .. _ __ 4()
Mean lin es _______ . _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ 5 Position of Aerodynamic Center __ . ______________ . __ .. ___ 43:
NACA 6-Series Airfoils________________________________ 5 High-Lift Devices_ _ _ __ __ ___ _ _ _ _ _ _ _ _ _ _ _ __ __ __ __ __ _ ___ _ 43:
N um bering system _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 5 Lateral-Control Devices ___________________ .. _ _ _ _ _ _ _ _ _ _ _ 43
Thickness distribu tions _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 6 Leading-Edge Air Intltkes __________ .. _ _ _ _ _ __ __ _ _ _ _ _ _ __ _ 49
Mean lines ___ _____________________ .. _____ .. ______ 6 In terference __ .. _________________________ .. ____________ . 50
~
NACA 7-Series Airfoils __________ ~· ___ :.:_= _____________ ~_ 7 ApPI,ICATION TO WINO DESIGN __________ . ___ .. ______________ 51
NUmcering system_ _ _____ ___ __ ___ _____ __ ____ __ ___ 7 Application of Section Data __________________________ .. 51
Thir,kness distributions_ _ _ _ __ __ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ __ _ 7 Selection of Root Section ___ ._ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ 51
THEORETICAL CONSIDERATIONS __________ . ______ .. _________ .. 8 Selection of Tip Section ____ .. ________________ ... _ _ _ _ _ _ _ _ 52
Pressure Distributions _______________ c _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 8 CONCLUSIONS _________________ .. _________________ .. _ _ _ __ _ _ _ 52
Methods of derivation of thickness distributions_ _ _ _ 8 ApPENDIX--METHODS 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
Symbols ___ .. _____________ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 54
Effect of camber on pressure distribution ___ .. _____ .. _ _ 13
Critical Mach Number___ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ __ _ _ __ ___ _ _ _ _ 13 Measurement of Lift.. ______ . ______ ... _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ 55
Moment Coefficients___ __ __ _ ___ _ _ __ __ ___ ___ __ ___ _____ _ 14 Measurement of Drag .. ______________________________. _ 56
Methods of calculation ____ . _______ . ______ .. __ ._____ 14 Tunnel-Wall Corrections _____ .. _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ 57
Numerical exapl pIes _ . _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ 14 Correction for Blocking at High Lifts ______ . _ _ _ _ _ _ _ _ _ _ _ _ 59
Comparison w.ith Experiment.. ____________________ .. _ _ _ _ 59
Angle of Zero Lift_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 14
REFERENCES _____________ .. ______________________________ 60
Methods of calculation ______________________ .... _ _ _ _ 14
TABLES ___________________ .... ___ .. ________________________ 64
Numerical examples______________________________ 14
SUPPLEMENTARY DATA:
Description of Flow around Airfoils ___ ~-~~~-:c __- ___ ~______ 15 I-Basic Thickness Forms _______ .. ____ . _. ___ . _____ . _ ___ 69
EXPERIMENTAL CHARACTERISTICS_ _ _ __ _ _ __ _ _ __ _ _ __ _ _ __ _ _ _ _ _ 16- J.I-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___ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 12~
III
REPORT No. 824
SUMMARY OF AIRFOIL DATA
By IRA /,H . ABBOTT, ALBERT E. VON DOENHOFF, and LOUIS S. STIVERS, JR.
SUMMARY Recent information on the aerodynamic characteristics of
NACA airfoils is presented. The historical development of
Recent airfoil data for both flight and 'wind~tunnel tests have
NACA airfoils is briefly reviewed. New data are presented
been collected and correlated insojar as possible. The flight
that permit the rapid calculation of the approximate pressure
data consist largely of drag measurements made' by the wake~
distributions for the older NACA four-digit and five-digit
survey method. Most of~he data on airjoil section characteris~
airfoils by the same methods used for the N ACA 6-series
tics were obtained in the Langley two-dimensionallow~turbulence
airfoils. The general methods used to derive the basic thick
pressure tunnel. Detail data necessary for the application of
ness forms for N ACA 6- and 7- series airfoils together with
NAOA 6~series airfoils to wing design are presented in sup
their corresponding pressure distributions are presented.
plementary figures, together with recent datajor the NAOA 00-,
14-, 24-, 44-, and 230-series airjoils. The general methods Detail data necessary for the application of the airfoils to
wing design are presented in supplementary figures placed at
used to derive the basic thickness jorms jor NAOA 6- and
the end of the paper. The report includes an analysis of
7 -series airjoils and the'ir corresponding pressure distributions
are presented. Data and methods are given jor rapidly obtain the lift, drag, pitching~moment, and critical-speed charac:'
teristics of the airfoils, together with a discussion of the
ing the approximate pressure distributions jor N AOA 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 oj 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.
of application.
