NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
REPORT No. 824
SUMMARY OF AIRFOIL DATA By IRA H. ABBOTT, ALBERT E.
VON
DOENHOFF,
and LOUIS S. STIVERS, Jr.
1945
AERONAUTIC SYMBOLS 1. FUNDAMENTAL AND DERIVED UNITS English
Metric Symbol Unit
Abbrevia-tion
Length ______ Time _____ ___ Force ___ _____
t F
meter __________________ second _________________ weight of) kilogram _____
m s kg
Power _______ Speed _______
P V
horsepower (metric) _____ {kilometers per hour ______ meters per second _______
---------kph
l
Abbreviation
Unit
foot (or mile) _________ ft (or rni) second (or bour) _______ sec (or hr) weight of 1 pound _____ lb
mps
horsepower ___________ hp miles per hOuL _______ mph feet per second ________ fps
2. GENERAL SYMBOLS
w
u
m I
Weight=mg Standard acceleration of gravity=9.80665 m/s 2 or 32.1740 ft/sec 2 Mass=W g Moment of inertia=mP. (Indicate axis of radius of gyration k by proper subscript.) Coefficient of viscosity
Kinematic viscosity Density (mass per unit volume) Standard density of dry air, 0.12497 kg_m- 4_s2 at 15° C and 760 mm; or 0.002378 Ib-ft-4 sec2 Specific weight of "standard" air, 1.2255 kg/ms or 0.07651 lb/cu ft JI
p
3. AERODYNAMIC SYMBOLS
s S~
G b c A
Area Area of wing Gap Span Chord
11
Angle of setting of wings (relative to thrust line) Angle of stabilizer setting (relative to thrust line) Resultant moment Resultant angular velocity
b' Aspect ratio, S
R
Reynolds number, p Vl wherelisalineardimen-
'Y
sion (e.g., for an airfoil of 1.0 ft chord, 100 mph, standard pressure at 15° 0, the corresponding Reynolds number is 935,400; or for an airfoil of 1.0 m chord, 100 mps, the corresponding Reynolds number is 6,865,000) Angle of attack Angle of downwash Angle of attack, infinite aspect ratio Angle of attack, induced Angle of attack, absolute (measured from zerolift position) Flight-path angle
o
V
True air speed
q
Dynamic pressure,
L
Lift, absolute coefficient OL= q~
D
Drag, absolute coefficient OD= q~
~P V'
Profile drag, absolute coefficient
ODO=~
Induced drag, absolute coefficient OD j = qu ~~
D.
Parasite drag, absolute coefficient ODP= ~S
o
Cross-wind force, absolute coefficient 0 0 =
q~
fJ.
REPORT No. 824 SUMMARY OF AIRFOIL DATA By IRA H. ABBOTT, ALBERT E. VON DOENHOFF, and LOUIS S. STIVERS, Jr. Langley Memorial Aeronautical Laboratory Langley Field, Va.
I
National Advisory Committee for Aeronautics Headquarters, 1500 New Hampshire Avenue NW., Washington 25, D. O. Created by act of Congress approved March 3, 1915, for the supervision and direction of the scientific study of the problems of flight (U. S. Code, title 49, sec. 241). Its membership was increased to 15 by act approved March 2, 1929. The members are appointed by the President, and serve as such without compensation. JEROME C. HUNSAKER, Sc. D., Cambridge, Mass., Chairman LYMAN J. BRIGGS, Ph. D., Vice Chairman, Director, National Bureau of Standards.
AUBREY W. FITCH, Vice Admiral, United States Navy, Deputy Chief of Naval Operations (Air), Kavy Department.
CHARLES G. ABBOT, Sc. D., Vice Chairman, Executive Committee, Secretary, Smithsonian Institution.
WILLIAM LITTLEWOOD, M. E., Jackson Heights, Long Island, N. Y.
HENRY H. ARNOLD, General, "Gnited States Army, Commanding General, Army Air Forces, War Department.
FRANCIS W. REICHELDERFER, Sc. D., Chief, United States Weather Bureau.
WILLIAM A. M. Bl:RDEN, Assistant Secretary of Commerce for Aeronautics. VANNEVAR BUSH, Sc. D., Director, Office of Scientific Research and Development, Washington, D. C. WILLIAM F. DCRAND, Ph. D., Stanford Lniversity, California. OLIVER P. ECHOLS, !\iajor General, "Cnited States Army, Chief of Materiel, Maintenance, and Distribution, Army Air Forces, War Department.
LAWRENCE B. RICHARDSON, Rear Admiral, United States Navy, Assistant Chief, Bureau of Aeronautics, Navy Department. EDWARD 'VARNER, Sc. D., Civil Aeronautics Board, Washington,
D. C. ORVILLE WRIGHT, Sc. D., Dayton, Ohio. THEODORE P. WRIGHT, Sc. D., Administrator of Civil Aeronautics, Department of Commerce.
GEORGE W. LEWIS, Sc. D., Director of Aeronautical Research JOHN F. VICTORY, LL. M., Secretary HENRY J. E. REID, Sc. D., Engineer-in-Charge, Langley Memorial Aeronautical Laboratory, Langley Field, Va. SMITH J. DEFRANCE, B. S., Engineer-in-Charge, Ames Aeronautical Laboratory, Moffett Field, Calif. EDWARD
R. SHARP,
1,1,. B., Manager, Aircraft Engine Research Laboratory, Cleveland Airport, Cleveland, Ohio
CARLTON KEMPER, R. S., Executive Engineer, Aircraft Engine Research Laboratory, Cleveland Airport, Cleveland, Ohio
TECHNICAL COMMITTEES AERODYNAMICS
OPERATING PROBLEMS
POWER Pr,ANTS FOR AIRCRAFT
MATERIALS RESEARCH COORDINATION
AIRCRAFT CONSTRUCTION
Coordination of Research Needs of Military and Civil Aviation Preparation of Research Programs Allocation of Problems PrevenUon of Duplication
LANGLEY MEMORIAL AERONAUTICAL LABORATORY Langley Field, Va.
AMES AERONAUTICAL LABORATORY l\Ioffett Field, Calif.
AIRCRAFT ENGINE RESEARCH LABORATORY, Cleveland Airport, Cleveland, Ohio
Conduct, under unified control, for all agencies, of scientific research on the fundamental problems of flight
OFFICE OF AERONAUTICAL INTELLIGENCE, Washington, D. C.
Collection, classification, compilation, and diss~'minatiori of scientific and technical information on aeronauticll II
CONTENTS Page
SUMMARY _______ .. _- - - __ - - . __ - ____ - - __ - - __ ., . _ . _.. _.. _____ _ 1NTRoDucTION_ . ________________________ .. _"_C ___ .. _______ SYMBOLS ________________________ ._______________________ HIflTORICAL DE~·ELOPMENT .. ________________________ .. _ _ __ _ _ DESCRIPTION OF AIRFOILS ____________________________ .. __ _ _ :\fethod of Combining :.\Iean Lines and Thickness Distributions ______. ______________ .__________ ______ NACA Four-Digit Series Airfoils ________________ .. ______ Numbering system_ _ _____ _ _____ __ ___ __ _ _______ _ _ _ Thickness distributions ________ . _ _ __ ___ __ _ __ _ __ _ _ _ Mean lines ____________________________. _________ ~ NACA Fh'e-Digit Series Airfoils ____ .... _____________.___ _ Numbering system__ _ ___ _ ____ ___ ____ __ ___ ___ ____ _ Thickness distributions _________________ -~_c ____ ~c-_ Mean lines ______________________ .. _ ___ _ __ __ _ __ _ _ N ACA I-Series Airfoils ____ ... ____ . ______________ "~_-=-=Numbering system ___________ ~________________ ___ Thickness distributions _________________ . __________ Mean lin es _______. __ _ __ _ ___ __ _ __ _ _ _ __ __ _ __ _ __ _ _ _ NACA 6-Series Airfoils________________________________ N um bering system __ __ __ _ _ ____ _ _ __ _ _ ___ _ __ __ _ _ __ _ Thickness distribu tions _ _ _ _ __ __ __ _ _ __ __ __ _ __ _ _ ___ _ Mean lines ___ _____________________ .. _____ .. ______ NACA 7-Series Airfoils __________ ~· ___ :.:_= _____________ ~_ NUmcering system_ ______ ___ __ ___ _____ __ ____ __ ___ Thir,kness distributions_ _ ____ __ __ __ __ _ _ ___ __ _ _ ___ _ THEORETICAL CONSIDERATIONS __________ . ______ . _________ .. Pressure Distributions _______________ c _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Methods of derivation of thickness distributions_ _ _ _ Rapid estimation of pressure distributions ____ ~ __ _ _ __ Numerical examples_ __ _ _ __ __ __ __ _ _ ___ _ ___ _ __ __ __ _ Effect of camber on pressure distribution ___ .. _____ . _ _ Critical Mach Number___ __ __ __ __ __ _ _ __ __ __ ____ ___ _ __ _ Moment Coefficients___ __ __ ____ ____ __ ___ ___ __ ___ _____ _ Methods of calculation ____ . _______ . ______ .. __ ._____ Numerical exapl pIes _ . _ _ _ __ __ _ _ __ __ __ _ ___ __ _ _ __ __ _ Angle of Zero Lift_ _ _ _ __ __ __ _ __ _ ___ __ _ _ __ __ __ __ _ __ __ _ _ Methods of calculation ______________________ .... _ _ _ _ Numerical examples______________________________ Description of Flow around Airfoils ___ ~-~~~-:c __-___ ~______ EXPERIMENTAL CHARACTERISTICS_ __ __ _ ___ _ _ __ __ __ ____ _ __ _ _ Sources of Data _______ .. __________________________ . __ _ Drag Characteristics of Smooth Airfoils ________ .. __ _ __ __ _ Drag characteristics in low-drag range __ .. ______ . __ _ Drag characteristics outside low-drag range_ __ __ _ ___ _ ~
1 1 2 3 3 4 4 5 5 5 5 "5 5 5 5 5 5 5 5 6 6 7 7 7 8 8 8 10 12 13 13 14 14 14 14 14 14 15 1616 16 16 18
Page
EXPERIMENTAL CHARACTERISTIcs-Continued Drag Chara~teristics of Smooth Airfoils-·Continued Effects of. type of sectiOIl on drag charact.eristics .. ____ Effective aspect ratio ________. _________________ .. ___ Effect of surface irregularities on drag ____ . _____________ Permissible roughness ________ .. _________ __ ______ ___ Permissible waviness ______________________ ._ _____ __ Drag with fixed transition ___ . ___ .. _________________ Drag with practical construction methods_ __________ Effects of propeller slipstream and airplane vibration_~ Lift Characteristics of Smooth Airfoils_ ______________ ___ Two-dimensional dat9. __________ .. _________________ Three-dimensional data_ _ _________________________ Lift Characteristics of Rough Airfoils. _______________ ___ Two-dimensional data_ ___________ _________ _______ Three-dimensional data ______ .____ . ____ .. ______ .. __ __ Unconservatiye Airfoils ________ .... __ . _____ ... ____________ Pitching Moment ____________________ . ___________ .. ___ Position of Aerodynamic Center __ . ______________ . __ .. ___ High-Lift Devices_ ____ __ ___ ___________ __ __ __ ____ _ ___ _ Lateral-Control Devices ___________________ .. __ _________ Leading-Edge Air Intltkes __________ .. _____ __ __ ______ __ _ In terference __ .. _________________________ .. ____________ . ApPI,ICATION TO WINO DESIGN __________ . ___ .. ______________ Application of Section Data __________________________ .. Selection of Root Section ___ ._ _______________ ______ _____ Selection of Tip Section ____ .. ________________ ... _ _____ __ CONCLUSIONS _________________ .. _________________ .. _____ ___ ApPENDIX-- METHODS OF OBTAINING DATA IN THE LANGLEY Two-DIMENSIONAL Low-TURBULENCE TUNNELS_ __________ Description of Tunnels___ ___ ______________ __ ____ _____ Symbols ___ .. _____________ . _ ___________ ________ _____ Measurement of Lift.. ______ . ______ ... _______ _________ __ Measurement of Drag .. ______________________________._ Tunnel-Wall Corrections _____ .. ______ ____________ __ ____ Correction for Blocking at High Lifts ______ . _________ ___ Comparison w.ith Experiment.. ____________________ .. ____ REFERENCES _____________ .. ______________________________ TABLES ___________________ .... ___ .. ________________________ SUPPLEMENTARY DATA: I-Basic Thickness Forms _______ .. ____. _. ___ . _____ . _ ___ J.I-Data for Mean Lines_____________________________ III::""':Airfoil Ordinates_ ________ __ ______ __ __ __ ___ ______ IV-Predicted Critical Mach Numbers ______ .__________ V-Aerodynamic Characteristics of Various Airfoil Sections___ ________________ __ ________ _________ III
18 21 22 22 22 24 24 29 30 30 37 37 37 38 394() 43: 43: 43 49 50 51 51 51 52 52 54 54 54 55 56 57 59 59 60 64 69 89 99 113 12~
REPORT No. 824 SUMMARY OF AIRFOIL DATA By
/,
IRA
H.
ABBOTT, ALBERT
E.
VON DOENHOFF,
SUMMARY
Recent airfoil data for both flight and 'wind~tunnel tests have been collected and correlated insojar as possible. The flight data consist largely of drag measurements made' by the wake~ survey method. Most of~he data on airjoil section characteris~ tics were obtained in the Langley two-dimensionallow~turbulence pressure tunnel. Detail data necessary for the application of NAOA 6~series airfoils to wing design are presented in supplementary figures, together with recent datajor the NAOA 00-, 14-, 24-, 44-, and 230-series airjoils. The general methods used to derive the basic thickness jorms jor NAOA 6- and 7 -series airjoils and the'ir corresponding pressure distributions are presented. Data and methods are given jor rapidly obtaining the approximate pressure distributions jor N AOA fourdigit, five-digit, 6-, and 7-series airfoils. The report includes an analysis oj the lift, drag, pitchingmoment, and critical-speed characteristics of the airfoils, together 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 interference are briefly discussed. The data indicate that the effects oj surface condition on the l~ft and drag characteristics are at least as large as the effects of the airfoil sha,pe and must be considered in airfoil selection and the prediction of wing characteristics. Airjoils permUting extensive laminar flow, such as the NAOA 6-series airfoils, have much lower drag coefficients at high speed and cru~~sing lift coefficients than earlier types of airfoils if, and only if, the wing surfaces are suffic1~ently smooth and fair. The NAOA 6-scries airfoils also ha,1'e favorable crit?:cal-speed character'istics and do not appear to present 1Lnu8ual problems associated with the applicat1:on oj high-l'i:ft and lateral-control devices.
and
LOUIS S. STIVERS, JR.
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 N ACA 6-series airfoils. The general methods used to derive the basic thickness forms for N ACA 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 lateralcontrol devices, leading-edge air intakes, and interference are briefly discussed, together with aerodynamic. problems of application. Numbered figures 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 following headings: I-Basic Thickness Forms II-Data. for Mean Lines III-Airfoil Ordinates IV--Predicted Critical Mach Numbers V-Aerodynamic Charactel'is tics of Various Airfoil Sections These supplementary figures and tables present the basic data for the airfoils. SYMBOLS
INTRODUCTION
A considerable amount of airfoil data has been accumulated from tests in the Langley two-dimensional low-turbulence tunnels. Data ha,ve 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 ai.rfoil 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 t,hem insofar as possible.
aspect ratio Fourier series coefficients mean-line designation, fraction of chord from leading edge over which design load is uniform; in derivation of thickness distributions, ba,sic length usually considered unity wing span flap span, inboard flap span, outboard drag coefficient drag coefficient at zero lift lift coefficient increment of maximum lift cuused by flap deflection
2 C
Ca Cd
Cdml~ Cfi CfO
91 C
REPORT NO. 824-¡NATIONAL ADVISORY COMMITTEE FOR AERONAUTiC;:,
chord aileron chord section drag coefficient minimum section drag coefficient flap chord, inboard flap chord, outboard flap-chord ratio section aileron hinge-moment coefficient
(~) goc
increment of aileron hinge-moment coefficient at constant lift !lCHO hinge-moment parameter section lift coefficient Cl design section lift coefficient Cli moment coefficient about aerodynamic center Cma . e. moment coefficient about quarter-chord point Cme/ 4 Cn section normal-force coefficient D drag !lH . loss of total pressure free-stream total pressure h section aileron hinge moment exit height he k constant L lift M Mach number critical Mach number Mer typical points on upper and lower surfaces of airfoil OU,OL
XL Xu
abscissa of lower surface absciss!'\. of upper surface
G},.
chordwise position of transition distance perpendicular to chord mean-line ordinate ordinate of lower surface ordinate of symmetrical thickness distrihution ordinate of upper surface complex variable in circle plane complex variable in near-cireIe plane angle of attack
Y Ya YL YI Yu Z
z' a !lao .10
Ho
p
pressure coefficient
(P-Po) go
R Rer
critical pressure coefficient resultant pressure coefficient; difference between local upper- 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 pressure Reynolds number critical Reynolds number
s
pressure coefficient (H~o
P Po
pb/2V
f}o
P)
first airfoil thickness ratio second airfoil thickness ratio free-stream velocity inlet velocity local velocity increment of local velocity increment of local velocity caused by additional type of load distribution velocity ratio corresponding to thickness i1 velocity rat.io corresponding to thickness t2 distance along chord mean-line abscissa
sO
section aileron effectiveness parameter, ratio of change in section angle of attack to increment of aileron deflect,ion 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 design lift coefficient flap 01' aileron deflection; down deflection is positi,-e flap deflection, inboard flap deflection, outboard i\,irfoil parameter (IP-() value of E at trailing edge complex variable in airfoil plane angular coordinate of z'; also, angle of which tangent is slope of mean line . (TiP chord) taper ratIO Root chord
T
t urb u Ience fac t or (
Effective Reynolds number) Test Reynolds number
angular coordinate of z airfoil parameter determining radial co.)rdinato of z average value of 1ft
(~17r 50
2 ..
1ft dIP)
HISTORICAL DEVELOPMENT
The development of types of NACA airfoils now in common use was started in 1929 with a systematic investigation of a family of airfoils in the Langley variable-density tunnel. Airfoils of this family were designated by numbers having four digits, such as the NACA 4412 airfoil. All airfoils of this family had the same basic thickness distribution (reference 1), and the amount and type of camber was systematically varied to produce the family of related airfoils. This investigation of the NACA airfoils of the four-digit series produced airfoil sections having higher maximum lift coefficients and lower minimum drag coefficients than those of sections developed before that time. The investigation also provided information on the changes in aerodynamic characteristics resulting from variations of geometry of the mean line and thickness ratio (reference 1).
3
SUMMARY OF AIRFOIJ" DATA
The investigation was extended in references 2 and 3 to include airfoils with the same thickness distribution but with positions of the maximum camber far forward on the airfoil. These airfoils were designated by numbers having five digits, such as the NACA 23012 airfoil. Some airfoils of this family showed favorable aerodynamic characteristics except for a large sudden loss in lift at the stall. .Although these investigations were extended to include a limited number of airfoils with varied thickness distributions (references 1 and 3 to 6), no extensive investigations of thickness distribution were made. Comparison of experimental drag data at low lift coefficients with the, skinfriction coefficients for flat plates indicated that nearly all of the profile drag under such conditions was attributable to skin friction. It was therefore apparent that any pronounced 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 airstream 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 airfoils having favorable pressure gradients over a greater proportion of the chord than the airfoils developed in references 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 t.est equipment with very low airstream turbulence. This work was greatly encouraged by the experiments of Jones (reference 7), who demons~rated the possibility of obtaining extensive laminar layers in flight at relatively large Reynolds numbers. Uncert.ainty with 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 conditions of air-stream turbulence and Reynolds number. The resulting wind tunnels, the Langley two-dimensional lowturbulence 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; twodimensional flow is thus provided, which obviates difficulties previously encountered in obtaining section data from tests of finite-span wings and in correcting adequately for support interference (reference 8). Difficulty was encountered in attempting to design airfoils having desired pressure distributions because of the lack of adeql.late 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 the absence of a suitable theoretical method, the 9-percentthick symmetrical airfoil of the N ACA 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 N ACA 2- to 5-series sections (reference 11). Experience with these sections showed that none of the approximate methods tried was sufficien tly 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 cOplparatively large values of the Reynolds number if the airfoil surfaces were sufficiently 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 airfoils 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 designJift coefficient when sm09th, 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 thickness forms were derived by new and improved methods described herein in the section "Methods of Derivation of Thick.9.ess Distributions," in accordance 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 development 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 slilctions permit low pitching-moment coefficients with moderately high design lift coefficients at the expense of some reduction 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 N ACA families considered 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 supplementary figures by the methods described for each family of airfoils.
4
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAU'fICS
y
--- ---
Mean line
---
----
Chord Ime I
I
::OL(:X:L-)-:Y,;L~)-----~-------------
I
\ \
Xv =x-Y t sin 8 =x+Y, sin 8
Yu=Yc+y, YL =Yc -Yt
XL
\
\,
cos 8 cos 8
Rodius fhrou9h end of chord '(mean-line slope ot 05 percent chord)
1.00
SAMPLE CALCULATIONS FOR DERIVATION OF THE KACA 65,3-818, a=1.0 AIRFOIL
0 -.005 .05 .25 .50 .75 1.00
11,
11'
X
(0)
0
0 ;"(;0200
.-01324 .03831 .08093 .08593 .04456 0
tan 0
sin 0
cos 0
----------
"6:3i932'
'6:94765-'
(b)
.01264 .03580 .04412 .03580 0
' 0.33696 .18744 .06996 0 -.06996
----------
0 -.06979
.98288 .99756 1.00000 .99756
----------
----------
.18422 .06979
YI sin 0
y, cos 0
0
0 .00423 .00706 . 00565
0 -.00311
a
.01255 .03765 .08073 .08593 .04445
a
I
Xu
0
.ooon
.04294 .24435 .50000 .75311 1.00000
0
0 .01455 .05029 .11653 .13005 .08025 0
1!L
XL
1/U
I
0 -.01055 -.02501 -.04493 -.04181 -.00865
.00923 . C5706 .25565 .50000 .74689 1. 00000
a
Thickness distribution obtained from ordinates of the N A OA 65,3--018 airfoil. Ordinates of the mean line, 0.8 of the ordinate for c',= 1.0. , Slope of radius through end of chord. FIGURE I.-Method of combining mean lines and basic thickness forms.
o b
The process for combining a mean line and a thickness. distribution to obtain the desired cambered airfoil section is illustrated in figure 1. The leading and trailing edges are defined as the forward and rearward extremities, respectively, of the mean line. The chord line is defined as the straight line connecting the leading and trailing edges. Ordinates of the cambered airfoil are obtained by laying off the thickness distribution perpendicular to the mean line. The abscissas, ordinates, and slopes of the mean line are designated as Xc, Yc, and tan (J, respectively. If Xu and Yu represent, respectively, the abscissa and ordinate of a typical point of the upper surface of the airfoil and Yt is the ordinate of the symmetrical thickness distribution at chordwise position X, the upper-surface coordinates are given by the following relations: xu=X-Yt sin
(J
(1) (2)
The corresponding expressions for the lower-surface coordinates are (3) (4)
The center for the leading-edge radius is found by drawing a line through the end of the chord at the leading edge with the slope equal to the slope of the mean line at that point and laying off a distance from the leading edge along this line equal to the leading-edge radius. This method of construction causes the cambered a.irfoils to p.roject slightly forward
of the leading-edge point. Because the 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 through the end of the chord for such mean lines is usually taken as the slope of the mean line at ~=0.005. This
c
procedure is justified by the manner in which the slope increases to the theoretically infinite value as x/c approaches o. The slope increases slowly until very small values of x/c are reached. Large values of the slope are thus limited to values of x/c very close to 0 and may be neglected in practical airfoil design. Tables of ordinates are included in the supplementary data for all airfoils for which standard characteristics are presented. NACA FOUR-DIGIT-SERIES AIRFOILS
Numbering system.-The numbering system for the NACA airfoils of the four-digit series (reference 1) is based on the airfoil geometry. The first integer indicates the maximum value of the mean-line ordinate Yc in percent of the chord. The second integer indicates the distance from the leading edge to the location of the maximum camber in tenths of the chord. The last two integers indicate the airfoil thickness in percent of the chord. Thus, the NACA 2415 airfoil has 2-percent camber at 0.4 of the chord from the leading edge and is 15 percent thick. The first two integers taken together define the mean line. for example, the N ACA 24 mean line. The symmetrical airfoil sections representing the thickness distribution for a family of airfoils are designated by zeros for the first two integers, as in the case of the N ACA 0015 airfoil.
5
SUMMA RY OF AIRFOI L DATA
Thickn ess distrib utions. ---Data for the NACA 0006,0008, 0009, 0010, 0012, 0015, 0018, 0021, and 0024 thickness distrib utions are presen ted in the supple mentar y figures_ Ordina tes for interm ediate thicknesses may be obtain ed correc tly by scaling the tabula ted ordina tes in propor tion to the thickness ratio (reference 1). The leading-edge radius varies as the square of the thickness ratio. Values of (vIV)2, which is equiva lent to the low-speed pressur e distribution, and of vlV are also presen ted. These data were obtain ed by Theodo rsen's method (reference 9). Values of the velocity increm ents t::.va/F induce d by changing angle 01 attack (see section "Rapid Estima tion of Pressu re Distrib utions") are also presen ted for an additio nal lift coefficient of approx imately unity. Values of the velocity ratio v/V for interm ediate thickness ratios may be obtain ed approximately by linear scaling of the velocity increm ents obtain ed from the tabula ted values of v/V for the neares t thickness ratio; thus, (5)
Values of the velocit y-incre ment ratio !::.Va/V may be obtaine d for interm ediate thicknesses by interpo lation. Mean lines. -Data for the NACA 62,63, 64,65, 66, and 67 mean lines are presen ted in the supple mentar y figures. The data presen ted include the mean-line ordina tes yo, the slope dYeldx, the design lift coefficient eli and the correspondi ng design angle of attack ai, the momen t coefficient cmei4 ' the resulta nt pressure coefficient P R , and the velocity ratio !::.v/V. The theoret ical aerody namic charac teristic s were obtain ed from thin-airfoil theory . All tabula ted values for each mean line, accordingly, vary linearl y with the maximum ordina te Ye, and data for similar mean lines with different amoun ts of cambe r within the usual range may be obtain ed simply by scaling the tabula ted values. Data for the NACA 22 mean line may thus be obtain ed by multiplying the data for the N ACA 62 mean line by the ratio 2: 6, and for the NACA 44 mean line by multip lying the data for the NACA 64 mean line by the ratio 4:6. NACA 'FIVE.DI GIT-SER IES AIRFOIL S
system .-The numbe ring system for airfoils of git series ,is based on a combin ation of live-di the NACA charac teristic s and geometric charnamic theoret ical aerody 3). The first integer indicat es and 2 acteris tics (references of the relativ e magnit ude of terms in r cambe the amoun t ,pf lift coefficient in tenths design the ient; the design Wit coeffic The second and third . integer first the of is thus three-h alves the leading edge from e distanc the e indicat er integers togeth this distanc e in r; cambe um maxim the of n to the locatlo represe nted by r numbe the lf one-ha is chord percen t of the e the airfoil indicat s integer two last The these integers. 23012 airfoil NACA The chord. the of t thickne ss in percen maxim um its has 0.3, of ient coeffic lift ,aesign a, thus has ss ratio thickne a has and chord, the of t percen cambe r at U . of 12 percen~ Numberinl~
Thickn ess distrib utions .--The thickne ss distrib utions for airfoils of the N ACA 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 presen ted in the supple mentar y figures in the same form as for the mean lines given herein for the four-di git series. All tabula ted values for each mean line vary linearl y with the maxIm um ordina te or with the design lift coefficient. Thus, data for the NACA 430 mean line ma,y be obtain ed by multip lying the data for the NACA 230 mea,n line by the ratio 4:2 and for the NAOA 640 mean line by multip lying the data for the NACA 240 mean line by the ratio 6: 2. NACA l-SERIES AIRFOIL S
Numbe ring syster n.-The NACA I-series airfoils are designated by a five-digit 'numb er-as, for example, the NACA 16-212 section. The first integer represe nts the series designation. The second integer indicat es the distance in tenths of the chord from the leading edge to the positio n of minim um pressure for the symme trical section at zero lift. The first numbe r following the dash indicat es the amoun t of cambe r expressed in terms of the design lift coefficient in tenths, and the last two numbe rs togeth er indicat e the thickne ss in percen t of the chord_ The commonly used sections of this family have minim um pressure at 0.6 of the chord from the leading edge and are usually referre d to as the NACA 16-seI'ies sections. Thickn ess distrib utions .-Data for the NACA 16-006, 16-009, 16-012, 16-015, 16-018, and 16-021 thickne ss distrib utions (reference 10) are presen ted in the supple mentary figures. These data are similar in form to the data for those airfoils of the N ACA four-digit series, and data for interm ediate thickness ratios may be obtain ed in the same manne r. Mean lines. -The NACA 16-series airfoils as commo nly used are cambered with a mean line of the uniform -load type (a=1.0 ), which is described under the section for the N ACA 6-series airfoils that follows. If any other type of mean line is used, this fact should be stated in the airfoil d.esignation. NACA 6-SERIES AIRFOIL S
Numbe ring system .-The N ACA 6-set'ies airfoils are usually design ated by a six-digit numbe r togeth er with a statement showing the type of mean line used. For example, in the designation NACA 65,3-218, a=O.5 , the "6" is the series designation. The" 5" denote s the chordwise positio n of minim um pressure in tenths of the chord behind the leading edge for the basic symme trical 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 favorab le pressure gradien ts exist on both surfaces. The "2" following the dash gives the design lift eoefficient in tenths. The last two digits indicat e the airfoil thickne ss in percen t of the chord. The design ation" a=0.5 " shows the type of mean line used. When the mean-line designation is not given, it is unders tood that the uniform -load mean line (a= 1.0) has been used.
6
REPORT NO. 824-NA 'rIONA L ADVISO RY COMMI TTEE FOR AERON AUTICS
When the mean line used is obt.ained by combin ing more t.han one mean line, the design lift. coefficient used in t.he design ation is the algebraic sum of the design lift coefficients of the mean lines used, and the mea.n lines are described in the statem ent following the numbe r as in the following case: NACA 65,3-218
a=0.5 CII=O ..3 } { a=l.O ,' Cl =-0.1 i
Air'foils having a thickne ss distrib ution obtain ed by linearl y increas ing or decreasing the ordina tes of one of the originally derived thickness distrib utions are design ated as in the following example: NACA 65(318)-217, a=0.5 The significance of all of the numbe rs except those in the parenth eses is the same as before. The first numbe r and the last two numbe rs enclosed in the parenth eses denote , respectively, the low-dr ag range and the thickness in percen t of the chord of the originally derived thickness distrib ution. The more recent NACA 6-sories airfoils are derived as membe rs of thickne ss families having a simple relatio nship betwee n the conformal transfo rmatio ns for airfoils of different thickness ratios but having minim um pressur e at the samt;\ chord wise position. These airfoils are distinguished from thp earlier individ ually derived airfoils by writing the number indicat ing the low-dr ag ra.nge as a. subscr ipt; for exa.mple, NACA 65 3-218, a=0.5 For NACA 6-se1'ies airfoils having a thickne ss ratio less than 0.12 of the chord, the subscr ipt numbe r indicat ing the low-dr ag range should be less than unity. Rather than usc a fmctio nal numbe r, a subscr ipt of unity was originally employed for these airfoils. Since this usa.ge is not consist ent with the previo us definition of a numbe r indicat ing the lowdrag range, the designations of a.irfoil sections having a thickness ratio less than 0.12 of the chord are now given withou t such a numbe r. As an example, an N AOA 6-series airfoil having a thickne ss ratio of 0.10 of the chord would be design ated: NAOA 65-210 Ordina tes for the basic thiclniess distrib utions design ated by a subscr ipt are slightly different from those for the correspondi ng individ ually derived thickne ss distrib utions. As before, if the ordina tes of the basic thickne ss distrib ution have been changed 1)Y a factor, the low-dr ag range and thickness ratio of the original thickne ss distrib ution are enclosed in parenth eses as follows: NAOA 65(318)-217, a=O.5
If, howevPJ', the ordina tes of a basic thickness distrib ution having a thickne ss ratio less than 0.12 of the chord have been changed by a factor, 'the numbe r indicat ing the low-drag range is elimin ated and only the original thickne ss ratio is enclosed in parenth eses as follows: NACA 65(10)-211 If the design lift coefficient in tenths or the airfoil thickne ss in percen t of chord are not whole integers, the numbe rs giving these quanti ties are usually enclosed in parenth eses as in the following designation:
NACA 65(318)-(1.5) (16.5), a=O.5 Some early experim ental airfoils are design ated by the insertion of the letter "x" immed iately preceding the hyphen as in the designation 66,2x-115. Thickn ess distrib utions .-Data for availab le N AOA 6-series thickne ss forms are presen ted in the supple mentar y figures. These data are compa rable with the similar data for airfoils of the NACA four-digit series, except that ordinates for interm ediate thicknesses may not be correct ly obtained by scaling the tabula ted ordina tes propor tional to the thickness ratio. This metho d of changi ng the ordina tes by a factor will, however, produc e shapes satisfa ctorily approx imatin g membe rs of the family if the change in thickne ss ratio is small. Values of v/V and 6.v./V for interm ediate thickne ss ratios may be approx imated as described for the NACA four-digit series. Mean lines. -The mean lines commo nly used with the NACA 6-series airfoils produc e a uniform chordwise loading from the leading edge to the point ~=a and a linearl y decreasing load from this point to the trailing edge. Data for NAOA 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 presen ted in the supple mentar y figures. The ordina tes were compu ted by the following formula, which represe nts a simplification of the original expression for mean-line ordina tes given in reference 11:
x x~ -cx loge c+ U- h cI
(6)
where
1 [1
1
]
h= - -2 (1-a)2 10ge (l-a) -- (1-a)2 +U I-a . 4 The ideal angle of attack lift coefficient is given by
IXI
corresponding to the design Cit
cx(==- h 27l'(a+ D
The data are presen ted for a design lift coefficient Cit equal to unity. All tabula ted values vary directl y with the design lift coefficient. Oorres pondin g data for similar mean lines with other design lift coefficients may accordingly be obtaine d simply by multip lying the tabula ted values by the desired design lift coefficient. In order to cambe r NAOA 6-series airfoils, mean lines are usually used having values of a, equal to or greater than the distanc e from the leading edge to the locatio n of minim um pressure for the selected thickne ss distrib ution at zero lift. For special purposes, load distrib utions other than those corresponding to the simple mean lines may be obtaine d by combin ing two or more types of mean line having positive or negativ e values of the design lift coefficient. The geome tric
7
SUMMARY OF AIRFOIL DATA
and aerodynamic characteristics of such combinations may be obtained by algebraic addition of the values for the component mean lines. NACA 7-SERIES AIRFOILS
Numbering system.-The NACA 7-series airfoils are designated 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 surface, in tenths of the chord from the leading edge, of the region of favorable pressure gradient at the design lift coefficient. 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 numbers 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 surfaces, the same design lift coefficient, and the same maximum thickness as the original airfoil but having a different meanline combination or thickness distribution would have the
serial letter "B." Mean lines used for the NACA 7-series airfoils are obtained by combining two or more of the previously described mean lines. A list of the thickness distributions and mean lines used to form these airfoils is presented in table 1. The basic thickness distribution is given a 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 designation NACA 747 A015 even though minimum pressure occurs at O.4c on 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 7series thickness distributions are presented in the supplementary figures. These thickness distributions are individually 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 their characteristic features. Values of (V/V2) and of v/V for thinner or thicker thickness distributions may be approximated by the method of equation (5). If the change in thickness ratio is small, tabulated values of I1V a /V may be applied'directly with reasonable a.ccuracy.
20 I.B
V
1.6
1.4
k"
V
l
!
I
I
""
I
1 ~ ~.
_I 1 1 -----. NACA 747AOl5 basic rhicimess distribution
/
(v)'1.0 I /' ---- k .8
f---
,NACA 747A315 '(upper surface) II
I
1.2
-- r-
r:-:JCA I
,"" "-
""
----- :----... ~
74~A3~5
(lower surface)
"" "'" "-
!
I
'-.
"-
"'"
.6 .4
.2
o
.3
.I
.5
.4
.6
.7
.8
.9
1.0
xlc FIGURE
2.-Theoretical pressure distribution for the NACA 747A315 airfoil section at the design lift coefficient and the NACA 747AOlij husir thickness dis:l'ibuUOll.
TABLE I.-ANALYSIS OF AIRFOIL DE.RIVATION Airfoil designation
Basic thickness form
Mellon-line combination 1
1_ _ _ _ -;-_ _ _--;-_ _ _ _ , _ _ _
a=O
a=O.l
a=0.2
_,_----;--------.-----;-----,------;----,---1
a=0.3
747A315 ________ 747A015 ____________________________ "" ______________________________ _ 747A415 ________ 747A015 ____________________________________________________________ _
I
a=0.4
a=0.5
a=0.6
0.763 .763
The numbers in the various columns headed "Mean-line combination". indicate the magnitude orthe design lift coefficient used.
a=0.7
=O:!~
a=0.8
a=0.9
a=1.0
::::::::::::: :::::: ::::::: ----ii:ioo----
8
REPOR'l' NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
THEORETICAL CONSIDERATIONS PRESSURE
this circle in complex coordinates is
(7)
z=aefo+iq,
DISTRIBUTION~
A knowledge of the pressure distribution over an airfoil is desimble for structural design and for estimation of the critical 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 usually advisable to relate the airfoil characteristics to the pressure distribution rather than 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 N ACA 6and 7-series airfoils, together with their corresponding pressure distributions, are derived by means of conformal transformations. 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 shows schematically 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 aiD. The equation of
where
z ¢ a 1/10
complex variable in circle plane angular coordinate of z basic length usually considered unity constant determining radius of, circle
This true circle is transformed into an arbitrary, almost circular curve by the relation ~,
='_= e(f-fol+i{O-q,) z
(8)
the equation of the almost circular curve is z' =ae f +iO
(9)
where
z'
complex variable in near-circle plane
ae f
radial coordinate of
f}
angular coordi.nate of z'
z'
In order Jor the transformation (8) to be conformal, it is necessary that the quantity (f}-r/» (given the symbol -E) be the conjugate function of (1/I-if;0); that is, if E is represented by a Fourier series of the form Z-p/one \ - - - - - - - j L - - - - " - - - l
'" '" e=L: An sin n</>-L: Bn cos n</> 1 1
then (if;-1/Io) is given by the relation '"
'"
1
1
(1/1-1/10)="'22 An cos nr/>+::8 Bn sin nr/> =-.'= e
fll ->;.)4-I(S-tJ)
z
This relationship indicates that, if the function E(r/» is given, (1/1-1/10) can be calculated as a function of r/>. Means of performing this calculation are presented in reference 13. The transformation relating the almost circular curve to tbe airfoil shape is (10)
Z-p/one f-------,fL------'L----,
where f is the complex va.'iable in the airfoil plane. The coordinates of the airfoil x and yare the real and imaginary parts of f, respectively. These coordinates are given hy the relations .c= 2a cosh 1/1 cos 8 (11) y=2a sinh 1/1 sin f}
(12)
The velocity distribution in terms of the airfoil parameters 1/1 and € is given exactly for perfect fluid flow by the expression v
f=Xri y FIGURE
3.-Transformations used to derive airfoils nnd calculate pressure distributionR.
[sin
(ao+¢)+~in (aO+€TE)] efO
V= ~ (sinh21/1+sin28) [( 1-
:;y +(~~)]
(13)
9
SUMMA RY OF AIRFOI L DATA .16
where
.08
r
v
free-stream velocity
ao
section angle of attack
0/0
average value of 0/ (i1f'L
"\ '--
o
ETE
d¢; dE dfjJ'dfjJ.
0/ de/> )
The basic symme trical shapes were derived by assuming suitabl e values of de/de/> as.a functio n of e/>. These values were chosen on the basis of pr~vious experience and are subjec t to the eonditi ons that
L1J"~=o
appr~ximately proportional to
1
dtPJ
~
'\
j
II
\ /
/ /
V
1\
~J
\
-.16
/
Ir h
"'" "j
~
/ ,
V i
.24
~
--1\ i
V
V
V
\
V
.08
o
V
\' \
>I,e I
o
\
j V
1\ C\
-.08
-.IB '---.
"'/ II
/E
~
----
+J;
(see refrren ce 14), the initiall y assumed values of df/de/> were altered by a process of successive approx imatio ns until the desired type of velocity distrib ution was obtaine d. After the final values of 0/ and e were obtaine d, the ordina tes of thr basic thickness distrib ution were compu ted by equatio ns (11) and (12). When these compu tations were made, it appear ed that there was an optimu m value of the leading-edge radius dependent. upon the airfoil thickne ss and the positio n of minim um pressure. If the leading-edge radius was too small, a premature peak in the pressure distrib ution occurred in the immed iate v-icinity of thr leadi.ng edge as the angle of att.ack was increas rd. If the leading-edge radius was too large, a premat ure peak occurre d a few prrcen t of the chord behind thr lrading edge. With the COrI'rct l(lading-edge radius t.he pressure distribut.ion became nearly flat over the forward portion of the airfoil before the norma l leading-edge peak formed at the higher lift coefficients. Curves of the param eters 0/, f, dl/;/de/>, de/de/> plotted agains t e/> for the NACA 64 3-018 airfoil section are given in figure 4. Experi ence has shown tl~at, ,,,,hen the thickness ratio of an originally derived basic form was increased merely by multiplying all the ordina tes by a consta nt factor, an unnecessarily large decrease in the critical speed of the resultin g section occurred. Reduc ing the thickness ratio in a similar manne r caused an unnecessarily large decrease in the low-drag range. For this reason, each of the earlier N ACA 6-series sections was individ ually derived. It was later found that it was possible
\V\
dlf.-I
\dfjJ
\
.16
and de/de/> at e/> is equal to df/dcp at -cp. These conditions are hecessary for obtain ing closed 'symm etrical shapes. Values of fCe/» were obtain ed simply by integra ting ;; de/>. Values of o/(cp) were found by obtaini ng the conjug ate of the curve of eCe/» and adding a value % suffieient to make the. ,'alue of 0/ equal to zero at cp=1f'. This condition assures a sharp trailing-edge sbape. Inasm uch as small change s in the velocity distrib ution at any point of the surface are
V
/
!
... ·dE
/
~
V
-.08
value of e at trailing edge
/
/
i
2 1J"
~
/
local velocity over surface of airfoil ':I.
2
/
I
'"
~--
4
/ 5
V-
/
..- f--_ ..
6
~.'I"
tP, radians
;he XACA 643-018 airloil. FIGURE 4.-Variat ion of airfoil parameter s,p, E'~' !~ with", for section basic thickness form.
t.o derive basic airfoil parame ters I/; and e that could be multip lied by a eonsta nt faetor to obtain airfoils of variou s thickness ratios, withou t ha.ving the aforementioned limitations in the resultin g sect.ions. Each of the more recent families of NACA 6-series airfoils, in which numeri cal subscripts are used in the designation, having minim um pressur e at a given chordwise position was obtain ed by scaling up and down the basic values of the airfoil parame ters 1/;, and E.
(V))
Theore tical pressur e distrib utions (indica ted by for a, family of N ACA 65-series a.irfoils covering n range of thickness ratios are given in figure .5 (a). This figure shows the typical increase in the magnit ude of the favora ble pressure gradie nt, increase in maxim um velocity over the surface, and increase in the relativ e pressure recovery over the rear portion of the airfoil' with increase in thickness ratio. Figure 5 (b) shows the pressure distrih ution for a series of bnsic thickness forms having a thickness ratio of 0.15 and having minim um pressure at various chordwise positions. The value of the minim um pressure coefficient is seen to decrease and the magnit ude of the pressure recove ry over the renr portion of the airfoil to increase with the rearwa rd movem ent of the point of minim um pressure.
10
REPOR'!' NO. 824-NATIONAL ADVISORY COMMIT'!'EE FOR AERONAU'rtCS 2.8
28
, , , , , , 24
-
_---------'------
-
MACA MACA NACA MACA
65,-012 652 -015 65-018 65.-021
c:::
-~
/.6
~ ~--
(V!
64 -oJs
~
I-- -------- MACA 65,-015 ' _ - - - NACA 6~-015 r-- - - - NACA 67,1-015
NACA 64,-015
f;;::{
-
c::==::::::=-
-""\
c::==::::::=-
MACA 652 -015
.-:-
--' --- ~
"
NACA 65.-015
/6
(VI
~~
"
~
-:::c== ~,
. /2
MACA 65.J-0I8
',' ~ ~
.8
l'-~
f
u. ~
=-~
=
--
-
~ -,~
~
\
c
" ~~ ~,~
.8
MACA 654-021
.4
:=:::::::=-
NACA 6tJ,-015
-~
c
:::>
NACA 67,/-015
.4
(a)
o
~ ~4C~
2.4 20
20
1.2
====-
MACA 65,-012
(b)
.2
.4
.:rIc
.6
.8
1.0
o
.2
.4
.:ric
.6
.8
1.0
(a) Variation with thickness. (b) Variation with position of minimum pressure. FIGURE 5.-Theoretical presmre distributions for some basic symmetrical NACA 6-series airfoils at zero lift.
