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NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
REPORT No. 824
¸
_/i< [
SUMMARY OF AIRFOIL DATA
t_,-_G,
}-
.._vll#11_! H. ABBOTT, ALBERT E. YON DOENHOFF
"_ ; and LOUIS S. STIYERS, Jr.
1945
._-= -::_ : For sale by the Superintendent of Doeunxents, U.S. Go,, i_ment Printing Ofnce. Washington 25.D.C.:: : __:._._ ' .......... Price tlJ0
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REPORT No. 824 q
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
P
National Advisory Comnfittee for Aeronauticstteadquarter_', 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
Bureau of Standards.
CH._RLES G. ABBOT, So. D., Vice Chairnmn, Executive Committee,
Secretary, Smithsonian Institution.
]tENR'¢ H. ARNOLD, General, United States Army, Comnianding
General, Army Air Forces, War Department.
_rlI,I,IAM A. M. BURI)EN, Assistant Secretary of Commerce for
Aerolmutics.
VANNEVAR BUSH, Sc. 1)., Director, Office of Scientific Research
and Devclot)ment, Washington, D. C.
WILLIAM F. I)URAND, Ph.D., Stanford Ulfiversity, California.
OLIVER 1 ). E(:HOLS, Major General, United Status Army, Chief
of Mat6rM, Maintenance, and l)istribmion, Army Air Forces,
War Depart nlent.
AUBREY W. FITCH, Vice Admiral, United States Navy, Deputy
Chief of Naval Operations (Air), Navy Department.
WILL1AM LITTLEWOOI), M. E., Jackson Heights, Long Island,
N.Y.
FRANCIS W. REICHFLDERFER, So. D., Chief, United States
Weather Bureau.
LAWRENCE B. RICHARDSON, Rear Admiral, Untied States Navy,
Assistant Chief, Bureau of Aeronautics, Navy Departmdnt.
EDWARD WARNER, So. D., Civil Aeronautics Boar(t, Washington,
D.C.
ORVILLE WRI(;HT, So. D., Dayton, Ohio.
THEODORE P. _Valt;wr, So. D., Ad,ninistrator of Civil Aero-
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
II
OFFICE OF AERONAUTICA|, INTELLIGENCE, Washinglon, I). C.
('olleetion, classification, compilation, and d|'ssemimltion of scientific and technical information on ae,'onauties
CONTENTS
Page
SUMMARY .............................. 1
INTRODUCTION ................... 1
SYMBOLS ................................... 1
HISTORICAL DEVELOPMENT ..................... 2
DESCRIPTION OF AIRFOILS ........................ 3
Method of Combining Mean Lines and Thickness
Distributions ............................. 3
NACA Four-Digit Series Airfoils ............ 4
Numbering system ................. 4
Thickness distributions ............... 5
Mean lines_ : ................... 5
NACA Five-Digit Series Airfoils ......... 5
Numbering systeni ................. 5
Thickness distributions ............... 5
Mean lines ..................... 5
NACA 1-Series Airfoils .............. 5
Numbering system ............... 5
Thickness distributions .............. 5
Mean lines ................... 5
NACA 6-Series Airfoils .............. 5
Nunabering system ................. 5
Thickness distributions ............ 6
Mean lines ................ 6
NACA 7-Series Airfoils ..................... 7
Numbering system ........... 7
Thickness distributions ............. 7
THEORETICAL CONSIDERATIONS ............... 8
Pressure Distributions ................... 8
Methods of derivation of thickness distributions __ 8
Rapid estimation of pressure distributions ..... 10
Numerical examples ................... 12
Effect of camber on pressure distribution ...... 13
Critical Mach Number .................. 13
Moment Coefficients ................ 14
Methods of calculation ......... 14
Numerical examples ............. 14
Angle of Zero Lift ................. 14
Methods of calculation .............. 14
Numerical examples ............... 14
Description of Flow around Airfoils ....... 15
EXPERIMENTAL CHARACTERISTICS ............... 16
Sources of Data .................... 16
Drag Characteristics of Smooth Airfoils .......... 16
Drag characteristics in low-drag range ........... 16
Drag characteristics outside low-drag range ........ 18
Page
iil
EXPERIMENTAL CHARACTERISTICS--Continued
Drag Characteristics of Smooth Airfoils--Continued
Effects of type of section on drag characteristics ..... 18
Effective aspect ratio ..................... 21
Effect of surface irregularities on drag ................. 22
Permissible roughness .......................... 22
Permissible waviness ......................... 22
Drag with fixed transition ............... 24
Drag with practical construction methods ...... 24
Effects of propeller slipstream and airplane vibration_ 29
Lift Characteristics of Smooth Airfoils .............. 30
Two-dimensional data .................. 30
Three-dimensional data ............... 37
Lift Characteristics of Rough Airfoils ........... 37
Two-dimensional data ........... 37
Three-dimensional data ................. 38
Unconservative Airfoils ..... : ....... 39
Pitching Moment ................... 40
Position of Aerodynamic Center ................ 43
High-Lift Devices ................. 43
Lateral-Control Devices ..................... 43
Leading-Edge Air Intakes .................. 49
Interference ............................ 50
APPLICATION TO WING DESIGN ............... 51
Application of Section Data ............... 51
Selection of Root Section .................. 51
Selection of Tip Section ................. 52CONCLUSIONS ................................. 52
APPENDIX--_IETHODS OF OBTAINING DATA IN THE LANGLEY
Two-DIMENSIONAL Low-TuRBULENCE TUNNELS ......... 54
Description of Tunnels .................. 54
Symbols ..................... __ .... 54
Measurement of Lift ..................... 55
Measurement of Drag .................. 56
Tunnel-Wall Corrections ............... 57
Correction for Blocking at High Lifts ........ 59
Comparison with Experiment ............ 59
REFERENCES ......................... 60
TABLES ......................... 64
SUPPLEMENTARY DATA :
I--Basic Thickness Forms .............. 69
II--Data for Mean Lines ................ 89
III--Airfoil Ordinates .................... 99
IV--Predicted Critical Mach Numbers ............... 113
V--Aerodynamic Characteristics of Various Airfoil
Sections ........................... 129
REPORT No. 824
SUMMARY OF AIRFOIL DATA
By IRA H. ABBOTT, ALBERT E. VON DOENHOFF, and Lovls S. STIVERS, JR.
SUMMARY
ReceT_t airfoil data for both flight and wind-tunnel tests have
been collected and correlated insofar as possible. The flight
data consist largely of drag measurements made by the wake-
survey method. Most of the data on airfoil section characteris-tics were obtained in the Langley two-dimensional low-turbulence
pressure tunnel. Detail data necessary for the application o]
NACA 6-series airfoils to wing design are presented in sup-
plementary figures, together with recent data for the NACA 00-,
1_-, 2_-, _-, and 230-series airfoils. The general methods
used to derive the basic thickness forms for NACA 6- and
7-series airfoils and their corresponding pressure distributions
are presented. Data and methods are given for rapidly obtain-
ing the approximate pressure distributions .for NACA four-
digit, five-digit, 6-, and 7-series airfoils.
The report includes an analysis of the lift, drag, pitching-
moment, and critical-speed characteristics of the airfoils, to-
gether with a discussion of the effects of surface conditions.Data on high-lift devices are presented. Problems associated
with lateral-control devices, leading-edge air intakes, and inter-
ference are briefly discussed. The data indicate that the effects
of sub:face condition on the lift and drag characteristics are at
least as large as the effects of the airfoil shape and must be
considered in airfoil selection and the prediction of wing charac-
teristics. Airfoils permitting extensive laminar flow, such as
the NACA 6-series airfoils, have much lower drag coe_icients
at high speed and cruising lift coeficients than earlier types of
airfoils if, and only if, the wing surfaces are suy_ciently smooth
and fair. The NACA 6-series airfoils also have favorable
critical-speed characteristics and do not appear to present
unusual problems associated with the application of high-liftand lateral-control devices.
INTRODUCTION
•A considerable amount of airfoil data has been accumulated
from tests in the Langley two-dimensional low-turbulencetunnels. Data have also been obtained from tests both in
other wind tunnels and in flight and include the effects of
high-lift devices, surface irregularities, and interference.Some data are also available on the effects of airfoil section
on aileron characteristics. Although a large amount of these
data has been published, the scattered nature of the data
and the limited objectives of the reports have prevented
adequate analysis and interpretation of the results. The
purpose of this report is to summarize these data and to
correlate and interpret them insofar as possible.
Recent information on the aerodynamic characteristics of
NACA airfoils is presented. The historical development of
NACA airfoils is briefly reviewed. New data are presented
that permit the rapid calculation of the approximate pressure
distributions for the older NACA four-digit and five-digit
airfoils by the same methods used for the NACA 6-series
airfoils. The general methods used to derive the basic tki_k-
ness forms for NACA 6- and 7-series airfoils together with
their corresponding pressure distributions are presented.
Detail data necessary for the application of the airfoils to
wing design are presented in supplementary figures placed at
the end of the paper. The report includes an analysis of
the lift, drag, pitching-moment, and critical-speed charac-
teristics of the airfoils, together with a discussion of the
effects of surface conditions. Available data on high-lift
devices are presented. Problems associated with lateral-
control devices, leading-edge air intakes, and interference
are briefly discussed, together with aerodynamic problems
of application.
Numbered figuces are used to illustrate the text and to
present miscellaneous data. Supplementary figures and
tables are not numbered but are conveniently arranged at
the end of the report according to the numerical designation
of the airfoil section within the follo_'ing headings:I--Basic Thickness Forms
II--Data for Mean Lines
III--Airfoil Ordinates
IV--Predicted Critical Mach Numbers
V--Aerodynamic Characteristics of Various AirfoilSections
These supplementary figures and tables present the basicdata for the airfoils.
A
An, B,a
b
b_
bIo
C,
CDL 0
_5¥ 1
SYMBOLS
aspect ratioFourier series coefficients
mean-line designation, fraction of chord from lead-
ing edge over which design load is uniform; in
derivation of thickness distributions, basic length
usually considered unity
wing spanflap span, inboard
flap span, outboard
drag coefficient
drag coefficient at zero liftlift coefficient
increment of maximum lift caused by flap deflection
1
¢
Ca
Ca
Cdmi n
cf_
¢fo
cf
c
CH
_eu
ACH_
V_
el l
Cma. c,
Cmc/4
Cn
D
AH
Hoh
h,k
L
M
M.OU, OL
P
Per
P.
P
PO
pb/2V
qoR
Re,
S
tl
t:V
At"
AVa
(") qV
x
xc
REPORT N'O. 824--NATIONAL ADVISORY COMMITTEE, FOR AERONAUTICS
chord
aileron chord
section drag coefficient
minimum section drag coefficient
flap chord, inboardflap chord, outboard
flap-chord ratio
section aileron hinge-moment coefficient (q_c_)
increment of aileron hinge-moment coefficient atconstant lift
hinge-moment parametersection lift coefficient
design section lift coefficient
moment coefficient about aerodynamic center
moment coefficient about quarter-chord pointsection normal-force coefficient
dragloss of total pressure
free-stream total pressure
section aileron hinge moment
exit heightconstant
liftMach number
critical Mach number
typical points on upper and lower surfaces of airfoil
pressure coefficient (_L_oP°)qcritical pressure coetficient
resultant pressure coefficient; difference between
local ul)per- and lower-surface pressure coefficients
local static pressure; also, angular velocity in roll in
pb/2V
free-stream static pressure
helix angle of wing tip
free-stream dynamic pressureReynolds number
critical Reynolds mmfl)er
pressure coefficient (_)
first airfoil thickn(.ss ratio
second airfoil thickness ratio
free-stream velocity
inlet velocity
local velocity
increment of local vdocity
increment of local velocity caused 1)y additional
type of load distribution
velocity ratio correspon(ling to thi('kness t,
velocity ratio corresponding to thi(,l_ness t2
distance along chordmean-line abscissa
XL
Xu
(x),,Y
Yc
yL
yt
Yvz
z p
Ol
A(_ o
A5
Ol lo
Ol o
Aot o
Oti
_.TE
0
T
¢
_o
abscissa of lower surface
abscissa of upper surface
chordwise position of transition
distance perpendicular to chordmean-line ordinate
ordinate of lower surface
ordinate of symmetrical thickness distribution
ordinate of upper surface
complex variable in circle plane
complex variable in near-circle plane
angle of attack
section aileron effectiveness parameter, ratio of
change in section angle of attack to increment ofaileron deflection at a constant value of lift
coefficient
angle of zero lift
section angle of attack
increment of section angle of attack
section angle of attack corresponding to designlift coefficient
flap or aileron deflection; down deflection is positive
flap deflection, inboard
flap deflection, outboard
airfoil parameter (6--0)value of e at trailing edge
complex variable in airfoil planeangular coordinate of z' ; also, angle of which tangent
is slope of mean line
{ Tip chord "_taper ratio \Root chord/
{Effective Reynohls number'_turbulence factor \ Test Reyimldsnumber ]
angular coordinate of z
airfoil parameter determining radial coordinate of z
average value of _b (21r£2_ ¢ d_)
HISTORICAL DEVELOPMENT
The development of types of NACA airfoils now in con>mon use was started in 1929 with a systenmtic investigation
of 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 of
this 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. This
investigation of the NACA airfoils of the four-digit series
produced airfoil se(,tions having higher maximum lift
coefficients and lower minimum drag co(,flieients than those
of sections developed before that time. The investigation
also provided infornmtion on the changes in aerodynamic
characteristics resulting from wtriations of geometry of the
mean line and thickness ratio (reference 1).
SU_/IMARY OF AIRFOIL DATA 3
The investigation was extended in references 2 and 3 toinclude airfoils with the same thickness distribution but
with positions of the maximum camber far forward on theairfoil. These airfoils were designated by numbers having
five digits, such as the NACA 23012 airfoil. Some airfoilsof this family showed favorable aerodynamic characteristics
except 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 (references 1 and 3 to 6), no extensive investigations of
thickness distribution were made. Comparison of experi-
mental drag data at low lift coefficients with the skin-
friction coefficients for fiat plates indicated that nearly all
of the profile drag under such conditions was attributable
to skin friction. It was therefore apparent that any pro-
nounced reduction of the profile drag must be obtained by a
reduction of the skin friction through increasing the relative
extent of the laminar boundary layer.
Decreasing pressures in the direction of flow and low air-stream turbulence were known to be favorable for laminar
flow. An attempt was accordingly made to increase the
relative extent of laminar flow by the development of ah'-
foils having favorable pressure gradients over a greater
proportion of the chord than the airfoils developed in refer-
ences 1, 2, 3, and 6. The actual attainment of extensive
laminar boundary layers at large Reynolds numbers was a
previously unsolved experimental problem requiring the
development of new test equipment with very low air-
stream turbulence. This work was greatly encouraged by
the experiments of Jones (reference 7), who demonstrated
the possibility of obtaining extensive laminar layers in flight
at relatively_ large R_l,,,_u_l_ ,_u,,,_,s.l"_ TT,_..._._.;_,._._._jwith
regard to factors affecting separation of the turbulent
boundary layer required experiments to determine the
possibility of making the rather sharp pressure recoveries
required over the rear portion of the new type of airfoil.
New wind tunnels were designed specifically for testing
airfoils under conditions closely approaching flight condi-
tions of air-stream turbulence and Reynolds number. The
resulting wind tunnels, the Langley two-dimensional low-
turbulence tunnel (LTT) and the Langley two-dimensional
low-turbulence pressure tunnel (TDT), and the methods
used for obtaining and correcting data are briefly described
in the appendix. In these tunnels the models completely
span the comparatively narrow test sections; two-
dimensional flow is thus provided, which obviates difficulties
previously encountered in obtaining section data from
tests 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 lack
of adequate theory. The Theodorsen method (reference 9),
as ordinarily used for calculating the pressure distributions
about airfoils, was not sufficiently accurate near the leading
edge 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 (reference 10)
was obtained by empirical modification of the previously
used thickness distributions (reference 4). These NACA
16-series sections represented the first family of the low-drag
high-critical-speed sections.
Successive attempts to design airfoils by approximate
theoretical methods led to families of airfoils designated
NACA 2- to 5-series sections (reference 11). Experience with
these sections showed that none of the approximate methods
tried was sufficiently accurate to show correctly the effect
of changes in profile near the leading edge. Wind-tunnel
and flight tests of these airfoils showed that extensive laminar
boundary layers could be maintained at comparatively large
values of the Reynolds number if the airfoil surfaces were
smfficiently fair and smooth. These tests also provided
qualitative information on the effects of the magnitude of
the favorable pressure gradient, leading-edge radius, and other
shape variables. The data also showed that separation of
the turbulent boundary layer over the rear of the section,
especially with rough surfaces, limited the extent of laminar
layer for which the airfoils should be designed. The air-
foils of these early families generally showed relatively low
maximum lift coefficients and, in many cases, were designed
for a greater extent of laminar flow than is practical. It was
learned that, although sections designed for an excessive
extent of laminar flow gave extremely low drag coefficients
near the design lift coefficient when smooth, the drag of such
sections became unduly large when rough, particularly at lift
coefficients higher than the design lift. These families of
airfoils are accordingly considered obsolete.The NACA 6-series basic _hickness forms were derived by
new and improved methods described herein in the section
"Methods of Derivatinn of Thick-noss Distributions," in ac-
cordance with design criterions established with the objective
of obtaining desirable drag, critical Mach number, and
maximum-lift characteristics. The present report deals largely
with the characteristics of these sections. The develop-
ment of the NACA 7-series family has also been started.
This family of airfoils is characterized by a greater extent of
laminar flow on the lower than on the upper surface. These
sections permit low pitching-moment coefficients with mod-
erately high design lift coefficients at the expense of somereduction in maximum lift and critical Mach number.
Acknowledgement is gratefully expressed for the expert
guidance and many original contributions of Mr. Eastman
N. Jacobs, who initiated and supervised this work.
DESCRIPTION OF AIRFOILS
METHOD OF COMBINING MEAN LINES AND THICKNESS DISTRIBUTIONS
The cambered airfoil sections of all NACA families con-
sidered herein are obtained by combining a mean line and a
thickness distribution. The necessary geometric data and
some theoretical aerodynamic data for the mean lines and
thickness distributions may be obtained from the supple-
mentary figures by the methods described for each family ofairfoils.
4 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Y
• 10 t Ou(a'_
0 _'_. ' 1;I Chord hne
', "uc(_L, VL) _ -I ',, Rodius t,hrocgh end o£ chord
Ioli "(meon-h'me 5/ope Of" _5 percent c,boFd)
/
zu=x-y _ s_n 8 yu=yc.yt cos 8xc=z+y r s/n 0 YL=YO-Yt COS 8
SAMPLE CALCULATIONS FOR DERIVATION OF THE NACA 65,3-818, a=l.O AIRFOIL
1.00
O• 005• 05• 25.50• 75
1.00
yJ(_)
0.01324.0383l.080_]•08593.0445fi
0
y¢(b)
0• C0200• 012£;4.03580.04412.03580
0
tan 8
• 18744•06996
0--. 06996
sin 0
0. 31932.18422.00979
0-. 06979
cos 0
O. 94765•98288•99756
1.00000•99756
yt sin 0
0.00423.00706
.005650
--.003110
Yt cos 0
0.01255.03765-08073•08593-04445
0
_u
0•00077•04294• 24435
•50000• 75311
1. 00000
yu
O• 01455• 05029• 11653• 13O05• 08025
0
XL
0• 00923• 05706• 25565.50000• 74689
1.00000
yL
0--.01055--.02501--.04493--.04181--.008650
• Thickness distribution obtained from ordinates of the NACA 65,3-018 airfoil.
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 forms•
The process for combining a mean line and a thicknessdistribution to obtain the desired cambered airfoil section is
illustrated in 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 straigllt
line connecting the leading and trailing edges. Ordinates of
tim canibered airfoil are obtained by laying off the thickness
distribution 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 the
upper surface of the airfoil and y_ is the ordinate of tlle
symmetrical tllickness 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 are
x,.=x+y_ sin 0 (3)
YE=--Y_--yt cos 0 (4)
The center for the leading-edge radius is found by drawing
a line through tlle end of tlle chord at tlie leading edge with
the slope equal to the slope of the mean line at tllat point
and laying off a distance from the leading edge along tllis line
equal to the leading-edge radius. Tliis method of construc-
tion causes tile cambered airfoils to project sliglitly forward
of the leading-edge point. Because tim slope at the leading
edge is theoretically infinite for the mean lines having a
theoretically finite load at the leading edge, the slope of the
radius througli tlle end of tlle chord for such mean lines is
usually taken as tlle slope of the niean line at x--0.005. Thisc
procedure is justified by the nulnner in wllicll the slope
increases to tlle theoretically infinite vahle as x/c approaches
0. Tlle slope increases slowly until vel T snmll values of x/c
are reached. Large vahles of tlle slope are tllus limited to
vahles of x/c very close to 0 and may be neglected in practical
airfoil design.Tables of ordinates are included in the supplenlentary data
for all airfoils for wtlicll standard characteristics are presented
NACA FOUR-DIGIT-SERIES AIRFOILS
Numbering system.--The nunlbering system for theNACA airfoils of tlle fonr-(ligit series (reference 1) is based
on tlle airfoil geometry. Tile first integer indicates theinaxilmml value of the mean-line ordinate y_ in percent of tlle
cllord. Tlle second integer indicates the (listance from the
lea(ling edge to the location of tim maxinuml camber intentlls of the cllord. The last two integers indicate tlle
airfoil ttlickness in percent of the cllord. Thus, tlle NACA
2415 airfoil has 2-percent camber at 0.4 of ttle chord from tlle
leading 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 sections representing tlle thickness distribution for a
family of airfoils are designated by zeros for tile first two
integers, as in the case of tlle NACA 0015 airfoil.
SUMMARY OF AIRFOIL DATA 5
Thickness distributions.--Data for the NACA 0006, 0008,
0009, 0010, 0012, 0015, 0018, 0021, and 0024 thickness
distributions are presented in the supplementary figures.
Ordinates for intermediate thicknesses may be obtained
correctly by scaling the tabulated ordinates in proportion to
the thickness ratio (reference 1). The leading-edge radius
varies 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 were
obtained by Theodorsen's method (reference 9). Values of
the velocity increments Ava/I" induced by changing angle ofattack (see section "Rapid Estimation of Pressure Distribu-
tions") are also presented for an additional lift coefficient of
approximately unity. Values of the velocity ratio v/V for
intermediate thickness ratios may be obtained approxi-
mately by linear scaling of the velocity increments obtainedfrom the tabulated values of v/V for the nearest thickness
ratio; thns,
tl 1 (5)
Values of the velocity-increment ratio hva/V may be obtained
for intermediate thicknesses by interpolation.
Mean lines.--Data for the NACA 62, 63, 64, 65, 66, and 67
mean lines are presented in the supplementary figures.The data presented include the mean-line ordinates y_, the
slope dyJdx, the design lift coefficient c, and the corre-
sponding design angle of attack a,, the moment coefficient
C,n_,,,, the resultant pressure coefficient PR, and the velocity
ratio Av/V. The theoretical aerodynamic characteristics
were obtained from thin-airfoil theory. All tabulated values
for each mean line, accordingly, vary linearly with the maxi-
mum ordinate y_, and data for similar mean lines with
different amounts of camber within the usual range may be
Obtained simply by scaling the tabulated values. Data
for the NACA 22 mean line may thus 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 for
the NACA 64 mean line by the ratio 4:6.
NACA FIVE-DIGIT-SERIES AIRFOILS
Numbering system.--The numbering system for airfoils of
the NACA five-digit series is based on a combination of
theoretical aerodynamic characteristics and geometric char-
acteristics (references 2 and 3). The first integer indicates
the amount of camber in terms of the relative magnitude of
the design lift coefficient; the design lift coefficient in tenths
is thus three-halves of the first integer. The second and third
integers together indicate the distance from the leading edge
to the location of the maximum camber; this distance in
percent of the chord is one-half the number represented by
these integers. The last two integers indicate the airfoil
thickness in percent of the chord. The NACA 23012 airfoil
thus has a design lift coefficient of 0.3, has its maximum
camber at 15 percent of the chord, aml has a thickness ratioof 12 percent.
Thickness distributions.--The thickness distributions for
airfoils of the NACA five-digit series are the same as those
for airfoils of the NACA four-digit series.
Mean lines.--Data for the NACA 210, 220, 230, 240, and
250 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 line
vary linearly with the maximum ordinate or with the designlift coefficient. Thus, data for the NACA 430 mean line
may be obtained by multiplying the data for the NACA 230mean line by the ratio 4:2 and for the NACA 640 mean line
by multiplying the data for the NACA 240 mean line bythe ratio 6 :2.
NACA 1-SERIES AIRFOILS
Numbering system.--The NACA 1-series airfoils are des-
ignated by a five-digit number--as, for example, the
NACA 16-212 section. The first integer represents the
series designation. The second integer indicates the dis-
tance in tenths of the chord from the leading edge to the
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 liftcoefficient in tenths, and the last two numbers togetherindicate the thickness in percent of the chord. The com-
monly used sections of this family have minimum pressure
at 0.6 of the chord from the leading edge and are usuallyreferred to as the NACA 16-series sections.
Thickness distributions.--Data for the NACA 16-006,
16-009, 16-012, 16-015, 16-018, and 16-021 thickness
distributions (reference 10) are presented in the supplemen-tary figures. These data are similar in form to the data for
those airfoils of the NACA four-digit series, and data forintermediate thickness ratios may be obtained in the samemanner.
Mean lines.--The NACA 16-series airfoils as commonlyused are cambered with a mean line of the uniform-load
type (a=l.0), which is described under the section for the
NACA 6-series airfoils that follows. If any other type ofmean line is used, this fact should be stated in the airfoil
designation.NACA 6-S_.RIESAIRFOILS
Numbering system.--The NACA 6-series airfoils are usu-
ally designated by a six-digit number together with a state-
ment showing the type of mean line used. For example,
in the designation NACA 65,3-218, a=0.5, the "6" {sthe series designation. The "5" denotes the chordwise
position of minimum pressure in tenths of the chord beifind
the leading edge for the basic symmetrical section at zero
lift. The "3" following the comma gives the range of lift
coefficient in tenths above and below the design lift coefficient
in which favorable pressure gradients exist on both surfaces.
The "2" following the dash gives the design lift coefficientin tenths. The last two digits indicate the airfoil thickness
in percent of the chord. The designati0n "a=0.5" shows
the type of mean line used. When the mean-line designa-tion is not given, it is understood that the uniform-load
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
than one mean line, the design lift coefficient used in the
designation is the algebraic sum of the design lift coefficientsof the mean lines used, and the mean lines are described in
the statement following the number as in the following ease:
(a=0.5, cli=0.3 tNACA 65,3-2181a=1.0 ' c,_=--0.11
Airfoils having a thickness distribution obtained by linearly
increasing or deereasing the ordinates of one of the originallyderived thickness distributions are designated as in the follow-
ing example:NACA 65(318)-217, a=0.5
The significance of all of the numbers except those in the
parentheses is the same as before. The first number and thelast two numbers enclosed in the parentheses denote, respec-
tively, the low-drag range and the thickness in percent ofthe chord of the originally derived thickness distribution.
The more recent NACA 6-series airfoils are derived as
members of thickness families having a simple relationshipbetween the conformal transformations for airfoils of different
thickness ratios but having minimum pressure at the same
ehordwise position. These airfoils are distinguished from
the earlier individually derived airfoils by writing the num-
ber indicating the low-drag range as a subscript ; for example,
NACA 653-218, a=0.5
For NACA 6-series airfoils having a tlfickness ratio less
than 0.12 of the chord, the subscript number indicating the
low-drag range should be less than unity. Rather than usea fractional number, a subscript of unity was originally em-
ployed for these airfoils. Since tt, is usage is not consistentwith the previous definition of a number indicating the low-
drag range, the designations of airfoil sections having a thick-
ness ratio less than 0.12 of the chord are now given without
such a number. As an example, an NACA 6-series airfoil
having a thickness ratio of 0.10 of the chord would be
designated:NACA 65-210
Ordinates for the basic thickness distributions designated by
a subscript are slightly different from those for the corre-
sponding individually derived thickness distributions. Asbefore, if the ordinates of the basic thidkness distribution
have been changed by a factor, the low-drag range and thick-
ness ratio of the original thickness distribution are enclosed
in parentheses as follows:
NACA 65(a_8)-217, a=0.5
If, however, the ordinates of a basic thickness distributionhaving a thickness ratio less than 0.12 of the chord have been
changed by a factor, the number indicating the low-drag
range is eliminated and only the original thickness ratio isenclosed in parentheses as follows:
NACA 65c10)-211
If the design lift coefficient in tenths or the airfoil thickness
in percent of chord are not whole integers, the numbers
giving these quantities are usually enclosed in parentheses as
in the following designation:
NACA 65(3_s)-(1.5)(16.5), a=0.5
Some early experimental airfoils are designated by the in-sertion of the letter "x" immediately preceding the hyphen
as in the designation 66,2x-115.Thickness distributions.--Data for available NACA 6-series
thickness forms are presented in the supplementary
figures. These data are comparable with the sinfilar datafor airfoils of the NACA four-digit series, except that ordi-
nates for intermediate thicknesses may not be correctly ob-
tained by scaling the tabulated ordinates proportional to thethickness ratio. This method of changing the ordinates by
a factor will, however, produce shapes satisfactorily approx-
imating members of the family if the change in thickness
ratio is small. Values of v/V and hvdV for intermediate
thickness ratios may be approximated as described for the
NACA four-digit series.Mean lines.--The mean lines commonly used with the
NACA 6-series airfoils produce a uniform chordwise loading
from the leading edge to the point -=a and a linearly de-c
creasing load from this point to the trailing edge. Datafor NACA mean lines with values of a equal to 0, 0.1, 0.2,
0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 are presented in the
supplementary figures. The ordinates were computed by
the following formula, wlfich represents a simplification of
the original expression for mean-line ordinates given inreference 11 :
Y¢--c--2r(a+l)Cq ll_la[l(a x)-"log_la_X
61(l--X) 2 log. (1-- x)+14 (1--c/--4x'_" 1(a_;)2 _
:log_ ;+g-h c} (6)
where
• 1 [ (1 1) 1]g=--l--a a2 _log, a- +
[ 1 (1--a)2]h=l_ al 21 (l_a)2 log. (1--a) -- _ +g
The ideal angle of attack a: correst)onding to the design
lift coefficient is given by
(?l t = -- ]b eli
27r (a+ 1)
The data are presented for a design lift coefficient c,
equal to unity. All tabulated values vary directly withthe design lift coefficient. Corresponding data for similar
mean lines with other design lift coefficients may accordingly
be obtained simply by multiplying the tabulated values by
the desired design lift coeffieicnt.hi order to camber NACA 6-series airfoils, mean lines are
Usually used having vahles of a equal to or greater than thedistance from the leading edge to the location of nfinimum
pressure for the selected thickness distrilmtion at. zero lift.
For special purposes, load distrihutions other than those
corresponding to the simple mean lines may be obtaiz_ed 1)y
combining two or more types of mean line having positive or
negative values of the design lift coefficient. The geometric
SUMMARY OF AIRFOIL DA'I_A
and aerodynamic characteristics of such combinations ,nay be
obtained by algebraic addition of the values for the compo-nent mean lines.
NACA 7-SERIES AIRFOILS
Numbering system.--The NACA 7-series airfoils are desig-
nated by a number of the following type (reference 12):
NACA 747A315
The first number "7" indicates the series number. The
second number "4" indicates the extent over the upper sur-
face, in tenths of the chord from the leading edge, of the
region of favorable pressure gradient at the design lift coeffi-cient. The third number "7" indicates the extent over the
lower surface, in tenths of the chord from the leading edge,
of the region of favorable pressure gradient at the design lift
coefficient. The significance of the last group of three num-bers is the same as for the previous NACA 6-series airfoils.
The letter "A" which follows the .first three numbers is a
serial letter to distinguish different airfoils having parameters
that would correspond to the same numerical designation.
For example, a second airfoil having the same extent of
favorable pressure gradient over the upper and lower sur-
faces, the same design lift coefficient, and the same maximum
thickness as the original airfoil but having a different mean-line combination or thickness distribution would have the
Z© m
7
serial letter "B." Mean lines used for the NACA 7-series
airfoils are obtained by combining two or more of the pre-viously described mean lines. A list of the thickness dis-
tributions and mean lines used to form these airfoils is pre-
sented in table I. The basic thickness distribution is givena designation similar to those of the final cambered airfoils.
For example, the basic thickness distribution for the
NACA 747A315 and 747A415 airfoils is given the designationNACA 747A015 even though minimum pressure occurs at 0.4con both upper and lower surfaces at zero lift. Combination
of this thickness distribution with the mean lines listed in
table I for the NACA 747A315 airfoil changes the pressure
distribution to the desired type as shown in figure 2.Thickness distributions.--Data for available NACA 7-
series thickness distributions are presented in the supple-mentary figures. These thickness distributions are indi-vidually derived and do not form thickness families. The
thickness ratio may, however, be changed a moderate
amount--say 1 or 2 percent--by multiplying the tabulated
ordinates by a suitable factor without seriously altering theircharacteristic features. Values of(v/V2)and of v/V for thinn(,r
or thicker thickness distributions may be approximated bythe method of equation (5). If the change in thickness ratio
is small, tabulated values of Ava/V may be applied directlywith reasonable accuracy.
/.8
/'_ u/ ,per sur'foce)
/" NHCA 747A{215 basle _ _,
12 / "r,5/c,k'rvess d/t_tribu//on _ M
\\
\
.6
.4
0 ./ .2 .3 .d .5 .C .7 .8 ._ L0
x_e'
FIGURE 2.--Theoretical pressure distribution for the NACA 747A315 airfoil section at the design lift coefficient and the NACA 747A015 basic thickness distribution.
TABLE I.--ANALYSIS OF AIRFOIL DERIVATION
Mean-line combination _ I
IAirfoil
designation
747A315 ........ I
747A415 ........ ]
Basic thicknessform
a=0
747A015 ......................
747A015 .......................
a =0.1 a =0.2 a =0.3 a =0.4 a =0.5 a=0.6 a =0.7 a=0.8 a =0.9 a=l.0
....................................... I .763 .............
The numbers in the various columns headed "Mean-line combination" indicate the magnitude of the design lift coefficient used.
8 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
THEORETICAL CONSIDERATIONS
PRESSURE DISTRIBUTIONS
A knowledge of the pressure distribution over an airfoil is
desirable for structural design and for estimation of thecritical Mach number and moment coefficient if tests are not
available. The pressure distribution also exerts a strong
or predominant influence on the boundary-layer flow and,
hence, on the airfoil characteristics. It is therefore usuallyadvisable to relate the airfoil characteristics to the pressure
distribution rather tllan directly to the airfoil geometry.Methods of derivation of thickness distributions,--As
mentioned in the section "Historical Development," the
basic symmetrical thickness distributions of the NACA 6-and 7-series airfoils, together with their corresponding pres-
sure distributions, are derived by means of conformal trans-formations. The transformations used to relate the known
flow about a circle to that about an airfoil section were
developed by Theodorsen in reference 9. Figure 3 showsschematically the significance of the various phases of the
process.The circle about which the flow is originally, calculated has
its center at the origin and a radius of ae ¢°. The equation of
Z%_ I_21?t ?
Z'-plone
a(-2
FIGURE 3.--Transformations used to derive airfoils find calculate pressure distributions.
this circle in complex coordinates is
z = ae ¢o+_*
where
(7)
z complex variable in circle plane
angular coordinate of z
a basic length usually considered unity
_0 constant determining radius of circle
This true cir('le is transformed into an arbitrary, ahnost
circular curve by the relation
z>-= e (_-¢0)+i(0-_) (8)Z
the equation of the ahnost circular curve is
Z _ = gee+ io
where
z' complex variable in near-circle plane
ae_ radial coordinate of z'
0 angular coordinate of z'
(9)
In order for the transformation (8) to be conformal, it is
necessary that the quantity (0--_b) (given the symbol --_)
be the conjugate function of (_b--_0) ; that is, if _ is represented
by a Fom'ie," series of the form
_=_, A, sin 7_--_ B_ cos n4,1 l
then (4_--¢0) is given by the relaLion
1 1
This relationship indicates that, if tile flmction e(¢) is given,
(_b--¢0) can be calculated as a function of q_. Means of
performing this calculation arc presented in reference 13.
The transformation relating the ahnost circular curve to
the airfoil shape isa 2
_=z'-l-z, (10)
where _" is the comph,x variable in the airfoil plane. The
coordinates of tile airfoil x and y ave the real and imaginary
parts of i', respectively. These coordinates are given by therclatio,s
x=2a cosh _bcos 0 Ill)
y=2a sinh 4, sin 0 (12)
The veh)city distril)ution in terms of the airfoil 1)arameters
and e is given exaetiy for perfect fluid tlow by the expression
v [sin (ao+4,)+sin (ao+_r_:)] e_°
V--_ (sinh2_ + sin'20) _(1--d¢ ) +(-d_ ) _
(13)
k
SUMMARY OF AIRFOIL DATA
where
v local velocity over surface of airfoil
V free-stream velocity
ao section angle of attack
¢0 average value of ¢ (lf02_ _d_b)
er_ value of e at trailing edge
The basic symmetrical shapes were derived by assumingsuitable values of de�do as a function of 4_. These vahws were
chosen on the basis of previous experience and are subject tothe conditions that
0_4, =0
and de/dr_ at 4 is equal to de�d4) at --q_. These conditions
are necessary for obtaining closed symmetrieal shapes.de
Values of _(¢) were obtained simply by integrating d4_d4.
Values of ¢(4) were found by obtaining the conjugate of thecurve of e(¢) and adding a value _0 sufficient to make _evalue of _ equal to zero at ¢=7r. This condition assures asharp trailing-edge shape.
Inasmuch as small changes in the velocity distribution at anyde
point of the surface are approximately proportional to 1-t-d_
(see reference 14), the initially assumed values of de/deo werealtered by a process of successive approximations until thedesired type of velocity distribution was obtained. After thefinal values of _ and e were obtained, the ordinates of the basicthickness distribution were computed by equations (11)
and (12).
When these computations were made, it appeared that there
was an optimum value of the leading-edge radius dependentupon the airfoil thickness and the position of minimum
pressure. If the leading-edge radius was too small, a pre-mature peak in the pressure distribution occurred in the
immediate vicinity of the leading edge as the angle of attackwas increased. If the leading-edge radius was too large, apremature peak occurred a few percent of the chord behind the
leading edge. With the correct leading-edge radius, thepressure distribution became nearly flat over the forward
portion of the airfoil before the normal leading-edge peakformed at the higher lift coefficients. Curves of the param-eters ¢, e, d_/dep, de/dep plotted against _ for the NACA643-018 airfoil section are given in figure 4.
Experience has shown that, when the thickness ratio of an
originally derived basic form was increased merely by multi-plying all the ordinates by a constant factor, an unnecessarilylarge decrease in the critical speed of the resulting sectionoccurred. Reducing the thickness ratio in a similar manner
caused an unnecessarily large decrease in the low-drag range.For this reason, each of the earlier NACA 6-series sections was
individually derived. It was later found that it was possible
9
-./60 2 3z W 5 6 PTr
¢_, roc//bns
FIGURE 4.--Variation of airfoi! parameters ¢, e, _, d_ with tb for the NACA 643-018 air foil
section basic thickness form.
to derive basic airfoil parameters ¢ and e that could bemultiplied by a constant factor to obtain airfoils of various
thickness ratios, without having the aforementioned limita-tions in the resulting sections. Each of the more recentfamilies of NACA 6-series airfoils, in which numerical sub-scripts are used in the designation, having minimum pressureat a given chordwise position was obtained by scaling up anddown the basic values of the airfoil parameters _band e.
Theoretical pressure distributions(indicated bY(v) _)
for a family of NACA 65-series airfoils covering a range ofthickness ratios are given in figure 5 (a). This figure showsthe typical increase in the magnitude of the favorable pressuregradient, increase in maximum velocity over the surface, and
increase in the relative pressure recovery over the rear portionof the airfoil with increase in thickness ratio. Figure 5 (b)shows the pressure distribution for a series of basic thickness
forms having a thickness ratio of 0.15 and having mininmmpressure at various chordwise positions. The value of theminimum pressure coefficient is seen to decrease and the
magnitude of the pressure Fecovery over the rear portion ofthe airfoil to increase with the rearward movement of thepoint of minimum pressure.
10 REPORT NO. 824--NATION _L ADVISORY COMMITTEE FOR AERONAUTICS
Z8
EO
/6
(?)'/.2
.8
.4
........ _,'_CA CSe O/5----N_CAC_ 0/8 ___NAC_65,-OZJ
(a)
%
NAC_ E,5_-02;
rv'AC_ 642-015
IVAC_ G6_ 015
A<ACA 67,,/ 0'5
0 .Z ...4 6 .8 LO 0 .2 4 .6 .8 LO
_1_ _1_(a) Variation with thickness. (b) Variation with position of minimum pressure.