Data on high-lift devices are presented. Problems associated
Numbered figures are used to illustrate the text and to
with lateral-control devices, leading-edge air intakes, and inter
present miscellaneous data. Supplementary figures and
ference are briefly discussed. The data indicate that the effects
tables are not numbered but are conveniently arranged at
oj surface condition on the l~ft and drag characteristics are at
the end of the report according to the numerical designation
least as large as the effects of the airfoil sha,pe and must be
of the airfoil section within the following headings:
considered in airfoil selection and the prediction of wing charac
I-Basic Thickness Forms
teristics. Airjoils permUting extensive laminar flow, such as
II-Data. for Mean Lines
the NAOA 6-series airfoils, have much lower drag coefficients
III-Airfoil Ordinates
at high speed and cru~~sing lift coefficients than earlier types of
IV--Predicted Critical Mach Numbers
airfoils if, and only if, the wing surfaces are suffic1~ently smooth
V-Aerodynamic Charactel'is tics of Various Airfoil
and fair. The NAOA 6-scries airfoils also ha,1'e favorable
Sections
crit?:cal-speed character'istics and do not appear to present
These supplementary figures and tables present the basic
1Lnu8ual problems associated with the applicat1:on oj high-l'i:ft
data for the airfoils.
and lateral-control devices.
SYMBOLS
INTRODUCTION
aspect ratio
A considerable amount of airfoil data has been accumulated Fourier series coefficients
from tests in the Langley two-dimensional low-turbulence mean-line designation, fraction of chord from lead
tunnels. Data ha,ve 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, ba,sic length
high-lift devices, surface irregularities, and interference. usually considered unity
Some data are also available on the effects of ai.rfoil section wing span
on aileron characteristics. Although a large amount of these flap span, inboard
data has been published, the scattered nature of the data flap span, outboard
and the limited objectives of the reports have prevented drag coefficient
adequate analysis and interpretation of the results. The drag coefficient at zero lift
purpose of this report is to summarize these data and to lift coefficient
correlate and interpret t,hem insofar as possible. increment of maximum lift cuused by flap deflection
2 REPORT NO. 824-·NATIONAL ADVISORY COMMITTEE FOR AERONAUTiC;:,
C chord XL abscissa of lower surface
Ca aileron chord Xu absciss!'\. of upper surface
Cd section drag coefficient G},. chordwise position of transition
minimum section drag coefficient
Cdml~
flap chord, inboard Y distance perpendicular to chord
Cfi
flap chord, outboard Ya mean-line ordinate
CfO
YL ordinate of lower surface
91
flap-chord ratio
C YI ordinate of symmetrical thickness distrihution
section aileron hinge-moment coefficient (~) Yu ordinate of upper surface
goc Z complex variable in circle plane
increment of aileron hinge-moment coefficient at z' complex variable in near-cireIe plane
constant lift a angle of attack
!lCHO hinge-moment parameter !lao
section aileron effectiveness parameter, ratio of
Cl section lift coefficient .10 change in section angle of attack to increment of
design section lift coefficient
Cli aileron deflect,ion at a constant value of lift
moment coefficient about aerodynamic center
Cma.e. coefficient
moment coefficient about quarter-chord point
Cme/4 angle of zero lift
C section normal-force coefficient
n section angle of attack
D drag
increment of section angle of attack
!lH . loss of total pressure
Ho section angle of attack corresponding to design
free-stream total pressure
lift coefficient
h section aileron hinge moment
he exit height flap 01' aileron deflection; down deflection is positi,-e
flap deflection, inboard
k constant
flap deflection, outboard
L lift
i\,irfoil parameter (IP-()
M Mach number
value of at trailing edge
Mer critical Mach number E
s complex variable in airfoil plane
OU,OL typical points on upper and lower surfaces of airfoil
O angular coordinate of z'; also, angle of which tangent
(P-Po)
p pressure coefficient is slope of mean line
go
critical pressure coefficient . (TiP chord)
taper ratIO Root chord
resultant pressure coefficient; difference between
local upper-and lower-surface pressure coefficients Effective Reynolds number)
P T t urb u Ie nce f ac t or ( Test Reynolds number
local static pressure; also, angular velocity in roll in
pb/2V angular coordinate of z
Po
free-stream static pressure airfoil parameter determining radial co.)rdinato of z
pb/2V helix angle of wing tip average value of 1ft (~17r 502 1ft dIP)
f}o free-stream dynamic pressure ..