The pressure distribution for one of the basic symmetrical thickness 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 flat 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 lead~ng edge. Rapid estimation of pressure distributions.-In the discussion that follows, the term "pressure distribution" is used to signify the distribution of the static pressures on the upper
5.0
4.0
3.0
(v! 2.0
FIGURE 6.-Theoretical pressure distribution for the N ACA 65.-015 airfoil at several lift . coefficients.
and lower surfaces of the airfoil along the chord. The term "load distribution" is used to signify the distribution along the chord of the 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 the methods of the previous section. Although this method is not unduly laborious, the computations required are too long to permit quick and easy calculations for large numbers of airfoils .. The need for a simple method of quickly obtaining pressme distributions with engineering accuracy has led to the development of a method (reference 15) combining features of thin- and thick-airfoil theory. This simple method makes use of previously calculated characteristics of a limited number of mean lines and thickness distributions that may be combined to form large numbers 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 and (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 thin airfoil, or (if the thin airfoil 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 small angles of attack, is substantially equal to a lift coefficient Cit, which is designated the ideal or design lift coefficient. If, moreover, the camber of the mean line is changed by multiplying the mean-line ordinates by a constant factor, the resulting load distribution, the ideal or design angle of attack at and the design lift coefficient Cl i may be obtaIned simply by mUltiplying the original values by the same fnctor. The characteristics of a large number of mean lines are presented in both graphical and tabular form in the supplementary figures. The load-distribution data are presented both in the form of the resultant pressure. coefficient P R and in the form of the corresponding velocityincrement ratios !.lv/V. For positive design lift coefficie~ts, these velocity-increment ratios are positive on the upper
11
SUMMA RY OF AIRFOI L DATA
!'Iudace and negative on the lower surface; the opposite is true for negativ e design lift coefficients. The second load distribution, which results from changing the angle of attack, is designated herein the" additio nal load distrib ution" and the corresponding lift coefficient is deRignated the" additio nal lift coefficient." This additio nal load distrib ution contrib utes no momen t about the quarte r-chord point and, according to thin-airfoil theory, is indepe ndent of the airfoil geometry except for angle of attack. The additional load distrib ution obtain ed from thin-airfoil theory is of limited practic al application, however, because this simple theory leads to infinite values of the velocity at the leading edge. This _difficulty is obviat ed by the exact thick-airfoil theory (reference 9) which also shows that the additio nal load distrib ution is neither completely indepe ndent of the aidoil shape nor exactly a linear function of the lift coefficient. For this reason, the additio nal load distrib ution ha,s been calculated by the method s of reference 9 for each of the thickness distrib utions presen ted in the supple mentar y figures. These data are presented in the form of velocity-increment rat.ios AVa/V corresponding to an additio nal lift coefficient of approx imately unity. For positive additio nal lift coeffic:ients, these. velocity-increment ratios are positive on the upper surfaces and negat.ive on the lower surfaces; the opposite is true for negative additio nal lift coefficients. In additi~n to the pressure distributions associated with thes~ two load distrib utions, anothe r pressu re' distrib ution exists which is associated with the basic symmetrical thickness form or thickness distrib ution of the airfoil. This pressure distribution has been calculated by the method s described in the previous section for the condition of zero lift and is presen ted in the supple mentar y figures as which is equiva lent at low Mach numbe rs to the pressure coefficient S, and as the local velocity ratio VIV. This local velocity ratio is always positive and is the same for corresponding points on the upper and lower surfaces of the thickness form.¡ The velocity distrib ution about the airfoil is thus considered to be composed of three separa te and indepe ndent component s as follows: (1) The distrib ution corresponding to the velocity distributi on over the basic thickness form at zero angle of attack (2) The distrib ution corresponding to the design load distrib ution of the mean line (3) The distrib ution corresponding to the additio nal load distrib ution associated with angle of attack The velocity-increment ratios AviV and At'a/V corresponding to components (2) and (3) are added to the velocity ratio corresponding to compo nent (1) to obtain the total velocity at one point, from which the pressure coefficient S is obtain ed; thus, (14)
('f;)2,
When this formula is used, values of the ratios corresponding to one value of x are added togeth er and the resulting value of the pressure coefficient S is assigned to the airfoil surface It t the same value of X.
The values of. v/V and of ~v/V in equatio n (14) should, of course, correspond to the ¡airfoil geometry. Metho ds of obtain ing the proper values of these ratios from the values tabula ted in the supple mentar y figures are presen ted in the previous section "Descr iption of Airfoils. " When the ratio AvalV has the value of zero, the resulting distrib ution of the pressure coefficient S will correspond approximately to the pressure distrib ution of the airfoil section at the design lift coefficient Cl i of the mean line, and the lift coefficient may be assigned this value as a first approximation. If the pressure-distribution diagram is integrated , however, the value of Cl will be found to be greate r than Cli by an amoun t depend ent on the thickness ratio of . the basic thickness form. at some desired be usually The pressure distrib ution will this For Cli' to onding specified lift coefficient not corresp .obvalue some d assigne be purpose the ratio ~va/V must a by ratio this of value ted tained by multip lying the tabula be may factor this n imatio factor j(a). For a first approx assigned the value (15)
where CI is the lift coeffici(1nt for which the pressure distrib ution is desired. If greater accuracy is desired, the value of j(a) may be adjuste d by trial and error to produce the actual desired lift coefficient as determined by integra tion of the pressure-distribution diagram. Althou gh this metho d of superposition of velocities has inadeq uate theoretical justification, experience has shown that the results obtain ed are adequa te for engineering use. In fact, the results of even the first approximations agree well with experimental data and are tl,dequate for at least prelim inary consideration and selection of airfoils. A comparison of a first-approximation theoretical pressure distribution with an experimental distrib ution is shown in figure 7.
c __ _~ NACA '66(215) -2/6, a
~ 06
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for the N ACA
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 potential flow'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 ifllow. Numerical examples.-The following numerical examples are included to illustrate the method of obtaining the firstapproximation pressure distributions: Example 1: Find the pressure coefficient S at the station x=0.50 on the upper and lower surfaces of the NACA 65 3-418 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 65 3-018 basic thickness form with the a= 1.0 .type mean line cambered to a design lift coefficient of 0.4. The following data are obtained from the supplementary figures for this thickness form and mean line at x=0.50:
v
V=1.235
The supplementary figures give a value of 1.182 for v/V atx=0.25 for the NACA 65 2-015 basic thickness form. The desired value of v/V is obtained by applying formula (5) as follows: v 14 V=(1.182-1) 15+1 =1.170 From the supplementary figures the following values of AVa/V are obtained at x=0.25 for the following basic thickness forms:
By interpolation the value of AVa/V of 0.287 may be assigned to the 14-percent-thick form. The desired value of AVa/V is then computed as follows by use of equation (15):
~=0.157
A'v a V =(0.287) (0.6-0.2)
~=0.250 The desired. value of AVa/V is computed as follows by use of equation (15):
A~a=(0.157)(0.2-0.4)
=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 multiplying the tabulated value by the design lift coefficient. Thus,
=-0.031 The desired value of AV/V is obtained by multiplying the tabulated value by the design lift coefficient as stated in the description of the NACA 6-series airfoils. Thus,
AV V = (0.250) (0.4)
~ = (0,333) (0.2) =0.067 Substituting the foregoing values in equation (14) gives the values of S as follows: For the upper surface
=0.100 S= (1.170+0.067 +0.115)2
Substituting these values in equation (14) gives the following values of S: For the upper surface
=1.828 For the lower surface S= (1.170-0.067 -0.115)2
S= (1.235+0.100-0.031)2
=1.700 For the lower surface S= (1.235-0.100+0.031)2
=1.360 Example 2: Find the pressure coefficient S at the station x=0.25 on the upper and lower surfaces of the NACA 65(215)-214, a=0.5 airfoil at a lift coefficient of 0.6. The airfoil designation shows that this airfoil was obtained by combining a thickness form obtained by multiplying' the ordinates of the NACA 652-015 form by the factor 14/15 with the a=0.5 type mean line cambered to a design lift coefficient of 0.2.
=0.976 Example 3: Find the pressure coefficient S at the station x=0.30 on the upper and lower surfaces of the NACA 2412 airfoil at a lift coefficient of 0.5. The description of airfoils of the NACA four-digit series shows that the necessary data may be found from the NACA 0012 thickness form and 64 mean line in the supplementary figures. From these figures the following data are obtained: At x=0.30 v V=1.162 At x=0.30
A~a=0.239
SUMMARY OF AIRFOIL DATA
For the NACA 64 mean line at x=0.30 b.1) V=0.260
For the NACA 64 mean line
The values of b.v/V llnd eli corresponding to the airfoil geometry are obtained by multiplying the foregoing values by the factor 2/6 as explained in the description of these airfoils; thus,
~=(0.260)(i) =0.087
elt=(0.76)(~) =0.253
The desired value of b.va/V is obtained from equation (15) as follows:
t:,.~a= (0.239) (0.5-0.253)
at the design lift coefficient is to separate the pressures on the upper and lower surfaces by an amount corresponding approximately 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 design lift 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 concentrating 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/e at the position of minimum pressure on the basic thickness distribution. If a mean line with a smaller value of a is used, the possible extent, of laminar flow along the upper surface will be reduced. CRITICAL MACH NUMBER
=0.059
Substituting the proper values in equation (14) gives the values of S as follows: For the upper surface
S= (1.162+0.087+0.059)2 = 1.712
For the lower surface S= (1.162-0.087 -0.059)2 = 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
The critical speed is defined as the free-stream speed at which the velocity at any point along the surface of the airfoil reaches the local velocity of sound. If the maximum valueof the low-speed pressure coefficient S is known either experimentally or from theoretical methods, the criti~al Mach, number may be predicted approximately by the Von Karman. method (reference 19). A curve relating the critical Mach. number and the low-speed pressure coefficient S has been calculated from the equations of reference 19 and included in. the supplementary figures. These predicted critical Mach. numbers are useful for preliminary considerations in the¡ absence of test data and appear to correspond fairly well to the Mach numbers a t which the local velocity of sound is. reached in the high-critical,speed range of lift coefficient~ This criterion does not, howe~~r, appear to predict accurately, \
28
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1.0
14
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
the Mach numbers at which large changes in airfoil characteristics occur, especially when sharp pressure peaks exist at the leading edge. A discussion of the characteristics of airfoil sections at supercritical Mach numbers is beyond the scop'e of this report. For convenience, curves of predicted critical Mach number plotted against the low-speed section lift coefficient have been included in the supplementary figures for a number of airfoils. High-speed lift coefficients may be obtained by multiplying the low-speed lift coefficient by the factor 1
.
..jl"'::'W· 'I'he critical Mach numbers have been predicted from theoretical pressure distributions. For airfoils of the NACA four- and five-digit series and for the NACA 7-series airfoils, the theoretical pressure distributions were obtained by Theodorsen's method. For the other airfoils the theoretical pressure distributions were obtained by the approximate method described in the preceding section. The data in the supplementary figures show that, for any one type of airfoil, the maximum critical Mach number decreases rapidly as the thickness is increased. The effect of camber is to lower the maximum critical Mach number and to shift the range of high critical Mach numbers iii 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 in the supplementary figures shows that N ACA 6-series sections have consi<ierably higher maximum critical Mach numbers than NACA 24-, 44-, and 230-series airfoils of corresponding thickness ratios.
NACA 64 mean line in the supplementary figures. moment coefficient for this mean line is -0.157. required value is then 4 cmc /4 ·( -0.157) "6
The The
=-0.105 ANGLE OF ZERO LIFT
Methods of calculation.-Values of the ideal or design angle of attack at corresponding to the design lift coefficient Cit 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 from the data by using the theoretical value of the lift-curve slope for thin airfoils, 2'lr per radian. The value of alo in degrees is then (16) The tabulated values of aj 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 preliminary design, they should not be used without experimental verification for such purposes as establishing the washout of a wing. ./ Numerical exampl~s·./: The method of comPlltlng alo is illustrated in the following e~amples: / Example 1: Find th~ theoretical angle of zero lift of the NACA 65 2-515, a=0.5 airfoil. This airfoil number indicates a design lift coefficient of 0.5. Dll,ta for the NACA a=0.5 mean line indicate that ai=3.04° when Clt=1.0. The desired value of aj is then
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. These values were obtained from thin-airfoil theory and may be scaled up or down linearly with the design lift coefficient or with the mean-line ordinates. These theoretical values are sufficiently accurate for preliminary considerations, but experimental values should be used for stability and control calculations. Numerical examples.-The following numerical examples illustrate the methods of calculating the moment coefficients: Example 1: Find the theoretical moment coefficient about the quarter-chord point for the NACA 65 2-215, a=0.5 airfoil. The designation of the airfoil shows that the design lift coefficient of this airfoil is 0.2. From the data on the NACA a=0.5 type mean line included inthe supplementary figures, the value of C"'c/4 is -0.139 for a design lift coefficient of 1.0. The desired value of the moment coefficient. is accordingly Cmc /4=(-0.139) (0.2)
a;= (3.04) (0.5)
=1.52° Substituting in equation (16) gives
=-3.0° Example 2: Find the theoretical angle of zero lift for the NACA 2415 airfoil. The description of the N ACA four-digit-series airfoils shows that the required values of at and Cl i may be obtained by multiplying the corresponding values for the N ACA 64 mean line (see supplementary figures) by a factor 2/6; then a,=(O.74)
(~)
=0.25°
CI,;~(0.76) (~) =0.253
=-0.028 Example 2: Find the theoretical moment coefficient about the quarter-chord point for the NACA 4415 airfoil. From the description of the N ACA four-digit series airfoils, the required data is found to be presented for the
(57.3) (0.5) 2'lr
alo=1.52
and from equation (16) (57.3) (0.253) 2'lr =-2.0°
SUMMARY OF AIRFOIL DATA DESCRIPTION OF FLOW AROUND AIRFOILS
Perfect-fluid theory postulates that the flow follow the airfoil contour smoothly at all angles of attack with no loss of energy. Consequently, perfect-fluid theory itself gives no information concerning the profile drag or the maximum lift of airfoil sections. The explanation of these phenomena is found from a consideration of the effects of viscosity, which are of primary importance in a thin region near the 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 large number 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 the portions closer to the surface, the distribution of average velocity 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 layer developed under otherwise identical conditions. Skin friction is therefore higher for turbulent boundary-layer flow than for laminar flow. When the pressures along the airfoil surface are increasing in the direction of flow, a general deceleration takes place. At the outer limits of the boundary layer this deceleration takes place in accordance with Bernoulli's law. Closer to the surface, 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 for particles 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 flow against the adverse pressure gradient. If the rise in pressure is sufficiently great, portions of the fluid within the boundary layer 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 boundary layers are much more resistant to separation than are laminar layers. Laminar boundary layers can only exist for a relatively shQrt distance in a region in which the pressure increases in the direction of flow. Formulas for calculating many of the boundary-layereharacteristics 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 concerning the factors controlling this phenomenon. Laminar separation on wings is usually not permanent at flight values of the Reynolds number except when it occurs near the leading edge 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 location of the first minimum-pressure point on both upper and
15
lower surfaces. If the region of laminar flow is extensive, separation occur", 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 boundary layer 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 anywhere upstream of the calculated laminar separation point. For low and moderate lift coefficients where inappreciable separation occurs, the airfoil profile drag is largely caused by skin 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 accuracy from boundary-layer theory by use of the methods of references 23 and 24. As the lift coefficient of the airfoil is increased by changing the angle of attack, the resulting application of the additional type of lift distribution moves the minimum-pressure point upstream 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 velocity of flow over the surfaces, causes the drag to increase with lift coefficient. In the case of many of the older types of airfoils, this forward movement of transition is gradual and the resulting variation of drag with lift coefficient occurs smoothly. The pressure 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 coefficients. A sharp increase in drag coefficient to the value corresponding to a forward location of transition on the upper surface results. Such sudden shifts in transition give the typical drag curve for these airfoils with a "sag" or "bucket" in the low-drag range. The same characteristic is shown to a smaller degree by some of the earlier airfoils such as t~e NACA 23015 when tested in fl, low-turbulence stream. At high lift coefficients, a large part of the drag is contributed 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 turbulence 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 reestablishment of flow following laminar separation is unduly delayed by low Reynolds numbers, the turbulent layer will separate from the surface near the trailing edge and will cause large drag increases. The eventual loss in lift with increasing angle 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 in reference 5.
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
16
.06
EXPERIMENTAL CHARACTERISTICS
,~
.04
rJ' ....:
.03
SOURCES OF DATA
The primary source of the wind-tunnel data presented is from tests in the Langley two-dimensional low-turbulence pressure timnel (TDT). The methods, used to obtain and correct 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 other NACA wind tunnels. In each case, the source of the data is indicated and the testing techniques and corrections used were conventional unless otherwise indicated. Most of the flight data consist of drag measurements made by the wake-survey method on either the airplane \\ing or it "glove" fitted over the wing as the test specimen. Whenever 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 cofficient form by compressible-flow methods. In the case of all such NACA 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 SMOOTd AIRFOILS
Drag characteristics in.low~drag range.--The value of the drag coefficient in the low-drag range for smooth airfoils is mainly a function of the Reynolds number and the relative extent of the laminar layer and is moderately affected by the airfoil thickness ratio and camber. The effect on minimum drag of the position of minimum pressure which determines the possible extent of laminar flow is shown in figure 9 for some NACA 6-series airfoils. The data show a regular decrease in drag coefficient with rearward movement of minimum pressure. o INAtA
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FIGUllE
tested was a practical-construction model. It may be noted that the drag coefficient for the NACA 65 3-418 airfoil at low Reynolds numbers is substantially higher than that of the NACA 0012, whereas at high Reynolds numbers the opposite is the case. The higher drag of the NACA 65 3-418 airfoil section at low Reynolds 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 Reynolds number. These data illustrate the inadequacy of low Reynolds number test data either to estimate the full-scale characteristics or t~ determine the relative merits of airfoil sections at flight Reynolds numbers (references 25 and 26). The variation of minimum drag coefficient with camber is shown in figure 11 for a number of smooth 18-percent-thick NACA 6-series airfoils. These data show very little change .016
o NACA 64r2/5 o NACA 652-2/5 {> NACA 66,-215 <:7 NACA.67,/-i?15
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9.-Variation of minimum drag coefficient with position of minimum pressure for some N ACA 6 series airfoils of the Same camber and thickness. R = 6 X 10'.
FiGURE
The variation of minimum drag coefficient with Reynolds number for several airfoils is shown in figure 10. The drag coefficient generally decreases with increasing Reynolds num . ber up to Reynolds numbers of the order of 20 X 106 • Above this Reynolds number the drag coefficient of the NACA 65(420-420 airfoil remained substantially constant up to a Reynolds number of nearly 40X 106 • The earlier increase in drag coefficient shown by the NACA 66(2x15)-U6 airfoil may be caused by surface irregularities because the specimen
o FIGURE
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ll.-'-Variation of minimum section drag coefficient with camber for several NACA 6·series airfoil sections of I8-percent thickness ratio. R = 9 X I()<l:
17
. SUMMARY OF AIRFOIL DATA
in nlllllmum 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 thickness ratio for a number of NACA airfoil sections ranging in thickness from 6 percent to 24 percent of the chord. The minimum drag coefficient is seen to increase with increase in thickness ratio for ea,ch airfoil series. This increase, however, is greater for the NACA four- and five-digit-series airfoils (fig. 12 (a)) than for the N ACA 6-scries airfoils (figs, 12 (b) to 12 (e)). 016 Rough
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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 thickness. It has been possible to design airfoils of 12~percent thickness with a total theoretical low-drag range of lift coefficients of 0.2. This theoretical range increases by ~pprox 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 9 X 106 . Figure 13 also shows a characteristic tenclE'ncy for the drag to increase to some extent toward the upper end of the low-drag range for moderately cambered airfoils, pai'ticularly for the thicker airfoils. All data for the X ACA 6-series airfoils show a decrease in the extent of the IO\'l-drag range with increasing Reynolds number. Extrapolation of the rate of decrease observed at Reynolds numbers below 9X 106 would indicat(> a vanishingly small low-drag range at flight values of the Reynolds number. Tests of a carefully constructed model of the XACA 65(421)-420 airfoil showed, however, that the rate of reduction of the low-drag range with increasing Reynolds number decreased markedly at Reynolds numbers above 9X 10 6 (fig. 14). These data indicate that the extent of the low-drag range of this airfoil is reduced to about olH'-half the theoretical value at a Reynolds number of 35 X 106 •
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FrGt!RE 13.-Drag characteristics of some XACA 54·series airfoil sections of ,-urious thicknesses, cambered to a design lift coefficient of 0.4. R = 9 X 10'; TDT tests 682, 733, 735,
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(a) XACA four- and five·digit series. (b) XACA 63·series. (el XACA 64-series. (d) X .'I.e A 55·series. (e) XAC A 66-series, FIGFRE 12.-Variation of minimum section drag coefficient with airfoil thickness ratio for several NACA airfoil seNions of differel1', cal"bc~s in both smooth and rough conditions. R = 6 X 106•
and 691.
The values of the lift coefficient for which low d.rag is obtained are determined largely by the amount of camber. The lift coefficient at the center of the low-drag range corresponds approximately to the design lift coefficient of the mean line. The effect on the drag characteristics of various amounts of camber is shown in figure 15. Section data indicate 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.)
18
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
'c.4
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Section lift coeffic/ent, fl 15.-Drag characteristics of some NACA 65-seriesairfoil sections of 18 percent thickness with various amounts of camber. R = 6 X 106; TDT tests 163, 314, 802, 813, and 830.
FIGURE
The location of the low-drag range shows some variation from that predicted by simple thin-airfoil theory; This departure appears to be a function of the type of mean line used (reference 27) and the airfoil thickness. The effect of airfoil thickness is shown in figure 13, from which the center 'of the low-drag range is seen to shift to higher lift coefficients with increasing airfoil thickness. This shift is partly explained by the increase in lift coefficient above the design lift coefficient for the mean line obtained when the velocity increments caused by the mean lirie are combined with thp velocity distribution for the basic thickness form according to the approximate methods previously described.
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 and low-cambered airfoils, for which the lift coefficient at the upper end of the low-drag range is moderate, this high rate of increase does not continue. (See fig. 15.) For highly cambered sections; for which the lift at the upper end of the low-drag range is already high, the drag coefficient shows a continued rapid mcrease. Comparison of data for airfoils cambered with a uniformload 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 coefficient.s at high lift coefficients (fig. 16 'and reference 27). Data for many of the airfoils given in the supplementary figures s~ow large reductions in drag with increasing Reynolds number at high lift coefficients. This scale effect is too large to be accounted for by the normal variation in skin 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 (reference 28). Effects of type of section on drag characteristics.-A comparison of the drag characteristics 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 coefficients corresponding to high-speed flight, and this margin may usually be maintained through the range of lift coefficients useful for cruising by suitable choice of camber. The NACA 6-series sections show the higher maximum values of the lift-drag ratio. At high values of the lift coefficient, however, the earlier NACA sections have generally lower drag coefficients than the NACA 6.-series airfoils.
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FIGURE 16.-Comparison of the aerodynamic characteristics of the NACA 653-418 and NACA 65.-418,
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FIGURE 17.-Comparison of the ~erodynamic characteristics oC some NAC.'\. airfoils from tests in the Langley two·dimensional low-turbulence pressure tUIlIlCI.
.8
1.2
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21
SUMMARY OF AIRFOIL DATA
Effective aspect ratio.-The combination of high drags at high lift coefficients, low drags at moderate lift coefficients, and the nonregular variation of drag with lift coefficient shown by the NACA 6-series airfoils may lead to paradoxical results when the span-efficiency concept (reference 29) is used for the calculation of airplane performance. In the usual application of this concept, the airplane drag charactc!ristics are approximated by a curve of the type (17) This curve is usually matched to the actual drag characteristics at a rather low and at a moderately high value of the lift coefficient (reference 30). The application of this concept to two hypothetical airplanes with N ACA 230-. and (}5~.series sections, respectively, is illustrated in figure 18 (a). The wing drags of the airplanes have been calculated by adding the induced drags corresponding to an aspect ratio of 10 with elliptical loading to the profile-drag coefficients of the NACA 23018 and 653-418 airfoils. These sections are considered representative of average wing sections for a large airplane of this aspect ratio. Ordinate scales are given in figure 18 (a) for the wing drag and for the total airplane drag coefficients obtained by adding a representative constant value of ./0
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IWinb; NACA 24/5 wing; aspect ratio, 8 NACA 652 -415 winq; effective aspect ratio, 6.97 NACA 24/5 win91 effective aspect rafio, 746
.06
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-
.O{)
!
I
0.0150 to the wing drag coefficients. The resulting drag coefficients have been approximated by two curves corresponding to equation (17) and matched to the drag curves at lift coefficients of 0.2 and 1.0. These two curves correspond to effective aspect ratios of 9.29 for the airplane with NAOA 23018 sections and of 8.30 for the airplane with NACA 65 3-418 sections and illustrate the typical large reduction in the effective aspect ratio obtained with such sections. It should be noted, however, that although equation (17) provides a reasonably satisfactory approximation to the drag of the airplane with NACA 23018 sections, such is not the case for the airplane with the NAOA 653-418 section. The most important reason for using high aspect ratios on large airplane3 is to reduce the drag at cruising lift coefficients and 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 NACA 653-418 sections (19.8 as compared with 18.5) despite the fact that this airplane shows the lower effective aspect ratio. Figure 18 (b) shows a similar comparison with similar results for two airplanes of aspect ratio 8 and NACA 2415 and 652-415 airfoils. It is accordingly concluded that the effective aspeCt ratio is not a satisfactory criterion for use in airfoil selection .
-
y
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Lift coe ffl'cient,
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(b) NACA 65,-415 and 2415 wings of aspect ratio 8.
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 NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONATT'I'ICS 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 was shown to result from forward movement of transition, substantial drag inGrements resulted from surface roughness in the region of turbulent flow. It is accordingly important to maintain smooth surfaces even when extensive laminar flow cannot be expected, but the gains that may be expected from maintaining smooth surfaces are grAater for NACA 6or 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 numbers 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 the permissible roughness will vary directly with the chord of the 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 waxing a sllrfacethat is not Iterodynamically smooth wiH, of course, result in improvement and such finishes may be of considerable practical value because deterioration of. the finish may be easily Seen and pmlsibly postponed. Large models having chord lengths of 5 to 8 feet tested in the Langley twodImensional low-turbulence tunnels are usually finished by sanding in the chordwise direction with N o. 3~0 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' rougher surface 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-series 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 than small depressions. Dust particles, for example, are more effective than ,small scratches in producing transition if the material at the edges of the scratches is not forced above the general surface level. Dust particles adheI:ing to the oil left on airfoil surfaces by fingerprints may be expected to cause transition at high Reynolds numbers. Transition spreads from an individual disturbance with an included angle of about 15° (references 31 and 33). A few scattered specks, especially near the leading edge,' will cause the flow to be largely turbulent. This fact makes necessary an extremely thorough inspection if. low drags are to be realized. Specks sufficiently large to cause . premature transition on full-size wings can be felt by hand. The inspection procedure used in the Langley two-dimensional low-turbulence tunnels is to feel the entire surface by hand after which the surface is thoroughly wiped with a dry cloth. It has been noticed that transition resulting froin individual C
small sharp protuberances, in contrast to waves, tends to occur at the protuberance. Transition caused by surface waviness appears to approach t:Qe waVe gradually as the Reynolds number or wave size is increased. The height of a small cylindrical protuberance necessary to cause transition when located at 5 percent of the chord with its axis normal to the surface is shown in figure 19. These data were
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2
3
4
5
6
--
7
Wing Reynolds number, R
8
9
IOxIO'
19.-Variation with wing Reynolds number of the minimum height of a cylindrical protuberance necessary to cause premature transition. Protuberance has 0.035·inch diameter with axis normal to wing surface and is located at 5 percent chord of a 9O·inch·chord symmetrical 6-series airfoil section of 15·percent thickness and with minimum pressure at 70 percent chord.
FIGURE
obtained at rather low values of the Reynolds number and show a large decrease in allowable height with increase in Reynolds number. This, effect of Reyn?lds number on permissible surface roughness is also evident in figure 20, in which a sharp increase in drag at a Reynolds number of approximately 20 X 106 occurs for the model painted with camouflage lacquer. The magnitude of the favorable gradient appears to have a small effect on the permissible surface roughness for laminar flow. Figure 21 shows that the roughness becomes more important at the extremities of the low-drag range where the favorable pressure gradient is reduced on one surface. The effect of increasing the Reynolds number for a sllrface of marginal smoothness, which has an effect similar to increasing the surface roughness for a given Reynolds number, is to reduce rapidly the extent of the 19w-drag range and then to increase the minimum drag coefficient (fig. 21). The data of figure 21 were specially chosen to show this effect. In most cases, the effect of Reynolds number predominates over the effect of decreasing the magnitude of the favorable pressure gradient to such an extent that the only effect is the elimination of the low-drag range (reference 34). Permissible waviness.-More difficulty is generally encountered in reducing the waviness to permissible values for the maintenance of laminar flow than in obtaining the required surface smoothness. In addition, the specification of the required freedom from surface waviness is more difficult than that of the required surface smoothness. The problem is not limited merely to finding the minimum wave size that will cause transition under given conditions because the number of waves and the shape of the waves require consideration.
23
SUMMARY OF AIRFOIL DA'l'A ~
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Reynolds number, R (a) Smooth condition; TDT test 328. (b) Lacquer camouflage unimproved after painting; TDT test 461.
FIGrRE 20.-· Yariation
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o 149
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of drag codl:cient with Reynolds numhr for a 6O-inch·chord model of the NACA 65(-121)-420 airfoil for two surface conditions .
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FIGURE
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o
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21.-Drag characteristics of N AOA 65(",)-420 airfoil for two surface conditions. TDT tests 300 and 486.
If the wave is sufficiently large to affect the pressure distribution in such a manner that laminar separation is encountered, there is little doubt that such a wave will cause premature transition at all useful Reynolds numbers. A relation between the dimension€; 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 pressure gradient increases with the pressure gradient. Large negative pressure gradients would therefore appear to be favorable for wavy surfaces. Experimental results have shown 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 on the upper surface are given in figure 22. Marked increases in the drag corresponding to a rapid forward movement of the transition point were not noticeable below a Reynolds number of 44 X 106 • On the other hand, transition has been caused at comparatively low Reynolds numbers by a series of small waves with a wave height of the order of a few tenthousandths of an inch and a wave length of the order of 2 inches on the same 60-inch-chord model. For the types of wave usually encountered on practicalconstruction wings, the test of rocking a straightedge over the surface in a chord wise direction 'is a fairly satisfactory criterion. The straightedge should rock smoothly without jarring or clicking. The straightedge test will not show the existence of waves that leave the surface convex, such as the wave of figure 22 and the series of small waves previously mentioned. Tests of a large number of practical-construction models, however, ·have shown that those models which passed the straightedge test were sufficiently free of small waves to permit low drags to be obtained at flight values of the Reynolds number. It is not feasible to specify construction tolerances on airfoil ordinates with sufficient accuracy to ensure adequate freedom from waviness. If care is taken to obtain fair surfaces, normal tolerances may be used without causing serious alteration of the drag characteristics.
24
ItEPORT NO. 824-NATIONAL ADVISORY COMMITTEE F'OR AERONAUTICS /Cenfer of wave
-.~c:-r =-1 Departure from fair
-------60"--------~-
'
airfoil surface
/
- f-----'
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D
4
8
12
16
cO ~
28 J2 J6 Winq Reynolds number. R
24
40
44
48
5exlD¡
FIGl'RE 22.-Expcrimental curve showing variation of drag corffici~nt with Hcynolds number for the N ACA 65(421)-420 airfoil section with a small amount of surface waviness.
Dra.g with fixed transition.---If the airfoil surface is sufficiently 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 increment in minimum drag coefficient cau~ed by the smallest roughness capable of producing transition is nearly as great as 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 sufficiently large to cause transition at all Reynolds numbers considered, the drag of the airfoil with roughness only at the leading edge decreases with increasing Reynolds number (fig. 10 and reference 36). The effect of fixing transition by means of a roughness strip of carborundum of O.Oll-inch grain is shown in figur(~ 24. The minimum drag increases progressively with forward movement of the roughness strip. The effE'ct 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 coefficients for the NACA 65(223)-422 and 63(420)-422 airfoils were nearly the same throughout most of the lift range when the extent of laminar flow was limited to 0.30c. All recent airfoil data obtained in the Langley two-dimensional low-turbulence pressure tunnel include results with roughened leading edge, and these data are included in the supplementary figures. Tests with roughened leading edge were formerly made. only for a limited number of airfoil sections, especially those having large thickness ratios (reference 37). The standard roughness selected for 24-inchchord models consists of O.Oll-inch carborundum grains applied to the airfoil surface at the leading edge over a surface length of 0.08c measured from the leading edge on both surfaces. The grains are thinly spread to cover 5 to 10 percent of this area. This standard roughness is considerably more severe than that caused by the usual manufacturing irregularities 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 number 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-series airfoils are less than the values 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 condition than in the smooth condition. Drag with practical construction methods.-The section drag coefficients of several airplane wings have been measured in flight by the wake-survey method (reference 38), and a number of practical-construction wing sections have been tested in the Langley two-dimensional low-turbulence pressure tunnel at flight values of the Reynolds number. Flight data obtained by the NACA (referenee 38) arc summarized in figure 26 and some data obtained by the Consolidated Vultee Aircraft Corporation are presented in figure 27. Data obtained in the Langley two-dimensional lowturbulenee pressure tunnel for typical praetical-construction sections are presented in figures 28 to 32. Figure 33 presents a comparison of the drag coefficients obtained in this wind tunnel 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 experimental error. All wings for which flight data art' pres('nted in figure 2() were earefully finished to produce smooth surfaces. Great care was taken to reduce surface waviness to a minimum for all the sections except the NACA 2414.5, the N-22, the Republic 8-3,13, and the NACA 27-212. Curvature-gage measurements of surface wavinE'ss for some of these airfoils are presented in referE'nce 38. Surface eonditions corresponding to the data of figure 27 arc descri.bed in the figure. These data show that the sections permitting extensive laminar flow had substantially lower drag coefficients when smooth than the other sections.
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FIGURE 23.-Lift and drag characteristics of an NACA 63(420)-422 airfoil with various degrees of roughness at the leading edge. ~
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27
SUMMA RY OF AIRFOI L DATA
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CA
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various airfoilS. 26.-Comp arison of section drag coefficients obtained in flight on Tests of N A CA 27-212 and 35--215 sections made on gloves.
1.6
30 x/O S
-grain 25.-Drag characteristics of two NACA 6·series airfoils with O.Oll·inch roughness at 0.30e. R=26XI0 6•
The wind-t unnel tests of practic al-cons tructio n wing sections as delivered by the manuf acturer showed minim um drag coefficients of the order of 0.0070 to 0.0080 in nearly all cases rpgardless of the airfoil section used (figs. 28 to 32). Such values may be regard ed as typical for good curren t constru ction practic e. Finishi ng the sections to produc e smooth surfaces always produc ed substa ntial drag reducti ons althoug h considerable waviness usually remained. None of the sections tested had fair surfaces at the front spar. Unless speeial care is taken to produc e fair surfaces at the front spar, the resultin g wave may be expected to cause transit ion either at the spar locatio n or a short distanc e behind it. One practic al-eons tructio n specimen tested with smooth surfaces mainta ined relativ ely low drags up to Reyno lds numbe rs of approx imatel y 30X10 6 (NACA 66(2x1 5)-116 airfoil of fig. 10)~ This specim en had no spar forwar d of about 35 percen t chord from the leading edge and no spanwise stiffeners forwar d of the spars. This type of constru ction resulte d in unusua lly fair surfaces and is being used on some moder n high-p erform anee airplanes. A compa rison of the effect of airfoil section on the minimum drag with practic al-cons truetio n surfaces is very diffieult because the quality of the surface has more effect on the drag than the type of section. Probab ly the best comparison can be obtain ed from pairs of models constru eted at
~ 4, 2-(1. 4}(.13.5}
.64 .48 .32 Section lift coefficie nt, c l
./6
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V FIGURE
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NACA 65(223)-422 (modified)
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o FIGURE
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Lift coe fficient,
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condition 27.-Conso lidated·Vu ltee flight measurements of the effect of wing surface on drag of an NACA 66(215)-1(14.5) wing section.
the same time by the same manuf acturer s. Data for such pairs of models are presen ted in figures 30 to 32. The results indicat e that as long as curren t constru ction practic es are used the type of section has relativ ely little effect at flight . values of the Reyno lds numbe r for militar y airplanes.
28
REPORT NO. 824- TATIONAL ADVISORY COMMITTEE FOR AERO
AUTICS
<J ~.01Z..-'--r-'r-.--'-.-r-'--.-'r-.--.-.-r-~-.-'
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o
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1
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o
ondilion of model c, '0'079 As r~c~lV~d III + ,077 Painted with gray primer surfacer x ,074 Camouflage poinled with
~
FIGURE 29.-Variation of drag coefficient with Reynolds number for the NACA 23016 ai rfoil
23015 (approx) as bUilt
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Turbulent.·
()
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FIGURE 28.-Drag scale etTect on lOO'inch-chord practical-construction model of tbe NAC.'. 65(216)-3( 16.5) (approx .) airfoil section. cl=0.2 (approx.).
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J , I 1 1 ,I 1 1 I . NACA 65(216)-411(approx.) as built
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FIGURE 3O.-D rag characteristics of the NACA 65(216)-417 (approx.) and NACA 23015
ift'"
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---- /'
t
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(approx.) airfoil sections built by practical'construction methods by the same manufact urer. R= 1O.23Xl()6.
o
4
8
12 16 20 24 Reynolds number, R
28
32x10'
FIGURE 31.-8cale 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.
,[1 16
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8
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28
32x10'
FIGURE 32,-Drag scale effect for a model of the ACA 65-series airfoil section, 18,27 percent thick, and the Davis airfoil section, 18,27 percent thick, built by practical·construction
methods by the same man ufacturer. cl= 0.46 (approx.) .
o
4
FIGUR E 33,-Comparisoo
8
or
12 16 20 24 Reynolds number, R
28
J2xIO '
drag coefficients measured in Hight and wind tWlJlel for t he NACA 0012 airfoil section at zero lift.
29
SUMMARY OF AIRFOIL DATA
·0/6
I,clab'5\";Yo!, )'h i-i!.}aJc;' J,~)
10 ~ ~<
surface and 0.1 Dc on lower surfacl3 c,=Q4D o NACA 23015' (appro x.) with de-lcer removed I_L <> NACA 65(2/6)-215, 0=0,8wllh QD75c de-ieer }c=029 /', NACA 65(216)-215, 0=0.8 with de-ieer removed I'
............
.....,.
0.
:
j....".- I--
4
8
16
12
20
24
28
32
44
40.
36
48
52xlO
•
Reynolds number, R
FIGURE 34.- Effect of de-ieers on the drag of two practical-construction airfoil sections with relatively smooth surfaces.
o
Important savings in drag may be obtained at high Reynolds numbers by keeping the surfaces smooth even if extensive laminar flow is not realized. Drag increments resul ting from surface roughness in turbulent flow have been shown to be important (reference 31). The effects of surface roughness on 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 of scale 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 boundary layer with fixed transition are presented in reference 39, The effect of the application of de-icers to the leading edge of two smooth airfoils is shown in figure 34. The de-icer "boots" were installed in both cases by the manufacturer to
ct
I I
represent good typical installations. The mmlmum drag coefficients 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 slipstream on transition or airfoil drag; the data that are available do not show consistent results. This inconsistency may result 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 measurements 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 l these data seem to preclude very 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
L.
1
20
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-9
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in s//Dsfreom t=-.
i-- :;--\R/qhf wing section outside slipstream
c:
~Cl
~O
~ Airfoil sections Root, NACA 66(2xI5J-DI8 Tip, NACA 67, 1-1/.3)15 Aspect ratio, 5.98 J Propeller tip radius-
o Riqht winq sectionl--10
. I)o IArope I ler wmdmll mg L\ Propeller removed
outSide S!iPstre~L Left wing section in slipstream o Power on Power off 0
~
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19
~~ ~
~
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6 5 4 '.3 2 DistanceJr~m.. f!ROdel cepfer line, ft
o
FIGURE 35.-The effect of propel«lr operation on section drag coefficient of a fighter-type airplane from tests of a model in the Langley 19-foot pressure tunnel. CL=O.lO; R=3.7Xl06.
.!
.£' ..3 .4 Section lift coeffiCient,
.5
.6
Cl
FIGURE 36.-Flight measurements of transition on an NACA 66-series wing within ana outside the Slipstream.
30
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
of the chord in the slipstream. Other unpublished NACA flight data on transition on an 8-3,14.6 airfoil in the slipstream 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 sufficiently wide. Some unpublished flight data showed small but consistent rearward 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 attributed to vibration. Recent tests in the Ames full-scale tunnel showed premature adverse scale effect on drag coefficients measured by the wake-survey method when a model-support strut vibrated.
airfoil section. For the NACA 6-series airfoils this lift coefficient is approximately in the center of the low-drag range. For airfoils having thicknesses in the range from 6 to 10 percent, the NAOA four- and five-digit series and the NAOA . 64-series airfoil sections have values of lift-curve slope very close to the value for thin airfoils (271' per radian or 0.110 per degree). Variation in Reynolds number between 3XI06 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. The airfoil thickness and the type of thickness distribution appear to be the primary variables. For the NAOA four- and five-digit-series airfoil sections, the liftcurve 'slope decreases with increase in airfoil thickness. For the NAOA {i-series airfoil sections, however, the liftcurve slope increases with increase in thickness and forward movement of the position of minimum pressure of the basic thickness form at zero lift. Some N AOA 6-series airfoils show jogs in the lift curve LIFT CHARACTERiSTICS OF SMOOTH AIRFOILS at the end of the low-drag range, especially at low Reynolds numbers. This jog becomes more pronounced with increase Two-dimensional data.-As explained in the section "Angle of camber or thickness and with rearward movement of the of Zero Lift," the angle of zero lift of an airfoil is largely position of minimum pressure. on the basic thickness form. determined by the camber. Thin-airfoil theory provides a This jog decreases rapidly in severity with increasing Reymeans for computing the angle of zero lift from the mean-line nolds number, becomes merely a change in lift-curve slope, data presented in the supplementary figures. The agreeand is practically nonexistent at a Reynolds number of ment between the calculated and the experimental angle of zero lift depends on the type of mean line used. Comparison , 9 X 106 for most airfoils that would be considered for practical application. This jog may be a consideration in the selection of the experimental values of the angle of zero lift obtained from the supplementary figures and the theoretical values of airfoils for small low-speed airplanes. An analysis of the flow conditions leading to this jog is presented in refertaken from the mean-line data shows that the agreement is ence 28. good except for the uniform-load type (a=1.0) mean line. The variation of maximum lift coefficient with airfoil The angles of zero lift for this type mean line generally have thickness ratio at a Reynolds number of 6 Xl 06 is shown in values more positive than those predicted. The experi~ figure 39 for a number of N AOA airfoil sections. The airfoils mental va,lues of the angles of zero lift for a number of NACA for which data are presented in this figure have a range of four- and five-digit and NACA 6-serie::; airfoils are presented thickness ratio from 6 to 24 percent and cambers up to in figure 37. The. airfoil thickness appears to have little effect 4 percent chord. From the data for the NAOA four- and on the value of the angle of zero lift regardless of the airfoil five-digit-series airfoil sections (fig. 39 (a»), the maximum series. For the NACA four-digit-series airfoils, the angles of lift coefficients for the plain airfoils appear to be the greatest zero lift are approximately 0.93 of the value given by thinfor a thickness of 12 percent. In general, the rate of change airfoil theory; for the NACA 230-series airfoils, this factor is 'of maximum lift coefficient with thickness ratio appears approximately 1.08; and for the NAOA 6-series airfoils with to be greatest for· airfoils having a thickness less than 12 uniform-load type mean line, this factor is approximately percent. The data for the NAOA 6-series airfoils (figs. 0.74. 39 (b) to 39 (e» also show a rapid increase in maximum lift The lift-curve slopes (fig. 38) for airfoils tested in the coefficient with increasing thickness ratio for thickness 'Langley two-dimensional low-turbulence pressure tunnel are ratios of less than 12 percent. For NAOA 6-series airfoil higher than those previously obtained in the tests reported sections cambered to give a design lift coefficient of not more in reference 8. It is not clear whether this difference in slope than 0.2, the optimum thickness ratio for maximum lift is caused by the difference in air-stream turbulence or by coefficient appears to be between 12 and 15 percent, except the differences in test .methods, since the section data of for the airfoils having the position of minimum pressure at reference 8 were inferred from tests of models of aspect ratio 6. 60 percent chord. The optimum thickness ratio for the The present values of the lift-curve slope were measured for NAOA 56-series sections cambered for a design lift coeffia Reynolds number of 6 X 106 and at values of the lift coefficient of not more than 0.2 appears to be 15 percent or greater. cient approximately equal to the design lift coefficient of the
31
SUMMARY OF AIRFOIL DATA
f--
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I
ODD} 14 (4-digit)
I-- ~ 0
0.24 f-- _ D 44
1
eli
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A
'1
,
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- -
(a)
(b)
4 8 12 16 20 Airfoil thickne%, percent of chord
.,
24
8 12 16 20 Airfoil thickness, percent of chord (b) NACA 63-serles.
1
I c-
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f-- ,-0 0
I-- f-
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i
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(c)
4
8 /2 16 20 Airfoil thiCKness; percent of chord'
4
8 12 16 20 Airfoif thickness, percent of chord
24
(d) NACA 55-series.
(c) NACA 64-series.
r eli
I - - I-
f-'-
00 .2
1-°
.4
D
tr- j---.
-0
0
v
(e)
4
8
Q
m
m
24
..clirfo!1 thickness, percenf of chord (e) NACA 66-series.
FIGURE 37.-Measured section angles of zero lift for a number of NACA airfoil sections of various thicknesses and camber. R=6XI06•
24'
32
ImpORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
Flab-qed
s';"mb~/s
indicate rough conditlori ::Smoofh
r
':;
-
'""""1
-
-
'-4i
-
Series 00 14 (4-digit)
-
- - -
0 0
<> 24 /:;
(a.)
l-
I-'
r t-.~ "Rough
-
Rou¢"':·~
e'i
0
0
.2
<> (b)
10 12 14 16 1/3 20 Airfoil thickness, percent of chord
- _.
... -'!
1 'I
44
" 230 (5-digif)
8
-
,'Smooth
22
8
/:;
.4
17
.6
/0
/2 14 16 18 20 Airfoil thickness, percent of chord
(a) N A CA four- and five-digit series.
22
24
(b) NACA 63-scries.
-1'tI° 4 ~~.1 ,Smooth
:,Smoofh :
:..l?
.,
«!l
--
- -
..... t--
:#oug'h
--
-~ t--_
I.
''Rough
o ~;
(el 6
0
.1
<>
.2 .4 .. 6
.6
\7
8
-
c,j
<> (d)
10 12 14 /6 18 20 Airfoil thickness, percent of chord
22
8
.z
/:;
.4
17
.6
10 12 14 16 18 20 Airfoil thickness, percent of chord
(c) NACA M-series.
I--
0
0
22
24
(d) NACA 65-series.
\Smooth
--
..; 0
-
::j
eli
0
<>
(e) 6
8
'"
0
---.-'> "- "Rough
.z
~
,4
10 12 14 16 18 20 Airfoil fhickness, percent of chord
22
24
(e) N A CA 66-series. FIGURE 38.-Variation of lift-curve slope with airfoil thickness ratio and camber for a number of NACA airfoil sections in both the smooth and rough conditions. R=6XI06.
The available data indicate that a thickness ratio of 12 percent or less is optimum for airfoils having a design lift coefficient of 0.4. The maximum lift coefficient is least sensitive to variations in position of minimum pressure on the basic thickness form for airfoils having thickness ratios of 6, 18, or 21 percent. The maximum lift coefficients corresponding to intermediate thickness ratios increase with forward movement of the position of minimum pressure, particularly for those airfoils having design lift 'coefficients of 0.2 or less. The maximum lift coefficients of moderately cambered
~NACA
6-series sections increase with increasing camber (fig. 39 (b) to 39 (e». The addition of camber to the symmetrical 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 decreases as the airfoil thickness increases beyond 12 or 15 percent. The available data indicate that the combination of a 12percent-thick section and a mean line cambered for a design lift coefficient of 0.4 yields the highest maximum lift coefficient.
33
SUMMARY OF AIRFOIL DATA
2.B
28
\-
%1';;>-
oo 14 -e--
/
() ;:4 4-digit
/
~ 1.6
/'
c:
.0
..::
I
~ 1.2 Vl
/
/'
V--
-- -,,,,-. .
~'
o
4
/
0
-)!>
.2 .4
'<7
.6
(<::
~~
~
.:::
/2
20
/6
C"
0 0
",-
....-Z.4 I:;
_0
k
0
./
.2
.4 t- 'V ·6 '00
h
I;
.\1)
.i3 ..:: 'Qy.2.0 ()
" {: "" 1.6
't:J
~
.I
>:>
.., ."-
r,
.4
~ , r-o:~ --
,~
l:"'__
v .6
c:
o
~
5 ·sx
~
1.2
4
·17
.'