FIGURE 5.--Tbcorctical pressure distributions for some basic symmetrical NACA 6-series airfoils at zero lift.
The pressure distribution for one of the basic symmetricalthickness distributions at various lift coefficients is shown in
figure 6. At zero lift the pressure distributions over the
upper and lower surfaces are the same. As the lift coefficient
is increased, the slope of the pressure distribution over the
forward portion of the upper surface decreases until it becomes
fiat at a lift coefficient of 0.22 (the end of the low-drag range).
As the lift coefficient is increased beyond this value, the usual
peak in the pressure distribution forms at the leading edge.
Rapid estimation of pressure distributions.--In the dis-
cussion that follows, the term "pressure distribution" is used
to signify the distribution of the sbltic pressures on the upper
5O
z]O
30
_C
LO
FIGURE 6.--Theoretical pressure distribution for the NACA 652-015 airfoil at several liftcoefficients.
and lower surfaces of the airfoil along the chord. The term
"load distribution" is used to signify the distribution along
tli_ chord of tim normal force resulting from the difference in
pressure on the upper and lower surfaces.
The pressure distribution about any airfoil in potential
flow may be calculated accurately by a generalization of themethods of tile previous section. Although this method is
not unduly laborious, the computations required are too
long to permit quick and easy calculations for large numbersof airfoils. The need for a simple methotl of quickly obt'lining
pressure distributions with engineering accuracy has led tothe development of a methotl (reference 15) combining
features of thin- and thick-airfoil theory. This simple
method makes use of previously calculated characteristicsof a limited number of mean lines and thickness distributions
that may be combinetl to form large mlmbers of airfoils.
Thin-airfoil theory (references 16 to 18) shows that the
load distribution of a thin airfoil may be considered to consist
of: (1) a basic distribution at the ideal angle of attack aml
(2) an additional distribution proportional to the angle of
attack as measured from the ideal angle of attack.
The first load distribution is a function only of the shape of
the tllin airfoil, or (if the thin _lirfoil is considered to be a
mean line) of the mean-line geometry. Integration of this
load distribution along the chord results in a normal-force
coefficient which, at snmll angles of attack, is substantially
equ.fl to a lift coefficient c_, which is designated the ideal
or design lift coefficient. If, moreover, the camber of the
mean line is changed by multiplying tile mean-line ordinates
by a constant factor, the resulting load distribution, tim
ideal or design _lngle of attack _ and the design lift coelticient
c _ may be obtained sinll)ly by multiplying the original Wthles
by the same fi_ctor. The cllar_lcteristics of a large number of
mean lines are presented in both graphical and tabular form
in the supplementary figures. The lo_ld-distribution data
are presented both in the form of the resultant pressurecoefficient Pn and in the form of the corresponding velocity-
increment ratios A_/V. For positive design lift coefficients,
these velocity-increment ratios are positive on the upper
k
SUl_IMARY OF AIRFOIL DATA 11
surface and negative on the lower surface; the opposite is
true for negative design lift coefficients.
The second load distribution, which results from changing
the angle of attack, is designated herein thc "additional load
distribution" and tile corresponding lift coefficient is desig-nated the "additional lift coefficient." This additional load
distribution contributes no moment about the quarter-chord
point and, according to thin-airfoil theory, is independent of
the airfoil geometry except for angle of attack. The addi-
tional load distribution obtained from thin-airfoil theory is
of limited practical application, however, because this simple
theory leads to infinite values of the velocity at the leading
edge. This difficulty is obviated by the exact thick-airfoil
theory (reference 9) which also shows that the additional load
distribution is neither completely independent of the airfoil
shape nor exactly a linear function i_f the lift coefficient.
For this reason, the additional load distribution has been
calculated by the methods of reference 9 for each of the thick-
ness distributions presented in the supplementary figures.
These data are presented in the form of velocity-increment
ratios Ava/V corresponding to an additional lift coefficient of
approximately unity. For positive additional lift coeffi-
cients, these velocity-increment ratios are positive on the
upper surfaces and negative on the lower surfaces; the
opposite is true for negative additional lift coefficients.
In addition to the pressure distributions associated with
these two load distributions, another pressure distribution
exists which is associated with the basic symmetrical thick-
ness form or thickness distribution of the airfoil. This pres-
sure distribution has been calculated by the methods
described in the previous section for the condition of zero
lift and is presented in the supplementary figures as
which is equivalent at low Much numbers to the pressure
coefficient S, and as the local velocity ratio v/V. This
local velocity ratio is always positive and is the same for
corresponding points on the upper and lower surfaces of thethickness form.
The velocity distribution about the airfoil is thus considered
to be composed of three separate and independent com-
ponents as follows:
(1) The distribution corresponding to the velocity dis-tribution over the basic thickness form at zero angle ofattack
(2) The distribution corresponding to the design loaddistribution of the mean line
" (3) The distribution corresponding to the additional load
distribution associated with angle of attack
The velocity-increment ratios At,/V and ht,,/V correspond-
ing to components (2) and (3) are added to the velocity
ratio corresponding to component (1) to obtain the total
velocity at one point, from which the pressure coefficient S
is obtained; thus,
S_(v±A vV± _)2 (14)
When this formula is used, values of the ratios corresponding
to one value of x are added together and the resulting value
of the pressure coefficient S is assigned to the airfoil surfaceat the same value of x.
The values of v/V and of Av/V in equation (14) should,
of course, correspond to the airfoil geometry. Methodsof obtaining the proper values of these ratios from the values
tabulated in the supplementary figures are presented in the
previous section "Description of Airfoils."
When the ratio AvdV has the value of zero, the resulting
distribution of the pressure coefficient S will correspondapproximately to the pressure distribution of the airfoil
section at the design lift coefficient cz_ of the mean line, and
the lift coefficient may be assigned this value as a first ap-proximation. If the pressure-distribution diagram is inte-
grated, however, the value of ct will be found to be greaterthan cu by an amount dependent on the thickness ratio ofthe basic thickness form.
The pressure distribution will usually be desired at some
specified lift coefficient not corresponding to ca. For this
purpose the ratio AvdV must be assigned some value ob-
tained by multiplying the tabulated value of this ratio by a
factor y(a]. For a first approximation this factor may be
assigned the value
f(_) =c,-c,, (15)
where c_ is the lift coefficient for which the pressure distribu-
tion is desired. If greater accuracy is desired, the value of
dr(a) may be adjusted by trial and error to produce tim
actual desired lift coefficient as determined by integration
of the pressure-distribution diagram.
Although tiffs method of superposition of velocities has
inadequate theoretical justification, experience has shown
that the results obtained are adequate for engineering use.
In fact, the results of even the first approximations agre6
well widL experimeh_al dat_ and are adequate for at least
preliminary consideration and selection of airfoils. A com-
parison of a first-approximation theoretical pressure distri-
bution with an experimental distribution is shown in figure 7.
NACA t7612/5]-216, a = 06
2.O
Upper sc*_face_
/1.2 ..-o-- -'oN
.8
.4
\
-- Theory
o Exp er,).en /
0 .2 .4 .8 .8 LO
_/c
FIGURE 7.--Comparison of theoretical and experimental pressure distributions for tile NAC A
66(215)-216, a = 0 6 airfoil, c_ = 0.23.
12 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Some discrepancy naturally occurs between the results of
experiment and of any theoretical method based on potentialflow because of the presence of the boundary layer. These
effects are small, however, over the range of lift coefficients
for which the boundary layer is thin and the drag coefficient
is low.
Numerical examples.--The following numerical examples
are included to illustrate the method of obtaining the first-
approximation pressure distributions:
Example 1: Find the pressure coefficient S at the stationx=0.50 oll the upper and lower surfaces of the NACA
653-418 airfoil at a lift coefficient of 0.2.From the description of the NACA 6-series airfoils, it is
determined that this airfoil is obtained by combining the
NACA 65a-018 basic thickness form with the a=l.0 type
mean line cambered to a design lift coefficient of 0.4. The
following data are obtained from the supplenumtary figuresfor this thickness form and mean line at x=0.50:
The desired value of A_',/V is computed as follows by use of
equation (15):AVa-V =(0.157) (0.2--0.4)
= --0.031
Tile desired value of Av/V is obtained by:nmltiplying the
tabulated vahlc by the design lift coefficient as stated in the
description of Ill(' NACA 6-series_airfoils. Thus,
A'b'V = (0.250) (0.4)
=0.100
Substituting these values in equation (14) gives the following
vahws of S:
For the upl)cr surface
S= (1.235+ 0.100-- 0.031 )2
= 1.700
For the lower surface
S= (1.235-- 0.100_-0.031) 2
-=1.360
Examl)h, 2:Fin(1 the t)rcssu,'e ('oetti(;i(,nt N a! the station
x=-0.25 on the llt)])er altd lower Slll'faces of the NACA
(i5(2L,,) 214, a=-0.5 airfoil at a lift (,o(,tli(,imtt of 0.(i.
The airfoil designation shows that this airfoil was ol)laincd
by cmnl)ining a thickness form obtain(,d |)y multilllying Ilwordinates of Ill(, NACA 652 015 form 1)y the factor 14/15
with the a=0.5 type mean line (,aml)ered to a design liftcoefficient of 0.2.
The supplementary figures give a value of 1.182 for v/Vatx=0.25 for the NACA 652-015 basic thickness form. The
desired value of v/V is obtained by applying formula (5)as follows:
14V=(1.182-- 1) 15 +1
=1.170
From the supplementary figures the following values of5v_/V are obtained at x = 0.25 for the following basic thickness
foI'm s:
Thickness form .... ?_ at _25
NACA 6,52 015 ............ 0.290
NACA 651 012 ................. 282 .
By interpolation the value of A_a/V of 0.287 may be
assigned to the 14-percent-thick form. The desired value ofAv_/V is then computed as follows by use of equation (15):
AVa=(0 287) (0.6--0.2)V "
=0.115
Data presented in the supplementary figures for the a=0.5
type mean lines give the value of 0.333 for Av/V at x=0.25.As stated in the description of the NACA 6-series airfoils,
the, desired value of Av/V is obtained by multiltlying the
tabulated value by the design lift coefficient. Thus,
A/;
-v= (0.333) (0.2)
=-0.067
Substituting the foregoing values in equation (14) gives thevalues of S as follows:
For the upper surface
S= (1.170q- 0.067-_- 0.115) 2
-----1.828
For the lower surface
S= (1.170-- 0.067-- 0.115) 2
----0.976
Example 3: Find the pressure coefficient S at tim station
x=0.30 on the upper and htwcr surfaces of the NACA 2412airfoil at a lift coefficient of 0.5.
The description of airfoils of the NACA four-digit series
shows that tit(, necessary data may be found fi'om the NACA0012 tlfickncss form and 64 lnt.q(.u line in the supph,mentary
tigures. From these tigurcs lit(, folh)wing data are obtained:
At x=0.30Y
V---l.162
At x=0.30
k
SUMMARY OF AIRFOIL DATA 13
For the NACA 64 mean line at x=0.30
A?) 9V=0.-60
For the NACA 64 mean line
c4=0.76
The values of Av/V and c_ corresponding to the airfoilgeometry are obtained by multiplying the foregoing values
by the factor 2/6 as explained in the description of theseairfoils ; thus,
Av 2
=0.087
ch= (0.76)( 2 )
----0.253
The desired value of Ava/V is obtained from equation (15)as follows:
Av_ _ (0.239) (0.5-- 0.253)V--
=0.059
Substituting the proper values ill equation (14) gives thevalues of S as follows:
For the upper surface
S= (1.162+0.087+0.059) 2
=1.712
For the lower surface
S= (I. i 6z -- O.08] -- o. obu)
=1.032
Effect of camber on pressure distribution.--At zero lift. the
pressure distributions over the upper and lower surfaces of
a basic symmetrical thickness distribution are, of course,
identical. The effect of camber on the pressure distribution
£8
2.4
zo
L6
ZE
.8
.4
0
f....L-_
./
,/
-- Upper surf oce I |
! .._.m cA 65_-0/5/ ./VJOA 65z-_/5
.A/ACA 65s415 -
._(4 15E6/5
• I
<:%
._ .6
_r/c
(a) Amount of camber.
.8 ZO
NACA 652-0/5
A/ACA 65_-2/5
,vAc_ 65_-4/5
at the design lift coefficient is to separate the pressures on
the upper and lower surfaces by an amount correspondingapproximately to the design load distribution of the mean
line. When the local value of the design load distribution is
positive, the pressure coefficient S on the upper surface is
increased (decreased absolute pressure) whereas that on the
lower surface is decreased. This effect is shown in figure 8 (a)for various amounts of camber.
The maximum value of the pressure coefficient on the upper
surface at the design lift coefficient increases with the designlift coefficient and for a given design lift coefficient increases
with decreasing values of a. The result is to cause the critical
Mach number at the design lift coefficient to decrease with
increasing camber or with the use of types of mean line con-
centrating the load near the leading edge. Figure 8 (b)shows that the location of minimum pressure on both surfaces
is not affected if a type of mean line is used having a value of
a at least as large as the value of x/c at the position ofminimum pressure on the basic thickness distribution. If a
mean line with a smaller value of a is used, the possible extentof laminar flow along the upper surface will be reduced.
CRITICAL MACH NUMBER
The critical speed is defined as the free-stream speed at
which the velocity at any point along the sm'face of the air-foil reaches the local velocity of sound. If the maximum value
of the low-speed pressure coefficient S is known either experi-mentally or from theoretical methods, the critical Mach
number may be predicted approximately by the Von K_irmfin
method (reference 19). A curve relating the critical Muchnumber and the low-speed pressure coefficient S has beencmcmaued flulu the of _u and included ineq tlgt uLuhb 1 (fl el l:_ltt;e
the supplementary figures. These predicted critical Maeh
numbers are useful for preliminary considerations in the
absence of test data and appear to correspond fairly well to
the Math numbers at which the local velocity of sound is
reached in the high-critical-speed range of lift coefficient.
This criterion does not, however, appear to predict accurately
ZO
/i.aCl_ 65r015
/VAC,4 65_-415, a=0.3
A'ACA 65c4/5 , a=05
/V4C,4 65E4/5, c_:07
A_C_ 65E4/5
FIGURE 8.--Effect of amount and type of camber on pressure distribution at design lift,
14 REPORT NO. 824--NATIONAL ADVISORY COM:MITTEE FOR AERONAUTICS
the Mach numbers at which large changes ill airfoil char-
actcristies occur, especially when sharp pressure peaks exist
at the leading edge. A discussion of the characteristics of
airfoil sections at supercritical Math numbers is beyond the
scope of this report.For convenience, curves of predicted critical Math num-
ber plotted against the low-speed section lift coemcient have
been included in the supplementary figures for a number of
airfoils. High-speed lift coefficients may be obtained by
multiplying tire low-speed lift coefficient by the factor1- • The critical Math numbers have been predicted
_/1--M 2front theoretical pressure distributions. For airfoils of the
NACA four- and five-digit series an(l for the NACA 7-series
airfoils, the theoretical pressure distributions were obtained
by Theodorsen's method. For the other airfoils the theo-
retical pressure distributions were obtained by the approxi-mate method described in the preceding section.
The data in the supplementary figures show that, for any
one type of airfoil, the maxilnum critical Maeh numberdecreases rapidly as the thickness is increased. The effectof camber is to lower the maximum critical Maeh number
and to shift the range of high critical Maeh numbers in the
same manner as for the low drag range. For common types
of camber the minimum reduction in critical speed for a
given design lift coefficient is obtained with a uniform load
type of mean line. A comparison of the data presented inthe supplementary figures shows that NACA 6-series see-tions have considerably higher maximum critical Math
numbers than NACA 24-, 44-, and 230-series airfoils of
corresponding tlfiekness ratios.
MOMENT COEFFICIENTS
Methods of calculation.--Theoretical moment coefficients
may be approximated directly from the values presented in
the supplementary figures for the various mean lines. Thesevalues were obtained front thin-airfoil theory aim may be
scaled up or down linearly with the design lift coefficient orwith the mean-line ordinates. These theoretical vahles are
sufficiently accurate for preliininary considerations, but ex-
perimental values shouht be used for stability and controlcalculations.
Numerical examples.--The following nmnerical examples
illustrate the nwtlm(ts of calculating the moIne,_t coefficients:
Exainple 1: Find the theoretical moment eoefiicient about
the qimrter-chord point for the NACA 652 215, a=0.5airfoil.
The designation of the airfoil shows that the (h,sign lift(.oellicient of tiffs airfoil is 0.2. Froin the dala on the
NACA a--0.5 type mean line inch,led in the SUl)l)MIwniary
tigures, the value of c,,_; 4 is --0.139 for a design lift ('oeffi('ientof 1.0. The desired vahw of the nmment ('ocfli('icnt is
ae(.ordinglyc,,,c,,= (-0.1:_9) (o.2)
= --0.028
ExaInl)le 2: Find the theoretical monwnt ('oeffi('icnt al)out
the quarter-chord point for the NACA 4415 airfoil.From tim description of the NACA four-digit series
airfoils, the required data is found to be presented for the
NACA 64 mean line in tlle sut)plementary figures.
moment coefficient for this mean line is --0.1_7.
required value is then4
Cmc/4= (-0"157)
= --0.105
The
The
ANGLE OF ZERO LIFT
Methods of calculation.--Values of the ideal or design
angle of attack o_ corresponding to the design lift coefficient
c_ are included among the data for the various mean lines
presented in the supplementary figures. The approximate
values of the angle of zero lift may be obtained front the
data by using the theoretical value of the lift-curve slope
for thin airfoils, 27r per radian. The value of a: 0 in degreesis then
57.3 (16)alo=ai-- 21r ch
The tabulated values of a_ may be scaled linearly with
the design lift coefficient or with the mean-line ordinates.
Although these theoretical angles of zero lift may be useful
in prelimiimry design, they should not be used without
experimental verification for such purposes as establishing
the washout of a wing.
lgumerieM examples.--The inethod of computing az0 is
illustrated in the following exainph,s:
Example 1: Find the theorctical angle of zero lift of the
NACA 65.2--515, a=0.5 airfoil.Tiffs airfoil number indicates a design lift coefficient of
0.5. Data for the NACA a=0.5 mean line indicate that
a_=3.04 ° when c,=l.0. Tilt' desired value of a_ is then
c_= (3.04) (0.5)
=1.52 °
Substituting in equation (16) gives
.52-- (57.3) (0.5)at0= 1 27r
= --3.0 °
Examlih, 2: Fin(I the theoreti('al angh, of zero lift for theNACA 2415 airfoil.
The descrilition of the NACA four-digit-series airfoils
shows tlmt tile required values of a_ and cq may be obtained
by multiplying the corresllonding values for the NACA 64
mean line (see supplementary tigures) by a factor 2/6; then
=0.25 °
c_= (().76)('_-)
--0.253
and from equation (16)
a,0=0.25 (57.3)(0.253)2rr
= --2.0 °
L
SUMS,IARY OF AIRFOIL DATA 5
DESCRIPTION OF FLOW AROUND AIRFOILS
Perfect-fluid theory postulates that tile flow follow tile
airfoil contour smoothly at all angles of attack with no loss
of energy. Consequently, perfect-fluid theory itself givesno information concerning the profile drag or the maximum
lift of airfoil sections. The explanation of these pllenomena
is found from a consideration of the effects of viscosity,which are of primary importance in a thin region near tile
surface of the airfoil called the boundary layer.
Boundary layers in general are of two types, namely,laminar and turbulent. The flow in the laminar layer is
smooth and free from any eddying motion. The flow in the
turbulent layer is characterized by the presence of a largenumber of relatively small eddies. Because the eddies in the
turbulent layer produce a transfer of momentum from the
relatively fast-moving outer parts of the boundary layer to
tile portions closer to the surface, the distribution of averagevelocity is characterized by relatively higher velocities near
the surface and a greater total boundary-layer thickness in
a turbulent boundary layer than in a laminar boundary layerdeveloped under otherwise identical conditions. Skin fric-
tion is therefore higher for turbulent boundary-layer flowthan for laminar flow.
When the pressures along the airfoil surface are increasing
in the direction of flow, a general deceleration takes place. Atthe outer limits of the boundary layer this deceleration takes
place in accordance with Bernoulli's law. Closer to tile sur-
face, no such simple law can be given because of the action
of the viscous forces within the boundary layer. In general,
however, the relative loss of speed is somewhat greater forparticles of fluid within the boundary layer than for those at
the outer limits of the layer because the reduced kinetic
energy of the boundary-layer air limits its ability to flowagainst the adverse pressure gradient. If the rise in pressure
is sufficiently great, portions of the fluid within the boundarylayer may actually have their direction of motion reversed
and may start moving upstream. When this reverse occurs,
the flow in the boundary layer is said to be "separated."
Because of the increased interchange of momentum from
different parts of the layer, turbulent boundal T layers are
nmch more resistant to separation than are laminar layers.Laminar boundary layers can only exist for a relatively short
distance in a region in which the pressure increases in the
direction of flow. Formulas for calculating many of the
boundary-layer characteristics are given in references 20 to 22.
After laminar separation occurs, the flow may either
leave the surface permanently or reattach itself in the form
of a turbulent boundary layer. Not much is known concern-
ing the factors controlling this phenomenon. Laminar sep-
aration on wings is usually not permanent at flight values of
the Reynolds number except when it occurs near the leadingedge under conditions corresponding to maximum lift. The
size of the locally separated region that is formed when the
laminar boundary layer separates and the flow returns to the
surface decreases with increasing Reynolds number at a
given angle of attack.
The flow over aerodynamically smooth airfoils at low and
moderate lift coefficients is characterized by laminar boundary
layers from the leading edge back to approximately the loca-
tion of the first minimum-pressure point on both upper and
lower surfaces. If the region of laminar flow is extensive,separation occurs immediately downstream from the location
of minimum pressure (reference 20) and the flow returns to
the surface almost immediately at flight Reynolds numbers
as a turbulent boundary layer. This turbulent boundarylayer extends to the trailing edge. If the surfaces are not
sufficiently smooth and fair, if the air stream is turbulent,
or perhaps if the Reynolds number is sufficiently large, tran-
sition from laminar to turbulent flow may occur anywhereupstream of the calculated laminar separation point.
For low and moderate lift coefficients where inappreciable
separation occurs, the airfoil profile drag is largely caused byskin friction and the value of the drag coefficient depends
mainly on the relative amounts of laminar and turbulent
flow. If the location of transition is known or assumed, the
drag coefficient may be calculated with reasonable accuracyfrom boundary-layer theory by use of the methods ofreferences 23 and 24.
As the lift coefficient of the airfoil is increased by changingthe angle of attack, the resulting application of the additional
type of lift distribution moves the minimum-pressure pointupstream on the upper surface, and the possible extent of
laminar flow is thus reduced. The resulting greater propor-
tion of turbulent flow, together with the larger average veloc-ity of flow over the surfaces, causes the drag to increase withlift coefficient.
In the case of many of the older types of airfoils, this
forward movement of transition is gradual and the resultingvariation of drag with lift coefficient occurs smoothly. Thepressure distributions for NACA 6-series airfoils are such as
to cause transition to move forward suddenly at the end of
the low-drag range of lift coetlicients. A sharp increase in
drag coefficient to the value corresponding to a forward loca-
tion of transition on the upper surface results. Such sudden
shifts in transition give the typical drag curve for these air-
foils with a "sag" or "bucket" in the low-drag range. The
same characteristic is shown to a smaller degree by some ofthe earlier airfoils such as the NACA 23015 when tested ina low-turbulence stream.
At high lift coefficients, a large part of the drag is contrib-
uted by pressure or form drag resulting from separation of
the flow from the surface. The flow over the upper surface is
characterized by a negative pressure peak near the leading
edge, which causes laminar separation. The onset of tur-bulence causes the flow to return to the surface as a turbulent
boundary layer. High Reynolds numbers are favorable to
the development of turbulence and aid in this process. If
the lift coefficient is sufficiently high or if the reestablish-
ment of flow following laminar separation is unduly delayed
by low Reynolds numbers, the tm'bulent layer will separate
from the surface near the trailing edge and will cause large
drag increases. The eventual loss in lift with increasingangle of attack may result either from relatively sudden
permanent separation of the laminar boundary layer near
the leading edge or from progressive forward movement of
turbulent separation. Under the latter condition, the flow
over a relatively large portion of the surface may be separated
prior to maximum lift. A more extended discussion of the
flow conditions associated with maximum lift is given inreference 5.
16 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
EXPERIMENTAL CHARACTERISTICS
SOURCES OF DATA
The primary source of the wind-tunnel data presented isfrom tests in the Langley two-dimensional low-turbulence
pressure tunnel (TDT). The methods used to obtain andcorrect the data are summarized in the appendix. Design
data obtained from tests of 2-foot-chord models in this
tunnel are presented in the supplementary figures.
Some wind-tunnel data presented were obtained in otherNACA wind tunnels. In each case, the source of tlle data
is indicated and the testing techniques and corrections usedwere conventional unless otherwise indicated.
Most of the flight data consist of drag measurements made
by the wake-survey method on either the airplane wing or a
"glove" fitted over the wing as the test spe(,imen. When-evcr the measurements were obtained for a glove, this fact
is indicated in the presentation of the data. All data obtained
at high speeds have been reduced to coeffii'ient form by
compressible-flow methods In the case of all suchNACA flight data, precautions have been taken to ensure
that the results presented are not invalidated by cross
flows of low-energy air into or out of the survey plane.
DRAG CHARACTERISTICS OF SMOOTH AIRFOILS
Drag characteristics in low-drag range.--The value of the
drag coefficient in the low-drag range for slnooth airfoils is
mainly a function of the Reynolds number and the relative
extent of the laminar layt,r and is moth, rately affected by theairfoil thickness ratio and eamber. The effee.t on minimum
drag of the position of minimum l)l'essure which detel'mines
the possible extent of laminar flow is shown in figure 9 forsome NACA 6-series airfoils. The data show a regular
decrease in drag coefficient with rearward inovenlent of
nfinimum pressure.
c .0/_ ----- o AIA(A 63:-215
_ ul?6 ......
_ OC:
b
•_ o i
A,'ACA 6d_-215k_
.... ¢, ,'¢AC4 65_-L_15
.Oi,P _ NACA dY6_-2/5v NA_ C7,1-L_15
2 .3
' i i i
f I " : "
.z .5 .6 .7 .8"-" Po5/t/Dn of m/nlrnurn pr-essuFe, x_/e
FIGURE 9.--Variation of ndnimum drag coefficient with position of minimum l)ressIIre fors/nne N AC A 6-series airfoils of the same camber aml thickness. R = 6 X 10%
The variation of minimmn drag (,oeflieient with Reynohls
number for sevt,ral airfoils is shown in figure 10. The th'ag
coelii('ieId, gelwrally decreases with iucreasing Reynohls num-
i)er up to Rt,ynolds numbers of the order of 20X 10t Above
this Reynohts mmfl)er tht_ drag coefficient of the NACA
65(4o.1)-420 airfoil remained substantially constant up to a
RcynohIs munbt, r of n.early 40)< 105 The earlier ine|'ease indrag coefli('icnt shown by,the NACA 66(2x15)-116 airfoil
may be i'aused by sm'face irregularities because the specimen
FIGURE 10.--Variation of minimuln section drag coefficient with Reynohls number for several
airfoils, togelher with laminar and turbtflent skin-friction coefficients for a flat plate.
tested was a practical-construction model. It may be noted
that the drag coefficient for the NACA 65_-418 airfoil at low
Reynohls numbers is substantially higher than that of the
NACA 0012, whereas at high Reynolds mm_bers the opposite
is the ease. The higher drag of the NACA 65a-418 airfoil
section at low Reynohts numbers is caused by a relatively
extensive region of laminar separation downstream of the
point of minimum pressure. This region decreases in size
with increasing Reynohts nunfl)er. These data illustrate the
inadequacy of low Reynohls number test data either to esti-nlatc the full-s('ale characteristics or to detel'mil_e the relative
merits of airfoil sections at flight Reynt>hls mmfl)ers (refer-
enecs 25 and 26).The variation of minimum drag coefiieient with cambcr is
shown in figure 11 for a number of smooth 18-percent-thickNACA 6-series airfoils. These data show very little change
J I.%.0/2 --. t_
t_
r_t_
_ .008
._.
._ .0_
0
i
.... r ¸-- 1 -q --
0 65-seriesA 66--,_eri_v 653-8/8
v_____ ___---.>_--
i2 .4 .6
Des/on sechb_ Ii'ft coefT;c_e_ ¢_;
_ _
.8
FIGURE ll.--Variation of itliniinllnI section drag eoeffieielfl with camber for several NACA
6-series airfoil sections of 18-percent thickness ratio. R = 9 X 10_.
L .....
SUM_IARY OF AIRFOIL DATA 17
in nfinimum drag coefficient with increase in camber. A
large amount of systematic data is included in figure 12 to
show the variation of minimum drag coefficient with thick-
ness ratio for a number of NACA airfoil sections ranging inthickness from 6 percent to 24 percent of the chord. The
minimum drag coefficient is seen to increase with increase in
thickness ratio for each airfoil series. This increase, how-
ever, is greater for the NACA four- and five-digit-series air-
foils (fig. 12 (a)) than for the NACA 6-series airfoils (figs.12 (b) to 12 (e)).
.o/o ___ .__17ou_, _ .......
• 012 -- ._moot_,
L! y2t l- 2 _
(__._-.
004
0/2 ----
_ 00,
_" (b).g.0 0
<<.OlZ
qJ
C:)k_
.OOd
b .oo4
__._ .0/2
I--" Ser-I'em
o oo]m /4+ z4, (4-_),'# _
44 [
---- v 230 (5-d,g#) -I
- __--6-- "-_-
..-0
ct i
oOo .2a .4v .6
__. - -_
.... + -[
q
..... 0 " - k'- "_
i
o O---cJ ./<:> .2 --A .4_
I!
(d)
012 ._
.o08 I c,,I o 0
o .2
.004 _ _ + _ _ .4I >----e_ I
0 d- 8 12 I _ 20 24 Z8 ,.72/17-fell /h,,c/_f_ess,pe_ce, _t<;i o_'o,,<I
(a) NACA four- and five-digit series.(b) NACA 63-series.(c) NACA 64-series.(d) NACA 65-series.(e) NACA 66-series.
C/i
oO --
,_" .4---
v .6
FIGURE 12.--Variation of minimum section drag coefficient with airfoil thickness ratio forseveral NACA airfoil sections of different cambers in both smooth and rough conditions.R = 6X 10_.
The data presented in the supplementary figures for the
NACA 6-series thickness forms show that the range of lift
coefficients for low drag varies markedly with airfoil thick-
hess. It has been possible to design airfoils of 12-percent
thickness with a total theoretical low-drag range of lift coeffi-
cients of 0.2. This theoretical range increases by approx-imately 0.2 for each 3-percent increase of airfoil thickness.
Figure 13 shows that the theoretical extent of the low-drag
range is approximately realized at a Reynolds number of
9X10% Figure 13 also shows a characteristic tendency for
the drag to increase to some extent toward the upper end of
the low-drag range for moderately cambered airfoils, par-
ticularly for the thicker airfoils. All data for the NACA
6-series airfoils show a decrease in the extent of thelow-drag
range with increasing Reynolds number. Extrapolation of
the rate of decrease observed at Reynolds numbers below
9 X 10_ would indicate a vanishingly small low-drag range at
flight values of the Reynolds number. Tests of a carefully
constructed model of the NACA 65(,2,-420 airfoil showed,
however, that the rate of reduction of the low-drag range
with increasing Reynolds number decreased markedly at
Reynolds numbers above 9_ 10 _ (fig. 14). These data indi-
-cate that the extent of the low-drag range of this airfoil is
reduced to about one-half the theoretical value at a Reynoldsnumber of 35X10%
.032
.028
•02d
d
•_-. 020.0
(5
o .016
b
._ .012
0
%. 008
.004
Io IVACA 84,-412
_] IVACA 84_-d15
0 NAC,4 6%-418
z_ AIACA 64,-,¢21
I I I I II I
\
i
0-/.6 -1.2 -.8 -.4 0 .d .8 L2 L6
Section lift coefficient, e,
FIGURE 13.--Drag characteristics of some NACA 64-series airfoil sections of various thick.nesses, cambered to a design lift coefficient of 0.4. R = 9 X 10_; TDT tests 682, 733, 735,and 691.
The values of the lift coefficient for which low drag is
obtained are determined largely by the amount of camber.
The lift coefficient at the center of the low-drag range corre-
sponds approximately to the design lift coefficient of themean line. The effect on the drag characteristics of various
amounts of camber is shown in figure 15. Section data indi-
cate that the location of the low-drag range may be shifted
by even such crude camber changes as those caused by small
deflections of a plain flap. (See supplementary fig.)
REPORT N',O. S2-t--NATIONAL ADVISO'RY COMMITTEE) FOR AERONAUTICS
-4
I-.& 4
I
0 4 8 12 /6' 20 2d 28 3Z×/O _
Reyno ds flute, bet-, FI
(a) Variation of upper and lower limits of low-drag range with Reynolds number.
/._q -LZ_ :8 :4 O .4 .8 12 L65_chbn hf! co_ffJk_k_?t, q
(b) Section drag characteristics at various Reynolds numbers.
FIGURE 14.--Yariation of low-drag range with Reynolds number for the NACA 65142D-420 airfoil. T I)T tests 3(X1, 312, and 329.
i '
o '_;424 _5,,-018.028 o AAC4 _5_-ZI8
z_ /V,IC,4 G5_-6'18--- 7 A/ACA _5,3-_1_ I
•OO#
o-I.o" -1.2 -.8 -.4 0 .4 8 L2 1.6
Sectlon I/fl coeff/c/erTf_ c,
.Fw, U_E 15.--Drag characlcrislics of some NACA 65-series airfoil sections of 18 percent thick-
hess with various amounts of carol)or. A' = 6 X 106; T I)T tests 163, 314,802, 813, and f#10.
The location of the low-drag range shows some variation
from that predietcd by simple thin-airfoil theory. This de-
parture appears to I)e a function of the type of mean line
used (refert,nee 27) and the airfoil thickness. The effect of
airfoil thM:ness is shown in figure 13, from wlfich the center
of the low-drag range is seen to shift to higher lift coefficients
with increasing airfoil thickness. This shift is partly ex-
plained by the increase in lift coefficient above the design
lift eoetticient for the mean line obtained when the velocity
increments caused by the mean line are combined with the
velocity distribution for the basic thickness form according
to the approximate methods previously describe(1.
Drag characteristics outside low-drag range.--At the end
of the low-drag range the drag increases rapidly with increase
in lift coefficient. For symmetrical anti low-<'ambered air-
foils, for which the lift coefficient at the upl)er end of the
low-drag range is moth, rate, this high rate of increase does
not continue. (See fig. 15.) For highly eaml)ered sections,
for which the lift at the upper end of the low-drag range is
already high, the drag coefficient shows a continued rapid
increase.
Comparison of data for airfoils cambered with a uniform-
load mean line with data for airfoils cambered to carry the
load farther forward shows that the uniform-load mean line
is favorable for obtaining low drag coefficients at high lift
coefficients (fig. 16 and reference 27).
Data for many of the airfoils given in the supplementary
figures show large reductions in drag with increasing Reynohls
m_mher at high lift coefficients. This scale effect is too large
to be accounted for by the normal variation in sldn friction
and appears to be associated with the effect of Reynolds
number on the onset of turbulent flow following laminar
separation near the leading edge (refiwenee 28).
Effects of type of section on drag characteristics.--A com
parison of the drag ehara('teristies of the NACA 23012 and of
three NACA 6-series airfoils is presented in figure 17. The
drag for the NACA 6-series sections is substantially lower
than for the NACA 23012 section in the range of lift, coeffi-
cients corresponding to high-speed flight, anti this margin
may usually be maintained through the range of lift coeffi-
cients useful for cruising by suitable choice of camber.
The NACA 6-series sections show the higher maxinmm values
of the lift-drag ratio• At high values of the lift ('oeflicient,
however, the earlier NACA sections have generally lower
drag coefficients than the NACA 6-series airfoils.
SUMMARY OF AIRFOIL DATA 19
I
I -
I
i
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i
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i
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" i .... I.....
i
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v
I' I" I" i •
20 REPORT NO. 824--NATIONAL ADVISORY COMS]ITTEE FOR AERONAUTICS
"1"_'o 'lu_./o./,,/dooo 4ua_o.w
q5
k
SUMMARY OF AIRYOIL DATA 21
Effective aspect ratio.--The combination of high drags athigh lift coefficients, low drags at moderate lift coefficients,and the nonregular variation of drag with lift coefficientshown by the NACA 6-series airfoils may lead to para-doxical results when the span-efficiency concept (reference 29)is used for the calculation of airplane performance. In theusual application of this concept, the airplane drag charac-teristics are approximated by a curve of the type
C_-_ CDL=o-]-kCL _ (17)
This curve is usually matched to the actual drag character-istics at a rather low and at a moderately high value of thelift coefficient (reference 30).
The application of this concept to two hypothetical air-planes with NACA 230- and 65-series sections, respectively,is illustrated in figure 18 (a). The wing drags of the air-planes have been calculated by adding the induced dragscorresponding to an aspect ratio of 10 with elliptical loadingto the profile-drag coefficients of the NACA 23018 and653-418 airfoils. These sections are considered representa-tive of average wing sections for a large airplane of thisaspect ratio. Ordinate scales are given in figure 18 (a),forthe wing drag and for the total airplane drag coefficientsobtained by adding a representative constant value of
0.0150 to the wing drag coefficients. The resulting dragcoefficients have been approximated by two curves corre-
sponding to equation (17) and matched to the drag curvesat lift coefficients of 0.2 and 1.0. These two curves corre-
spond to effective aspect ratios of 9.29 for the airplane withNACA 23018 sections and of 8.30 for the airplane with
NACA 653-418 sections and illustrate the typical largereduction in the effective aspect ratio obtained with suchsections.
It should be noted, however, that although equation (17)provides a reasonably satisfactory approximation to thedrag of the airplane with NACA 23018 sections, such is notthe case for the airplane with the NACA 653-418 section.
The most important reason for using high aspect ratios onlarge airplanes is to reduce the drag at cruising lift coefficientsand to obtain high maximum values of the lift-drag ratio.For the two wings considered, the maximum value of this
ratio is appreciably higher for the airplane with NACA653-418 sections (19.8 as compared with 18.5) despite thefact that this airplane shows the lower effective aspect ratio.Figure 18 (b) shows a similar comparison with similarresults for two airplanes of aspect ratio 8 and NACA 2415and 652-415 airfoils. It is accordingly concluded that theeffective, aspect ratio is not a satisfactory criterion for use inairfoil selection.
./0
.O2
(JO
.07
._ .06 ._
r_ .o3
.o4
.0_ oD
.07-- -- m
I I
.0/
.02
.0/
o /- / S .o, /
/ o / I0 .2 .4 .6 .8 1.0 L2 0 .2 .4 .6 .8 1.0 L2
Lift coefficient, CL L/T/ coeffi'c/en_ _z
(a) NACA 65a-418 and 23018 wings of aspect ratio 10. (b) NACA 65m-415and 2t15 wings of aspect ratio 8.
I I I I t I I I I I ./0 | I I I I I I I I I I I
/VACA 65_-418 w_bg; ospec/ rohb, I0.-- .08 --JF o /v_g{'lt 65z-415 wing; o.tpecf r-oho, 8 __/Vt4Ct4 23018 w/n_,, aspect f'of/o, I0 [] IVACtl Z415 wln_, .aspect r-alia, 8
.... IVACA G53-418 w_ny_ _ I .09 A!ACA 65_-41E w_n_effective aspect rot/b, 830 effective ospect rot]o, 6.97 I/
AIACA 2,.7018 wt½g_ _ . .07 NACA 8415 w_77g_ _ • "_I effective osl_ecf rob'o, 9.29 _ I I I effeeh've aspect robo, 7 416 z/
i" it.06
¢ /'c2.O7
, . / ,"• qa
i'i/ 06o 7"i/ ,4/r-plane t_
t_<<,: _ .04 % o:o.oo63+ o.o4z_ c_,. _P/ ,_,L:_,=,'_n
FiGurE 18.--Comparison of finite aspect-ratio drag characteristics for two types of airfoils obtained by adding the induced drag corresponding to an elliptical span loading
to the section drag coefficients.
22 REPORT N_O. 824--N_ATIONTAL ADVISO'RY COMMIITTEE FOR AERONAUTICS
EFFECT OF SURFACE IRREGULARITIES ON DRAG
Permissible roughness.--Previous work has shown large
drag increments resulting from surface roughness (reference
31). Although a large part of these drag increments wasshown to result from forward movement of transition, sub-
stantial drag increments resulted from surface roughness in
the region of turbulent flow. It is accordingly important tomaintain smooth surfaces even when extensive laminar
flow cannot be expected, but the gains that may be expected
from maintaining smooth surfaces are greater for NACA 6-or 7-series airfoils when extensive laminar flOWS are possible.