R Reynolds number
Rer critical Reynolds number HISTORICAL DEVELOPMENT
s P)
pressure coefficient (H~o
The development of types of NACA airfoils now in com
first airfoil thickness ratio mon use was started in 1929 with a systematic investigation
second airfoil thickness ratio of a family of airfoils in the Langley variable-density tunnel.
free-stream velocity Airfoils of this family were designated by numbers having
inlet velocity four digits, such as the NACA 4412 airfoil. All airfoils of
local velocity this family had the same basic thickness distribution (refer
increment of local velocity ence 1), and the amount and type of camber was systemati
increment of local velocity caused by 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 sections having higher maximum lift
velocity ratio corresponding to thickness i1
coefficients and lower minimum drag coefficients than those
of sections developed before that time. The investigation
velocity rat.io corresponding to thickness t2
also provided information on the changes in aerodynamic
distance along chord characteristics resulting from variations of geometry of the
mean-line abscissa mean line and thickness ratio (reference 1).
SUMMARY OF AIRFOIJ" 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. N ACA 2-to 5-series sections (reference 11). Experience with
.A lthough 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 sufficien tly 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 cOplparatively large
friction coefficients for flat plates indicated that nearly all values of the Reynolds number if the airfoil surfaces were
of the profile drag under such conditions was attributable sufficiently 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 air 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 designJift coefficient when sm09th, the drag of such
previously unsolved experimental problem requiring the sections became unduly large when rough, particularly at lift
development of new t.est 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 demons~rated The NACA 6-series basic thickness 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 Reynolds numbers. Uncert.ainty with "Methods of Derivation of Thick.9.ess 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 slilctions 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 N ACA families con
of adeql.late 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 N ACA 16-series (reference 10) airfoils.
4 REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAU'fICS
y
- - - ---
--M-ean l-ine- --
Chord Ime
I
I
I\\ \ ::OL(:X:L-)-:Y,;L~)-----~------------- XXLv ==xx+-YY,t ssiinn 88 YYLu ==YYcc -+Yyt, ccooss 88
\, Rodius fhrou9h end of chord
'(mean-line slope ot 05 percent chord) 1.00
SAMPLE CALCULATIONS FOR DERIVATION OF THE KACA 65,3-818, a=1.0 AIRFOIL
X (101)' (1b1), tan 0 sin 0 cos 0 YI sin 0 y, cos 0 I Xu I 1/U XL 1!L
0- .005 0 .-01324 0 ;"(;0200 -' -0--.3-3-6-9--6- "6:3i932' '6:94765-' 0 .00423 0 .01255 0. ooon 0 .01455 0 .00923 -0.0 1055
.05 .03831 .01264 .18744 .18422 .98288 .00706 .03765 .04294 .05029 . C5706 -.02501
.25 .08093 .03580 .06996 .06979 .99756 . 00565 .08073 .24435 .11653 .25565 -.04493
.50 .08593 .04412 0 0 1.00000 0 .08593 .50000 .13005 .50000 -.04181
.75 .04456 .03580 -.06996 -.06979 .99756 -.00311 .04445 .75311 .08025 .74689 -.00865
1.00 0 0 ---------- ---------- ---------- a a 1.00000 0 1. 00000 a
o Thickness distribution obtained from ordinates of the N A OA 65,3--018 airfoil.
b Ordinates of the mean line, 0.8 of the ordinate for c',= 1.0.