/-
.8
Ii --- --
/~:
.0-
'z.8 ~ ° • ,,<)
--- ~
/ --"': , "
,
-
,
/
Airfoil with sp/d flop
c--
I
--
.~
.\.)
~ 20
r,
.2 .4
'<7
.6
.e
~ I-"'
0
Plain airfoil
--J~
<lJ
'"
Y ~,
/'
~'.:
Airfoil with split flop
-'"'{:f " I , ):Y
...;:::"
1.2
V V
./
-;? k
~ ,- )o0--
_..
-
-.
-l>.
J)~
I
<:::::--
-1--- - -- - -
~
Plain airfoil
-0
-0
-- Rouqh
I I Smooth
(d)
24
4
8
/2
/6
20
C4
Airfoil thickness, percent of chord
2.8
eli
0
~
.2
1:'2.4 1-6 .4 00 .~
/;
<.;:::
V
.'>
l:>
.2
~ 20 o I.)
'"
.4
V j.Y
----
~ P-Q-
{:
"" 1.6
.-' --
~
h
V
,
,,~
,
'/
Xf'
p--.
I
--
:
~ -t>
Airfoil with splif flap
if
c:
-6
.0
..::
V ,.....-- f-O"
o
'iJ,!.2
3
?
.§l< . 8
~
--l--£ .c-
.(e)
o
NACA Go-series.
Symbols with flogs correspond to Simulated split flop deflected 60'?.
f-O 0
.4
~
I?l'
><.J'
(d)
""•
N
,>:>
/ ) ,/" ,
~.
(e) N ACA 64 serIes.
",-
20
1.6
~
/2
.;,yJ
1=""
-§ .8 x
16 20 Airfoil thickness, percent of chord
8
¢
~
-
I I STOO(h 4
/) /;
-;:::
-- ----- Rough (c)
'"II 0....... u
I- ~
.2 .4
.6 00
<t:: -:::: """" -=~~ -'::L.£
.,
16
l--? v_ /'~
0
I;
\.)
,0-
--":; ~~~
Smooth
12
8
'V
()
~
--
Plain oirfoil
'6
~::-
..0-
.- ,IJ-
eli
<-:,2.4 <.;:::
, .J))'
~
t::S.,
"t>-
(b) NACA 63-series.
/'
J/ 7
V
/
.--
Airfoil thickness, percent of chord
~
t:::-; V"
if
~
II
o
24
i--
~
~
V
,
_.-- -:..-- Rough (b)
(a) NAOA fonr- and five·digit serie3.
2.8
Airfoil with split flop
,
........
~ -0-
Airfoil thickness, percent of chord
i
/
I. L
....
.
-- f--. h...
V
Plain airfoil
--- '~
,
'(f
~
~p
,,
/,/' ~
~
~'
, if' ,/, , ::7 ~~
... ---- Rough SiOO{h
8
.4
.6
>:>
II
(al
.4
,......
[.AI"" -:/
v/ -/ -:,j! .-,
:c
1-0-r- " 4 -= """'- ..:::; ~
--0 -
'V 0
144-digit
tJ ~
t--..
%'1
<)
rl;
Airfoil wITh spM flap
o~23~~~ 00
~--
...
44r~
6
(P / -v,..'
0
f-
4
8
-
V
-
--
_.<>.-
,-- -0'
-- --- --
I
Plain airfoil
-<> -0
-- - --- Rough
I I Sroih 12
/6
20
24
Airfoil Thickness; percent of chord (e) NACA GO-series. FIGURE 39.-Variatioll of maxiwum section lift coefficient with airfoil thickness ratio and camber for several NACA airfoil sections with and without simulated split flaps and standard roughness. R=6X106•
34
REPORT NO. 824-NATIONAL ADVISOIW 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 airfoils such as the N ACA 230-series sections with the maximum camber far forward show large values of maximum lift. Airfoil sections with maximum camber far forward and with thickness ratios of 6 to 12 percent usually stall from the leading edge with large sudden losses in lift. A more desirable gradual stall is obtained when the location of maximum camber is farther back, as for the NACA 24-,44-, and 6-series sections with normal types of camber. 2.0
y-- r-
~
I,.--- f -
Reynolds number o 6.0x10 6 o 9.0
o
.2
.4 .6 Type of camber, a
.8
1.0
FIGURE 40.-Variation of maximum lift coefficient with type of camber for some NACA 65a-418 airfoil sections from tests in the Langley two-dimensional low-turbulence pressure tunnel.
A comparison of the maximum lift coefficients of NACA 64-series airfoil sections cambered for a design lift coefficient of 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 of the NACA 44-series sections in all cases. The NACA 230series airfoil sections have maximum lift coefficients somewhat 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 3 X 106 to 9 X 106 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 t024 percent is favorable and nearly independent of the airfoil thickness. IIwreasing the Reynolds number from 3 X 106 to 9 X 106 results in an increase in the maximum lift cO('fficient of
approximately 0.15 to 0.20. The scale effect on the NACA 00- and 14-series airfoils having thickness ratios less than 0.12c is very small. The scale-effect data for the NACA 6-series airfoils (figs. 41 (c) tv 41 (f» do not show an entirely systematic variation. In general, the scale effect is favorable for these airfoil sections. For the NACA 63- and 64-series airfoils with small camber, the increase iIi maximum lift coefficient with increase in Reynolds number is generally small for thicknes.s ratios of less than ·12 percent but is somewhat larger for the thicker 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 of 26X106 • The values of the maximum lift coefficient presented were obtained for steady conditions. The maximum lift coefficient 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 deflected 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 show a considerable increase in maximum lift coefficient with increase in thickness ratio. Corresponding data for the NACA 44-series airfoils wit,h thickness ratios from 12 to 24 percent show very little variation in maximum lift coefficient with thickness. For NACA 6-sel'ies 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, depending 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 N ACA 6-series airfoils are essentially the same regardless of thickness ratio and position of minimum pressure on the basic thickness form. The maximum lift coefficient decreases with rearward movement of minimum pressure for the airfoils having t,hickness ratios between 9 and 18 percent.
35
SUMMARY Ol!' AIRFOIL DATA
2 .0
2..0
;.c::
>-=-
R o J.OxIO·
.6
i"--..
6'~T <> 9.0
I-- o
..<>
I'b.
.21-- e:. 6.0 Standard r
NACA 24-series (4-digit)
--;::: ~
.8
~k
r-..... Dr. f::::
/'
J.6
~
~
f:::;: ~ .... ;;:: b:" r-::::- ~ i,.- 1--6::: ~ ~
6 2
~
2
~
~
I"--
~
f0- r-,
'-...... ""~
r- J-o.. r--..,;; ~ ~
-
'-"l ~
I. 2
Symbols with flags correspond to cu ·O.6
6
t--.
!o=,
~ i-'
2. 0
.........
NACA ~4-ser/es (4-dlqit)
/. 6
NACA DO-series (4-digit)
A
(a)
--
-0-.
8 (b)
IA
8
r-..... ~
~~ .........
~
2
"""" ~ I::::-..... ....... ~
~ .r.
.2
.6
NACA 23O-series (5-diq/t)'
8
NACA 14-series (4-digit) I.2
t--.
:.--
I. 2
~
.8 .6
::::."..
~
~
~ r-..
ughness
I ~
-
I. (5
~ 6
~ ........,
~
V
~ i'D v ~~
.P-
'"
C,j=O.4 and 0.6
r--; t:- "0
r-- t--
~
e'i =0.2
t-i>
V
el; =0.4 and 0.0
~
;l; y
i'-- h,.. ::::::::: c- 1-0
V-
~
~ r--....
i=O
cl;=O.c
VII
c:
:2
(J (\)
"'1 =0.1
if
8
v,
~ 1.6
8 ........ v
~ .B
....
.§
=0
~ 1.2
.8
!.6
V V
1.2
.....~ ?-- h:,. -.......::: r-.
r-
-:::,~ ...tc
t1'
x
r--.... I'<>
kf I..---' / '
b
(e)
C'i
c1i =o.4 and 0.8
\-0
1-0
!,-,:::
::J
~
/'-.,
IB (d)
~~
\'0... t--.
?-- t-o
CI'=O
I-
-....
1.6
C'I
0-
=0.4
V
/.2 1.8
1.6 ..4' ......
1.2
~
~V
#
..-'
.......
R"" k
t-...... fO
c1j =0.2
V)'"
1.2
.8
I~ 'F/
1.2
lL V /.
(e)
~
4
8
-
Ie
J...6-. t--
"0
~
I
....., cll=O
/.2
\
i
m~I
..A
.b-
~
(f) 16
eO
e'l = 0.2
~V l--- ,-~
>--
1.6
:>-- 1-0
C4
Airfoil thickness, percent of chord
028
32
4
'" t....- f-"
c11·O
V ..... ~ ~
8 12 18 20 ?4 Airfoil thickness) percent of chord
28
32
(b) NACA four- and five-digit series. (a) N ACA four-digit series. (d) NACA 54-series. (c) NACA 63-serles. (f) NACA 66-series. (e) NACA 65-series. FIGVI\& 41.-Variation of maximum section lift coefficient with airfoil thickness ratio at several Reynolds numbers for a number of NACA airfoil sections of different cambers.
~ ~
3.6
.2
3.2
~o
2.8
-.2
.036
r--- r-- r--
1/ f'-- r--
0
I - -~
.2
.4
:x/c
.032
I--1.0
.8
.6
.028
pj
.024
2.4-
\:':l "d
o
20
i:¥
I;>
"... 020
z
o
.....
~
'v
1.6
~ ~ If ~(T (>-~
10>,.. !-J2~
~-
~p;;?
...:-1.2
I'-'
~
.8
0
t.)
!
:g
t.:l
.016
is'
-fs
L>.p...
'V~
.012
.~ .,..
lp 18W
~,\ I'-
~
~ .008
L
.4
~ .....
f/
1\ I~lu..,
II
~
z
'1' .1\,
-'-c
<.>
o Z
> t:'" > ~ ...... Ul o
l(fJ
:--r I'D
'h ~V;
i'ilt-: ::::i~
~-...; ~ r-"~
?
<::::
"c:
~
"""I
o
J/
.,
(¥)
<lJ
I€l r!: )-I...p- f-o
~
~ "--
c:
:~
1,,- -1'~
I~
V,
>- f-:::: r1::f':::: r:; ~
~
(l
.004
o
?' .... ?' ,.., .....
\.J
~
I'" 0
16
'-
H H M M "'1
o
r--
j
o
~
-.4
}
I
,
> M
~
-
I
o ~ >-
w );i
-.8 -'l
IC
..,..,
A;
1
-1.2
d ,......,
.,.cW
(")
Ul
~
a
R
6. 0 X,!.06
o 10.0 <> 14.0
-I. 5
" 20.0 v 26.0
1
I -2.0 -32
I -24
-16
-8
0
Section angle of coftuck,
8 IXo,
16 deq
24
J::
"I.e
F,GURE 42.-LiCi and drag characteristics of the NACA (,1(420)-422 airfoil at
-/.2
-.8
-.4
0..4
Secfion lift coefficient, c 1 hi~h
Reynolds numbo.r. 1'1)1' tests 228 and 255,
.8
1.2
/.f'
37
SUMMARY 0]' AIRFOIL DATA
Substantial increments in maximum lift coefficient with increase in camber are shown for the N ACA 6-series airfoils of moderate thickness ratios (10 to 15 percent chord) with split 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 15 percent, the maximum lift coefficients of the N ACA 63- and 64-series airfoils cambered for a design lift coefficient of 0.4 equipped with split flaps are greater than the corresponding maximum lift coefficients of the NACA 44-series airfoils. Three-dimensional data.-No recent systematic threedimensional wing data obtained at high Reynolds numbers are available, so that it is difficult to make any comparison with the section data. When the maximum-lift data for three-dimensional wings are compared with section data, account should be taken of the span load distribution over the wing. The predicted maximum lift coefficient for the wing will be somewhat lower than the maximum lift coefficients of the sections used because of the nonuniformity of the spanwise distribution of lift coefficient. The difference amounts to about 4 to 7 percent for a rectangular wing with an aspect ratio of 6. Maximum-lift data obtained from tests of a number of wings and airplane models in the Langley 19-foot pressure tunnel are presented in table II. Although section data at the Reynolds numbers necessary to permit a detailed comparisonare not available, the maximum lift coefficient for plain wings given in table II appears to be in general agreement with values expected from section data. The data for the airplane'models are presented to indicate the maximum lift coefficients obtained with varIOUS airfoils and eonfigurations. LIFT CHARACTERISTICS OF ROUGH AIRFOILS
Two-dimensional data.-Most recent airfoil tests, especially of airfoils with the thicker 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 NACA 63(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 0.20e from the leading edge have littie 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 decrease the mt-curve slope, particularly for the thicker airfoils having the position of minimum pressure far back. These data are for a Reynolds number of 6X 106 • Maximum-
20
...... l - - I--
.--
~ I---
, .-
I
o 0.002 roughness o .004 roughness o .01/ roughness LI Smooth
o FIGURE
4
Ie 16 Reynolds number, R
8
cO
e4x/O'
43.-Effects of Reynolds number on maximum section lift coefficient CI max of the N ACA 63(420)-422 airfoil with roughened and smooth leading edge.
lift-coefficient data at a Reynolds number of 6 X 106 for a large number of NACA airfoil sections with standard roughness are presented in figures 39 and 41. The variation of maxi~um 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 of these airfoils other than the N ACA OO-series airfoils of 6 percent thickness. For a given thickness ratio greater than 15 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 thickness 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, however, is about the same for the airfoils with standard roughness as for the smooth sections. The maximum lift coefficient of airfoils with standard roughness generally decreases somewhat with rearward movement of the position of minimum pressure except for airfoils having thickness ratios greater than 18 percent, in which case some slight gain in maximum lift coefficient results from 3, rearward movement of the position of minimum pressure. Except for the NACA 44-series airfoils of 12 to 1.'5 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 airfoils of comparable thickness. Standard roughness causes decrements in maximum lift coefficient of the airfoils with split flaps that are substantially the same as those observed for the plain airfoi.ls.
38
REPORT NO. 824-NATIONAL ADVISORY COMMl'l"l'J£E FOR AERONAUTICS
20
1.6
I II
~ ~R,, I
-,V
\
b
I
II ~
\.J'
4
I
~
I
Jo
I
V
o
8
16
24
o
(b) NACA 2415.
lnl
1/
JJ r'tJ
1.2
J.~/ ~'l,
!.O
"....
'>-'
.~ .8
J
<.J
~
I/;V j V W
;}, tv
QJ
.6
S --J
J
/
VI
W 4
j
jf
1I
[; Model (Longley 19-foot pressure tunnel) Airplane I I I o Sealed condition } (Langle fi II-scale o Service conddlon Lj t::nnel)
I
I
I
I
1I o
I
I
I I
I
: \ \
I I
\~
/
o As delivered by shop, TDT test 494
o Final condition, TOT test 523
-8
17
o
8 (c)
16
24
32
NACA 23012.
H.-Lift characteristics of the NACA 23012, 2412, and 2415 airfoil sections as affected by normal model inaccuracies. R=9X10 6 (approx.).
I....) C-;-== J S=-'"'
.2
I
~
7
r-
FIGURE
I
Final condition, TOT test 498
1=
1.4
•I
~
II
%shop, . TDT test 64
8 16 24 Section angle of attack, a" de-:)
-8
P""I I I
J
(e)
(a) NACA 2412. FIGURE
)
1/
(b)
'-8
o
j
II
II
-4
\.J
""
~
J
(e)
()
I
If-
o As delivered
o As delivered by shop, TOT test 4158 o Final condition, TOT test ':CO
J
o
1
!t>..
/I¢
4
8 12 115 Angle of atfack, a, deg
20
24
45.-The effects of surface conditions on the lilt characteristics of a fighter-type 'airplane. R=2.8X106•
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. Examples 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 model inaccuracies 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 factors besides the airfoil sections affect the maximum lift coefficient of airplanes. Such factors as roughness, leakage, leading-edge air intakes, armament installations, nacelles, and fuselages make it difficult to correlate the airplane maximum lift with the airfoils used, even when the flaps are retracted. The various flap configurations used make such a correlation even more difficult when the flaps are deflected. When the flaps were retracted, both the highest and the lowest maximum lift coefficients obtained in recent tests of airplanes and complete mock-ups of conventional configurations 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 Reynolds number. 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 wljll as a lower lift-curve slope. Some improvement in the airplane lift characteristics was obtained by sealing leaks. These results show that airplane lift characteristics are strongly affected by details not reproduced on large-scale smooth models.
39
SUMMARY OF AIRFOIL DATA I. 6
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46.-The effect on the lift characteristics of fixing the transition on a model in the Lang]ey 19-foot pressure tunnel. R=2.7XI06, (Model with Davis aifroil sections.)
FIGURE
Lift characteristics obtained in the IJangley 19-foot pressure 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 Ilft-curve slope was decreased throughout most of the lift range with fixed transition. The maximum lift coefficient was decreased in one case 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 largp- spar depths require the use of thick root 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
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47,-The effect on the lift characteristics of fixing the transition on a model in the Langley 19-foot pressure tunnel. R=2.7XlO.6. (Model with N ACA airfoil sections.)
FIGURE
drag coefficient at high lift coefficients. The resulting drag coefficients may be excessive at cruising lift coefficients for heavily loaded, high-altitude airplanes. Airfoil sections that have suitable characteristics when smooth but have excessive drag coefficients when rough at lift coefficients corresponding to cruising or climbing conditions are classified as unconservative. The decision as to whether a given airfoil section is conservative 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 inoperative in icing conditions or after suffering damage in combat 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 leading edges. The variation of this critical lift coefficient with airfoil 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 COMMITTEE FOR AERONAUTICS Series 0
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FIGURE 4B.-Variation of the lift coefficient corresponding to a drag coefficient of 0.02 with thickness and camber for a number of N'ACA airfoil sections with roughened leading edges. R=6XI06•
position o~ 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 the critical lift coe'lficient. 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 6XI06 • 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 num bel' of 6 X 10 6 if the roughness is confined to the leading edge. PITCHING MOMENT
The variation of the quarter-chord pitching-moment coefficient at zero angle of attack with airfoil thickness ratio and camber is presented in figure 50 for several NACA airfoil sec.tions. The quarter-chord pitching-moment coefficients of the NACA four- and five-digit-series airfoils become less negative with increasing airfoil thickness. Almost no variation in quarter-chord pitching-moment coefficient with airfoil thickness ratio or position of minimum pressure is shown by the NACA 6-series aiffoil 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 coefficient and theoretical values for the mean lines is presented in figure 51. The experimental values of the moment coefficients for NACA 6-series airfoils cambered with the uniformload 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 uniformload 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 mean line. 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 becomes more negative with increasing thickness for all the airfoils tested. For the thicker NACA 6-series sections the magnitude of the moment coefficient increases with rearward movement of the position of minimum pressure.
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42
REPOR'f NO. 824-NATIONAL ADVISORY COMMITTEE FOR AEHONAUTICS I
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R=6XI06•
43
SUMMARY OF AIRFOIL DATA -. I 6'
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HIGH-LIFT DEVICES
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increasing thickness. For the N ACA 6-series airfoils, the opposite appears to be the case.
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FIGURE 51.-Comparison of theoretiml and measured pitching-moment coefficients for some NACA airfoils. R=6X10', POSITION OF AERODYNAMIC CENTER
The variation of chordwise position of the aerodynamic center corresponding to a Reynolds number of 6 X 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 thickness 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 chord wise position of the aerodynamic center is ahead of the quarter-chord point and moves forward with increase in thickness ratio. The chordwise position of the aerodynamic center is behind the quarter-chord point for the NACA 6-series airfoils 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 of chordwise position of the aerodynamic center with camber or position of minimum pressure on the basic thickness form for these airfoils. The data of reference 43 show important forward movements 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
Lift characteristics for two NACA 6-series airfoils equipped with plain flaps are presented in figure 53. These data show that the maximum lift coefficient increases less rapidly with 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 maximum-lift increments for the 12-percent-thick sections were only about three-fourths of that increment for the 16-percentthick 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 obsolete Langley variable-density tunnel (reference 45) and in the Langley 7- by lO-foot tunnel (reference 46). Tests of a number of slotted flaps on N ACA 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 the N ACA 230series 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 obtained for one of the flaps. Lift characteristics for the NACA 65 3-118 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 moderately thick N ACA 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 supports, 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 shape on 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 AaolAo is plotted against the aileron-chord ratio Calc 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.
44
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS ,---r-,~--
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FIGURE 52.-Variation of section chordwise position of tne aerodynamic center with airfoil thickness ratio for several NACA airfoil sections of different cambers. R=6Xl()6.
32
45
SUMMARY OF AIRFOIL DATA 2.8
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FWURE 53.-Maximum lift coefficients for the NACA 65,3-618 and NACA 66(215)-216 air· foils fitted with O.20-airfoil-chord plain flaps. R=6XlO'.
FWURE 54.-Maximum lift coefficients for some NACA airfoils fitted with O.20-airfoil·chord split flaps.
The data show no large consistent trends of aileron-effectiveness variation with airfoil section for a wide range of thickness distributions 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 threedimensional data. The analysis that follows is considered suitable for comparing the relative merits of ailerons from two-dimensional data. Two-dimensional data are presented in the form of the eq uivalent change in section angle of attack Aao required to maintain a constant section lift coefficient for various deflections of the aileron from neutral. This equivalent change in angle of attack is plotted against the hinge-moment parameter ACHO, which is the product of the aileron deflection from neutral and the resulting increment of hinge-moment
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 Aao for a given value of the hinge-moment parameter, the more ad vantageous the combination should be for providing a large value of pb/2V for a given control force. The assumption 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 twodimensional characteristics of different ailerons.
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SUMMARY OF AIRFOIL DATA
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1.2
1.0
LlC'I' predicted
V
57.-Comparison between measured values of the increments In lift coefficients due t.o flap deflection and values predicted from two-dimensional data. Split flap.
FIGURE
~(
2.4
V
/
/ ,/
/
I .
1.0
/
1
1
1
1
i
'/
.2
.4
o
L/
I
1
!
,8
/
V
V
.2
V
/
V
V
8
0
0
0
0
V 0
.4
.6
.8
1.0
1.2
LlC,,} predicted
5S.-Comparison between measured values of the increments In lift coefficients due to flap dellection and values predicted from two-dimensional data. Slotted lIap.
FIGURE
(b)
20
40 Flop deflection,
80
60
oJ)
90
deg
(a) Flap configuration. (b) Maximum lift characteristics. :FIGURE
I
.8
J-q .4
o
1
L me of ogree/nenf between meosured t--- and predictd results......
56.-Flap configuration and maximum lift coefficients for the NACA 653-118 airfoil with a double slotted flap. R=6X106,
48
REPORT NO. 824-NATIONAL ADVISORY COMMIT'l'EE FOR AERONAUTICS
SUPPLEMENTARY INFORMATION REGARDING TESTS OF TWO-DIMENSIONAL MODELS
I
Symbol
Basic airfoil
Air-flow characteristics - - - - - - - - - - - - - - - - Reference
Type of flap
I
TIM
------;--- NACA
+
NACA 0015 _________________________________________________ do ______________________________ _
1. 93
.10
1.4XI06
56
X
NACA 23012, __________ . ____ . ___ . ______ . ____ ..• ___ .. __ . ___ .. do ___ ... ___ ... _._, .. _.. ____ .. __ ..
1. 60
.11
2.2XIO'
57,48
o
NACA 66(2xI5)-OlU _
Plain, straight contour ___ ... ____ ... _
1. 93
.10
1.4XI0'
<>
NACA 66-009._ ... ____ ... ___ "' __________ .. _____ .. ___ "'_ Plain __ ..• _._ .... _.... _____ .... __ ..• _
1. 93
.11
l.4XlO'
A
NACA 63,4-4(17.8) (approx.) ______ . _______ . __ ._ . _____ . Internally balanced __ .... ___ ._. __ ._.
(I)
.17
2.5X106
59
\1
NACA 66(2xI5)-216, a=0.6. _________ . _____ .. ___ ... ___ .. _.. ,.do.... __ ..... ___ .... ___ .. ______ ._
(I)
.18
5.3XlO'
59
C> <l
NACA 66(2xI5)-116, a=O.6 .. __________ . ____'. __________ .. ___ do _______________________________ _
(I)
.14
6.0XJO'
59
NACA 64,2-(1.4) (13.5) _____ .. ___________ . ____ . __ ______ _ Plain_.______ • ____ .. ______ . _____ .. __ ._
<I)
!7
NACA 65,2-318 (approx.) ________ ._ .... ________ ... __ .. _ Internally balanced ____________ .. __ _
(1)
'q
NACA 63(420)-521 (approx.) __ .. ______ .. _______________ .. __ do .. ___ .... _______________ . _____ _
(I)
c,..
NACA 66(215)-216, a=O.6 __ .. ,_ .. ______ . ___ . ___ .. ____ . _' ___ do._ .. __________ .. ______________ _
<I)
.d
NACA 66(215)-014.. ____
o
NACA 66(215)-216, a=O.6 ____ ._ ._. ___ .. _. _______ . ____ . _______ do _______________________ • ______ _
<I)
NACA 65,-415 _______ .. ________ . ___ . ______ . ________________ .do_. ____ • ________________ • ______ _
<I)
.13
6.0X106
[}
NACA 653-418 ___ • ____ . _______
do ______________________________ _
(I)
.13
6.0XI0 6
62
Q
NACA 65,-421. ___ . ___ ._. __ . ___________ .. ___ . ______ . ________ do ______________________________ _
(I)
.13
6.0X10 6
62
o
NACA 65(112)-213 .. ________ . _____ . _____ ._. __ .. ______ ._. __ Internally balanced. _______ ._. _____ _
(I)
.14
8.0XJ06
--------
o
NACA 745.A317 (approx.). _____________ . ___ .. ___ ... _. ____ • ___ do ___ ..... _... __ .... __ .. _._ ... __ .
(I)
.13
6.0XlO'
o
NACA 64,3-013 (approx.)_. _______ .. ____ ... ____________ . ____ do __________ . ___________________ _
<I)
.13
6.0X!06
l:>
NACA 64,3-1(15.5) (approx.). ____ . ____ . __ . __________________ do ______________________________ _
(1)
.13
6.0XlO'
o
I
R
OO~~~=~~~~=~~~~~~~~~~= --;,lain __~==~~=~~~~~~~ ----~;_- --~~-- -=~~~~~-r~~~;-
00
___ "
____ . . ____ •
.00 ____ •
___ •
_____ •
_____ •
______ •
Plain ______ .. ________________ • ______ _
,___
_________
58
13.0XIO'
1.93
.14
6.0XI0'
.20 to .48 .09
8.0X1Q6 2.8XI0 6 to 6.8X10 6 1.2XI06
59
}
61
6.0X1Q6 62
Approaching 1.00.
.8
.8
.... . . .. . / / ' . --- -.. . . v ,, LV< ,
~1~·6
/'"
Theoretical
.;
<I)
QJ
c:QJ :,
IJ
,,
~ .4 "QJ
,,
c:
~
,,
::;:
()
c:
I
.~
..... .2 <J
J
,,
,,
:;:;
J?
,
V
/
,
,,'
~V
17
- --Experimenfal
~ I/) III t
..- .-
QJ
...." "
J.P 'V
,
(j
~ .4 -,.; QJ
,
t
0
(J
t
:g ~
+
, !sf
~
--
.."..
s: /[7
/'
V
V
"./
" /'"
~
V
0
/9- --- --E~perimental
iP
/
I I
,,
"
. ..
.,
.
!oP"x
I I
.2
,,-
, .-
./
I
""
/
,,
I
t
c;,£o
/
V"
I
V
(a)
.1
.2
A ileron chord ratio, calc
(a) IJ range from 0° to 10°. FIGURE
Thgoretical-
tJl
." ~.6
<;.<
,'V //
o
60
.3
.4
o
V
(b) .1
.2 Aileron chord ratio,
calc
.3
.4
(b) IJ range from 0° to 20°.
59.-Variation of section aileron effectiveness with aileroll-chord ratio for true·airfoil·contour ailerons without exposed overhang balance on a number of airfoil sections. Gaps sealed; c,=O.
49
SUMMARY OF' AIRFOIL DATA
-
I Basic airfoil
Air-flow characteristics CI
'l'ype of aileron (I)
-----------f
M
R
0.10 .18 .33
1.4XI06 4.0X106 9.0X106
Basic airfoil
Reference
------------- - - - - - - - - . - - --- - - - - - - - -
I 1
NACA 0009 NACA 64,2-(1.4) (I3.5)
NACA~66(215)-216, a=0.6_
0 .150 .100
0.20c plain 0.187c plain 0.20c plain
1 1
~
1. 93 (')
(~)
I
Reference
Type of aileron
CI
------------- ---- ---------- ---NACA 66(215)-216.a =0.6 NACA 63,4-4(17.8)(approx.)
63
0.100 .450
0.20c plain 0.20c with 0.43c, internal balance
64 ----
----
64
8
Trne airfoil contoUl". Approaching 1.00.
LI6/~
Aileron deflecfion, deg
6
NACA 63,
4~4( 11.8) (opprox.j-.,-:
...: .... ---
...:.,
4
2
. _.r... _ -/2-
f\ if;";'-
1\
C "
" ~:--
NACA 66(215)-216, a=Q6-""
~,
---)
Ef'
'\
'. ~-.(.\
'~ , ~
Stroi hi sided
-2
"
-4 ~.:::-
~
~;""'....--
(
;~~~
-'
-4r-r-+-+-~~-r-r_+_+~I-4~~2-~~,~,~+-+-~
rAileron defleelion, deq
L---rr
~'"''
-- ".
-6
~
.--- "12
.
---
p;;...-
V 471
--- '-a, li" "
"':.::::~ ...
' "
True airfoil contou?)-
",
"
V -_:. '.
-8 -.0018 -.0016 ~0014 -.OOlc ,DOlO ~0008 :0006 :0004 :0002 .1cu radians
o,
;biJ,
I
o
61.-Variation of the hinge-moment parameter ACH5 with the equivalent change in section angle of attack required to maintain a constant section !itt coefficient for deflection of true-airfoil-contour and straight-sided ailerons on the NACA 63,4-4(17.8) (approx.) and the NAC A 66(215)-216, a=O.6 airfoil sections. Gaps sealed.
FIGURE
FIGURE 60.-Variation of the hinge-moment parameter ilea a with the equivalent chan~e in section angle of attack required to maintain a constant section lift coefficient for deflection of the aileron on the N ACA 0009, N ACA 64,2-(1.4)(13.5), and N ACA (\6(215)-21(\, a=O.6 airfoil sections. Gaps sealed.
For the purpose of evaluating the effect of airfoil shape on the aileron characteristics, it is desirable to make the comparison 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 tIll' range of deflection for which data are available. The NACA 64,2-(1.4) (13.5) airfoil shows appreciably smaller valuE'S of 6.CIIO for a given value of 6.0:0 than the other sections prE'sented. 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 ailE'rons instE'ad of ailerons of true airfoil contour are shown in figure 61 for two N ACA 6-series airfoils. One of the two combinations for which data are available was provided with an internal balance whE'reas the other combination was without balance. This differencE' prevents any comparison between the two combinations but doE'S not affect comparison of the two contours for each case. For the NACA 66(215)-216, a=O.6 airfoil, the straight-sided aileron has more desirable characteristics for tll(' range of deflections for which dat.a arE' avail-
able. It appears, however, that the straight-sided aileron would be lE'sS advantageous than the aileron of true contour for positive dE'flections greater than 12°. In the case of the NACA 63,4-4(17.8) (approx.) airfoil, the straightsidE'd aileron appears to have no advantage over the aileron of true airfoil contour. The advantage of using straightsided ailerons appears to depend markedly on the airfoil used but sufficient data are not available to determine the significant airfoil parameters. Figure 62 shows that in one case the effE'ct of leading-edge roughness on the aileron characteristics is unfavorable. LEADING-EDGE AIR INTAKES
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 velocity ratios. 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 airfoils. 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 Langley Laboratory indicate that shapes such as those of reference 65 have low maximum lift coefficients. Recent data show
50
REPORT NO. 824-NATIONAL ADYlSORY COMMITTEE FOR AERONAUTICS
8 t:--
-16·.
6
-.... i--!<§mooth
Roughness ot leading edqe.-->
~~~
:::--. --.::.:,r12 ::::- ~ -I-
4
~ fX'-8 .~
2
-4-~··
Q\
1\
~_ 0
'I!
J"::V
"'I
-2
INTERFERENCE
~V
-4
r- I--
Aileron deflection, deg -12" <'-,.
-6
--
/'/ >.5·"8
-~
,/
,/
----
-8
~OOI8 ~OOI6 ~OOI4 ~OOI2 ~OOIO ~0008 ~0006 ~0004 ~OOO2
that air-intake shapes can be provided for such airfoil sections with desirable air-intake characteristics and without loss in maximum lift coefficient (fig. 63). Some pressuredistribution data for the air intakes shown in figure 63 indicate that the critical speed of the section has been lowered only slightly and that falling pressures in the direction of flow were maintained for some distance from the leading edge on both surfaces at lift coefficients near the design lift coefficient for the section. Sufficient information is not available to permit such desirable configurations to be designed without experimental development.
0
twHo, radians FIGURE 62.-Variation of the hinge·moment parameter !1cH6 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 64,2-(1.4)(13.5) airfoil section, smooth and with roughness at the leading edge of the airfoil. (For description of aileron, see fig. 60.)
The main problem of interference at low Mach numbers)s considered to be that of avoiding boundary-layer separation resulting from rapid flow expansions caused by the addition of induced velocities about bodies and the boundary-layer accumulations near intersections. No recent systematic investigations of interference such as the investigation of reference 66 have been made. Some tests have been made of airfoil sections with intersecting flat plates (reference 67). These configurations may be considered to represent approximately the condition of a wing intersection with a large flat-sided fuselage.:.i:1n
24-inch chord 1.6
1.4
#
J
I
,!-e =0.186 ..• p
1.2
.p-
lei 'l
1V t
.., .8
,
~
~
/.2
./
~ ",
~. v.
.V' he" 1.135
V
·····he ~ 1./35
VV
J
IJ
I
11
\\
,a L
Ii /
Configuration R o Plain airfoil 3.0" I O't - - o Ducfed model (low flow) .,. 2.4
I
<> Oucted model
I
-8
qo
v. he =0.186 (V'
\
V /
,tJH - , he =0.186
1\
j /
-I.e -16
~
0
(high flpw)
\ 11V
.2
r:I
2.4
8
16 Section onqle of attock, «"
24 deq
o
;\
~4
If
o
X
u
...r/' ~
r . tJ H, he =/.135
qOI
.4
Sedion lift
I
.8 coerric~'enf,
FIGURE 63.-Lift and flow characteristics of an )<ACA 7·scries type airfoil section with leading·edge air intake.
J !.2 C1
/.0
51
SUMMARY OF AIRFOIL DATA
this case, the interference may be considered to result from the effect on the wing of the fully developed turbulent boundary layer on the fuselage or flat plate and the accumulation of boundary layer in the intersection. These tests showed little interference except in cases for which the boundary layer on the airfoil alone was approaching conditions of separation 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 fl.ow are presented in references 68 to 70. The data appear to indicate that the interference problems for conservative NACA 6-series sections are similar to those encountered with other types of airfoil. The detail shapes 'for optimum interfering bodies and fillets may, however, be different for various sections if local excessive expansions in the flow are to be avoided. Some lift and drag data for an airfoil with pusher-propellershaft housings are presented in reference 71. These results indicate that protuberances near the trailing edge of wings should be carefully designed to avoid unnecessary drag increments. Another type of interference of particular importance for high-speed airplanes results in the reduction of the critical Mach number of the combination because of the addition of the induced velocities associated with each body (reference 72). This effect may be kept to a minimum by the use of bodies with low induced velocities, by separation of interfering bodies to the greatest possible extent, and by such selection and arrangement of combinations that the points of maximum induced velocity for each body do not coincide.
Detail consideration of the various factors affecting wing design lies outside the scope of this report. The following discussion is therefore limited to some important aerodynamic features that must be considered in the application of the data presented.
The usual wing theory assumes that the resultant air force and moment on any wing section are functions of only the section lift coefficient (or angle of attack) and the section shape. According to this assumption, the air forces and moments on any section are not affected by adjacent sections or other features of the wing except as such sections or features affect the lift distribution and thus the local lift of the section under consideration. These assumptions obviously are not valid near wing tips, near discontinuities in deflected flaps or ailerons, near disturbing bodies, or for wings with pronounced sweep or sudden changes in plan form, section, or twist. Under such circumstances, cross flows result in a breakdown of the concept of two-dimensional flow over the airfoil sections. In addition to th('se cross flows, induced effects exist that are equivalent to a change in camber. Such effects are particularly marked near the wing tips for wings of normal plan form and for wings of low aspect ratio or unusual plan form. Liftingsurface theory (see, for example, reference 81) provides a means for¡ calculating wing characteristics more accurately than 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 for structural design, such distributions are not suitable for predicting maximum-lift and stalling characteristics. Until sufficient data are obtained to permit the prediction of the maximum-lift and stalling characteristics of wings with discontinuities, these characteristics may best be estimated from previous results with similar wings or, in the case of unusual configurations, should be obtained by test. The characteristics of intermediate wing sections must be known for the application of wing theory, but data for such sections are seldom available. Tests of a number of such intermediate sections obtained by several manufacturers for wings formed by straight-line fairing have indicated that the characteristics of such sections may be obtained with reasonable accuracy by interpolation of the root and tip characteristics according to the thickness variation.
APPLICATION OF SECTION DATA
SELECTION- OF ROOT SECTION
APPLICATION TO WING DESIGN
Wing characteristics are usually predicted from airfoilsection data by use of methods based on simple lifting-line theory (references 73 to 76). Application of such methods to wings of conventional plan form without spanwise discontinuities yields results of reasonable engineering accuracy (reference 77), especially with regard to such important characteristics as the angle of zero lift, the lift-curve slope, the pitching moment, and the drag. Basically similar methods not requiring the assumption of linear section lift .characteristics (references 78 and 79) appear capable of yielding results of greater accuracy, especially at high lift coefficients. Further refinement may be made by consideration of the chordwise distribution of lift (reference 80). Wings with large amounts of sweep require special consideration (reference 81).
The characteristics of a wing are affected to a large extent by the root section. In the case of tapered wings formed by straight-line fairing, the resulting nonlinear variation of section along the span causes the shapes of the sections to be predominantly affected by the root section over a large part of the wing area. The desirability of having a thick wing that provides space for housing fuel and equipment and reduces structural weight or permits large spans usually leads to the selection of the thickest root section that is aerodynamically feasible. The comparatively small variation of minimum drag coefficient with thickness ratio for smooth airfoils in the normal range of thickness ratios and the maintenance of high lift coefficient for thick sections with flaps deflected usually result in limitation of thickness ratio by characteristics other than maximum lift and minimum drag.
52
HEPORT 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 margin exists between the critical Mach number and the Mach number at which the drag increases sharply. As airplane speeds increase, it becomes increasingly difficult and finally impossible to avoid the drag increases resulting from compressibility effects by reduction of the airfoil thickness ratio. In the cases of airplanes of such low speeds that compressibility considerations do not limit the thickness ratio to values less than about 0.20, the maximum thickness ratio is limited by excessive drag coefficients at moderate and high lift coefficients with the surfaces rough. In these cases, tho 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 of multiengine 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 conditions at moderately high lift coefficients will indicate an optimum aspect ratio beyond which corresponding increases in aspect ratio and root thickness ratio will result in reduced performance. 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 armament installations. Attainment of extensive laminar flows is, therefore, less likely on the inboard 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 N ACA 63-series will provide advantages if the sections are thick, because such sections are more conservative than those permitting more extensive laminar 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 maxiInurn 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 the tip section than at the root section tor tapered wings because of the lower Reynolds number of fhe tip section. For wings with small camber, the most effective way of increasing the section maximum lift coefficient is to increase the camber. The amount of camber used will be limited in most cases by either the critical-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 complicates the design of the lateral-control system and increases its weight. The use of a type of camber that carries the lift farther forward on the section and thus relieyes the ailerons will, however, have little effect on the maximum lift coefficient of the section unless the maximum-camber position is well forward, as for the N ACA 230-series sections. In this case a sudden loss of lift at the stall may be expected. The effects 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 characteristics of the wing. If the root sections are at least moderately thick, it is usually desirable to select a tip section with a somewhat reduced thickness ratio. This reduction in thickness ratio, together with the absence of induced velocities from interfering bodies, gives a margin in critical speed that permits the camber of the tip section to be increased. This reduction in thickness ratio will probably be limited by the loss in maximilm lift coefficient resulting from too thin a section. A small amount of aerodynamic washout may also be useful as an aid in the avoidance of tip stalling. The permissible amount of washout may not be limited by the increase in induced drag, which is small for 10 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 the 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 outboal"d sections. Thus, such combinations as an NACA 230-series root section with an NACA 44-series tip section or an N ACA 63-series root section with an N ACA 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 particularly 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. :a.:fost of the data, particularly for the lift, drag, and pitching-moment characteristics, were obtained at Reynolds numbers from 3 to 9XI0 6 â&#x20AC;˘ 1. Airfoil sections permitting extensive laminar flow, such as 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 wing surfaces are fair and smooth.
53
SUMMARY OF AIRFOIL DATA
2. Experience with full-size wings has shown that extensive lnminnr flows nre obtainable if the surface finish is as smooth ns thnt provided by sanding in the chordwise direction with No. 320 curborundmn paper and if the surface is free from smull scattered defects and specks. Satisfactory results are usually obtained if the surface is sufficiently fair to permit n straightedge to be rocked smoothly in the chordwise direction without jarring or clicking. 3. For ,vings 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 minimum drag coefficient for such wings depend primarily on the surface condition rather than on the airfoil section. 4. Substantial reductions in drag coefficient at high Reynolds numbers may be obtained by smoothing the wing 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-series airfoils. The NACA 230-series airfoils have somewhat higher maximum lift coefficients for thickness ratios less than 0.20. 6. The maximum lift coefficients of airfoils with flaps are about the same for moderately thick NACA 6-seriessections as for the NACA 23012 section but appear to be considerably lower for thinner N ACA 6-series sections. 7. The lift-curve slopes for smooth N ACA 6-series airfoils are slightly higher than for N ACA 24-, 44-, and 230-series airfoils and usually exceed the theoretical value for thin airfoils. 8. Leading-edge roughness causes large reductions in maximum lift coefficient for both plain airfoils and airfoils equipped 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 having the position of minimum pressure far back. 10. Characteristics of airfoil sections with the expected surface conditions must be known or estimated to provide a satisfactory basis for the prediction of the characteristics of practical-construction wings and the selection of airfoils for such wings. 11. The N A CA 6 series airfoils provide higher critical Mach numbers for high-speed and cruising lift coefficients than earlier types of sections and have a. reasonable range of lift coefficients within which high critical Mach numbers may be obtained. 12. The NACA 6-series sections provide lower predicted critical ::\-fach numbers at moderately high lift coefficients than the earlier types of sections. The limited data available suggest, however, that the NACA 6-series sections retain satisfactory lift characteristics up to higher Mach numbers than the earlier sections. 13. The NACA 6-series airfoils do not appear to present unusual problems with regard to the application of ailerons. 14. Problems associated with the avoidance of boundarylayer separation caused by interference are expected to be similar for conservative NACA 6-series sections and other good airfoils. Detail shapes for optimum interfering bodies and fillets may be different for various sections if local excessive 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 experimental development.
LANGLEY ::\-IEMORIAL AERONAUTICAL LABORATORY, NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS, LANGLEY FIELD,
VA., March 5,1945.
APPENDIX METHODS OF OBTAINING DATA IN THE LANGLEY TWO·DIMENSIONAL LOW.TURBULENCE TUNNELS By
MILTON M. KLEIN
DESCRIPTION OF TUNNELS
The Langley two-dimensional low-turbulence tunnels are closed-throat wind tunnels having rectangular test sections 3 feet wide and 7% feet high and are designed to test models completely spanning the width of the tunnel in twodimensional flow. The low-turbulence level of these tunnels, amounting to only a few hundredths of 1 percent, is achieved by the large contraction ratio in the entrance cone (approx. 20: 1) and by the introduction of a number of finewire small-mesh turbulence-reducing screens in the widest part of the entrance cone. The chord of models tested in these tunnels is usually about 2 feet, although the characteristics at low lift coefficients of models having chords as large as 8 feet may be determined. The Langley two-dimensional low-turbulence tunnel operates at atmospheric pressure and has a maximum speed of approximately 155 miles per hour. The Langley twodimensional low-turbulence pressure tunnel operates at pressures up to 10 atmospheres absolute and has a maximum speed of approximately 300 miles per hour at atmospheric pressure. Standard airfoil tests in this tunnel a,re made of 2-foot-chord wooden models up to Reynolds numbers of approximately 9X 106 at a pressure of 4 atmospheres absolute. The lift and drag characteristics of airfoils tested in these tunnels are usually measured by methods other than the use of balances. The lift is evaluated from measurements of the pressure reactions on the floor and ceiling of the tunnel. The drag is obtained from measurements of static and t9tal pressures in the wake. Moments titre usually measured by a balance.
C/
F
wake (Ho~HI)
He max
a B C Cd
ca'
54
••
An coefficients of potential function for a symmetrical body fraction of chord from leading edge over which design load is uniform dimensionless constant determining width of wake chord drag coefficient corrected for tunnel-wall effects drag coefficient uncorrected for tunnel-wall effects drag coefficient measured in tunnel section lift coefficient corrected for tunnelwall effpcts
maximum value of He tunnel height
hT
K=c/ Cd
L
L' m
n
,SYMBOLS
AI, A 2 ,
section lift coefficient uncorrected for tunnelwall effects design lift coefficient lift coefficient measured in tunnel moment coefficient about quarter-chord point corrected for tunnel-wall effects moment coefficient about quarter-chord point measured in tunnel average of velocity readings of orifices on floor and ceiling used to measure blocking at high lifts average value of F in low-lift range potential function used to obtain 'I)-factor total pressure in front of airfoil total pressure in wake of airfoil coefficient of loss of total pressure III the
T
true lift resulting from a point vortex lift associated with a point vortex as measured by integrating manometers upstream limit of integration of floor and ceiling pressures downstream limit of integration of floor and ceiling pressures resultant pressure coefficient; difference between local upper- and lower-surface pressure coefficients static pressure in the wake free-stream dynamic pressure static-pressure coefficient (HoqO
P)
static-pressure coefficient in the wake
(Ho qo 8
U
v ~V
PI)
distance along airfoil surface velocity, due to row of vortices, at any point along tunnel walls free-stream velocity increment in free-stream velocity due to 'blocking
SUMMARY OF AIRFOIL DATA
V' V" v w
corrected indicated tunnel velocity tunnel velocity measured by static-pressure orifices local velocity at any point on airfoil surface potential function for flow past a symmetrical body distance along chord' or center line of tunnel
(B:w)
y
variable of integration
Y
distance perpendicular to stream direction ordinate of symmetrical thickness distribution distance perpendicular to stream direction from position of Hcmax
ilt Yw
z
1/a 1/b 1/x
A
slope of surface of symmetrical thickness distribution complex variable (x+iy) angle of zero lift section angle of attack corrected for tunnelwall effects. section angle of attack measured in tunnel strength of a single vortex ratio of measured lift to actual lift for any type of lift distribution 'IJ-factor for additional-type loading 'IJ-factor for basic mean-line loading 'IJ-factor applying to a point vortex component of blocking factor dependent on shape of body quantity used for correcting effect of body upon velocity measured by static-pressure orifices component of blocking factor dependent on size of body potential function stream function
55
The factor 'T]x was obtained as follows: The image system which gives only a tangential component of velocity along the tunnel walls is made up of an infinite vertical row of vortices of alternating sign as shown in figure 64. If the sign of the vortex at the origin is assumed to be positive, the complex . potential functionj for this image system is ir I . h 'I1'zir I . h (Z-ihT) j =2'11' og sm 2hT -2'11' og sm '11' ~
(18)
where
r strength of a single vortex z complex variable (x+iy) hT tunnel height y .+
+"+
Upperwo//....
m
n
Lower woll·· ....