No accurate method of specifying the surface condition
necessary for extensive laminar flow at high Reynolds num-
bers has been developed, although some general conclusions
have been reached. It may be presumed that for a given
Reynolds number and chordwise position, the size of thepernlissible roughness will vary directly with the chord ofthe airfoil. It is known, at one extreme, that the surfaces
do not have to be polished or optically smooth. Such
polishing or waxing has shown no improvement in tests in
the Langley two-dimensional low-turbulence tunnels when
applied to satisfactorily sanded surfaces. Polishing or waxinga surface that is not aerodynamically smooth will, of course,
result in improvement and such finishes may be of consider-
able practical value because deterioration of the finish may
be easily seen and possibly postponed. Large models having
chord lengths of 5 to 8 feet tested in the Langley two-dimensional low-turbulence tunnels are usually finished by
santling in tile chordwise direction with No. 320 carborundum
paper when an aerodynamically smooth surface is desired.
Experience has shown the resulting finish to be satisfactory
at flight values of the Reynolds number. Any i'oughersurface texture should be considered as a possible source of
transition, although slightly rougher surfaces have appeared
to produce satisfactory results in some cases.
Wind-tunnel experience in testing NACA 6-st,ries sections
and data of reference 32 show that small protuberances
extending above the general surface level of an otherwise
satisfactory surface are more likely to cause transition thansinall del)ressions. Dust particles, for examph,, are more
effective than small scratches in producing transition if the
nmtt, l'ial at the edges of the seratcht,s is not forced above the
general surface level. Dust particles adhering to the oil
h,ft on airfoil surfaces 1)y fingerprints may be expected to
cause transition at high Reynohls numl)t,i's.
Transition spreads from an individual disturt)ance with an
incluth,tl angle of al)out 15 ° (references 31 and 33). A few
s('altercd spc('ks, especially near the h, ading edge, will cause
the flow to l)e largely turbulent. This fact Inakes necessary
an extrenlcly thorough inspection if low drags are to be
i'ealiz_,d. SI)ecks suiticit, nily large to cause premature
trallsition on full-size wings can I)e felt by hand. The in-
sl)ectioll procedurt, used in the Langley two-dimensional
low-tul'bulencc tunnels is to feel the t,ntire surface by hand
aft(,r which the surface is thoroughly wiped with a dry cloth.
It has been noticed that transition resulting froin individual
small sharp protuberances, in contrast to waves, tends to
occur at the protuberance. Transition caused by surface
waviness appears to approach the wave gradually as the
Reynolds number or wave size is increased. The height
of a small cylindrical protuberance necessary to cause transi-
tion when located al_ 5_,percent of the chord with its axis
normal to the suTfface is shown in figure 19. These data were
• _.050
__
_.030
] I.o,o
\
I 2 3 d 5 © f 8
W/mg }_egmo./o's nurnD_F, R
c
lOxlO"
FmURE 19.--Variation with wing Reynolds number of the minimum height of a cylindrical
protuberance necessary to cause premature transition. Protuberance has 0.035-inch di-
ameter with axis normal to wing surface and is located at 5 percent chord of a 90-inch-chord
symmetrical 6-series airfoil section of 15-percent thickness and with minimum pressure at
70 percent chord.
obtained at rather low values of the Reynolds number and
show a large decrease in allowable height with increase in
Reynohls nunfiier. This effect of Reynolds munl)er on
permissit)h' surface roughness is also evidt,nt in figure 20,
in which a sharp incrt,ase in drag at a Reynohls numt)er of
approxiInately 20X106 occurs for the model painted with
canmullage lacquer.
The niagnitude of the favorable gradient appears to have a
small effect on the permissible surface I'oughnt'ss for laminar
flow. Figure 21 shows that the roughness 1)ecoInes more
important at the extremities of the low-drag range wliere
the favorable pressure gradient is rciluced on one surface.
The effect of increasing the Reynolds nuinber for a sui'facc
of inarginal snloothness, which has an effect similar to in-
creasing the surface roughness for a given Reynohls number,
is to reduce rapidly the extent of the low-drag range and
then to increase tlie minimum drag cocfficient (fig. 21).
The data of figure 21 were specially chosen to show this
effect. In nmst cases, the effect of Reynohls numt)er pre-dominates over the effect of decreasing the magnitude of the
favorable pressure gratlient to such an extent that the only
effect is the eliinination of the low-drag range (refereuce 34).Permissible waviness.---More difficulty is generally cn-
counteretl in reducing the waviness to perInissil)h, values forthe maintenan('e of laminar flow than in obtainillg the re-
quired surface sInoothness. In addition, the specification
of the required freetlom fronl surface waviness is moreilifficult than that of tile rt, quired surface smoothness. Tile
prot)h,m is not linfite(l inerely to finding the nlinimuln waw'size that will cause transition undt,r given eon(litions t)ecausethe Immbt, r of waves and the shapt, of the waw,s require
consideration.
SUMMARY OF AIRFOIL DATA
¢°/6' I ' I [ --_-
i .o/z[ ! i i
I I J I i :
Og _
OE t t f I I I I
8 12 /5 20 2_ Z8
.016 .....
o/2
I
_ .006 --
t 004 _ _-O<
ibl I I0 4 8 /2 16 20
(
!
i'
.72 36 40 44 4_ 52 55 60×10 _
Reynolds number, R
i
i I
-.9--
!i i- ! ....
i !
I36 ZO 4W
I
t I24 28 3E 48 5Zx/O °
Reynolds number, 19
(a) Smooth condition; TDT test 328.
(b) Lacquer camouflage unimproved after painting; TDT test 461.
FIGURE 20.--Variation of drag coefficient with Reynolds number for a 60-inch-chord nmdel of the NACA 65(m)-420 airfoil for two surface conditions.
23
.012 -o
"_- -v
0.008
(b
.0/_-_, I IRI ] i I I I i 1 I l I
-o 15.3 x I0 _ Smoolh cond/h'om
/49 ] I I I J I248 } Synthet;c enomel camoo,_loge uv,,'?h-34(? ol/ _,oecks cur off uv Ch b/ode I
_46 J
t
,d 0 .d .8 1.2
fiechbn //ffcoeff/c/e,g/,q
LO 20
FIGURE 21.--Drag characteristics of NACA 65(4:1)-4.'20 airfoil for two surface conditions.
TDT tests 300 and 486.
If the wave is sufficiently large to affect the pressuredistribution ,in such a manner that laminar separation isencountered, there is little doubt that such a wave will cause
premature transition at all useful Reynolds numbers. A re-lation between the dimensions of a wave and the pressure
distribution may be found by the method of reference 35.The size of the wave required to reverse the favorable pres-
sure gradient increases with the pressure gradient. Largenegative pressure gradients would therefore appear to be
favorable for wavy surfaces. Experimental results haveshown this conclusion to be qualitatively correct.
Little information is available on waves too small to cause
laminar separation or even reversal of the pressure gradient.Data for an airfoil section having a relatively long wave onthe upper surface are given in figure 22. Marked increasesin the drag corresponding to a rapid forward movement ofthe transition point were not noticeable below a Reynoldsnumber of 44X l0 _. On the other hand, transition has beencaused at comparatively low Reynolds numbers by a seriesof small waves with a wave height of the order of a few ten-thousandths of an inch and a wave length of the order of2 inches on the same 60-inch-chord model.
For the types of wave usually encountered on practical-construction wings, the test of rocking a straightedge overthe surface in a chordwise direction is a fairly satisfactorycriterion. The straightedge should rock snmothly withoutjarring or clicking. The straightedge test will not show theexistence of waves that leave the surface convex, such as thewave of figure 22 and the series of small waves previouslymentioned. Tests of a large number of practical-constructionmodels, however, have shown that those models whichpassed the straightedge test were sufficiently free of smallwaves to permit low drags to be obtained at flight values ofthe Reynolds number.
It is not feasible to specify construction tolerances on air-foil ordinates with sufficient accuracy to ensure adequatefreedom from waviness. If care is taken to obtain fair
surfaces, normal tolerances may be used without causingserious alteration of the drag characteristics.
24 REPORT NO. 8241NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
..(enfer of wove,.--4-
60"
.005"
i_ _
Oepor/ure f/orr/ fOIr
olT-fo/I surfooe
C "008
i_•oo8
0
.004
.g.oo_
I I
0 4 8 / 2 / d ZO 2# 28 32 36 40 44. 48 E2 x I 06
Win_ Reynolds number, t_
FIGURE 22.--Exlx, rimental curve showing variation of drag coefficient with Reynolds number for tim NACA 65(4m-420 airfoil section with a small amount of surface waviness.
Drag with fixed transition.---If the airfoil surface is suffi-
ciently rough to cause transition near the leading edge, large
drag increases are to be expected. Figure 23 shows that,although the degree of roughness has some effect, the incre-
ment in minimum drag coefficient caused by the smallest
roughness capable of producing transition is nearly as greatas that caused by much larger grain roughness when the
roughness is confined to the leading edge. The degree of
roughness has a much larger effect on the drag at high lift
coefficients. If the roughness is sufiiciently large to cause
transition at all Reynohls numbers considered, the drag of
the airfoil with roughness only at the h,ading edge decreases
with increasing Reynolds number (fig. l0 and reference 36).
The effect of fixing transition by means of a roughness
strip of carborundum of 0.01 I-inch grain is shown in figure 24.
The minimum drag increases progressively with forward
movement of the roughness strip. The effect on the drag
at high lift coefficients is not progressive; the drag increases
rapidly when the roughness is at the leading edge. Figure 25
shows that the drag coeiilcients for the NACA 65(223)_ 422
and 63(420) 422 airfoils were nearly the same tllroughout
most of the lift range when the extent of laminar flow waslimited to 0.30c.
All recent airfoil data obtained in the Langley two-dimen-
sional low-turbulence pressure tunnel iiwlude results with
roughened h,ading edge, and these data are included in the
supph, mentary figures. Tests with roughened leading edge
were formerly made only for a limited numi)er of airfoil
sections, especially those having large thickness ratios
(reference 37). The siandard roughness seh,eted for 24-inch-chord models consists of 0.011-inch (,arl)orundum grains
applied to the airfoil surface at the h,ading edge over a surface
length of 0.08c measured from the leading edge on 1)oth sur-
faces. The grains are thinly spremt to cover 5 to l0 percent
of this area. This standm'd roughness is consideral)ly more
severe t llml that caused by the usual manufacturing irregu-larities or deterioration in service but is considerably less
severe than that likely to be encountered in service as a
result of accumulation of ice or mud or damage in military
combat.
The variation of minimum drag coefficient with thickness
ratio for a mlmber of NACA airfoils with standard roughness
is shown in figure 12. These data show that the magnitudes
of the minimum drag coefficients for the NACA 6-sm'iesairfoils are less than the vahles for the NACA four- and
five-digit-series airfoils. The rate of increase of drag with
thickness is greater for the airfoils in the rough conditionthan in the smooth ('ondition.
Drag with practical-construction methods. The section
drag coefficients of several airplane wings have 1)een measured
in flight by the wake-survey method (reference 38), and anumher of practical-construction wing sections have been
tested in tin, Langley two-dimensional low-turbulence
pressure tunnel at flight vahws of the Reynohls number.
Flight data obtained by the NACA (reference 38) are sum-
marized in figure 26 and some data obtained by the Consoli-dated Vultee Aircraft Corporation are presented in figure 27.
Data obtained in the Langh,y two-dimensional low-
turl)ulence pressure tunnel for typical practical-construction
sections are presented in figures 28 to 32. Figure 33 presentsa comparison of the drag eoetficients obtained in this wind
tmmel for a model of the NACA 0012 section, and in flight
for the same model mounted on an airplane. For this case,
the wind-tunnel and flight data agree to within the experi-
nlental erl'or.
All wings for wllich flight data are presented in figure 26
were carefully finished to produce smooth surfaces. Greatcare was taken to reduce surface waviness to a minimum
for all the sections except tile NACA 2414.5, the N-22, the
Republic S 3,13, and the NACA 27-212. Curvature-gagenwasurenwnts of surface waviness for some of these airfoils
are l)resented in reference 38. Surface conditions correspond-
ing to the data of figure 27 are described in the figure.These data show that the sections permitting extensive
lamifmr flow had substantially lower drag coefficients whensmooth than the other sections.
k
SUMMARY OF AIRFOIL DATA 25
%
%
%
% %I"
%
26 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
%
%(5
%
k
SUMMARY OF AIRFOIL DATA 27
FIGURE 25.--Drag characteristics of two NACA 6-series airfoils with 0.011-inch-grainroughness at 0.30c. R=26X10_.
The wind-tunnel tests of practical-construction wing sec-
tions as delivered by the manufacturer showed minimum
drag coefficients of the order of 0.0070 to 0.0080 in nearly all
cases regardless of the airfoil section used (figs. 28 to 32).
Such values may be regarded as typical for good current
construction practice. Finishing the sections to produce
smooth surfaces always produced substantial drag reductions
although considerable waviness usually remained. None of
the sections tested had fair surfaces at the front spar. Unless
special care is taken to produce fair surfaces at the front spar,the resulting wave may be expected to cause transition either
at the spar location or a short distance behind it. One
practical-construction specimen tested with smooth surfaces
maintained relatively low drags up to Reynolds numbers
of approximately 30X10 ° (NACA 66(2x15)-116 airfoil offig. 10). This specimen had no spar forward of about 35
percent chord from the leading edge and no spanwise stiffeners
forward of the spars. This type of construction resulted in
unusually fair surfaces and is being used on some modernhigh-performance airplanes.
A comparison of the effect of airfoil section on the mini-
mum drag with practical-construction surfaces is very diffi-cult because the quality of the surface has more effect on
the drag than the type of section. Probably the best com-
parison can be obtained from pairs of models constructed at
,32x/06
\-'NACA 35-215
24
, ,_--¢_p_b/,c s-s,/}"-_
_ NACA 2414.5"__--NACA8 I ._" ", I rqNACA 27-212- x "RepubDb S-3,13
Q,I '"N-22
0 I
ff.O06 I"_-_ ,dbhb g-3,/3--.
66,2-2(14.z)
/V-22. .-_- -_.Repub/,'c ,_L 3_/ /
I /_/ "'NAOA 35-2/5
//,I/" "'A,AC,_6_,2-2(_4.7)//I I i
"NA CA 2 7-2/2"_.oo,_ ',,, / I
D0 .16 .32 .48 .64 .80 .96
Sechon I/f/ coefficien_ ez
FIC,L'RE 26.--Comparison of section drag coefficients obtained in flight on various airfoils.Tests of NACA 27-212 and 35-215 sections made on gloves.
L7 I 2 .3 .4 .5 .6
Lift coefhcler% C_
F]ov_ 27.--Consolidated-Vultee flight measurements of the effect of wing surface conditionon drag of an NACA 66(215)-1(14.5) wing section.
the same time by the same manufacturers. Data for such
pairs of models are presented in figures 30 to 32. The results
indicate that as long as current construction practices are
used the type of section has relatively little effect at flight
values of the Reynolds number for military airplanes.
28 REPORT NO. 8 2 4-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
3 -- 012 F G c x $ 008
8 6
c,
& 004
< $ 4 ' A ' 1; ' ik ' 2L ' A ' 2; ' 3L ' 3Lcxld6
Reynolds number, R
NACA 65(216)-3(16.5) (approx.) airfoil section. c1=0.2 (approx.). FIGURE 28.-Drag scale effect on 100-inch-chord practical-construction model of the
,016
Q
C ,012 .a, .u < \
Y.-
8 F? &
,008
C ;" ,004 CI a, v,
0 -.2 0 .2 .4 .6 .8 1.0
Section lift coefficient, c,
FIGURE 30.-Drag characteristics of the NACA 65(216)-417 (approu.) and KAC-4 23015 (approx.) airfoil sections built by practicalconstruetim methods by the same manu- facturer. R=10.23XW.
Reynolds number, R
FIGURE %.-Variation of drag coefficient with Reynolds number for the NACA 23016 airfoil section together with laminar and turbulent skin-friction coefficients for a flat plate.
016 3 -+.-
5 012 z 8 009 8 6
8
i,
Q
$ 004 i i,
0 8 12 16 20 24 28 32x10' Reynolds number, R
FIGLRE 31.-Scale effect on drag of the NACA 66(215)-116 and NACA 23016 airfoil sections built by practical-construction methods by the same manufacturer and tested as received.
FIGCRE 32.-Drag scale effect for a model of the S A C A BS-series airfoil section. 15.2i percent thick, and the Davis airfoil section, 18.Z percent thick, hriilt by practical-construction methods by the same manufacturer. ci=O.4G (appros.).
Reynolds number, f?
FIGL-RE 33.-Comparison of drag coefficients measured in flight and wind tunnel for the iYAC.4 0012 airfoil section at zero lift.
.016"
.2.0lg --
0
_ .00_
_ 004
O
©
SUMMARY OF AIRFOIL DATA
IIIIIIIIIIII111.11-- 0 N_CA 23015 (opprox.)_i?h de-icer O08e on upper I
5urfoce ond O/Oc on lower surfoce _ Q=O.WO
-- a NACA Z30/5 (opprox.) with die-leer removed ]_0 NACA 65(216)-215, o=g28 w/lh 0075e de-icer" l
-- Z_ NACA 85{2/d)-2/5 G=(2.8 _/lh de-icer /-emoved _ °r(229__
W 8 12 16 20 Zd 28 32 36 40 4W 48
Reynolds mumber, R
FIGURE 34.--Effect of de-leers on the drag of two practical-construction airfoil sections with relatively smooth surfaces.
Important savings in drag may be obtained at highReynolds numbers by keeping the surfaces smooth even if
extensive laminar flow is not realized. Drag increments result-ing from surface roughness in turbulent flow have been shown
to be important (reference 31). The effects of surface roughnesson the variation of drag with Reynolds number are shown
in figure 29, in which the favorable scale effect usually expected
at high Reynolds numbers was not realized. This type ofscale effect may be compared with that shown for the NACA
63(420)-422 airfoil with rough leading edge but otherwise
smooth surfaces (fig. 10). Drag increments obtained in
flight resulting from roughness in the turbulent boundarylayer with fixed transition are presented in reference 39.
The effect of the application of de-icers to the leading edgeof two smooth airfoils is shown in figure 34. The de-icer
"boots" were installed in both cases by the manufacturer to
L '&
Cg
_---7
A/rfo,/sechons
RoOf, /VACA 88(2x15;-0/8Tzp, N_OA 87, /-(/.3)/5
Aspecf Folio, 5.98 IPropeller tip rod/us--_
o Propeller w/bdmH//h_z_ Propeller removed
I
_--o
£
3 Z I 0Z 6 5 4
OJstonce from mode/ renter hne_ f/
FIGURE 35.--The effect of propeller operation on section drag coefficient of a fighter-type air-
plane from tests of a model in the Langley 19-foot pressure tunnel. CL= 0.10; R=3.TX 106.
918392--51--3
52x106
29
0
E
0
f
0
<
Mo
k(5
FIGURE
_xlO6
,Left wing section,/-L in s//ps_reom
oucs[de sl/pxfreom
.GO
.20 _.
0 .I .Z .3 .4 .5 .6
Sect�on lift coeff/c/em/; c,
-<
o f?/ght wing seclior_ --ou'l side slipstfeom
/ eft wln9 secfionL -in sh;osfreom
[3 Pow6f" on
0 Power off
\%_
36.--Flight measurements of transition on an NACA 66-series wing within and
outside the slipstream.
represent good typical installations. The minimum dragcoefficients for both sections with de-icers installed were of
the order of 0.0070 at high Reynolds numbers.
Effects of propeller slipstream and airplane vibration.-
Very few data are available on the effect of propeller slip-
stream on transition or airfoil drag; the data that are avail-
able do not show consistent results. This inconsistency mayresult from variations in lift coefficient, surface condition,
air-stream turbulence, propeller advance-diameter ratio, and
number of blades. Tests in the Langley 8-foot high-speed
tunnel indicated transition occurring from 5 to 10 percent of
the chord from the leading edge (reference 40). Drag measure-
ments made in the Langley 19-foot pressure tunnel (fig. 35)indicated only moderate drag increments resulting from a
windmilling propeller. Although the data of figure 35 may
not be very accurate because of the difficulty of making
wake surveys in the slipstream, these data seem to precludevery large drag increments such as would result from move-
ment of the transition to a position close to the leading edge.
These data also seem to be confirmed by recent NACA flight
data (fig. 36), which show transition as far back as 20 percent
3O
Q
of the chord in the slipstream. Other unpublished NACA
flight data on transition oil an S-3,14.6 airfoil in the slip-stream indicated that laminar flow occurred as far back
as 0.2c.
Even less data are available on the effects of vibration on
transition. Tests in the Langley 8-foot high-speed tunnel
(reference 40) showed negligible effects, but the range of
frequencies tested may not have been sufficientlywide. Some
unpublished flight data showed small but consistent rear-
ward movements of transition outside the slipstream when
the propellers were feathered. This effect was noticed even
when the propeller on the opposite side of the airplane from
the survey plane was feathered and was accordingly attrib-uted to vibration. Recent tests in the Ames full-scale tun-
nel showed premature adverse scale effect on drag coefficients
measured by tlle wake-survey method when a model-supportstrut vibrated.
REPORT :NO. 8 2 4--;N'ATION'AL ADVISORY COMMITTEE FOR AERONAUTICS
LIFT CHARACTERISTICSOF SMOOTHAIRFOILS
Two-dimensional data.--As explained in the section "Angle
of Zero Lift," tile angle of zero lift of an airfoil is largely
determined by the camber. Thin-airfoil theory provides a
means for computing the angle of zero lift from the mean-line
data presented in the supplementary figures. Tile agree-
ment between the calculated and the experimental angle of
zero lift depends on the type of mean line used. Comparison
of the experimental values of the angle of zero lift obtained
from the supplementary figures and the theoretical values
taken from the mean-line data shows that the agreement is
good except for the uniform-load type (a----1.0) mean line.
The angles of zero lift for this type mean line generally have
values more positive than those predicted. The experi-mental values of the angles of zero lift for a number of NACA
four- and five-digit and NACA 6-series airfoils are presented
in figure 37. The airfoil thickness appears to have little effect
on the value of the angle of zero lift regardless of the airfoil
series. For tile NACA four-digit-series airfoils, the angles of
zero lift are approximately 0.93 of the value given by thin-airfoil theory; for tile NACA 230-series airfoils, this factor is
approximately 1.08; and for the NACA 6-series airfoils with
uniform-load type mean line, this factor is approximately0.74.
The lift-curve slopes (fig. 38) for airfoils tested in the
Langley two-dimensional low-turbulence pressure tunnel are
higher than those previously obtained in the tests reported
in reference 8. It is not clear whether this difference in slope
is caused by the difference in air-stream turbulence or by
the differences in test methods, since the section data of
reference 8 were inferred from tests of models of aspect ratio 6.
The present values of the lift-curve slope were measured fora Reynohls number of 6XI06 and at values of the lift coeffi-
cient aplJroximately equal to the design lift coefficient of the
airfoil section. For the NACA 6-series airfoils this lift coeffi-
cient is approximately in the center of the low-drag range.For airfoils having thicknesses in the range from 6 to 10 per-
cent, the NACA four-and five-digit series and the NACA
64-series airfoil sections have values of lift-curve slope very
close to the value for thin airfoils (27r per radian or 0.110 per
degree). Variation in Reynolds number between 3 X 106 and
9X 106 and variations in airfoil camber up to 4 percent chord
appear to have no systematic effect on values of lift-curve
slope. Tile airfoil thickness and the type of thickness
distribution appear to be the primary variables. For the
NACA four- and five-digit-series airfoil sections, the lift-
curve slope decreases with increase in airfoil thickness
For the NACA 6-series airfoil sections, however, the lift-
curve slope increases with increase in thickness and forward
movement of the position of minimum pressure of the basicthickness form at zero lift.
Some NACA 6-series airfoils show jogs in the lift curve
at the end of the low-drag range, especially at low Reynolds
numbers. This jog becomes more pronounced with increaseof camber or thickness and with rearward movement of tile
position of minimum pressure on tile basic thickness form.
This jog decreases rapidly in severity with increasing Rey-
nolds number, becomes merely a change in lift-curve slope,
and is practically nonexistent at a Reynolds number of9 X 106 for most airfoils that would be considered for practical
application. This jog may be a consideration in the selection
of airfoils for small low-speed airplanes. An analysis of
the flow conditions leading to tiffs jog is presented in refer-ence 28.
The variation of maximum lift coefficient with airfoil
thickness ratio at a Reynolds number of 6X 106 is shown in
figure 39 for a number of NACA airfoil sections. The airfoilsfor which data are presented in this figure have a range of
thickness ratio from 6 to 24 percent and cambers up to
4 percent chord. From the data for the NACA four- and
five-digit-series airfoil sections (fig. 39 (a)), the maximumlift coefficients for the plain airfoils appear to be the greatest
for a thickness of 12 percent. In general, the rate of change
of maximum lift coefficient with thickness ratio appears
to be greatest for airfoils having a thickness less than 12percent. The data for the NACA 6-series airfoils (figs.
39 (b) to 39 (e)) also show a rapid increase in maximum liftcoefficient with increasing thickness ratio for thickness
ratios of less than 12 percent. For NACA 6-series airfoil
sections cambered to give a design lift coefficient of not more
than 0,2, the optimum thickness ratio for maximum lift
coefficient appears to be between 12 and 15 percent, excep!
for the airfoils having the position of minimum pressure at
60 percent chord. The optimunl thickness ratio for the
NACA 66-series sections cambered for a design lift coeffi-
cient of not more than 0.2 appears to be 15 percent or greater
SUMMARY OF AIRFOIL DATA 31
-4--
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230 {5-d/git )
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I °
(b) NAOA 63-series.
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4 8 /2 16 ZO
A_rfo/l thickness, percenf of chord
(e)NACA66-series.
24
FIaURZ 37.--Measured section angles of zero lift for a number of NACA airfoil sections of various thicknesses and camber. R=6XI(_.
Z4
24
32 REPORT NO. 8 2 4--1_TATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
./2
Q..
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I I l l I I [ I
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.-Smooth
Rough->
22 24
i =--a,_-' -'_{--i- --_ - -
C h
o 0
o ./!0 .2L_ .41
/0 12 f4 16 ,8 20
A/rfo// th/ckness, percent of chord
(c) NACA 64-series.
,.Sin oo fh
- :,Rouglh
22 24
-- ---'._--t_ ..... -_ ,_"x
(b)
6
.-Smooth
"Rouqh
Ctl
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(b) NACA C_-series.
22 24
./Z
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.o_(d)
8
,,Smooth
",,
c,_o 0
.d
.6
/6 /8
"ROUgh
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A/rfo// th/ckness, percent of cho,_d
(d) NACA 65-series.
FIGURE 38.--Variation of lift-curve slope
¢J
./2
.I0)
&% .08
0%
o 0
0 .2.4
i
8 '0 '_ '4 16 18 20 22
A/rfo// /h/ckness, percent of chord
_:- .Smoo /h:_L_
.I Ix _,'Rough
2d
(e) NACA66-series.
with airfoil thickness ratio and camber for a number of NACA airfoil sections in both the smooth and rough conditions, R=6)<10 _.
The available data indicate that a thickness ratio of 12
percent or less is optimum for airfoils having a design liftcoefficient of 0.4.
The maxinmm lift coefficient is least sensitive to variations
in position of minimum pressure on the basic thickness formfor airfoils having thickness ratios of 6, 18, or 21 percent.
The maximum lift coefficients corresponding to intermediatethickness ratios increase with forward movement of the
position of minimum pressure, particularly for tltose airfoils
having design lift coefficients of 0.2 or h,ss.The maximum lift coefficients of modcratcly cambered
NACA 6-series sections increase with increasing camber
(fig. 39 (b) to 39 (e)). The addition of camber to the sym-metrical airfoils causes the greatest increments of maximum
lift coefficient for airfoil thickness ratios varying from 6 to
12 percent. The effectiveness of camber as a means of
increasing the maximum lift coefficient generally decreasesas the airfoil thickness increases beyond 12 or 15 percent.The available data indicate that the combination of a 12-
percent-thick section and a mean line cambered for a designlift coefficient of 0.4 yiehls the highest maximum lift
coefficient.
[
SUMMARY OF AIRFOIL DATA 33
J.8
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28
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bolh/8 /2 /6 ZO
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(b) NACA 63-series.
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splff flop
Plo/noi_£oil
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(e) NAOA64series.
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sph/ flop
Plo_kno,k-foil
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#20co
Cz;
LoO¢ .Z
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8 12 15 _0
_/_foi/ th/c/rmess, perce_t of c/_ord
(d) NAOA6,5-series.
A_t'fo# w/lh
spht flop
Plaina_ f ofl
Z4
2.8
_'_.4
_20ot_
_ /.8
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I I I I4 8 /g 16 ZO 24
Airfoil fhiclr_ess, percemf of c/_ord
(e) NAOA 66-series.
Alr-_off with
sp/i/ flop
P/o/'noff-foil
FIGURE 39.--Variation of maximum section lift eoe_eient with airfoil thickness ratio and camber for several NACA airfoil sections with and without simulated split flaps and standardroughness, R=fXIO_.
34 REPORT :NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The variation of maximum lift with type of mean line is
shown in figure 40 for one 6-series thickness distribution.
No systematic data are available for mean lines with values
of a less than 0.5. It should be noted, however, that airfoilssuch as the NACA 230-series sections with the maximum
camber far forward show large values of maximum lift.Airfoil sections with maximum camber far forward and with
lhickness ratios of 6 to 12 percent usually stall from the
leading edge with large sudden losses in lift. A more de-
sirable gradual stall is obtained when the location of maxi-mum camber is farther back, as for the NACA 24-, 44-, and
6-series sections with normal types of camber.
2.O
_/.8
q)0
.8(9COO)
f
Reyno/ds numbero _OxlO_c_ 9.0
0 .2 .4 .6 .8 1.0
Type of combeG a
FIGURE 40.--Variation of maximum lift coefficient with type of camber for some NACA
653-418 airfoil sections from tests in the Langley two-dimensional low-turbulence pressuretunnel.
A comparison of the maximum lift coefficients of NACA64-series airfoil sections cambered for a design lift coefficientof 0.4 with those of the NACA 44- and 230-series sections
(fig. 39) shows that the maximum lift coefficients of the
NACA 64-series airfoils are as high or higher than those ofthe NACA 44-series sections in all cases. The NACA 230-
series airfoil sections have maximum lift coefficients somc-
what higher than those of the NACA 64-series sections.
The scale effect on the maximum lift coefficient of a large
number of NACA airfoil sections for Reynolds numbers
from 3X10 _ to 9X108 is shown in figure 41. The scale
effect for the NACA 24-, 44-, and 230-series airfoils (figs.
41 (a) and 41 (b)) having thickness ratios from 12 to 24 percent
is favorable and nearly independent of the airfoil thickness.
Increasing the Reynolds number from 3X106 to 9X106results in an increase in the maximum lift coefficient of
approximately 0.15 to 0.20. The scale effect on the NACA
00- and 14-series airfoils having thickness ratios less than0.12c is very small.
The scale-effect data for the NACA 6-series airfoils (figs.
41 (c) to 41 (f)) do not show an entirely systcmatic variation.
In general, the scale effect is favorable for these airfoilsections. For the NACA 63- and 64-series airfoils with
small camber, the increase in maximum lift coefficient with
increase in Reynolds number is generally small for thickness
ratios of less than 12 percent but is somewhat larger for thethicker sections. The character of the scale effect for the
NACA 65- and 66-series airfoil sections is similar to that for
the NACA 63- and 64-series airfoils but the trends are not
so well defined. In most cases the scale effect for NACA
6-series airfoil sections cambered for a design lift coefficient
of 0.4 or 0.6 does not vary much with airfoil thickness ratio.
The data of figure 42 show that the maximum lift coefficient
for the NACA 63(420)-422 airfoil continues to increase with
Reynolds number, at least up to a Reynolds number of26X 106.
The values of the maximum lift coefficient presented were
obtained for steady conditions. The maximum lift coeffi-
cient may be higher when the angle of attack is increasing.
Such a condition might occur during gusts and landing
maneuvers. (See reference 41.)
The systematic investigation of NACA 6-series airfoils
included tests of the airfoils with a simulated split flap de-flected 60 °. It was believed that these tests would serve as
an indication of the effectiveness of more powerful types of
trailing-edge high-lift devices although sufficient data to verify
this assumption have not been obtained. The maximum lift
coefficients for a large number of NACA airfoil sections
obtained from tests with the simulated split flap are presented
in figure 39.
The data for the NACA 00- and 14-series airfoils equipped
with split flap for thickness ratios from 6 to 12 percent showa considerable increase in maximum lift coefficient with in-
crease in thickness ratio. Corresponding data for the NACA
44-series airfoils with thickness ratios h'om 12 to 24 percent
show very little variation in maximum lift coefficient withthickness. For NACA 6-series airfoils equipped with split
flaps the maximum lift coefficients increase rapidly with
increasing thickness over a range of thickness ratio, the range
beginning at thickness ratios between 6 and 9 percent, depend-
ing upon the camber. The upper limit of this range for the
symmetrical NACA 64- and 65-series airfoils appears to be
greater than 21 percent and for the NACA 63- and 66-series
airfoils, approximately 18 percent. Between thickness ratios
of 6 and 9 percent the values of maximum lift coefficient for
the symmetrical NACA 6-series airfoils are essentially the
same regardless of thickness ratio and position of minimum
pressure on the basic thickness form. The maximum liftcoefficient decreases with rearward movement of minimum
pressure for the airfoils having thickness ratios between 9 and
18 percent.
SUMMARY OF .AIRFOIL DATA 35
L2 i -_
/ c "/
IVACA 14-5er/es (Z-d/g f]/.2
.8
/_m /.5
(a) _7._ IVACAOO-ser/e.s(d-d/q/t)
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1.2 X ,_ -z_
u "0 .6Cb
1.6 _ /6
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I. C "_ _ "-'_- _ >" I. _?
_""_--_-_ 04 end 0.6
16: 1.8
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CW
(d)
f T/_CA
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Z l-ser_es !-dig/i) .._
-___._ ___ -o c.:O._, and 0.6
LZ "..o L2i.
4 8 12 I_ ZO 24 Z8 ?2 0A,7-foil thickness, pea'cent of chord
(a) NAOA tou_-di_it series,(e) NACA &'l-serieso(e) NACA 6_series,
/f
.J
! f
"o
,,v:O,/
Cli : 0
e,_ : O.4
_ _.-__ __._
I -_" _ "-o c_ :0.2
4 8 I_ I_ 20 24 28 ?gAirfoil thickness_ percent of cMord
(b) N.&O.& four- and. fiTe,-di6it _erie&(d) NACA 64-series.(f) NAOA 66-series,
Fleisll_ 41.--Vuriation of maximum section lift coefficient with airfoil thickness ratio at several Reynolds numbers for a number of NACA airfoil sections of different cambers.
36 REPORT NO. 824--NATIO:N'AL ADVISORY COMMITTEE :FOR AERONAUTICS
c_
/
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f15
%
i
i
I!
i
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I
i
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P._ _uq/o/jjaoo Eo_p LIo/(oa S
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r
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k
SUMMARY OF AIRFOIL DATA 37
Substantial increments in maximum lift coefficient with
increase in camber are shown for the NACA 6-series airfoils
of moderate thickness ratios (10 to 15 percent chord) withsplit flaps. For the airfoils having thickness ratios of 6
percent and for the airfoils having thickness ratios of 18 or 21
percent, the maximum lift coefficient is affected very little by
a change in camber. For thickness ratios greater than 15percent, the maximum lift coefficients of the NACA 63- and
64-series airfoils cambered for a design lift coefficient of 0.4
equipped with split flaps are greater than the correspondingmaximum lift coefficients of the NACA 44-series airfoils.
Three-dimensional data.--No recent systematic three-
dimensional wing data obtained at high Reynolds numbers
are available, so that it is difficult to make any comparisonwith the section data. When tile maximum-lift data for
three-dimensional wings are compared with section data,
account should be taken of the span lc.ad distribution overthe wing. The predicted maximum lift coefficient for the
wing will be somewhat lower than the maximum lift coeffi-
cients of the sections used because of the nonuniformity ofthe spanwise distribution of lift coefficient. The difference
amounts to about 4 to 7 percent for a rectangular wing withan aspect ratio of 6.
Maximum-lift data obtained from tests of a number of
wings and airplane models in the Langley 19-foot pressuretunnel are presented in table II. Although section data at
tlle Reynolds numbers necessary to permit a detailed com-
parison are not available, the maximum lift coefficient for
plain wings given in table II appears to be in general agree-ment with values expected from section data. The data for
the airplane models are presented to indicate the maximumlift coefficients obtained with various airfoils and
configurations.
LIFT CHARACTERISTICS OF ROUGH AIRFOILS
Two-dimensional data.--Most recent airfoil tests, espe-cially of airfoils with the {hicker sections, have included tests
with roughened leading edge (reference 37), and the available
data are included in the supplementary figures.
The effect on maximum lift coefficient of various degrees
of roughness applied to the leading edge of the NACA63(420)-422 airfoil is shown in figure 23. The maximum lift
coefficient decreases progressively with increasing roughness
(reference 36). For a given surface condition at the leading
edge, the maximum lift coefficient increases slowly with
increasing Reynolds number (fig. 43). Figure 24 shows that
roughness strips located more than 0.20c from the leadingedge have little effect on the maximum lift coefficient or
lift-curve slope. The results presented in figure 38 show
that the effect of standard leading edge roughness is to de-
crease the lift-curve slope, particularly for the thicker air-
foils having the position of minimum pressure far back.
These data are for a Reynolds number of 6 >( 106. Maximum-
2.O
/.6
q)
z2
o O.OOP r-oughness
o .00_I r-ouqhness _
1_ .O/ /Smoofhr-Oughness
0 4 8 /2 /6 2(7 24x/8"Revno/ds number, }:1
FIGURE 43.--Effects of Reynolds number on maximum section lift coefficient c_... of theNACA 63(420)-422 airfoil with roughened and smooth leading edge.
lift-coefficient data at a Reynolds number of 6X106 for a
large number of NACA airfoil sections with standard rough-
ness are presented in figures 39 and 41: The variation ofmaximum lift coefficient with thickness for the NACA four-
and five-digit-series airfoil sections shows the same trends
for the airfoils with roughness as for the smooth airfoils
except that the values are considerably reduced for all ofthese airfoils other than the NACA 00-series airfoils of
6 percent thickness. For a given thickness ratio greater than15 percent, the values of maximum lift coefficient for the
four- and five-digit-series airfoils are substantially the same.Much less variation in maximum lift coefficient with thick-
ness ratio is shown by the NACA 6-series airfoil sections in
the rough condition than with smooth leading edge. The
maximum lift coefficients of the 6-percent-thick airfoils are
essentially the same for both smooth and rough conditions.
The variation of maximum lift coefficient with camber, how-
ever, is about the same for the abfoils with standard rough-ness as for the smooth sections. The maximum lift coeffi-
cient of airfoils with standard roughness generally decreases
somewhat with rearward movement of the position of mini-
mum pressure except for airfoils having thickness ratios
greater than 18 percent, in which case some slight gain inmaximum lift coefficient results from a rearward movement
of the position of minimum pressure.
Except for the NACA 44-series airfoils of 12 to 15 percent
thickness, the present data indicate that the rough NACA
64-series airfoil sections cambered for a design lift coefficient
of 0.4 have maximum lift coefficients consistently higher than
the rough airfoils of the NACA 24-, 44-, and 230-series air-
foils of comparable thickness. Standard roughness causesdecrements in maximum lift coefficient of the airfoils with
split flaps that are substantially the same as those observedfor the plain airfoils
918392--51----4
38 REPORTNO.824--NATIONALADVISORYCOMMITTEEFORAERONAUTICS
/.6
_1.2 -- --
_.8_
._..zl
(a)=4
-8 0
/ "\b
ii /' tt
/ ( /o AS do/ivened by shop, d _ As rich'repealby shop, m As delivered by shop,
TDT lest 468 TDT test 464 / TOT test 494-0 Fsnol condition, / o Fl:_ol condition o FiY_olcondition,TDT t_st 520 TOT test 498 TOT test 523
/(b) (c)_/
8 15 24 -8 0 8 15 24 -8 0 8 155echbn ongle of o/tock, _ deq.
(a) NAOA 2412. (b) NACi 2415. (c) NACA 23012.