, Slope of radius through end of chord.
FIGURE I.-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 the 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 through the end of the chord for such mean lines is
of the mean line. The chord line is defined as the straight
usually taken as the slope of the mean line at ~=0.005. This
line connecting the leading and trailing edges. Ordinates of c
the cambered airfoil are obtained by laying off the thickness procedure is justified by the manner in which the slope
distribution perpendicular to the mean line. The abscissas, increases to the theoretically infinite value as x/c approaches
ordinates, and slopes of the mean line are designated as Xc, o. The slope increases slowly until very small values of x/c
Yc, and tan (J, respectively. If Xu and Yu represent, respec are reached. Large values of the slope are thus limited to
tively, the abscissa and ordinate of a typical point of the values of x/c very close to 0 and may be neglected in practical
upper surface of the airfoil and Y t is the ordinate of the airfoil design.
symmetrical thickness distribution at chordwise position X, Tables of ordinates are included in the supplementary data
the upper-surface coordinates are given by the following for all airfoils for which standard characteristics are presented.
relations:
xu=X-Yt sin (J (1) NACA FOUR-DIGIT-SERIES AIRFOILS
Numbering system.-The numbering system for the
(2)
NACA airfoils of the four-digit series (reference 1) is based
on the airfoil geometry. The first integer indicates the
The corresponding expressions for the lower-surface coordi
maximum value of the mean-line ordinate Yc in percent of the
nates are
chord. The second integer indicates the distance from the
(3) leading edge to the location of the maximum camber in
tenths of the chord. The last two integers indicate the
(4) airfoil thickness in percent of the chord. Thus, the NACA
2415 airfoil has 2-percent camber at 0.4 of the chord from the
The center for the leading-edge radius is found by drawing leading edge and is 15 percent thick.
a line through the end of the chord at the leading edge with The first two integers taken together define the mean line.
the slope equal to the slope of the mean line at that point for example, the N ACA 24 mean line. The symmetrical air
and laying off a distance from the leading edge along this line foil sections representing the thickness distribution for a
equal to the leading-edge radius. This method of construc family of airfoils are designated by zeros for the first two
tion causes the cambered a.irfoils to p.roject slightly forward integers, as in the case of the N ACA 0015 airfoil.
5
SUMMARY OF AIRFOIL DATA
000T9h, ic0k0n1e0s,s d0i0s1t2ri, bu0t0i1o5n,s .-0-0-1D8a, ta0 f0o2r1 ,t hea nNd A0C0A24 0 0t0h6ic,0k0n0e8ss, airTfohiilcs konfe sths ed Nis AtriCbAu tifoivnes-.d-i-gTith es etrhieisc kanrees sth dei sstarmibeu taiso ntsh ofsoer
distributions are presented in the supplementary figures_ for airfoils of the NACA four-digit series.
Ooctvtb(hhvobaurIeerrtdVtrai i ie)oevtin2hsncnea, it le,tcl oawdeykcsas nh ibn bteiytdyycfsh o h siesrT o nc irfhcsaas i relnqtvieeointuolmqedgVa uro erm( itrenrvhase teareesfdeolne e fittr' :aansea:t. btnlvte msauhct o/eoleFe at thpth1iteinthr)oched.de kdis u cn oelckToenr(enrdswthedseeie-fen dsse bssa.pr ly teeee nmearscTcadd haet ihiinay npoen 9 grs.pg)e- eb.resi eonsd dVpuggVaoro eaeaatr bla nutltruid geaaoeiswlidnsesn tie erutoo0riode1s ff 2lfivmmino5afaeu 0tMr,at yry h,-cn em debol ai ileeenngisfna aeioflnetimab ic rnbistelleaieyey nnirf s nietowte..seh r-s imde.Dta hTb rra aeahytAts thu a ipmleosfl r o ,f uem ot4rlsad rt:ae tbi2ahxnptu thIeltaalyeme an dmi tdfunN eo emgidrAfna o t n Cohtrvth rehaAltdei lhenu di e 2neeNas 1sasutN 0At apge,Af Cip of2voOolrA2ere rA0 n mew,t4 a hhe63i2cetn4e03hh 0rt 0 N ae ,mtmri mhAny2eee e 4Ca afaf0donAnin,ger sualll2tiiiirnghnn3nedne0esee
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 l-SERIES AIRFOILS
intermediate thickness ratios may be obtained approxi Numbering systern.-The NACA I-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; thus, series designation. The second integer indicates the dis
tance in tenths of the chord from the leading edge to the
(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 !::.Va/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 yo, the referred to as the NACA 16-seI'ies sections.