.-
FIGURE
64.-Image system for calculation of ~·ractor in the Langley two·dimensional low·turbulence tunnels.
The velocity u, due to the row of vortices, at any point along the tunnel walls where hT
y=""2
is then obtained as MEASUREMENT OF LIFT
The lift carried by the airfoil induces an equal and opposite reaction upon the floor and ceiling of the tunnel. The lift may therefore be obtained by integrating the pressure distribution along the floor and ceiling of the tunnel, the integration being accomplished with an integrating manometer. Because the pressure field theoretically extends to infinity in both the upstream and the downstream directions, not all the lift is included in the length over which the integration is performed. It is therefore necessary to apply a correction factor'T] that gives the ratio of the measured lift to the actual lift for any lift distribution. The calculation was performed by first finding the correction factor 'lJx applying to a point vortex and then determining the weighted average of this factor over the chord of the model.
r
'I1'X
u=2h T sech hT
(19)
where x is the horizontal distance from the point on the wall to the origin. The resultant pressure coefficient P R is then given by 4u PR==V
2r
'I1'X
=hTVsech hT
(20)
where V is the free-stream velocity. The lift manometers integrate the pressure distribution along the floor and ceiling from the downstream position n to the upstream position m (fig. 64). For a point vortex
56
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
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 (21)
The values of 'YJb and 'YJa 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 'YJb is the 1]-factor corresponding to the basic mean-line loading (indicated by the value of a) and 'YJa is the 'YJ-factor for the additional type of loading as given by thin-airfoil theory: a
where qo is the free-stream dynamic pressure. The true lift L resulting from the point vortex is given by
1.0 .8 .6 .4 .2
L=2Qor
0.934; .9342 .9336 .9330 .9325 .9322
o
V
'Ia=O.92U6
The correction factor
'YJx
1 = hT
is then
in-x m-x
7rX
sech -h dx T'
which yields (22) In the Langley two-dimensional low-turbulence tunnels, 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 1]x against x for the Langley two-dimensional low-turbulence pressure tunnel is shown in figure 65. The 1]-factor for a given lift distribution is obtained from the expression
Jrchord 'YJ=f chord
11'YJ"
d (~)
l1d
(X) -
C
C
In order to check the variation of 'YJa with variations in the additional type of lift distribution, the value of 'YJa was recalculated for the class C additional lift distribution given in figure 6 of reference 74. The value of 'YJa for this case was 0.9304, as compared with 0.9296 for a thin airfoil. Because of the small variation of 'YJa with the type of additional lift, the value for thin-airfoil additional lift was used for all calculations. The lift coefficient of the model in the tunnel uncorrected for blocking c/ is given in terms of the lift coefficient measured in the tunnel CIT and the design lift coefficient of the airfoil Cit by the following expression: (24)
Because 'YJb does not differ much from 'YJa, 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 distribution over the airfoil in the turinel does not agree exactly with the assumed lift distribution. Because of the small variations of 'YJ 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 distribution of the lift reaction along the tunnel walls are small.
1.0
MEASUREMENT OF DRAG ~r-
.8
---
i---...
t--
.6
.4
The drag of an airfoil may be obtained from observations of the pressures in the wake (reference 84). An approximation to the drag is given by the loss in total pressure of the air 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 Ho and HI, respectively, the drag coefficient obtained from loss of total pressure Cd T is =
Cd
o
-2 ~ 0 I 2 3 4 5 6 Disfonce downsfream from reference point in funnel, x) ft
FIGURE 65.-Lift efficiency factor n. for a point vortex situated at various"positions along the center line of the tunnel.
T
r
Jwake
Hc
dyw
(25)
C
where
He coefficient of loss of total pressure in the wake (Ho-_HI) Qo
57
SFMMARY OF AIRFOIL DATA
Yw
d istanc(' perpendicular to stream direetion of fI ema ;:
froIll
-:-.. t---, :-
position 10
;---- t----
--;--..
If thr static pressure in the wak(, is rrpresented by PI! the tl'U(, drug coeffieient uncorrected for bloeking shown to be (refel'l'nee 84)
ca'
.9
may be B
(26)
r--
r-- --;--..
t---
.7
-t--
t----
r-- t--
I------
t-- t--
r--- r--
t-- r----
f-
l-J-i:
.9
r----.-
1'---
.5
~
tZ
q,
t-- I---
I---
.8 "~
~
1_ WaKe depth
"(mo,)
r-- r----
-- -r---1.0
I--- I'-i"---j-....
.6 I--- l-- cc'=Kcdr
· th ' I' stati<,-pl'essure COl'ffi' ('len t'm th . e wak-e Ho-PI --_. 8 1 IS qo The assumption is made that the variation of total pressure acrcss tIl(' wake can be represented by a normal probability curve. Tht' drag cOPfficient ca' is tllPn easily obtainable from measurements of CdT by means of a factor K, the ratio of c/ to Cd T , which depC'uds only on 8 1 and the maximum value of lIe. If the maximum value of He is rt'prf'sentf'd by H emax ' tIl(' NlllH tiOll of the normal probability cune is
r--
/'--.
K
'WI l{'re
S, 1./
t---- r-I--
t--
r---.,.
r-- t--. t--
l'--.~
f"".-
~
~
""-.
S' _ Sfa Ie pressure - - t - q,
f-- j..--'.J:.....
~
I--- :--.....
I'-.... ~
----
'-...
~
""
.4
.I
.3
.4
.5
.6
.7
.8
.9
J.O
FH.CRE tl(t--Plot of ](us u function of l1c maz with 8 1 as U paramC'ter.
TIll' pou'lltial function w for a symm('trical body IS ginll b~-
where B is a dinH'llSiollless eonstnnt that determines the width of the wlIk(,. If a ('onvenient varinble of intpgration
. K'IS ..- .. IS use(1, t IIe ratIO Y = Byw' c
(28)
where ,. is tlll' fl'('l'-str('am veloeity and the coefficients AI, A 2 , • • • H1'(' comph,x. If the tunnel ht'ight is large COIllpal'l'd to tIl(' size of tIll' body, POW('I'S of liz greater than 1 may b(, Iwgl(>ded and
(29)
and is ind('pend<'llt of the width of the wah. TIl(' quantity K has b('PI1 evaluatpd for variolls values of He rna;c and 8 1 bv . .. assuming 8 1 to b(' constant aeross thE' wake. The drag coeffieipnt c/ may thus be obtained from tunn('l mNl.sur('ments of Cd T , He mu , and 8 1 • A plot of K as a funetion of He mn with 8 1 as param('t!:'r is given in figurE' 66. A paralIc,1 t1'l'atmpnt of this probll'm is given in rpfrr(,lH'P 85. TUNNEL-WALL CORRECTIONS
In two-dim(,llsional flow, the tunnE'1 walls may be eOllV(,I1iently eOllsid(,l'('(i as having two distinct dff'cts upon thE' flow over a mod('l in a tunnrl: (1) an inerease in the frE'e-stream velocity in titP neighborhood of thE' model bpcausr of a (;onstrietion of tIl<' flow and (2) a distortion of the lift distribution from tIl!' indu(,E'd curvature of the flow. The inca-cast' in fn.>('-str('am vplocity caused by the tunnel walls (blocking pfl'Pet) is obtaill('d from consideration of an infinite vprtieal "ow of imag('s of a symmetrical body as given in rpf(,I'('I\(,(, 86; tll(> irriag('s rl'pn'sent the ('fl'(>d of th(' tunnd wnlls.
This opl'l'Htion is ('quivaknt to rpplacing the body by a eil'elc of whieh the doublpt strength is 2'llA I ; the term AI/z repn'Sl'nts thr disturbnnec to the fr('('-stn'am flow. The total indu('pd Y('locity at the center of tIl(' body dw' to all thf' imng('s is ('XP"('ss('d ill l'('f(,l'en('(' 86 as (30)
where the term Al is the same as the term
"41
'At2 V of
reference 86. For eOllveniellep in tunnd cal('ulatiolls, the t'xpressioll of AF may be written
AV
V=Au
(31)
where (32) (33)
The faetor 0' d('pends only Oil the size of the body and is easily calculatE'd. The factor A depends on the shape of the body and is more diffi('ult tocttlculate. For bodi('s such as
58
REPORT NO. 824-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
A=l: .fol ~ V~l+(~J dG)
sponding points of the upper and lower surfaces, and
{ y de{! may be replaced by an integration over the upper
.10
surface; therefore,
fo z
(34)
where v is the velocity at any point on the airfoil surface and dy ddx is the slope of the airfoil surface at any point of which the ordinate is Yt.
y de{! (counterclockwise direction)
or
Reversing the path of integration, replacing de{! by vds, replac-
y
ing ds by ods
..... 路路路路Polh of Inlegralien
u,
fa z~~ dz will
depend only on the term -Adz and, from the theory of residues, is given by
r
dWd z=-211'~'A 1 Jo z dz
but dw
z dz dz=z dw =
(x+iy) (dcjJ+i dt/;)
where e{! is the potential function and if; is the stream function. On the surface of the body dif;=O, so that
r z dd z dz= Jo{ x de{!+i Jo{ y de{! W
Jc
(35)
Since the body is symmetrical, the term x de{! will have equal numerical values but opposite signs at corres,Ponding points of the upper and lower surfaces, and
~
11'.10 c V
In order to obtain this expression, consider the flow past a symmetrical body as shown in figure 67. The potential function for this flow is given by equation (28). Differentiating and multiplying equation (28) by z gives
The line integral about a closed curve
~ 1 +d:~2 dx, and solving for A = lC~~l gives A=.16 (I'lL
.1.'
FIGURE 67.-Sketch for derivation of A-factor.
vanish.
~~ dz=2i f
fax de{! will
The term y de{! will have equal values at corre-,
11 +(dyt)J d(~) -V dx c
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 .}xists in the measured tunnel velocity'because of the interference effects of the model upon the velocity indicated by the staticpressure 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 distribution along the streamline halfway between the upper and the lower tunnel walls for Rankine ovals of various sizes and thickness 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 A and a factor ~ which depended upon the 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 approximately 0.002. In order to calculate the effect of the tunnel walls upon the lift distribution, 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 when the 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 refer to the coefficients measured in the tunnel: cl=[1-2A(o+~) -u]cz'
(37)
59
SUMMARY OF AIRFOIL DATA
-(1+) '+ d'id 4uc me /4' ,-UIl'Io, Ull'o
Il'o-
CI
Il'o
(38) (39)
·,
4 UC m
14'
I n t he f oregolllg equatlons, the terms ,CI d 'IdeCXo " UCXI0 ,and uc/14 are usually negligible for 2-foot-chord models in the Langley two-dimensional low-turbulence tunnels. When the effect of the tunnel walls on the pressure distribution over the model is small, the wall effect on the drag is merely that corresponding to an increase in the tunnel E!peed. The correction to the drag coefficient is therefore given by the following relation: ' ca=[1-2A(u+m ca'
from unity in the high-lift range for ap.y airfoil tested in the tunnel; this variation indicates a change in blocking at high lifts. A plot of FIFo against angle of attack cxo' for a 2-footchord model of the NACA 643-418 airfoil is given in figure 68. The quantity FIFo is nearly constant for values of cxo' up to 12°; but for values of Il'o' greater than 12°, FIFo increases and the increase is partIcularly noticeable at and over the stall. 1.20 1.10
f/.oo
~r-
o ,.."...
>-.
:r-o-
V
.90
(40) .80
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 therefore 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 appreciably. 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.
-16
-12
-8 -4 0 4 8 Geometric angle of attacK,
12 /6 deg
a;,
20
24
FIGURE 68.-Additional blocking factor at the tunnel walls plotted against angle of attack for the NACA 643-418 airfoil.
A theoretical comparison was made of the blocking factor Au and the velocity measured by the floor and ceiling orifices
for 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 Au and the change in F to be unique for chord ler gths up to 50 inches in that different bodies having the same blocking factor Au gave approximately the same value of F. For chords up to 50 inches, the relationship is A:=0.45
(~ -1)
(41)
CORRECTION FOR BLOCKING AT mGH LIFTS
SO long as the flow follows the airfoil surface, the foregoing relations account for the effects of the tunnel walls with sufficient accuracy. When the flow leaves the surface, the blocking increases because of the predominant effect of the wake upon the free-stream velocity. Since the wake effect shows up primarily in the drag, the increase in blockilig 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-dimensional low-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
where A VIV is the true increment in tunnel velocity due to blocking; The foregoing relation :was adopted to obtain the correction to the blocking in the range of lifts where
~o >1.
Considerable uncertainty exists regarding the correct numel1ical 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, the correction amounts to only about 2 percent at maximum lift for 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.
60
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
.0
V I. 2
f\ r
iit" ~
!
8
I
\,
I
If A
I
11
1
~
!
!I
-. 4
) '\ (a)
(~V -/6
II
I
/
.8
t Airfoil A
I Ai~fOil ~
1I
K
/
If
0
V
!
/
.4
.2
/
!
II
Pressure distribution, TDT test 640 Iregratinq manomrer, TDr fest 618
o Airfoil B Airfoil
l
Pressure distnbution, rDr test 655 I Integratin$. manometer, TDT test 6 3 and 654
-
(b)
o
-8
8
/6
24 32 -24 -16 Section angle of attack, «OJ deg
o
~8
8
32
24
16
(b) Comparison for airfoil B.
(a) Comparison for airfoil A.
FIGURE 69.-Comparison between lifts obtained from pressure·distribution measurements and lifts obtained from rea~tions on the 1100r and ceiling of the tunnel.
1 l 1 Chord. in.
2.0
~ Jl""'~r";'fed tor blocking ~ J~ cor;"ecfed for' b/~ckinq
/.6
/.8 1.2
V'
<:!
/.6
l r
/.4
I
/.2
II
1/
II
.,&;; ~
\
~~
\
~~
1\
\
'" , ~
.8 .6
.4 .2
-1.2
-24
~
~
o Balance o Integrating manometer_
j
~.B
i"-
---' >-
S 1.0
I
_J
17 <1 V
-16
-8 0 8 16 Section angle of attock, «., deg
24
FIGURE 70.-Comparison between lifts obtained from balance measurements and from reactions on the floor and ceiling of the tunnel.
o
.I
.2
.3
.4
.5
.6
.7
.8
.9
:x/c
FIGURE 71.-Comparison between corrected arid uncorrected pressure distributions for two chord sizes of a symmetrical NACA 6-series airfoil of l(i·percent thickness. ,"0=0·,
SUMMARY OF AIRFOIL DATA
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 theoretical correction factor (equation (40)) and the experimentally derived corrections of reference 88. The theoretical correction factors were found to be in good agreement with those obtained experimentally. In order to check the validity of the 'I-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 'I-factor has also been checked by comparison of the lift obtained _from balance measurements with the integratingmanometer values in figure 70. Finally, a check has been made of the method of correcting pressure distributions (reference 87) for NACA 6-series airfoils of two chord lengths at zero angle of attack in figure 71, in which the pressure coefficients are plotted against chordwise position x/c. The agreement between the corrected pressure distributions for both models verifies the method of making the tunnel-wall corrections. REFERENCES 1. Jacobs, Eastman N., Ward, Kenneth E., and Pinkerton, Robert M.: 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 the Variable-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: Aerodynamic Characteristics 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. Jacobs, 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 Compressibility Burble. NACA Rep. No. 763, 1943. 11. Jacobs, Eastman N.: Preliminary Report on Laminar-Flow Airfoils and Jirew Methods Adopted for Airfoil and Boundary-Layer Investigations. NACA ACR, June 1939.
61
12. Von Doenhoff, Albert E., and Stivers, Louis S., Jr.: Aerodynamic Characteristics of the NACA 747A315 and 747A415 Airfoils from Tests in the NACA Two-Dimensional Low-Turbulence Pressure Tunnel. NACA CB No. L4I25, 1944. 13. Naiman, Irven: Numerical Evaluation by Harmonic Analysis of 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. N ACA 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. N ACA Rep. No. 383, 1931. 19. Von Karman, Th.: Compressibility Effects in Aerodynamics. Jour. Aero. ScL, 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. N ACA ACR, Aug. 1941. ' 22. Von Doenhoff, Albert E., and Tetervin, Neal: 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. L4Gl4, 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 MeanLine Loading on the Aerodynamic Characteristics of Some LowDrag 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 Calculation 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(421)-420, a=1.0 Airfoil Section. NACA CB No. L4Gl7, 1944. -
62
REPORT NO. 824-NATIONAL 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. Zalovcik, John A., and Wood, Clotaire: A Flight Investigation of the Effect of. Surface Roughness on Wing Profile Drag with Transition Fixed. NACA ARR No. L4I25, 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. Silverstein, Abe, Katzoff~ S., and Hootman, James A.: Comparative Flight and Full-Scale Wind-Tunnel Measurements of the Maximum Lift of an~~iIi?lane. NACA Rep. No. 618, 1935. 42. Sweberg, Harold H., and . Dirigeldein, Richard 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, Harold S.: Effects of TrailingEdge Modifications on Pitching-Moment Characteristics of Airfoils. NACA CB No. L4I30, 1944. 44. Fullmer, Felicien F., Jr.: Wind-Tunnel Investigation of NACA 66(215)-216, 66,1-212, and 651-212 Airfoils with 0.20-AirfoilChord Split Flaps. NACA CB No. L4G10, 1944. 45. Abbott, Ira H., and Greenberg, Harry: Tests in the VariableDensity Wind Tunnel of the N. A. C. A. 23012 Airfoil with Plain and Split Flaps. NACA Rep. No. 661, 1939. 46. Wenzinger, Carl J., and Harris, Thomas A.: Wind-Tunnel Investigation of N. A. C. A. 23012, 23021, and 23030 Airfoils with Various Sizes of Split Flap. NACA Rep. No. 668, 1939. 47. Bogdonoff, Seymour M.: Wind-Tunnel Investigation of a LowDrag 'Airfoil Section with a Double Slot,ted Flap. NACA ACR No. 3120, 1943. ' 4S. Wenzinger, Carl J., and Harris, Thomas A.: Wind-Tunnel Investigation of an N. A. C. A. 23012 Airfoil with Various Arrangements of Slotted Flaps. NACA Rep. No. 664, 1939. 49. Wenzinger, Carl J., and Harris, Thomas.A.: Wind-TunneIInvest.igation of an N. A. C. A. 23021 Airfoil with Various Arrangements of Slotted Flaps. NACA Rep. No. 677, 1939. 50. Swanson, Robert S., and Crandall, Stewart M.: Analysis of A vailable Data on the Effectiveness of Ailerons without Exposed Overhang Balance. NACA ACR No. L4E01, 1944. 51. Street, William G., and Ames, Milton B., Jr.: Pressure-Distribution Investigation of an ,N. A. C. A. 0009 Airfoil with a 50Percent-Chord Plain Flap and Three Tabs. NACA TN No. 734, 1939. 52. Ames, Milton B., Jr., and Sears, Richard 1.: Pressure-Distribution Investigation of an N. A. C. A. 0009 Airfoil with an SO-PercentChord Plain Flap and Three Tabs. N ACA TN No. 761, 1940. 53. Ames, Milton B., Jr., and Sears, Richard I.: Pressure-Di!~tribution Investigation of an N. A. C. A. 0009 Airfoil with a 30-PercentChord Plain Flap and Three Tabs .. NACA TN No. 759, 1940. 54. Sears, Richard I.: Wind-Tunnel Investigation of Control-Surface Characteristics. I-Effect of Gap on the Aerodynamic Characteristics of an N ACA 0009 Airfoil with a 30-Percent-Chord Plain Flap. NACA ARR, June 1941.
55. Jones, Robert T., and Ames, Milton B., Jr.: Wind-TUlinel Investigation of Control-Surface Characteristics. V-The Use of a Beveled Trailing Edge to Reduce the Hinge Moment of a Control Surface. NACA, ARR, March 1942. 56. Sears, Richard r., and Liddell, Robert B.: Wind-Tunnel Investigation of Control-Surface Characteristics. VI-A 30-PercentChord Plain Flap on the NACA 0015 Airfoil. NACA ARR, June 1942. 57. Wenzinger, 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 1.., and Lockwood, Vernard E.: Wind-Tunnel Investigation of Control-Surface Characteristics. XIII-Various Flap Overhangs Used 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. Denaci, H. G., and Bird, J. D.: Wind-Tunnel Tests of Ailerons at Various Speeds. II-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 Effectiveness of 0.20-Airfoil-Chord Plain Ailerons of True Airfoil Contour on N ACA 65r 415, 653-41S, 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 Investigation of the Effects of Profile Modifications and Tabs on the Characteristics of Ailerons on a Low Drag Airfoil. N ACA Rep. No. S03, 1944. 65. Von Doenhoff, Albert E., and Horton, Elmer A.: Preliminary Investigation in the NACA Low-Turbulence Tunnel of LowDrag-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. 6S. 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 Characteristics of a Thick Low-Drag Airfoil Critically Affected by Leading-Edge Roughness. NACA CB No.3D27, 1943. 70. Allen, H. Julian, and Frick, Charles W., Jr.: Experimental Investigation of a New Type of Low-Drag Wing-Nacelle Combination. NACA ACR, July 1942. 71. Abbott, 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, March 1940. 73. Anderson, Raymond F.: Determination of the Characteristics of Tapered Wings. NACA Rep. No. 572, 1936. 74. Jacobs, Eastman N., and Rhode, R. V.: Airfoil Section Characteristics as Applied to the Prediction of Air Forces and Their Distribution on Wings. NACA Rep. No. 631, 1938.
SUMMARY OF AIRFOIL DA'l'A
75. Soule, 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 the Stalling of Tapered Wings. NACA ARR, Jan. 1943. 77. Anderson, Raymond F.: The Experimental and Calculated Characteristics 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 Load Distributions. 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 SweptBack Wing. NACA ARR, Oct. 1942. 82. Pearson, H. A.: Span Load Distribution for Tapered Wings with Partial-Span Flaps. NACA Rep. No. 585, 1937.
63
83. Pearson, Henry A., and Anderson, Raymond F.: Calculation of the Aerodynamic Characteristics of Tapered Wings with PartialSpan Flaps. NACA Rep. No. 665, 1939. 84. The Cambridge University Aeronautics Laboratory: The Measurementof 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 Determining Wing Profile Drag in Flight. Jour. Aero. ScL, vol. 7, no. 7, May ]940, pp. 295-301. 86. Glauert, H.: Wind Tunnel Interference on Wings, Bodies and Airscrews. R. & M. No. 1566, British A. R. C., 1933. 87. Allen, H. Julian, and Vincenti, Walter G.: Interference in a TwoDimensional-Flow Wind Tunnel with the Consirleration of the Effect of Compressibility. NACA Rep. No. 782, 1944. 88. Fage, A.: On the Two-Dimensional Flow past a Body of Symmet.rical Cross-Section Mounted in a Channel of Finite Breadth. R. & M. No: 1223, British A. R. C., 1929.
TABLE
H.-MAXIMUM LIFT AND STALLING CHARACTERISTICS OF MODELS TESTED IN THE NACA 19-FOOT PRESSURE TUNNEL Contlguration
Flap angle (deg)
Flap
Flap.chord (percent c)
Geometric characteristics
Model Plan view
Outboard
Inboard
Front view
~fi
·------1---------1----'---,---
Jr. I cr,
I cr.
br,
I
II
1
1 Split
I
60
1 1
I I
Sections: Root: NAGA 66(215)-216 Tip: NAGA 66(215)-216 A=7.00
c--:-------=--=:J
I I
T I 1 -1---1
---I
Fowler
Sections: Root: NAGA 66(215)-116 Tip: NACA 66(215)-216 A=7.0
~
I
~=0.5
Geometric washout, 1.50 .j,
--I
Sections: Root: NACA 65(318)-{)19 Tip: NAGA 65(318)-{)15 A=7.36
~
_ _ _I
washout; 3.6
Sections; Root: NAGA 65(318)-{)19 Tip; NACA 65(318)-{)15 A=7.36
~ ~
30
60
10
1
1 I
I
I
j
I
37
I
10
I
20
1
I
20
30
30
-J.
Stalling characteristi cs
2.6 3.6 4.6
1.72 1. 78 1.84
2.6 3.6
1.94 1. 98 2.07
-J.
4.6
1. 97 2.03 2.06
2.6 3.6 4.6
2.04 2.11 2.15
2.6 3.6 4.6
2.40 .2.50 2.51
2.6 3.6 4.6
2.43 2.49 2.52
2. lX106
1. 15 1.29 1. 27
Abrupt stall progresses from root toward tip for flaps neutral and p~rtial span flaps detlected; no data for fnll-span· flaps
j
o
o
30
I
30
I
I
I 1.
I I 1 1
.j,
30
53
37
2.8 3.3 1
I
35
30
30
j
I
2. I 2.9 3.4
2.44
I
2. I
2.36 2.49
I
2.9 3.4
1
00 ~
>I>
~
~ ..... o ~
With flaps neutral, satisfactory; with flaps deflected, extremely abrupt stall envelops entire wing
2.49
2.54
3.13 3.31 3.29
None
3.0XJ06
1.18 1. 37 1.43
5. I
7.4
Noue
3.3XI0' 5.6 7.2
a=0.6 Tip; NACA 66(215)-(1.8)12, a=O.6 A =5.82 X=0.46 . Geometric washout, 2.50
Pliin
1
Nine 1
1
-J.
I-o-'=='-y-'-_-_=_:_~ ~6-0-'---I
. .-.--.
I
1
50
_... _..
I
I
Abrupt stall with satisfactory progression to· ward tips
-J.
_ _ •______________ :-----.,
I
I
78 • 3.3 5.2 5.8
1 55 • 2.10 2.19 2.21
Unsatisfactory stall; a strong outflow resulted in severe tip stall
~ ~ .....
...., >-3
trl trl
"'J
o
> trl o ~ > q
::tI
>-3 .....
I Abrupt stall wit~ satisfactory. progresslOn to· ward UPO;
~_ _ ,,,,,:~,
, I
o
::tI
::tI
1.17 1.31 1. 34
'-~-:~-X-1;; -i-:-~~-I
1
-J.
Sl.....
Ul
><i
1----1--1--1--\-·-1---1--1---1---1--None
~ >
o o
1--1--1--1--1---1---- ·--1 None
~
>-3 ~
2.29
2. I 2.9 3.4
~
.."
?
I-~I--I--I-.--I--I--I------I
I
Geometric washout, 4.00 Sweep back of 0.25 chord line 21.930
~
1.26 1. 36 1. 41
2.6 3.6
~=0.25
-====
3.6 4.6
4.6
I
1 1
CLmr.u:
0
se~gf:~ACA66(215)-(1.S)(15.5), v
Fowler
1
I
~=O.25
I~metric
IV
.j,
I
1
III
I !
~=1.00
Geometric washout, 0.00
1
63
I
I
I
II
10
20
1
R
bro
1No~~ -Non~ No:I-~ne 1- 2. 6XIO~·
None
None
Flap span (percent b)
~
,----
o
Ul
VI
-
C ---.::J
b:=J ==
t}::=-
Sections: Root:NACA66(215)-(1.8) (15.5), a=0.6 Tip: NACA 66(215)-(1.8)12, a=0.6 A =5.82 >'~0.46
Plain
I 1
None
0
II
,1.
.10
--.6.--
25
------
L
.
I I I
-._----
-------
60
-------
3.3XI0' 5.3 6.0
1.34 1.39 1.39
-------
3.3 5.1 5.8
1.87
1
Geometric washout, 2.50
1.91 1.92
Abrupt stall with satisfactory progression toward tips
-- -- --- ---
I VIl
1
~
D
I~
Sections: Root: Mod. N ACA 65,3-318, a=O.8 Tip: Mod. NACA 65(318)-316, a=0.8 A=8.09 >'=0.5 Geometric washout, 0.00
Double slotted ,1.
Double slotted ,1.
0
0
2.1
2.5
.10
48
55
30
,1.
1
,1.
,1.
I
I
I
5.1XlO'
1.33
5.1
2.85
Satisfactory
I
I I
\
-- - - - - - -
(\
I I
I
VUI
-.~
C-==
=-=0==
- P'
V
Sections: Root: NACA 67(115)-116 Tip: NACA 67,1-115 A=6.7 >'=0.4 Geometric washout, 2.00
Zap
I
,1. Split ,l-
Zap
IX
X
~ ~
V
r
---.
60 ,l-
-v
None Split
None ,l-
55
d ~ -, ,------
\r-
'v-o-.
-
-
sr~ v
V
• Propellers win<lmi!ling.
60 ,l-
.!-
1.32 2.25 2.77 1. 91 2.22
I
No data
I
I
I I
w q ~
~
~
>1
-------
20
-----.-
60
·
-------
3.5X10'
----.-- 3.6
138 1. 97
:......
Satisfactory
~ ";j
Sections: Root: N ACA 64(215)-418 Tip: NACA 66,2x-415 A=8.92 >'=0.33 Geometric washout, 1.00
None Split
None
---55--
-------
./.
Split
,l-
55
20
.!-
------20
60
·
.!-
t::1
~
-------
--ao---
3.5XlO' 3.6 3.5
1.42 1.87 2.11
Satisfactory
-------------
4.0XlO' 4.1
1.47 1. 95
Satisfactory
------ -~
Sections: Root: NACA 64(215)-418 Tip: NACA 66,2x-415 A=8.92 ),,=0.33 Geometric washout, 1.00
None Split
None
.\.
55
Extensible slotted
None
0
.------
I
35
-_.----
-------
20
-------
60
·
--- - - - - -- --- ----
t
---:'. l1t c:t
,l-
20 ,l-
2.4XI0' 2.4 2.4 2.5 2.5
- - - - - - -- . - -
V
XII
38
60
S
II
XI
35
1 1 1 381 20
t<
V
----
60
35
o";j
.
d~b v
-=0=
Sections: Root: NACA 64(215)-418 Tip. N A CA 66,2x-415 A=8.92 >.=0.33 Geometric washout, 1.00
0
,1. 48
- - -- - - --
:
f\
~
0 48 ,l-
I
,lNone Split
~=-
Sections: Root: NACA 63(420)-418, a=l.O Tip: NACA 65M15. a=1.0 A=7.77 >'=0 ..10 Geometric washout, 2.8 0
1 Split
1
60
-------
25
-------
70
3.1XlO' 4.1 4.8
01.37 01.42 01.45
-------
3.1 4.0 4.9
<>2.19
3.1 4.1 4.8
02.00 02.06 02.06
I I -------
-.-._--
-- - - -- --
I
---- .. --
--~----
02.20 02.21
I
I Sati.factory
I
I ·1
I ~
Cl
TABLE II.-MAXIMUM LIFT AND STALLING CHARACTERISTICS OF MODELS TESTED IN THE NACA 19-FOOT PRESSURE TUNNEL-Concluded
~ ~
---
I
Configuration
Plan view
Front view
F
Inboard
Outboard
tJ"
None
None
-----.-
Split
~-~
lL-d
XIII
----~
Sections: Roots: NACA 66(215)-016 Tip: NACA_66(215)-o16 A =5.34> >'=0.68 Geometric:washout, 0.00
Extensible trailing edge
1
V Split
Extensible slotted
,....
c:.L Ol1,:J
XIV
~
Sections: Root: NACA65(318)-1(18.5) Tip: NACA 66(215)-216 A=5.52 >'=0.48 Geometric washout, 3.0 0
V I
XV
--XVI
I .J.
Slotted
Split
I I
I I
.J. None
I I I I
I I
1
~ ~
45 j
I
1 60
Flap span (percent b)
~---==; p-~
~~
.J.
---- - - --
R
CLma~
2.4XI0 6 3.8 5.3
1. 21 1.37 1.45
20
-------
I
-._-._-
II
20
I
-l-
I I I
.(,
65
----._-
2.4 3.8 5:4
1. 76 1. 89
I I
-._----
2.5 3.7 5.2
1. 72 1.86
30
2.4 3.6 5.3
I I
35
-------
50
-------
50
-------
I I
-
1 I .J.
I I I I I
.J.
~
Sections: Root: NACA 23015.6 Tip: NACA 23009 A=5.5 >'=0.52 Geometric washout, 0.00
Slotted
None
0
I
1 1
50
-------------
20
II
.J.
1.00
1. 98~
2.03 2.13
3.8 5.3
2.01 2.15 2.21
3.6X1Q6 5.1 61
1. 32 1.42 1. 46
3.6 5.2 6.3
2.27 2.34 2.37
2.4
-------
-------
-------
3.5 4.9 5.9
2.04 2.13 2.16
-------
1
-------
3.5 4.S 5.9
2.02 2.12 2.17
I
-------------
60
I
.J.
l:d Satisfactory
1.99
I I
-------
Stalling characteristif!S
bl.
----.-- ------. ---- .. -- -------
60
1
bl,
---- ----
t::l 'tJ
o ~
Z
? 00 .,..
II>-
Abrupt stall with satisfactory progression toward tips
~
> >-3 t-<
o Z > t"' >
~ rJl
-.-----------
3.4XI06 4.8 5.6
1. 55 1.58 1.60
3.4 4.8 5.6
2.46 2.50 2.52
o Very abrupt stall, leftwing stalling very rapidly, for all conditions
~
c
o
~ ~
t-<
p.
. )::=='"
I
c"
CI.
1
Extensible slotted
==--A==-
Sections: Root: NACA 66,2-118 Tip: NACA 66(2x15)-1l6 A=6.9 Geometric washout, 2.0 0
I
1
-=Q==
Sections: Root: NACA 65 (216)-215, a=0.8 Tip: NACA 65(216)-215, a=0.5 A=9.08 >'=0.45 Geometric washout, 1.00 0.2 chord line straight
None
I I I
0
38
1
---------- - -3.0XlO' 24 50 -------
-------
-------
I
-------
.J.
-------
I
1
45
-------
I I
I I I
1
-------
-------
I
---- --
1
-------
4.1 5.0
2.9 4.0 4.9 4.9 4.9
~
1.34 1.47 1.50
Extremely abrupt stall, left wing stalls first for the extensible slotted flap, satisfactory for split flap
2.01 2.15 2.21 '2.29 'I. 98
-=Q=.
g >
t::l !:O
o
z:
g;
----
>-3 t-<
Double slotted
.1-
Double slotted
.J.
0 55
.J.
0
.J.
25
25
25
61;
31
3.6X1Q6 3.1 2.8
1.38 2.45 2.69
31
3.6X10 6 3.1 2.8
1.37 2.44 2.76
1 1 1 1
rJl
Satisfactory
- - - - - -- Sections: Root: NACA 65 (216)-215, a=0.8 Tip: NACA 65(216)-215, a=0.5 A=9.08 >'=0.45 Geometric washout, 1.00 -0.10 chord line straight
t::l t::l "'!
C
~
XVIII
Flap chord (percent c)
--- - - - - - -- 0 ------- 20 ------- 60 -------
V
C:(f.D:-::::>
---r 1
1 sPt
I
a/.
60
,....
Split
XVII
Flap angle (deg)
Flap Geometric characteristics
Model
Double slotted
Double slotted
.1-
.J.
0 55
.J.
0
.J.
25
25
1
25
I .J.
65
1 1
.------
Satisfactory I
I
XIX
~
---I
-w-
Sections: Root: NACA 65(216)-215, a =0.8 Tip: NACA 65(216)-215, a=0.5 A =9.08 ).=0.45 Geometric washout, 1.0 0 1.1 chord line straight
Donble slotted
DOUble slotted ,J..
.l-
~
.l-
~
Sections: Root: NACA 65(216)-215, a=O.S Tip: NACA 65(216)-215, a=0.5 A=9.08 ),=0.45 Geometric washout, 1.00 0.20 chord line straight
Double slotted
.l-
Double slott!,d ,J..
None
None
o
55 ,J..
'---I
~
---,
XXII
25
25
65
31
1 1 1 1
3.6X106 3.1 2.S
o .~
25
25
65
1 1 1
'==:::::!-
~
Sections: Root: NACA 66,2-11S Tip: NACA 66(2x15)-1l6 A=6.25 1<=0.35 Geometric washout, 2.5 0 0.375 chord line straight
p
~
-==
±-
$
Sections: Root: NACA 66,2-11S Tip: NACA 66(2x15)-1l6 A=6.25 1<=0.35 Geometric washout, 2. 50 0.375 chord line straight
T
j Split
31 1
.l-
5.5X106 5.5 5.5
1.45 2. 37
2.6.'\
1 - - 1 - -_ _ _ __ 2.9X106 4.0 4.9
45
: : : -: II j 1 50
1
60
60
,j,
20
40
1 Satisfactory
1.23
1.43 1. 51
3.0 4.0 4.9
1. 80
3.0 4.3 5.1
1.90 2.01 2.04
5.2
2.43
t~
1 Satisfactory
rJ2
q ~ ~
1--1--1--1--1--1--11---
None
None
Split
i
---,
1. 45 1 UnsatisfactorY, severe tip 2.57 stall for all conditions 2. 86 except full-span flap
1--1-------
1-·- 1 - - 1 - - 1 - - 1 - - 1 II
XXI
o
.l-
25
1_ _1___1_ _ 1_ _ 1_ _ 1
10:- ---
XX
o
55
45
1_ ... __ -1 20
'- _____ -1 50
4.1XlO' 4.9
1.50 1.60
4.1
2.02
~
Satisfactory
....t:"'
1-----1--1--1--1--1--1--11--CJ
XXIII
~ ~== $
/---/
XXIV
None
Split
1
~
Sections: Root: NACA 66,2-118 Tip: NACA 66(2x15)-1l6 A=6.1 1<=0.47 Geometric washout, 2. 5° 0.375 chord line straight
None
1______ -1
20
. ______ , 50
Split
None
1
45
1.38 1.57 1.61
2.9 4.1 5.0
1. 83 1.99 2.02
0
~
Sections: Root: N ACA 65(223)-221, a=1.0 Tip: NACA 66(215)-316, a=0.6 A=12.S 1<=0.33 Geometric washout, 0.0°
Fowler
I
1
20
. ______ , 50
2.9X10· 4.2 5.0
1.34 1. 56 1.63
3.0
1.85 1.92 2.0l
4.2 5.1
1---1
1L9l iE:LJ:t
.--.~.-
45
2.9XlO' 4.1 4.9
~
I Satisfactory
:>
1--1--1--1--1--1--1---
~\~
~
t:j
None
c.
---I
XXV
Sections: Root: NACA 66,2-118 Tip: NACA 66(2xI5)-116 A=6.25 ).=0.35 Geometric washout, 2.50 0.375 chord line swept for· ward3.5°
~ > .... ~ o
Satisfactory
1--1--1--1-_1,_ __ None
1
o 40
IS
63
1
1
I
1. 5X106 2.2 2.8
1.17 1.27 1.37
1.4 1.9 2.7
2.21 2.23 2.30
I
Poor, initial stall Occurs at tips
• Fillets removed.
t::.l
--l
SUMMARY OF AIRFOIL DATA
69
SUPPLEMENTARY DATA I-BASIC THICKNESS FORMS Page
N AC A 0006 ___________________________________________ _ N ACA 0008 ____________________________________________ _ N AC A 0009 ____________________________________________ _ N ACA 0010 ____________________________________________ _ N ACA 0012 ____________________________________________ _ NACA 0015 ____________________________________________ _ N ACA 001.8- ___________________________________________ _ N ACA 0021 ____________________________________________ _ N ACA 0024 ____________________________________________ _ NACA 16-006 ____ - ______________ - - ____ - - _- - - - - _- - - _- _- -NACA 16-009 __________________________________________ _ N ACA 16-012 ____ - _____________________________________ _ NACA 16-015 __________ - __ - - -" _- - - _- - - -- - - - - - - - - - - - - - - -N ACA 16-018__________________________________________ _ N ACA 16-021- ________________________ - - _- _- - ___ - - - - _- -N ACA 63,4-020_________________________________________ _ ~
NACA NACA N ACA N ACA N ACA N ACA N ACA N ACA N ACA NACA NA'CA NACA
63-006 ____ - _______ - - _- - _- - - _- _- - - - - - - - - - - - - - - - - -63-009 __________________________________________ _ 63-010 __________________________________________ _ 631-012 _____________________________ - - __ - _____ - -632-015 _________________________________________ _ 63 3-018 _________________ - _- _- _- - - _- _- - - - - - - - - - - -63c 021 ____________ - _- __ - - - _- _- - - _- _- - - - - - - ___ - -64,2-015 _________________ - ________ .___ - ____ - - ___ -_ 64-006 _____________ - _- ___ - __ - __ - - _- - - - __ - - -'. - - - -64-008 _______________ - ______________ - - ___ " _- __ - -64-009 ______ ._________________________ - _____ - __ - -64-010 .. ____________________________________ - __ - __
70 70 70
71 71
71 72 72 72 73 73 73 74 74 74 75 75 75 76 76 76 77 77 77 78 78 78 79
Page
NACA 641-012 _________________________________________ _ N ACA 6~-015 _________________________________________ _ NACA 643-018 _______________________________ c _________ _ N ACA 644-02L ________________________________________ _ N ACA 65,2-016 _________________________________________ _ N ACA 65,2-02L _______________________________________ _ N ACA 65,3-018_________________________________________ _ N ACA 65-006 ________________ . ________________ .. ________ _ N ACA 65-008 __________________________________________ _ N ACA 65-009 __________________________________________ _ NACA 65-010 __________________________________________ _ NACA 651-012 _________________________________________ _ NACA 652-015 _________________________________________ _ N ACA 653-018 _______________________________________ - __ N A C A 65c02 L ________________________________________ _ N ACA 66,1-012-- _______________________________________ _ N ACA 66,2--015-- ___________ - - ____ - ____ - - ___ - - __________ _ N ACA 66,2-01L _____________________ .__________________ _ NACA 66-006 __________________________________________ _ N ACA 66-008 __________________________________________ _ N A C A 66-009 __________________________________________ _ N ACA 66-010_ _____________ ________________ ___________ _ N ACA 661-012 _________________________________________ _ N ACA 66 2-015 _____________________________ - - __ - _- - __ - __ N A C A 663-018 _________________________________________ _ NACA 66c 02L ____________________________ - ___ - _- - __ - __ N A C A 67,1-01 L _______________________________________ _ NACA 747 AOI5 _________________________________ - _- - ____ _
79 79 80 80 80 81 81 81 82 82 82 83 83 83 84 84 84 85 85 85 86 86 86 87 87 87 88 88
70
REPORT NO. 824--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 2.0 NACA 0006 BASIC THICKNESS FORM X
(percent c)
1.6
-
1.2
(-r;)'
:---r--
-
I-- ::---
0 .li 1.25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80
~
.8 NACA 0006
90
95 100
11 (percent c)
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
(DIV)' 0 .880 1.117 1.186 1..217 1. 225 1.212 1. 206 1.190 1.179 1.162 1.136 1.109 1.086 1. 057 1. 026 .980 .949 0
vlV
I
0 .938 1.057 1.089 1.103 1.107 1.101 1.098 1. 091 1.086 1.078 1.066 1.053 1.042 1.028 1.013 .990 .974 0
AD./V
3.992 2.015 1.364
.984
.696 .562 .478 .378 .316 .272 .239 .189 .162 .123 .097 .073 .047 .032 0
.4 L. E. radius: 0.40 percent c
r---
o NACA 0008 BASIC THlOK;);ESS FORM
x
1.6
(percent 0)
I'
1.2
r--
I
--
~
-,
r-- I--
.8 NACA 0008
.4
0 .5 1.25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100
11 (percent 0) 0
---i:263--1.743 2.369 2.800 3.121 3.564 3.825 3.961 4.001 3.869 3.529 3.043 2.443 1.749 .965 .537 .084
(vi V)'
vlV
d"./F
0 .792 1.103 1.221 1.272 1.284 1. 277 1.272 1. 259 1. 241 1.223 1.186 1.149 1.111 1.080 1.034 .968 .939
0 .890 1. 050 1.105 1.128 1.133 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 .017 .031 0
---
... --------
L. E. radius: 0.70 percent c
V-
.-
I'-..
o NACA 0009 BASIC THlCKXESS FORM
1.6
1.2
x
(
----
(percent c)
(t>fV)'
vlV
Av.IV
- - - - ----- ----0
~
r-- :---
t--
'\
.8
NACA 0009
\
.4
V-
.5 1. 25 2.5 5.0 7.5 10 15 20 25 30
40
50 60 70 80 90 95 100
0
--T42Q--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
L. E. radius: 0.89 percent c
I'---
o
y (percent c)
.6
1.0
0 .750 1.083 1.229 1. 299 1. 310 '1. 309 1. 304 1. 293 1.275 1.252 1.209 1.170 1.126 1.087 1.037 .984 .933 0
0
.866 1.041 1.109 1.140 1.145 1.144 1.142 1.137 1.129 1.119 1.100 1.082 1.061 1.043 1.018 .982 .966 0
0.595 1. 700 1.283 .963 .692 .560 .479 .380 .318 .273 .239 .188 .151 .120 . .095 .070 .046 .030 0
71
SUMMARY OF AIRFOIL DATA. 2.0 NACA 0010 BASIC THICKNESS FORM
x
(per~nt c)
(percent c)
1.6
0
r-- r--
(
--
--
---r---
(';\7I))' .8
......
........
'\\
~----------
1. 578 2.178 2.962 3.500 3.902 4.455 4.782 4.952 5·002 4.837 4.412 3.803 3.053 2.187 1.207 .672 .105
60
70
80
NACA 0010
0
0
.5 1.25 2.5 5.0 7.5 10 15 20 25 30 40 50
90 95 100
(v/V)2
.712 1.061 1. 237 1.325 1. 341 1.341 1.341 1. 329 1. 309 1.284 1. 237 1.190 1.138 1.094 1.040 .960 .925 -----------
--
v/V
I:1v.jV
0 .844 1.0ao 1.112 1.151 1.158 1.158 1.158 1.153 1.144 1.133 1.112 1.091 1.067 1.046 1.020 .980 .962 -----------
2.372 1.618 1. 255 .955 .690 .559 .479 .380 .318 .273 .239 .188 .150 .119 .094 .069 .045 .030 0
.4 L. E. radius: 1.10 percent c
V-
I'---
o NACA 0012 BASIC THICKNESS FORM
1.6
1.2
x
---r--
(
----~
. . . r---
r--
.........