FIGURE 44.--Lift characteristics of the NACA 23012, 2412, and 2415 airfoil sections as affected by normal model inaccuracies. R=9X106 (approx.).
24 .72
I
q_
k) ._)" .--
.Z i _ . Z<:<_.'c'/ pFC_UFe tunne/)
/ ,0 ci f, iIl-_ccale(L rocjlc_ty ?-u,mPTeI)
II0
:_ / O J U /Y / 5 ZO Zd
FIOUliE 45.--The effects of surface conditions on the lift characteristics of a fighter-type
airplane. R=2.SX106.
The maximum lift coefficient may be lowered by failure to
maintain the true airfoil contour near the leading edge, but
no systematic data on this effect have been obtained. Ex-
amples of this effect that were accidentally encountered are
presented in figure 44, in which lift characteristics are given
for accurate and slightly inaccurate models. The modelinaccuracies were so small that they were not found previous
to the tests.
Three-dimensional data.--Tests of several airplanes in the
Langley full-scale tunnel (reference 42) show that many fac-tors besides the airfoil sections affect the maximmn lift co-
efficient of airplanes. Such factors as roughncss, leakage,
leading-edge air intakes, armament installations, nacelles,
and fuselages make it difficult to correlate the airplane maxi-mum lift with the airfoils used, even when the flaps are
retracted. The various flap configurations used make sucha correlation even more difficult when the flaps are deflected.
When the flaps were retracted, both the highest and thelowest maximum lift coefficients obtained in recent tests of
airplanes and complete mock-ups of conventional configura-tions in the Langley full-scale tunnel were those obtained
with NACA 6-series airfoils.Results obtained from tests of a model of an airplane in
the Langley 19-foot pressure tunnel and of the airplane in
the Langley full-scale tunnel are presented in figure 45.Both tests were made at approximately the same Reynoldsnumber. The results show that the airplane in the service
condition had a maximum lift coefficient more than 0.2
lower than that of the model, as well as a lower lift-curve
slope. Some improvement in the airplane lift characteristicswas obtained by scaling leaks. These results show that air-
plane lift characteristics are strongly affected by details not
reproduced on large-scale smooth models.
SUMMARY OF AIRFOIL DATA 39
_2
;0
i
J
2i! ---
-4 0 4 8 /2 /6 20
Anqle of o/toch_ _ deg24
FIGURE 46.--The effect on the lift characteristics of fixing the transition on a model in theLangley 19-foot pressure tunnel. R=2.7XlO 6. (Model with Davis airfoil sections.)
Lift characteristics obtained in the Langley 19-foot pres-
sure tunnel for two airplane models in the smooth condition
and with transition fixed at the front spar are presented in
figures 46 and 47. In both cases, the lift-curve slope was de-
creased throughout most of the lift range with fixed transi-tion. The maximum lift coefficient was decreased in onecase but was increased in the other case.
UNCONSERVATIVE AIRFOILS
The attempt to obtain low drags, especially for long-range
airplanes, leads to high wing loadings together with relatively
low span loadings. This tendency results in wings of high
aspect ratio that require large spar depths for structural
efficiency. The large spar depths require the use of thickroot sections.
This trend to thick root sections has been encouraged by
the relatively small increase in drag coefficient with thickness
ratio of smooth airfoils (fig. 12). Unfortunately, airplane
wings are not usually constructed with smooth surfaces and,
in any case, the surfaces cannot be relied upon to stay smooth
under all service conditions. The effect of roughening the
leading edges of thick airfoils is to cause large increases in the
0 A,'olur_o/tr-onsi/l'On
o 7r-m?s/h'on f/xod ot. IOe
I
_¢ 8 12 16 ZO 24 28Angle of o;/och, v(, dec3
FIGURE 47.--The effect on the lift characteristics of fixing the transition on a model in the
Langley 19-foot pressure tunnel. R=2.TX106. (Model with NACA airfoil sections.)
drag coefficient at high lift coefficients. The resulting dragcoefficients may be excessive at cruising lift coefficients for
heavily loaded, high-altitude airplanes. Airfoil sections thathave suitable characteristics when smooth but have excessive
drag coefficients when rough at lift coefficients corre-
sponding to cruising or climbing conditions are classified asuneonservative.
The decision as to whether a given airfoil section is conserv-
ative will depend upon the power and the wing loading of
the airplane. The decision may be affected by expected
service and operating conditions. For example, the ability
of a multiengine airplane to fly with one or more engines in-
operative in icing conditions or after suffering damage incombat may be a consideration.
As an aid in judging whether the sections are conservative,
the lift coefficient corresponding to a drag coefficient of 0.02
was determined from the supplementary figures for a large
number of NACA airfoil sections with roughened leadingedges. The variation of this critical lift coefficient with air-
foil thickness ratio and camber is shown in figure 48. These
data show that, in general, the lift coefficient at which the
drag coefficient is 0.02 decreases with rearward movement of
40 REPORT NO. 824--NATIONAL ADVISORY COMEMITTEE FOR AERONAUTICS
LO
0 4 8 12 16 20 24 28 32
Airfoil #h/ckness, percen/ of chord
(a) NACA four- and five-digit series.
(b) NACA 63-series.
(e) NACA 64-series.
(d) NACA 65-series.
(e) NACA. 66-series.
FIGVnE 48.-Variation of the lift coefficient corresponding to a drag coefficient of 0.02 with
thickness and camber for a number of NACA airfoil sections with roughened leading edges.
Rffi6X106.
position of minimum pressure. The thickness ratio for
which this lift coefficient is a maximum usually lies between
12 and 15 percent; variations in thickness ratio from this
optimum range generally cause rather sharp decreases in thecritical lift coefficient. The addition of camber to the
symmetrical airfoils usually causes an increase in the critical
lift coefficient except for the very thick sections, in which case
increasing the camber becomes relatively ineffectual and may
be actually harmful. All the data of figure 48 correspond to
a Reynolds number of 6X106. As shown in figure 49, the
drag coefficient at flight values of the Reynolds number may
be considerably lower than the drag coefficient at a Reynolds
number of 6X 106 if the roughness is confined to the leading
edge.
PITCHING MOMENT
The variation of the quarter-chord pitching-moment coef-
ficient at zero angle of attack with airfoil thickness ratio and
camber is presented in figure 50 for several NACA airfoil
sections. The quarter-chord pitching-moment coefficients of
the NACA four- and five-digit-series airfoils become less
negative with increasing airfoil thickness. Almost no varia-
tion in quarter-chord pitching-moment coefficient with air-
foil thickness ratio or position of minimum pressure is shown
by the NACA 6-series airfoil sections. As might be expected,
increasing the amount of camber causes an almost uniform
negative increase in the pitching-moment coefficient.As discussed previously, the pitching moment of an airfoil
section is primarily a function of its camber, and thin-airfoil
theory provides a means for estimating the pitching moment
from the mean-line data presented in the supplementary
figures. A comparison of the experimental moment coeffi-cient and theoretical values for the mean lines is presented
in figure 51. The experimental values of the moment coeffi-cients for NACA 6-series airfoils cambered with the uniform-
load type mean line are usually about three-quarters of the
theoretical values (figs. 50 and 51). Airfoils employing mean
lines with values of a less than unity, however, have moment
coefficients somewhat more negative than those indicated by
theory. The use of a mean line having a value of a less than
unity, therefore, brings about only a slight reduction in
pitching-moment coefficient for a given design lift coefficient
when compared with the value obtained with a uniform-
load type mean line. The experimental moment coefficients
for the NACA 24-, 44-, and 230-series airfoils are also less
negative than those indicated by theory but the agreement
is closer than for airfoils having the uniform-load type meanline.
The pitching-moment data for the airfoils equipped with
simulated split flaps deflected 60 ° (fig. 50) indicate that the
value of the quarter-chord pitching-moment coefficient be-
comes more negative with increasing thickness for all theah'foils tested. For the thicker NACA 6-series sections the
magnitude of the moment coefficient increases with rearward
movement of the position of minimum pressure.
SUMMARY OF AIRFOIL DATA 41
I I
%
! !
42 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
C
.cj
CO
t,_ 2
E
"_ _..3
(a) NACA four and five-digit serif.
'"¢-- o 0 --
El .f
_ I zx .4
2
-'_0 4 8 12 16 2o LwAiPfoil ti_icHmems> pel-r_mf of chor-d
0
COO
C_ -.2
q)
(b!_ all0
Ie _ -_S- I_ _o 24 z_
A it" fo/I fh,,'ol_n_mj percent of chr_,4
(b) blACA63-seri_s.
(c) NACA64-series.
]L'8
fr
1
I
0
._ -./
G
Ii
."1_{3o
= " o ' "",,io :_7 _ +_,o ,:Lk,
---+- ..... i
I i
' I
-- ..__.____ _
' _
4 8 IZ IG 20Al'rfoi/ thichness_ per-ce_f of cho_-d
(d) NACA 65-series.
I !i
I
O0 ___© .?
_xt .,d_ __
---T-- --
" 2_ Z8
' I
__ ]
oO- b .z
A .':7
24 28/1,'r'fo, "1 t'_/c'tw_es'% percenf of chord
(e) NACA 66-series.
F_(iullE 50.--Variation of sect ion quarter-chord pitching-moment coefficient (measured at an angle of attack of 0 a) with airfoil thickness ratio for several NACA airfoil sections of different cam her,
R=6X10_,
SUMMARY OF AIRFOIL DATA 43
_5
-./2
_ _./
_ -.08
'_ -.04(3_d
6_3-61 _ a-05,,,, /
/654-42/, a=GS,, 7 o'"
--6,ga- 41_ 0=0.5,,'
6_ 4-,_go. a:a_ i/.6_(2/:_)_z/8o/_:._-24z_
//
/65_-6/8-"
.-654-42/,-65o-415
-#3. 4-420
/
/ t/ "" "'6"6(21_)-21 _ a-O.6
d--230/2
7 I0 -.02 -.O_Z -.06 -.OB -.10 -.Ig -.14 -.16
Theore//co/ rnomenf coefficl'en/ for _I_ oirfoilrneon /i77e obou f quor/er- chord'po/7_f
FIGURE 51.--Comparison of theoretical and measured pitching-moment coefficients for some
NACA airfoils. R=6X10_.
POSITION OF AERODYNAMIC CENTER
The variation of chordwise position of the aerodynamiccenter corresponding to a Reynolds number of 6X 106 for a
large number of NACA airfoils is presented in figure 52.From the data given in the supplementary figures there
appears to be no systematic variation of chordwise position
of aerodynamic center with Reynolds number. The data
for the NACA 00- and 14-series airfoils, presented for thick-
ness ratios less than 12 percent, show that the chordwise
position of the aerodynamic center is at the quarter-chord
point and does not vary with airfoil thickness. For the
NACA 24-, 44-, and 230-series airfoils with thickness ratios
ranging from 12 to 24 percent, the chordwise position of the
aerodynamic center is ahead of the quarter-chord point andmoves forward with increase in thickness ratio.
The chordwise position of the aerodynamic center is behind
the quarter-chord point for the NACA 6-series ah'foils and
moves rearward with increase in airfoil thickness, which is
in accordance with the trends indicated by perfect-fluid
theory. There appears to be no systematic variation ofchordwise position of the aerodynamic center with camber or
position of minimum pressure on the basic thickness form forthese airfoils.
The data of reference 43 show important forward move-
ments of the aerodynamic center with increasing trailing-edge
angle for a given airfoil thickness. For the NACA 24-, 44-,
and 230-series airfoils (fig. 52) the effect of increasing
trailing-edge angle is apparently greater than the effect of
increasing thickness. For the NACA 6-series airfoils, theopposite appears to be the case.
HIGH-LIFT DEVICES
Lift characteristics for two NACA 6-series airfoils equippedwith plain flaps are presented in figure 53. These data
show that the maximum lift coefficient increases less rapidlywith flap deflection for the more highly cambered section.
Lift characteristics of three NACA 6-series airfoils with split
flaps are presented in reference 44 and figure 54. The maxi-
mum-lift increments for the 12-percent-thick sections were
only about three-fourths of that increment for the 16-percent-thick section. The maximum lift coefficient for the thicker
section with flap deflected is about the same as that obtained
for the NACA 23012 airfoil in the now obgolete Langley
variable-density tunnel (reference 45) and in the Langley7- by 10-foot tunnel (reference 46).
Tests of a number of slotted flaps on NACA 6-series
airfoils (supplementary figures and reference 47) indicate that
the design parameters necessary to obtain high maximum
lifts are essentially similar to those for the NACA 230-
series sections (references 48 and 49). Lift data obtained
for typical hinged single slotted 0.25c flaps (fig. 55 (a)) on
the NACA 63,4-420 airfoil are presented in figure 55 (b).
A maximum lift coefficient of approximately 2.95 was ob-
tained for one of the flaps. Lift characteristics for the
NACA 653-118 airfoil fitted with a double slotted flap
(reference 47 and fig. 56 (a)) are presented in figure 56 (b).
A maximum lift coefficient of 3.28 was obtained. It may
be concluded that no special difficulties exist in obtaining
high maximum lift coefficients with slotted flaps on moderatelythick NACA 6-series sections.
Tests of airplanes in the Langley full-scale tunnel (reference
42) have shown that expected increments of maximum lift
coefficient are obtained for split flaps (fig. 57) but not for
slotted flaps (fig. 58). This failure to obtain the expected
maximum-lift increments with slotted flaps may be attributed
to inaccuracies of flap contour and location, roughness near
the flap leading edge, leakage, interference from flap sup-
ports, and deflection of flap and lip under load.
LATERAL-CONTROL DEVICES
An adequate discussion of lateral-control devices is outside
the scope of this report. The following brief discussion is
therefore limited to considerations of effects of airfoil shapeon aileron characteristics.
The effect of airfoil shape on aileron effectiveness may be
inferred from the data of figure 59 and reference 50. The
section aileron effectiveness parameter Aa0/Aa is plotted
against the aileron-chord ratio cJc for a number of airfoils
of different type in figure 59. Also shown in this figure
are the theoretical values of the parameter for thin airfoils.
.22
26
.24
28
REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
8 / 2 /8 20 24
Airfo// fh/ckness, percent of chord
(a) NACA four- and five-digit series.(c) NACA 64.series.
4 28 32 240 4 8 12 16 20 24 28 32
A/r£oi/ ÷hickness, /oercenf of chord
(b) NAOA _-se_les.(d) NACA 65.series.
(e)NAOA 66-se,rles.
Fmul_ 52.--Variation of section ch0rdwise position of the aerodynamic center with airfoil thickness ratio for several NACA airfoil sections of different cambers. Rffi6Xl0 I.
L
SUMMARY OF AIRFOIL DATA 45
/VACA 66(215)-216-.
J
-20 0 20 40 60 80
Flop def/ecfionj 6:, deg
FIC,URE 53.--Maximum lift coel_cients for the NACA 65,3-618 and NACA 66(215)-216 air-foils fitted with 0.20-airfoil-chord plain flaps. R=6X10 _.
The data show no large consistent trends of aileron-effective-ness variation with airfoil section for a wide range of thick-ness distributiotls and thickness ratios. In order to evaluate
aileron characteristics from section data, a method of analysis
is necessary that will lead to results comparable to the usual
curves of stick force against helix angle pb/2V for three-
dimensional data. The analysis that follows is considered
suitable for comparing the relative merits of ailerons fromtwo-dimensional data.
Two-dimensional data are presented in the form of the
equivalent change in section angle of attack Aao required tomaintain a constant section lift coefficient for various de-
flections of the aileron from neutral. This equivalent change
in angle of attack is plotted against the hinge-moment param-eter 5cRa, which is the product of the aileron deflection
from neutral and the resulting increment of hinge-moment
/i ,_' 11
P if
..4,_4"
//S" I)_ -4
.:.:;';"
/¢(opprox.)
o NACA 66(2/5J-2/6 G.Ox/OeNACA 23012 3.5
"from f'ef.. 45) (e:£)-o NACA ©_I-212 6.00 NACA 651-21-P 6.0
0 20 40 60 ,90 I00
Flop deflection, 6:: deg
FIGURE 54.--Maximum lift coefficients for some NACA airfoils fitted with 0.20-airfoil-chord
split flaps.
coefficient based on the wing chord. This method of analysis
takes into account the aileron effectiveness, the hinge
moments, and the possible mechanical advantage between
the controls and the ailerons. The larger the value of Aa 0
for a given value of the hinge-moment parameter, the more
advantageous the combination should be for providing a
large value of pb/2V for a given control force. The assump-
tion that the aileron operates at a constant lift coefficient
as the airplane rolls is not entirely correct, however, and
involves an overestimation of the effect of changing angle
of attack on the hinge-moment coefficient. In addition,
the span of the ailerons and other possible three-dimensional
effects are not considered. In spite of these inaccuracies,
the method provides a useful means of comparing the two-
dimensional characteristics of different ailerons.
46 REPORT NO. 824------NATIONAL ADVISORY COMMITTE'E FOR AERONAUTICS
I
\
SUMMARY OF AIRFOIL DATA 47
S
000- --_
• 781Flop r-efroc/ed
I ,..Flop pofh
-.2/z r/op)X_,\/
808 plvof o
/-/0t9 piVOT TPom U .---" f_ _7._ o _,._
to 45 ° deflect/on-'" de-fle-cfion
Flop de_leefed 65 _
3.2
28
2.4
I
_d
:< 1.6
_ /.2
._.
.8
//
/
/
.4
(b)
0 20 40 60 80 IO0
Flop deflection, 6_ deg
(a) Flap configuration.(b) Maximum lift characteristics.
FIGURE 56.--Flap configuration and maximum lift coefficients for the NACA 65_-118 airfoil
with a double slotted flap. R=6X10 _.
.8
//
I I 1 I I I I I I//,_ of ogreemem/ be/_veen fneosLyr-ed
GrTd pred/'c'e_ f_'_:_S_/7_S- 1, '
//
JX
0 .2 .4 .6 .8 LO L2
ACL,. pr-edlcted
FIGURE 57.--Comparison between measured values of the increments in lift coefficients due
to flap deflection and values predicted from two-dimensional data. Split flap.
LO
.8
.2/
/
i
Vo
[
/ i4 .6 .8
_1o
0 .2 LO LZ
A£'_,, p_ed/cfed
FIGURE 58.--Comparison between measured values of the increments in lift coefficients dueto flap deflection and values predicted from two-dimensional data. Slotted flap.
48 REPORT NO. 8 2 4--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
SUPPLEMENTARY INFORMATION REGARDING TESTS OF TWO-DIMENSIONAL MODELS
Symbol
o
+
X
C]
0
A
_7
b
p"
r,,
0
c_
[3-
q
0
Basic airfoil Type of flap
NACA 0009 ......................................... Plain ................................
NACA 0015 ............................................ do ............................
NACA 23012 ............................................... do ...............................
NACA 66(2x15)-009 ................................... Plain, straight contour ..............
NACA 66-009 ....................................... Plain ...............................
NACA 63,4-4(17.8) (approx.) ............................ Internally balanced .................
NACA 66(2x15)-216, a=0.6 .................................. do .............................
NACA 66(2x15)-I16, a=0.6 ................................ do .............................
NACA 04,2-(1.4) (13.5) ................................ Plain .............................
NACA 65,2-318 (approx.) .............................. Internally balanced ...............
NACA 63(420)-521 (approx.) ............................. do ..........................
NACA 66(215)-216, a=O.6 ................................. do ..............................
NACA 66(215)-014 .......................... Plain ..........................
NACA 66(215)-216, a=0.6 ............................. do ............................
NACA 652-415 ............................................. do .............................
NACA 653 418 ......................................... do ..............................
NACA 651-421 ............................................ do ..............................
NACA 65o1_)-213 .................................... Internally balanced .................
NACA 745A317 (approx.) ................................. do ..............................
NACA 64,3-013 (approx.) ................................... do .............................
NACA 64,3-1(15.5) (approx.) ................................ do ..............................
i Approaching 1.00.
Air-flow characteristics
T
1.93
1.93
1.60
1.93
1.93
(1)
(1)
0)
0)
(1)
0)
0)
1.93
(')
0)
(1)
(1)
(1)
(1)
0)
(1)
M
O. 08
.10
.11
• 10
.11
.17
.18
.14
.14
.20to• 48.09
.13
.13
.13
.14
.13
.13
• 13
Reference
R
51 to 55
56
57, 48
58
59
59
59
59
l 60
61
62
02
62
1.4XIO 6
2.2X106
1.4X106
1.4XlO 6
2.5X108
5.3X106
6.0XlO 6
13.0XlO 6
6.0XlO _
8.0Xl082.8X10 _
to6.8X10 _1.2XlO 8
6.0XlO _l
6.0XlO_
6.0X10 t
6.0XlO 6
8.0XIO 6
6.0XlO 8
6.0XlO 6
6.0XIO 6
.8
,_o "Theoretical .... vl _ _.6 Th_oreticol- ,'" i li
o - ,2-" "" _ "'Exloerimen¢ol _ " 7
q) f#
Z " //ss _ s
! ,/
iii i P" 1(a) _// (b)0 ./ ._- .3 .4 0 .I .Z .3 .d
A ;/eron chord rot/G ca/e A/le/'or) chord ro#/o, male
(a) $ range from 0° to 10% (b) ,_range from 0° to 20 °.
FI6UEE 59.--Variation of section aileron effeetiveness with aileron chord ratio for true-airfoil-contour ailerons without exposed overhang balance on a number of airfoil sections.
Gaps sealed; el=0.
SUMMARY OF AIRFOIL DATA 49
Basic airfoil
NACA 0009
NACA 64,2-(1.4) 03.5)NACA 66(215)-216, a=0.6_
ct Type _/)aileron Air-flow characteristics Refer-..... • AI R ence
O 0.20cplain 1.93 0.10 ] 1.4X10 e 63• 150 0.187cplain (_) I .18 I 4-0X106 / - - I
/ "100/ 0.20c plain I (') I "33t 9.OXi0' I 64 I
True airfoil contour.
2 Approaching 1.00.
O>
I I I
N_O_ 0009, ,..
.' "" -. ,-N/_CA 6d, 2-(Lzl) (125)
-/ U"
/'
-2
-4l
-6
I
dNeror? de2flec//om, c/eg, ._ /_v- _ I--- / / "- /2 .---_ "'"
/6 ..---- ----"
'_,,
-8
-.0018 -.0016 =00141 -.0012 -.0010 =0008 :O00B :00041 =0002 0
A ¢=_, rad/ons
FmtTI_E 60.--Variation of the hinge-moment parameter Ae_l with the equivalent change in
section angle of attack required to maintain a constant section lift coefficient for deflection
of the aileron on the NACA 0009, NACA 64,2-(1.4)(13.5), and NACA 66(215)-216, a=0.6
airfoil sections. Gaps sealed.
For the purpose of evaluating the effect of airfoil shape onthe aileron characteristics, it is desirable to make the com-
parison with unbalanced ailerons to avoid confusion. Plots
of the parameters for plain unbalanced flaps of true airfoil
contour on three airfoil sections are shown in figure 60.The characteristics of the NACA 66 (215)-216, a = 0.6 section
are essentially the same as those for the NACA 0009 airfoil
within the range of deflection for which data are available•
The NACA 64,2-(1.4)(13.5) airfoil shows appreciably
smaller values of AcH_ for a given value of Aao than the other
sections presented. No explanation for this difference can
be offered, although some of the difference may result from
the slightly smaller chord of the flap for this combination.
The effects of using straight-sided ailerons instead of ailer-
ons of true airfoil contour are shown in figure 61 for twoNACA 6-series airfoils. One of the two combinations for
which data are available was provided with an internalbalance whereas the other combination was without balance•
This difference prevents any comparison between the two
combinations but does not affect comparison of the two
contours for each case. For the NACA 66(215)-216, a=0.6
airfoil, the straight-sided aileron has more desirable charac-
teristics for the range of deflections for which data are avail-
Basic airfoil el
NACA66(215) 216,a=0.61 0.1OO INACA 63,4-4(17.8) (up- .450
prox.) I I
1Type of aileron Refer- |
enee /
O.2Oc plain " ---_-4 -[
0.20c with 0.43c! inter-
----[hal balance
FIGURE 61.--Variation of the hinge-moment parameter Acg6 with the equivalent change in
section angle of attack required to maintain a constant section lift coefficient for deflection
of true-airfoil-contour and straight-sided ailerons on the NACA 63,4-4(17.8) (approx.)
and the NACA 66(215)-216, a=0.6 airfoil sections. Gaps sealed.
able• It appears, however, that the straight-sided aileron
would be less advantageous than the aileron of true contour
for positive deflections greater than 12 °. In the case of
the NACA 63,4-4(17.8) (approx.) airfoil, the straight-sided aileron appears to have no advantage over the aileron
of true airfoil contour. The advantage of using straight-
sided ailerons appears to depend markedly oll the airfoil used
but sufficient data are not available to determine the signif-
icant airfoil parameters. Figure 62 shows that in one case
the effect of leading-edge roughness on the aileron character-istics is unfavorable.
LEADING-EDGEAIRINTAKES
The problem of designing satisfactory leading-edge air
intakes is to maintain the lift, drag, and critical-speed
characteristics of the sections while providing low intake
losses over a wide range of lift coefficients and intake velocityratios. The data of reference 65 show that desirable intake
and drag characteristics can easily be maintained over a
rather small range of lift coefficients for NACA 6-series air-foils. The data of reference 65 show that the intake losses
increase rapidly at moderately high lift coefficients for the
shapes tested. Unpublished data taken at the LangleyLaboratory indicate that shapes such as those of reference65 have low maximum lift coefficients. Recent data show
50 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
8
6
Roughness of
..#" _.-/6 .... _ <_-Smoofh
/eod/bg edge--" _ "-- ._
-4
- --,-/2
4 "_
0
< /
/
--- -- Aileron de{lection, d_g'-- 12"_
-8-.0018:0016 -.0014 -.00/2:0010 =0008:0006 --.0004 --.0002 0
ACH_ _ rod�ORS
FIGURE 62.--Variation of the hinge-moment parameter AeH6 with the equivalent change insection angle of attack required to maintain a constant section lift coefficient for deflectionof the aileron on the NACA 64,2-(1.4)(13.5) airfoil section, smooth and with roughness atthe leading edge of the airfoil. (For description of aileron, see fig. 60.)
that air-intake shapes can be provided for such airfoil sec-tions with desirable air-intake characteristics and without
loss in maximum lift coefficient (fig. 63). Some pressure-distribution data for the air intakes shown in figure 63 in-dicate that the critical speed of the section has been loweredonly slightly and that falling pressures in the direction offlow were maintained for some distance from the leadingedge on both surfaces at lift coefficients near the design liftcoefficient for the section. Sufficient information is not
available to permit such desirable configurations to be de-signed without experimental development.
INTERFERENCE
The main problem of interference at low Math numbers isconsidered to be that of avoiding boundary-layer separationresulting from rapid flow expansions caused by the additionof induced velocities about bodies and the boundary-layeraccumulations near intersections. No recent systmmaticinvestigations of interference such as the investigation ofreference 66 have been made.
Some tests have been made of airfoil sections with in-
tersecting flat plates (reference 67). These configurationsmay be considered to represent approximately the conditionof a wing intersection with a large flat-sided fuselage In
/.6
h_,:o./8_.../[/.2
, /
" [_ ,
, /%=4
/'Zt-hd/_7.)
24-I'nc/_ chord
1.4
/J
_ S-. = ,
Co_flgsur'aflbn R-o P/o/k? o/7-fo//--- 30×10' --
n ZJuc/-ed mode/
(low flow) .2.4_00ueted mode/
:_'1> 1.0
k.
7. '
.,i !he =0.186
-'o'/ ",. ,,,• =. .V, he 1135
f43"-- 0"-'_"_
V,. h¢ =_186(V'
C0 8 IG 24 =4 O .4 .8 1.2
Sect�on ong/e of offock, _, deg Secf/bn h'ft coefhc(enf, ¢_
FIGURE 63.--Lift and flow characteristics of an NACA 7-series type airfoil section with leading edge air intake.
l
/.6
SUMMARY OF AIRFOIL DATA
this case, the interference may be considered to result fromthe effect on the wing of the fully developed turbulent bound-
ary layer on the fuselage or flat plate and the accumulation ofboundary layer in the intersection. These tests showed
little interference except in cases for which the boundarylayer on the airfoil alone was approaching conditions ofseparation such as were noted with the less conservative
airfoils at moderately high lift coefficients.Some scattered data on the characteristics of nacelles
mounted on airfoils permitting extensive laminar flow arepresented in references 68 to 70. The data appear to in-dicate that the interference problems for conservative NACA6-series sections are similar to those encountered with other
types of airfoil. The detail shapes for optimum interferingbodies and fillets may, however, be different for varioussections if local excessive expansions in the ftow are to beavoided.
Some lift and drag data for an airfoil with pusher-propeller-shaft housings are presented in reference 71. These resultsindicate that protuberances near the trailing edge of wingsshould be carefully designed to avoid unnecessary dragincrements.
Another type of interference of particular importance forhigh-speed airplanes results in the reduction of the criticalMach number of the combination because of the addition of
the induced velocities associated with each body (reference72). This effect may be kept to a minimum by the use ofbodies with low induced velocities, by separation of inter-fering bodies to the greatest possible extent, and by suchselection and arrangement of combinations that the pointsof maximum induced velocity for each body do not coincide.
APPLICATION TO WING DESIGN
Detail consideration of the various factors affecting wingdesign lies outside the scope of this report. The followingdiscussion is therefore limited to some important aerodyna-mic features that must be considered in the application ofthe data presented.
APPLICATION OF SECTION DATA
Wing characteristics are usually predicted from airfoil-
section data by use of methods based on simple lifting-linetheory (references 73 to 76). Application of such methodsto wings of conventional plan form without spanwise discon-
tinuities yields results of reasonable engineering accuracy(reference 77), especially with regard to such importantcharacteristics as the angle of zero lift, the lift-curve slope,the pitching moment, and the drag. Basically similarmethods not requiring the assumption of linear section lift
characteristics (references 78 and 79) appear capable ofyielding results of greater accuracy, especially at high liftcoefficients. Further refinement may be made by consider-ation of the chordwise distribution of lift (reference 80).Wings with large amounts of sweep require special consider-ation (reference 81).
51
The usual wing theory assumes that the resultant air forceand moment on any wing section are functions of only thesection lift coefficient (or angle of attack) and the sectionshape. According to this assumption, the air forces andmoments on any section are not affected by adjacent sectionsor other features of the wing except as such sections orfeatures affect the lift distribution and thus the local lift of
the section under consideration. These assumptions ob-viously are not valid near wing tips, near discontinuities indeflected flaps or ailerons, near disturbing bodies, or forwings with pronounced sweep or sudden changes in planform, section, or twist. Under such circumstances, cross flowsresult in a breakdown of the concept of two-dimensionalflow over the airfoil sections. In addition to these
cross flows, induced effects exist that are equivalent to achange in camber. Such effects are particularly markednear the wing tips for wings of normal plan form and forwings of low aspect ratio or unusual plan form. Lifting-surface theory (see, for example, reference 81) provides a
means for calculating wing characteristics more accuratelythan the simple lifting-line theory.
Although span load distributions calculated for wings with
discontinuities such as are found with partial-span flaps(references 82 and 83) may be sufficiently accurate forstructural design, such distributions are not suitable forpredicting maximum-lift and stalling characteristics. Untilsufficient data are obtained to permit the prediction of themaximum-lift and stalling characteristics of wings withdiscontinuities, these characteristics may best be estimatedfrom previous results with similar wings or, in the case ofunusual configurations, should be obtained by test.
The characteristics of intermediate wing sections must beknown/or the application of wing tileory, but da_a for suchsections are seldom available. Tests of a number of such
intermediate sections obtained by several manufacturers folwings formed by straight-line fairing have indicated that thecharacteristics of such sections may be obtained with reason-able accuracy by interpolation of the root and tip character-istics according to the thickness variation.
SELECTION OF ROOT SECTION
The characteristics of a wing are affected to a large extent
by the root section. In the case of tapered wings formed bystraight-line fairing, the resulting nonlinear variation of sec-tion along the span causes the shapes of the sections to bepredominantly affected by the root section over a large partof the wing area. The desirability of having a thick wingthat provides space for housing fuel and equipment and re-duces structural weight or permits large spans usually leads
to the selection of the thickest root section that is aerody-namically feasible. The comparatively small variation ofminimum drag coefficient with thickness ratio for smoothairfoils in the normal range of thickness ratios and the main-
tenance of high lift coefficient for thick sections with flapsdeflected usually result in limitation of thickness ratio bycharacteristics other than maximum lift and minimum drag.
52 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
The critical Mach number of the section is the most serious
limitation of thickness ratio for high-speed airplanes. It is
desirable to select a root section with a critical Mach number
sufficiently high to avoid serious drag increases resulting from
compressibility effects at the highest level-flight speed of the
airplane, allowance being made for the increased velocity of
flow over the wing resulting from interference of bodies and
slipstream. Available data indicate that a small marginexists between the critical Mach number and the Mach num-
ber at which the drag increases sharply. As airplane speeds
increase, it becomes increasingly difficult and finally impos-
sible to avoid the drag increases resulting from compressibil-
ity effects by reduction of the airfoil thickness ratio.In tile cases of airplanes of such low speeds that compressi-
bility considerations do not limit the thickness ratio to valuesless than about 0.20, tlle maximum thickness ratio is limited
by excessive drag coefficients at moderate and high liftcoefficients with the surfaces rough. In these cases, the
actual surface conditions expected for the airplane should be
considered in selecting the section. Consideration should
also be given to unusual conditions such as ice, mud, and
damage caused in military combat, especially in the case ofmultiengine airplanes for which ability to fly under such
conditions is desired with one or more engines inoperative.
In cases for which root sections having large thickness ratios
are under consideration to permit the use of high aspect ratios,
a realistic appraisal of the drag coefficients of such sections
with the expected surface comtitions at moderately high lift
coefficients will indicate an optinmm aspect ratio beyond
which corresponding increases in aspect ratio and root thick-
ness ratio will result in reduced perforinance.
Inboard sections of wings on conventional airplanes are
subject to interference effects and may be in the propeller
slipstream. The wing surfaces are likely to be roughened by
access doors, landing-gear retraction wells, and armamentinstallations. Attainment of extensive laminar flows is,
therefore, less likely on the itlt)oard wing panels than on the
outboard panels. Unless such effects are minimized, little
drag reduction is to be expected from the use of sections
permitting extensive laminar flow. Under these conditions,the use of sections such as the NACA 63-series will provide
advantages if the sections are thick, because such sections aremore conservative than those permitting more extensivelaminar flow.
SELECTION OF TIP SECTION
In order to promote desirable stalling characteristics, the
tip section should have a high maximum lift coefficient and
a large range of angle of attack between zero and maxi-
mum lift as compared with the root section. It is also
desirable that the tip section stall without a large sudden loss
in lift. The attainment of a high maximum lift coefficient is
often more difficult at tile tip section than at the root section
for tapered wings because of the lower Reynolds number of
the tip section. For wings with small camber, the most
effective way of increasing tile section maximum lift coeffi-cient is to increase the camber. The amount of camber used
will be limited in most cases by either the criticM-speed
requirements or by the requirement that the section have
low drag at the high-speed lift coefficient.
The selection of the optimum type of camber for the tip
section presents problems for which no categorical answers
can be given on the basis of existing data. The use of a type
of camber that imposes heavy loads on the ailerons compli-
cates the design of the lateral-control system and increases
its weight. The use of a type of camber that carries the liftfarther forward on the section and thus relieves the ailerons
will, however, have little effect on the maximum lift coeffi-cient of the section unless the maximum-camber position is
well forward, as for the NACA 230-series sections. In this
case a sudden loss of lift at the stall may be expected. Theeffects on the camber of modifications to the airfoil contour
near the trailing edge, which may be made in designing the
ailerons, should not be overlooked in estimating the charac-
teristics of the wing.If the root sections are at least moderately thick, it is
usually desirable to select a tip section with a somewhatreduced thickness ratio. This reduction in thickness ratio,
together with the absence of induced velocities from inter-
fering bodies, gives a margin in critical speed that permits the
camber of the tip section to be increased. This reduction inthickness ratio will probably be limited by the loss in maxi-
mum lift coefficient resulting from too thin a section.
A small amount of aerodynamic washout may also be
uscfnl as an aid La the avoidance of tip stalling. The per-
missible amount of washout may not be limited by the in-
crease in induced drag, which is small for 1° or 2 ° of washout
(reference 73). The limiting washout may be that which
causes the tip section to operate outside the low-drag range
at the high-speed lift coefficient. This limitation may be
so severe as to require some adjustment of the camber to
permit Lhe use of any washout.A change in airfoil section between the root and tip may
be desirable to obtain favorable stalling characteristics or
to take advantage of the greater extent of laminar flow that
may be possible on the outboard sections. Thus, such com-binations as an NACA 230-series root section with an NACA
44-series tip section or an NACA 63-series root section with
an NACA 65-series tip section may be desirable.It should be noted that the tip sections may easily be so
heavily loaded by the use of an unfavorable plan form as to
cause tip stalling with any reasonable choice of section and
washout. Both high taper ratios and large amounts of
sweepback are unfavorable in this respect and are particu-
larly bad when used together, because the resulting tip stall
promotes longitudinal instability at the stall in addition to
the usual lateral instability.
CONCLUSIONS
The following conclusions may be drawn from the data
presented. Most of the data, particularly for the lift, drag,
and pitching-moment characteristics, were obtained at
Reynolds numbers from 3 to 9 X 106.
1. Airfoil sections permitting extensive laminar flow, suchas the NACA 6- and 7-series sections, result in substantial
reductions in drag at high-speed and cruising lift coefficients
as compared with other sections if, and only if, the wingsurfaces are fair and smooth.
SUMMARY OF AIRFOIL DATA 53
2. Experience with full-size wings has shown that extensivelaminar flows are obtainable if the surface finish is as smooth
as that provided by sanding in the chordwise direction with
No. 320 carborundum paper and if the surface is free from
small scattered defects and specks. Satisfactory results
are usually obtained if the surface is sufficiently fair to permit
a straightedge to be rocked smoothly in the chordwise direc-
tion without jarring or clicking.3. For wings of moderate thickness ratios with surface
conditions corresponding to those obtained with current
construction methods, minimum drag coefficients of the
order of 0.0080 may be expected. The values of the mini-
mum drag coefficient for such wings depend primarily onthe surface condition rather than on the airfoil section.
4. Substantial reductions in drag coefficient at high
Reynolds numbers may be obtained by smoothing thewing surfaces, even if extensive laminar flow is not obtained.
5. The maximum lift coefficients for moderately cambered
smooth NACA 6-series airfoils with the uniform-load type
of mean line are as high as those for NACA 24- and 44-seriesairfoils. The NACA 230-series airfoils have somewhat
higher maximum lift coefficients for thickness ratios lessthan 0.20.
6. The maximum lift coefficients of airfoils with flaps are
about the same for moderately thick NACA 6-series sections
as for the NACA 23012 section but appear to be considerablylower for thinner NACA 6-series sections.
7. The lift-curve slopes for smooth NACA 6-series airfoils
are slightly higher than for NACA 24-, 44-, and 230-series
airfoils and usually exceed the theoretical value for thinairfoils.
8. Leading-edge roughness causes large reductions in
maximum lift coefficient for both plain airfoils and airfoilsequipped with split flaps deflected 60 °. The decrement in
maximum lift coefficient resulting from standard roughness
is essentially the same for the plain airfoils as for the airfoils
equipped with the 60 ° split flaps.
9. The effect of leading-edge roughness is to decrease the
lift-curve slope, particularly for the thicker sections havingthe position of minimum pressure far back.
10. Characteristics of airfoil sections with the expected
surface conditions must be known or estimated to provide asatisfactory basis for the prediction of the characteristics of
practical-construction wings and the selection of airfoils
for such wings.
11. The NACA 6"-series airfoils provide higher critical
Mach numbers for high-speed and cruising lift coefficients
than earlier types of sections and have a reasonable rangeof lift coefficients within which high critical Mach numbersmay be obtained.
12. The NACA 6-series sections provide lower predictedcritical Mach numbers at moderately high lift coefficients
than the earlier types of sections. The limited data avail-
able suggest, however, that the NACA 6-series sections retain
satisfactory lift characteristics up to higher Mach numbersthan the earlier sections.
13. The NACA 6-series airfoils do not appear to presentunusual problems with regard to the application of ailerons.
14. Problems associated with the avoidance of boundal T-layer separation caused by interference are expected to besimilar for conservative NACA 6-series sections and other
good airfoils. Detail shapes for optimum interfering bodiesand fillets may be different for various sections if local exces-sive expansions in the flow are to be avoided.
15. Satisfactory leading-edge air intakes may be provided
for NACA 6-series sections, but insufficient information exists
to allow such intakes to be designed without experimentaldevelopment.