slope dYeldx, the design lift coefficient eli and the corre Thickness distributions.-Data for the NACA 16-006,
sponding design angle of attack ai, the moment coefficient 16-009, 16-012, 16-015, 16-018, and 16-021 thickness
cramteii4o' th!:e:. vr/Ve.s ulTtahnet ptrheesosruertei ccaole fafiecrioednty nPaRm, iacn dc htahrea cvteerliosctiictys dtaisrtyr ifbiguutiroens.s (Trehfeerseen dcea ta10 a) rea rsei mprielasre ninte fdo rinm tthoe tshuep dpaletma efonr
were obtained from thin-airfoil theory. All tabulated values those airfoils of the N ACA 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 Ye, 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=1.0), which is described under the section for the
plying the data for the N ACA 62 mean line by the ratio 2: 6, N ACA 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. d.esignation.
NACA 6-SERIES AIRFOILS
NACA 'FIVE.DIGIT-SERIES AIRFOILS Numbering system.-The N ACA 6-set'ies airfoils are usu
ttattiitptttchhshhnochhhe aeeettNe eiturmeeoc h u sctsgradkrheNmueb ieemen sbesnehrtAsteei itrsoaiitncs lr gch Csuotoastaisnre o fncAlte n ig a gaWt,e(nl taelU rte-h~i ,erle,pihptvao ts erffh ase e.eoen pc ecslycrr-d oeviracedhgsoyer emneTionitcffnsnngce f reh baideotdimtlnceem tsihif oit f c r ie.e tlfti ss2a-honc ai etT ntfcet moser ha; co itht n fnteehah tteieeehhs drxfaet-rc s fwee rih nm,ihtci3ma c saouoddhic)s iln mu.erieo tf sbdteno imsrebnttra.fitdag hT g ie ts,sneteon erechhtaTgcirf diaene .lnecenhm i g0 rsduffeorfs .t b ieTrm3 ns ahroeNlc,ys hinaa bmrontsaeAdt;s heedti i evrfsaaCitntgfc emchs ehirtAeoct ca eeieho ommsiitg fpeteiml n2oescrenba dd3re rkeatgi t0 i smntdanhasnii1reianniteneiiar2nnatctsd f dx iuntgto soiaae eic dcc itmniidrlenhhearersa d fft ait utboohoegrooirimdiiynfsfes foll amitplticiTittnihlhnnnhoiofle hoeey t esew.ntep n f it etfhtl de htsinie "yereocieiTsats2ccisp rnhhd eiehi"hed seongnin o n.esewftno ftfo sag io"atifivnom n ldtg T3leo femggenoti "dhrdens iwata e vgneihittfbbgaiemihe teonollynnhn e leagunafl , s cos oaml t pthtitiaw riynho rNos tb teipene iprwtonAxs deh i.rvgss d-uoe .eC ud e sa so rtiueAsdTsfabgheud nhiTn iaeg.rhmd tg hds eg i6ertienc eei5sbcarivou Wa" sn, dee3imdmntsl in5so-oheyt e md2"beownelmst1 iinedhntianc 8smgrttd e ea h h,gnte t tetehseheoidnaxutav e greaodtios=te isiseetethfcsomtOie dts egatnhsoit.e.th lng h e5"hn aae ner s, ieantl r b Fehl i-c=wfifcoulretoohfitahti0n titnr oitlnh ei .ochec erf5g etdhon o oshe"xado e ue"ria b afemfrrc6sofftdmsefskiit f"ah-ihwccaz nglpc oiiioeltieenleenwiesreanisnsafode s,dsst.t t
mean line (a= 1.0) has been used.
of 12 percen~.