.8
1\
NACA 0012
.4
(perc~nt c)
(percent c)
,,---
0
---i:S94--2.615 3.555 4.200 4.683. 5.345 5.737 5.941 6.002 5.803 5.294 4.563 3.664 2.623 1.448 .807 .126
40
50 60 70 80 90 95 100
vlV
I:1v.IV
0 .640 1. 010 1. 241 1. 378 1. 402 1.411 1.411 1. 399 1. 378 1. 350 1.288 1.228 1.166 1.109 1.044 .956 .906 0
0 .800 1.005 1.114 1.174 1.184 1.188 1.188 1.183 1.174 1.162 1.135 1.108 1.080 1. 053 1.022 .978 .952 0
1.988 1.475 1.199 .934 .685 .558 .479 .381 .319 .273 .~9
.187 .149 .118 .092 .068 .044 .029 0
L. E. radius: 1.58 percent c
c--=:-- .
r'--
0 .5 1.25 2.5 5.0 7.5 10 15 20 25 30
(vi V)'
o
--
1.6
/
I.~
I
NACA 0015 BASIC THICKNESS FORM
r-......
~
r--......
~
~ .........
'1\
.8
\
NAtA 0015
-
- r-----
"--o
.2
(percent c)
----
(ilt
V
u
x
(percent c)
.:rIc
.6
.8
0
0 .5 1.25 2.5· 5.0 7.5 10 15 20 25 30 40 50
---2:367--3.268 4.443 5.250 5.853 6.682 7.172 7.427 7.502 7.254 6.617 5.704 4.580 3.279 1. 810 1. 008 .158
60
70 80 90 95 100 I
L. E. radius: 2.48 percent c
/.0
(vIV) ,
vlV
I:1v.IV
0 .546 .933 1. 237 1.450 1.498 1. 520 1. 520 1.510 1.484 1. 450 1. 369 1. 279 1. 206 1.132 1.049 .945 .872 0
0 .739 .966 1.112 1.204 1. 224 1. 233 1.233 1. 229 1.218 1.204 1.170 1.131 1.098 1.064 1.024 .972 .934 0
1.600 1.312 1.112 .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 2.0 NACA 0018 BASIC THICKNESS FORM
1.6
1.2
c---:-
.~
-.....
(
~
I
,
'" ""-
0
~
t--- -.....
~ I"--..
i !
""'"1\
.8
\'
NACA 0018
.4
,..--
;---
:/
o "'-- r--
/.6
I
t-- r-I-------- r----
-
i
t--- t--
""'" """
I
J ~
~
I, I I
~
~
-
- t--'----
'/ ~
! - -l - -
~ -........
(
'"
""1\ \
----
x
(percent c) 0
.5 1.25 2.5 5 7.5 10 15 20 25 30 40 .10 60 70 80 90 95 100
I
flv.iF
0 .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
0 .682 .926
1. 103 1.228 1. 264 1.276 1. 278 1. 275 1. 262 1. 247 1. 205 1. 15·i 1.116 1. 074 1. 025 .966 .914 0
1.342 1.178 1.028 .86l .662 .55fi
.4i9 .381 .320 .274 .238 .184 .144 .113 .087 .063 .039 .025 0
v/V
(vIF)'
0
0 .. _---------
3.315 4.576 6.221 7.350 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
.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
.397 .787 1.182 1. 543 1.682 1. 734 1. 756 1. 742 1. 706 1.664 1..538 1. 388 1. 284 1.177 1. 055 .916 .801 0
1l.v(dV'
1.167 1. 065 .946 .818 .648 .550 .478 .381 .320 .274 .2.~8
.183 .142 .111 .084 .061 .037 .023 0
L. E. radius: 4.85 percent c
e----
x
~r--~
~
-',! r--...
'"
NACA OON
- ---
1/ ~
~ .'T
zlc
y (percent c)
(V/V)2
----
""-
,
.C
11 (percent c)
;
r--
(percent c)
.8
o
v/v
NACA 0024 BASIC THICKNESS FORM
1.2
.4
I
L. E. radius: 3.56 percent c
~i
I
J
0 ----------2.841 3.922. 5.332 6.300 7.024 8.018 8.606 8.912 9.003 8.705 7.941 6.845 5.496 3.935 2.172 1.210 .189
(v/VP
- - - - - - - - - - - - - .. - -
NACA 0021 BASIC THICKNESS FORM
NACA 0021
/.6
.5 1.25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100
y (percent 0)
l - -i-'-'
.8
o
:
~
1.2
.4
(percent 0)
.6
~
\
\I
'---- r--
f-.-- ~ .8
~ 1.0
0 .5 1. 25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100
0 ________ w
__
3.788 5.229 7.109 8.400 9.365 10.691 11.475 11.883 12.004 11.607 10.588 9.127 7.328 5.247 2.896 1. 613 .252
L. E. radius: 6.33 percent c
0 .335 .719 1.130 1.548 1. 748 1. 833 1.88S 1.871 1. 822 1.777 1. 631 1. 450 1.325 1.203 1. 065 .891 .773 0
I
v/V
fll'./V
0 .579 .848 1. 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
1. 050 .964 .870 .771 . 6.~2 . .142 .470 .383 .321 .274 .238 .181 .140 .109 .082 .059 .035 .022 0
73
SUMMARY OF AIRFOIL DATA
20
NACA 16-006 BASIC THICKNESS FORM
/. 6
x
1/ (percent c)
(pCrcent c)
/. e
- -----..
r
(v)'
\
8 NACA 16-006
0
0 1. 25 2.5 5.0 7.5 10 15 20 30 40 50 60 70 80 90
\
.646 .903 1. 255 1. 516 1.729 2.067 2.332 2.709 2.927 3.000 2.917 2.635 2.099 1. 259 .707 .060
05
100
4
(vIF)' 0 1.059 1. 085· 1. 097 1.105 1.108 1.112 1.116 1.123 1.132 1.137 1.141 1.132 1.104 1. 035 .962 0
vlF 0
1. 029 1. 042
1.047 1. 051 1.053 1. 055 1.057 1.060 1. 054 1. 066 1. 068 1. 064 1. 051 1. 017 .981 0
Av./F 5.471 1. 376 .980 .689 .557 .476 .379 .319 .244 .196 .160 .130 .104 .077 .049 .032 0
L. E. radius: 0.176 percent c
0
NACA 16-009 BASIC THICKNESS FORM
I. 6
1
'V
(percent c)
(perc;nt c)
(vi F) ,
vjF
Av./F
1 - - - - --------1----- -------1-----3.644 o o o o
1.2
1. 25 2.5 5.0 7.5
-- ~
,--
10
\
.8
\
NACA 16-009
I
90 80 95 100
.4
-
t...--
o
15 20 80 40 50 60 70
---
1. 021 1. 053 1. 067 1. 073 1. 076 1. 081 1.085 1. 091 1. 096 1.100 1.106 1. 099 1. 075 1. 022 .969
1. 330
.964 .684 .5M
.475 .378 .319 .245 ,197 .160 .131 .103 .076 .047 .030
L. E. radius: 0.3g6-percent c
J---
NACA 16-012 BASIC THICKNESS FORM
/
(percent c)
-
~
o
~
\
.8 NACA 16-012
.4
---
---' .2
.4
.rIc
.6
.8
\
---
I-
'-......2
o
1.109 1.139 1.152 1.158 1.168 1.177 1.190 1. 202 1.211 1.214 1. 206 1.156 1.043 .939
r---
x
(v)"
1. 042
o o o ---------------------------------- '
u;
I.e
.969 1. 354 1. 882 2.274 2.593 . 3.101 3.498 4.063 4.391 4.500 4.376 3.952 3.149 1. 888 1. 061 .090
1. 25 2.5 5.0 7.5 10 15 20 30 40 50 60 70 80 90 95 100
y (percent c)
o
1. 292
1. 805 2.509 3.032 3.457 4.135 4.664 '5.417 5.855 6.000 5.835 5.269 4.199 2.517 1. 415 .120
(vjF) ,
o
1.002 1.109 1.173 1.197 1. 208 1. 223 1. 237 1. 257 1.271 1. 286 1. 293 1. 275 1. 203 1.051 .908
o
vlF
o
1.001 1. 053 1.083 1. 094 1.099 1.106 1.112 1.121 1.128 1.134 1.137 1.129 1. 097 1. 025 .953
o
"-v.iF 2.624 1. 268 .942 .677 .1)51 .473 .378 .319 .245 .197 .161 .131 .102 .075 .045 .027
o
----------' -----..!.----~--.-------L. E. radius: 0.703 perccnt c
74
_ REPOR'!' NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
'20
NACA 16-015 BASIC THICKNESS FORM
/.6
x
11 (percent c)
(vIV)'
0 1. 25 2.5 5.0 7.5 10 15 20 30
0 1. 615 2.257 3.137 3.790 4. 322 5.168 5,830 6.772 7.318 7.500 7.293 6.587 5.248 3.147 1. 768 .150
0 .956 1.105 1. 200 1.239 1. 256 1. 278 1. 297 1. 327 1. 349 1. 364 1.374 1. 348 1. 254 1,053 .875 0
(percent c)
--'
~t-..
L.--- I--./
1.2
/
(vt
'\
.-
\
.8
40
50
60
'\
70 80 90 95 100
, NACA 16-015
.4
V-
~ I--.
tJ.v.IV
.978 1.051 1.095 1.113 1.121 1.130 1.139 1.152 1,161 1.168 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
0
L. E. radius: 1.100 percent c
r--- r-.... L---V-
~
t'/V
o NACA 16-018 BASIC THICKNESS FORM
/.6
x
11 (percent c)
(v/V) ,
0 1. 25 2.5 5.0 7.5 10 15 20 30 40 50
0 1. 938 2.708 3.764 4.548 5,186 6.202 6.996 8.126 8.782 9.000 8.752 7.904 6.298 3.776 2.122 .180
0 .903 1.09,2 1.217 1.271 1. 302 1. 332 1. 357 1. 399 1. 426 1,447 1. 452 1. 421 1. 306 1. 051 .837 0
(percent c)
/,E
(
/'
,...-
V-
"""
~
\
,
,
\
.8 NACA 16-018
.4
V o
lop
-
I--
\
1--r--..
'--1---
-
60
70 80 90 95
vlV 0 .950 1. 045 1.103 1.128 1.141 1.154 1.165 1.183 1.194 1.203 1. 205 1.192 . 1.143 1. 025 .915 0
tJ.v.IV 1. 744 1.140 .883 .657 .541 .468 .376 .318 .245 .198 .162 .131 .102 .073 .042 .024 0
L. E. radius: 1.584 percent c
V--
.I-- ~
NACA 16-021 BASIC THICKNESS FORM
1.6
!---1.2
I
I---r-
~
1\
7
'\
1\ \
.8 NACA 16-0EI
'"
-
v- L.--f"-- r--
1---:
I-
.2
.4
~/c
.6
x
11 (percent c)
(o/V) ,
vlV
tJ.v.IV
0 1.25 2.5 5,0 7.5 10 15 20 30 40 50
0 2.261 3.159 4.391 5.306 6,050 7.236 8.162 9.480 10.246 10.500 lO,211 9.221 7.348 4.405 2.476 .210
0 .826 1. 062 1.221 1. 295 1. 342 1. 391 1. 419 1. 474 1. 506 1. 535 1. 536 1. 495 1. 361 1.039 .801 0
0 .909 1. 031 1.105 1.138 1.159 1.179 1.191 1. 214 1.227 1. 239 1.239 1. 223 1.166 1.019 .895 0
1. 574 1. 069 .828 .640 .534 .463 .374 .317 .245 .198 .162 .131 .102 .072 .041 .023 0
(percent c)
V
\
i-- r----... !---V
.8
1.0
60
70 , 80
90
95 100
L. E. radius: 2.156 percent c
75
SUMMARY OF AIRFOIL DATA 2. .0
NACA 63,4-020 BASIC THICKNESS FORM
~
I.B
Va
V
V o
~"" ~ ~
/
/ AI/
I
x
~~
-;44 fower surface)
.8
I
~
-.;;;;:
II V V-
I
•••• .c. ".44 (upper surface)
~
/
.2
I
~ -.......::
~
NAOA 63,4-020
- t----r-- r--
I--
'-- r--
~ L--- ~
"
I. 2
ff?'
(VfV)2
vfV
Av.IV
0 .5 .75 1.25 ·2.5 5.0 7.5 10 15 20 25 30 35 40 45
0 1. 714 2.081 2.638 3.606 4.947 5.964 6.800 8.090 9.006 9.630' 9.955 9.978 9.765 9.366 8.819 8.143 7.351 6.464 5.496 4.466 3.401 2.342 1.348 .501 0
0 .444 .605 .820 1.080 1. 277 1. 383 1. 456 1.551 1. 614 1. 659 1. 689 1.630 1.567 1.500 1.433 1. 362 1. 288 1. 213 1.137 1. 059 .978 .896 .811 .728 .651
0 .666' .778 .906 1.039 1.130 1.176 1.207 1.245 1.270 1.288 1. 300 1. 277 1.252 1. 225 1.197 1.167 1.135 1.101 1. 066 1.029 .989 .947 .901 .853 .807
1.395 1.280 1.201 1. 072 .846 .645 .543 .475 .386 .330 .289· .257 .219 .192 .169. .148 .128 •• 112 .097
55 60 65 70 75 80 85 90 95 100
,
.084
.071 .059 ;046 .036 .023 O·
NACA63-006 BASIC THICKNESS FORM
~-, [""
1/
L. E. radius: 3.16 percent c
~
_.cz =.03 (upper surface)
,,0
(percent c)
50
I .0
I
(percent c)
"
I
~
-:03 (lower surface)
roo-
..........
r---.
B NACA 63-006
4 i..--
x (percent c)
(per~nt c)
(vi V) ,
.IV
A••IV
0 .5 .75 1. 25 2.5 5 7.5 10 15 ·20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 109
0 .503 .609 .771 1.057 1.. 462 1.766 2.010 2.386 2.656 2.841 '2.954 3.000 2.971 2.877 2.723 2.517 2.267 1.982 1.670 1. 342 1. 008 .683 .383 .138 0
0 .973 1.050 1. 080 1.110 1.130 1.142 1.149 1.159 1.165 '1.170 1.174 1.170 1.164 1.151 1.137 1.118 1.096 1. 074 1.046 1.020 .. 994 .965 .936. .910 .886
0 .986 1.025 1.039 1.054 1. 063 1.069 1.072 1.077 1. 079 1.082 1.084 1.082 1.079 1.073 1.066 1.·057 1.047 1.036 1. 023 1.010 .997 .982 .967 .954 .941
4.483 2.110 1.778 1. 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
0 NACA 63-009 BASIC T1HCKNESS FORM
x
(perc~nt c)
0
0 .749 .906 1.151 1.582 2.196 2.655 3.024 3.591 3.997 4.275 4.442 4:500 4.447 4.296 4.056 3.739 3.358 2.928 2.458 '1.966 1.471
(percent c)
(·fV)'
vlV
Av.IV
0 .941 1.001 1. 025 1.063 1.086 1.098 1.105 1.114 1.120 1.124 1.126 1.125 1.120 1.111 1.099 1.084 1.068 1.051 1.032 1.012 :992
3:058 1. 889 1.647 .1.339 .961 .689 .560 . .484 .386 .324 .281 .248 .220 .196 .175 .156 .140 .124 .109 .095 .082 .069 .057 .044 .• 030' 0
1.6
1.2
'I;<-
,,
",,,, ...
c, =.08 (upper surface)
~
1 0 ...
V
---.08 (lower. surface).
(vt
I
-..;;:::
.5
~~
.75 1.25 2.5 5 7.5
10
"'-
.8 NACA 8:1"'009
""
.4 I..---:
~
o
.2
.4
.¥<Ic
.6
.8
/.0
15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
.990
.550 .196 0
. L. ,E. radius: 0.631 percent c
0
.885
1.002 1.051 1.130 1.180 1.205 1. 221 1. 241 1.255 1.264 1.269 1. 265 1. 255 1.235 1.208 1.175 1.141 1.104 1.065 1.025 .984 .942 .903 .868 .838
.971
.950. .932 .915
76
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS NACA 63-010 BASIC THICKNESS FORM
.6°= ~[TII 1,- L.) .. ~j-
----- I - - ..--. - -
.--~ . -.-----.-
2.
/ ' .c, =.10 (upper surface)
,
2
~t•. /)'
I.
1
'(/.~-.!o I
\~-
--~::::::::.....
(°'>--
10wer I'
surfacel--":::::::::~~· --.-------... ) ~
~-~L- ~r'
1/ 8
r
~~
I
-
1---+-----1----1--- NACA 83-010··-+---1---1----1
I
.4r--+~4--~_4--!~_+-~-~_+-~
z
'1/
(peJ'cent c)
(percent c)
(VIV)2
vfV
I
"'v.IV
- - - - ----- ------ ------ ------' 0
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 80 85 90 95 100
.829 1.004 1. 275 1. 756 2.440 2.950
3.362 3.994 4.445 4.753 4.938 5.000 4.938 4.7GG 4.496 4.140 3.715 3.234 2.712 2.166 1. 618 1.088 .604 .214 0
0 .841 .978 1. 037 1.131 1.193 1.223 1.245 1. 270 1. 285 1. 295 1.302 1. 299 1. 286 1.2G2 1. 231 1.193 1.154 1.113 1. 069 1. 025 .979 .935 .893 .853 .822
2.775 1. 825 1. 603 1.316 .952 .687 .500 .484 .386 .325 .2S2 .218 .220 .196 .175 .156 .139 .123 .108 .094 .081 .069 .056 .043 .030 0
0 .917 .989 1.018 1.063 1.092 1.10() 1.116 1.127 1.13~
1. 138 1.141 1.140 1.134 1.123 1.110 1.092 1. 074 1.055 1.034 1. 012 .989 .967 .945 .924 .907
L. E. radius: 0.770 percent c Or-~--_+---L·-~---L--~--~--+_--~~
NACA 63,-012 BASIC THICKNESS FORM Z
I.B
----=
_--------C', :./4 (upper
V0/ K:', ---
U?
(vl 1/1/
---
-t3::=:
"-.14 fower
surface)
~
,
surface)-........:::~ ~
--..::::
.8
..........
'1/
(percent c)
(percent c)
0 .5 .75 1. 25 2.5 5 7.5 10 15 20 25 30 35 40 45
0 .985 1.194 1.519 2.102 2.925 3.542 4.039 4.799 5.342 5.712 5.930 6.000 5.920 5.704 5.370 4.935 4.420 3.840 3.210 2.556 1. 902 1. 274 .707 .250 0
50
.4
r.---
-
-r'--
'--'--0
I---
vfV
I
",v.IV
-.---.
55 60 65 70 75 80 85 90 95 100
NACA 63,-012
(VIV)2 0 .750 .925 1.005 1.129 1. 217 1. 261 1. 294 1.330 1. 349 1. 362 1.370 1. 366 1. 348 1. 317 1. 276 1. 229 1.181 1.131 1.076 1. 023 .969 .920 .871 .826 .791
2.336 1.695 1. 513 1. 266 .933 .682 .559 .484 .387 .326 .283 .249 .221 .195 .174 .155 .137 .121 .106 .091 .079 .067 .055 .042 .029 0
0 .866 .962 1.003 1.063 1.103 1.123 1.138 1.153 1.161 1.167 1.170 1.169 1.161 1.148 1.130 1.109 1.087 1.063 1.037 1. 011 .984 .959 .933 .909 .889
-------------~----------------
L. E. radius: 1.087 percent c
NACA 632-015 BASIC THICKNESS FORM
/.8
-
f
.........
......-- ..-1.2
(vi .8
I
i/ I
/
--.
._._-
0
---------r-=:~ ~ ~
/---.22 fower surface)
~
--
~
~
1----..
. -'---.-
~
'&.
.........
.4
/ -~
--1----1--
'-r-.. 0
.2
(percent c) 0
-_.-.
1
x
__ .c, =.22 (upper surfaoe)
.5 . 75 1. 25 2.5 5 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
'II
!
(percent c) 0 1.204 1. 462 1. 878 2.610 3.648 4.427 5.055 6.011 6.693 7.155 7.421 7.5CO 7.386 7.099 6.665 6.108 5.453 4.721 3.934 3.119 2.310 1. 541 .852 .300
0
L. E. radius: 1.594 percent c
.4
.rIc
.8
.8
1.0
(V/V)2
vlV
0
0
· 600 · 822 · 938 1.105 1. 244 1. 315 1.360 1.415 1. 446 1.467 1. 481 1.475 1. 446 1.401 1. 345 1.281 1. 220 1.155 1.0.85 1.019 .953 .894 .839 .789 .750
· 775 · 907 · 969 1. 051 1.115 1.147 1.166 1.190 1.202 1.211 1. 217 1. 214 1. 202 1.184 1.160 1.132 1.105 1.075 1.042 1.009 .976 .946 .916 .888 .866
I
I
",v.IV 1. 918 1. 513 1. 379 1.182 .903 .674 .557 .484 .388 .330 .286 .251 .222 .196 .174 .153 .135 .118 .102 .088 .076 .063 .051 .039 .026 0
77
SUMMARY OF AIRFOIL DATA 2.0
NACA 633-018 BASIC THICKNESS FORM ,
/,c,
~.32
( C(
...--
V
I V'"/ / ' I/ I I
-........
""~ ~
""~
.8
~~
I
.4
,~
1.6
(v) .8
.4
V
./
o
=.38 (upper
~ '" ~ ~
~
,-
NACA 634 -021
---:::
V-
~t---..
--
~
~
~ r---
I---
(vfV) ,
0
.441 .700 .848 1. 065 1. 260 1.360 1. 424 1. 500 1. 547 1. 579 1. 598 1. 585 1. 550 1. 490 1.411 1.330 1. 252 1.170 1. 087 1. 009 .933 .868 .807 .753 .712
y
o
o
.5 .75 1. 25 2.5 5 7.5 10 15 20 25 30 35 40 45
.275 .564 .725 1.010 1. 260 1.394 1. 487 1. 592 1.655 1.698 1. 721 1. 709 1.654 1. 578 1.479 1.380 1. 281 1.180 1.084 .994 .911 .839 .774 .721 .676
1. 583 1. 937 2.527 3.577 5.065 6.182 7.080 8.441 9.410 10.053 10.412 10.500 10.298 9.854 9.206 8.390 7.441 6.396 5.290 4.160 3.054 2.021 1.113 .392
no
55 60 65 70 75 80 85 90 95 100
o
j..--
L.--- ~
(II/V)'
(percent c)
o
~~
-.38 dower surface)
0 1. 404 1. 713 2.217 3.104 4.362 5.308 6.068 7.225 8.048 8.600 8.913 9.000 8. 845 8.482 7.942 7.256 6.455 5.567 4.622 3.650 2.691 1. 787 .985 .348 0
x (percent c)
surface)
""
.-- ..........
V
I / I II'" / I I V
/c,
0
c)
I
vfV
tl.v./V
I- - - - - -
0 .664 .837 .921 1. 032 1.122 1.166 1.193 1. 225 1. 244 1. 257 1. 264 1. 259 1. 245 1. 221 1.188 1.153 1.119 1. 082 1.043 1.004 .966 .932 .898 .868 .844
1.639 1. 361 1. 258 1.105 .871 .663 .553 .484 .390 .333 .289 .253 .223 .197 .173 .152 .133 .115 .099 .084 .072 .059 .048 .036 .024 0
NACA 63,-021 BASIC THICKNESS FORM I
,,"\
I (percent I
L. E. radius: 2.120 percent c
l..---
t--
~~ ''/
1.2
- r-- I--- -
~
a
"
t---- r--
/
I
~
NACA 63.-018
f.--
V o
~
y
(percent c) .5 .75 1. 25 2.5 5 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
~
'.32 dower surrace)
(~r
x
~
1.6
1.2
(upper surfaco)
v/V
o
.524 .751 .851 1.005 1.122 1.181 1. 219 1. 262 1. 286 1.303 1. 312 1.307 1. 286 1. 256 1. 216 1.175 1.1~2
1.086 1. 041 .997 .954 .916 .880 .849 .822
d •• /V 1. 439 1. 236 1.156 1.034 .842 .653 .550 .484 .392 .335 .291 .255 .225 .198 .173 .150 .130 .1l2 .096 .081 .068 .057 .046 .035 .023
o
L. E. radiu.: 2.650 percent c
NACA 64,2-015 BASIC THICKNESS FORM
1.0 ~
-
/ /'" V /
1.2
// .8
__ c z =.20 (upper surface)
,,
x c) . (percent
~~ ~~ ~~
0
~
-.20 fower surface) I
~~
I
~
I
" '"
NACA 64,2-015
.4
'-V-
o
-
l--.2
.4
.8
I
y (percent
(v/l')'
c)
v/v
tlv./v
- - - - - --------- -------- - - - - - - -------
--
:-~
.8
1.0
.5
.75 1. 25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 . 100
0 1.216 1.453 1. ~29 2_ 538 3.514 4.243 4.838 5.781 6.464 6.967 7.307 7.481 7.480 7.268 6.850 6.311 5.670 4.944 4.158 3.338 2.506 1. 698 .961 .351 0
.
L. E. radius: 1.65 percent c
0
0
.710 .825 .962 1. 122 1. 234 1. 288 1. 323 1.371 1.401 1. 422 1. 441 1. 458 1.471 1.432 1. 366 1. 299 1. 234 1.16R 1.102 1·039 .973 .910 .849 .791 .739
.843 .908 .981 1.059 1.111 1.135 1. 150 1.171 1.184 1.192 1. 200 1. 207 I. 213 1.197 1.169 1.140
1.111
1. 081 1.050 1.019 .986 .g54 .921 .889 .860
1. 930 1500 1. 359 1.161 .911 .678 .553 .477 .383 .325 .285 .253 .227 .202 .175 .156 ; 137 .122 .102 .086 .080 .071 .056 .039 .027 0
78
HEPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS NACA 64-006 BASIC THICKNESS FORM
20 x
1.6
1.2
,
(ill V
----- --
.. .' .. --- (:, ... 02 (upper surface)
,,0
~
I
...... ~ ..
--.02 (lower surrace)
.8
r--.
(percent c)
(pertent c)
0 .5 .75 1.25 2.5 5.0 7.5 10 15 20 25 30 35 40 45
0 .494 .596 .754 1.024 1.405 1.692 1. 928 2.298 2.572 2.772 2.907 2,981 2.995 2.919 2.775 2.575 2.331 2.050 1.740 1. 412 1.072 .737 .423 .157 0
50 55
'50
65 70 75 80 85 90 95 100
NACA 84-008
.4
(ofV) ,
ofV
t;.o./V
0 .995 1.058 1.085 1.108 1.119 1.128 1.134 1.146 1.154 1.160 1.164 1.168 1.171 1.160 1.143 1.124 1.102 1.079 1.0M 1.028 1.000 .970 .939 .908 .876
0 .997 1.029 1.042 1.053 1. 058 1.062 1.065 1.071 1. 074 1.077 1. 079 1.081 1.082 1.077 1. 069 1.060 1. 050 1.039 1.027 1. 014 1.000 .985 .969 .953 .936
4.623 2.175 1. 780 1.418 .982 .692 .560 .483 .385 .321 .279 .246 .220 .198 .178 .158 .142 .126 .112 .098 .085 .072 .060 .047 .031 0
L. E. radius: 0.256 percent c
o NACA 64-008 BASIC THICKNESS FORM
1.6
.. -
,.0 12
____ c, :.04 (upper surface)
~-
;
f? ~
~ -----.04 {ower surface ~
~
.8
~ ............
NACA 84~OO8
.4
-"........
o
x (percent c)
11 (percent c)
(vfV) ,
v/V
t;.o./V
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 SO 85 90 95 100
0 .658 .794 1. 005 1. 365 1.875 ,2.259 2.574 3.069 3.437 3.704 3.884 3.979 3.992 3.883 3.684 3.411 3.081 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. 225 1.230 1. 235 1. 220 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~ 080 1.086 1. 093 1. 099 1.103 1.107 1.109 1. 111' 1.105 1. 091 1.078 1. 064 1. 050 1. 034 1. 016 .997 .978 .958 .937 .916
3.M4 1. 994 1. 686 1. 367 .969 .688 .560 .480 .385 .323 .279 .246 .220 .198 .176 .158 .141 .125 .110 .096 .083 .071 .059 .046 .031 0
L. E. radius: 0.455 percent c
NACA 64-000 BASIC THICKNESS FORM
x
1.6 ,
,0 1.2
(vY
, , .. ---
----c,=.06 (upper surroC'e)
:
/7
V
.J
~ :::,...
~- --coe
(ower
sur~~
----+=i--
.8
--
~
I ' ............
NACA 84-009
'.4 t..---"
r-o
.2
.6
.8
·1.0
(percent c)
(percent c)
11
(v/V)'
v/V
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 80 85 90 95 100
0 .739 .892 1.128 1. 533 2.109 2.543 2.S98 3.455 3.S68 4.170 4.373 4.479 4.490 4.364
0 .872 .990 1. 075 1.131 1.166 1.186 1.200 1. 221 1. 236 1.246 1. 255 1.262 1.267 1.246 1. 217 1.183 1.149 1.112 1.073 1.033 .992 .950 .907 .865 .822
0 .934 .995 1.037 1.063 1.080 1.089 1. 095 1.105 1.112 1.116 1.120 1.123 1.126 1.116 1.103 1.088 1.072 1.055 1.036 1.016 .996" .975 .952 .930 .907
4.1~6
3.826 3.452 3.026 2.561 2.069 1. 564 1.069 .611 .227 0
L. E. radius: 0.579 percent c
t;.v.IV 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
I
79
SUMMARY OF AIRFOIL DATA
1'. 0
NACA 64-010 BASIC THICKNESS FORM
x
,.
,-cz "'.08 ~
I. ZO.
K __
V f
---
(upper surface)
,
~~-..:::::
--.08 (lower svrface)
~~
f'
\
8
NACA 64-010
"
.,.
-
L.----
I'--
(percent c)
0
0 .820 .989 , 1.250 1.701 2.343 2.826 3:221 3.842 4.302 4.639 4.864 4.980 4.988 4.843 4.586 4.238 3.820 3.345 2.827 2.281 1.722 1.176 .671 .248 0
.5 .75 1.25 2.5 5 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
/. 6
(vI V)' 0
.834 .962 1.061 1.130 1.181 1.206 1.221 1.245 1.262 1.275 1.286 1.295 1.300 1.279 1.241 1.201 1.161 1.120 1.080 1.036 .990 .944 .900 .850 .805
vlV 0
.913 .981 1.030 1.063 1. 087 1.098 1.105 1.116 1.123 1.129 1.134 1.138 1.140 1.131 1.114 1.096 1.077 1.058 1.039 1.018 .995 .972 .949 .922 .897
Av.IV 2.815 1.817 1. 586 1.313 .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
0
NACA 641-012 BASIC 'rHICKNESS FORM
x (percent c)
,
/. {)
-I /,c, =./Z (upper surfaoe)
/.2
II
(percent c)
~V
~ -....:
---
~
-(/
~
K_';12 (lower surface)
~~
r
8 (
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 80 85
,
~~
NAOA 041 -012
--
,--e---..:...
90
95 100
(percent c)
11
(vI V)'
V/V
t.v./V
0 .978 1.179 1.490 2.035 2.810 3.394 3.871 4.620 5.173 5.576 5.8# 5;978 5.981 5.798 ,5.480 5.056 4.548 3.974 3.350 2.695 2.029 1.382 .786 .288 0
0 .750 .885 1.020 1.129 1.204 1.240 1. 264 1.296 1.320 1.338 1.351 1.362 1.372 1.335 1.289 1.243 1.195 1.144 1.091 1.037 .981 .928 .874 .825 .775
0 .866 .941 1.010 1.063 1.097 1.114 1.124 1.139 1.149 1.156 1.162 1.167 1.171 1.156 1. 136 1.115 1.093 1.070 1.044 1. 018 .990 .963 .935 .908 .880
2.379 1. 663 1. 508 1.271 .943 .685 .569 .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
o NACA 64.-015 BASIC THICKNESS FORM
1."6
.8
I
--
I- /-- V--V ,,/
/.2
x
'~ZZ
/
~KA
~
...........
NACA 642 -015
.4 ~
'-- r-.-.... o
~~
" ~~
II
~
x.c2 (upper surface)
~~
(lower surface)
I
-- - ~
.2
.4
(percent c)
(percent c)
"
(oJV)'
vlV
Av./17
0 .5, .75 1. 25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 56 60 65 70 75 80 85, 90 95 100
0 1.208 1.456 1.842 2.028 3.004 4.240 4.842 5.785 6.480 6.985 7.319 7.482 7.473 7.224 6.810 6.266 5.620 4.895 4.113 3.296 2.472 1.677 .950 .346 0
0 .670 .762 .896 1.113 1.231 1;284 1.323 1.375 1.410 1.434 1.454 1.470 1.485 1.426 '1.365 1.300 1.233 1.167 1.101 1.033 .967 .902 .841 .785 .730
0 .819 .873 .947 1.055 1.109 1.133 1.150 1.172 1.187 1.198 1.206 1.213 1.218 1.195 1.168 1.140 1.110 1.080 1.049 1.016 .983 .950 .917 .886 .855
1.939 1.476 1.354 1.188 .916 .'670 .559 .482 .389 .326 .285 .250 .225 .202 ' .179 .158 .135 .121 .105 .090 .078, .065 .054 .041 .031 0
/
.6
~
.8
/.0
L. E. radius: 1.590 percent c
80
REPORT NO. 824-NATIONAL ADVISORY COMMI'fTEE FOR AERONAUTICS NACA 613-018 BASIC THIOKNESS FOJlM
2.0
---,---------------. (perc~nt c) I
l~c,=.3e (upper surface) 1.6
/" /.2
.8
--
V
fr
7 v'-I ./
/f--. ~
o
~
~
-
- ------
r--
1\
----~\
/
V
V
/ 1/,
t---
I---
_..
( /0
II
V /'
--
V
,"'..
,......-
V-
v<_. __ --.20 fower
~
surface)
~
=f
~
"~
8 '(
~
65 70 75 m 85 90 95 100
J-- t--.
o
.C'
.4
.6 a:>/C
.m
.m
.~
.937
.051
.•
.~
.747 .695
.864 .834
0
.027
0 1.646 1. 985 2.517 3.485 4.871 5.915 6.769 8.108 9.095 9.m7 10.269 10.481 10.431 ]0.030 9.404 8.607 7.678 6.649 5.549 4.416 3.287 2.213 1. 245 .449 0
1~=-I_~l_'T__ '-_ tJ.".:__ I o
0
. 462 . 603 .759 1.010 1. 248 1. 358 1. 431 1. 527 1. 593 1. 654 1. 681 1. 712 1. 709 1.607 1. 507 1.406 1.307 1. 209 1.112 1.020 .932 .851 .778 .711 .653
. 680 . 776 .871 1.005 1.117 1.165 1.196 1.236 1. 262 1. 281 1. 297 1.308 1.307 1. 268 1. 228 1.186 1. 143 1.099 1.055 1.010 .965 .923 .882 .844 .808
I,
1. 458 1. 274 1. 203 1.084 .878 .665 . .157 486 .395 .335 .293 .259 .232 .202 .178 .IM .134 .116 .099 .084 .071 .059 .047 .036 .022 0
c)
0
. ,)
I---
.75 1. 25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
.-
1.0
65,2-016 BASIC THICKNESS FORM
(perc~~t I (perc~nt I
t--.
.8
I
(percent c)
c)
(l>jl')'
I
tJ.v.IV
- - - - - - - - - - - - - - - - - - - - -------
1--~ ~
~ t---
. 200 .177 .154 .134 .117 .102 . 088 .071
.879
.400
~ACA
NAGA 65, 2-0/6
~
1. 265 1. 232 1.198 1.164 1.128 1. 091 1. 053 1. 014
L. E. radius: 2.884 percent c
4
V
1.646 1.360 1. 269 1. 128 .904 .669 .558 . 486 .391 .331 .288 .255
.m
y
I
I
60
""""-
f
0
.5 .75 1. 25 2.5 .0;.0 7.5 10 15 20 25 30 35 40 45 50 55
J-- ~ ~
~
.•
1. 951
l.m
:r (percent c)
___ c,= .20 (upper surface) I---
~
I..
~~
.739 .840 .920 1. 039 1.115 1.152 1. 17.5 1. 204 1. 224 1. 239 1. 250
I L. E. radius: 2.208 percent c
,
~
1. 600 1.518 1. 436 1. 354 1.272 1.190 1. 109 1. 028
&m
95 100
1----1---!-.
..
!6
1.~
8. 952 8.630 8.114 7.445 6.658 5.782 4. 842 3.866
tJ.v.IV
NACA 64.-021 BASIC THICKNESS FORM
~~
- r--
~
~o
M 40 45 50 55 60 65 70 75
90
I--
.-- I-'-NAGA 64,-02/
L V
0
.546 .705 . 862 1. 079 1. 244 1. 327 1. 380 1. 450 1. 497 1. 535 1. 562
,
~
I.
viI'
0
0
--·.44 (lower surface)
(v/V)'
0 1.428 1. 720 2. 177 3.005 4.186 5.076 5. 803 6.942 7.782 8.391 8. 7R9
85
K,:·c,=.44 (upper surface)
/
'0
~
I
.5 .75 1. 25 2. 5 5.0 7.5 10 15 20 25
m
~~
~
1.2
~
"" ~'\
~
/
/0
.8
~
- --r---- -
.-.
-
(
..4
~~
-NACA 643 -0/8
.4
1.2
~~
----.32 ~ower surface)
7
1.6
o
--- ~ ~ '"'-....
V
(pergent c)
0 1. 202 1. 423 1. 796 2.507 3.543 4.316 4.954 5.958 6.701 7.252 7.645 7.892 7.995 7.938 7.672 7.184 6.495 5.647 4.713 3.738 2.759 1.817 .982 .340
I
0
L. E. radius: 1.704 percent c
I
0
.560 .690 .812 1. 068 1. 217 1.287 ·1.328
~1.379
'1. 409 1. 433 1. 453 1. 469 1.484 1. 497 1. 491 1. 421 1.328 1. 235 1.147 1.05fi .970 .886 .816 .769 .733
0
.748 .831 .918 1. 033 1.103 1.134 1.152 1.174 1.187 1.197 1. 205 1. 212 1. 218 1. 224 1. 221 1.192 1.152 1.111 1.071 1.028 .985 .941 .903 .877 .856
1. 950 1. 650 1. 500 1. 275 .920 .680 .545 .480 .390 .325 .285 .255 .225 .200 .180 .160 .140 .125 .110 .095 .080 .066 .050 .040 .025 0
81
SUMMARY OF AIRFOIL DATA 2
NACA'
.0 x (percent c)
~- C', =.2 (uPper surface)
-~
",.-
/
.6
l.---
0-_
V V
v--
~
/
/ 1/
I.2
.8
- '---.2 fower sur'fqce)
t\
~
~
I
~
~
If '/
~
'"~
NACA 65,2-023
4
V
----
V
~
~r0
I---
c.---
~
y, (percent c)
(vIV)2 0
0 1. 664 2.040 2.628 3.715 5.300 6.478 7.433 8.889 9.917 10.648 11.142 11.423 11.499 11.361 10.949 10.179 9.108 7.848 6.461 5.015 3.618 2.345 1.258 .439 0
.400 .500 .682 .943 1. 232 1.375 1.467 1. 577 1.628 1. 655 1. 677 1.694 1. 708 1.716 1. 712 1.606 1.428 1. 274 1.135 1. 003 .893 .803 .732 .682 .651
vlV
Ilv';v
0 '.632 .707 .826 .971 1.110 1.173 1.211 1. 256 1. 276 1. 286 1.295 1. 302 1. 307 1.310 1. 308 1. 267 1.195 1.129 1. 065 1.001 .945 .896 .856 .826 .807
1. 414, 1. 161 1. 084 .967 .811 .633 .539 .479 .380 .324 .281 .247 .220.
I
.198 .178 .161 .147 .110 .096 .093 .080 .053 .035 .022 .018 0
L. E. radius: 2.955 percent c
x (percent c)
I
1/
(percent c)
(vIV)2
v/V
1l".IV
0 .650 .,750 .872 1.020 1.179 1.263 1.320 1.393 1.439 1.473 1.502 1.526' 1. 546 1. 562 1.513 1.433 1.348 1. 258 1.169 1.079 .992 .905 .818 .738 .658
0 .806 .866 .934 1. 010 1.086 1.124 1.149 1.180 1.200 1.214 1.226 1. 235 1.243 1. 250 1.230 1.197 1.161 1.122 1.081 1. 039 .996 .951 .904 .859 .811
1.750 1.387 1.268 1.108 .800 .677 .568 .489 .395 .334 .292 .260 .232 .209 .186 .165 .142 .123 .107 .093 .080 .066 .054 .040 .024 0
_._-(!,=.32 (upper surface)
1 I. 8 /
.. --0 ~
/
c7
! 1/
'{ .8
-
.5 .75 1. 25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85, 90 95 100
BASIC THICKNESS FORM
NACA 65,3-Q18 BASIC THICKNESS FORM
.'
1.2
0
I
65,2-02.~
/
~~
~
~~
/
~
----:32 (lower surface)
/
I I
~
~
"~
"-
NACA 65,3-018
- --
--
I'--.r---to
-~
~
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 80 85 90
95
r---
100
~
0 1.324 1. 599 2.004 2.728 3.831 4.701 5.424 6.568 7.434 8.093 8.568 8.868 8.900 ' 8.916 8.593 8.045 7.317 6.450 5.486 4.456 3.300 2.325 1.324 .492 0
L. E.'radius: 1.92 percent
c
NACA 65-Q06 BASIC THICKNESS FORM
x
(percent c)
/6
0
____ .(!,=.Ol (upper surface) ,-
.--0
~
--- -- -
~
---~O/
I """'" fower,surface)
r=-r--..
~
~
.8 NACA65-00B
A
.5 .75 1.25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 00 95 100
11 (percent c) 0
.476 .574 .717 .956 1.310 1.589 1.824 2.197 .2.482 2.697 2.852 2.952 2.998 2.983 2.900 2.741 2.518 2.246 1.935 1.594 1.233 .865 .510 .195
o.
L. E. radius: 0.240 percent c
o
.2
.4
.0
.8
1.0
(v/l?)'
"IV
I!.v.IV
0 1. 044 1.055 1.063 1. OSI 1.100 1.112 1.120 1.134 1.143 1.149 1.155 1.159 1.163 1.166 1.165 1.145 1; 124 1.100 1. 073 1.044 1.013 .981 .944 .002
0 1.022 1.027 1.031 1.040 1.049 1.055 1.058 1. 065 1.069 1.072 1.075 1.077 1.078 1.080 1.079 1.070 1.060 1.049 1.036 1.022 1.006 .900 .972 .950 .926
4.815 2.110 1.780 1.300 .965 .695 .560 .474 .381 .322 .281 .247 .220 .198 .178 .160 .144 .128 .114 .100 .086 .074 .060 .046 .031 0
.858
82
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS NACA 65-008 BASIC THICKNESS FORM
200 x
1.6
1.2
.c, "'.04 (upper surf'ace)
~
r.-
V
'.
I~
"":0+ (lower surface)
~
~
...........
.8
~
NACA 65-008
(percent c)
(percent c)
11
(vfV)'
0 .5 .75 1.25 2.5 5.0 7.5 10 15 20 25 30 35
O· .627 .756 .945 1. 2t17 1.745 2.118 2.432 2.931 .3.312 3.599 3.805 3.938 3.998 3.974 3.857 3.688 3.337 2.971 2.553 2.096 L617 1.131 .664 .252 0
0 .978 1.010 1.043 1. 08t1 1.125 1.145 1.158 1.178 1.192 1.203 1. 210 1.217 1.222 1.226 L222 1.193 L 168 1.130 1.094 1.055 1.014 .971 .923 .873 .817
40
45 50 55 60 65 70 75 80 85
90
·4
.95 100
I
v/V
AV./V
0 .989 1.005 1. 021 1. 042 1. 061 1. 070 1. 07t1 1.085 1. 092 1.097 1.100 1.103 1.105 1.107 1.105 1.092 L078 1.068 1.046 1.027 1.007 .985 .961 .934 .904
3.695 2.010 1.61ltl 1. 340 .95t1 .689 .560 .477 .382 .323 .281, .248 .221 .199 .178 .160 .145 .128 .113 .098 .084 .012 .059 .044 .031 0
.,-
r--
L. E. radius: 0.434 percent c
o
NACA 65-009 BASIC, THICKNESS FORM
x
(percent c)
,1.6
.()
:'c, =.06 (upper surf'ace) , O.
1.2
---
K. '1/ If
~
.. ·.06 (lower 8urrace)
~
.8
"""~
45
50 55
60
NACA 65-009
.4
.5 .75 L25 2.5 5.0 7.5 10 15 20 25 30 35 40
65 70 75 80 85
--
90
95 100
....-
1/
(percent c) 0
.700 .845 1.058 1. 421 1. 961 2.383 2.736 3.299 3.727 4.050 4.282 4.431 4.49t1 4.469 4.336 4.086 3.743 3.328 2.856 2.342 1.805 1.260 .738 .280 0
vlV
(v/V)' 0
Av./V
0
.945 .985 L037 L089 1.134 1.159 L 177
3.270 1.962 1. 655 1. 315 .,950 .687 .560 .477 .382 .323 .280 .248 .220 .198 .178 .160 .144 '.128 .111 .097 .084 .071 .051l .044 ..030 0
.1l12 .992 L018 L044 1.065 1.077 1.085 1.095 1.103 L 109 L113 1.116 1.119 L 122 1.118 L 105 L089 L070 L050 L029 l.ootl .981 .955 .925 .898
1.200
1. 216 L229 1.238 1.246 1.252 L258 1. 250 L220 L185 1.145 L 103 1.059 1. 013 .968 .912 .856 .797
I--
o
L. E. radius: 0.552 percent c
NACA 6lHl10 BASIC THICKNESS FORM :&
1.6
(/ -
,ie, =.08 (upper surface) :
O.
I.e Ir-t
(vr
~
!--
~
\08 (lower surra'ce)
~
r( .8
~
"'- ~
(perJnt c)
(vi V)'
0
0 .772 .932 1.169 1.574 2.177 2.647 3.040 3.666 4.143 4.503 4.760 4.924 4.996 4.968 4.812 4.530 4.146 3.682 3.156 2.584 1.987 L3g5 .810 .306 0
0 .911 .960 1. 025 1.086 1.143 1.177 1.197 1.224 1.242 1.257 1.268 1.277 1.284 1.290 1.284 1.244 1.202 1.158 1.112 1.062 1.011 .958 .903 .844 .781
.5
.75 L25 2.5 5.0 7.5 10 15 20 25 30 35
40
45 50 55 60 85 70 75 80 85
NACA 65-010
90
VI'--
o
(percent c)
95 100
.Z
.4
.6
.8
/.0
L. E. radius: 0.!l87 percent c
I
v/V 0 .954 .980 1.012 1.042 1.069 L085 1.094 1.106 1.114 1.121 1.126 1.130 1.133 1.136 1.133 I.U5 1.096 1.076 1.055 1.031 L005 .979 .1l50 .919
.884
I
Av./V 2.967 1.911 1.614 1.292 .932 .679 .558 .480 .383 .321 .280 .248 .222 .199 .179 .160 .141 .126 ; 110 .097 .082 .070 .058
.045
.030
0
83
SUMMARY OF AIRFOIL DATA
.
2.0
x
/.6
--,,~--
1.2
----c, ... 12 (upper surface)
r- ~ e---V_
I{/
(vt I(
~~
~
--olE (lower surface)
~
.8 NACA 65,-012
"
i'-..