LANGLEY I_/_EMORIAL J_kERONAUTICAL LABORATORY,
NATIONAL .ADVISORY COMMITTEE FOR .AEROI_AUTICS,
LANGLEY :FIELD, VA., March 5, 1945.
APPENDIX
METHODS OF OBTAINING DATA IN THE LANGLEY TWO-DIMENSIONAL LOW-TURBULENCE TUNNELS
By MILTONM. KLEIN
A1, A2, . . . A,
a
B
c
ca
Cd p
Cd T
Ct
54
DESCRIPTION OF TUNNELS
The Langley two-dimensional low-turbulence tunnels areclosed-throat wind tunnels having rectangular test sections3 feet wide and 7_/ feet high and are designed to test modelscompletely spanning the width of the tunnel in two-dimensional flow. The low-turbulence level of these tunnels,
amounting to only a few hundredths of 1 percent, is achievedby tile large contraction ratio in tile entrance cone (approx.20:1) and by the introduction of a number of fine-wire small-mesh turbulence-reducing screens in the widest
part of tile entrance cone. The chord of models tested inthese tunnels is usually about 2 feet, although thecharacteris-tics at low lift coefficients of models having chords as large
as 8 feet may be determined.The Langley two-dimensional low-turbulence tunnel oper-
ates at atmospheric pressure and has a maximum speed ofapproximately 155 miles per hour. The Langley two-dimensional low-turbulence pressure tunnel operates at pres-sures up to 10 atmospheres absolute and has a maximumspeed of approximately 300 miles per hour at atmosphericpressure. Standard airfoil tests in this tunnel arc made of2-foot-chord wooden models up to Reynolds numbers ofapproximately 9 X 106 at a pressure of 4 atmospheres absolute.
The lift and drag characteristics of airfoils tested in thesetunnels are usually measured by methods other than the useof balances. The lift is evaluated from measurements of the
pressure reactions on the floor and ceiling of the tunnel. Thedrag is obtained fl'om measurements of static and totalpressures in the wake. Moments are usually measured by abalance.
SYMBOLS
coefficients of potential function for asymmetrical body
fraction of chord from leading edge overwhich dcsign load is uniform
dimensionless constant determining widthof wake
chord
drag coefficient corrected for tunnel-walleffects
drag coefficient uncorrected for tunnel-walleffects
drag coefficient measured in tunnelsection lift coefficient corrected for tunnel-
wall effects
C l t
el i
el T
Cmc/4
Creel4 t
F
Fo
YIio
HI
Hcm(lx
hT
K = cd'Cd T
LL t
m
n
PR
Pl
q0
S
S,
VAV
section lift coefficient uncorrected for tunnel-wall effects
design lift coefficientlift coefficient measured in tunnelmoment coefficient about quarter-chord
point corrected for tunnel-wall effectsmoment coefficient about quarter-chord
point measured in tunnelaverage of velocity readings of orifices on
floor and ceiling used to measure blockingat high lifts
average value of F in low-lift rangepotential function used to obtain n-factortotal pressure in front of ah.foiltotal pressure in wake of airfoilcoefficient of loss of total pressure in the
wake (H°_0H')
maximum value of II_
tunnel height
true lift resulting from a point vortexlift associated with a point vortex as
measured by integrating manometersupstream limit of integration of floor and
ceiling pressuresdownstream limit of integration of floor
and ceiling pressuresresultant pressure coefficient; difference
between local upper- and lower-surface
pressure coefficientsstatic pressure in the wakefree-stream dynamic pressure
static-pressure coefficient (_)
static-pressure coefficient in the wake
distance along airfoil surface
velocity, due to row of vortices, at anypoint along tunnel walls
free-stream velocityincrement in free-stream velocity due to
blocking
t
!
V"
v
Y
Yyt
Yw
dy_dx
z
Ol Io
O_ o
!OL 0
F
V_
*/b
W
A
SUMMARY OF AIRFOIL DATA
corrected indicated tunnel velocitytunnel velocity measured by static-pressm'e
orifices
local velocity at any point on airfoil surfacepotential function for flow past a symmetri-
cal bodydistance along chord or center line of
tunnel
variable of integration (-_)
distance perpendicular to stream directionordinate of symmetrical thickness distri-
bution
distance perpendicular to stream direction
from position of Hc_a_
slope of surface of symmetrical thicknessdistribution
complex variable (x+iy)angle of zero liftsection angle of attack corrected for tunnel-
wall effects
section angle of attack measured in tunnelstrength of a single vortex
ratio of measured lift to actual lift for anytype of lift distribution
v-factor for additional-type loadingv-factor for basic mean-line loading_-factor applying to a point vortexcomponent of blocking factor dependent on
shape of body
quantity used for correcting effect of bodyupon velocity measured by static-pressureorifices
component of blocking factor dependent onsize of body
potential functionstream function
MEASUREMENT OF LIFT
The lift carried by tile airfoil induces an equal and oppositereaction upon the floor and ceiling of the tunnel. The liftmay therefore be obtained by integrating the pressure dis-tribution along the floor and ceiling of the tunnel, the inte-gration being accomplished with an integrating manometer.Because the pressure field theoretically extends to infinity inboth the upstream and the downstream directions, not all thelift is included in the length over which tile integration isperformed. It is therefore necessary to apply a correctionfactor _ that gives the ratio of the measured lift to the actual
lift for any lift distribution. The calculation was performedby first finding the correction factor _ applying to a pointvortex and then determining the weighted average of thisfactor over the chord of the model.
55
The factor _ was obtained as follows: The image systemwhich gives only a tangential component of velocity along thetunnel walls is made up of an infinite vertical row of vorticesof alternating sign as shown in figure 64. If the sign of thevortex at the origin is assumed to be positive, the complexpotential function/for this image system is
iF _rz iF log sinh 7r (18)J----2_l°g sinh 2hr 27r - \ 2hr )
where
F strength of a single vortex
z complex variable (x+iy)
hr tunnel height
.+ 4- .+
hr
l
"-_ "-m _ x Upper" _volL.,, n
i7 u _Pos///on of po/mf vorfex x
Z_ o_vef" _c_//--""
•+ .,_,.
FIGURE 64.--Image system for calculation of _-factor in the Langley two-dimensional
low-turbulence tunnels.
The velocity u, due to the row of vortices, at any pointalong the tunnel walls where
hry=-_
is then obtained as
1_ 7rX
u=2_ r sech hr (19)
where x is the horizontal distance from the point on the wallto the origin. The resultant pressure coefficient PR is thengiven by
PR=_
2r _x=h_ sech hr (20)
where V is the free-stream velocity.The lift manometers integrate the pressure distribution
along the floor and ceiling from the downstream position nto the upstream position m (fig. 64). For a point vortex
56 REPORT :NO. 824--:NATIONAL ADVISORY COMMITTEE FOR AERO=NAUTICS
located a distance x from the origin along the center line of
the tunnel, the limits of integration become n--x and m--x.The lift L' associated with a point vortex, as measured by
the integrating manometers, is given by
L ' = qoPR dx (21)l--X.
where q0 is the free-stream dynamic pressure.The true lift L resulting from the point vortex is given by
L 2q0r=V
The correction factor yz is then
which yields
1 _ n-z _X
=_-I-zarJ,_ sech hr dx
(22)2 Fe-'_/h_(e_'/hT--e'm/hr)7_=_ tan-I L 1_ e-_/hre_(m+'__)/h_ -J
In the Langley two-dimensional low-turbulence tunne!s,
the orifices in the floor and ceiling of the tunnel used to
measure the lift extend over a length of approximately 13
feet. A plot of _ against x for the Langley two-dimensional
low-turbulence pressure tunnel is shown in figure 65. The
_-factor for a given lift distribution is obtained from the
expression
z©
.8
.6
.4
.2
-2 -/ 0 I 2 3 4t 5 6
D/sfonce downs/reom from reference po/nf /r_ funn_,/_ x_ ff
FIGURE 65.--Lift efficiency factor v# for a point vortex situated at various positions along thecenter line of the tunnel.
The values of _b and _a for the Langley two-dimensional
low-turbulence pressure tunnel are given in the following
table for a model having a chord length of 2 feet, where _b is
the _-factor corresponding to the basic mean-line loading(indicated by the value of a) and va is the _-factor for the
additional type of loading as given by thin-airfoil theory:
a yb
1.0 0.9347.8 .9342.6 .9336.4 .9330.2 .9325
0 .9322
_o=0.9296
In order to check the variation of _ with variations in the
additional type of lift distribution, the value of _ was re-calculated for the class C additional lift distribution given in
figure 6 of reference 74. The value of _, for this case was0.9304, as compared with 0.9296 for a thin airfoil. Because
of the small variation of _ with the type of additional lift,the value for thin-airfoil additional lift was used for all cal-
culations. The lift coefficient of the model in the tunnel
uncorrected for blocking c{ is given in terms of the lift co-
efficien_ measured in the tunnel Czr and the design lift coeffi-
cient of the airfoil c_, by the following expression:
c,__CZT__I/___I)Z _ "qa _V]a Cl_
(24)
Because _ does not differ much from n_, it is not necessary
that the basic loading or the design lift coefficient be known
with great accuracy.Because of tunnel-wall and other effects, the lift distribu-
tion over the airfoil in the tunnel does not agree exactly withthe assumed lift distribution. Because of the small varia-
tions of n with lift distribution, errors caused by this effect are
considered negligible. It can also be shown that errors caused
by neglecting the effect of airfoil thickness on the distri-
bution of the lift reaction along the tunnel walls are small.
MEASUREMENT OF DRAG
The drag of an airfoil may be obtained from observations
of the pressures in the wake (reference 84). An approxi-
mation to the drag is given by the loss in total pressure of theair in the wake of the airfoil. The loss of total pressure is
measured by a rake of total-pressure tubes in the wake.
When the total pressures in front of the airfoil and in the
wake are represented by H0 and //1, respectively, the drag
coefficient obtained from loss of total pressure cd r is
Ca7,--"f,_w_k_HJyw (25)
where
H_ coefficient of loss of total pressure in the wake (Ho--HI"_\ qo /
SU_IMARY OF AIRFOIL DATA
y_ distance perpendicular to stream direction from position
of H_ma _
If the static pressure in the wake is represented by Pl,
the true drag coefficient uncorrected for blocking ca' may beshown to be (reference 84)
fwo ' dY c (26)
where $1 is the static-pressure coefficient in the wake Ho--p_q0
The assumption is made that the variation of total pressure
across the wake can be represented by a normal probabilitycurve. The drag coefficient Cd' is then easily obtainable frommeasurements of CaT by means of a factor K, the ratio of cd'
to c_r, which depends only on S_ and the maximum value of
He. If the maximum value of Hc is represented by H_ax,
the equation of the normal probability curve is
_(Bvoy
where B is a dimensionless constant that determines the
width of the wake. If a convenient variable of integration
y_=By_ is used, the ratio K isc
C tK_ t'a
Cd T
2 1_ _'_ _/_HH_ (1--_/1----_) dY (27)--._Hcmax,)-_,
and is independent of the width of the wake. The quantity
K has been evaluated for various values of H¢_,x and S_ by
assuming S_ to be constant across the wake. The dragcoefficient Cd' may thus be obtained from tunnel measure-
ments of QT, H¢_, and S_. A plot of K as a function of H_,_
with $1 as parameter is given in figure 66. A parallel treat-ment of this problem is given in reference 85.
TUNNEL-WALL CORRECTIONS
In two-dimensional flow, the tunnel walls may be conven-
iently considered as having two distinct effects upon the flowover a model in a tunnel: (1) an increase in the free-stream
velocity in the neighborhood of the model because of a
constriction of the flow and (2) a distortion of the lift
distribution from the induced curvature of the flow.
The increase in free-stream velocity caused by the tunnelwalls (blocking effect) is obtained from consideration of an
infinite vertical row of images of a symmetrical body as
given in reference 86; the images represent the effect of thetunnel walls.
57
' --_:_.. _..
.6 --- cjKc_,7 _
--H, = 14/QA'e dP,p/h
I qol I_ ,_fO//c pressuro
.,4
30 .I .8 .3 .4
x,/./
.8 _
.5 .C .7 .8 .9 1.0
FIGURE 66.--Plot of Kas a function of He °. with S_ as a parameter.
The potential function w for a symmetrical body isgiven by
A_w=Vz+_+¢+ ... +_ (28)
where V is the free-stream velocity and the coefficients A_,A_, . . . are complex. If the tunnel height is large com-
pared to the size of the body, powers of 1/z greater than 1may be neglected and
w---- Vz-4-_ (29)
This operation is equivalent to replacing the body by a circle
of which the doublet strength is 2rA1; the term A_/z repre-sents the disturbance to the free-stream flow. The total
induced velocity at the center of the body due to all theimages is expressed in reference 86 as
AV-- A1 _2--_rr2 _ (30)
1where the term A, is the same as the term_ kt2V ofreference 86.
For convenience in tunnel calculations, the expression ofAV may be written
AVV =Aa (31)
where
71"2 // C "_2
(32)
A 16A1: c-_-V (33)
The factor a depends only on the size of the body and is
easily calculated. The factor A depends on the shape of thebody and is more difficult to calculate. For bodies such as
58 REPORT NO. 8 2 4--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Rankine ovals and ellipses, simple formulas may be obtained
for calculating A. In the general case, the value of A may
be obtained from the velocity distribution over the body by
the expression
(34)
where v is the velocity at any point on the airfoil surface and
dyt/dx is the slope of the airfoil surface at any point of which
the ordinate is yr.
I, ds . . .... t_J/h of lnlegr'ohor7
FIGURE 67.--Sketch for derivation of A-factor.
In order to obtain this expression, consider the flow past a
symmetrical body asshown in figure 67. The potentialfunction for this flow is given by equation (28). Differen-
tiating and multiplying equation (28) by z gives
dw A 2A2 nA,Z_z= VZ-z' "'"Z 2 Z n
fc ewThe line integral about a dosed curve z_ dz will
depend only on the term --A,/z and, from the theory of
residues, is given by
fc d_w dz-- --27riA,Z dz --
butd_o
z -_ dz = z dw
= (x÷ iy) (d_ + i de)
where _ is the potential function and ¢ is the stream func-
tion. On the surface of the body de-=0, so that
.!; z -_dwdz=fc xd++i fc y d, (35)
Since the body is symmetrical, the term x de will have
equal numerical values but opposite signs at corresponding
of the upper and lower surfaces, and I;x dq_ willpoints
vanish. The term y dq_ will have equal values at corre-
spending points of the upper and lower surfaces, and
fcy dep be replaced an integration over the uppermay by
surface; therefore,
fz _ dz----2i y d4_ (counterclockwise direction)
or
,fA,=--_ y de
Reversing the path of integration, replacing d_b by vds, replac-
-t-d-Y} dx, and solving for A= c_V-V givesing ds by " dx
,_,orly ,,/, Kx)_.j0 cV
where the integration is taken from the leading edge to the
trailing edge over the upper surface.
In addition to the error caused by blocking, an error exists
in the measured tunnel velocity because of the interference
effects of the model upon the velocity indicated by the static-
pressure orifices located a few feet upstream of the model
and halfway between floor and ceiling. In order to correct
for this error, an analysis was made of the velocity distribu-
tion along the streamline halfway between the upper and thelower tunnel walls for Rankine ovals of various sizes and thick-
ness ratios. The analysis showed that the correction could
be expressed, within the range of conventional-airfoil
thickness ratios, as a product of a thickness factor given
by the blocking factor h and a factor ( which depended uponthe size of the model and the distance from the static-pressure
orifices to the midchord point of the model. The corrected
indicated tunnel velocity V' could then be written
V'= V"(1 ÷A}) (36)
where V" is the velocity measured by the static-pressure
orifices. In the Langley two-dimensional low-turbulence
tunnels, the distance from the static-pressure orifices to the
midchord point of the model is approximately 5.5 feet; the
corresponding value of _ for a 2-foot-chord model is approxi-
mately 0.002.In order to calculate the effect of the tunnel walls upon the
lift distril)ution, a comparison is made of the lift distribution
of a given airfoil in a tunnel and in free air on the basis of
thin-airfoil theory. It is assumed that the flow conditions
in the tunnel correspond most closely to those in free air whenthe additional lift in the tunnel and in free air are the same
(reference 87). On this basis the following corrections are
derived (reference 87), in which the primed quantities referto the coefficients measured in the tunnel:
c_= [1-- 2A(a÷ _) -- a]c_' (37)
SUMMARY OF AIRFOIL DATA 59
4 ffCme 14t t
_0----(l+¢)a0'-_ dc_'/dao' ¢aZo (38)
!
c_c/_= [1-- 2A(¢+ _)]c_¢/4'-_ a _ (39)
4(7Cmc/4 t
In the foregoing equations, the terms dc//dao ), aaZo, and acz'/4
are usually negligible for 2-foot-chord models in the Langleytwo-dimensional low-turbulence tunnels.
When the effect of the tunnel walls on the pressure distri-
bution over the model is small, the wall effect on the drag is
merely that corresponding to an increase in the tunnel speed.
The correction to the drag coefficient is therefore given by the
following relation:
cd= [1 --2A (_-_ _)] c_' (40)
Similar considerations have been applied to the development
of corrections for the pressure distribution in reference 87.
Equation (40) neglects the blocking due to the wake, such
blocking being small at low to moderate drags. The effect
of a pressure gradient in the tunnel upon loss of total pressure
in the wake is not easily analyzed but is estimated to be small.
The effect of the pressure gradient upon the drag has there-
fore been disregarded. When the drag is measured by a
balance, the effect of the pressure gradient upon the drag is
directly additive and a correction should be applied. For
large models, especially at high lift coefficients, the effect of
the tunnel walls is to distort the pressure distribution appre-
ciably. Such distortions of the pressure distribution may
cause large changes in the boundary flow and no adequate
corrections to any of the coefficients, particularly the drag,can be found.
CORRECTION FOR BLOCKING AT HIGH LIFTS
So long as the flow follows the airfoil surface, the foregoingrelations account for the effects of the tunnel walls with suffi-
cient accuracy. When the flow leaves the surface, the block-
ing increases because of the predominant effect of the v_ake
upon the free-stream velocity. Since the wake effect shows
up primarily in the drag, the increase in blocking would
logically be expressed in terms of the drag. The accurate
measurement of drag under these conditions by means of a
rake is impractical because of spanwise movements of low-
energy air. A method of correcting for increased blocking
at high angles of attack without drag measurements has
therefore been devised for use in the Langley two-dimensionallow-turbulence tunnels.
Readings of the floor and ceiling velocities are taken a few
inches ahead of the quarter-chord point and averaged to
remove the effect of lift. This average F, which is a measure
of the effective tunnel velocity, is essentially constant in the
low-lift range. The quantity FIFo, where Fo is the average
value of F in the low-lift range, however, shows a variation
from unity in the high-lift range for any aix foil tested in the
tunnel; this variation indicates a change in blocking at high
lifts. A plot of FIFo against angle of attack s0' for a 2-foot-
chord model of the NACA 643-418 airfoil is given in figure 68.
The quantity FIFo is nearly constant for values of a0' up to12°; but for values of a0' greater than 12 °, FIFo increases and
the increase is particularly noticeable at and over the stall.
/.20_
/'/_
-16 -12 -8 -4 0 4 8 /2 /8 28 Z4
Geornefr-/c ongTIc of c_ttoo/_, _, _/_9
FmURE 88.--Additional blocking factor at the tunnel walls plotted against angle of attack
for the NAC._ 6,t3-418 airfoil.
A theoretical comparison was made of the blocking factor
Aa and the velocity measured by the floor and ceiling orificesfor a series of Rankine ovals of various sizes and thickness
ratios. The quarter-chord point of each oval was located at
the pivot point, the usual position of an airfoil in the tunnel.
The analysis showed the relation between the blocking factor
Aa and the change in F to be unique for chord lengths up
to 50 inches in that different bodies having the same blocking
factor Aa gave approximately the same value of F. For
chords up to 50 inches, the relationship is
AV
where AV/V is the true increment in tunnel velocity due toblocking. The foregoing relation was adopted to obtain the
Fcorrection to the blocking in the range of lifts where F0 ) 1.
Considerable uncertainty exists regarding the correct
numerical value of the coefficient occurring in equation (41).
If a row of sources, rather than the Rankine ovals used in
the present analysis, is considered to represent the effect of
the wake, the value of the coefficient in equation (41) would
be approximately twice the value used. Fortunately, thecorrection amounts to only about 2 percent at maximum liftfor an extreme condition with a 2-foot-chord model. Further
refinement of this correction has therefore not been attempted.
COMPARISON WITH EXPERIMENT
A check of the validity of the tunnel-wall corrections has
been made in reference 87, which gives lift and moment
curves for models having various ratios of chord to tunnel
height, uncorrected and corrected for tunnel-wall effects.
6O REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
/.2
q.8
_.4
.v.
.0
-.4
-.8
c_ J
_24 -15
/
!//
/ //Io Airfoil A Pressure d/str/butiom, /o AL"fo/I B Pressure distribuhbn,
J
TDT test 640 TDT test 6_55 II-Airfoil A Imleqrahh_ momorne, ter, z A/rfoll B ImlegrohDq monometer_
-8 0 8 /6 24 32 -Z4 -15" -8 0 8 IO Z4 3,2
Sechbn onqle of ottock, a'o,deg
(a) Comparison for airfoil A.
/
(b) Comparison for airfoil B.
FIGURE 69.--Comparison between lifts obtained from pressure-distribution measurements and lifts obtained from reactions on the floor and ceiling of the tunnel.
/.6
/.2
.8
0
£
t_..4
-.8
//
/
o BolonceN InfegrOfln _ monometer_
-Z 4 -/6 -8 0 8 / 6 24
__ech'on ongle of o/to,-h, oto, dec]
FIGURE 70.--Comparisou between lifts obtahmd from balance measurements and fromreactions on the floor and ceiling of the tunnel.
o gO uncorrected for" block/rago 45 I I I I Iz_ 90' correcled for- blocA'imgo 45
I
,,-" \
",I
,%\\
%"I
0 .I .2 3 4 .5 .6 .7 .8 .9x/c
FIGURE 71.--Comparisonbetween correctedand uncorrectedpressuredistributionsfortwo
chordsizesofa symmetrical NACA 6*seriesairfoilof15-percentthickness,a0=0°.
L,
SUMMARY OF AIRFOIL DATA 61
The general agreement of the corrected curves shows that
the method of correcting the lifts and moments is valid.
A comparison is made in reference 87 between the theoreti-
cal correction factor (equation (40)) and the experimentally
derived corrections of reference 88. The theoretical cor-
rection factors were found to be in good agreement with those
obtained experimentally.
In order to check the validity of the n-factor, a comparison
has been made of lift values obtained from pressure dis-
tributions with those obtained from the integration of the
floor and ceiling pressures in the tunnel A comparison for
two airfoils given in figure 69 shows that the two methods of
measuring lift give results that are in good agreement. The
n-factor has also been checked by comparison of the lift
obtained from balance measurements with the integrating-
manometer values in figure 70.
Finally, a check has been made of the method of correcting
pressure distributions (reference 87) for NACA 6-series air-
foils of two chord lengths at zero angle of attack in figure 71,
in which the pressure coefficients are plotted against chord-
wise position x/c. The agreement between the corrected
pressure distributions for both models verifies the method of
making the tunnel-wall corrections.
REFERENCES
I. Jacobs, Eastman N., Ward, Kenneth E., and Pinkerton, RobertM.: The Characteristics of 78 Related Airfoil Sections from
Tests in the Variable-Density Wind Tunnel. NACA Rep.
No. 460, 1933.
2. Jacobs, Eastman N., and Pinkerton, Robert M.: Tests in theVariable-Density Wind Tunnel of Related Airfoils Having the
Maximum Camber Unusually Far Forward. NACA Rep.
No. 537, 1935.
3. Jacobs, Eastman N., Pinkerton, Robert M., and Greenberg,Harry: Tests of Related Forward-Camber Airfoils in the
Variable-Density Wind Tunnel. NACA Rep. No. 610, 1937.
4. Stack, John, and Von Doenhoff, Albert E.: Tests of 16 Related
Airfoils at High Speeds. NACA Rep. No. 492, 1934.
5. Jacobs, Eastman N., and Sherman, Albert: Airfoil Section
Characteristics as Affected by Variations of the Reynolds
Number. NACA Rep. No. 586, 1937.
6. Pinkerton, Robert M., and Greenberg, Harry: AerodynamicCharacteristics of a Large Number of Airfoils Tested in the
Variable-Density Wind Tunnel. NACA Rep. No. 628, 1938.
7. Jones, B. Melvill: Flight Experiments on the Boundary Layer.Jour. Aero. Sci., vol. 5, no. 3, Jan. 1938, pp. 81-94.
8. Jaeobs, Eastman N., and Abbott, Ira H.: Airfoil Section Data
Obtained in the N.A.C.A. Variable-Density Tunnel as Affected
by Support Interference and Other Corrections. NACA Rep.No. 669, 1939.
9. Theodorsen, Theodore: Theory of Wing Sections of Arbitrary
Shape. NACA Rep. No. 411, 1931.
10. Stack, John: Tests of Airfoils Designed to Delay the Compress-
ibility Burble. NACA Rep. No. 763, 1943.
11. Jacobs, Eastman N.: Preliminary Report on Laminar-Flow Airfoilsand New Methods Adopted for Airfoil and Boundary-Layer
Investigations. NACA ACR, June 1939.
12. Von Doenhoff, Albert E., and Stivers, Louis S., Jr.: AerodynamicCharacteristics of the NACA 747A315 and 747A415 Airfoils
from Tests in the NACA Two-Dimensional Low-Turbulence
Pressure Tunnel. NACA CB No. L4125, 1944.
13. Naiman, Irven: Numerical Evaluation by Harmonic Analysisof the e-Function of the Theodorsen Arbitrary-Airfoil Potential
Theory. NACA ARR No. L5H18, 1945.
14. Theodorsen, Theodore: Airfoil-Contour Modification Based on
e-Curve Method of Calculating Pressure Distribution. NACA
ARR No. L4G05, 1944.
15. Allen, H. Julian: A Simplified Method for the Calculation of
Airfoil Pressure Distribution. NACA TN No. 708, 1939.
16. Munk, Max M.: Elements of the Wing Section Theory and of
the Wing Theory. NACA Rep. No. 191, 1924.
17. Glauert, H.: The Elements of Aerofoil and Airscrew Theory.
Cambridge Univ. Press, 1926, pp. 87-93.
18. Theodorsen, Theodore: On the Theory of Wing Sections with
Particular Reference to the Lift Distribution. NACA Rep.No. 383, 1931.
19. Von K_rm_n, Th.: Compressibility Effects in Aerodynamics.
Jour. Aero. Sci., vol. 8, no. 9, July 1941, pp. 337-356.
20. Von Doenhoff, Albert E.: A Method of Rapidly Estimating the
Position of the Laminar Separation Point. NACA TN No.
671, 1938.
21. Jacobs, E. N., and Von Doenhoff, A. E.: Formulas for Use in
Boundary-Layer Calculations on Low-Drag Wings. NACA
ACR, Aug. 1941.
22. Von Doenhoff, Albert E., and Tetervin, Neah Determination of
General Relations for the Behavior of Turbulent Boundary
Layers. NACA Rep. No. 772, 1943.
23. Squire, H. B., and Young, A. D.: The Calculation of the Profile
Drag of Aerofoils. R. & M. No. 1838, British A. R. C., 1938.
24. Tetervin, Neal: A Method for the Rapid Estimation of Turbulent
Boundary-Layer Thicknesses for Calculating Profile Drag.
NACA ACR No. L4G14, 1944.
25. Quinn, John H., Jr., and Tucker, Warren A. : Scale and Turbulence
Effects on the Lift and Drag Characteristics of the
NACA 653-418, a= 1.0 Airfoil Section. NACA ACR No. L4Hll,1944.
26. Tucker, Warren A., and Wallace, Arthur R.: Scale-Effect Tests
in a Turbulent Tunnel of the NACA 653-418, a-----1.0 Airfoil
Section with 0.20-Airfoil-Chord Split Flap. NACA ACR No.
L4122, 1944.
27. Davidson, Milton, and Turner, Harold R., Jr.: Effects of Mean-
Line Loading on the Aerodynamic Characteristics of Some Low-
Drag Airfoils. NACA ACR No. 3127, 1943.
28. Von Doenhoff, Albert E., and Tetervin, Neal: Investigation of
the Variation of Lift Coefficient with Reynolds Number at a
Moderate Angle of Attack on a Low-Drag Airfoil. NACA
CB, Nov. 1942.
29. Oswald, W. Bailey: General Formulas and Charts for the Calcula-
tion of Airplane Performance. NACA Rep. No. 408, 1932.
30. Millikan, Clark B.: Aerodynamics of the Airplane. John Wiley
& Sons, Inc., 1941, pp. 108-109.31. Hood, Manley J.: The Effects of Some Common Surface
Irregularities on Wing Drag. NACA TN No. 695, 1939.
32. Loftin, Laurence K., Jr.: Effects of Specific Types of Surface
Roughness on Boundary-Layer Transition. NACA ACR No.
L5J29a, 1946.
33. Charters, Alex C., Jr. : Transition between Laminar and Turbulent
Flow by Transverse Contamination. NACA TN No. 891, 1943.
34. Braslow, Albert L.: Investigation of Effects of Various Camouflage
Paints and Painting Procedures on the Drag Characteristics of
an NACA 65(_21)-420, a-----1.0 Airfoil Section. NACA CB No.
L4G17, 1944.
918392--51--5
62 REPORT NO. 824--:N'ATIO/_AL ADVISORY COMMITTEE FOR AERONAUTICS
35. Jones, Robert T., and Cohen, Doris: A Graphical Method of
Determining Pressure Distribution in Two-Dimensional Flow.
NACA Rep. No. 722, 1941.
36. Abbott, Frank T., Jr., and Turner, Harold R., Jr.: The Effects
of Roughness at High Reynolds Numbers on the Lift and Drag
Characteristics of Three Thick Airfoils. NACA ACR No.
L4H21, 1944.
37. Jacobs, Eastman N., Abbott, Ira H., and Davidson, Milton:
Investigation of Extreme Leading-Edge Roughness on Thick
Low-Drag Airfoils to Indicate Those Critical to Separation.
NACA CB, June 1942.
38. Zalovcik, John A.: Profile-Drag Coefficients of Conventional
and Low-Drag Airfoils as Obtained in Flight. NACA ACR
No. L4E31, 1944.
39. Zaloveik, John A., and Wood, Clotaire: A Flight Investigation of
the Effect of Surface Roughness on Wing Profile Drag with
Transition Fixed. NACA ARR No. L4125, 1944.
40. Hood, Manley J., and Gaydos, M. Edward: Effects of Propellers
and of Vibration on the Extent of Laminar Flow on the
N. A. C. A. 27-212 Airfoil. NACA ACR, Oct. 1939.
41. Silverstcin, Abe, Katzoff, S., and Hoot.man, James A.: Com-
parative Flight and Full-Scale Wind-Tunnel Measurements of
the Maximum Lift of an Airplane. NACA Rep. No. 618, 1938.
42. Sweberg, Harold H., and Dingeldein, ]_ichard C.: Summary of
Measurements in Langley Full-Scale Tunnel of Maximum
Lift Coefficients and Stalling Characteristics of Airplanes.
NACA Rep. No. 829, 1945.
43. Purser, Paul E., and Johnson, Itarold S.: Effects of Trailing-
Edge Modifications on Pitching-Moment Characteristics of
Airfoils. NACA CB No. L4130, 1944.
44. Fulhner, Felicien F., Jr.: Wind-Tulmel Investigation of NACA
66(215)-216, 66,1-212, and 65,-212 Airfoils with 0.20-Airfl)il-
Chord Split Flaps. NACA CB No. 1,4G10, 1944.
45. Abbott, Ira H., and Greenberg, IIarry: Tests in tim Variable-
Density Wind Tunnel of the N. A. C. A. 23012 Airfoil with
Plain and Si)lit Flaps. NACA Rep. No. 661, 1939.
46. Wenzinger, Carl J., and Harris, Thomas A.: Wind-Tunnel Investi-
gation of N. A. C. A. 23012, 23021, and 23030 Airfoils with
Various Sizes of Split Flap. NACA Rep. No. 668, 1939.
47. Bogdonoff, Seylnour M.: Wind-Tunnel Investigation of a Low-
Drag Airfoil Section with a Double Slotted Flap. NACA ACR
No. 3120, 1943.
48. Wenzinger, Carl J., and Harris, Thomas A.: Wind-Tunnel Investi-
gation of an N. A. C. A. 23012 Airfoil with Various Arrangemez_ts
of Slotted Flaps. NACA Rep. No. 664, 1939.
49. Wenzinger, Carl J., and Harris, Thomas A.: Wind-Tunnel Investi-
gation of an N. A. C. A. 23021 Airfoil with Various Arrangements
of Slotted Flaps. NACA Rep. No. 677, 1939.
50. Swanson, Rol)ert S., and Crandall, Stewart M.: Analysis of Avail-
able Data on the Effectiveness of Ailerons wit, hour Exposed
Overhang Balance. NACA ACR No. L4E01, 1944.
51. Street, William G., and Ames, Mil(;on B., Jr.: Pressure-Distribu-
tion Investigation of an N. A. C. A. 0009 Airfoil with a 50-
Percent>Chord Plain Flap and Three Tabs. NACA TN No.
734, 1939.
52. Ames, Milton B., Jr., and Sears, Richard I.: Pressure-Distribution
Investigation of an N. A. C. A. 0009 Airfoil with an 80-Percent-
Chord Plain Flap and Three Tabs. NACA TN No. 761, 1940.
53. Ames, Milton B., Jr., and Sears, Richard I.: Pressure-Dislribution
Investigation of an N. A. C. A. 0009 Airfoil with a 30-Perc(,nt-
Chord Plain Flap and Three Tails. NACA TN No. 759, 1940.
54. Sears, lliehard I.: Wind-Tunnel lnvestigalion of Control-Surface
Characteristics. I--Effect of Gap on lhe Aerodynamic Charac-
teristics of an NACA 0009 Airfoil with a 30-Percent-Chord
Plain Flal). NACA ARR, June 1941.
55. Jones, Robert T., and Ames, Milton B., Jr.: Wind-Tunnel Inves-
tigation of Control-Surface Churacteristics. V--The Use of a
:Beveled Trailing Edge to Reduce the Hinge Moment of a
Control Surface. NACA ARR, March 1942.
56. Sears, Richard I., and Liddell, Robert B.: Wind-Tunnel Investiga-
tion of Control-Surface Characteristics. VI--A 30-Percent-
Chord Plain Flap on the NACA 0015 Airfoil. NACA ARR,
June 1942.
57. Wcnzinger, Carl J., and Delano, James B.: Pressure Distribution
over an N. A. C. A. 23012 Airfoil with a Slotted and a Plain Flap.
NACA Rep. No. 633, 1938.
58. Gillis, Clarence L., and Lockwood, Vernard E.: Wind-Tunnel
Investigation of Control-Surface Characteristics. XIII--Various
Flap Overhangs U'sed with a 30-Percent-Chord Flap on an
NACA 66-009 Airfoil. NACA ACR No. 3G20, 1943.
59. Rogallo, F. M.: Collection of Balanced-Aileron Test Data. NACA
ACR No. 4All, 1944.
60. Dcnaci, H. G., and Bird, J. D.: Wind-Tunnel Tests of Ailerons at
Various Speeds. ]I--Ailerons of 0.20 Airfoil Chord and True
Contour with 0.60 Aileron-Chord Sealed Internal Balance on the
NACA 66,2-216 Airfoil. NACA ACR No. 3F18, 1943.
61. Purser, Paul E., and Riebe, John M.: Wind-Tunnel Investigation
of Control-Surface Characteristics. XV--Various Contour
Modifications of a 0.30-Airfoil-Chord Plain Flap on an
NACA 66(215)-014 Airfoil. NACA ACR No. 3L20, 1943.
62. Braslow, Albert L.: Wind-Tunnel Investigation of Aileron Effec-
tiveness of 0.20-Airfoil-Chord Plain Ailerons of True Airfoil
Contour on NACA 652-415, 653-418, and 654-421 Airfoil Sections.
NACA CB No. L4H12, 1944.
63. Sears, Richard I., and Purser, Paul E.: Wind-Tunnel Investigation
of Control-Surface Characteristics. XIV--NACA 0009 Airfoil
with a 20-Percent-Chord Double Plain Flap. NACA ARR
No. 3F29, 1943.
64. Crane, Robert M., and Holtzclaw, Ralph W.: Wind-Tunnel Inves-
tigation of the Effects of Profile Modifications and Tabs on the
Characteristics of Ailerons on a Low Drag Airfoil. NACA Rep.
No. 803, 1944.
65. Von Doenhoff, Albert E., and Horton, Elmer A.: Preliminary
Invcstigation in the NACA Low-Turbulence Tunnel of Low-
Drag-Airfoil Sections Suitable for Admitting Air at the Leading
Edge. NACA ACR, July 1942
66. Jacobs, Eastman N., and Ward, Kenneth E.: Interference of Wing
and Fuselage from Tests of 209 Combinations in the N. A. C. A.
Variable-Density Tunnel. NACA Rep. No. 540, 1935.
67. Abbott, Ira H.: Interference Effects of Longitudinal Flat Plates on
Low-Drag Airfoils. NACA CB, Nov. 1942.
68. Ellis, Macon C., Jr.: Some Lift and Drag Measurements of a
Representative Bomber Nacelle on a Low-Drag Wing--II.
NACA CB, Sept. 1942.
69. Ellis, Macon C., Jr.: Effects of a Typical Nacelle on the Charac-
teristics of a Thick Low-Drag Airfoil Critically Affected by
Leading-Edge Roughness. NACA CB No. 3D27, 1943.
70. Allen, tI. Julian, and Frick, Charles W., Jr.: Experimental Investi-
gation of a New Type of Low-Drag Wing-Nacelle Combination.
NACA ACR, July 1942.
71. AI)bott, Frank T., Jr.: Lift and Drag Data for 30 Pusher-Propeller
Shaft Housings on an NACA 65,3-018 Airfoil Section. NACA
ACR No. 3K13, 1943.
72. Robinson, Russell G., and Wright, Ray H.: Estimation of Critical
Speeds of Airfoils and Streamline Bodies. NACA ACR, March1940.
73. Anderson, Raymond F.: Determination of the Characteristics of
Tapered Wings. NACA Rcp. No. 572, 1936.
74. Jacol)s, Eastman N., and Rhode, R. V.: Airfoil Section Charac-
teristics as Applied to the Prediction of Air Forces and Their
Distribution on Wings. NACA Rep. No. 631, 1938.
SUMMARY OF AIRFOIL DATA 63
75. Soul_, H. A., and Anderson, R. F.: Design Charts Relating to the
Stalling of Tapered Wings. NACA Rep. No. 703, 1940.
76. Harmon, Sidney M.: Additional Design Charts Relating to theStalling of Tapered Wings. NACA ARR, Jan. 1943.
77. Anderson, Raymond F.: The Experimental and Calculated Char-
acteristics of 22 Tapered Wings. NACA Rep. No. 627, 1938.
78. Tani, Itiro: A Simple Method of Calculating the Induced Velocity
of a Monoplane Wing. Rep. No. 111 (Vol. IX, 3), Aero. Res.
Inst., Tokyo Imperial Univ., Aug. 1934.
79. Sherman, Albert: A Simple Method of Obtaining Span LoadDistributions. NACA TN No. 732, 1939.
80. Jones, Robert T.: Correction of the Lifting-Line Theory for the
Effect of the Chord. NACA TN No. 817, 1941.
81. Cohen, Doris: Theoretical Distribution of Load over a Swept-
Back Wing. NACA ARR, Oct. 1942.
82. Pearson, H. A.: Span Load Distribution for Tapered Wings with
Partial-Span Flaps. NACA Rep. No. 585, 1937.
83. Pearson, Henry A., and Anderson, Raymond F.: Calculation of
the Aerodynamic Characteristics of Tapered Wings with Partial-
Span Flaps. NACA Rep. No. 665, 1939.
84. The Cambridge University Aeronautics Laboratory: The Measure-
ment of Profile Drag by the Pitot-Traverse Method. R. & M.
No. 1688, British A. R. C., 1936.
85. Silverstein, A., and Katzoff, S.: A Simplified Method for Determin-
ing Wing Profile Drag in Flight. Jour. Aero. Sci., vol. 7, no. 7,
May 1940, pp. 295-301.
86. Glauert, H.: Wind Tunnel Interference on Wings, Bodies and
Air, crews. R. & M. No. 1566, British A. R. C., 1933.
87. Allen, H. Julian, and Vincenti, Walter G.: Interference in a Two-Dimensional-Flow Wind Tunnel with the Consideration of the
Effect of Compressibility. NACA Rep. No. 782, 1944.