"
(percent c)
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 80 85
0 .923 1.109 1.387 1.875 2.606 3.172 3.647 4.402 4.975 5.406 5.716 5.912 5.997 5.949 5.757 5.412
95 100
~-
l--- e--
I
vlV
!;v.IV
0
0
.848 .935 1.000 1.082 1.162 1. 201 1.232 1.268 1.295 1.316 1.332 1.343 1. 350 1. 357 1.343 1. 295 1.243 1.188 1.134 1.073 1.010 .949 .884 .819 .748
.921 .967 1.000 1.040 1. 078 1. 096 1.110 1.126 1.138 1.147 1.154 1.159 1.162 1.165 1.159 1.138 1.115 1. 090 1.065 1. 036 1.005 .974 .940 .905 .865
2.444 1.776 1.465 1.200 .931 .702 .568 .480 .389 .326 .282 .251 .223 .204
.188 .169 .145 .127 .111 .094 .074 .062 .049 .038 .025 0
NACA 60',-015 BASIC THICKNESS FORM
x (percent c)
.. --- ___ c,=.22 (upper surface)
'f
(
-
~
~
f-"'
V
v-
~
~
........
0
~
- ~~
~
--.22 (lower surfac~
I
/
~
'"
NACA 65.-015
-.---r--
.4
I--
/
~
r-- r--
f..--
y
(percent c)
(vi V)'
!;v~IV
vlV
- - - - ----- ----- ------ ------
I.B
o
4.943
4.381 3.743 3.059 2.345 1.630 .947 .356 0
(vIV) ,
L. E. radius: 1.000 percent 'c
o
.8
I
-I-
r---- '----
/.2
II
(percent c)
90
.4
NACA 65!-012 BASIC THICKNESS FORM
r--
.5 .75 1. 25 2.5 5.0 7.5 10 15 20 25 30 35 40' 45 50 55 60 65 70 75 80 85 90 95 100
0 1.124 1. 356 1. 702 2.324 3.245 3.959 4.555 5.504 6.223 6.764 7.152 7.396 7.498 7.427 7.168 6.720 6.118 5.403 4.600 3.744 2.858 1.977 1.144 .428 0
0
.654 .817 .939 1.063 1.184 1. 241 1. 281 1.336 ' 1.374 1.397 1.418 1.438 1. 452 1. 464 1. 433 1.369 1. 297 1.228 1.151 ],077 ],002 .924 .846 .773 .697
2.038. 1. 729 1.300 1.156 .920 .682 .563 .487 .393 .,334
0
.809 .004 .969 1.031 1.088 1.114 1.132 1.15R 1.172 1.182 1.191 1.199 1. 205 1. 210 1.197 1.170 1.139 1.108 ].073 1.038 1.001 .961 .920 .879 ' .835
.290
.255 .227 .203 .184 .160 .143 .127 .109 .096 .078 .068 .052 .038 .026 0
~
L. E. radius: 1.505 percent c
NACA 65,-{)18 BASIC THICKNESS FORM
1.6
~ --.,,-I V ~ / v""'" ~ V
1.2
~
L
x
,_-- c,=.3E (upper surface)
"
/
(percent c)
.8
r-----"
0 .5 .75 1.25 2.5
!~
'/ j
I .4
y--
5.0
--
"-'---o
~
NACA 653 -018
r-
.2
.4
;rIc
---.6
r'.
7.5 10 15 20 25 30 35 40 45 50 55
60
65
70 75 80 85 00 95 100
r--i - ~
(oIV)'
vlV
~
.8
LO
0 1.337 1.608 2.014 2.751 3.866 4.733 5. 457 6.606 7.476 8.129 8.595 8.886 8.999 8.001 8.568 8.008 7.267 6.395 5.426 4.396 3.338 2.295 1.319 .400 0
L. E. radius: 1.96 percent c
!;v.IV
-----
----- ------
---o3E (lower surface)
(vt
v
(percent c)
0
.625 .702 .817 1.020 1.192 1.275 1.329 1.402 1.452 1.488 1. 515 1.539 1; 561 1.578 1.526 1.440 1.353 1.262 1.170 1.076 .985 .896 .813 .730 .657
0
.791 .8.38 .004 1.010 1.092 1.129 1.153 1.184 1.205 1. 220 1.231 1.241 1.249 1.256 1.235 1.200 1.163 1.123 1.082 1.037 .992 .947 .002 .854 .811
1. 746 1.437 1.302 1.123 .858 .650 .542 .474 .385 .327 .285 .251 .225 .203 .182 .157 .137 .118 ;104 .087 .074 .062 .050 .039 .026 0
84
REPORT NO. 824-NATIONAL ADVISORY COMMIT'fEE FOR AERONAUTICS 2.0
I
{
r--
'\
1.8
.I.e
/'
01
----
/
./
/,
I /
h ~
V
x
(percent c)
~"'\ f\ ~
"'" K\ '"
. '.44 (lower surf'ace)
"~~~
,/
o
NACA 65.-021 BASIC THICKNESS FORM
I
l\
I / .8
/ I Y
I
I
.... c, =.41 {upper surface}
NACA 654 -02/
- I-- I--1--1-
).---
~ t--- t--
I--:~
).---
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 80 85 90 95 100
I
I
y (percent c)
(v/V) ,
v/v
I
!!.Va/V
I
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
I
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 1. 293 1.371 1. 469 1. 533 1. 580 1. 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 1.137 1.171 1.212 1.238 1.257 1.273 1.286 1.296 1.304 1. 278 1.228 L 182 1.134 1.085 1.036 .985 .934 .882 .833 .785
L. E. radius: 2.50 percent c
NACA 66,1-012 BASIC THICKNESS FORM
/.6
I
,
;:V---
Vq 1.2
(vJ .8
I--'"
,
.A =./2 (upper surface)
~
J.--- +-
'--Ii? (lower surface)
rl
I'
~
"
1'-.
NACA 66,1-0/2
--
l,..---
I'-o
"'-
~ ~
(percent c)
x
y (percent c)
(v/V)'
v/V
!!'Va/V
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 80 85 90 95 100
0 .900 1.083 1. 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 4.535 3.789 2.964 2.098 1. 244 .477 0
0 .854 .902 .964 1.069 1.138 1.175 1. 201 1. 237 1.257 1. 272 1.284 1. 293 1.302 1. 309 1.313 1.320 1.327 1.297 1. 221 1.143 1. 061 .974 .885 .792 .701
0 .924 .950 .982 1.034 1. 067 1.084 1. 096 1.112 1.121 1.128 1.133 1.137 1.141 1.144 1.146 1.149 1.152 1.139 1.105 1. 069 1.030 .987 .941 .890 .837
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 .041 .028 0
L. E. radius: 0.893 percent c
NACA 66,2-015 BASIC THICKNESS FORM
I
I x
:c, =.20 (upper surf'ace) :
/.8
,.0.,
I.R
( (vl V .8
"
--- :---r-
----
~
V
.'\.
~~
路路路路.EO (tower surface)
I
I
NACA '66,i?-0I5
.4
V- ~
"'-----r -
o
.E
.4
.6
-
f--
I-" I---- f...--
.8
0
0 1.110 1. 329 1. 645 2.229 3.086 3.757 4.337 5.255 5.964 6.516 6.933 7.230 7.415 7.495 7.460 7.294 6.961 6.405 5.597 4.652 3.616 2.545 1.488 .560 0
10
""
r--- b -
(percent c)
.5 .75 1. 25 2.5 5.0 7.5
~~
1.0
y
(percent c)
15 20 21i 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
L. E. radius: 1.384 percent c
(vW) ,
0
.700 .870 .940 1.048 1.154 1.210 1. 244 1.290 1.323 1. 342 1.359 1.374 1.387 1. 397 1. 407 1.415 1. 421 1. 372 1. 267 1.162 1.057 .953 .848 .743 .640
v/V 0 .837 .933 .970 1.024 1.074 1.100 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
AVa/V 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
85
SUMMARY OF AIRFOIL DATA
2..0
NACA 66,2-018 BASIC THICKNESS FORM
I i I
-
.8
/0
V 2
V,
/
If /V
8
J--I-
,
_c,=.22 (upper surfac6j
-~
~~
/
.5 .75 1. 25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
I~
NACA fi6,2-0/8
80
-
4
V 0
,
0
~~
~ 22 fower surroce)
'II
(perc~nt c)
1---
'---t--- t - -
I--- I-l---
L.---
85 00 95 100 j;--
F
.5 .75 1. 25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Ai'Of (upper surface)
'I
!'--- t-....
'.'Of (lower surfoce)
"'-.
.8
I
NACA 88-008
""
1
.4
I
vjlT
I
av.IV
0
0 1. 438 1. 730 2.180 2.938 3.984 4.804 5.486 6.541 7.342 7.957 8.419 8.741 8.933 8.998 8.934 8.719 8.316 7.629 6.657 5.523 4.296 3.027 1. 789 .672 0
.590 .740 .918 1. 084 1. 217 1. 285 1. 325 1. 373 1. 401 1. 422 1.440 1. 456 1. 468 1. 478 1. 488 1. 497 1. 502 1. 442 1. 314 1.185 1.059 .936 .817 .700 .594
1.659 1. 317 1. 209 1.091 .867 .665 .544 .469 .379 .323 .282 .251 .224 .201 .181 .162 .146 .134 .102 .089 .078 .064 .052
0
.768 .860 .958 1.041 1.103 1.134 1.151 1.172 1.184 1.192 1.200 1. 207 1. 212 1. 216 1. 220 1. 224 1. 226 1. 201 1.146 1. 089 1. 029 .967 .004 .837 .771
.O(l
0
.027
NACA 66-006 BASIC THICKNESS FORM
0
/0
(vIF)!
L. E. radius: 2.30 percent c
6
"
I
t-
x (percent c)
1.2
(percXnt c)
- - - - - - - - - - - ------- - - - - - - - - - -
I
I
o
y
(percent
c)
0
.461 .554 .693 .918 1. 257 1. 524 1. 752 2.119 2.401 2,618 2.782 2.899 2.971 3.000 2.985 2.925 2.815 2.611 2.316 1. 953 1. 543 1. 107 .665 .262 0
(./V),
v/V
----0 1. 052 1. 057 1.062 1.071 1. 086 1.098 1.107 1.119 1.128 1.133 1. 138 1.142 1.145 1.148 1.151 1.153 1. }.i5 1.154 1.118 1. 081 1. 040 .996 .948 .890 .822
I
0 1. 026 1.028 1. 031 1. 035 1. 042 1. 048 1. 052 1. 058 1.062 1. 064 1.067 1.069 1. 070 1. 071 1.073 1. 074 1. 075 1. 074 1. 057 1.040 1.020 .998 .974 .943 .907
/lva/V 4.941 2.500 2.020 1. 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: 0.223 percent c
NACA 66-008 BASIC THICKNESS FORM
x
y
(pereent c)
(percent c)
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 80 85 90 95 100
0 .610 .735 .919 1. 219 1. 673 2.031 2.335 2.826 3.201 3.490 3.709 3.865 3.962 4.000 3.978 3.896 3,740 3.459 3.062 2.574 2.027 1. 447 .864 .338 0
(v/V)'
vjV
av./v
Ul
,f. =.03 (upper ,surfoce)
,-0
Id?
~
, 1 l ~03 (lower surface)
""'"~
"- ..........
"'"
.8 NACA 68-008
.4
--
-
r-I
.2
.4
<rIc
.6
.8
1.0
L. E. radius: 0.411 percent c
0
.968 1. 023 1. 046 1.078 1.107 1.128 1.141 1.158 1.171 1.178 1.186 1.191 1.196 1. 201 1. 205 1. 208 1.213 1. 202 1.1.56 1.103 1. 048 .989 .926 .855 .768
0
.984 1.011 1. 023 1. 038 1. 052 1.062 1. 068 1:076 1.082 1.085 1. 089 1. 091 1. 094 1.096 1.098 1. 099 1. 101 1. 096 1. 075 1. 050 1. 024 .994 .962 .925 .876
3.794 2.220 1. 82" 1.388 .949 .689 .552 .474 .379 .321 .278 .246 .220 .198 .178 .161 .145 .130 .115 .101 .087 .073 .058 .045 .029 0
86
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS NACA 66-009 BASIC THICKNESS FORM
2.0 x
1.6
I.E
,
~
I ::::<:,....--:05 (lower surface)
"-
I(
"-
.8
(perlent c)
0
0 .687 .824 1.030 1.368 1.880 2.283 2.626 3.178 3.601 8.927 4.173 4.848 4.457 4.499 4.475 4.381 4.204 3.882 8.428 2.877 2.263 1.611 .961 .374 0
.5
.75 1.25 2.5 ,5.0 7.5 10 15 20 25 30 85 40 45 50 55 60 65 70 ·75 80 85 90 95 100
/0, ~.05 (upper surface)
/0
(percent c)
"-
NACA 56-DOB
.4 V""'-
(v/V)'
v/v
0
0
.930 .999 1.036 1. 079 1.119 1.142 1.159 1.178 1.190 1.201 1.210 1.217 1.221
.964 .999 1.018 1.039 1.058 1.069 1.077 1.085 1.091 1,096 1.100 1.103 1.105 1.108 1.110 1.112 1.114 1.109 1.083 1.055 1.025 .992 .957 .916 .864
1.228
1.232 1.237 1.240 1.230 1.172 1.113 1.050 .985 .915 .839 .747
M./V 3.352 2.100 1.750 1.340 .940 .686 .552 .473 .379 .323 .280 .246 .220 .197 .178 .161 .145 .130 .116 .100 .085 .071 .057
:043
.028
0
L. E. radius: 0.530 percent c
I
o NACA 66-OlO BASIC THICKNESS FORM
x
1.6 /e, =.07 (upper surface)
/.2
or;;k -
,..---
~ "-
-;07 fower surface)
If
"'
.8
~
""
NACA 6{]-010
-I---
t---r--
1/
(percent c)
(percent c)
0
0 .759 .913 1.141 1. 516 2.087 2.536 2.917 3.530 4.001 4.363 4.636 4.832 4.953 5.000 4.971 4.865 4. 665 4.302 3.787 3.176 2.494 1.773 1.054 .408 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 80 85 90 95 100
(v/V) , 0
.896 .972 1.023 1. 078 1.125 1.154 1.174 1.198 1.215 1.226 1.236 1.243 1.249 1.25. 1.261 1.265 1.270 1.250 1.190 1.121 1.052 .979 .904 .821 .729
v/V 0
.947 .986 1.011 1.038 1.061 1.074 1.084 1.095 1.102 1.107 1.112 1.115 1.118 1.120 1.123 1.125 1.127 1.118 1.091 1.059 1.026 .989
.951
.906 .854
Il.v./V 3.002 2.012 1.686 1.296 .931 .682 .551 .473 .379 .322 .279 .246 .220 .198 .178 .161 .146
• ISO
.114 .099 .085 .070 .056
.043
.027 0
~
L. E. radius: 0.662 percent c
o
NACA 661-012 BASIC THICKNESS FORM
x
(percent c) /0,
I =.Ie (upper surface)
r; -- --
0
/
/,2
---
,
-
~~
~
0
f-
~ --':IE
I'
(lower surface)
~
((
" "~
,8 NACA 66,,-012
.5 .75 1.25 2.5 5 7.5 10 15 20 25 30 35 40 45 50 55 60
65
---
-
I--
'--
o
f..--.2
·4
.6
---
.8
70 75 80 85 90 95 100
1.0
1/
(percent c) 0
.906 1.087 1.358 1. 808 2.496 3.037 3.496 4.234 4.801 5.238 5.568 5.803 5.947 6.000 5.965 5.836 5.588 5.139 4.515 3.767 2.944 2.083 1.234 .474 0
L. E. radius: 0.952 percent c
(v/V) , 0
.800 .915 .980 1. 073 1.138 1.177 1. 204 1.237 1.259 1.275 1.287 1.297 1. 303 1.311 1.318 1.323 1.331 1. 302 1. 221 1.139 1. 053 .96E .879 .788 .687
v/v 0
.894 .957 .990 1. 036 1. 067 1.085 1. 097 1.112 1.122 1.129 1.134 1.139 1.142 1.145 1.148 1.1501.154 1.141 1.105 1.067 1.026 .984 .938 .888 .829
Il.v./V 2.569 1.847 1.575 1.237 .913 .674 .549 .473 .380 .323 .280 .246 .221 .197 .176 .162 .147 .132 .113 .098 .084 .069 .053 .040 .031 0
87
SUMMARY OF AIRFOIL DATA
20
NACA 66z-{)15 BASIC THICKNESS FORM
x
(percent c)
I
11
(percent c)
(v/V) •
0 I.J22 1.343 1. 675 2.235 3.100 3.781 4.358 5.286 5.995 6.543 6.. 956 7.250 7.430 7.495 7.450 7.283 6.959 6.372 5.576 4.632 3.598 2.530 1. 489 .566 0
0 .760 .840 .929 1. 055 1.163 1. 208 1.242 1. 288 1.817 1.840 1. 356 1.370 1.380 1.391 1. 401 1.411 1.420 1.867 1.260 1.156 1. 053 .949 .847 .744 .639
----- - - - - /. 6
I.
_---ct =.:! (upper ,-'
surface) ~
~~
v----
...-1--ELY14 I
~~
power surface)
8
1/
"\
NACA 662 -0/5
-- -- --
4
-
,.--I-:-'-- I--o I I
,~
1.8
1.2
.8
0/
.. - _--c,_.3 (u~Der
-
V
../'"
/ /--
:...---
I/
I
NACA 68s -0/8
.4 ~
V ~
o '"
J
~
I
lJ
1.2
/'
V
.4
V o
:;;;;0-
----/ " /'
(vt / /' I /1
I I I -
--
--····c,-.4 (upper surface)_
.-
-----.4 fower surface)
" - -- ---"
,
,-
'- r--- .2
",
I--- l--
~
.4
a:/c
.8
--
V
.8
2.139 1.652 1:431 1.172 .895 .663 .547 .473 .381 .822 .280 _.248 .222
.200
.180 .163 .146 .131 .118 .096 .080 .065 .051 .039 .025 0
L~
(percent c)
11
(V/V)2
0 1.323 1.571 1.952 2.646 3.690 4.513 5.210 6.333 7.188 7.848 8.346 8.701 8.918 8.998 8.942 8.733 8.323 7.580 6.597 5.451 4.206 2.934 1. 714 .646 0
0 .650 .. 735 .850 1. 005 1.154 1. 234 1.285 1. 350 1. 393 1.423 1. 445 1. 464 1.481 1.496 1. 509 1.522 1. 534 1.438 1. 302 1.172 1.045 .922 .803 .692 .581
viv 0
.806 .857 .897 1.002 1. 074 1.111 1.134 1.162 1.180 1.193 1. 202 1. 210 1. 217 1.223 1.228 1. 234 1.238 1.199 1.141 1.083 1. 022 .950 _ .896 .832 .166
t;.v./V 1..773 1. 456 1. 312 1.121 .858 .649 .545 .472 .381 .323 .282 .250 .223 .201 .181 .163 .147 .131 .114 .095 .077 .061 .048 .037 .022 0
E. radius: 1.955 percent c
NACA 66.-{)21 BASIC THICKNESS FORM
'\~ I \ ~ ~~
I--
0 .5 .75 1. 25 2.5 5 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
x
I
~
I-I--
\
N4CA 884 -02/
0 .872 .9)6 .964 1. 027 1. 078 1.099 1.114 1.134 1.148 1.158 1.164 1.170 1.175 1.179 1.184 1.188 1.192 1.169 1.122 1. 075 1.026 .974 .920 .863 .799
t;.v./V
NACA 66s-{)18 BASIC THICKNESS FORM
x
~
I
L. E. radius:' 1.435 percent c
(percent c)
- ---
t--
1.8
p-
~~
I
v/V
•
f--
-~~t\
~ I--
----
"
,
surfacp)
--;3 fower surface}
I
.8
~
0 .5 .75 1. 25 2.5 5 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
I
""-
1.0
11
(percent c)
(percent c)
(v/V) 2
0 .. 5 .75 1. 25 2.5 5 1.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
0 1.525 1.804 2.240 3.045 4.269 5.233 6.052 7.369 8.376 9.1539.138 10.154 10.407 10.500 10.434 10.186 9.692 8.793 7.610 6.251 4.796 3.324 1.924 .717 0
0 .580 .635 .755 .952 1.143 1. 246 1.318 1.405 1. 459 1. 499 1. 528 1. 551 1.574 1.594 1.611 1.629 1. 648 1.508 1.335 1.176 1. 031 .891 .763 .648 .539
90
95 100
L. E. radius: 2.550 percent c
v/V
t;.v./V
----0 .761 .797 .869 .976 1. 069 1.116 1.148 1.185 1. 208 1.224 1. 236 1. 245 1.255 1.263 1. 269 1.276 1.284 1.228 1.155 1. 084 1. 015 .944 .873 .805 .734
1.541 1.314 1. 218 1.054 .828 .635 .542 .472 .381 .324 .283 .251 .224 .202 .183 .165 .148 .132 .114 .093 .073 .058 .046 .034 .020 0
88
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAU'l'ICS
e.o
NACA 67,1-015 BASIC THICKNESS FORM
x
,
/.6
i.e
(v/
/'
V/ '(
I-~ I.--(...:---I - -
,
V'-, '- -./2
f-
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 80 85 90 95 100
~
power surface)
\~
.8
\
NACA 67,/-0/5
- r--
.4
V- I----
-
r--I---
a I
~
~
I
y,0 / " ~V r-:: ~ ~ -...:: /-'-:2c fower (/ ~
.4
t.---
NACA U7AOl5
~
r--..: I---
o
.2
"
"-
r-- !--
I--+I---- I-<ric
.6
0 .650 .970 1.059 1.140 1. 209 1. 239 1. 259 1.285 1.304 1. 318 1.330 1.341 1. 351 1. 360 1.368 1.375 1. 381 1. 388 1.390 I. 321 1.176 1. 018 .864 .712 .570
0 .806 .985 1. 029 L068 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.M2 1. 560 1. 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
v I:>.v./V (v/F)' v/V (percent c) - - - - - - - - - - - - - - - - - - - - - ------.
~
--
0 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 6.905 6.402 5.621 4.540 3.327 2.021 .788 0
x (percent c)
/ /
/ I
I:>.v./F
NACA 747A015 BASIC THICKNESS FORM
surfac~
.8
v/F
L. 1'~. radius: 1.523 percent c.
~
/.2
(II/V)'
I--
__ -c, =.ec (upper surface)
1.6
y (percent c)
- - - - - - - - - - - - - - - - - - ------- -------
,c, ",./2 (upper surface)
: , (
(percent c)
I
I
I
.8
1.0
0 .5 .75 1. 25 2.5 5 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
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
L. E. radius: 1.544 perceut c
0 .660 .799 .942 1.100 1. 201 1. 259 1. 295 1.339 1.369 1. 390 1. 409 1.423 1.435 1. 391 1. 348 1. 306 1. 265 1. 221 1.178 1.115 1. 027 .938 .852 .774 .703
0 .812 .894 .971 1.049 1.096 1.122 1.138 1.156 1.170 1.179 1.187 1.193 1.198 1.179 1.161 1.143 1.125 1.105 1. 085 1. 056 1. 013 .969 .923 .880 .838
2.028 1. 680 1. 560 1. 325 .990 .695 .551 .465 .383 .324 .283 .252 .224 .199 .176 .156 .1~ .1 .108 .093 .079 .065 .052 .040 .02!l .018
SUMMARY OF AIRFOIL DATA
89
II-DATA FOR MEAN LINES Page
Page
N ACA NACA NACA NACA NACA NACA N ACA N ACA NACA NACA NACA
mean mean mean mean mean mean mean mean mean mean mean
line line line line line line line line line line line
62_ __ ______ ____________________ ______ __ _ 90 63______________________________________90 64______________________________________ 90 65______________________________________ 91 66______________________________________ 91 67 _____________ .. __________________ . ___·__ 91 2.10_ _ ____________________________ _______ 92 220_ _ ___________________________________ 92 230 _________________________ .. ___________ 92 240_____________________________________ 93 250 __ .. ________________________ .. _________ 93
NACA mean line a=O _____ ,______________________________ NACA mean line a=O.L_________________________________ NACA mean line a=0.2 ________ ._________________________ NACA mean line a=0.3 _________________ "________________ NACA mean line a=O.4_ _ _ ______ ___ ___ ____ ___ ___ ____ _____ . NACA mean line a=O.5__________________________________ NACA mean line a=0.6_ _ _ __ __ ______ __ ____ ___ ____ ___ _____ N ACA mean line a = 0.1- _ _ _______________________________ NACA mean line a=O.&_ _ ________________________________ N ACA mean line a=0.9_ _ ___ __ ______ _________ ____ ___ _____ NACA mean line a=1.0__________________________________
93 94 94 94 95 95 95 96 96 96 97
90
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
3.0 NACA MEAN LINE 62
2.0
el,=0.90
h
I~ r-
---
o
--
x
(percent c)
(percent c)
dll,/dx
PR
tlv/V=P.Ri4
0 .726 1. 406 2.625 3.656 4.500 5.625 6.000 5.977 5.906 5.625 5.156 4.500 3.656 2.625 1.406 .727 0
0.80000 .56250 .52500 .45000 .37500 .30000 .15000 0 -.00938 -.01875 -.03750 -.05625 -.07500 -.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 .741 .635 .525 .377 .261 0
0 .171 .258 .328 .376 .413 .451 .383 .318 .279 .238 .211 .185 .159 .131 .094 .065 0
1/,
------ ------
r--- r---
..........
0 1. 25 2.5 5.0 7.5
~
NACA 62
mean line
.~ .2
lO
15 20 25 30 40 50 60 70 80 90 95 100
l-
~
o
em",= -0.113
--
/
1.0
",,=2.81°
NACA MEAN LINE 63
2.0
e,,=0.80
..P-"
x
1.0
I
r-. I"'---.
V
(percent e)
r-- t---
t--
II o
--I--. '~
NAt;'A 83
mean line Yc
c .2
o
0 1. 25 2.5 5.0 7.5 lO
15 20 25 30 40 50 60 70 80 90 95 100
"'1=1.60°
em". = -0.134
(percent c)
dll,/dx
PR
tlv/V=PR/4
0 .489 .958 1.833 2.625 3.333 4.500 5.333 5.833 6.000 5.878 5.510 4.898 4.041 2.939 1. 592 .827 0
0.40000 .38333 .36667 .33333 .30000 .26667 .20000 .13333 .06667 0 -.02449 -.04898 -.07347 -.09796 -.12245 -.14694 -.15918 -.17143
0 .389 .553 .788 .940 1.066 1.220 1. 259 1. 233 1.160 .949 .850 .762 .673 .560 .406 .291 0
0 .097 .138 .197 .235 .267 .305 ,315 .3G8 .290 .237 .213 .191 .168 .140 .102 .073 0
11,
.I---
----NACA MEAN LINE 64
2. 0 e,,=0.76
I. 0
/
-
V
t-- r---
V
1--- r-...
0
~
NACA 64
mean line 2
o
I
-
I--.2
r-- I.4
.Jt'/c
.8
.8
1.0
. (percent e)
x
y, (percent e)
0 1.25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100
0 .369 .726 1. 406 2.039 2.625 3.656 4.500 5.156 5.625 6.000 5.833 5.333 4.500 3.333 1.833 '.958 0
a;=0.74°
em,'I=-0.157 •
dy,/dx
PR
tlv/V=PR/4
0.30000 .29062 .28125.26250 .24375 .22500 .18750 .15000 .11250 .07500 0 -.03333
0 .257 .391 .546 .668 .748 .871 .966 1.030 1.040 .999 .910 .827 .750 .635 .466 .334 0
0 .064 .098 .137 .167 .187 .218 .242 .258 .260 .250
~.06667
-.10000 -.13333 -.16667 -.18333 -.20000
.228
.207 .188 .159 .117 .084 0
91
SUMMARY OF AIRFOIL DATA 3.0 NACA MEAN LINE 65 CI 1 =0.75
2.0 x
1.0
~
o
1/
Cme/I =
-0.187
1/,
dy,/dx PR Avj1T=PR/4 (percent c) (percent c) ------- - - - - - - -------- - - - - - - --------
--
,r--
~
'\ NACA 65
mean line
!ft ..? c
o
Q'i=Oo
- -
-
f.---
--
0 1. 25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100
0
0.24000 .23400 .22800 .21600 .20400 .19200 .16800 .14400 .12000 .09600 .04800 0 -.04800 -.09600 -.14400 -.19200 -.21600 -.24000
.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
.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
r--. NACA MEAN LINE 66
20
-cI 1 =0.76
x
(percent c)
1.0
--V o
~ f.---
f.---
1/,
-
~
0 1. 25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100
""\
NACA 66
Yo .2 c
- :---
0.20000 .19583 .19167 .18333 .17500 .16667 .15000 .13333 .11667 .10000 .06667 .03333 0 -.07500 -.15000 -.22500 -.26250 -.30000
.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
0
.135 .244 .334 .408 .466 .557 .635 .700 .750 .827 .910 .999 1. 040 .966 .748 .546 0
0 .J34 .061 .084 .102 .117 .139 .159 .175 .188 .207 .228 .250 .260 .242 .187 .137 0
t-- t---.
NACA MEAN LINE 67
/.0
i/
~~
.......
~
--
L
I-"'~
1-""""
X
\
(percent c) -------
\
NACA 67
1& .2 c
••
..?
>_h
.4
x/c
.6
a:"i=-1.60o
cI 1=0.80
mean line
o
'I' = -0.222
dy,/dx PR AV/V=PR/4 - - - - - - - - - - - - - - - - -------
0
2.0
o
Cm
II
(percent c)
------- ------
mean line
a
",=-0.74°
.8
--
0 1. 25 2.5 5 7.5 10 15 20 25 30 40 50 60 70
80
90 95 100
r-...
/.0
y,
I
(percent c)
dy,/dx
0 .212 .421 .827 1. 217 1. 592 2.296 2.939 3.520 4.041 4.898 5.510 5.878 6.000 5.333 3.333 1. 833 0
0.17143 .16837 .16531 .15918 .15306 .14694 .13469 .12245 .11020 .09796 .07347 .04898 .02449 0 -.13333 -.26667 -.33333 -.40000
Cm,"=-0.266
PR
AV/V=PR/4
------- ------ - - - - - - - - - - - - - 0 .137 .195 .291 .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 .29'0 .315 .267 .197 0
92
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 3. 0
I
1
!
NACA MEAN LINE 210
II
2. 0
I i I
/\
\
1.0
I
r-- t-I
o
NACA 210
mean line
i
Yc
7" .2.
X
(percent e)
ai=2.09°
y, (percent e)
em ~'I = -0. 006
dy,/dx
PR
AV/V=PR/4
------- ------- - - - - - - - ------- ------0 1. 25 2.5 5.0 7.5 10 15 20 25 30 40 50' 60 70 80 90 95 100
\ .........
e,,=0.30
0.59613 .36236 .18504 -.00018
0
.596 .928 1. 114 1. 087 1. 058 .999 .940 .881 .823 .705 .588 .470 .353 .235 .118 .059 0
0
1. 381 1. 565 1. 221 .781 .626 489 .408 .348 .302 .242 .198 .160 .128 .098 .065 .044 0
-.01175
I
I
0
.345 .391 .305 .195 .156 .122 .102 .087 .075 .061 .049 .040 .032 .025 .016 .011 0
I
I J
o
NACA MEAN LINE 220
2.0
e.,=0.30
! x
,..--"
(percent c)
I
1.0
!""-
o
Yo ('
0 1. 25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100
----
~--
em",= -0. OlD
dy,/dx
PR
AV/V=PR/4
------- ------- -------- -------- --------
\
~
y, (percent c)
ai=1.86°
NACA 220
mean line
,.,
.C
0.39270 .31541 .24618 .13192 .04994 .00024
0 .442 .793 1. 257 1. 479 1. 535 1. 463 1. 377 1. 291 1. 205 1.033 .861 .689 .516 .344 .172 .086 0
0
.822 1. 003 .988 .900 .8t)! .615 .465 .378 .326 .253 .205 .169 .135 .100 .064 .040 0
-.01722
0
.206 .251 .247 .225 .200 .154 .116 .095 .082 .063 .051 .042 .034 .025 .016 .010 0
o
NACA MEAN LINE 230
20
c.,=0.30
1.0
V~
...............
r--
o NACA 230
mean line ~•. 2
o
.2
.4
riC
.0
.8
1.0
x (percent e)
(percent e)
0 1. 25 2.5 6.0 7.5 10 15 20 25 30 ·40 50 60 70 80 90 95 100
0 .357 .666 1.155 1.492 1. 701 1.838 1. 767 1. 656 1;546 1.325 1. 104 .883 .662 .442 .221 .110 0
1/,
a,=1.65° dy,jdx 0.30508 .26594 .22929 .16347 .10762 .06174 -.00009 -.02203
-.02208
em". = -0.014
I
PlI
AVjV=PlIj4
0 .628 .673 .791 .853 .859 .678 .519 .419 .361 .274 .217 .177 .144 .105 .069 .042 0
0 .132 .168 .198 .213 .215 .170 .130 .105 .090 .069 .054 .044 .036 .026 .017 .011 0
93
SUMMARY OF AIRFOIL DATA
3.0 NACA MEAN LINE 240 Cli=1.45°
c,;=0.30
Cm'I' = -0.019
2.0 x
(percent c)
y, (percent c)
------- - - - - 0
1. 25
/.0
!
r-----..
/
2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100
-
I-- r--
'0
N;1cA NO mean line
1& .2 e
dy,/dx
PR
AVjV=PR/4
-------- ------- ------C.25233 .22877 .20625 .16432 .12653 .09290 .03810 -.00010 -.02169
0 .301 .572 1. 035 1. 397 1.671 1. 991 2.079 2.018 1. 890 1. 620 1.350 1. 080 .810 .540 .270 .135 0
-.02700
0 .377 .491 .625 .718 .750 .677 .556 .477 .410 .304 .234 .186 .150 .110 .071 .047 0
0 .094 .123 .156 .180 .188 .169 .142 .119 .103 .076 .0f,9 .047 .038 .028 .018 .012 0
o NACA MEA:\, LINE 250
2.0 X
(percent c)
c,,=0.30
ai=1.26°
y, (percent c)
dy,/d.r
Cm c/4=-O.026
PR
At,/V=PR/4
- - - - - - - -------- ----------- -------- --------
/.0
/' o
0 1. 25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100
- - ---- NACA 250
tnean line
Yo
C
-:>
.cc
0.21472 .19920 .18416 .15502 .12909 .10458 .06162 .02674 -.00007 -.01880
0
.258 .498 .922 1.277 1. 570 1. 982 2.199 2.263 2.212 1. 931 1. 609 I. 287 .965 .644 .322 .161 0
-.03218
,
0
.281 .369 .477 .552 .592 .624 .610 .547 .470 .346 .255 .197 .154 .119 .076 .051 0
0 .070 .092 .119 .138 .148 .156 .153 .137 .117 .087 .064 .049 .038
.oao
.019 .013 0
o NACA MEAN LINE a=O c,,=1.0
2.0
..............
~r-...
1.0
x
(percent c)
'~
0
.............
~, ~
o
'---
NACA Q=O
mean line
o
dy,/dx
Cm,I' = -0.083
PR
AV/V=PR/4
- - - - - - - - - - - - - - - - - - ------- -------
..............
~
y, (percent c)
Q:i=4.56°
I--
.4
.:rIc
.8
.8
to
.5 .75 1.25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0
.460 .641 .964 1. 641 2.693 3.507 4.161 5.124 5.747 6.114 6.277 6.273 6.130 5.871 5.516 5.081 4.581 4.032 3.445 2.836 2.217 1. 604 1.013 .467 0
---O~75867---
.69212 .60715 .48892 .36561 .29028 .23515 .15508 .09693 .05156 .01482 -.01554 -.04086 -.06201 -.07958 -.09395 -.10539 -.11406 -.12003 -.12329 -.12371 -.12099 -.11455 -.10301 -.07958
----------1. 990 1. 985 1. 975 1. 950 1. 900 1. 850 1. 800 1.700 1.600 1. 500 1. 400 1.300 1.200 1.100 1.000 .900 .800 .700 .600 .500 .400 .300 .200 .100 0
---O~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
94
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS NACA MEAN LINE a=O.1
3.0
C mc14 =-O.OF6
x
(percelJt c)
20 '--
i'---- r---..
------ ~ --o
'" /'--....
5. 0 7. 5 10 15 20 25 30 35 40 45 50 li5 60 65 70 75 80 85 90 95 100
~
NACAa:QI mean line
o~
c)
dll,jdx
PR
I
-
I-
-
2. 689 3. 551 4.253 .5. 261 5. 905 6. 282 6.449 6.443 6.296 6. 029 5.664. 5.218 4.706 4.142 3.541 2.916 2.281 1. 652 1. 045 .482 0
. 38235 .31067 .25057 . 16087 . 09981 . 05281 .01498 -.01617 -.04210 -. 06373 -.08168 -.09637 -.10806 -.11694 -.12307 -.12644 -. 1269..~ -.12425 -.11781 -.10620 -.08258-
1. 313
I. 212
1.111
I. 010
.909 .808 .707 .606 .505 .404 .303 .202 .101
o
a,=4.17"
o
Po
1. 667
O. 417
1. 563 1. 459 1. 355 1. 250 1.146 1.042 .938 .834 .729 .625 .521 .417 .313 .208 .104
.391 .365 .339 .313 .287 .260 .234 .208 .182
-- : ~-- --~;al-- -~~~]~i~-!I-~=~~ -~~~~~~-l\
I'---.. ..............
~ t-.....
"'/'--....
o
, I
I-...
NACA a=QE mean line .2
o
-,
! I "tv-P"'I
Cm,/I=-0.094
~',J "'~, 'J I "", I
J!s c
.429 .404 .379 .354 .328 .303 .278 .253 .227 .202 .177 .152 .126 .101 .076 .050 .025
I. 7li I. 616 I. 515 I. 414
NACA MEAN LINE a=0.2
-......;., 1.0
AV/T'=PRj4
,--------.-:~------------------
CI,=l.O
~
I
~- -~j--~§~')-~=:::--~.-~-::-
~k
1.0
y, (perc~nt
-
......-I---
t---
2.5 5. 0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
I. 530 2. 583 3.443 4. 169 5.317 6.117 6. 572 6. 777 6.789 6. 646 6. 373 5. 994 5. 527 4.989 4.396 3. 762 3.102 2.431 l. 764 1. 119 .518 0
.47592 . 37661 .31487 . 26803 . 19373 . 12405 . 06345 . 02030 -.01418 -. 04246 -. 06588 -. 08522 -. 10101 -'.11359 -.12317 -. 12985 -.13.363 -. 13440 -. 13186 -.12541 -. JI361 -. 0~941
o
.156 .130 .104 .078 .052 .026
o
NACA MEAN LINE a=0.3 CI,=1.0
ai=3.84°
Cm,,,= -0.106
20
'-..... !.O
y, x (percent c) (percent c) ------- --------
~,
0
-.......
~~ ~~
o NACA a=Q3 mean lioe
Yc c .2
V.......o .2
I---I - - ~ .4
.8
1.0
.5 .75 1. 25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0
.389 .546 .832 1.448 2.458 3.293 4.008 5.172 6.052 6.685 7.072 7.175 7.074 6.816 6.433 5.949 5.383 4.753 4.076 3.368 2.645 1. 924 1. 224 .570 0
---------I dy,jdx
----ii:~553ii--
.60524 .54158 .45399 .36344 .30780 .26621 .20246 .15068' .10278 .04833 -,00205 -. O~710 -,06492 -.08746 -.10567 -.12014 -.13119 -.13901 -.14365 -.14500 -.14279 -.13638 "':.12430 -.09907
PR
AvjT7=PR/4
-----------
-.---------
1.538
0.385
1. 429 1. 319 1.209 1.099 .989 .879 .769 .659 .549 .440 .330 .220 .110 0
.367 .330 .302 .275 .247 .220 .192 .165 .137 .110 .082 .055 .028
0
95
SUMMARY OF AIRFOIL DATA NACA MEAN LINE a=O.4
3.0
-------------------------_._CI,=1.0
(perc~nt c) (perg~nt c)
2.0
---~~-- --~. ~
1.0
. 75 1. 25 2. 5 .1. 0 7. 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
r--......
~
~
~
0
~
NACA a 0A 2
mean line .2
0
~----
- -
c-
r--
3:--
dy,/dx
I
. 514 . 784 1. 367 2. 330 3. 131 3.824 4. 968 5. 862 6. 546 7. 039 7.343 7.439 7. 275 6. 929 6.449 5.864 5.199 4.475 3.709 2.922 2. 132 1. 361 .636 0
. 57105 . 51210 . 43106 . 34764 . 29671 .25892 . 20185 . 15682 . 11733 . 07988 .04136 -.00721 -.05321 -. 08380 -.10734 -.12567 -.13962 -.14963 -.15589 -.15837 -. 15683 -.15062 -.13816 -.11138
~
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 80 85 90 95 100
,
0
~
NACA a=D.5
mean line 2
t--t-r--I--
I---
0
~
1.310 1.190 1.071 .952 .833 .714 .595 .476 .357 .238 .119
.327 .298 .268 .238 .208 .179 .149. .119 .089 .060 .030
o
o
Cm,/.=-0.139
ai=3.04°
___
~
0.357
NACA MEAN LINE a=O 5
~~~~~I~er~~nt~J ___ dY,/~ ~
1. 429
I--.
.0
~
f>.vjV=P~/4
-~~O:6~~~-I-~~~~=- -~~~~~~-
CI,=l.O
I .0
PR
0 .345 .485 .735 1.295 2.205 2.970 3.630 4.740 5.620 6.310 6.840 7.215 7.430 7.490 7.350 6.965 6.405 5.725 4.955 4.130 3.265 2.395 1. 535 .720 0
-------------
;
0.58195 . 53855 .43360 .40815 .33070 .28365 .24890 .19690 .15650 .12180 .09000 .05930 .02800 -.00630 -.05305 -.09765 -.12550 -.14570 -.16015 -.16960 -.17435 -.17415 -.16850 -.15561> -.12660
_~_J_:~:~~~~ -----------
-----------
1. 333
0.333
1.200 1. 067 .933 .800 .667 .533 .400 .267 .133 0
;300 .267 .233 .200 .167 .133 .100 .067 .033 0
NACA MEAN LINE a=0.6
CI,=1.0
",,=2.58°
Cm,I<=-0.158
0 X
(percent c)
1/,
(percent c)
dy,/dx
PR
f>.v/V=PR/4
- - - - - - - - - - -------- ------- -----
~
1.0
""~
o NACA a=O.fJ
mean line lie
C
""-.,
'"
!> .<;
o
0 .5 .75 '1. 25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55
eo
--
J...-.2
xlc
.6
-
t--- r-- I-.8
1.0
65 70 75 80 85 90 95 100
0 .325 .455 .695 1. 220 2.080 2.805 3.435 4.495 5.345 6.035 6.570 6.965 7.235 7.370 7.370 7.220 6.880 6.275 5.505 4.630 3.695 2.720 1. 755 .825 0
-------------
0.54825 .50760 .45615 .38555 .31325 .26950 .23730 .18935 .15250 .12125 .09310 .06660 .04060 .01405 -.01435 -.04700 -.09470 -.14015 -.16595 -.18270 -.19225 -.19515 -.19095 -.17790 -.14550
-----------
-----------
1. 250
0.312
1. 094 .938 .781 .625 .469 . ;112 .156 0
.273 .234 .195 .156 .117 .078 .039 0
96
REPOR'l' NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS NACA MEAN LINE a=0.7
3.0
--
, CI,=1.0 y,
x
(percent c)
"-
/.0
"'-
~ NACA a=O.l mean line
"
.C;
-----
-----
0
------------0.51620 .47795 .42960 .36325 .29545 .25450 .22445 .17995 .14595 .11740 .09200 .06840 .04570 .02315 0 -.02455 -.05185 -.08475 -.13650 -.18510 -.20855 -.21955 -.21960 -.20725 -.16985
.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 0
-.............
(perc~nt ~L
"" ~
o NACA a=0.8 mean line '" ."-
-r--- -
---
!---
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 80 85 90 95 100
x
(percent c)
~
\
NACA a=0.9 mean/ine
+.2 o
....-- ~
.2
~
.4
.8
.8
-----------
1.176
0.294
I
.980 .784 .588 .392 .196
.245 .196 .147 .098 .049 0
0
0 .287 .404 .616 1.077 1. 841 2.483 3.043 3.985 4.748 5.367 5.863 6.248 6.528 6.709 6.790 6.770 6.644 6.405 6.037 5.514 4.771
C m ,/.=-0.202
~~~
_ _ I___
-------------
0.48535 .44925 .40359 .34104 .27718 .23868 .21050 .16892 .13734 .11101 .08775 .06634 .04601 .02613 .00620 -.01433 -.03611 -.06010 -.08790 -.12311 -.18412 -.23921 -.25583 -.24904 -.20385
3.683
2.435 1.163 0
~_I~~=p~
-----------
-----------
1. III
0.278
.833 .556 .278
.208 .139 .069 0
0
NACA MEAN LINE a=O.9
20
o
ai=1.5·lo
(perg:nt c) -' __
Cl,=1.0
1.0
-----------
NACA MEAN LINE a=O.R CI,=1.0
I.p
o
!:J.vjl'=Puj4
PH
-
EO
Yc C
-0.179
dy,jdx
(percent c)
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 80 85 90 9.1 100
~
o
o
C m./. =
----- ------ ------ ------- -------
20
Yc C
Q'i=2.09°
~ 1.0
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 80 85 90 95 100
Qi=O.90°
1/,
Cm,/.= -0.225
dy,jdx I (percent c) I-------
0 .269 .379 .577 1.008 1. 720 2.316 2.835 3.707 4.410 4.980 5.435 5.787 6.045 6.212 6.290 6.279 6.178 5.981 5.681 5.265 4.714 3.987 2.984 1.503 0
----0:45482-.42064 .37740 .31821 .25786 .22153 .19500 .15595 .12644 .10196 .08047 .06084 .04234 .02447 .00678 -.01111 -.02965 -.04938 -.07103 -.09583 -.12605 -.16727 -.25204 -.31463
-.26086
PR
I
t:J.v/'V=Pllj4
--
-----------
-----------
1.053
0.263
.526 0
.132 0
97
SUMMARY OF AIRFOIL DATA .:J.O NACA MEAN LINE a=1.0 Cl,=l.O x
C.O
(percent c)
y,
(percent c)
ai=Oo
Cm",=-0.250
Pn
dy,/dx
AV/V=Pn/4
- - - - - - ---,----- - - - - - - - -------- - - - 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 80 85 90 95 100
/.0
o NACA a=I.O mean line Yo .C £'
o
---
.4
x/c
.6
.8
-
i--1.0
0
. 250 .350 .535 .930 1. 580 2.120 2.585 3.365 3.980 4.475 4.860 5.150 5.355 5.475 5.515 5.475 5.355 5.150 4.860 4.475 3.980 3.365 2.585 1. 580 0
----.---.----
0.42120 .38875 .34770 .29155 .23430 .19995 .17485 . 13805 .11030 .08745 .06745 .04925 .03225 .01595 0 -.01595 -.03225 -.04925 -.06745 -.08745 -.11030 -.13805 -.17486 -.23430
---.---------
I
--.--------
_.--.----- .
1. 000
0.250
-------.---
-----------
SUMMARY OF AIRFOIL DATA
99
III-AIRFOIL ORDINATES Page
K A C A OOOL _- - - - - ___ - - - - __ - ________ .. __________________ 100 KACA 0009______ ________ _______ ___ __________ _______ ____ 100 N ACA 1408 _______________________ . _________ ___________ 100 NACA 1410______ _______________________________________ 100 KACA 1412 _____________ - - ______________ .__ ______ __ __ ____ 100 100 NACA 2412 ____ .__ - ____ -- _____ "__ ________ ___ _______ ______ NACA 241L. _________ - ____ ___ ___ _____ __ ______ __ ________ 100 N ACA 2418 ___________ - __________________ _______________ 100 NACA 242L __________ ~ _____________ .__ ______ ___ __ _____ __ 100 NACA 2424____ __ ___ ________ ________ __ ___ ____________ ___ 100 NACA 4412_____________________________________________ 101 . NACA 4415 ___________ ~_________________________________ 101 N ACA 4418_ _____ ______ _________________________________ 101 N ACA 442L _________ _ ______________________ ________ ____ 101 N ACA 4424____ _______ _______________________ __________ _ 101 N ACA 23012 ______ - __ - - - - - - - - - ___ - - - - __ - __ c _ _ _ _ _ _ _ _ _ _ _ _ _ 101 N ACA 23015 _____________________________________ .. ____ __ 101 NACA 23018____________________ ________________________ 101 N ACA 2302L ______ _____________ ________________________ 101 NACA 23024 _______________________ ~ __ ______ ___ _________ 101 NACA 63,4-420 _____________________________.___________ 102 102 NACA 63,4-420, a=;0.3 ____.______________________________ NACA 63(420)-422_ ___ ____ _______ __ _____ ___ _____ __ __ ____ 102 102 N ACA 63(420)-517 _____ .. _________________________________ N ACA 63-006 __ "_ ____ _____ __________ ____________________ 102 NACA 63-009 ____ ~ ____ -_ ____ __ ___ ___ ___ _______ __________ 102 N ACA 63-206_ _______ ___________________________________ 102 102 N ACA 63-209 _______________________________ . ___________ c NACA 63-210_ ______ ______ __ __ ____ __ ___ ___ __ ___ _________ 102 NACA 63\-012 ____________________ .. ______________ ------102 N ACA 63\-212_ _ _ ____ _____________ ___________ ___________ 103 N ACA 63\~412_ _____ ________ __ _________________________ _ 103 N AC A 63r O15 ____________________________________ _____ 103 N ACA 63r 215_ __ _______________________________________ 103 N ACA 63r 415_ ________________ _________________________ 103 N ACA 63r 615_ __ ___ __________ ___________ _______________ 103 N ACA 63 3-018_ __ __ __________________________________ ___ 103 NACA 633-218 _______________ ~_ _________ ____ _________ ___ 103 NACA 633-418 ___ .. __ ~____ _______________________________ 103 N ACA 63 3-618_ __ __________ _____________________________ 103 N ACA 634-021.. ________________________________. _________ 104 N ACA 63r 22L ______________________________________ ___ 104 N ACA 634-421.. __________ . ___ . __ . _______ ___ _____________ 104 NACA 64-006______ ______ ____ ___________ ________________ 104 NACA 64-0'09___________________________________________ 104 NACA ·64-108 __________________ . ___ .____ ._ ___ ______ _____ __ 104 NACA 64-110 _________________ c__ __ _ _ _ __ _ _____ __________ 104 N ACA 64-206_ ____________________ __ _________________ ___ 104 NACA 64-208 ____________________ .. __. _ . _____ .. ___ __ ___ ____ 104 N AC A 64-209 _________ __________________________________ 104 NACA 64.,-210.______ . ___ . _______________ ._. ______________ 105 NACA 64\-012 _____________ . ________________ .. ________ ._ _ 105 NACA 64\-112 __________ .______________________ _________ 105 NACA 64\-212_ _ _ __________ _____ _ ______ ___ ______________ 105 N ACA 64\-412 _______________ .. ____ .. _.. _____ _ _____________ 105 N AC A 64r O15 ____________ . ____ _________________________ 105 NACA 64 2-215 __________________________________ .. _______ . 105 NACA 642-415 _____________________ " ____________. _____ ~__ 105 NACA 64:>018 __________________________ "_______________ 105 ~
Page
NACA 643-218 ______________________________________ .___ N ACA 64 3-418_ _ _ ____________ ____________________ __ _____ N ACA 643-618 ____ - ____ ._ _____________ __ _________ ________ N ACA 644-02L _ _ __________________________________ ____ _ NACA 64r 22L _________________________ .. -----__ ___ ___ __ N ACA 6~-42L _ ~ ________ __ ____________ ____________ _____ N ACA 65, 3-018 _____ .. ___ __________________ ______ ___ _ ____ N ACA 65,3-418, a=Q.8 ______________ .. ______________ _____ NACA 65, 3-618 ____ -- _____________________ ~____________ NACA 65(216)-415, a=0.5 _____ .__________________________ N ACA 65-006 _________________________________________. __ N ACA 65-009 ____ - - __ - __________ ___________________ _____ NACA 65-206 ________ - _____ _____ _ __ __ ___ __ ___ ___ __ _ _____ N ACA 65-209___ __ ______ ____ _____ _______ ______ __________ N ACA 65-210 ____ .. ___ - ____ __ _____ ___ __ __ ___________ _____ N ACA 65-410___ _____ _____________ __ _____ ___ ______ ______ N ACA 65\-012_ - _ __ ___ ___ _____ ___________ _____ _____ ___ __ N ACA 6k212_ _ _ ________________ _____________ ______ ___ _ NACA 65\-212, a=0.6 ____________________ --------------cN ACA 65\-412_ _ _ __ __ ___ __________ ______ ____ ___ ____ ___ __ N ACA 652-015_ _ _ _______________________________________ N ACA 65 2-215 _______ - _______________ _____ _________ _____ N ACA 65r 415_ - _____ - ______,_ __ ____________________ _____ NACA 65r 415, a=0.5 _____________ ~______________________ NACA 65:>018 ________ .. _____________________________ ,,--N ACA 653-218 _________ .. _______________ ____________ _____ N ACA 653-418_ _ _ ___________ ____________________ ________ NACA 653-418, a=0.5 _____ "______________________________ N ACA 653-618_ _ _ ______ ____ ______ ______ ____________ _____ NACA 653-618, a=0.5 _______________________________ ._____ N ACA 654-021.. _ _ __________________________________ _____ N ACA 654-221.. - _____ - - - ___ - ___________ - ___________ _____ N ACA 654-421.. ___________ .. ______________________ c _ _ _ _ _ _ NACA 65r 421, a=0.5____________________________________ N ACA 65(211)-114.. __ - __ - _____ - ___________ - ____________ __ __ N A C A 65(12!)-·420 _______ - ___ .. ____________ - _____ .. ___ .. _ ____ _ N ACA 66,1-212 _______ - __ .. __ - - - ________ - - ___________ _____ N ACA 66(215)-016 _____________________ - ___________ ___ __
105 106 106 106 106 1')6 106 106 106 106 106 107 107 107 107 107 107 1Q7 107 107 107 108 108 108 108 108 108 108 108 108 108 109 109 109 109 109 109 109
N ACA 66(215)-216_ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - c NACA 66(215)-216, a=0.6_______________________________ _ N ACA 66(215)-416 _________ - - .. _- - __ - __ - - _- - __ - - ____ - - ___ NACA 66-006___________ ________________________________ N ACA 66-009 _________________________ .. - __________ ______ N ACA 66-206 ________________ - ________ - - ________________ N ACA 66-209 ___________ .. ___ - _________ - _- ________ ______ N ACA 66-2lO_ ____________________________________ ______ NACA 66\-012_ _ _ ___ ____ ________ ____________ ______ _ _____ NACA 66 1-212_ _ _ __ ___ __ ____ ___ ___________________ ______ NACA 66r 015 _______________ - _________ - _- ________ ______ N ACA 66 2-215 _______________ - ___________ - ___________ - __ N ACA 66r 415 ___________ " _- _- _________ - _- - __ - _______ ___ NACA 66:>018_ _ _ __ _____ __ ________________ _______ ___ ____ NACA 66:>218_.______ ____________________ _______________ NACA 66 -418 _________ ._ _____ _____________ __ ___ ____ ____ 3 NACA 66r 02L _ _ ___ __ ______ ________________ ______ ____ __ N ACA 66~-22L _ _ _ __________________ _____________ _______ N ACA 67,1-215 _____________________________ .. ____ ____ ____ N ACA 747 A315 _______________________ .. _- __________ ~ ___ __ N ACA 747 M15 ______ ________________ ,,_ __ _______ _____ ___ _
109 109 109 110 110 110 110 110 110 110 110 110 110 111 111 III 111 111 111 111 III
NACA 0006
NACA 0009
NACA 1408
NACA 1410
NACA 1412
[Stations and ordinates given In percent of airfoil chord]
[Stations and ordinates given In percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given In percent of airfoil chord]
Upper surface
Lower surface
Upper surface Station
Or<'Jnat~·
Ordinate Station Ordinate
---- - - - ---- - 0 1.25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100 100
0 .95 1.31 1.78 2.10 2.34 2.67 2.87 2.97 3.00 2.90 2.65 2.28 1.83 1.31
.72
.40 (.06) 0
0 -.9(> -1.31 -1.78 -2.10 -2.34 -2.67 -2.87 -2.97 -3.00 -2.90 -2.65 -2.28 -1.83 -1.31 -.72 -.40 (-.06) 0
0 1.25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100 100
L. E. radius: 0.40
Upper surface
Lower snrface
-----Station Ordinate Station ---------
---~---
~----
,
I
0 1. 25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100 100
0 1. 42 ·1.96 2.67 3.15 3.51 4.01 4.30 4.46 4.50 4.35 3.97 3.42 2.75 1.97 1.09 .60 (.10) 0
0 1.25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100 100
0 -1.42 -1.96 -2.67 -3.15 -3.51 -4.01 -4.30 -4.46 -4.50
i
~4.35
-3.97 -3.42 -2.75 -1.97 -1.09 -.60 (-.10) 0
Upper surface
Lower surface
Station
Ordinate Station Ordinate
---- - - - ---- - - 0 1.189 2.418 4.896 7.386 9.883 14.889 19.904 24.926 29.950 40.000 50.020 60.034 70.041 80.039 90.027 95.016 100.000
0 1.324 1.862 2.602 3.138 3.558 4.171 4.574 4.819 4.939 4.869 4.502 3.931 3.193 2.305 1.271 .698 .084
0 1.311 2.582 5.104 7.614 10.117 15.111 20.096 25.074 30.050 40.000 49.980 59.966 69.959 79.961 89.973 . 94.984 100.000
0 -1.200 -1.620 -2.134 -2.458 -2.682 -2.953 -3.074 -3.101 -3.063 -2.869 -2.556 -2.153 I -1.693 -1.193 -.659 -.378 -.084 I
L. E. radius: 0.70 Slope of radius through L. E.: 0.05
L. E. radius: 0.89
.
-I
NACA 241 8
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
I
Station
I
Station
Ordinate .Station Ordinate
ioo
-2~i5
2.99 4.13 4.96 5.63 6.61 7.26 7..67 7.88 7.80 7.24 6.36 5.18 3.75 2.08 1.14 (.13) -----
0 0 -1.65 1. 25 -2.27 2.5 -3.01 i 5.0 -3.46 , 7.5 . -3.75 10 15 -4.10 -4.23 20 -4.22 I 25 -4.12 30 -3.80 40 -3.34 50 -2.76 60 -2.14 I 70 -1.50 80 -.82 90 95 -.48 (-.13) , 100 100 o
I
I
L. E. radius: 1.58 Slope of radius through L. E.: 0.10 --'
- -
Ordinat~
Lower surface
I
StatIOn Ordinate'
- - - ---- - - - - - -
- - ---- ---- - - 0 1. 25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70. 80 90 95 100
Upper surface
I ----
0 1.25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100 100
-2~7i
3.71 5.07 6.06 6.83 7.97 8.70 9.17 9.38 9..25 8.57 7.50 6.10 4.41 2.45 1. 34 (.16) -----
0 1.25 2.5 5.0 7.5 10 15 20 25 30 40 ' 50 60 70 80 90 95 100 100
Ordinate Statiou
Ordinate
I
---------- ---0 1.174 2.398 4.870 7.358 9.854 14.861 19.880 24.907 29.937 40.000 50.025 60.042 70.051 80.049 90.034 95.021 100.000
0 1.639 2.297 3.194 3.837 4.338 5.062 5.531 5.809 5.940 5.836 5.385 4.692 3.804 2.741 1. 513 .832 .105
0 -1. 515 -2.055 -2.726 -3.157 -3.462 -3.844 -4.031 -4.091 -4.064 -3.836 -3.439 -2.914 -2.304 -1.629 -.901 -.512 -.105
0 1.326 2.602 5.130 7.642 10.146 15.139 20.120 25.093 30.063 40.000 49.975 59.958 69.949 79.951 89.966 94.979 100.000
I I
Upper surface
Lower surface
Station Ordinate Station Ordinate ------- ---- - 0 1.158 2.378 4.845 7.330 9.824 14.833 19.857 24.889 29.925 40.000 50.029 60.051 70.061 80.058 90.040 95.025 100.000
0 1. 954 2.733 3.786 4.537 5.118 5.951 6.486 6.799 6.940 6.803 6.267 5.453 4.413 3.178 '1. 753 .966 .126
0 1.342 2.622 5.155 7.670 10.176 15.167 20.143 25.111 30.075 40.000 49.971 59.949 69.939 79.942 89.960 94.975 100.000
0 -1. 830 -2.491 -3.318 -3.857 -4.242 -4.733 -4.986 -5.081 -5.064 -4.803 -4.321 -3.675 -2.913 -2.066 -1.141 -.646 -.126
!:d
I':l "d
o
~
Z
?
00 ~
0 -2.06 -2.86 I -3.84 , -.4.47 -4.90 -5.42 -5.66 -5.70 -5.62 -5.25 -4.67 I -3.90 -3.05 -2.15 -1.17 -.68 (-.16) 0
Upper surface
Lower surface
------Station Ordinate Station Ordinate - - - ---.- - - - - - 0 1.25 2.5 5.0 7;5 10 15 20 25 30 40 50 60 70 80 90 95 100 100
-3:28 4.415
6.03 7.17 8.05 9.34 10.15 10.65 10.88 10.71 9.89 8.65 7.02 5.08 2.81 1. 55 (.19)
-
0 1. 25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 10.0 100
0 -2.45 -3.44 -4.68 -5.48 -6.03 -6.74 -7.09 . -7.18 -7.12 -6.71 -5.99 -5.04 -3.97 -2.80 -1.53 -.87 (-.19) 0
L. E. radius: 3.56 Slope·of radius through L. E.: 0.10
L. E. radius: 2.48 Slope of radius through L. E.: 0.10 I
L. E. radius: 1.10 Slope of radius through L. E.: 0.05
>l>-
I
L. E. radius: 1.58 Slope of radius through L. E.: 0.05
z ~ ......
NACA 241 5
Lower surface
Statiou
l
o o
---
NACA 241 2
Upper surface
Lower surface
- - - - - - - - -- - - - -
-
NACA 2421
NACA 2424
[Stations and ordinates given in percent of airfoil chord] Upper surface
Lower surfac~
Station
Ordinate Station
0 1. 25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100 100
0 1.2& 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100 100
Ordinate
----------- - 3.87 5.21 7.00 8.29 9.28 10.70 11.59 12.15 12.38 12.16 11.22 9.79 7.94 5.74 3.18 1. 76 (.22) -----
o Z >t"' >t:l -< ...... Ul o
0
~2.82
-4.02 -5.51 -6.48 -7.18 -8.05 -8.52 -8.67 -8.62 -8.16 -7.31 -6.17 -4.87 -3.44 -1.88 -1.06 (-.22) 0
L. E. radius: 4.85 Slope of radius through L. E.: 0.10 --
[Stations and ordinates given in percent of airfoil chord] Upper surface
0
~ ~
Lower surface
...... >-l >-l
----- - -
.885 2.012 4.380 6.820 9.300 14.333 19.427 24.555 29.700 40.000 50.U8 60.203 70.244 80.233 90.161 95.098 100.000
0 3.892 5.449 7.552 9.052 10.215 11.888 12.959 13.593 13.874 13.606 12.532 10.903 8.824 6.352 3.502 1. 930 -------
I':l I':l
0 0 1.615 -3.646 2.988 -4.965 5.620 -6.614 8.180 -7.692 10.700 -8.465 15.667 -9.450 20.573 -9.959 25.445 ~10.155 30.300 -10.124 40.000 -9.606 49.882 -8.644 59.797 -7.347 69.756 -5.824 79.767 -4.130 89.839 -2.280 94.902 -1.292 100.000 0
L. E. radius: 6.33 Slope of radius through L. E.: 0.10
>1
C":l
o
Station Ordinat3 Station Ordinate
----
!:d
>:rJ
o
!:d
~
!:d
o Z >-
~......
C":l
Ul
I
NACA 441 2
NACA 441 5
NACA 441 8
NACA 4421
NACA 4424
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinaws given in percent. of airfoil chord]
[Stations and ordinaws given in percent of airfoil chord]
[Stations and ordinaws given in percent of airfoil chord]
Upper surface
Lower surface
Station Ordinate Station Ordinate
---- - - - --_. ---0 1.25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100 100
0 2.44 3.39 4.73 5.76 6.59 7.89 8.80 9.41 9.76 9.80 9.19 8.14 6.69 4.89 2.71 1. 47 (.13)
-------
0 1.25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100 100
0 -1.43 -1.95 -2.49 -2.74 -2.86 -2.88 -2.74 -2.50 -2.26 -1.80 -1.40 -1.00 -.65 -.39 -.22 -.16 (-.13) 0
L. E. radius: 1.58 Slope of radius through L. E.: 0.20
Upper surface
Lower surface
-----Station Ordinate Station Ordinaw
- - - - ---- - - - - - 0 1. 25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100 100
3.07 4.17 5.74 6.91 7.84 9.27 10.25 10.92 11.25 11.25 10.53 9.30 7.63 5.55 3.08 1.67 (.16)
0 1. 25 . . 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100 100
0 -179 -2.48 -3.27 ~3. 71 -3.98 -4.18 -4.15 -3.98 -3.75 -3.25 -2.72 -2.14 -1.55 -1.03 -.57 -.36 (-.16) 0
L. E. radius: 2.48 Slope of radius through L. E.: 0.20
Station Ordinate Station Ordinate
--- ----
0 1. 25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100 100
Upper surface
Lower surface
Upper surface
--3~76-
5.00 6.75 8.06 9.11 10.66 11.72 12.40 12.76 12.70 11.85 10.44 8. 55 6.22 3.46 1. 89 (.19)
I -------
0 1.25 2.5 5.0 7.5 10 15 20
25 30 40 50
6a
70 80 90 95 100 100
0 -2.11 -2.99 -4.06 -4.67 -5.06 -5.49 -5.56 -5.49 -5.26 -4.70 -4.02 -3.24 -2.45 -1.67 -.93 -.55 (-.19) 0
L. E. radius: 3.56 Slope of radius through L. E.: 0.20
Station
Station Ordinaw Station Ordinaw
- - - - --- - - - - ----
-
0 1. 21; 2.5 5.0 7 . .5 10 15 20 25 30 40 50 60 70 80 90 95 100 100
4.45 .5.84 7.82 9.24 10.35 12.04 13.17 13.88 1!.27 14.16 13.18 11.60 9.50 6.91 3.85 2.11 (.22)
-----
30
40 50 60 70 80 90 95 100 100
-----Ordinaw Station Ordinate -----~
0
0 -2.42 -3.48 -4.78 -5.62 -6.15 -6.7.1 -6.9g -6.92 -6.76 -6.16 -5.34 -4.40 .. -3.35 -2.31 -1.27 -.74 (-.22) 0
0 1.25 2.5 5.0 7.5 10 15 20 25
Lower surface
Upper surface
Lower surface
.530 1.536 3.775 6.153 8.611 13.674 18.858 24.111 29.401 40.000 50.235 60.405 70.487 80.464 90.320 95.196 100.000
0 3.964 5.624 7.942 9.651 11.012 13.045 H.416 15.287 15.738 15.606 14.474 12.674 10.312 7.447 4.099 2.240 -----
0 1. 970 3.464 6.225 8.847 11. 389 16.326 21.142 25.889 30.599 40.000 49.765 59.595 69.513 79.536 89.680 94.804 100.000
0 -3.472 -4.656 -6.006 -6.931 -7.512 -8.169 -8.416 -8.411 -8. 238 -7.'606 -6.698 -5.562 -4.312 -3.003 -1.655 ~.964
0
L. E. radius: 6.33 Slope of radius through L. E.: 0.20
L. E. radius: 4.85 Slope of radius through L. E.: 0.20
-------
Ul
o
-
-
~ ~
>-
~
NACA 2301 2
NACA 2301 5
NACA 2301 8
[Stations and ordinaws given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinaws given in percent of airfoil chord]
Upper surface
Lower stuface
Station- Ordinaw Station Ordinate
---- --- --- - - 0 1.25 2.5 5.0 7.5 10 15 20
25 30 40 50 60 70 80 90 95 100 100
2.67 3.61 4.91 5.80 6.43 7.19 7.50 7.60 7.55 7.14 6.41 5.47 4.36 3.08 1.68 .92 (.13) -----
0 1. 25 2.5 5.0 7.5 10 15 20 25 30 40 50 .60 70 80 90 95 100 100
0 -1.23 -1.71 -2.26 -2.61 -2.92 -3.50 -3.97 -4.28 -4.46 -4.48 -4.17 -3.67 -3.00 -2.16 -1.23 -.70 (-.13) 0
. L. E. radius: 1.58 Slope of radius through L. E.: 0.305 ----
----
Upper surface
Lower surface
Station Ordinate Statio!l Ordinaw
---
0 1. 25 2.5 5.0 7.5 10 15 20 25 30 40 50
60 70 80 90 95 100 100
-3~34
4. 44 5.89 6.90 7.64 8.52 8.92 9.08 9.05 8.59 7.74 6.61 5.25 3.73 2.04 1.12 (.16) -----
0 1.25 2.5 5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100 100
0 -1.M -2.25 -3.04 -3.61 -4.09 -4.84 -5.41 -5.78
-5.96 -5.92 -5.50 -4.81 -3.91 -2.83 -1.59 -.90 (-.W)
0
L. E. radius: 2.48 Slope of radius through L. E.: 0.305 ----
---------
Upper surface
---- ---
Lower surface
Station OrdiDaw Station Ordinate
---- - - - - - - - - - 0 1.25 2.5 5.0 7.5 10 15 20
25 30 40 50 60 70 80 90 95 100 100
4.09 5.29 6.92 8. 01 8.83 9.86 10.36 10.56 10.55 10.04 9.05 7.75 6.18 4.40 2.39 1. 32 (.19)
0 1. 25 2.5 5.0 7.5 10 15 20 21\ 30 40 50 60 70 80 90 95 100 100
0 -1.83 -2.71 -3.80 -4.60 -5.22 -6.18 -6.86 -7.27 -7.47 -7.37 -6.81 -5.94 -4.82 -3.48 -1. 94 -1. 09 (-.19) 0
I,. E. radius: 3.56 Slope of radius through L. E.: 0.305
NACA 2302 4
NACA 2302 1 [Stations and ordinates given in percent of airfoil chord] Upper surface
---- ---
Station Ordinate Station Ordinaw -4~87 6. 14
7.93 .9.13 10.03 11.19 11.80 12.05 12. 06 11.49 10.40 8.90 7.09 5.05 2.76 1.53 (.22)
20
25 30 40 50 60 70 80 90 95 100 100
-----
0 -2.08 -3.14 -4.52 -5.55 -6.32 -7.51 -8. 30 -8.76 -8. 95 -8.83 -8.14 -7.07 -5.72 -4.13 -2.30 -1.30 (-.22) 0
0 1. 25 2.5
5.0 7.5 10 15 20 25 30 40 50 60 70 80 90 95 100 100
-
-
Lower surface
StatioD Ordinate Station Ordinate
---- ---- ---- - - - 0 .277 1.331 3.853 6.601 9.423 15.001 20.253¡ 25.262 30.265 40.256 50.235 60.202 70.162 80.116 90.064 95.036 100
0 4.017 5.764 8.172 9.884 11. 049 12.528 13.237 13.535 13. 546 12.928 11.690 10. 008 7.988 5.687 3.115 1. 724
-----
>-.... ~o .... t" t:1
~ >-
0 0 2.223 -3.303 3.669 -4. 432 6.147 -5.862 8.399 -6.860 10.577 -7.647 14.999 -8.852 19.747 -9.703 24.738 -10.223 29.735 -10.454 39.744 -10.278 49.766 -9.482 59.798 -8.242 69.838 -6.664 79.884 _4.803 89.936 -2.673 94.964 -1.504 0 100
L. E. radius: 6.33 Slope of radins through L.E.: 0.305
L. E. radius: 4.85 Slope of radius through L. E.: 0.305 --
"l
[Stations and ordinaws given in percent of airfoil chord] Upper surface
Lower surface
---- - - - ---- - - 0 1. 25 2.5 5.0 7.5 10 15
o
~
-.---
--
-
-
-----
I--'
or-'-
i-<
NACA 63,4-420
NACA 63A-420
NACA 63(420)-422
NACA 63(420)-51 7
NACA 63-006
[Stations and ordinates given in percent of airfoil chord]
a=0.3
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinat.:ls given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
J,ower surface
Upper surface
--------Station Ordinate Station Ordinate - - - --- - - 0 .215 .430 .887 2.082 4.538 7.024 9.526 14.554 19.603 24.663 29.732 34.S03 39.874 44.940 50.000 55.052 60.095 65.127 70.148 75.156 80.150 85.129 90.094 95.047 100
0 1.790 2.196 2.827 3.954 5.557 6.793 7.817 9.424 10.589 11.414 11.895 12.036 11.906 11.556 11.025 10.333 9.492 8.523 7.438 6.253 4.990 3.684 2.379 1. 131 0
0 .785 1.070 1. 613 2.918 5.462 7.976 10.474 15.446 20.397 25.337 30.268 35.197 40.126 45.060 .10.000 54.948 59.905 64.873 69.852 74.844 79.850 84.871 89.906 94.953 100
:~1.590
=g~
[Stations and ordinates given in percent of airfoil chord] Upper surfncc
I
------
I
---
I _ _ _-_-1 wwer surface
Station Ordinate Station Ordinate I
I
-3.210 -4.293 -5.097 -5.749 -6.732 -7.405 -7.834 -8. 007 -7.916 -7.622 -7.176 -6.613 -5.953 -5.208 -4.403 -3.MO -2.673 -1.806 -.992 -.311 .133 0
L. E. radius: 3.16 Slope of radius through I,. E.: 0.168
0 .065 .260 .691 1.856 4.268 6.771 9.280 14.347 19.4.18 24.604 29.808 35.00S 40.145 45.243 50.308 55.344 60.353 65.339 70.305 75.256 80.197 85.13-1 90.073 95.025 . 100.000
,
0 1.814 2.241 2.912 4.128 5.878 7.237 8.366 10.132 11.4IO 12.296 12.781 12.848 12.594 12.089 II. 388 JO.516 9.497 8.357 7.120 5.807 4.453 3.108 1.836 .728 0
0 .935 1. 240 1.809 3.144 .5.712 8.229 10.720 15.6.53 20.542 25.396 30.192 34.992 39.855 44.757 49.692 54.656 59.647 64.661 69.695 ' 74.744 79.803 84.866 89.927 94.975 100.000
0 -1.502 -1.805 -2.244 -2.968 I -3.914 -4.601 -5.158 i -5.996 -6.570 -6.948 -7.125 -7.108 -6.934 I
=~:~b
I
-5.756 -5.189 -4.553 -3.856 ' -3.111 -2.337 i -1.568 -.856 I -.272 i 0
L. E. radius: 3.16 Slope of radius through L. E.: 0.262
I
-----Station Ordinate Station Ordinate - - - - - - ----- - 0 .187 3.98 .850 2.041 4.492 6.977 9.478 14.509 19.563 24.630 29.705 34.784 39.861 44.934 50.000 55.057 60.104 65.140 70.163 75.172 80. Ie,S 85.142 90.103 95.051 100.000
0 1. 959 2.402 3.088 4.312 6.050 7.387 8.496 路10.231 11.489 12.377 12.890 13.034 12.883 12.493 11.907 11. 147 10.227 9.169 7.988 6.700 5.329 3.918 2.513 1.181 0
Upper surface
Lower surface
0
.S13
I. 102
1.650 2.959 5.508 8.023 10.522 15.491 20.437 25.370 30.295 35.216 40.139 45.066 50.000 54.943 59.896 64.860 69.837 74.828 79.835 84.8.18 89.897 94.949 100.000
0 -1.759 -2.122 -2.660 -3.568 -4.786 -.1.691 -6.428' -7.539 -8.305 -8.797 -9.002 -8.914 -8.599 -8.113 -7.495 -6.767 -5.943 -5.049 -4.100 -3.120 -2.145 -1.226 -.445 .083 0
Lower surface
I
------I
I
1
i
~
I
I
Upper snrfflce
o
0 1.551 1.912 2.477 3.498 4.966 6.104 7.050 8.542 9.633 10.416 10.887 11. 0.13 10.977 10.699 10.254 9.660 8.92.1 8.067 7.099 6.030 4.877 3.668 2.434 1.213 0
0
.800
I. 088
1.634 2.942 5.489 8.004 10.503 15.473 20.422 25.358 30.285 35.209 40.134 45.064 50.000 54.945 59.899 64.865 69.843 74.834 79.841 84.863 89.900 94.950 100.000
Lower surface
Station Ordinate Station Ordinate
Station Ordinate Station Ordinate
---- - - - - - - - - - -
---- ------- - 0 .200 .412 .866 2.058 4.511 6.996 9.497 14.527 19.578 24.642 29.715 34.791 39.866 44.936 50.000 55.055 60.101 65.135 70.157 75.166 80.159 S5.137 90.100 95.050 100.000
Upper surface
0 -1.301 -1.562 -1.941 -2.568 -3.386 -3.984 -4.466 -.1.178 -5.653 -5.940 -6.027 -.1.903 -5.621 -5.223 -4.738 -4.184 -3.569 -2.917 -2.239 -1.554 -.897 -.304 .150 .367 0
0 .5 .75 1.25 2.5 5.0 7.5 10 15 20 25 30 35 40 4.1 50 55
60 65 70 75 80 85 90 95 100
0
0
.503 .609 .771 1.057 1. 462 1. 766 2.010 2.386 2.656 2.841 2.954 3.000 2.971 2.877 2.723 2.517 2.267 I. 982 I. 670 I. 342 1.008 .683 .383 .138 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 80 85 90 95 100
0 -.503 -.609 -.771 -1.057 -1.462 -1.766 -2.010 -2.386 -2.656 -2.841 -2.954 -3.000 -2.971 -2.877 -2.723 -2.517 -2.267 -I. 982 -1.670 -1.342 -1.008 -.683 -.383 -.138 0
!:d t'i
'"d
o
!:d >-:3
Z
?
00 t>:)
H>-
I
z e3.... o
Z
J,. E. radius: 3.82 Slope of radius through L. E.: 0.168
L. E. radius: 0.297
L. E. radius: 2.283 Slope of radius through L. E.: 0.211
-
---
-
__ J
-
~ ~ -< .... [IJ.
o
NACA 63-009
NACA 63-206
NACA 63-209
NACA 63-210
NACA 631-012
[Stations and ordinates riven in p('rcent of airfoil chord]
[Stations and ordinat", given in perccnt of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinatl's given in pe.rcent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
Station
Upper surface
Lower surface
Upper suriace
.5
.75
1.25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 tiS
70 75 80 85 90 95 100
0
.5 .75 1. 25 2.5 5.0 7.5 10 15 20 25 30 35 40 4.5 . 50 55 60
65 70 75 80 85 90 95 100
0
I
-3.358 -2.928 -2.458 -1.966 -1. 471 -.990 -.550 196
0.
i
0 .458 .703 I. 197 2.438 4.932 7.429 9.930 14.934 19.941 24.950 29.960 34.970 39.981 44.991 50.000 55.008 60.015 65.020 70.023 75.023 80.022 85.019 90.013 95.006 100.000
0
.551 .677 .876 I. 241 I. 776 2.189 2.526 3.058 3.451 3.736 3.926 4.030 4.042 3.972 3.826 3.612 3.338 3.012 2.642 2.237 I. 804 ]. 356 .900 .454 0
0
.042 .797 1. 3.03 2.562 5.068 7.571 10.070 15.066 20.059 25.050 30.040 35.030 40.019 45.009 50.000 54.992 59.985 64.980 69.977 74.927 79.978 84.981 89.987 94.994 100.000
0 -.451 -.537 -.662 -.869 -1.144 -1.341 -1.492 -1. 712 -1. 859 -1. 946 -1.982 -I. 970 -1.900 -I. 782 -1. 620 -1.422 -1.196 -.952 -.698 -.447 -.212 -.010 .134 .178 0
1,. E. radius: 0.297 Slope of radius through L. E.: 0.0842
L. E. radius: 0.631 -
--
-
------ - - - - - - - - -
- - - ---- ---- - - -
0 -.749 -.906 -1.151 -1. 582 I -2.196 : -2.655 I -3.024 -3.591 I -3.997 -4.275 -4.442 -4.500 -4.447 ' -4.296
=gg~
Station IOrdinate Stat.ion Ordinate
Station Ordinate Station Ordinate
Ordinate Station Ordinate 0 .749 .906 1.151 I. 582 2.196 2.655 3.024 3.591 3.997 4.275 4.442 4.500 4.447 4.296 4.056 3.739 3.358 2.928 2.458 1.966 1.471 .990 .550 .196
Lower surface.
Upper surface
Lower surface
- - - - - - --------
---- ------ ---0
UppP,' surface
J.lowcr surface
0
I
I
I
.437 .680 1.170 2.408 4.897 7.394 9.894 14.901 19.912 24.925 29.940 34.956 39.971 44.986 50.000 55.012 60.022 65.029 70.033 75.034 80.032 85.027 90.019 95.009 100.000
0
.796 .973 1. 255 I. 765 2.510 3.077 3.539 4.263 4.792 5.169 5.414 5.530 5.518 5.391 5.159 4.834 4.429 3.958 3.430 2.861 2.267 1.668 1.067 .512 0
0
.563 .820 1.330 2.592 5.103 7.606 10.106 15.099 20.088 25.075 30.060 35.044 40.029 45.014 50.000 54.988 59.978 路64.971 69.967 74.966 79.968 84.973 89.981 94.991 100.000
0 -.696 -.833 -1.041 -1. 393 -1.878 -2.229 -2.505 -2.917 -3.200 -3.379 -3.470 -3.470 -3.376 -3.201 -2.953 -2.644 -2.287 -I. 898 -I. 486 -1. 071 -.675 -.317 -.033 .120 0
L. E. radius: 0.681 Slope of radius through L. E.: 0.0842
I
Station Ordinate Station ordina~1
---0 .430 .669 1.162 2.398 4.886 7.382 9.882 14.890 19.902 24.917 29.933 34.951 39.968 44.985 50.000 55.013 60.024 65.032 70.036 75.038 SO. 036 85.030 90.021 95.010 100.000
0
.876 1.107 1.379 1. 939 2.753 3.372 3.877 4.665 5.240 5.647 5.910 6.030 6.009 5.861 5.599 5.235 4.786 4.264 3.684 3.061 2.414 1. 761 1. 121 .530 0
0
.570 .831 I. 338 2.602 5.114 7.618 lO.ll8 15.lIO 20.098 25.083 30.067 35.049 40.032 45.015 50.000 54.987 59.976 64.968 69.964 74.962 79.964 84.970 89路979 94.990 100.000
0 -.776 -.967 -1.165 -1.567 -2.121 -2.524 -2.843 -3.319 -3.648 -3.857 -3.966 -3.970 -3.867 -3.671 -3.393 -3.045 -2.644 -2.204 -1.740 -1.271 -.822 -.415 -.087 .102 0
L. E. radius:路 0.770 Slope of radius through L. E.: 0.0842
I I
I
I I
Upper surface
~~
20 25 30 35 I
I
t'i t'i
Station Ordinate Station Ordinate
.5 .75 1.25 2.5 5.0 7.5
40
45 50 55 60 65 70 75 SO 85 90 95 100
0
.985 ].194 ].519 2.102 2.925 3.542
g~~
5.342 5.712 5. 930 6.000. 5. 920 5. 704 5.370 4. 935 4. 420 3.840 3. 210 2.556 1. 902 1. 274 .707 .250 0
L. E. radills: 1.087
0
.5 .75 1.25 2.5 5.0 7.5
~~
20 25 30 35 40 45 50 55 60 65 70 75 SO 85 90 95 100
><j
o
0 -.985 -1.194 -1.519 -2.102 -2.925 -3.542
=t~~~
-5.342 -5.712 -5.930 -6.000 - 5. 920 - 5. 704 -5.370 -4. 935 -4.420 -3.840 -3.210 -2.556 -I. 902 -1. 274 -.707 -.250 0
~
.... ..., ...,
I .Lower surface
---- ---- - - - - - - - o
~ S "" (l
!:d
~
g;
Z
>-
I
d
....>-3
(l
[IJ.
NACA 631-212
NACA 631-412
NACA 632-015
NACA 632-215
NACA 632-41 5
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinaj;es gben in percent oj airfoil chord] ,
;Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
Stations and ordinates given in percent of airfoil chord]
~
Upper surface Station
I~
o I .417 .657 1.145 2.378 4.863 7.358 9.859 14.S68 19.882, 2{.900
I
~n~1
39.962 44.982 50.000 55.016 60.029 65.038 70.043 75.045 80.042 85.035 90 .. 025 95.012 100.000
0 1.0.32 1.260 1.622 2.284 3.238 3.963 4.554 5.470 6.137 6.606 6.901 7.030 6.991 6.799 6. 473 6.030 5.491 4.870 4.182 3.451 2.698 ' 1.947 1.224 .566 0
Lower surface
Upper surface
Lower surface
,
I
i
Station Ordinate o
,0 -.932 .583 .843 -1.120 1.355 -1.408 2.622 -1.912 5.137 -2.606 7.642 -3.115 10.141 -3.520 15. 132 : -4.124 20.118 -4.545 25.100 -4.816 30.080 -4.957 35. OW -4.970 40.038 -4.849 45.018 -4.609 50.,000 -4.267 54.984 -3.~ 59.971 -3.349 64.962 -2.810 69.957 ·-2.238 74.955 -1.661 79.958 -1.106 84.965 -.601 -.190 89.975 94.988 .066 100.000 0
L, E. radius: 1.087 Slope of radius through L. E.: 0.0842
Station
Ordinate Station Ordinate
--0 .336 .•167 1.041 2.257 4.727 7.218 9.718 14.735 19.765 24.800 29.840 34.882 39.924 44.964 50.000 55.031 60.057 65.076 70.087 75.089 80.084 85.070 90.049 95.023 100.000
0 1.071 1. 320 1. 719 2.460 3.544 4.379 .1.063 6.138 6.929 7.499 7.872 8.059 8.062 7.894 7.576 7.125 6.562 5.899 5.153 4.344 3.492 2.618 1. 739 .881 0
0 .664 .933 1. 459 2.743 5.273 7.782 10.282 15.265 20.235 25.200 30.160 35.118 40.076 45.036 50.000 54.969 59.943 64.924 69.913 74.911 79.916 84.930 89.951 94.977 100.000
- - - - -1
0 -'.871 -1.040 -1.291 -1. 716 -2.280 -2.685 -2.995 -3.446 -3.745 -3.919 -3.984 -3.939 -3.778 -3.514 -3.164 -2.745 -2.278 -1. 779 -1. 265 -.764 -.308 .074 .329 .383 0
Uppe,r surface
i Station Ordinate Station Ordinate ---- ------ ---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 80 85 90 95 100
L. E. radius: 1.087 Slope of radius through L. E.: 0.1685
Upper surface
Lower surface
0 1.204 1. 462 1.878 2.610 3.648 4.427 5.055 6. on 6.693 7.155 7.421 7.500 7.386 7.099 6.665 6.108 5.458 4.721 3.934 3.119 2.310 1.541 .852 .300 0
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 80 85 90 95 100
Lower surface
I
Station Ordinate Station Ordinate
0 .399 .637 1.120 2.348 4.829 7.323 '9.823 14.834 19.852 24.875 29.900 34.926 39.952 44.977 50.000 55.019 60.035 65.047 70.053 75.055 • 80.051 85.043 90.030 95.014 100.000
~6.011
-6.693 -7.155 -7.421 -7.500 -7.386 -7.099 -6.665 -6.108 -5.453 -4.721 -3.934 -3.119 -2.310 -1. 541 -.852 -.300 0
L. E. radius: 1.594
0 1.250 1.528 1. 980 2.792 3.960 4.847 5.569 6.682 7.487 8.049 8.392 8.530 8. 457 8.194 7.768 7.203 6.524 5.751 4.906 4.014 3.105 2.213 1.368 .616 0
0 .601 .863 1. 380 2.652 5.171 7.677 10.177 15.166 20.148 25.125 30.100 35.074 40.048 45.023 50.000 54.981 59.965 64.953 69.947 74.945 79.949 84.957 89.970 94.986 100.000
- - - --- - - - - - -
0 -1.150 -1.388 -1.766 -2.420 -3.328 -3.999 -4.535 -5.336 -5.895 -6.259 -6.448 -6.470 -6.315 -6.004 -5.562 -5.013 -4.382 -3.691 -2.962 -2.224 -1.513 -.867
-.334
0 .300 .525 .991 2.198 4.660 7.147 9.647 14.669 19.705 24.750 29.800 34.852 39.C05 44.955 50.000 55.039 60.070 65.093 70.106 75.109 80.102 85.085 90.059 95.028 100.000
I
.016 0
L. E. radius: 1.594 Slope ofradius through L. E.: 0.0842
Lower surface'
Station Ordinate Station Ordinate
---- --- ---- - -
0 -1. 204 -1.462 -1.878 -2.610 -3.648 -4.427 -5.055
Upper surface
0 1.287 1.585 2. 074 2.964 4.264 5.261 6.077 7.348 8279 8.941 9.362 9.559 9.527 9.289 8.871 8.298 7.595 6.780 5.877 4.907 3.900 2.885 1.884 .931 0
0 .700 .975 1.509 2.802 5.340 7.853 10.353 15.331 20.295 25.250 30.200 35.148 40.095 45.045 50.000 54.961 59.930 64.907 69.894 74.891 79.898 84.915 89.941 94.972 100.000
0 -1.087 -1.305 -1.646 -2.220 -3..000 -3:565 , I -4.009 -4.656 -5.095 -5.361 -5.474 -5.439 -5.243 -4.909 -4.459 I -3.918 -3."311 -2.660 -1.989 -1.327 , -.716 -.193 .184 .333 I 0
L. E. radius: 1.594 SlopeofradiusthroughL. K: 0.1685
,
U2
c:l ~ ~
~
><:
o>rj :> .....
NACA 6~2-615'
NACA 633-01 8
NACA 633-21 8
NACA 633-41 8
NACA 633-61 8
[Stations and ordinates given in percent of ' airfoil chord]
[Stations and ordinates given in percent of airfoil chord] ,
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
Upper surface
I
I'()wer surface
Station Ordinate Station Ordinate
--0 .205 .418 .866 2.050 4. 492 6.973 9.473 14. 504 19. 558 24.625 29.700 34.778 39.857 44.932 50.000 55.058 60.105 65.139 70.159 75.163 80.153 85.127 90.089 95.042 100.000
0 1.317 1.634 2.159 3.129 4.560 5.667 6.578 8.010 9.066 9.830 10.331 10.587 10.598 10.384 9.974 9.393 8.665 7.809 6.847 5.800 4.693 3.555 2.398 ' 1.245 0
0
..795 1.082 1.634 2.950 5.508 8.027 10.527 15.496 20.442 25.375 30.300 35.222 40.143 45.068 50.000 54.942 59.895 64.861 69.841 74.837 79.847 84.873 89.911 94.958 100.000
0 -1.017 -1.214 -1. 517 -2.013 -2. 664 -3.123 -3.476 -3.972 -4.290 -4.460 -4.499 -4.407 -4.172 -3.814 -3.356 -2.823 -2.239 -1. 629 -1.015
-.430
.083 .483 .704 .651 0
Upper surface
Lower surface.
I
Station Ordinate Station Ordinate
-----0
.5
.75 1.25 2.5 , 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 7., 80 85 90 95 100
0 1.404 1.713 2.217 3.104 4.362 5.308 6.068 7.225 8.048 8.600 8.913 9:000 8.845 8.482 7.942 7.256 6.455 5.567 4.622 3.650 2.691 1. 787 .985 .348 0
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 80 85 90 95 100
0 -1.404 -1.713 -2.217 -3.104 -4.362 -5.308 -6.068 -7.225 -8.048 -8.600 -8.913 -9.000 -8.845 -8.482 -7.942 -7.256 -6.455 -5.567 -4.622 -3.650 -2.691 -1. 787 -.985
Upper surface
0
Upper surface
Station Ordinate Station Ordinate
---- - - - ----- - 0 .382 .617 1.096 2.319 4.796 7.288 9.788 14.801 19.822 24.850 29.880 34.911 39.943 44.973 50.000 55.023 60.042 65.055 70.062 75.064 80.059 85.049 90.034 95.016 100.000
-.348
Lower surface
0 1.449 1.778 2.319 3.285 4.673 5.728 6.581 7.895 8.842 9.494 9.884 10.030 9.916 9.577 9.045 8.351 7.526 6.597 5.594 4.544 3.486 2.459 1. 501 .664 0
Lower surface
Upper surface
I
;0
Station Ordinate Station Ordinate
Lower surface
0
0 .618 -1.349 .88.3 -1.638 1.404 -2.105 2.681 -2.913 5.204 -4.041 7.712 -4.880 10.212 -5.547 15.199 -6.549 20.178 -7.250 25.150 -7.704 30.120 -7.940 35.089 -7.970 40.057 -7.774 45.027 -7.387 50.000 -6.839 54.977 -6.161 59.958 -5.384 64.945 -4.537 69.938 -3.650 74.936 , -2.754 79.941 .-1.894 84.951 -1.113 89.966 -.467 94.984 -.032 100.000 0
0
.267 .487 .945 2.140 4:59.3 7.077 9.577 14.602 19.645 24.699 29.760 34.823 39.886 44.946 50.000 55.046
60.083
'65.110 70.125 75.128 80.119 85.099 90.069 95.032 100.000
0 1.484 1.833 2.410 3.455 4.975 6.139 7.087 8.560 9.632 10.385 10.854 11.058 10.986 10.1\72 10.148 9.446 8.596 7.626 6.564 5.438 4.280 3.130 2.017 .978 0
0
.733 1.013 1.555 2.860 5.407 7.923 10.423 15.398 20.355 25.301 30.240 35.177 40.114 45.054 50.000 54.954 59.917 64.890 69.875 74.872 79.881 84.901 89.931 94.968 100.000
Station Ordinate Station
o ..... t"
C;
,
- - - --- ---- ----
"1
Ordinat~
:> ..., :>
- - - - --- - - - - - 0
0 -1. 284 -1. 553 -1.982 -2.711 -3.711 -4.443 -5.019 -5.868 -6.448 -6.805 -6.966 -6.938 -6.702 -6.292 -5.736 -5.066 -4.312 -3.506 -2.676 -1.&18 -1.096 -.438 .051 .286 0
.156 .a61 .797 1.965 4.393 6.868 9.367 14.404 19.469 24.549 29.640 34.734 39.829 44.919 50.000 55.069 60.125 65.164 70.187 75.191 SO. 178 85.147 90.103 95.048 100.000
0 1.511 1. 878 2.491 3.616 5.268 6.542 7.586 9.219 10.418 11. 273 11.822 12.086 12.0.16 11.767 1l.251 19. 541 9.667 8. 655 7.534 6.330 5.073 3.800 2.531 1. 293 0
0 .844 1.139 1. 703 3.035 5.607 8.132 10.63.3 15.596 20.531 25.451 30.360 35.266 40.171 45.081 50.000 54.931 59.875 64.836 69.813 74.809 79.822 84.853 89.897 94.952 100.000
0 -1.211 -1.458 -1.849 -2.500 -3.372 -3.998 -4.484 -5.181 -5.642 -5.903 -5.990 -5.906 -5.630 -5.197 '-4.6.33 -3.971 -3.241 -2.475 -1.702 -.960 -.297 .238 .571 .603 0 I
L. E. radius: 1.594 Slope Qfradius through L. E.: 0.2527
L. E. radius: 2.120 --
I
L. K radius: 2.120 Slope of radius through L. E.: 0.0842
L. E. radius: 2.120 Slope of radius through L,K: 0.1685 -
-
----
- -
L. E. radius: 2.120 Slope of radius through L. E.: 0.2527 -
--
-
I-'-
8
.....