88. Fage, A. : On the Two-Dimensional Flow past a Body of SymmetricalCross-Section Mounted in a Channel of Finite Breadth.
R. & M. No. 1223, British A. R. C., 1929.
_4 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
SUMMARYOFAIRFOILDATA 65
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66 REPORT NO. 824--NATIONAL ADVISORY COMMITTE_ FOR AERONAUTICS
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SUM1VIARY OF AIRFOIL DATA 67
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SUMMARY OF AIRFOIL DATA 69
SUPPLEMENTARY DATA
I--BASIC THICKNESS FORMS
Page
NACA 0006 ........................................... 70
NACA 0008 ....................................... 70
NACA 0009 ...................................... 70
NACA 0010 .......................................... 71
NACA 0012 ....................................... 71
NACA 0015 .................................... 71
NACA 0018 ......................................... 72
NACA 0021 ...................................... 72
NACA 0024 ........................................... 72
NACA 16-006 ...................................... 73
NACA 16-009 ....................................... 73
NACA 16-012 ........................................ 73
NACA 16-015 .......................................... 74
NACA 16-018 .......................................... 74
NACA 16-021 ........................................ 74
NACA 63,4-020 .......................................... 75
NACA 63-006 ........................................... 75
NACA 63-009 ......................................... 75
NACA 63-010 .......................................... 76
NACA 631-012 ........................................ 76
NACA 632-015 ......................................... 76
NACA 633-018 ...................................... 77
NACA 634-021 ......................................... 77
NACA 64,2-015 ......................................... 77
NACA 64-006 ............................................ 78
NACA 64-008 ........................................... 78
NACA 64-009 ............................................ 78
NACA 64-010 ........................................... 79
Page
NACA 641-012 .......................................... 79
NACA 642-015 ........................................ 79
NACA 643-018 ....................................... 80
NACA 644-021 .......................................... 80
NACA 65,2-016 ....................................... 80
NACA 65,2-023 ......................................... 81
NACA 65,3-018 ......................................... 81
NACA 65-006 ........................................... 81
NACA 65-008 ........................................... 82
NACA 65-009 ........................................ 82
NACA 65-010 .......................................... 82
NACA 65r012 .......................................... 83
NACA 652-015 .......................................... 83
NACA 653-018 .......................................... 83
NACA 65,-021 ......................................... 84
NACA 66,1-012 .......................................... 84
NACA 66,2-015 .......................................... 84
NACA 66,2-018 .......................................... 85
NACA 66-006 ........................................... 85
NACA 66-008 ........................................... 85
NACA 66-009 ........................................... 86
NACA 66-010 ........................................... 86
NACA 661-012 .......................................... 86
NACA 662-015 ......................................... 87
NACA 663-018 .......................................... 87
NACA 664-021 .......................................... 87
NACA 67,1-015 .......................................... 88
NACA 747A015 .......................................... 88
918392- 51.---6
70 REPORT NO. 8 2 4----NATIONAL ADVISORY COMMITTEE :FOR AERONAUTICS
,)z
2.0
1.8
.8
.4
-- NACA 000@
/.d
.8
-- N/CA 0008 ....
.4
NACA 0006 BASIC THICKNESS FORM
z y v/V AvJV(percent c) (percent c) O'/V)2
0
.5
]. 25
2.5
5.0
7.5
10
15
2O
25
30
40
5O
60
7O
80
9O
95
100
0
.947
1. 307
1.777
2. 100
2.341
2. 673
2. 869
2.971
3. 001
2. 902
2. 647
2. 282
1. 832
1.312
.724
.403
.063
0
• 880
1. 117
1.186
1. 217
1. 225
1. 212
1.206
1. 190
1, 179
1. 162
1. 136
1. 109
1. O86
1. 057
I. 026
.980
.949
0
0
• 938
1.057
1.089
1. 103
1. 107
1. 101
1.098
1.091
1.086
1.078
]. 066
1. 053
1.042
1. 028
1. 013
• 990
• 974
0
3. 992
2.015
1. 364
.984
• 696
• 562
.478
•378
.316
.272
• 239
.189
• 152
• 123
• 097
• 073
• 047
.032
0
L. E. radius: 0.40 percent c
NACA 0008 BASIC TIIICKNESS FORM
x y v� V ArJ V(perccnt c) (percent c) (v/V):
0
.5
1.25
2.5
5.0
7.5
10
15
20
25
3O
40
5O
60
7O8O
90
95
100
0
1.2(_
1. 743
2. 369
2. 800
3. 121
3. 564
3. 825
3.901
4.001
3. 869
3. 529
3.043
2. 443
1.749
• 965
• 537
.084
0
• 792
1. 103
1. 221
1. 272
1..Z_4
1.277
1.272
1. 259
1.24l
1. 223
1. 186
1. 149
1.11!
1.080
1.034
• 968
.939
0
.890
1. 050
1. 105
1. 128
1. 533
1. 130
1. 128
1. 122
1. 114
1. 106
1. 089
1. 072
1. 054
1. 039
1.017
.984
.969
2.900
1. 795
1,310
.971
694
.561
.479
.379
• 318
• 273
.239
• 188
• 152
.121
.096
• 071
• 047
.031
0
L. E. radius: 0.70 percent c
/,6
12 fr----
0 .2
N,4CA 0009 --
II
•4 .6 .8 kOx]e
NACA 0009 BASIC TtlICKNESS FOR1V[
x Y (r/I')2 vl V AvJ V(percent c) (percent c)
0
.5
1.25
2.5
5.0
7.510
15
2O
25
30
40
5O
6O
70
8O
9O
95
100
0
1. 420
1. 961
2. 666
3,150
3.512
4.009
4.303
4.456
4.501
4.352
3.971
3.423
2.748
1.967
1.086
.605
.095
0
• 750
1. 083
1. 229
1. 299
1,310
1. 309
1. 304
1. 293
1. 275
1.252
1. 209
1. 176
1.126
1. 087
1. 037
• 984
.933
0
0
.866
1,041
1,109
1,140
1,145
1.144
5,142
1.137
1.129
1.119
1.100
5.(}82
1.061
1.()43
1.018
.982
.l_i6
0
0.595
1,700
1.283
.963
.692
.560
.479
.380
.318
.273
.239
.188
.15I
.120
.095
.070
.046
.030
0
L. E. radius: 0.89 percent c
SUMMARY OF AIRFOIL DATA 71
2.0
1.6
1.2
.8
.4
f
NACA 0010
NACA[0010 BASIC:THICKNESS FORM
x y(percent c) (percent c) (v/V)_ v/V avdV
0.5
1.252.55.07.5
101520253040506O70809095
I00
0
1. 5782.1782. 9623.5003. 9024. 4554. 7824.9525.0024.8374. 4123. 8033.0532.1871. 207• 672.105
0.712
1.061
0•844
1.0301. 2371. 325
1. 3411.3411,3411.3291.3091.2841.2371.1901.1381.0941. 040
.960• 925
1.1121.1511.1581.1581.1581.1531.1441.1331.1121. 0911. 0671.0461. 020
.980
.962
L. E. radius: 1.10 percent c
2. 3721. 6181.255
.955
.690• 559.479.380.318.273• 239• 188.150• 119.094.069.045.030
0
1.6
/.2
.8
.4
ff
o
NACA 00/2
jl jI
NACA 0012 BASIC THICKNESS FORM
(percent c)
0.5
I. 252.55.07.5
1O1520253040506O70809O95
100
Y(percent c)
0
1.8942.6153.5554.2004.6835.3455.7385,9416. 0025. 8035. 2944. 5633. 6642.6231.448
.807.126
(v/V) 2
0.640
1. OlO1. 2411.3781".4021. 4111.4111.3991.3781. 3501. 2881.2281. 1661. 1091. 044
• 956.996
O
vlV
O.800
1• 0051. 1141,1741.1841.1881.1881. 1831.1741.1621.1351.1081. 0801. 0531. 022
.978• 952
O
L. E. radius: 1.58 percent c
Av d V
1. 9881. 4751.199• 934.685.558.479.381.319
.273
.249
.187
.149
.118
.092
.068• 044.029
0
t
_,//'
I.G
/.8
.8
.4
f
0
1
.2
"-....
NACA 00/5
.4
1---------
.6.v/c
I
.8 /.0
NACA 0015 BASIC TRICKNESS FORM
z Y (vl I')_ vl V Avol V(percent c) (percent c)
O.5
1, 252.55.07.5
lO152025304O5O6O7O8O9O95
100
0
2. 3673.2684. 4435. 2505. 8536. 6827.1727. 4277. 5027. 2546. 6175. 7044.5803.2791. 8101.008
.158
0.546• 933
1.2371. 4501. 4981. 5201. 520
1. 5101.4841. 4501. 3691. 2791. 2061.1321. 049
•945.872
0
O• 739.966
1. 1121. 2041. 2241. 2331• 2331. 2291. 2181.2041. 1701. 1311.0981.0641. 024.972• 934
O
L. E. radius: 2.48 percentc
1.6001.3121. 112
.900
.675
.557• 479.381.320• 274.239.185• 146• 115• 090• 065• 041• 027
0
72 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
2.O
/.6
/.2
.8
.4
0
/6
_2
.8
.4
0
L5
ZE
.8
.4
0
__4
I---- NACA 0018
"----4-------..__..__..___._._
1
I
\
ICACA 0024
I._ .6 .8 LO
x/c
NACA 0018 BASIC THICKNESS FORM
x y(percent c) (percent c)
0 0
.5
1.25 2.841
2. 5 3.922
5. 0 5. 332
7.5 6.300
l0 7. 024
15 8.018
20 8.606
25 8.912
30 9. 003
40 8. 705
50 7. 941
60 6.845
70 5.496
80 3.935
90 2. 172
95 1.210
100 .189
(vl I ")
o
• 465
• 857
1.217
1. 507
1. 598
1. 628
1.633
1.625
1. 592
1. 556
1.453
1.331
1. 246
1. 153
1. 051
.933
.836
0
v� I."
0
.682
• 926
1.103
1. 228
1.264
1.276
1. 278
1. 275
1. 262
1. 247
1.205
1. 154
1.116
1.074
1.025
• 966
• 914
0
AvJ V
1. 342
1.178
1. 028
.861
• 662
• 555
• 479
• 381
.320
• 274
• 238
• 184
.144
.113
.087
.063
• 039
.025
0
L. E. radius: 3.56 percent c
NACA 0021 BASIC THICKNESS FORM
x Y (v/_r).. vl v Av./V(percent c) (percent c)
O
.5
1.25
2.5
5
7.5
10
15
20
25
30
40
50
60
70
80
9O
95
lOO
0
3.315
4. 576
6. 221
7. 35O
8. 195
9. 354
10. 040
10. 397
10. 504
10. 156
9. 265
7. 986
6. 412
4. 591
2. 534
1. 412
• 221
0.397
• 787
1. 182
1.543
1. 682
1. 734
1. 756
1. 7421. 706
1. 664
1. ,5,38
1. 388
1. 284
1. 177
1.055
.916
.801
0
0
• 630
• 887
1. 087
1.242
1.297
1.317
1. 325
1. 320
1. 306
1. 290
1. 240
1. 178
1. 133
1. 085
1.027
• 957
• 895
0
1.167
1. 065
• 946
•818
• 648
• 550
• 478
• 381
• 320
• 274
• 238
.183
.142
.Ill
• 084
• 061
• 0,37
• 023
0
L. E. radius: 4.85 percent c
NACA 0024 BASIC THICKNESS FORM
x
(percent c)
0
.5
1.25
2.5
5.0
7.5
10
15
20
25
30
40
5060
70
8O
9O
95
100
Y(percent c)
0
.... _:isg-5.229
7.109
8.400
9.365
I0.691
11.475
11,883
12. 004
11.607
10. 588
9.127
7.328
5. 247
2.896
1.613
.252
(vl V )'
0.335
.719
1. 130
1 548
1. 748
1. 833
1.888
1. 871
1. 822
1. 777
1. 631
1. 450
1. 325
1.203
1. 065
.891
• 773
0
v/V
0
.579
.848
I. 063
1. 244
1. 322
1.354
1.374
1.368
1,350
1.333
1.277
1.204
1.151
1.097
1.032
.944
.879
0
At'./1"
1. 050
.964
.870
.771
• (_32
.542
.476
• 383
• 321
.274
• 238
• 181
• 140
• 109
• 082
.059
• 0:15
• 022
0
L.E. radius: 6.33percent c
SUMMARY OF AIRFOIL DATA 73
2.0
/.8
/.2
.8
.4
0
f_
NACA 16-006
NACA 16-006 BASIC THICKNESS FORM
(percel) t c)
0i. 252.55.07.5
10152O30405O6O708O9O95
100
Y(percent c)
0• 646.903
1. 2551. 5161. 7292. 0672. 3322. 7092, 9273.0002.9172. 6352. 0991. 259
• 707• 060
(v/V) 2
01. 0591. 0851. 0971.1051.1081.1121.1161. I231.1321.1371.1411.1321.1041. 035
.9620
v/v
01. 0291. 0421. 0471. 0511. 0531.055I. 0571. 0601. 0641. 0661. 0681,064
1. 0511. 017
•981
0
L. E. radius: 0.176 percent e
Avo/V
5. 4711. 376
.980•689• 557• 476•379.319.244.196.160.130.104
.077• 049
•0320
/.6
1.2
,8
.4
0
f
NACA 16-009
iJ
NACA 16-009 BASIC THICKNESS FORM
(percent c)
01.252.55.07.5
10152O3040506070809O95
1O0
Y(percent c)
O.969
1. 3541. 8822. 2742. 5933.1013.4984.0634. 391
- 4. 5004. 3763. 9523.1491. 8881. 061
•090
(v/V)
01. 0421.1091.1391.1521.1581.1681.1771.1901. 202i. 2111. 2141. 2061.1561. 043
.9390
vlV
01. 0211. 0531. 0671. 0731.0761.0811.0851. 0911.0961.1001.1061.0991.0751.022
.9690
L. E. radius: 0.396 percent c
Av./V
3. 6441. 330
.964•684•554• 475•378.319.245.197• 160• 131.103.076• 047
.0300
/,6
/,2
.8
.6
f11-_
(
_-..,...,.,.__..,--,._.__
\
NACA 18-012
Ji
>
0 .2 .4 .6 .,9 1,0
z/v
NACA 16-012 BASIC THICKNESS FORM
x y(percent c) (percent c) (vlV)2 vlV Avd V
01.252.55.07.5
I0152030405060708O9095
1O0
01. 2921. 8052. 5093.0323.4574.1354.6645.4175. 8556. 000•5. 8355. 2694.1992. 5171.415
.120
01.0021.1091.1731.1971. 2081. 2231. 2371. 2571.2711.2861.2931.2751.2031.051
.9080
01. 0011. 0531. 0831. 0941. 0991. 1061. 1121. 1211. 1281. 1341. 1371.1291. 0971. 025
• 9530
L. E. radius: 0.703 percent c
2.6241. 268
• 942.677.551.473.378•319.245.197
.161
.131
.102
.075
.045
.0270
74 REPORT NO. 82 4--NATION_AL ADVISORY COMMIT-TEE FOR AERONAUTICS
'20
1.6
/.2
.8
.d
.______. _ ..---._
_.__
..... I ...... : ....
........ NACA 16-015 --
m _ .
f
NACA 16-015 BASIC THICKNESS FORM
r� V Avd Vx y(percent c) (percent
0 0
1.25 1. 615
2. 5 2. 257
5. 0 3. 137
7.5 3.79010 4.322
15 5. 168
20 . 5. 830
30 6. 772
40 7. 318
50 7. 500
60 7. 293
70 6. 587
80 5. 248
90 3. 147
95 1. 768
100 .150
c) (vlV)2
0
.956
1.105
1. 200
1. 239
1. 256
1. 278
1. 297
1. 327
1. 349
1. 364
1. 374
1. 348
I. 254
1. 053.875
0
L. E. radius: 1.lO0 percent c
0
• 978
1. 051
1. 095
1. 113
1. 121
1. 130
1. 139
1. 152
1. 1611. 168
1. 172
1. 161
1.120
1. 026
• 935
0
2. 041
1. 209
• 916
• 668
• 547
• 471
• 377
• 318
• 245
• 197
• 161
• 131
• 102
• 074
• 043
.025
0
/.6
/2
.8 m
.4
J
f
NACA 16-0/8
..____---
NACA 16-018 BASIC THICKNESS FORM
x y v� V Ava/V(percent c) (percent
0
i. 25
2.5
5.0
7.5
10
15
20
30
40
50
6O
70
8O
9O
95
1O0
0
1. 938
2. 708
3. 764
4.548
5. 186
6. 202
6. 996
8. 126
8. 782
9.000
8. 752
7.9046. 298
3. 776
2.122
• 180
c) (v/V)2
0
• 903
1. o_
1. 217
1.271
I. 302
1. 332
I. 357
I. 399
1. 4261. 447
1. 452
1. 421
1. 306
1. 051
• 837
0
0
.950
1. 045
1.1031.128
1. 141
1.1541.165
1. 183
1.194
1.2(}3
1. 205
1. 192
I. 143
1. O25
• 915
O
1. 744
1. 140
• 883
.657
.541
.468
• 376
• 318
• 245
• 1(}8
• 162
.131
. 102
• 073
• 042
• 0240
L. E. radius: 1.584 percent c
/.8
.8
JJ
----J
//
.4 __ ....... _.rJ
f
0 .2
NACA 16-021
H
I
.6
%X - --
JJ
J
.8 lO
NACA 16-021 BASIC THICKNESS FORM
x Y (v/!/)2 vl V Av ./V(percent c) (percent c)
0
1.25
2.5
5.0
7.5
10
15
2O
30
40
5O
70
80
9(1
95
100
0
2. 261
3. 159
4. 391
5. 306
6. 050
7. 236
8. 162
9. 480
10. 246
10.500
10. 211
9. 221
7.348
4. 405
2. 476
• 210
0
• 826
1. 062
1. 221
1. 295
1. 342
1.39I
1. 4191. 474
1. 506
1. 535
1. 536
I. 495
I. 361
1. 039
• 80I
0
O
• 909
1. 031
1. 1051.138
1.159
1.179
1.191
1. 214
1. 227
1. 239
1. 239
1.2Z_
I, 166
1. 019
• 895
0
1. 574
1. 069
• 828
• 640
• 534
• 463• 374
• 317
• 245
• 198
• 162
• 131
• 102
• 072
• 041
• 023
0
I L. E. radius: 2.156 percent c
I_
SUMMARY OF AIRFOIL DATA 75
2.O
/.6
/<
I I I I..... c, : A4(upper surfoce)
NACA _3, 4-020
\
_J/
/F
NACA 63,4-020 BASIC TIIICKNESS FORM
x y(percent c) (percent c) (v/V)2 v/V J',v,/V
0.5• 75
1.252.55.07.5
1O152025303540455O5560657O758O859O95
16O
01. 7142. 0812. 6383.6064. 9475.9646.8008. 0909. 0069. 6309. 9559. 9789. 7659. 3668. 8198. 1437. 3516. 464
5. 4964. 4663. 4012. 342
1.348• 501
0
0•444•605•820
1. 080I. 2771. 3831.4561. 551l• 6141.6591.6891.6301.5671.5001.4331.3621.2881.2131.1371.059
• 978• 896• 811• 728• 651
0• 666• 778• 906
I. 0391.1301.1761.2071. 2451. 2701. 2881. 3001. 2771. 252l. 2251.1971.1671.1351.1011. O66l. 029
• 989• 947• 901• 853• 807
1. 3951. 2801. 2011. 072
• 846• 645• 543• 475• 386• 330• 289• 257• 219• 192• 169• 148• 128• 112• 097• 084• 071• 059• 046• 036• 023
0
L. E. radius: 3.16 percent e
NACA 63-006 BASIC THICKNESS FORM
x Y (vl V) _ vl V AVal V(percent c) (percent c)
/.6
.8
.4
f--cz =.0.3 (upper surface)is
-b "
"_.0,3 qower sur£oce) % _
NACA 6.3-006
f
0.5• 75
1.252.557.5
10152025303540455O556O65707580859O95
16O
0• 503• 609• 771
1. 0571.462I. 7662. OlO2. 3862. 6562. 8412. 954
3. O6O2. 9712. 8772. 7232. 5172. 2671. 9821. 6701. 3421. 008.683• 383• 138
O
6• 973
1.0501.0801. llO1. 1301. 1421. 1491. 1591. 1651. 1701. 1741. 1701. 1641. 1511. 1371. 1181.0961. 0741. 0461.020
•994• 965•936• 910• 886
O• 986
1.025l. 0391. 0541.063l. 0691• 0721.0771. 0791. 0821.0841.0821.0791.0731.066I. 0571. 047I. 0361.0231.010
• 997• 982• 967• 954• 941
4. 4832. ll01. 7781. 399
• 981• 692• 562• 484• 384• 321• 279• 245• 218• 196• 176• 158• 141• 125• 111• 098• 085• 073• 060• 047• 032
0
L. E. radius: 0,297 percent c
NACA 63-009 BASIC THICKNESS FORM
/.6
/.2
.,9
.4
O
s./
.... .08
fl
_ ---..,...._ _
.z
.c, =.08(upper surfoce)
(/o_er surface)
_ACA 63-009
I.4 .6 .8 10
x/v
x
(percent c)
0.5• 75
I. 252.55
7.51015
2O25
3O354O455O556O657O758O859O95
16O
Y(percent c)
0• 749• 906
1.1511. 5822.1962. 6553.0243.5913.9974. 2754. 4424. 5004. 4474.2964. 0563. 7393. 3582. 9282. 4581. 9661. 471
.990• 550• 196
0
L. E. radius: 0.631 percent c
(v/V) 2
0•885
l. 0021.051l. 130l. 180I. 2051. 2211.2411.2551.2641.2691.2651. 2551.2351. 2081.1751. 1411. 1041. 0651. 025
•984•942.903• 868• 838
v/v
0• 941
1. 0011. 025
1. 0631. 0861. 0981.1051.114
1.1201.124
1.1261.125
1.1201.1111.0991. 084I. 0681.0511.0321.012
•992•971•950•932.915
Av./ V
3.0581.8891.6471. 339• 961•689•560•484•386•324•281•248• 220• 196• 175• 156• 140• 124.16O•095•082•069•057•044• 030
0
76 REPORT NO. 8 2 4--_N'ATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
2O
/.6
/.2
.8
.4
/.6'
.8
:!ltt T!i]
/8
L2
,'VACA 23_-U/2
-- I
i._ ]
._ , J
f
_4
0 .Z .4 .6 .8 LO
NACA 63-010 BASIC TtIICKNESS FORM
x y Avo/V(percent c) (percent ,) (v/l')_ v/V
0
.5
• 75
1.25
2.5
5.0
7.5
10
15
2O
25
30
35
4O
45
5O
55
6O
65
7O
75
80
85
9O
95
16O
0
.829
1. 004
1. 275
1. 756
2. 440
2. 950
3. 362
3.9944. 445
4. 753
4. 938
5.01_)
4.9384. 766
4.496
4. 140
3. 715
3. 2342. 712
2.166
1.618
1. 088
. (')04
• 214
0
0
.841
.978
1. 037
1. 131
1.193
1.223
1. 245
1. 270
1. 285
1. 296
1. 302
1. 299
1. 286
1. 262
1. 231
1.11,13
I. 154
1.113
1. 069
1. 025
.979
.935
.893
• 853
.822
0
.917
• 989
1. 018
1. O63
1. 092
1. 106
1. 1161.1'27
1. 134
1. 138
I. 141
I. 140
1. 134
1.123
1. 110
1. 092
1. 074
1. 055
1. 034
1.012
• 989
• 967
.945
.924
• 907
2. 775
1. 825
1. 603
1.316
.952
• 687
.560
.484
.386
.325
• 282
.248
.220
• 196
• 175
• 156
• 139
• 123
.108
• 094
.081
• 069
• 056
• 043
• 030
0
L. E. radius: 0.770 percent e
NACA 63_-012 BASIC THICKNESS FORM
x y(percent c) (percent e) (v/V)2 v/V AV,,IV
.........................
O 0
• 5 .985
.75 1.194
1.25 1.519
2. 5 2.102
5 2. 925
7. 5 3. 542
lO 4. 039
15 4. 799
20 5. 342
25 5. 712
31) 5. 931t
35 6. 000
40 5. 92O
45 5. 7O4
5O 5.37O
55 4. (,135
6O 4.42O
65 3.84(I
7O 3. 210
75 2. 55(;
80 1. ,(}(}2
85 I. 274
90 .7(17
95 .250
16O 0
L E ral us 1 087 percent e
0
.7,50
.925
1. 005
1. 129
1. 217
1. 261
1.2194
1. 330
I. 349
1. 3112
1. 371)
1. 3116
I. 348
1.317
1. 2711
1.22(`}
I. 181
I. 131
I. 076
1. I)2t
• !,169
.920
.871
.826
• 791
0 2. 336
• 866 1. 695
• 962 1. 513
1. 003 1. 266
1. 063 .933
1.103 . (k_2
1. 123 .559
1. 138 .484
1. 153 .387
1.161 .326
1.167 .283
1.170 .249
1. 109 .221
1.16t .196
I. 148 .174
1.130 . 1.55
1.109 . 137
1.1187 .121
l. 0{;3 .11t6
1. (137 .091
1. Ol 1 .07(`t
• 984 .067
• 959 .055
.933 .042
• 909 .029
• 889 0
NACA (`)32 015 BASIC THICKNESS FORM
x
(percent c)
0
.5
• 75
1.25
2.5
5
7.5
10
15
2O
25
30
35
40
45
5O
55
6O
65
7O
75
80
85
_)
95
100
L. E. radius: 1.594 i)crccnt c
Y(percent c)
I ....
0
I. 204
1. 462
1. 878
2. 610 1. 105
3. 648 I. 244
4. 427 1. 315
5. 055 1.3ti0
6.011 1.415
6. 693 1. 446
7. 155 ,1. 467
7. 421 1. 481
7. 5(',0 1. 475
7. 386 1. 446
7. 009 1. 401
6. 665
6. 1085. 453
4. 721
3. 934
3. 119
2. 310
1. 541
.852
• 300
0
(v/1,')_ v� V Avo/V
0 0 1. 918
• 6O0 . 775 1. 513
• 822 .907 1. 371`I
• 938 .969 1. 1821. 051 . (,}03
1. 115 .674
1. 147 .5571. 166 .484
1. 190 .388
1. 202 .330
I. 211 .286
[. 217 .251
1. 214 .2221. 202 .196
1. 184 .174
1. 345 1. 160 .153
1. 281 1. 132 .135
1. 22(} 1.105 . 118
1. 155 1.075 .11)2
I. 085 1. 042 . 088
1. 019 1. 009 . 07(i
• 953 • 976 . 063
. 894 • 946 • I)51
. 839 • 916 . 039
• 789 • 888 . 026
• 7._10 .866 0
Z.O
/.6
1.2
.8
SUMMARY OF AIRFOIL DATA
.4
/.6
/.2
.8
I i
=. 32 surface)
":3Z _/ower purl'ace)
N40A 63_-018
/ --/
/
/ _ \_ .'e z = .38/upper
.._ '
/i-t "..,\;
/
/
o i
/
surface)
i/
NACA 633-018 BASIC THICKNESS FORM
x y(percent c) (percent c) (v/V)2 v] AvdV
0.5• 75
1.252.557.5
I0152O253O35404550556O657O758O859O95
100
01. 4041. 7132. 2173. 1044. 3625. 3086. 0687. 2258. 0488. 6008. 9139. 0008. 8458. 4827. 9427. 2566. 455
5. 5674. 622
3. 6502. 6911. 787
.985• 348
0
0• 441• 700• 848
1.0651. 2601. 3601. 424
1. 5001. 5471. 5701. 5981. 585
1. 5501. 4901.411
I. 330I. 252
1.1701. 0871. 009.933• 868.807• 753• 712
0.664•837.921
1. 0321. 1221. 1661. 1931. 2251. 2441. 2571.26_1. 2591. 2451. 2211. 1881.1,531. 1191. 0821. 0431. 004
• 966.932• 898• 868• 844
1. 6391. 3611.2581. 105
•871.663• 553.484• 390.333• 289• 253• 223• 197• 173• 152.133• 115• 099• 084• 072•059• 048• 036.024
0
L. E, radius: 2.120 percent c
NACA 634-021 BASIC THICKNESS FORM
x y(percent c) (percent c) (v/V)2 v/V Ar./V
01. 5831. 9372.5273. 5775. 0656, 1827.0808. 4419. 410
10. 05310.41210.50010.298
9. 8549. 2068. 3907.4416.3965.2904.16O3.0542.0211.113
• 3920
0• 275.564•725
1,0101. 2601. 3941. 4871. 5921. 6551. 6981. 7211. 7091. 6541. 5781. 4791. 3801. 2811.1801. 084
• 994.911• 839• 774• 721•676
0.524• 751• 851
1. 0051.1221.1811.2191. 2621. 2861. 3031. 312I. 3071. 286I. 2501. 2161.1751.1321,0861. 041
• 997• 954.916.880• 849• 822
0,5.75
I. 252.557.5
10152O2530354045,5O556O657O758O859O95
100
1. 4301. 2361.1561. 034
• 842• 653• 550• 484•392• 335• 291
•255• 225• 198
.173.150• 130• 112• 096• 081.068•057.046• 035.023
0
L. E. radius: 2,650 percent c
NACA 64,2-015 BASIC TIIICKNESS FORM
z Y (v/V)_ v/V AvdV(percent c) (percent c)
77
/.6
/.Z
.8
.4
S
/
/
/
///
//(-..: 20
..._..._l --
I
.e z =.ZO {upper surface)
I%.7owe,- surface)
-- /VAOA 54 2-015 --
If/
__1 /
0 .Z .4 .6 .8 LO
w/e
0.5• 75
1.252.55.07.5
1015202530354O455O556O657O758O859O95
16O
01. 2161. 4531. 8292. 5383.5144.2434. 8385. 7816. 4546,0677. 3077. 4817. 4807. 2686.8,506.3115. 6704. 9444.1583. 3382. 5061. 698
• 96l• 351
0
0.710.825• 962
1.1221. 234
1. 2881. 323
1. 3711. 4011. 4221. 441
l. 4581. 4711. 4321. 3661. 2991. 2341.16_I. 1021. 039
.973• 910• 849.791.739
6• 843• 908•981
!. 0591,1111,1351,1501. 1711.1841,1921.2001. 2071.213I. 1971. 1691.1401.1111. 0811. 0501.019
• 986• 954• 921• 889.860
L. E. radius: 1.65 percent c
1. 9361. 5001. 3591.161
.911
.678• 553• 477• 383• 325• 285• 253• 227• 202• 175.156• 137• 122• 102• 086• 080• 071• 656•039.027
0
78 REPORT NO. 824--NATIONtAL ADVISORY CO'MMIT'TEE :FOR AERONAUTICS
2O
L2
.8
.... el=.02 (upper surfoce)
l ', I.-........g..o {uppersu_fooe)
_"_ "-=06 lower surroco)l_l[
64-002 ---NA CA
4 .d
.8
0 .2'
i
L "" II
.8 /.o
NACA 64-006 BASIC THICKNESS FORM
32
(percent c)
0
•5
.75
1.25
2.5
5.0
7.5
10
15
20
25
30
35
40
45
5O
55
6O
6,5
7O
75
80
85
9O
95
100
Y(percent c)
0
.494
• 596
.754
1.024
1.405
1.692
1.928
2,298
2.572
2. 772
2.907
2.98l
2,995
2.919
2. 775
2. 575
2.331
2.0_)
1. 740
1.412
1.072
.737
.423
.157
0
(v/V)
O
.995
1.058
1,085
1. 108
1. 1191.128
1. 134
1. 146
1. 154
1.160
1.164
1. 168
1. 171
1,160
1.143
1.124
1.102
1. 079
1. 054
1. 028
1.000
• 970
.939
• 908
• 876
v� V Av ol V
0 4, 623
.997 2.175
1.o29 1,780
1.o42 1.418
1,o53 •982
1.o58 •692
1.o62 .560
1.065 .483
1.071 .385
1.074 .321
1.077 .279
1.079 ,246
1.081 ,220
1.082 •198
1.077 •178
1.069 .158
1.060 .142
1.050 •126
1.039 .112
1.027 •098
1.014 .085
1.000 .072
.985 .060
.969 .047
.9_3 .031
• 936 0
L. E. radius: 0.256 percent c
NACA 64-008 BASIC TItICKNESS FORM
(vlV) 2 vlV Av_IVz
(l)erqcnt c)
0
.5
.75
1.25
2.5
5.0
7.5
1O
15
20
25
30
35
4O
45
55
9O
65
7O
75
80
85
9O
95
19O
Y
(percent c)
0• 658
• 794
1. 005
1. 365
1. 875
2, 259
2, 574
3.069
3.437
3. 704
3.8_A
3.979
3. 9(}2
:{,8M3
3. 6M4
3,411
3. (181
2. 704
2.291
1. 854
1. 404
• 961
•550
• 206
0
0
.912
1,016
1.084
1.127
1,152
1.167
1.179
1.195
1.208
1.217
1.2125
1.230
1.235
I. 22(}
1.191
1.163
1.133
1.102
1.069
1.033
,995
•957
•918
.878
.839
0• 955
1. 008
1. 041
1. 062
1. 073
1.08()
1. ()g6
1. (}93
1. 099
1. 103
1. 107
1. It)9
1.111
1. 105
1. 091
1. 078
1. O64
1.0_)
1. 034
1. 016
•997
• 978
•958
• 937
• 916
3. 544
1. 994
1. 686
1. 367
• 969
• 688
• 560
,480
• 385
.323
• 279
• 246
• 220
• 198
• 176
• 158
• 141
• 125
• ll0
• 096
• 083
• 071
• 059
• 046
• 031
0
L. E. radius: 0.455 percent c
NACJ64-009 BASIC TIIICKNESS FORM
x Y (v/V)2 v� V Avo/V(percent c) (percent c)
0
.5
• 75
1.25
2.5
5.0
7.5
10
15
20
25
30
35
40
45
5O
55
6O
65
7O
758O
85
90
95
100
0• 739
.892
1.128
1.533
2, 109
2. 543
2.898
3.455
3.868
4. 170
4. 373
4. 479
4.490
4. 3644. 136
3. 826
3. 452
3. 026
2. 561
2. 069
1. 564
1. 069
• 611
• 227
0
0
.872
• 990
1. 075
1. 131
1.166
1.186
I. 200
1. 221
1. 236
1. 2461. 255
1.262
1. 2671. 246
1. 217
1. 183
1. 149
1. 112
1. 073
1. O33
• 992
• 950
• 907
.865
• 822
O
.934
.995
1.037
1.0(_{
1.080
1.089
1.095
1.105
1.112
1. 116
1•120
1.123
1.126
1. lit;
1.1_
1. 088
1. 072
1.055
1.036
1.016
.996
.975
• 952
.930
.907
3.130
1. 905
1. 637
1•340
.963
• 686
• 560
• 479
• 383
• 323
.281
• 248
• 221
.198
• 176
.158
• 140
• 125
• 109
• 095
• 082
• 070
• 057
• 044
• 030
0
L. E. radius: 0.579 l)erccnt c
SUMMARY OF AIRFOIL DATA 79
20
_ =.08 (Upp@r su/-fooe)
.4
/.6
/.2
.8
.4
1.6
NACA 64-010 BASIC THICKNESS FORM
I,E
.8
.4
o
NACA 64-0/0
(percent c)
0.5.75
1.252.557.5
1015202530354045505560657O7580859095
16O
Y(percent c)
0• 820• 989
1.2501. 7012. 3432. 8263.2213.8424. 3024. 6394• 8644. 9804.9884. 8434. 5864. 2383.8203.3452. 8272.2811. 7221. 176
• 671• 248
0
(vlV)2
0• 834• 962
I. 0611.1301.1811. 2061. 2211. 2451. 2621. 2751. 2861.2951. 3001.279I. 2411. 2011.1611.1201. 080I. 036
.990• 944.900• 850• 805
v/V
0• 913• 981
1. 0301.0631. 0871. 0981. 1051. 1161• 19-31. 1291. 1341. 1381. 1401. 1311. 1141.0961.0771.0581.0391.018
• 995• 972• 949• 922•897
AVo/V
2. 8151.8171. 5861.313
• 957• 684• 559• 480• 386• 325• 280• 246• 220• 199• 176• 158• 139• 124• 109• 095• 081• 069• 057• 044• 030
0
L. E. radius: 0.720 percent c
NACA 641-012 BASIC THICKNESS FORM
.et =./2 (upper xclrfcloe)
__-------
":/2 (lower surface l
• NAOA G4_-012
........,.,__ El i
x(percent c)
0.5• 75
1.252.55.07.5
10152O2530354046.5O556O6570
758085
9O95
19O
Y(percent c)
0• 978
1.1791. 4902. 0352. 8103.3943.8714. 6205.1735. 5765. 8445. 9785.9815. 7985. 4805.0564. 5483. 9743.3502. 6952. 0291. 382
• 786• 288
0
(v/V)_
0• 750• 885
1. 0201.1291. 2041. 2401.2641.2961.3201.3381.3511.3621.3721.335I. 2891.2431. 1951. 144
1.0911.037
• 981• 928
.874•825• 775
vlV
0•866• 941
1. Ol01. 063I. 097I. 1141. 1241. 1391. 1491 1561. 1621. 1671. 1711. 1561. 1361. 1151.0931.0701.0441. 018• 990• 963• 935.908• 880
Av,/V
2. 3791.6631.5081.271
•943• 685•559•482•388•328.281•247• 221• 199
• 177• 158• 138• 122
• 103• 088
•074• 063• 052• 045• 028
0
L. E. radius: 1.040 percent c
/,t
/
i _ .-re =._2 (upper surface)
NAOA 64z-0/5
i
ii
r
.4 .6 .8 LO_e
NACA 645 015 BASIC THICKNESS FORM
x
(percent c)
0,5• 75
1.252.55.07.5
10152025303540455O556O6570758O859O95
16O
Y(percent
01• 2081.4561.8422. 5283.5044. 2404. 8425. 7856. 4806. 9857. 3197. 4827. 4737. 2240. 8106. 2665.6204. 8954.1133.2962. 4721.677
• 950• 346
0
c) (vlV)2
o•670• 762•896
1.1131.231 _i. 2841.3231.3751.4101.4341.4541.4701,4851. 4201.3651. 3001.2331. 1671. 1011.033
• 967• 902•841• 785• 730
dv
O.819•873• 947
I. 0_51.1091.1331.1501.1721.1871.1981.2061.2131.2181. 1951. 1681. 1401. 1101.0801.0491. 010.983• 950• 917• 886• 855
L. E. radius: 1.590 percent c
av./V
1. 9391.476
1. 3541. 188
• 916• 670• 559• 482• 389• 326• 285
• 250• 225
• 202• 179• 158• 135• 121• 105• 090• 078.065• 054• 041• 031
0
80
.4
L6
L8
.B
.4
/.6--
L2
.8
.4
O
REPORT :NO. 8 2 4--:NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
_cz=.3Z (uppe: surfoce)
.... /7"_\
. ,- _\
] %NACA G4_-016
/
// . _:-v_=. 44 [upper surface)
..... i N4CA G%-021 --
I I
I
_ , ..'- __ e z =. 20 (upper
_. NACA 65,_:-0/6
.2 .4
l
surfoce)
I
.6 .8 1.0
NACA 6t3-018 BASIC THICKNESS FORM
x y _v,/V(percent c) (percent
0
1. 428
1. 720
2. 177
3.005
4. 186
5. 076
5. 803
6. 942
7. 782
8. 391
8. 789
8.979
8. 952
8. 630
8. 114
7.445
6.658
5. 782
4.842
3.866
2. 8&_
I.951
1.101
• 400
0
0
.5
• 75
1.25
2.5
5.0
7.5
10
15
2O
25
30
35
40
45
5O
55
6(1
65
7O
75
8O
85
9O
95
I0O
L. E. radius: 2.208 percent c
c) (v/l')_
0
• 546
• 705
• 862
1. 079
1. 244
1. 327
1. 380
1.4,50
1. 497
1. ,N_5I. 562
1. 585
1.6001. 518
1. 436
1. 354
1. 272
1.190
|. 109
1. 028
.952
v� V
o
•739
•840
•920
1. 039
1.115
l. 152
1.175
1. 204
1. 224
1. 239
1. 250
1. 259
1. 265
1. 232
1.198
1. 164
1. 128
1. 091
1. 053
1.014
• 976
.879 .937
• 812 .901
• 747 .864
•695 .8;/4
NA('A 644-021 BASIC TIIICKNESS FORM
1. 646
1.3(')0
1.269
1.128
• 904
• 669
• 558
• 486
•391
• 331
• 288
• 255
• 228
.200
• 177
.154
• 134
.117
• 102
• 088
• 074
• 063
.051
• 039
• 027
0
:r y(percent c) (1)ercent c)
0 0
.5 1.046
• 75 1. 985
1.25 2.517
2.5 3. 485
5.0 4.871
7.5 5.915
l0 6. 769
15 8. 108
20 9, 01.15
25 9. 807
30 10.269
35 10.481
40 IlL 431
45 I 0. 030
50 9. 404
55 8. 607
5O 7. 678
65 6, 649
70 5. M9
75 4. 416
80 3. 287
85 2. 213
9O I. 245
95 .449
1(10 0
L. E. radius: 2.8_4 percent c
%
(percent c)
0
.5
.75
1.25
2.5
5.0
7.5
10
15
20
25
3(}
35
40
45
59
55
(_)
65
71)
75
8O
85
90
95
100
(v/1 "': v� I: At,,/I"
0
.462
• 5O3
• 759
1. 010
1. 248
1. 358
1.43l
1. 527
1. 593
1. 654
I. 681
I. 712
I. 71)9
I. 607
I. 507
I. 406
1. 307
1. 209
1.112
1. 029
• 932
• 851
.778
.711
.653
0 1. 458
•680 1. 274
• 776 1. 203
• 871 1. 084
1. 005 .878
1. 117 ,665
1. 165 .557
1. 196 48(;
1. 236 .395
1. 262 .335
1.2Sl .29:1
1. 297 .251)
1.3[)_ .232
1.3O7 .202
1. 268 ,17g
1. 228 .155
1. 186 .134
1.143 . 111l. 099 .099
1.1155 .084
1.010 .07l. !)65 .059
• 923 .047
• 882 .036• 844 .022
• _(18 0
NACA 65,2-016 BASIC THICKNESS FORM
Y (v/132(percent c)
0 0
1.2O2 .5O0
l. 423 .69O
1. 796 .842
2. 507 1. 068
3.54;I 1. 217
4. 316 1. 287
4. 954 1. 328
5. 958 1.37!1
6. 701 1. 409
7. 252 1. 433
7. 645 1. 453
7. 892 I. 469
7. 995 1.4_4
7. (,)38 1. 4117
7.672 1.4!}I
7. 184 1. 421
6, 495 1. 328
5. 647 l. 235
4. 713 I. 147
3, 7;18 1. O56
2.75(,) .970
1.817 .886
•982 .816
.340 .769
0 .733
L. E. radius: 1.704 pereont c
v/l" _v./V
0 1. 959
.748 1. 650
. 831 1. 500
• 918 1. 275
1. 033 .9211
1. 103 • 689
1. ]34 • 545
1.152 .48O
1.174 .39(1
1. 187 .325
1.1 (.17 285
1.2(15 255
1. 212 225
1.21_ 200
l. 224 180
1. 221 160
1. 192 1411
I. 152 125
1. III ll0
1.071 995
1. 028 (180
.985 O66
• 941 .05O• !)03 .049
• 877 .025
.856 0
SUMMARY OF AIRFOIL DATA 81
f
/.6 ?>
Z/.2
.8
.4 /
/. er urfo e)
_.-_...__.........--
//
.,../
NACA 05,2-023 BASIC THICKNESS FORM
x y(percent c) (percent c) (v/V)2 v/V AvJV
0.5• 75
1.252.55.07.5
10152O253035
4O455O5560657O758O859O95
16O
O1. 6642. 0402. 6283. 7155. 3006. 4787. 4338. 8899. 917
10. 648ll. 142ll. 42311. 49911. 36110. 94910. 179
9. 1087. 8486. 4615. 0153.6182. 3451. 258
• 4390
O.400.500• 682• 943
1.2321. 3751.4671,5771.6281. 6551. 6771. 6941. 7081. 7161. 7121. 606I. 428I. 2741.135I. 003
• 893.803• 732• 682• 651
0• 632• 707• 826• 971
1. 1101.1731. 2111. 2561.2761. 2861. 2951. 3021. 3071.3101. 3081. 2671. 1951.1291. 0651.6Ol
• 945• 896• 856• 826• 807
1. 4141. 1611. 084
• 967• 811• 633• 539• 479• 380• 324• 281• 247• 229• 198• 178• 161• 147• 110• 096•093•080•053•035•022•018
0
L. E. radius: 2.955 percent c
NACA 65, 3-018 BASIC THICKNESS FORM
x y(percent c) (percent c) (v/V)_ v/V" Avo/V
.4
/I
/
IV4CA65,3-©/8
_--.---..._.__
//
0.5• 75
1.252.55.07.5
10152O253O3540455O5560657O758O859095
16o
01. 3241. 5992.0042. 7283.8314.7015. 4246. 5687. 4348.0938.,5688.8688.9908.9168.5938.0457.3176.45O5. 4864.4563.3902. 3251. 324
• 4920
0• 650• 750• 872
1.0201. 1791. 2631.3201.3931. 4391. 4731. 5021. 5261. 5461. 5621. 5131. 4331. 3481. 2581. 1691. 079
• 992• 905• 818• 738• 658
0• 806• 866• 934
1. el01.0861. 1241. 1491. 1801.2001. 2141.2261. 2351. 2431. 2501.2301.1971. 1611.1221.0811. 039
.996• 951• 904.859.811
1. 7501. 3871. 2681.108
•890• 677.568• 489•395•334• 292• 260• 232• 209• 186• 165• 142• 123• 107• 093.080.066• 054•040• 024
0
L. E. radius: 1.92 percent e
NACA 65-006 BASIC THICKNESS FORM
1.6
L2.-0
.8
.4--
.... :01
..... ez:.O/(upper surfoce]
(/o,,_r s_,-foc4 _
IVACA 55-006
.4 .6 .8 1.0ale
%(per_ntc)
0.5
• 751. 252.5
5.07.5
1015
2O253035404550556O65707580859O95
100
Y(percent c)
0• 476• 574• 717• 956
1.3101.5891.8242.1972. 4822. 6972. 8522. 9522.9982.9832.9002. 7412. 5182. 2461.9351.5941.233• 865• 510• 195
0
L. E. radius: 0.240 percent c
(v/V)2
01.044
1.0551.0631.0811.16O1. 112
1. 1201. 1341. 1431• 1491.1551. 1591.163
1.1661.165
1. 1451. 1241.16O1.0731.0441.013.981• 944• 902• 858
v/V
O1. 0221.0271.0311.0401,049l• 0551.0581.0651.0691.0721. 075
1.0771.0781.080
1.0791. 0701. 0601. 0491.0361. 0221.006• 990.972.950• 926
Av./V
4.815
2. 1101. 7801.390
• 965• 695• 560.474.381.322.281• 247• 220• 198• 178• 160• 144.128• 114.100• 086
•074.060•046.0310
82
2.O--
REPORT NO. 8 2 4--NATIONtAL ADA'ISORY COMMITq'EE FOR AERONAETICS
1.6
I _ _104 (_p_r SUr_OC_)
0
04 /ow,r
-4
/.6"
0
.8
/.5
NACA 65-008 BASIC TIIICKNESS FORM
(v/ V)2 v/ V AVJ V
/.8
.8
4/ACA 65-008
• 4 -- -
._l_____
__t-------
l e[ =.00 _upper surface)
x y
(percent c) (percent
0 0
.5 .627
• 75 .756
1.25 .945
2.5 1.267
5.0 1. 745
7.5 2.118
10 2.432
15 2.931
20 3.312
25 3.599
30 3.805
35 3.938
40 3.998
45 3.974
50 3.857
55 11._8
60 3.337
65 2.971
70 2. 553
75 2.096
80 1. 617
85 1.13l
90 .0(_
95 .252
100 0
c)
0
.978
1.010
1.043
1.086
1.125
1.145
1.158
1.178
1.192
1.203
1.210
1.217
1.222
1.226
1.222
1.193
1.1C_3
1.130
1.094
1.055
1.014
.971
.923
.873
.817
L. E. radius: 0.434 percent c
0
.989
1.005
1.021
1.042
1.061
1.070
1.076
1.085
1.092
1.097
1.100
1.103
1.105
1.107
1.105
1.092
1.078
1.0_3
1.046
1.027
1.1107
19_5
.961
.934
•904
3.695
2. 010
1. 696
1. 340
.956
• 689
.560
.477
• 382
• 323
.281
• 248
.221
• 199
.178
• 160
.145
.128
• 113
.098
.084
.072
.059
.044
.031
0
NACA 65-009
q --.08 (upper surface)
o
i l:O 0 /lower surfoce_ _
NACA 65-009 BASIC
x y(percent c) (percent c)
0 0
• 5 .700
.75 .845
1.25 1. 058
2. 5 1. 421
5.0 1. 961
7. 5 2.383
10 2. 736
15 ',1.299
20 3. 727
25 4. 050
30 4. 282
35 4.431
40 4. 496
45 4. 469
,_X) 4. 336
55 4.086
60 "1. 743
65 3. :/28
70 2. 850
75 2.1/42
80 1. 805
85 1. 200
90 .738
95 .280
100 0
L. E.
TIIICKNESS FORM
(vlV)2
O
• 945
• 985
1. 037
1. 089
1. 134
1. 159
1. 177
1. 2001. 216
1. 229
1,238
1. 246
1. 252
1. 258
1.2f10
1. 220
1. 185
1. 145
1. 103
1,059
1. 013
• 963
.912
.856
.797
v/v
0
.972
.992
1. 018
1. 044
1. 065
1. 077
1. 085
1. (195
1, 1()3
1. 109
1.113
1.116
1. 119
1. 122
1. 118
1.11)5
1.11_9
1. (170
1. 050
1. 029
1. 006
• 981
. (,t55
.925
.893
I
avo/ V
3. 270
1. 962
1. 655
1. 315
.950
• 687
• 500
.477
.382
.323
• 280
.24S
• 220
198178
160
144
128
111
.097
• 084
• 071
.059
• 044
.030
0
radius: 0.552 pcrecnt c
f__.._.. 1 --
_ ---.____ _
-- NACA 65-010
0 .2 .4 •6" .8 LO
,_i_
NACA65-010 BASIC TIIICKNESS FORM
.T
(t)ercent c)
0
.5
• ;5
1.25
2.5
5. 0
7.5
10
15
20
25
30
35
40
45
,5O
55
6O
65
70
75
8O
85
9O
95
100
Y(1)crccnt c)
0
.772
.932
1. 169
1. 574
2. 177
2. 647
3. 041)
3. 666
4. 143
4. 503
4. 760
4. 924
4.996
4. 003
(r/1 ")2
0
.911
.0(10
1. 025
1. 085
1. 143
1. 177
1. 197
I. 224
1. 242
1. 257
I. 268
1. 277
1.2_4
1. 290
r/V
0
• 954
• 980
1. 012
1. 042
1. 069
1. 085
1. 094
1.1110
l. ll4
1.121
1. 126
1. 130
1. 133
1. 136
4. 812 1.2_4
4. 530 I.244
4. 146 1. _02
3. 682 1.1 r_
3. 156 1. 112
2. ,584 1. 002
1. 987 1. Ol I
1. 385 .95_;
• 810 .9(_1
• 1106 .844
0 .781
I. 133
1.115
1. 990
I. 076
I. 055
I. 031
1. 005
.979
.950
• 919
• 8!44
L. E. radius: 0.687 perccnt c
avo/ V
2. 96)7
1.9ll
1.614
1. 292
• 932
• 679• 558
• 480
• 321
.2_0
• 248
.222
.199
• 17!)
.160
.141
.126
• 11()
• ()07
• 082
.070
• 058
• 045
.03O0
SUMMARY OF AIRYOIL DATA 83:
NACA 651-012 BASIC THICKNESS FORM
x y vl V Av_l V(percent c) (percent
/.6
/.2
.8
..4
0
/.6
/.2
.8
........ ¢z :-12 {upper surfoce)
--:/2 'lo..e,-s.,-:ooe)
NACA G5C012
flJ
O,,f
/
....... cz =.22 [Upper surfoce)
--.Z2 [/ower surfoce)
-- NACA 652-0/5
f
I
j ....-----
0.5• 75
1. 252.55.07.5
10152O253035404550556O657O758O859O95
100
0• 923
1.1091. 3871. 8752. 6063.1723. 6474. 4024. 9755. 4065. 7165. 9125. 9975. 9495. 7575. 4124.9434. 3813. 7433. 0592. 3451. 630
• 947• 356
0
c) (v/V)2-
o.848•935
1. 0001. 0821.1621. 2011.2321.268I.2951,3161.3321. 3431. 3501. 3571. 3431. 2951. 2431. 1881.1341. 0731. 010
• 949• 884.819.748
0• 021.967
1.0001.0401.0781.0961.1101. 1261. 1381. 1471.1541. 1591. 1621. 1651. 1591. 1381. 1151. 0901. 0651. 0361. 005
• 974.940.905
•865
2. 4441. 776
I. 4651.200• 931
• 702.568• 480.389.326.282.251.223• 204.188• 169.145.127•111.094• 074• 062• 049• 038• 025
0
L. E. radius: 1.6O0 percent e
NACA 6,_2-015 BASIC THICKNESS FORM
x y(percent c) (percent c) (v/V)2 v/V 2xvJV
01.1241. 356I. 7022. 3243.2453.9594.5555.5046. 2236. 7647. 1527. 3967. 4987. 4277.1686. 7206.1185. 4034.6003. 7442. 8581. 9771.144• 428
0
0• 654• 817.939
1. 0631.1841. 2411. 2811. 3361. 3741. 3971. 4181. 4381.4521. 464I. 4331. 3691. 2971. 2281.1511. 077I, 002
•924•846.773•697
0.809.904•969
1. 031l. 0881.1141.1321.1861.1721.1821.1911.199
1. 2051. 2101.1971.1701.139
1.1081. 0731. 038
1. 001•961.920.879.835
0.5•75
1.252.55.07.5
10152O253O3540455O556O657O758O859O95
16O
2.0381. 7201. 390I. 156
•920• 682• 563• 487• 393• 334.290• 255• 227• 203• 184.160•143.127•109•096•078•068.052• 038• 026
0
L. E. radius: 1.505 percent c
NACA 65a-018 BASIC THICKNESS FORM
x y(percent c) (percent c) (v/V)_ Avo/V
/2
.8
.4
sG
/
-x,
\
I / ""C,JS- "--:32 flower _urfoce)
,--- c:.32/upper surface)
NACA8#:0/8
f.___-----
.2
ff
.4 .6 .8 ZOxle
0.5.75
1.252.55.07.5
10152O2530354O455O556O
6570758O859O95
100
0l, 3371. 6082.0142. 7513.8664. 7335. 4576.6067. 4768.1298. 5958. 8868.9998.9018.5688. 0087. 2676. 3955. 4264. 3963. 3382. 2951.319
.4900
L. E. radius: 1.96 percent e
v/v
0 0• 625 .791• 702 .838• 817 .904
1. 020 1. 0101.192 1. 0921. 275 1.1291. 329 1.1531.402 1.1841. 452 1. 2051. 488 1. 2201.515 1.2311. 539 1. 241
1. 561 1. 2491. 578 1. 2561. 526 1. 2351.440 1.2001.353 1.163
1. 262 1.123l. 170 1. 0821. 076 1. 037
• 985 .992• 896 .947• 813 .902• 730 .854• 657 .811
1. 7461. 4371. 3021.123•858•650•542•474•385•327•285•251•225•203• 182• 157• 137• 118
• 104•087•074•062.050•039
•0260
84
2. O
/.0
/.2
.,9
.4
0
/.6
1,2
.8
.4
0
1.6------
/2
.B
.4
REPORT :NO. 8 2 4--NATIO:NAL ADVISORY COMMITTEE :FOR AERONAUTICS
0
/
//!I
J
/
\
J
fJ
'.44 ('lower surface)
UACA 654-0ZI
I I i l
,=.44 (upper surface)
\\
JJ
jJ
] lq =" 12 fuppet- surfoce}
_ __
NAC4 6_/-012--
_ __i jj
NACA 654-021 BASIC THICKNESS FORM
x y vl V AV.I V(percent c) (percent c) (v/V)2
0
.5
• 75
1.25
2.5
5.0
7.5
10
15
2O
25
3O
35
40
45
5O
55
6O
65
7O
75
8O
85
9O
95
100
0
1. 522
1. 838
2. 301
3.154
4. 472
5. 498
6. 352
7. 700
8. 720
9. 487
10. 036
10. 375
10. 499
10. 366
9. 952
9. 277
8. 390
7. 360
6. 224
5. 024
3.800
2. 598
1. 484
• 546
0
• 514
• 607
• 740
• 960
1. 186
I. 293
1.371
I. 469
1. 533
1. 580
l. 621
1. 654
1.680
1. 700
1. 633
1. 508
1. 397
1. 286
1. 177
1. 073
• 970
• 872
• 778
• 694
• 616
0• 717
• 779
• 860
• 980
1. 089
I. 137
1. 171
1. 212
1. 238
1. 257
1. 273
1. 286
1. 296
l. 304
1. 278
1. 228
1. 182
1. 134
1. 085
1. 036
• 985
• 934
• 882
• 833
• 785
1. 531
1. 333
1. 215
1. 062
• 838
• 649
• 544
• 478
.388
• 330
.289
255
229
206
184
158
139
120
101
• 087
• 073
• 058
• 047
• 035
• 020
0
E.
97
(percent c)
radius: 2.50 percent c
NACA 66,1-012 BASIC TI{ICKNESS FORM
Y
(percent c) (vl V) 2 vl V
40 0
• 854 .924
• 902 .950
.964 .982
1. 069 1. 034
1. 138 1. 067
1. 175 1. 084
I. 201 1. O96
1. 237 1. 112
1. 257 1. 121
1. 272 1. 128
1. 284 1. 133
1.29;t 1. 137
1. 302 1. 141
1. 309 1. 144
1,313 1. 146
1. 320 1. 149
1. 327 1. 152
1. 297 1. 139
1. 221 1. 105
1. 143 1. 069
1. 001 1. 030
• 974 .987
• 885 .941
• 792 .890
• 701 .837
0
.5
.75
1.25
2.5
5.0
7.5
10
15
2O
25
30
35
40
45
50
55
60
65
7O
75
80
85
9O
95
100
0
.900
1. 083
I. 343
1.803
2. 484
3.019
3. 482
4. 214
4. 779
5.218
5. 550
5. 786
5. 934
5. 998
5. 972
5. 844
5. 594
5. 165
4. &35
3.789
2. 964
2. 008
1. 244
• 477
0
AVa/ V
L. E. radius: 0.893 percent c
2. 555
1. 780
1. 540
1. 247
.925
.673
• 552
• 474
• 381
• 319
.280
• 248
• 220
• 195
.176
.161
• 144
• 130
• 117
.099,
.083
• 069
• 053
• 04l
• 028
0
c, =.20 (upper surface)
J
J
-%'""._0 ...... (lower surface)
- NACA 6_g-015
\
.2 .4 .5 .8 1.0
(percent c)
0 0
.5 1.110
• 75 1. 329
1.25 1. 645
2.5 2.229
5.0 3.086
7. 5 3.757
10 4.337
15 5.255
20 5.964
25 6. 516
30 6. 933
35 7. Z_0
40 7.415
45 7. 495
50 7.46O
55 7. 294
60 6.961
65 6. 405
70 5. 597
75 4. 652
80 3.616
85 2. 545
-90 1. 488
95 .560
100 0
L. E. radius: 1.384 percent c
:NACA 66,2-015 BASIC TIIICKNESS FORM
Y (vl V)n vl V . Avo/V(percent c)
0
• 700
• 870
• 940
1. 048
1.154
1. 2101. 244
1. 290
1.323
1. 342
1. 359
1. 374
1. 387
1. 397
1. 407
1.415
1.42|
1. 372
1. 267
1.162
1. 057
• 9,5,3
.848
• 743
• 640
0• 837
• 933
• 970
1. 024
1. 0741.10O
1.115
1.136
1.150
1.158
1.166
1. 172
1. 178
1.182
1.186
1.190
1. 192
1.171
1.126
1. 078
1. 028
• 976
• 921
• 862
.800
2. 085
1. 703
1. 382
1.156
• 898
• 656
.547
• 473
• 382
• 323
• 283
• 248
• 222
• 199
• 179
• 161
• 145
• 131
• 122
• 102
.080
.066
.050
• 037
• 025
0
SUMMARY OF AIRFOIL DATA 85
Z8
t2
.8
.4
o
!J
.-" vz: .22 [upper surfoce}
\\-
\
_i j
fJ
/.cz,.OI {upper Surfoce}Z2
/0 i. ('i
_---- ,.'Ol _/ower surfoce) _-.
.8
.4
o
NACA 60-006
-- ----------....______
NACA 66,2-018 BASIC THICKNESS FORM
x Y (vl I_)_ vl V Av°l V(percent c) (percent c)
0.5• 75
1.252.55.07.5
1015202530354045505560657O7580859O95
100
01. 4381. 730
2.1802. 9383.9844.8045. 4866, 5417. 3427.9578. 4198,7418. 9338. 9988. 9348. 7198.3167. 6296. 6575. 5234.2963. 0271. 789
•6720
0• 590.740• 918
1. 0841. 2171. 2851. 3251. 3731. 4011. 4221. 4401. 4561. 4681. 4781. 4881. 497I. 502I. 4421. 3141.1851. 059
•936.817• 700• 594
0• 768• 860• 958
1. 0411.1031.1341,1511.1721.1841.1921. 2001. 2071. 2121. 2161. 2201. 2241. 2261. 2011. 140I. 0891. 029
• 967• 904• 837• 771
1. 6591.3171. 2091. 091
• 867.665.544•4691379•323•282•251•224.2Ol•181• 162• 146• 134
.102• 089• 078• 064.052.041• 027
0
L. E. radius: 2.30 percent c
NACA 66-006 BASIC THICKNESS FORM
x y(percent c) (percent c) (vll')_ vlV AvUV
0• 461• 554
• 693• 918
1. 2571. 524
I. 7522. 1192. 4012. 6182. 7822. 8992. 9713,0002. 9852. 9252. 8152. 6112. 3161. 9531. 543
1. 107• 665• 262
0
01. 0521. 0571. 0621. 0711. 0861. 0981. 1071. 1191. 1281. 1331. 1381. 1421. 1451. 1481. 1511. 1531.1,551. 1541. 1181. 081I. O40
•996•948•890.822
0i. 0261. 0281. 0311. 0351. 0421. 0481. 0521. 0581. 0621. 0641. 0671. 0691. 070I. 0711. 0731. 0741. 0751. 0741. 0571. 0401. 020
•008•974•943•907
0.5• 75
1.252.55.07.5
10152O253035404550556O657O7580859O95
100
4. 9412.5002. 0201. 500
• 967.695.554.474.379• 320• 278• 245• 219• 197• 178• 161• 145• 130• 116• 102•089.075•061.047.030
0
L. E. radius: 01223 percent c
NACA 66_)8 BASIC THICKNESS FORM
x y v/V Av.I V(percent c) (percent16
,.D
.8
..4
/ .2
Ic_: 03 /upper surface)
\
-- --- NACA 66-008
i I r
.4 .6
_/c.B I.O
0.5• 75
1.252.55.07.5
10152O25303540455O556O657O758O859O95
19O
0• 610.735• 919
1. 2191. 6732. 0312. 3352. 8263. 2013.4903.7093.8653.9624.6O03.0783. 8963. 7403.459
3.0622. 5742. 0271. 447
•864•338
0
c) (v/V) 2
0•968
1. 023
1. 0461. O78
1.1071.1281.1411.1581.1711.1781.186
1.191]. 196
1. 2011. 205I. 2081. 2131. 2021.1'561. 103I. 048
• 980• 926• 855• 768
L. E. radius: 0.411 percent c
0•984
1. 0111. 0231. 0381. 0521. 0621. 068I. 0761. 0821. 0851. 089
1. 0911. 094
1. 0961. 0981. 099I. 1011. 0961. 0751. 050I. 024
• 994• 962• 925• 876
3. 794
2. 2201. 8251. 388
.949• 689• 552• 474• 379• 321• 278• 246• 220• 198• 178• 161• 145• 130• 115• lO1• 087• 073.058• 045• 029
0
86 REPORT NO. 824--N-ATION1ATJ, AD_ISORY COMMITTEE FOR AERONAUTICS
1.6
/.2
.8
.4
/.Z
.8
NACA 66-009 BASIC THICKNESS FORM
x y vlV AvolV(percent c) (percent
/e z =.05 /upper" surface)/G /
NACA 56-009
_ _ _________I If
O.5• 75
1.252.55.07.5
10152O253035404550556O6570758O859O95
16O
0• 687• 824
1.0301.3681.8802.2832. 6263.1783.6013. 9274.1734. 3484. 4574. 4994. 4754. 3814. 2043. 8823. 4282. 8772. 2631.611
• 961•374
0
c) (v/V)
0• 930.999
1.0361.0791.1191.1421.1591.1781.1901. 2011. 2101. 2171. 221
1. 2281. 2321. 2371. 240i. 2301. 1721.113i. 050• 985•915• 839•747
0• 964• 999
1.0181. 0391. 0581.0691. 0771. 0851.0911,0961.1001.1031.1051.1081.1101.1121.1141.1091.0831.0551. 025
.992•957•916•864
L. E. radius: 0.530 percent c
NACA 66-010 BASIC THICKNESS FORM
.4
,q =.07 (upper surface)
"f_'_'--- "-:0 7 _/ower surface)
( \
NACA 56-0/0
\\
x(percent c)
0.5• 75
I. 252.55.07.5
10152O2530354O455O556O65707580859095
16O
Y(percent c)
0• 759• 913
1.1411.5162. 0872. 5362.9173. 5304. 0014. 3634. 6364. 8324. 9535.0004. 9714. 8654. 6654. 3023. 7873.1762. 494I. 7731.054
• 4080
(vl V)_
0• 896• 972
1.0231.0781.1251.1541.1741.1981.2151. 2261,2361. 2431. 2491. 2551. 2611• 2651,2701.2501. 1901• 121I, 052
• 979.904• 821• 729
vlV
0• 947• 986
1. O111.0381. 0611.0741.0841. 0951. 1021.1071.1121. 1151. 1181.1201.1231.125
1.1271. 1181.0911.059
1.026• 989• 951.906• 854
L. E. radius: 0.602 percent c
/.6
,.G =.IZ (upper" sut'foce)/
,o I----
"<
NACA 561-012
\\
0 .Z -4
f___.._,I
.5 .8
\
/.0
NAGA 66r012 BASIC THICKNESS FORM
"1(percent c)
0.5• 75
1.252.557.5
10152O253035404550556O
657O758O859O95
100
Y(percent c)
0• 906
1. 0871.3581• 8O82. 4963.0373.4964. 2344. 8015. 2385. 5685.8035. 9476.0005. 9655. 8365. 5885.1394. 5153. 7672. 9442. 0831.234
• 4740
(vl V)
0.800.915•980
1.0731.1381.1771.2041.2371. 2591.2751.2871.2971. 3031.3111.3181.3231.3311.3021.2211.1391. 053
• 968• 879• 788• 687
vlV
0• 894•957• 990
1.0361.0671.0851. 0971. 1121. 1221. 1291.1341. 1391.1421. 1451. 1481.150I. 1541. 1411.1051. 0671.026
• 984• 938• 888• 829
L. E. radius: 0.952 percent e
3. 3522.16O1.7501. 340
• 940• 686• 552• 473• 379• 323• 280.246• 220• 197• 178• 161
• 145• 130• 116• 100• 085•071• 057•043•028
0
,_vd V
3. 0022.0121.6861.296
• 931• 682• 551• 473• 379• 322• 279.246• 220• 198• 178• 161• 146• 130• 114• 099• 085• 070• 056• 043• 027
0
Av,IV
2. 5691.8471.5751.237
•913• 674• 549• 473• 380• 323• 280• 246.221.197• 176• 162• 147• 132• 113• 098• 084• 069• 053• 040• 031
0
/.6
LZ
.8
.4
?
/
.... Cz=.2 (upper _urfoce).f
/z--._-E2_/ower surfoce)
NACA G02-015 •
\
/
pf
L6
L.2
.8
?//
.. ...... Cz=.3 (upper
/
/i/
---:3
I
surfoce)
",5,
'lower surfoc_
NACA -O/B
_/
2
0
:
o/
//....:4
//i/
(upper surfoce)
//
f/ovver surfoce)
NACA 884-0£'1
/
.6'
SUMMARY OF AIRFOIL DATA
NACA 662-015 BASIC THICKNESS FORM
x y(percent c) (percent c) (v/V) _ v/V AV./V
\
0.5• 75
1.252.557.5
1015202530354045505560657O7580859095
100
01.1221.3431.6752.2353.1003. 7814. 3585. 2865. 9956. 5436. 9567. 2507. 4307. 4957. 4507. 2836. 9596. 3725. 5764. 6323. 598
2. 5301.489
• 5660
0• 760• 840.929
1. 0551.163I. 208I. 2421.2881.3171.3401.3561. 3701.3801.3911.4011.4111.4201.3671.2601.1561.053
• 949• 847• 744• 639
0• 872
.916• 964
1. 0271. 0781. 0991.1141.1341.1481.1581.1641.1701.1751.1791.1841.1881.1921.1691.1221. 0751. 026
•974•920•863• 799
2.1391. 6521:431
1.172•895• 663• 547•473• 381• 322• 280.248• 222• 200• 180• 163• 146• 131• 113• 096• 080• 065• 051• 039• 025
0
\
//
\
>-
L. E. radius: 1.435 percent c
NACA 66_-018 BASIC THICKNESS FORM
x y(percent e) (percent v/V Av=/V
01.323
1. 5711. 052
2. 6463.69O4.5135. 2106. 3337.1887.8488.3468.7018.9188.9988.9428.7338.3237. 5806. 5975. 4514. 2062. 9341. 714
• 6460
e) (v/V)
0• 650• 735• 850
1. 0051.1541. 2341. 2851. 3501. 3931. 4231. 4451. 4641. 4811. 4961. 5091. 5221. 5341. 438
1.3021.172
1. 045• 922• 803• 692.587
0• 806• 857• 897
1. 0021. 0741.1111.1341.1621.1801.1931. 2021. 2101. 2171. 2231. 2281. 2341. 2381.1991.141I. 0831. 022
• 950
• 896• 832• 766
0.5• 75
1.252•557.5
lO152O25303540455055606570758O859O95
100
\\
//
•8 LO
1_. 7731. 4561.3121.121
•858• 649• 545• 472•381•323• 282• 250• 223• 201• 181.163• 147• 131• 114• 095• 077• 061• 048•037• 022
0
L. E. radius: 1.955 percent c
NACA 664-021 BASIC THICKNESS FORM
x y(percent c) (percent c) (v/V)2 v/V AVo/V
0• 580.635• 755•952
1.1431. 2461.3181.4051. 4591. 4991. 5281,5511.5741.5941. 6111. 6291. 6481. 5081. 3351.176I. 031
• 891• 763• 648
• 539
0• 761• 797• 869•976
1.0691.1161.1481.1851. 2081. 2241. 2361. 2451.2551. 2631. 269I. 2761. 2841.228
1.1551.0841.015
• 944• 873• 805• 734
0.5• 75
1.252.557.5
10152O2530354O455O556O65707580859O95
100
01. 5251. 8042. 2403.0454. 2695. 2336. 0527. 3698. 3769.1539. 738
10.15410. 40710.50010. 43410.186
9. 6928. 7937. 6106. 2514. 7963. 324I. 924
• 717
0
L. E. radius: 2.550 percent c
1. 547
1. 3141. 2181. 054
• 828• 635• 542• 472• 381.324.283•251• 224• 202• 183• 165• 148• 132.I14•093.073•058• 046.034• 020
0
87
88
2.0
/.6
/.2
.8
.4
/.2
.8
.4
REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 67,1-015 BASIC TItICKNESS FORM
x y v/V AvJ V(percent c) (percent
f_ ,'0
/ /-.
/
e z =./2 (upper
i
/
__..._------_..__.-----._
"--,/z (/ower_urfocd
surfoce)
\\
NACA 67,1-015
f
\
/-jl
0
.5
• 75
1.25
2.5
5.0
7.5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
8O
85
9O
95
100
O
1. 167
1. 394
1. 764
2. 395
3. 245
3. 900
4. 433
5. 283
5. 940
6. 454
6. 854
7. 155
7.359
7. 475
7. 497
7. 421
7. 231
6.9O5
"6. 402
5. 621
4.540
3.327
2. 021
• 788
0
c) (v/v)
O• 650
• 970
1. 059
1.140
1. 209
1. 239
1. 259
1.285
1. 304
1. 318
1. 330
I. 34l
1. 351
I. 360
1. 368
1. 375
1. 381
1. 388
1. 390
1. 321
1.176
1.018
• 864
• 712
• 570
0• 806
• 985
1. 029
1. 068
1.100
1.113
1.122
1.134
1.142
1. 148
1.153
1.158
1.162
1.166
1.170
1.173
1.175
1.178
1.179
1.149
1. 084
1. 009
• 930
• 844
• 755
2.042
I. 560
I. 370
1.152
.906
• 667
• 548
• 470
• 370
•312
• 276
• 248
• 221
• 201
• 180
• 160
• 142
• 124
• 111
• 108
• 094
• 071
• 060
• 045
• 025
0
,-O
y
/,
/f
.- e,_ =.22 _pper
/
" ":22 (lower sur face)
surfoee)
.%
NACA 747A0/5
-.-------_,_____.__ I /
.2 .4 .6_/_
/f/
.8 1.0
L. E. radius: 1.523 percent c.
NACA 747A015 BASIC THICKNESS FORM
z y(percent c) (percent c) (v/V)2 v/V Av_/V"
0
1. 199
1. 435
1. 801
2. 462
3.419
4. 143
4. 743
5. 684
6. 384
6. 898
7. 253
7. 454
7. 494
7.316
7. 003
6. 584
6. 064
5.449
4. 738
3. 921
3. 020
2. 086
1. 193
• 443
0
0
• 660
• 799
• 942
1,100
1. 201
1. 259
I. 295
1. 339
1.36(.}
1.39(}
1.4(}9
1. 423
1. 435
I. 391
1. 348
1,306
1. 265
1. 221
1.178
1.115
I. 027
• 938
• 852
• 774
• 703
O
• 812
• 894
• 971
1. 049
1. 096
1.122
1.1381.156
• 1.1701.179
1.187
1.1931.198
1.179
1.161
1.143
1.125
1.105
1. 085
1. 056
1,013
• 969
• 923
• 880
• 838
0
.5
• 75
1.25
2.5
5
7.5
10
15
2O
25
30
35
40
45
,5O
55
60
65
70
75
80
85
9O
95
100
L. E. radius: 1.544 percent c
2. 028
1. 680
1.5()0
1. 325
• 990
• 695
• 551
• 465
• 383
• 324
• 283
• 252
.224
• 199
• 176
• 156
• 138
• 122
• 108
• 093
• 079
• 065
• 052
• 040
• 02g
• 018
L iii ,
SUMMARY OF AIRFOIL DATA 89
II--DATA FOR MEAN LINES
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
Page
mean line 62 ................................ 90
mean line 63 ................................ 90
mean line 64 .................................. 90
mean line 65 .................................. 91
mean line 66 ................................. 91
mean line 67 ............................ 91
mean line 210 ................................. 92
mean line 220 ................................. 92
mean line 230 ..................................... 92
mean line 240 .................................... 93
mean line 250 ..................................... 93
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
Page
mean line a_ 0 .................................... 93
mean line a: 0.1 .................................. 94
mean line a:0.2 ............................... 94
mean line a:0.3 ................................ 94
mean line a:0.4 ............................... 95
mean line a=0.5 .............................. 95
mean line a:0.6 ............................. 95
mean line a:0.7 .......................... 96
mean line a_0.8 ................................. 96
mean line a=0.9 ............................. 96
mean line a= 1.0 ................................. 97
90 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
3O
2..O
&
/.0
Y_.2c
0
.2c
2..O
LO
y_c
l
II
NACA 62
-- meo i 1/770
1
I
i
NACA MEAN LINE 62
ezi=0.90 a_=2.8i o c_cl4 = --0.113
z Y ¢ dy ddx PR Av/V= PR/4(percent c) (percent c)
0
1.25
2.5
5,0
7,5
10
15
2O
25
30
40
5O
60
70
80
90
95
100
0
• 726
1. 406
2. 625
3. 656
4. 500
5. 625
6.09O
5.977
5. 906
5. 625
5. 156
4.50O
3. 656
2. 625
1. 406
• 727
0
0. 6OOO0
56250
52,5011
45(}90
37500
30000
15OOO
0
--. 00938
--. 01875
--. 0375O
--. 05625
--. 0759O
--. 09375
--. 11250
--. 13125
--. 14062
--. 15000
0• 682
1. 031
1. 314
1. 503
1. 651
1. 802
1. 530
1. 273
1. 113
•951
• 843
• 74I
• 635
• 525
• 377
• 261
0
NACA MEAN LINE 63
eli=0.80 ai=l.60 ° c,c14 =--0,134
9?
(percent c)
0
1.25
2.5
5.0
7.5
10
15
20
25
;10
40
50
60
70
80
9O
95
100
(percent c)
O
• 489
• 958
1. 833
2. 625
3. 333
4.59O
5. 333
5. 833
6. 6O0
5, 878
5. 510
4. N98
4. 041
2, 939
1. 592
• 827
0
dy c/dx
0. 40000
• 38333
• 36067
• 33333
• 30000
• 26667
• 20000
• 13333
• 00667
0
--. 02449
--. 04898
--. 07347
--. 0979O
--. 12245
--. 14694
--. 15918
--. 17143
PR
0
• 389
• 553
• 788
• 940
1. I)66
1. 221)
1. 259
I. 233
1,160
• 949
• 8,50
• 762
• 673
• 560
• 406
.291
0
NACA MEAN LINE 64
cli=0.76 ai=0.74 ° cm c/4 = --6.157
x
(percent c)
0
1.25
2.5
5.0
7.5
1O
15
20
25
30
40
5O
6O
70
8O
9O
95
10O
_c(percent c) dy c/dx
O. 30000
• 369
• 726
1. 406
2. 039
2. 625
3. 656
4. 560
5.156
5. 625
6. 09O
5. 833
5. 333
4. 500
3. 333
1. 833
• 958
0
.29062
.28125
.26250
,24375
• 2259O
.18750
.15O00
.1125o
.0759O
0
--. 03;133
--.06(_7
--. I(W_)(}
--. 13333
--. 16067
--• 183:13
--. 201_H)
PR
0
• 257
• 391
• 546
.668
• 748
.87l
• 966
l. 030
1. 040
• 9(39
• 910
• 827
• 7,5(}
•635
• 466
• 334
0
0
• 371
• 258
• 328
• 376• 413
• 451
• 383
• 318
• 279
238
• 211
• 185
• 159
• 131
• 094
• 065
0
AvlV=PR/4
0
• 097
• 138
• 197
• 235
• 207
• 305
.315
• 368
•290
• 237
• 213
• 19l
• 168
• 140
• 102
• 0730
AV/V= PR/4
0
• 064
• 098
• 137
• 167
• 187
.218
• 242
• 258
• 260
• 250
• 228
• 207
• 188
• 15O
.117
• 084
0
3.O
2.O
/.0
0
Yc.ZC
/
N,#C,4 55rneon //_e
------_...,..,._
SUMMARY OF AIRFOIL DATA
"\
NACA MEAN LINE 65
clt=0.75 ai=0 ° ¢me/4= --0.187
x Y _ dy c/d.v PR AV/V= PR/4(percent c) (percent C)
0
1.25
2.5
5.07.5
10
15
20
25
3O
40
5O6O
708O
9O
95
100
0
• 296
.585
1. 140
1. 665
2.160
3.060
3. 840
4.500
5. 040
5. 760
6. 000
5. 760
5. 040
3. 840
2. 160
1• 140
0
0. 24000
• 23400
• 22800
• 21600
.20400
.19200
.16800
.14400
• 12000
• 09690
.04800
0
--. 04800
--. 09600
--. 14400
--. 19200
--. 21600
--. 24000
O
.205
.294
• 413
.502
.571
.679
.760
.824
• 872
.932
• 951
• 932
• 872
• 760
• 571
.413
0
0
• 051
• 074
.103
.126
• 143
.170
.190
.206
• 218
• 233
• 238
• 233
.218
.190
.143
.103
0
91
O /
/f
2.0
p_
/.0
/0
Ye 2C
//
/I
f
/J
\
NACA MEAN LINE 66
csi=0.76 at=--0.74 ° Cmcl_= --0.222
X Ye
(percent c) (percent Pn Av/V'=PR/4
0
1.25
2.5
5.0
7.5
10
15
20
25
30
40
5O
6O
70
80
90
95
100
0• 247
• 490
.958
1. 406
1• 833
2. 625
3. 333
3. 958
4. 500
5. 333
5. 833
6. 000
5. 625
4. 500
2. 625
1. 406
0
c) dy ddz
0. 2000019583
19167
18333
1750016667
1500013333
11667
10000
06667
• 033330
--. 07500
--. 15000
--. 22500
--. 26250--. 30000
0
.135
•244
•334
.408
.466
•557
.635
•700
.75O
•827
.910
.999
1.040
.966
• 748
.546
0
0
• 034
• 061
• 084
• 102
• 117
• 139
.159
.175
.188
.207
.228
.250
• 260
• 242
• 187
• 137
0
2.O
p_
/.0
Y_T
/
NACA 07
mean hive
._______.-------"i I
0 .__
f
i
.6" .8 ZO
NAGA MEAN LINE 67
eli=0.80 ai=--l.60 ° c_¢/4= --0.266
z ye(percent c) (percent P_ Av/V=PR/4
0
1.25
2.55
7.5
1015
2O25
30
40
50
60
70
80
9O
95
100
0
.212
,421
.827
1.217
1.592
2.290
2.939
3.520
4.041
4.898
5.510
5.878
6.000
5.333
3.333
1.833
0
c) dy _/dx
0. 17143
• 16837
• 16531
• 15918
• 15306
• 14694
• 13469
• 12245
• 11020
• 09796
• 07347
• 04898
.02449
0
--. 13333
--. 26667
--. 33333
--. 40000
0
• 137
• 195
• 29t
• 356
• 406
• 483
• 560
•616
• 673
• 762
• 850
• 949
1. 160
1.259
1.066
.788
0
0
.034
• 049
.073
.089
.102
.121
.140
.154
.168
.191
.213
.237
.290
.315
.267
• 197
0
92 REPORT NO, 8 2 4--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
3O
2O
/.0
o
¢,
Y_.£12
2O
/0--
Y--£ 2(,
I i
i ! !!
i
i
i
iI i
]
---_c-----!
L
]
...... i
i
____ NACA 220! , meon line
I
]
i
!
l_r __
i
i
NACA 230
f_eor] line
r
.2
I.4 .8
i
i
LO
NACA MEAN LINE 210
cti=0. 30 ai=2. 09 ° cm c/4= -0.006
x Y _ Av/V= PR/4(percent c) (percent c)
0
1.25
2.5
5.0
7.5
10
15
_025
3O
4O
50
6O
7O
8O
9O
95
100
0
• 596
.928
1.114
1. 0871. 058
• 999
• 9411
• 881
• 823
.7{)5
• 588
.470
• 353
.2;15
.I18
• 059
0
• 36236
.18504
--. O0018
--. 01175
dy ddx PR
0. 59613 01. 381
565
221
781
626
489
408348
302
242
• 198
• 160
• 128
• 098
• 065
• 044
0
0
• 345
• 391
• 305
.195
• 156
.122
• 102
.087
• 075
• 061
• 049
• 040
• 032
.025
• 016
• 011
0
NACA MEAN LINE 220
czi=0. 30
x yc
(percent c) (percent c)
0 0
1.25 .442
2.5 .793
5.0 1,257
7.5 1. 479
10 1. 535
15 I. 463
20 1. 377
25 1. 291
30 1. 2115
40 1. 033
50 .861
60 .68(,}
70 .516
80 .344
90 .172
95 .086
100 0
ai=l. 86 ° grad4 = --0. 010
dy c/dx Pn AV/V= P_¢/4
0. 39270
• 31541
• 24618
• 1;1192
• 04994
.6O024
--. 01722
0
• 822
1. 003
• 988
• _)0
• 81)1
• 615
• 465
• 378
• 320
• 253
• 2O5
• 169
• 135
• 19O
• 064
• 040
0
0
• 206
• 251
• 247
• 225
• 2(X)
• 154
• 116
• 095
• 082
._)3
• 051
• 642
• 034
• 625
.016
.010
0
NACA MEAN LINE 230
C_i=0.30 _i= 1.65 ° C._14=--0.014
x y,(percent c) (percent
0
1.25
2.5
5.0
7.5
10
15
2O
25
30
40
5O
6O
70
80
9O
95
100
0
• 357
• 666
1. 155
1. 492
1. 701
1. 838
1. 767
1.656
1. 546
1.325
1. 104
• 883
• t)62
• 442
• 221
.110
0
c) dyo/dx
0. 30508
• 26594
• 22929
• 16347
• 10762
• 06174
--. 00009
--. 02203
--. 02208
PR AV/V= Pn/4
0 0
• 528 .132
• 673 .168
• 791 .198
• 853 .213
• 859 .215
• 678 .170
• 519 .130
• 419 .105• 361 .09_)
•274 .069
• 217 .054.177 .044
• 144 .036
• 105 .026
,069 .017
• 042 .0110 0
SUMMARY OF AIRFOIL DATA 93
L....
l
NACA MEAN LINE 240
oi=0.30 ,_i=1.45 ° c_c/4=--0.019
x Y_ dy ddx PR AV[ V=PR/4(percent c) (percent c)
01.252.55.07.5
101520253040506O70809O95
100
0.301• 572
1. 0351.3971.6711.9912. 0702. 0181. 8901. 6201. 3501•080
• 810• 540• 270• 135
0
0. 25213.22877• 20625• 16432• 12653• 09290• 03810
--. 09OlO--. 02169
--. 02700
0377491625718750677
• 566•477•410.304• 234• 186• 150• 110.071• 047
0
0•094•123.156• 180• 188• 169• 142• 119• 103• 075• 059• 047• 038• 028• 018• 012
0
NACA 250
mean h_e
NACA MEAN LINE 250
cq=0.30 ai=1.26 ° cm_/_= --0.026
x Y ° dy ddz PR Av] V= Pn]4(percent c) (percent c)
0. 21472 001.252.55.07,5
1015202530405O6070809095
I 100
0•258.498• 922
1.2771. 5701.9822.1992.2632•2121. 9311.6091. 287
.965
.644
.322
.1610
• 19920• 18416
• 15562• 12999• 10458• 06162• 02674
--. 00007--. 01880
--• 03218
.281• 369• 477.552.592• 624• 610• 547• 470• 346• 255• 107• 154• 119• 076• 05l
0• 070• 092• 119• 138• 148• 156• 153• 137• 117•087•064•049
•038•030• 019.013
0
0
f
/
.4 .6 .8 10
x(percent c)
0.5.75
1.252.5
• 6.07.5
10152025_0354O455O55606570758O859O95
100
NACA MEAN LINE a=O
cq=l•0 a,:=4.,56 ° cmd, =--0.083
//e(percent c)
0.469•641.964
1.6412.6933.5074.1615. 1245.7476. 1146.2776. 2736.1305,8715,5165•0814.5814.0323. 4452. 8362.2171•6041•013
.467
0
dy ddx P ,_
........................O: 75867 1.000
• 69212 1. 985
• 60715 1.975• 48892 1.950• 36561 1.900• 29028 1,850• 23515 1. 800• 15508 1. 700• 09693 1. 600• 05156 I. 500• 01482 1. 400
--. 01554 1. 300--. 04086 1. 200--. 06201 1.100--. 07958 1. (DO--. 09395 .900--. 10539 ,800--. 11406 .700--.12OO3 .609--. 12329 .500--. 12371 .400--. 12099 .300--. 11455 .200--. 16301 .16O--. 07958 0
At'/V= P R/4
0. 498• 496• 494• 488• 475• 463• 450• 425• 400• 375• 350• 325• 300•275• 250• 225• 200• 175•150• 125.100• 075• 050• 025
0
918392--51--7
94 REPORT NO. 8 2 4--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
30
LO
! ii
_.--._____
w
tO
__..... [ 177_on_! !l/me
.2 .4 .0 .8
NACA MEAN LINE a=0.1
eli=l.0 ai=4.43 ° cmc14=--0.086
x Y c PI_ AV/V= PR/4(percent c) (percent
.....................0
.5
.75
1.252.5
5,0
7.510
15
2O
25
30
35
40
45
50
55
6065
7O
75
80
85
9()
95
100
0
• 440
• 616
• 9331. 608
2. 689
3.55l
4, 253
5. 261
5, 9115
6. 282
6. 449
6. 443
6. 291;6. 029
5. 664
5.218
4. 7064. 142
3. 541
5.910
2. 281
1. 652
1.1145
• 482
0
c) ely o/dx
-- -bA:iiii -• 67479
• 59896
• 49366
• 38235
• 31067
• 25(157
• 16087
• 09981
• 0528l
• 01498
--. 01617
--. 94210
--. (111373
--, 08168
--. 09637--. I08()0
--. 11694
--. 12;I07
--, 15644
--. 1269:1
--. 12425
--. 11781
--. I 0(12(1
--. 0_258
1,818
1. 717
1. 616
1. 515
1. 414
1. 313
1. 212
l.lll
I. 010
• 91)9
• 808
• 707
• 606
• 505
• 404
• 3O3
• 2(15
• 101
0
0. 455
• 429
• 404
• 379
• 354
• 328
• 303
• 278
• 253
• 227
• 202
• 177
• 152
• 126
• 1Ol
• O76
• 059
• I125
0
NACA MEAN lANE a=().2
z
(percent c)
0
.5
.75
1.25
2,5
5.0
7.5
l0
15
20
25
30
35
40
45
50
55
611
65
7O
75
811
85
91)
95
100
Cli=l.O ai=4.17 ° e= /1=--0,094
(pcrecn t c)
0
• 414
• 581
• 882
1. E_O
2. 583
3,443
4. 169
5,317
6. 117
6. 572
6. 777
6. 789
6.646
6. 3T3
5. 994
5. 527
4. 98!1
4. 396
3. 762
3. 102
2. 431
1. 764
1. 119
• 518
0
dy d dz 1" _
O. 69492
• 64047
• 57135
• 475!12
• 3761iI 1. O17
• 314_7
• 26_03
• 19373
• 124(15
• (J6;145 I. 5(13
• I)2030 l, 459
--.OI41M 1.355
--. 04246 1.25/1
--. 06588 1. 146
--. 0_522 1. 042
--, 10101 .938
--. 11359 .834
--. 12317 .7'2!I
--. 12O_i5 .625
--. 1331i3 .521
--. 13440 .417
--. 13186 .3l: _I
--. 12541 .2(18
--. 11361 .104
--. I)$94 l 0
Av[ V=PR/4
0. 417
• 391
• 365
• 339
.313
• 287
• 2(;0
.234
• 208
• 182
.1_)
• 130
. 11(4
• 078
• 1152
• 020
0
NACA MEAN LINE a=0.3
el i= 1.0 ai=3.84 ° Cm ¢/_ = --0.106
.r
(percent c)
0
,5
• 75
1.25
2.5
5. 0
7.5
10
15
20
25
311
35
40
45
5O
55
66
65
7(1
75
8O
85
9O
95
160
(percent c)
0
• 389
• 5411
.832
1. 448
2. 458
3.2!)3
4,008
5. 172
6.1)52
6. 6M5
7. O72
7.175
7. 074
6. 816
6. 433
5. !14!)
5. 383
4. 753
4. (/711
3.368
2. 645
1. 924
1.22,1
• 57(/
0
dy#d.r
0. 65536
• (_1524
.54158
• 45399
• 36344• 30780
• 2O621
• 2O246
• 15068
• 111278
• 04_33
--. 002O5
--. 0:1710
--. ()6492
--. 0_746
--. 105(17
• 1201-1
• 1311!)
--, (3()1)1
--. 14365
--. 14500
--. 14279
--. 136;_;M
--. 12430
--. 09907
t'R At,/I "= Pt¢14
..... i......
1 53_ (1. ;:I_5
1. 429 .357
1. 319 .330
1.2{)9 ,302
1. 099 .275
• I)_;(,) .247
• _479 .220
• 769 .192
• 659 . 165
• 54!) . 137
• 440 . l l0
• 330 .082
• 22{) .055
• 110 . O28
0 0
SUMMARY OF AIRFOIL DATA 95
J.O
2.0
p_
/.0
Y.T2
c
ff
N*C* a=0.5mean line
NACA MEAN LINE a=0.4
Czi=l.O ai=3.46 ° Cm el4= --0.121
:_ Y ¢ dv _/dx PR AV/V'= Pn/4(percent c) (percent c)
0.5• 75
1.252.55.07.5
1015
20253O354045
5O55
6O65
7O75
8085
9695
100
(percent c)
0.5.75
1.252.55.07.5
101520253O354O4550556065707580859095
100
0• 366• 514,784
1. 3672. 3303. 1313.824
0. 61759.57105.51210.43106.34764• 29671.25892 1,429 0.357
4.19685. 8626, 5467,0397. 3437. 4397,2756.9296.4495. 8645. 1994, 4753. 7092. 9222, 1321. 361
.6360
.20185
.15682
.11733
.07988
.04136--.00721--.05321--.08380--.10734--.12567--.13962--.14963--.15589--.15837
--.15(383--.15062--.13816
1.3101.1901.07l
.952•833.714.595•476.357.238.119
--.11138
• 327• 298• 268• 238• 208.179• 149• 119• 089• 060• 030
0
NACA MEAN LINE a=0.5
Cl,;= 1.0 "ai=3.04 ° era j4= --0.139
Y¢(percent c)
0• 345.485• 735
1.2952. 2052. 9703. 6304. 7405.620 -6. 3106. 8497. 2157. 430
1 7. 490
7.3506. 9656. 4055.7254. 9554,130
-3.2652. 395
- 1. 535.720
0
dyddx PR
1. 333
_,v/"V= P n/4
0.58195•53855.48360• 10815133070.28365• 24890•19690.15_50.12180.O9OOO.05930.02800
--.00630--.05305--•09765--•12550--.14570--. 16015--.16960--•17435--.17415--.16850--.15565
1. 2001. 067
• 933• 800• 667.533• 400• 267• 133
0.333
• 300• 267• 233• 200
• 167• 133• 100• 067• 033
0--. 12660 0
NACA MEAN LINE a=0.6
c .=1,0 ai=2.58 ° e_,/4=--0,158
X Y" Av/V= PM4(percent c) (percent c)
-c-.g
f_I
f0 .z .4
N.AC.4 a:O.6
medm I/_e
q
,6 .8 ZO
0.5• 75
1.252.55.07.5
10152025303540455055_065707580859O95
100
0,325.455• 695
1. 2202•0802•8053.4354.4955,3456. _156.5706. 9657,2357.3707.3707. 2206.8806.275 '5.5054.£_03. 6952.7201. 755
.8250
dy ¢/dx P
......................0.54825
.50760• 45615
.38555
.31325.26950.23730
.18935• 15250 1.250
.12125
.09310
.00160
.04060
.014(15--.01435
--.04700--.09470--.14015 1.094--. 16595 . 938
--.18270 .781--.19225 .625--.19515 .469
--.19095 .312--.17790 .156--.14550 0
0.312
• 273• 234• 195.1,56• 117• 078•039
0
96 REPORT NO. 8 2 4--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA MEAN LINE a=0.7
cti=l.O a{=2.09 ° C_,14=--0.179
X Yc PR At] V_PR/4(percent c) (percent
.....................O
.5
.75
1.25
2.5
5.0
7.5
10
15
21)
25
30
35
40
45
5O
5560
65
711
7580
8590
95
100
0
• 305
• 425
• 655
1.160
1. 955
2. 645
3. 240
4.245
5. 060
5. 715
6. 240
6.635
6. 925
7. 095
7. 155
7.090
6. 900
6. 565
6. 030
5. 205
4. 215
3. 140
2. 035
• 965
I)
c) dy ddx
O. 51620
.47795
• 42960
• 36325
• 29545
• 25450
• 22445
• 17995
.14595
.11740• 09200
• 068411
.04570
• 023150
--. 02455
--. 05185
--./)8475
--. 13650
--. 18511)
--. 20855
--. 21955
--. 21960
--. 21)725
--. 16985
1. 176
.980
• 784
.588
• 392
• 196
0
O. 294
• 245
• 196
• 147
• 098
• 049
0
x
(percent c)
0
.5
.75
1.25
2.5
5.6
7.5
10
15
20
25
30
35
40
45
50
55
6O
65
7O
75
80
85
99
95
100
Cl,:= 1.0
NACA MEAN LINE a=0.8
ai= 1.54 ° c=,/4= -0.202
dy _/dx P R
0. 48535
.44925
• 40359
• 34104
.27718
.23868
• 2105O
.16892
• 13734
• lllOl• 118775 1. Ill
.06634
• 0461)1
• 0261::;
. O0620--. 0143;:;
--. 03611
--. 06010
--. 08790--. 12311
--. 18412
--. 23921 .833
--. 25583 .556
--. 24904 .278
--. 20385 0
Yc
(percent c)
• 287
.404
.616
1. 077
1. 841
2. 4833.043
3. 9854.748
5.367
5. 863
6. 248
6. 528
6. 709
6. 790
6. 770
6. 644
6. 405
6. 037
5. 514
4. 771
3. 683
2. 435
1.16;:;
O
Av/V= PR/4
0.278
• 208
.139
• 069
0
NACA MEAN LINE a=0.9
cq=l.0 ai=0.9(} ° Cm_/_ =-0.225
z
(percent c)
0
.5
• 75
1.25
2.5
5. 07.5
10
15
20
2530
35
40
45
50
55
60
65
70
75
_o85
99
95
100
ye(percent
0
• 269
.379
• 577
1. 008
1. 720
2. 316
2. 835
3.707
4.410
4. 980
5. 435
5. 787
6.045
c) dyJdz
0.45482
• 42'0(;4
•37740
.31821
•25786
.22153
• 19500
•15595
.12644
.10190
.08047
.I)6084
.04234
6. 212 .02447
6.290 .00678
6.279 --.01111
6.178 --. 029t;5
5. 981 --.04938
5.681 --. 071_1
5.265 --.09584:;
4.714 --.12605
3.987 --.16727
2. 984 --. 252(_
1. 503 --. 314{;3
O --. 26086
PR AV/V=Px/4
I. 05;:; O. 263
• 526 .132
0 0
SUMMARY OF AIRFOIL DATA 97
,2.ONACA MEAN LINE a=l.0
Czi=l.O oti_O ° Creel4= --0.250
z Y _ AV/V= Pn/4(percent c) (percent ¢)
Y_
C
f f_--------
.2
NAC,_
/_ e o /7
.4
a=LO//he
.8 /.©
0.5• 75
1.252.55.07.5
10152O25303540455055
6O657O
758O859O95
100
0• 250
• 350• 535• 930
1. 5802.1202. 5853.3653. 9804. 4754. 8605.1505. 3555. 475
-- 5. 5155.4755, 3555. 1504. 8604. 4753. 980
- 3. 365
2. 5851. 5800
dy_/dx PR
......................O. 42120
• 38875.34770
29155234301999517485138051103008745067450492503225 1.06O01595
0--. 01595--.03225--.04925--.06745--. 08745--. 11030--. 13805--. 17485--.23430
......................
0.250
SUMMARY OF AIRFOIL DATA 99
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
III--AIRFOIL ORDINATES
Page0006 .............................................. 100
0009 ............................................. i00
1408 ............................................. i00
1410 ............................................. 100
1412 ............................................. 100
2412 ............................................ 100
2415 ............................................. 100
2418 ............................................ 100
2421 ............................................ 100
2424 ............................................ 100
4412 .............................................. 101
4415 ............................................ 101
4418 ............................................ 101
4421 ............................................. 101
4424 ............................................ 101
23012 ........................................... 101
23015 ............................................ 101
23018 ............................................ 101
23021 ............................................ 101
23024 ............................................ 101
63,4-420 ........................................ 102
63,4-420, a=0.3 .................................. 102
63(420)-422 ....................................... 102
63(420)-517 ........................................ 102
63-006 ........................................... 102
63-009 ........................................... 10263-206 ........................................... 102
63-209 ........................................... 102
63-210 ........................................... 102
63,-012 ........................................... 102
63,-212 .......................................... 103
63,-412 .......................................... 103
632-015 ......................................... 103
632-215 ........................................... 103
632-415 .......................................... 103
632-615 .......................................... 103
633-018 .......................................... 103
633-218 .......................................... 103
633-418 .......................................... 103
633-618 ..................................... 103
634-021 ......................................... 104
634-221 ........................................... 104
634-421 ......................................... 10464-006 ..................................... 104
64-009 ............................................ 104
64-108 ........................................ 10464-110 .......................................... 104
64-206 .......................................... 104
64-208 ............................................ 104
64-209 ......................................... 104
64-210 ........................................... 105
641-012 .......................................... 105
641-112 ............................................ 105
641-212 ......................................... 105
641-412 .......................................... 105
642-015 .......................................... 105
642-215 ......................................... 105
642-415 .......................................... 105
643-018 ......................................... 105
Page
NACA 643-218 .......................................... 105
NACA 643-418 .......................................... 106
NACA 643-618 ........................................... 106
NACA 644-021 .......................................... 106
NACA 644-221 ............................................. 106
NACA 644-421 ........................................... 106
NACA 65, 3-018 ....................................... 106
NACA 65, 3-418, a=0.8 .................................. 106
NACA 65, 3-618 ....................................... 106
NACA 65(216)-415, a=0.5 ...... : .......................... 106NACA 65-006 ........................................... 106
NACA 65-009 ........................................... 107
NACA 65-206 ........................................... 107
NACA 65-209 ........................................... 107
NACA 65-210 ............................................ 107
NACA 65-410 ........................................... 107
NACA 651-012 .......................................... 107
NACA 651-212 .......................................... 107
NACA 651-212, a=0.6 .................................... 107NACA 65,-412 .......................................... 107
NACA 652-015 .......................................... 107
NACA 652-215 ........................................... 108
NACA 652-415 .......................................... 108
NACA 65_-415, a=0.5 ................................... 108
NACA 653-018 .......................................... 108
NACA 653-218 .......................................... 108
NACA 653-418 .......................................... 108
NACA 653-418, a=0.5 .................................... 108
NACA 653-618 .......................................... 108
NACA 653-618, a=0.5 .................................... 108
NACA 654-021 .......................................... 108
NACA 654-221 .......................................... 109
NACA 654-421 .......................................... 109
NACA 654-421, a=0.5 .................................... 109
NACA 65_215)-114 .......................................... 109
NACA 65c_21)-420 .......................................... 109NACA 66,1-212 ........................................... 109
NACA 66(215)-016 ...................................... 109
NACA 66(215)-216 ...................................... 109
NACA 66(215)-216, a=0.6 ................................ 109
NACA 66(215)-416 ...................................... 109NACA 66-006 ........................................... 110
NACA 66-009 ........................................... 110
NACA 66-206 ........................................... 110
NACA 66-209 ........................................... 110
NACA 66-210 ........................................... 110
NACA 66,-012 .......................................... 110
NACA 66,-212 .......................................... 110
NACA 662-015 .......................................... 110
NACA 665-215 .......................................... 110
NACA 66r-415 .......................................... 110
NACA 663-018 .......................................... 111
NACA 663-218 .......................................... 111
NACA 663-418 ........................................... 111
NACA 664-021 ........................................... 111
NACA 664-221 ........................................... 111
NACA 67,1-215 .......................................... 111NACA 747A315 .......................................... 111
NACA 747A415 ........................................... 111
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IV--PREDICTED CRITICAL MACH NUMBERS
Page
114Critical Mach number chart ...............................
Variation of critical Much number with low-speed section lift
coefficient:
For the NACA 0006, 0009, and 0012 airfoil sections ...... 115
For several NACA 14-series airfoil sections of various
thicknesses ........................................ 115
For several NACA 24-series airfoil sections of various
thicknesses ........................................ 116
For several NACA 44-series airfoil sections of various
thicknesses ........................................ 116
For several NACA 230-series airfoil sections of various
thicknesses ......................................... 117
For several NACA 63-series airfoil sections of various
thicknesses, cambered for various design lift coefficients_ _ 117
For several NACA 63-series symmetrical airfoil sections of
various thicknesses .............................. 118
For several NACA 63-series airfoil sections of various thick-
nesses, cambered for a design lift coefficient of 0.2 ...... 118
For several NACA 63-series airfoil sections of various thick-
nesses, cambered for a design lift coefficient of 0.4 ...... 119
For two NACA 63-series airfoil sections of different thick-
nesses, cambered for a design lift coefficient of 0.6 ....... 119
For several NACA 64-series symmetrical airfoil sections of
various thicknesses ................................. 120
For several NACA 64-series airfoil sections of various thick-
nesses, cambered for a design lift coefficient of 0.1 ...... 120
For several NACA 64-series airfoil sections of various thick-
nesses, cambered for a design lift coefficient of 0.2 ...... 121
For several NACA 64-series airfoil sections of various thick-
nesses, cambered for a design lift coefficient of 0.4 ...... 121
For two NACA 64-series airfoil sections of different thick-
nesses, cambered for a design lift coefficient of 0.6 ....... 122
Page
Variation of critical Mach number with low-speed section lift
coefficient--Continued
For several NACA 65-series symmetrical airfoil sections of
various thicknesses ................................ 122
For several NACA 65-series airfoil sections with a thickness
ratio of 0.18 and cambered for various design lift
coefficients ........................................ 123
For several NACA 65-series airfoil sections of various thick-
nesses, cambered for a design lift coefficient of 0.2 ...... 123
For several NACA 65-series airfoil sections of various thick-
nesses, cambered for a design lift coefficient of 0.4 ...... 124
For several NACA 65-series airfoil sections with mean line
of the type a=0.5 and cambered for a design lift coeffi-
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For two NACA 65-series airfoil sections of different thick-
nesses, cambered for a design lift coefficient of 0.6 ...... 125
For two NACA 65-series airfoil sections with mean line of
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for a design lift coefficient of 0.6 ..................... 125
For several NACA 66-series symmetrical airfoil sections of
various thicknesses ................................. 126
For several NACA 66-series airfoil sections of various thick-
nesses, cambered for a design lift coefficient of 0.2 ...... 126
For two NACA 66-series airfoil sections of different thick-
nesses, cambered for a design lift coefficient of 0.4 ...... 127
For several NACA 66-series airfoil sections with a thickness
ratio of 0.16 and cumbered for various design lift
coefficients ........................................ 127
For several NACA 6-series airfoil sections with different
positions of minimum pressure and various thicknesses,
cambered for various design lift coefficients ............ 128
For two NACA 7-series airfoil sections with a thickness ratio
of 0.15 and cambered for different design lift coefficients_ _ 128
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128 REPORT NO. 824--NATIONAL ADVISORY CO_IM;ITTEE FOR AERONAUTICS
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V--AERODYNAMIC CHARACTERISTICS OF VARIOUS AIRFOIL SECTIONS
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
0006 ................................... 131
0009 .................................... 132
1408 ................................. 133
1410 ................................. 134
1412 ................... • ....... 135
2412 ................................ 136
2415 .................................. 137
2418 ................................. 138
2421 ................................ 139
2424 ............................ 140
4412 ................................... 141
4415 ................................. 142
4418 ..................................... 143
4421 ............................. 144
4424 .............................. 145
NACA 23012 ................................ 146
NACA23015 ..................................... 147
NACA 23018 .......................... 148
NACA 23021 ........................... 149
NACA 23024 ........................ 150
NACA C3,4-420 ............................... 151
NACA 63,4-420 with 0.25c slotted flap
(a) ,Configuration ......................... 152
(b) Aerodynamic characteristics with hinge location 1 .... 1 53
(e) Aerodynamic characteristics with hinge location 2 .... 154
NACA 63,4-420, a=0.3 .................... 155
NACA 63(420) 422 ................................ 156
NACA 63(420)-517 ............................ 157
NACA 63-006 .............................. 158
NACA 63-009 .......................... 159
NACA 63-206 ............................... 160
NACA 63-209 ............................ 161
NACA 63 210 ............................... 162
NACA 631-012 .................................. 163
NACA 631-212 .................................. 164
NACA 631-412 .............................. 165
NACA 632-015 ................................ 166
NACA 632 215 .......................... 167
NACA 632-415 ................................... 168
NACA 632-615 ................................... 169
NACA 633 018 .............................. 170
NACA 633-218 ......................... 171
NACA _32-418 .............................. 172
NACA 6"3-618 ................................. 173
NACA 634 021 .............................. 174
NACA 634-221 .................................. 175
NACA 634-42l .............................. 176
NACA 64-006 ............................... 177
NACA 64 009 ................................ 178
NACA 64-108 ............................... 179
NACA 64-110 ............................. 180
NACA 64-206 ........................... 181
NACA 64-208 ................................ 182
NACA 64-209 ............................. 183
NACA 64-210 ............................ 184
NACA 641-012 ....................... 185
NACA641-l12 ......................... 186
NACA 64_-212 ........................... 187
NACA 641-412 ........................... 188
NACA 642-015 .............................. 189
NACA 642-215 .................................. 190
NACA 642-415 .................................... 191
NACA 643-018 ..................................... 192
NACA 643-218 ..................................... 193
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
Fage
6_3-418 ......................................... 194
643-618 ....................................... 195
644-021 ...................................... 196
644-221 ...................................... 197
644-421 ....................................... 198
65,3-018 ...................................... 199
65,3-418, a=0.8 ............................... 200
65,3-618 ........................... 201
65,3-618 with 0.20c scaled plain flap ............. 202
65(216)-415, a=0.5 ........................ 203
65-006 ........................... 204
65-009 ................................... 205
65-206 ........................... 206
65-209 ....................... 207
65-210 ................................. 208
65-410 ................................ 209
65r012 ............................ 210
651-212 .................... 211
NACA 651-212 _ith 0.20c split flap (lift and moment
characteristics) ....................... 212
NACA 651-212, a:0.6 ............................. 213
NACA 651-412 ............................... 214
NACA 65.o-015 .................... 215
NACA 652 215 .................................. 216
NACA 65..-415 .......................... 217"
NACA 652-415, a=0.5 .................... 218
NACA 653 018 .............................. 219
NACA 653-118 with 0.309c double slotted flap
(a) Configuration .......................... 220
(b) Aerodynamic characteristics ............... 221
NACA 65z-218 .............................. 222
NACA 653 418 ............................... 223
NACA 65z-418, o=0.5 ............. 224
NACA 65z-618 .................. 225
NACA 653-618, a=0.5 ..................... 226
NACA 654-021 .................................... 227
NACA 654 221 ...................................... 228
NACA 654-421 ................. 229
NACA 654-421, a=0.5 ............................... 230
NACA 65(21_)-114 .................................. 231
NACA 65(4211-420 ............ 232
NACA 66,1-212 ............................... 233
NACA 66,1-212 with 0.20c split flap (lift and moment
characteristics) ...................... 234
NACA 66(215)-016 ........... " ...................... 235
NACA 66(215)-216 ................................... 236
NACA 66(215) 216 with 0.20c sealed plain flap ............. 237
NACA 66(125)-216 with 0.20c split flap (lift and moment
characteristics) .................................. 238
NACA 66(215)-216, a=0.6 ......................... 239
NACA 66(215)-216, a=0.6 with 0.30c slotted and 0.10c plain
flap
(a)(b)(c)(d)
(e)
(f)
(g)
NACA
Airfoil-flap configuration .................. 240
Flap configuration ................................. 240
Aerodynamic characteristics. Slotted flap retraeted___ 241
Lift and moment eharaeteristies. Slotted flap
deflected 22 ° _ .......................... 242
Lift and moment eharaeterislies. Slotted flap
deflected 27 ° .............................. 243
Lift and moment characteristies. Slotted flap
deflected 32 °_ .............................. 244
Lift and moinent eharaet_eristies. Slotted flap
deflected 37 ° ................................... 245
66(215)-416 .................................... 246
130 REPORT NO. 8 2 4--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
].)age
NACA 66-006 ........................................... 247
NACA 66_)09 ........................................... 248
NACA 66-206 ........................................... 249
NACA 66-209 ........................................... 250NACA 66-210 ........................................... 251
NACA 66,-012 .......................................... 252
NACA 661-212 .......................................... 253
NACA 662-015 .......................................... 254
NACA 662-215 ........................................... 255
Page
NACA 662-415 .......................................... 256NACA 663-018 ....................................... 257
NACA 66,_-218 .......................................... 258
NACA 663-418 ........................................ 259
NACA 66_-021 ........................................ 260
NACA 664-221 ........... : .......................... 261
NACA 67,1-215 ......................................... 262NACA 747A315 ........................................... 263
NACA 747A415 ............................................. 264
SU_vIMARY OF AIRFOIL DATA 131
NACA 0006
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132 REPORT NO. 8241NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 0009
t
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918392--50--10
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NACA 1410
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SUI_IMARY OF AIRFOIL DATA 135
NACA 1 41 2
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136 REPORT NO. 824--NATIONAL ADVISORY COI_IMITTEE FOR AERONAUTICS
NACA 241 2
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SUM:2_IARY OF AIRYOIL DATA 137
NACA 2415
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NACA 241 8
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SUMMARY OF AIRFOIL DATA 139
NACA 2421
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140 REPORT 1NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 2424
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SUMMARY OF AIRFOIL DATA 141
NACA 441 2
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142 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 4415
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144 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 4421
%
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SUMMARYOFAIRFOIL DATA 145
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146 REPORT _TO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 2301 2
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SUMI_ARY OF AIRFOIL DATA 147
NACA 23015
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148 REPORT NO. 8 2 4--2_TATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 23018
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SUMMARY OF AIRFOIL DATA 149
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150 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE )'OR AERONAUTICS
NACA
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23024
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SUMMARY OF AIRFOIL DATA 151
NACA 63,4-420
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152 REPORT NO. 824--NATIONAL ADVISORY CO_MITTEE FOR AERONAUTICS
NACA 63,4-420 with flap
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SUMMARY OF AIRFOIL DATA 153
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154 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 63,4-420 with flap
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SUM._IARY OF AIRFOIL DATA 155
NACA 63,4-420, a = 0.3
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] 56 REPORTNO.824--NATIONALADVISORYCOM2_IITTEEFORAERONAUTICS
NACA 63(420)-422
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%
NACA 63(420)-517
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158 REPORT NO. 8 2 4--NATIONAL ADVISORY COh_MITTEE FOR AERONAUTICS
NACA 63-006
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SUI_MARY OF AIRFOIL DATA 159
NACA 63-009
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160 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 63-206
I
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SUMMARY OF AIRFOIL DATA 161
NACA 63-209
%
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162 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 63-21 0
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SUMMARY OF AIRFOIL DATA 163
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NACA 63t-01 2
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164 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 631-21 2 -
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SUMMARY OF AIRFOIL DATA 165
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166 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 632-01 5
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SUMMARY OF AIRFOIL DATA 167
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168 REPORT NO. 8 2 4--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 632-41 5
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SUM_v[ARY OF AIRYOIL DATA 169
NACA 632-61 5
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170 REPORT NO. 824--NATIO_N:AL ADVISORY C'OMMITTEE FOR AEtlONAUTICS
NACA 633-01 8
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SUI_cIARY OF AIR/OIL DATA 171
NACA 633-218
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172 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 633-41 8
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SUMMARY OF AIRFOIL DATA 173
NACA 633-618
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174 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 634-021
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S'U.I_,I.1V£ARY OF AIRFOIL, DATA 175
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176 REPORT NO. 8241NATIONAL ADVISORY COMMITTEE :FOR AERONAUTICS
NACA 634-421
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SUMMARY OF AIRFOIL DATA 177
NACA 64-006
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178 REPORT NO. 8 2 4--:NATIONAL ADVISORY COMhIITTEE 1,_,q_ A l,:l_{ }N .\ U T I CS
NACA 64-009
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SUMMARY 0F AIRFOIL DATA 179
NACA 64-108
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NACA 64-110
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SVM_AaV 0_ A_RrOIT, DATA 181
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NACA 64-208
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SUMMARY OF AIRFOIL DATA 183
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184 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 64-210
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SUMMARY OF AIRFOIL DATA 185
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186 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 641-1 12
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SUMMARY OF AIRFOIL DATA 187
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188 REPORT NO. 8 2 4--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 641-41 2
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SUMMARY OF AIRFOIL DATA 189
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190 REPORT N0. 8 2 4--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 642-21 5
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SUMMARY OF AIRFOIL DATA 191
NACA 642-415
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192 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 643-01 8
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194 REPORT NO. 8 2 4--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 643-41 8
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SUMMARY OF AIRFOIL DATA 195
NACA 643-61 8
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NACA 644-021
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198 REPORT NO. 824---NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 644-421
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SUMMARY OF AIRFOIL DATA 199
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NACA 65,3-418, a =0.8
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NACA 65,3-618
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202 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 65,3-618 with flap
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SUMMARY OF AIRFOIL DATA 203
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204 REPORT NO. 8 2 4--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 65-006
"_- (::b ".-. o4 cO _
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206 REPORT NO. 8 2 4--1_ATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 65-206
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208 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 65-210
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SUI_,ii"VIARY OF AIRFOIL DATA 209
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NACA 651-01 2
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651-212 with flap
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214 REPORT :NO. 824--NATIONAL ADVISORY COMMITTEE :FOR AERONAUTICS
NACA 651-412
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SUMMARY OF AIRFOIL DATA 215
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216 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 652-21 5
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218 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 652-41 5,
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220 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 653-118 with flap .
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NACA 653-11 8 with flap
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222 REPORT NO. 8 2 4--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 653-218
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a =0.5
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SUMMARYOFAIRFOIL DATA 225
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a = 0.5
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SUMMARY OF AIRFOIL DATA 227
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228 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 654-221
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SUMMARY OF AIRFOIL DATA 229
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a = 0.5
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NACA 65(215)-1 14
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232 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 65(421)-420
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NACA
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66(21 5)-21 6 with flap
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SUMMARY OF A]RVOIL DATA 241
NACA 66(215)-21 6, a = 0.6 with flap
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242 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
%
66(21 5)-216,
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%
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SUMMARYOFAIRYOILDATA 243
[[ Jill IJ r I
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NACA 66(215)-216, a = 0.6 with flap
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244 REPORT _0. 824--NATIONAL ADVISORY CO_I51ITTEE FOR AERONAUTICS
NACA 66(215)-216, a = 0.6 with flap
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SUMMARYOFAIRFOILDATA 245
El
LI
%
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246 REPORT NO. 8 2 4--NATIONAL ADVISORY COMI_IITTEE FOR AERONAUTICS
NACA 66(215)-416
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SUMMARY OF AIRFOIL DATA 247
NACA 66-006
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248 REPORT NO. 824--NATIO_TAL ADVISORY COMMITTEE FOR AERONAUTICS
%
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SUMMARY OF AIRFOIL DATA 249
NACA 66-206
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250 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 66-209
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SUMMARYOFAIRFOILDATA 251
NACA 66-210
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252 REPORT N0. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 661-01 2
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SUMMARY OF AIRFOIL DATA 253
%
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NACA 661-21 2
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918392--51--17
254 REFORT N0. 824--2_TATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 662-01 5
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SUMMARY OF AIRFOIL DATA 255
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25() REPORTNO.824--NATIONALADVISORYCOMMITTEEFORAERONAUTICS
NACA 662-415
I
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SUIVIIYIARY OF AIRFOIL DATA 257
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258 REPORT N0. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NACA 663-21 8
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SUMMARY OF AIRFOIL DATA 259
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NACA 663-418
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NACA 664-021
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REPORT :NO. 8 2 4--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
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SUMMARY OF AIRFOIL DATA
NACA 664-221
261
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262
NACA
REPORT _TO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
67,1 -215
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SUiVZIVZARY OF AIRFOIL DATA
NACA 747A315
263
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264 REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
i,/
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NACA 747A415
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Positive d/reetion_ ot axis and snslm (forces and momants_ are shown by arrows
Azis
SymoDmigz_on _1,
Lo_/tud/nsL..__ XI_rsL._. YNormAL ....
F_
_xmt,ltel'to II.zm)lyml0oL
XYZ
Moment about
Veeii;natlon 8_-
o
Pitebin<_ Myawim_.._I N
i
Positive D_ips-din_/oa tiou
L
_mX Piteb.__.
X""* Y Yaw ....
Velocities
i I "_AaSulsr
r
t
Absolute coefficients of moment
(rolling) (pit_) _sw_)
D Diameter
p Geometric pitch
p/D Pitch ratioV' Inflow velocity
V'. Slipstream velocity
T Thrust, absolute coefficient Cr='_---_
Q Torque, absolute coefficient Co=_
A
I hp----76.04 kg.m/s==550 ft-lb/secI metric horsepowerm0.9863 hp
t mph----0.4470 raps
1 mpsffi2.2369 mph
Angle of set of control surface (relstive to neutralposition), 8. (Indicate surface by proper subscript.).
4. PROPILLER SYMBOLS
P Power, absolute coe/_cient Cr==on-_
0. Speed-power coemcieut---- _/p-_
n Efficiencyn Revolutions per second, rps
. (&)S. NUMEIglCAL RELATIONS
1 lb--0.4536 kg
I kg==2.2046 lbI mi==1,609.35 re=ffiS,280 ft
1 m=ffi3.2508 ft