NACA 634-021
NACA 634-221
NACA 634-421
NACA 64-006
NACA 64-009
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chorli]
[Stations and ordinates given in percent of airfoil chord]
~persurf~1
Lower surface
Upper surface
--------Station Ordinate Station Ordinate
- - - - - - --- - - - 0 .5 .75 I. 2.5 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0 .5 .75 I. 2.'; 2.5 5.0
0 1.583 I. 937 2.527 3.577 5.065 6.182 7.080 8.441 9.410 10.053 10.412 10.500 10.298 9.854 9.206 8.390 7.441 6.396 5.290 4.160 3.054 2.021 I. 113 .392 0
7.5
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0 -1.583 -1.937 -2.527 -3.577 -5.065 -6.182 -7.080 -8.441 -9.410 -10.053 -10.412 -10.500 -10.298 -9.854 -9.206 -8.390 -7.441 -6.396 -5.290 -4.160 -3.054 -2.021 -1.113 -.392 0
I
I
I
i
I
Station
Station
Ordinate Station Ordinate
---- ---- - - - - - 0 .367 .600 I. 075 2.292 4.763 7.253 9.75.'l 14.767 19.792 24.824 29.860 34.897 39.934 44.969 50.000 55.027 60.048 65.063 70.071 75.073 80.067 85.056 90.039 95.018 100.000
0 1.627 2.001 2.628 3.757 5.375 6.601 7.593 9.111 10.204 10.946 11.383 11.529 11. 369 10.949 10.309 9.485 8.512 7.426 6.262 5.054 3.849 2.693 1.629 .708 0
0 .237 .452 .902 2.086 4.527 7.007 9.506 14.535 19.585 24.649 29.719 34.793 39.867 44.937 50.000 55.054 60.096 65.126 70.143 75.145 80.135 85.111 90.078 95.037 100.000
I
I
0 .763 1.048 1. 598 2.914 5.473 7.993 10.494 15.465 20.415 25.351 30.281 35.207 40.133 45.063 50.000 54.946 59.904 64.874 69.857 74.855 79.865 84.889 89.922 94.963 100.000
0 -1.461 -1. 774 -2.289 -3.181 -4.411 -5.314 -6.029 -7.082 -7.809 -8.257 -8.464 -8.438 -8.155 -7.664 -7.000 -6.200 -5.298 -4.335 -3.344 -2.367 -1.459 -.672 -.076 .242 0
I
I
0 .494 .596 .754 1.024 1.405 1. 692 1.928 2.298 2.572 2.772 2.907 2.981 2.995 2.919 2.775 2.575 2.331 2.050 1. 740 1.412 1.072 .737 .423 .157 0
0 .50 .75 I. 25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0
0
-.494 -.596 -.754 -1.024 -1.405 -1.692 -1.928 -2.298 -2.572 -2.772 -2.907 -2.981 -2.995 -2.919 -2.775 -2.575 -2.331 -2.050 -1.740 -1.412 -1.072 -.737 -.423 -.157 0
Lower surface
Upper surface
---- ------ - - -
---- ------ ---0 .50 .75 I. 25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
~
Station Ordinate Station Ordinate
Station Ordinate Statiou Ordiilate
Ordinate Station Ordinate 0 I. 661 2.054 2.717 3.925 5.675 7.010 8.097 9.774 10.993 11.837 12.352 12.558 12.439 12.044 11. 412 10.580 9.582 8.455 7.232 5.947 4.643 3.364 2.144 I. 022 0
Lower surface
Upper surface
Lower surface
- - - ---- - - - ----
0 0 .6.'l3 -1.527 .900 -1.861 1.425 -2.414 2.708 -3.385 5.237 -4.743 7.747 -5.75.'l 10.247 -6.559 15.233 -7.765 20.208 -8.612 25.176 -9.156 30.140 -9.439 35.103 -9.469 40.066 -9.227 45.031 -8.759 50.000 -8.103 54.973 -7.295 59.952 -6.370 64.937 -5.366 69.929 -4.318 74.927 -3.264 79.933 . -2.257 84.944 -1.347 -.595 89.961 -.076 94.982 100.000 0
L. E. radius: 2.650 Slope of radius through L. E.: 0.0842
L. E. radius: 2.650
Upper surface
Lower surface
o
I
i
I
.50 .75 1.25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0 .739 .892 1.128 1.533
0 .SO .75 1.25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
2.109
2.543 2.898 3.455 3.868 4.170 4.373 4.479 4.490 4.364 4.136 3.826 3.452 3.026 2.561 2.069 1.564 1.069 .611 .227 0
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 -4.364 -4.136 -3.826 -3.452 -3.026 -2.561 -2.069 -1. 564 -1.069 -.611
::0 t'l "d
o
~
>-:3
Z
?
00 ~
>I>
~ >-:3
-.227
o'-<
0
Z ;.-
1
L. E. radius: 2.650 Slope of radius through L. E.: 0.1685
L. E. radius: 0.579
L. E. radius: 0.256
t<
;.t:;)
--
< '-< 111 o ~
NACA 64-1 08
NACA 64-1 1 0
NACA 64-206
NACA 64-208
NACA 64-209
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord}
""
l.l
Lower surface
Upper surface Station
Ordinate Station Ordinate
- - - - - - - ---- - - - 0 .472 .719 1. 215 2.460 4.956 7.455 9.955 14.958 19.962 24.968 29.974 34.980 39.987 44.994 50.000 55.005 60.010 65.013 70:015 75.016 80.015 85.013 90.010 95.005 100.000
0 .682 .828 1.058 1.457 2.032 2.471 2.832 3.405 3.8.% 4.152 4.370 4.494 4.528 4.431 4.236 3.959 3.617 3.219 2.777 2.302 1.802 1. 297 .808 .364 0
0 .528 .781 1. 285 2.540 5.044 7. ,545 10.045 15.042 20.038 25.032 30.026 35.020 40.013 45.006 50.000 ,54.995 59.990 64.987 69.985 74.984 79.985 84.987 89.990 94.995 100.000
0 -.632 -.758 -.950 -1.271 -1.716 -2.047 -2.316 -2.733 -3.039 -3.256 -3.398 -3.464 -3.456 -3.335 -3.132 -2.86.'l ¡-2.545 ':"2.189 -1.805 -1.406 -1.006 -.625 -.292 -.048 0
Station
Lower surface
Upper surface
Ordinate Station Ordinate
Station
Ordinate Station Ordinate
--- ----
---- --- --- ----
0 .465 .712 I. 207 2.450 4.945 7.443 9.944 14.947 19.953 24.959 29.967 34.975 39.984 44.992 50.000 55.007 60.012 65.016 70.019 75.020 80.019 85.016 90.012 95.006 100. 000
0 .844 I. 02.'l 1.303 I. 793 2.500 3.037 3.479 4.178 4.700 5.087 5.350 5.495 5.524 5.391 5.138 4.786 4.356 3.860 3.313 2.729 2.120 1.512 .929 .406 0
Lowrr surface
Lower surface
Upper surface
-------0 .535 .788 1. 293 2.550 5.055 7.557 10.056 15.053 20.047 25.041 30.033 35.025 40.016 45.008 50.000 54.993 59.988 64.984 69.981 74. g80 79.981 84.984 89.988 94.994 100.000
0 -.794 -.953 -1. 195 -1.607 -2.184 -2. Ill;) -2.96.'l -3.506 -3.904 -4.191 -4.378 -4.465 -4.452 -4.295 -4.034 -3.690 -3.284 -2.830 -2.341 -1.833 -1.324 -.840 -.413 -.090 0
0 .459 .704 I. 198 2.440 4.934 7.432 9.933 14.937 19.943 24.952 29.961 34.971 39.981 44.991 50.000 55.008 60.015 65.020 70.023 75.025 80.024 85.020 90.015 95.007 100.000
0 .542 .664 .859 1. 208 1. 719 2. Il5 2.444 2.970 3. :367 3.667 3.879 4. OIl 4.066 4.014 3.878 3.670 3.402 3.080 2.712 2.307 1.868 1.410 .940 .473 0
0 .541 .796 1.302 2.560 5.066 7.568 10.067 15.06.'l 20.057 25.048 :lO.039 35.029 40.019 45.009 50.000 54.992 59.985 64.980 69.977 74.975 79.976 84.980 89.985 94.993 100.000
0 -.442 - . .524 -.645 -.836 -1.087 -1. 267 -1.410 -1.624 -I. 775 -1.877 -1. 935 -I. 951 -1.924 -1.824 -1.672 -1.480 -1.260 -1.020 -.768 -.517 -.276 -.064 .094 .159 0
Station Ordinate Station Ordinate
---- --------0 .445 .688 1.180 i 2.421 4.912 7.410 9.909 14.915 19.924 24.935 29.948 34.961 39.974 44.988 50.000 55.011 60.020 65.027 70.031 75.032 80.031 85.027 90.019 95.010 100.000
0 .706 .862 1.110 1.549 2.189 2.681 3.089 3.741 4.232 4.598 4.856 5.009 5.063 4.978 4.787 4. S06 4.152 3.733 3.263 2.749 2.200 1.634 1.067 .522 0
0 .555 .812 1.320 2.579 5.088 7.590 10.091 15.085 20.076 25.065 30.052 35.039 40.026 45.012 SO. 000 54.989 59.980 64.973 69.969 74.968 79.969 84.973 89.981 94.990 100.000
0 -.606 -.722 -.896 -1.177 -1.557 -1.833 -2.055 -2.395 -2.640 -2.808 -2.912 -2.949 -2.921 -2.788 -2.581 -2.316 -2.010 -1.673 -1.319 -.959 -.608
-.288 -.033
.UO
0
Upper surface
>-:3 >-:3
t'l t'l
Station Ordinate Station Ordinate
---- ------ - - 0 .438
.680
1.172 2.411 4.901 7.398 9.899 14.905 19.915 24.927 29.941 34.956 39.971 44.986 50.000 55.012 60.022 65.030 70.035 75.036 SO. 035 85.030 90.021 95.011 100.000
0 .786 .959 1. 2,~2 1. 716 2.423 2.965 3.413 4.127 4.66.'l 5.064 5.345 5.509 5.561 5.459 .5.239 4.921 4.523 4.056 3.533 2.964 2.360 1. 742 1.128 .543 0
0 .562 .820 1.328 2.589 5.099 7.602 10.101 15.095 20.085 25.073 30.059 35.044 40.029 45.014 50.000 54.988 59.978 64.970 69.965 74.964 79.965 84.970 89.979 94.989 100.000
L. E. radius: 0.720 Slope of radius through L. E.: 0.042 -
- -
L. E. radius: 0.256 Slope of radius through L. E.: 0.084 --
L. E. radius: 0.455 Slope of radius through L. E.: 0.084
"j
o
0 -.686 -.819 -1.018 -1.344 -1.791 -2.117 -2.379 -2.781 -3.071 -3.274 -3.401 -3.449 -3.419 -3.269 -3.033 -2.731 -2.381
~
;.t'l ~
o
~ ~'-<
l.l 111
~1.996
~1.589
-1.174 -.768 -.396 -.094 .089 0
-
L. E. radius; 0.579 Slope of radius through L. E.: 0.084 --
;::;:
~
Lower surface
I
E. radius: 0.455 Slope of radius through L. E.: 0.042 1,.
Upper surface
o
I I
NACA 64-210
NACA 641-012
NACA 641-112
NACA 641-212
NACA 641-412
[Stations and ordinates ~iven in percent of airfoil chord]
[Stations and ordinates given in percent of airfoiLchord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
Upper surface
Lower surface
------
Station Ordinate Station Ordinate
---- - - - - - - - - 0 .431 .673 1.163 2.401 4.890 7.387 9.887 14.894 19.905 24.919 29.934 34.951 39.968 44.985 50.000 55.0.14 -60.025 65.033 70.038 75.040 80.038 85.033 90.0.24 95.012 100.000
0 .867 1.056 1.354 1.884 2.656 3.248 3.736 4.514 5.097 5.533 5.836 6.010. 6.059 5.938 5.689 5.333 4.891 4.375 3.799 3.176 2.518 1.849 1.188 .564 0.
0 .569 .827 1.337 2.599 5.110 7.613 10.113 15.106 20.0.95 25.A81 30..066 35.0.49 40.032 45.0.15 50.000 54.987 59.975 64.967 69.962 74.960 79.962 84.968 89.977 94.988 100.000
0 -.767 -.916 -1.140-1.512 -2.024 -2.400 -2.70.2 -3.168 -3.505 -3.743 -3.892 -3.950 -3.917 -3.748 -3.483 -3.143 -2.749 -2.315 -1.855 -1.386 -.926
Upper surface
Station Ordinate Station Ordinate
- - -------- - 0.
0
-.154 .068 0.
0.
.978 1.179 1.490 2.035 2.810 3.394 3.871 4.620 5.173 5.576 5.844 5.978 5.981 5.798 5.4SO 5.056 4.048 3.974 3.350 2.695 2.0.29 1. 382 .786 .288 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 SO 85 90 95 100
-.503
Upper surface
Lower surface
.5 _ .75 1.25 2.5 5.0. 7.5 10 15 20 25 30. 35 40 45 50 55 60. 65 70 75 SO 85 90 95 100
0 -.978 -1.179 -1.490 -2.0.35 -2.810 -3.394 -3.871 -4.620 -5.173 -5.576 -5.844 -5.978 -5.981 -5.798 -5.480 -5.056 -4.048 -3.974 -3.350 -2.695 -2.0.29 -1.382 -.786 -.288 0
L. E. radius: 1.0.40
L. E. radius: 0..720 Slope of radius through L. E.: 0.084
Upper surface
Lower surface
Station Ordinate Station Ordinate
Station Ordiriate Station Ordinate
---- - - - - - - - - - -
- - - - - - - --0 - .459 .704 1.198 2_441 4.934 7.432 9.932 14.936 19.943 24.951 29.961 34.971 39.981 44.991 50.0.00 55.008 60.015 65.020 70..023 75.0.24 SO. 022 85.0.19 90.014 95.007 100.000
0 1.002 1.213 1.543 2.127 2.967 3.605 4.128 4.956 5.571 6.0.24 6.330. 6.493 6.517 6.346 . 6.0.32 5.604 5.084 4.489 3.836 3.143 2.427 _1. 718 1.044 .446 0.
0 .541 .796 1.302 2.559 5.0.66 7.568 10.068 15.0.64 20.0.57 25.0.49 30..0.39 35.0.29 40.019 45.009 50.000 04.992 59.985 .64.9SO 69.977 74.976 79.978 84.981 89.986 94.993 100..0.00
Upper surface
Lower surface
0 .418 .659 1.147 2.382 4.868 7.364 9.865 14.872 19.886 24.903 29.921 34.941 3R 961 44.982 50.000 55.0.16 60.0.29 65.0.39 70..045 75.047 80..045 85.0.38 90.0.27 95.0.13 10.0..000
0. -.952 -1.143 -1.435 -1. 941 -2.651 -3.181 -3.612 -4.284 -4.775 -5.128 -5.358 -5.463 -5.445 -5.250 -4.928 -4.508 -4.0.12 -3.459¡ -2.864 -2.247 -1.631 -1.046 -.528 -.130 0
I
L. E. radius: 1.040 Slope of radius through L. E.: 0.042
0. 1.0.25 1.245 1.593 2.218 3.123 3.815 4.386 5.291 5.968 6.470 6.815 7.008 7.0.52 6.893 6.583 6.151 5.619 5.004 4.322 3.590 2.825 2.0.54 1.303 .60.4 0
0
.582 .841 1. 353 2.618 5.132 7.636 10.135 15.128 20.114 25.0.97 30.0.79 35.0.59 40.0.39 45.0.18 50.000 04.984 59.971 64.961 69.955 74.953 79.955 84.962 89.973 94.987 100.0.0.0.
0 -.925 -1.105 -1.379 -1.846 -2.491 -2.967 -3.352 -3.945 -4.376 -4.680-4.871
6
0. 1.0.64 1. 305 1.690 2.393 3.430 4. 231 4.896 5.959 6.760 7.363 7.786 8.0.37 8.123 7.988 7.686 7.246 6.690 6.0.33 5.293 4.483 3.619 2.722 1.818 .919 0.
0.
.662 .931 1. 455 2.736 5.262 7.771 10..270. 15.255 20.228 25.195 30.158 35.118 40.0.77 45.0.37 50.000 54.968 59.941 64.922 69.910 74.906 79.911 84.924 89.945 94.973 tQQ.QOO
0. -.864 -1.025 -1.262 -1.649 -2.166 -2.535 -2.828 -3.267 -3.576 -3.783 -3.898 -3.917 -3.839 -3.608 -3.274 -2.866 -2.406 -1.913 -1.405 -.903 -.435 -.0.38 .250 .345 0.
U2
c:l
;:::
;:::.
L. E. radius: 1.0.40 Slope of radius through L. E.: 0.168
Q.Q~4 -
-
.338 .569 1.045 2.264 4.738 7.229 9.730 14.745 19.772 24.S05 29.842 34.882 39.923 44.968 50.000 5.5.0.32 60.0.59 65.0.78 70..0.90 75.0.94 80.0.89 . 85.0.76 90.0.55 95.0.27 100..000
~4._948
L. E. radius: 1.0.40. Slope of radius through L. E.:
Station Ordinate Station Ordinate
---- - - - - - - - - 0.
-4.910 -4.70.3 -4.377 -3.961 -3.477 -2.944 -2.378 -1.SOQ -1.233 -.7C8 -.269 .0.28
Lower surface
;..
~
-
o>:rj
NACA ~642-215
NACA 642-015
NACA 642-415
NACA 643-018
;..
....
NACA 643-218
~
"'1 [Stations and ordinates given in percent of airfoil chord] Upper surface Station
Lower surface
Ordinate Station Ordinate
---- - 0 .50. .75 1.25 2.5 5.0. 7.5 10 15 20. 2S 30. 3" 40. 45 50. 55 60. 65 70. 75 SO 85 90 95 100
0. 1.208 1. 456 1.842 2.528 3.50.4 4.240. 4.842 5.785 6.480. 6.985 7.319 7.482 7.473 7.224 6.810 6.266 5.620. 4.895 4.113 3.296 2.472 1. 677 .950. .346 0.
L. E. radius: 1.590
O. .50 .75 1. 25 2.5 5.0. 7.5 10 15 20 25 30. 35 40 45 50. 55 60. 65 70. 75 80. 85 90. 95 100
0. -1.208 -1.456 -1.842 -2.528 -3.504 -4.240. -4.842 -5.785 -6.480. -6.985 -7.319 -7.482 -7.473 -7.224 -6.810. -6.266 -5.620. -4.895 -4.113 -3.296 -2.472 -1.677 -.950
'j
[Stations and ordinates given in percent of airfoil chord] Upper surface
Lower surface
Upper surface
Station Ordinate Station Ordinate
---- - - - - - - - - 0.
.399 .637 1.122 2.353 4.836 7.331 9.831 11.840. 19.857 24.878 29.90.1 34.926 39.952 44.977 SQ. 000 55.0.20 60..0.36 65.048 70.0.55 75.058 SO. 0.55 ----sir.-ll4690..033 95.0.16 100.000
0. 1. 254 1.li22 1. 945 2.710. 3.816 4.661 5.356 6.456 7.274 7.879 8.290. 8. 512 8.044 8.319 7.913 7.361 6.691 5.925 5.0.85 4.191 3.267 2.349 1. 466 .662 0.
0 .601 .863 1. 378 2.647 5.164 7.669 10.169 15.160 20.143 25.122 30.099 35.0.74 40..048 45.0.23 50.000 04.980. 59.964 64.952 69.945 74.942 79.945 84.954 ¡89.967 94.984 100.000
0. -1.154 -1.382 -1. 731 -2.338 -3.184 -3.813 -4.322 -5.110 -5.682 -6.0.89 -6.346 -6.452 -6.40.2 -6.129 -5.70.7 -5.171 -4.549 -3.865 -3.141 -2.401 -1.675 -1.003 -.432 -.0.30. 0
L. E. radius: 1.590. Slope of radius through L. E.: 0.0.84 -
-------
--
[Stations and ordinates given in percent of airfoil chord]
Upper surface
Lower surface
Station \Ordinate Station Ordinate
Station Ordinate Station Ordinate 0
.299 .526 .996 2.207 4.673 7.162 9.662 14.681 19.714 24.756 29.S03 34.853 39.90.4 44.954 50..000. 55.0.40. 60..0.72 65.0.96 70..111 75.115 80.10.9 81i.Q92 90.066 95.0.32 100.000
0. 1. 291 1.579 2.0.38 2.883 4.121 5.0.75 5.864 7.122 8.0.66 8.771 9.260. 9.041 9.614 9.414 9.0.16 8.456 7.762 6.954 6.055 5.0.84 4.0.62 3.0.20. 1. 982 .976 0.
0.
.70.1 .974 1.504 2.793 5.327 7.838 10..338 15.319 20.286 25.244 30..197 35.147 40..0.96 45.046 50..000 04.960. 59.928 64.904 69.889 74.885 79.891 84.908 89.934 94.968 100.000
0. -1.0.91 -1.299 -1.610 -2.139 -2.857 -3.379 -3.796 -4.430. -4.882 -5.191 -5.372 -5.421 -5.330. -5.0.34 -4.60.4 -4.0.76 -3.478 -2.834 -2.167 -1.50.4 -.878 -.328 .0.86 .288 0
0.
.50
.75 1,25 2.5 5.0. 7.5 lO 15 20 25 30. 35 40. 45
50. 55 50 65 70. 75 80. 85 90. 95 100
I
0. 1.428 1. 720. 2.177 3.0.05 4.186 5.0.76 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 2.888 1.951 1.101 .400. 0
0.
.50. .75 1. 25 2.5 5.0. 7.5 10. 15 20. 25 30. 35 40. 45 50. 55 60 65 70. 75 80. 85 90 95 100.
0. -1.428 -1.720. -2.177 -3.005 -4.186 -5.0.76 -5.S03 -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 -2.888 -1.951 -1.10.1 -.400. 0.
--
l:::l
;.. >-3 ;..
Lower surface
Station Ordinate Station Ordinate
.380. .617 1.0.99_ 2.325 4.804 7.297 9.797 14.808 19.828 24.853 29.881 34.912 39.942 44.972 50.000 55.0.24 60.0.43 65.0.57 70..065 75.0.68 80.0.64 85.0.54 90.0.38 95.019 100.000
L. E. radius: 2.208
....ot"'
----------- - 0.
--
I
[Stations and ordipates given in percent of airfoil chord) Upper surface
Lower surface
- - -------- - -
L. E. radius: 1.590 Slope of radius through L. E.: 0..168 -
[Stations and ordinates given in percent of airfoil chord)
0. 1. 473 1. 785 2.279 3.186 4.497 5.496 6.316 7.612 8.576 9.285 9.750 10.009 10.0.23 9.725 9.217 8.040. 7.729 6.812 5.814 4.760 3.683 2.623 1. 617 .716 0.
0.
.620 .883 1.401 2.675 5.196 7.70.3 10.203 15.192 20.172 25.147 30.119 35.0.88 40..0.58 45.028 50..000 54.976 59.957 64.943 69.935 74.932 79.936 84.946 89.962 94.981 100.000
0 -1.373 -1. 645 -2.0.65 -2.814 -3.885 -4.-648 -5.282 -6.266 -6.984 -7.495 -7.816 -7.949 -7.881 -7.535 -7.0.11 -6.350 -5.587 -4.752 -3.870. -2.970 -2.0.91 -1.277 -.583 -.0.84 0.
L. E. radius: 2.208 Slope of radius through L. E.: 0..0.84
I
I-'-
o
CJ1
NACA 643-418
NACA 643-61 8
NACA 644-021
NACA 644-221
NACA 644..421
[Stations and ordinates given in percent 0 r airfoil chord] .
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
Upper surface
Lower surface
Station Ordinate Station ordinate-
-------0
.26.3 .486 .950 2.152 4.609 7.095 9.595 14.(iJ7 19.657 24.707 2<J.763 34.823 39.885 44.945 50.000 55.047 60.086 65.114 70.131 75.135 80.127 85. 108 90.077 95.037 100.000
0 1. 508 I. 840 2.370 3.357 4.800 5.908 6.823 8.277 9.366 10.176 10.730 11. 037 11.093 10.820 10.320 9.635 8. 799 7.841 6.784 5.654 4.477 3.294 2. 132 1. 030 0
I
0 .737 1.014 1.550 2.848 5.391 7.905 10.405 15.383 20.343 25.293 30.237 35.177 40.115 45.055 50.000 54.953 59.914 64.886 69.869 74.865 79.873 84.892 89.923 94.963 100.000
0 -1.308 -1.560 -1. 942 -2.613 -3.536 -4.212 -4.755 -5.585 -6.182 -6.596 -6.842 -6.917 -6.809 -6.440 -5.908 -5.255 -4.515 -3.721 -2.896 -2.074 -1.293 -.602 -.064 .234 0
L. E. radius: 2.208 Slope of radius through L. E.: 0.168
Upper surface
Station Ordinate Station Ordinate
- - - - - - - --- - - 0
.150 .359 .805 I. 982 4.417 6.895 9.395 14.427 19.486 24.560 29.645 34.735 39.827 44.917 50.000 55.071 60.129 n.1.171 70.196 75.203 80.191 85.161 90.115 95.056 100.000
0 1. 534 I. 885 2.452 3.518 5.093 6.312 7.322 8. 937 10.153 11.065 11. 698 12.065 12.163 1l.915 11.423 10.730 9.870 8.870 7.754 6.544 5.270 3.963 2.646 1. 344 ()
Upper surface
Lower surface
0 .850 1.141 1. 695 3.018 5.583 8.105 10.605 15.573 20.514 25.440 30.355 35.265 40.173 45.083 50.000 54.929 59.871 64.829 69.804 74.797 79.809 84.839 89.885 94.944 100.000
Lower surface
Upper surface
Station Ordinate Station Ordinate
Station Ordinate Station
---- --- --- ---0
0 -1.234 -1. 465 -I. 810 -2.402 -3.197 -3.768 -4.220 -4.899 -5.377 -5.695 -5.866 -5.885 -5.737 -5.345 -4.805 -4.160 -3.444 -2.690 -1.922 -I. 174 -.494 .075 .456 .552 0
.50 .75 1.25 2.5 5.0 7.5 10 Iii
20 25 30 35 40 45 50 55 60 65 70 75 80 8., 90 95 100
0 1. 646 1.985 2.517 3.485 4.871 5.915 6.769 8.108 9.095 9.807 10.269 10.481 10.431 10.030 9.404 8.607 7.678 6.649 5.549 4.416 3.287 2.213 1.245 .449 0
0 .50 .75 1.25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55
60 65 70 75 80 85 90 95 100
0 -1.646 -1.985 -2.517 -3.485 -4.871 -5.915 -6.769 -8.108 -9.095 -9.807 -10.269 -10.481 -10.431 -10:030 -9.404 -8.607 -7.678 -6.649 -5.549 -4.416 -3.287 -2.213 -1.245 -.449 0
L. E. radius: 2.884.
L. E. radius: 2.208 Slope of radius through L. E.: 0.253
Lower surface
0 .362 .596 1. 075 2.297 4.772 7.264 9.763 14.776 19.799 24.829 29.8t\1 34.897 39.933 44.968 50.000 55.027 60.050 65.065 70.075 75.077 80.073 85.061 90.044 95.021 100.000
I
0 1.690 2.649 2.618 3.665 5.182 6.334 7.282 8.778 9.889 10.701 '11.240 11.510 11. 502 11.125 10.507 9.702 8.749 7.679 6.521 5.310 4.082 2.885 1. 761 .765 0
0 .6.38 .904 I. 425 2.703 5.228 7.736 10.237 15.224 20.201 25.17l 30.139 35.103 40.067 45.032 50.000 54.973 59.950 64.935 69.925 74.92.3 79.927 84.939 89.956 94.979 100.000
J
~rdinate I
I
0 -1.590 -1.909 -2.404 -3.293 -4.550 -5.486 -6.248 -7.432 -8.297 -8..911 -9.296 -9.450 -9.360 -8.935 -8.301 -7.512 -6.607 -5.619 -4.577 -3.520 -2.490 -1.539 -.727 -.133 0
Upper surface Station
~
Lower surface
Ordinate Station
-------0 .227 .445 .903 2.096 4.545 7.028 9.528 14.553 19.599 24.657 29.723 34.794 39.865 44.936 50.000 55.055 60.099 65.131 70.150 75.154 80.145 85.122 90.087 95.042 100.000
0 1.723 2.101 2.707 3.834 5.482 6.744 7.786 9.442 10.678 11.591 12.209 12.539 12.572 12.220 11.610 10.797 9.819 8.708 7.491 6.203 4.876 3.556 2.276 1.079 0
I ordina~
0 .773 1.055 1.597 2.904 5.455 7.972 10.472 15.447 20.401 25.343 30.277 35.206 40.135 45.064 50.000 54.945 59.901 64.869 69.850 74.846 79.855 84.878 89.913 94.958 100.000
0 -1.523 -1.821 -2.27Q -3.090 -4.218 -5.048 -5.718 -6.750
I
-, .., I
-8.0n -8.321 -8.419 -8.288 ":'7.840 -7.198 -6.417 -5.535 -4.588 -3.603 -2.623 -1.692 -.864 -.208 .185 0 1
L. E. radius: 2.884 Slope of radius through L. E.: 0.084
-
L. E. radius: 2.884 Slope of radius through L. E.: 0.168 - - -
~
l'J
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NACA 65,3-018 [Stations and ordinates given in percent of airfoil chord] Upper surface
NACA 65,3-618
NACA 65,3-418
a=0.8 [Stations and ordinates given in percent of airfoil chordj
[Stations and ordinates giwn in airfoil chord]
Lower surface
Upper surface Upper surface
0 .5 .75 I. 25 2.5 5.0 7.5 10 15 20 25 30 3" 40 45 50 55 60 65 70 75 80 85 90 95 100
0 1.324 1.599 2.004 2.728 3.831 4.701 5.424 6.568 7.434 8.093 8.568 8.868 8.990 8.916 8.593 8.045 7.317 6.450 5. 4~6 4.456 3.390 2.325 1.324 .492 0
L. E. radius: 1.92
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 80 85 90 95 100
0 -1.324 -1..199 -2.004 -2.728 -3.831 -4.701 -5.424 -6.568 -7.43t -8.093 -8.568 -8.8flS -8.990 -8.916 -8.593 -8.045 -7.317 -6.450 -5.486 -4.456 -3.390 -2.325 -1.324 -.492 0
a=0.5
of
Station Ordinate Station Ordinate
Upper surface
---- --- --- ----
0 .248 .467 .931 2.131 4.578 7.053 9.544 14.558 19.592 24.641 29.700 34.765 39.8.35 44.932 49. 979 55.646 60.106 65.155 70.193 75.219 80.249 85.221 90.135 95.649 100.000
0 1. 416 1.736 2.224 3.133 4.542 5.672 6.617 8.149 9.319 10.233 10.909 II. 369 11.600 U.602 11.307 10.751 9.974 9.016 7.899 6.651 5.289 3.818 2.289 .930 0
0 .752 1.033 1.569 2.869 5.422 7.947 10.456 15.442 20.408 25.359 30.300 35.235 40.165 45.068 50.021 54.954 59.894 64.8·15 69.807 74.781 79.751 84.779 89.865 94.951 100.000
0 .176 .387 .R41 2.030 4.467 6.940 9.434 14.458 19.509 24.576 29.654 34.738 39.826 44.915 50.000 55.077 60.142 65.191 70.222 75.2.13 SO. 224 8.1.192 90.138 95.068 100.000
0 -1.184 -1.412 -I. 732 -2.273 -3.074 -3.688 -4.193 -4.957 -5.527 -5.937 -6.217 -6.361 -6.376 -6.230 -5.879 -5.339 -4.658 -3.880 -3.067 -2.251 -1.473 -.810 -.345 -.050 0
L. E. radiu~: 1.92 Slope of radius through L. E.: 0.194
0 1.434 1. 767 2.283 3.245 4.742 5.940 6.945 8. 565 9.806 10.767 11. 477 11.954 12.201 12.201 11.902 11.330 10.529 9.537 8.398 7.135 5.771 4.336 2.868 1.435 0
0 .824 1.113 1.659 2.970 5.533 8.060 10. .566 15.542 20.491 25.424 30.346 35.262 40.174 45.085 50.000 54. Q23 59.858 64.809 6~. 778 74.767 79.776 84.808 89.862 94.932 100.000
0 -1.134 -1.347 -1.641 -2.129 -2.846 I -3.396 ' -3.843 -4.527 -5.030 -5.397 -5.645 -5.774 -5.775 -5.631 -5.284 -4.760 -4.103 -3.357 -2.5f>6 -1. 765 -.995 -.298 .234 .461 0
L. E. radius: 1.92 Slope of radius through L. F.: 0.253 -
----
-
ordinate~
given in percent of airfoil chord]
Upper surface
Lower surface
Station
Station Ordinat, Stotion Ordinet, \
------- ---- - 0 .244 .469 .930 2.121 4.564 7.044 9.540 14.561 19.608 24.669 29.742 34.825 30.916 45.019 50.153 55.263 60.305 65.308 70.281 75.237 80.180 85.117 00.062 95.020 100.000
0 1.2.16 1. 498 1. 947 2.837 4.175 5.208 6.073 7.465 8.518 9.315 9.900 1().279 10.467 10.438 10.131 9.512 8.645 7.575 6.373 5.152 3.890 2.639 I. 533 .606 0
Lower surfaee
Lower surface
Station Ordinate Station Ordinate
- - - - - - - ---- - - - -
NACA 65-006 [Stations and
[Stations and ordinates given in percent of airfoil chord]
Lower surface
Station Ordinate Station Ordinate
---- --- ---- - -
perc~nt
NACA 65(21 6)-41 5
0 .7.56 1.031 1.570 2.879 5.436 7.956 10.460 15.439 20.392 25.331 30.258 35.175 40.084 44.981 49.847 54.737 59.695 64.692 69 .• 19 74.763 79.820 84.883 89.938 94.980 100.000
0 -.960 -1.110 -1.359 -1.801 -2.411 -2.832 -3.169 -3.673 -4.022 -4.267 -4.428 -4.•1;7 -4.523 -4.446 -4.251 -3.940 -3.521 -2.995 -2.409 -1.848 -1.278 -.723 -.305 -.030 0
Ordinato Station Ordinate
- - - - ._--- - - - - - 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 80 85 90 95 100
0 .476 .574 .717 .956 1.310 1.589 1.824 2.197 2.482 2.697 2.852 2.952 2.998 2.9S:l 2.900 2.741 2.518 2.246 1.935 I. 594 I. 233 .865 .510 .195 0
L. E. radius: 0.240 L. E. radius: 1.498 _ Slope of radius through .~~~ 0.233
0 .5 .75 1.25 2.5 5.0 7.5 10 15 20 25 30 35 40 4.1 50
55 60 65 70 75 80 81i 90 95 100
0 -.476 -.574 -.717 -.956 -1.310 -1.589 -1.824 -2.197 -2.482 -2.697 -2.852 -2.952 -2.998 -2.98.1 -2.900 -2.741 -2.518 -2.246 -1.9:15 -1.594 -1.233 -.865 -.510 -.195 0
U1
o
~
>1 (")
o
~
~ .....
>-3 >-l
l'J M "'l
o
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.....
(")
,p
NACA 65-009
NACA 65-206
NACA 65-209
NACA 65-21 0
(Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
UpPer surface
Lower surface
Upper surface
Station Ordinate Station Ordinate
---- - - - - - - - - 0 .5 .75 1. 25 2.5 5.0 7.5 10 15 20 25 30 35 40,
4S 50
55
60 65 70 75 80 85 90 95 100
0 .700 .845 1.058 1.421 1. 961 2.383 2.736 3.299 3.727 4.050 4.282 4.431 4.496 4.469 4.336 4.086 3.743 3.328 2.856 2.342 1.805 1,260 ,738 ,280 0
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 80 85 90 95 100
0 -.700 -.845 -1.058 -1.421 -1.961 -2.383 -2.736 -3.299 -3.727 -4.050 -4.282 -4.431 -4.496 -4.469 -4.336 -4.086 -3.743 -3.328 -2.856 -2.342 -1.805 -1.260 -.738 -,280 0
L. E. radius: 0.552
Station
Ordinate Station Ordinate
Upper surface
.460 .706 1.200 2.444 4.939 7.437 9.936 14.939 19.945 24.953 29.962 . 34.971 39.981 44.990 50.000 55.009 .60.016 65.022 70.026 75.028 . 80.027 .85.024 90.018 95.009 100.000
0 .524 .642 .822 1.140 1.625 2.012 2.340 2.869 3.277 3.592 3.824 3.982 4.069 '4.078 4.003 3.836 3.589 3.276 2.907 2.489 2.029 1.538 1.027 .511 0
0 .540 .794 1.300 2.556 5.061 7.563 10.064 15.061 20.055 25.047 30.038 35.029 40.019 45.010 50.000 54.991 59.984 64.978 69.974 74.972 79.973 84.976 89.982 94.991 100.000
0 -.424 -.502 -.608 -.768 -.993 -1.164 -1.306 -1. 523 -1.685 -1.802 -1.880 -1.922 -1.927 -1.888 -1. 797 -1.646 -1.447 -1.216 -.963 -.699 -.437 -.192 .007 .121 0
L. E. radius: 0.240 Slope of radius through L. E.: 0.084
Lower surface
Station Ordinate Station
--- ---0
I
Lower surface
Ordinate
---- - 0 ,441 .684 1.177 2.417 . 4.908 7.405 9.904 14.909 19.918 24.929 29.942 34.956 39.971 44.986 50.000 55.013 60.024 65.033 70.039 75.041 80.040 85.035 90.026 95.013 100.000
0 .748 .912 1.162 1.605 2.275 2.805 3.251 3.971 4.522 4.944 5.254 .1.461 5.567 5.564 5.439 5.181 4.814 4.358 3.828 3.237 2.601 1.933 1.255 .596 0
0
.559 .816 1.323 2.583 5.092 7.595 10.096 15.091 20.082 25.071 30.058 35.044 40.029 45.014 50.000 54. 987 59.976 64.967 69.961 74.959 79.960 84.965 89.974 94.987 100.000
0 -,648 -.772 -.948 -1.233 -1.643 -1.957 -2.217 -2.625 -2.930 -3.154 -3.310 -3.401 -3.425 -3.374 -3.233 -2.991 -2.672 -2.298 -1.884 .-1.447 -1.009 -.587 -.221 ,036 0
L. E. radius: 0.552 Slope of radius through L. E.: 0.084
Upper surface Station
NACA 65-41 0 [Stations and ordinates given in percent airfoil chord]
Lower surface
Upper surface
Ordinate Station Ordinate
Station
----------- - 0 .435 .678 1.169 2.408 4.898 7.394 9.894 14.899 19.909 24.921 29.936 34.951 39.968 44.984 50.000 55.014 60.027 65.036 70.043 75.045 80.044 85.038 90.028 95.014· 100.000
0 .819 .999 1.273 1.757 2.491 3.069 3.555 4.338 4.938 5.397 5.732 5.954 6.067 6.058 5.915 5.625 5.217 4.712 4.128 3.479 2.783 2.057 1.327 .622 0
0 .565 .822 1. 331 2.592 5.102 7.608 10.106 15.101 20.091 25.079 30.064 35.049 40.032 45.016 50.000 54.986 59.973 64.964 69.957 74.955 79.956 84.962 89.972 '94.986 100.000
Lower surface
Ordinate Station Ordinate
---- ------- - -
0 -.719 -.859 -1.059 -1.385 -1.859 -2.221 -2.521 -2.992 -3.346 -3.607 -3.788 -3.894 -3.925 -3.868 -3.709 -3.435 -3.075 -2.652 -2.184 -1. 689 -1.191 -.711 -.293 .010 0
0 .372 .607 1.089 2.318 4.797 7.289 9.788 14.798 19.817 24.843 29.872 34.903 39.936 44.968 50.000 55.029 60.053 65.073 70.085 75.090 80.088 85.076 90.057 95.029 100.000
L. E. radius: 0.687 Slope of radius through L. E.: 0.084
0
.861 1.061 1.372 1. 935 2.800 3.487 4.067 5.006 5.731 6.290 6.702 6.983 7.138 7.153 7.018 6.720 6.288 5.741 5.099 4.372 3.577 2.729 1.8·12 .937 0
0 .628 .893 1.411 2.682 5.203 7.711 10.212 15.202 20.183 25.157 30.128 35.097 40.064 45.032 50.000 54.971 59.947 64.927 69.915 74.910 79.912 84.924 89.943 94.971 100.000
0 -.661 -.781 -.944 -L191 -1.536 -1.791 -1.999 -2.314 -2.547 -2.710 -2.814 -2.863 -2.854 -2.773 -2.606 -2.340 -2.004 -1.621 -1.211 -.792 -.393 -.037 .226 .327 0
L. E. radius: 0.687 Slope of radius through L. E.: 0.168 -
NACA 651-012
NACA 651-212
[stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
Upper sUrface Station
Lower surface
Ordinate Station Ordinate
--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 80 85 90 95 100
0 .923 1.109 1. 387 le875 2.606 3.172 3.647 4.402 4.975 5,406 5.716 5.912 5.997 5.949 5.757 5.412 4.943 4.381 3.743 3.059 2.345 1.630 .947 .356 0
L. E, radius: 1.000
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 80 85 90 95 100
0 -.923 -1.109 -1.387 -1.875 -2.606 -3.172 -3.647 -4.402 -4.975 -5.406 -5.716 -5.912 -5.997 -5.949 -5.757 -5.412 -4.943 -4.381 -3.743 -3.059 -2,345 -1.630 -.947 -.356 0
Upper surface Station
Lower surface
Ordinate Station' Ordinate
- - - ---------
0
0
.423 .664 1.154 2.391 4.878 7.373 9.873 14.879 19.890 24.906 29.923 34.942 . 39.961 44.981 50.000 55.017 60.032 65.043 70.050 75.053 80.052 85.045 90.033 95.017· 100,000
.970 1.176 1. 491 2.058 2.919 3.593 4.162 5.073 5.770 6.300 6.687 6.942 7.068 7.044 6.860 6.507 6.C:!'4 5.411 4.715 3.954 3.140 2.302 1.463 ,672 0
0 0 -.870 ,577 ,836 -1.036 1.346 -1.277 2.609 -1.686 5.122 . -2.287 7.627 -2.745 1 10.127 -3.128 15.121 -3.727 20.110 -4.178 25.094 -4.510 30.077 -4.743 35.058 -4.882 40.039 -4.926 45.019 -4.854 50.000 -4.654 54.983 -4.317 59.968 -3.872 64. 957 -3.351 69.950 -2.771 74.947 -2.164 79.948 -1.548 -.956 - 84.955 -.429 89.967 -.040 94.983 O· 100,000
L. E, radius: 1.000 Slope of radius through L. E.:· 0.084 --
--
NACA 651-212
. a=0.6
[Stations and ordinates given in percent of airfoil chord] Upper surface Station 0 ,399 ,638 1.124 2.356 ,4.837 7.329 9.827 14.833 19.848 24.869 29.894 34.921 39.951 44.983 50.017 55. 051 60.094 65.123 70.124 75.112 80.090 85,064 90.036 95.013 100.000
Lower surface
Ordinate Station Ordinate
----
---- - 0 ,982 1.194 1. 520 2.113 3.017 3.728 4.330 5.298 6. 042 6.611 7.029 7.304 7.444 7.423 7.231 6.856 6.318 5.634 4.842 3.983 3.082 2.173 1.297 .521 0
0 .601 .862 1.376 2.644 5.163 7.671 10.173 15.167 20. 152 25.131 30.106 35.079 40.049 45.017 49.983 .54.949 59.906 64.877 69.876 74.888 79.910 84.936 89.964 94.987 100.000
L. E. radius: 1.000 Slope of radius through L.
NACA 651-412 [Stations and ordinates git'en in percent of airfoil chord]
0 -.852 -1.012 -1.242 -1.625 -2.185 -2.606' -2.956 -3.5iJo -3.904 -4.197 -4.401 -4.518 -4.550 -4.475 -4.283 -3.968 -3.566 -3.124 -2.640 -2.131 -1.604 -1.085 -.595 -.191 0
E.' 0.110
Upper surface Station
NACA 652-01 5 [Stations and ordinates given in percent of . airfoil chord]
Lower surface
U ppersurface
Ordinate Station Ordinate
Station
----------- - 0 .347 ,580 1.059 2.283 4.757 7.247 9.746 14.757 19.781 24.811
29.846
34.884 39.923 44.962 50.000 55.035 60.064 65.086 70.101 75.107 SO. 103 85.090
90.066
95.033 100.000
0 1.010 1.236 1.588 2.234 3.227 4.010 4.672 5.741 6.562 7.193 7.658 7.971 8.139 8.139 7.963 7.602 7.085 6.440 5.686 4.847 3.935 2.9.74 1.979 .986 0
0
.653
,920
1. 441 2.717 5.243 7.753 10.254 15.243 20.219 25,189 30.154 35.116 40.077 45.038 50.000 54.965 59.936 64. 914 69.899 74.893 79.897 84.910 89.934 94.967 100,000
Ordinate Station
Ordinate
- - ----------
0 -.810 -.956
0
.5 .75 1.25 2.50 5.00 7.50 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
~1.160
-1.490 -1. 963 -2.314 -2.604 -3.049 -3.378 -3.613 -3.770 -3.851 -3.855 -3.759 -3.551 -3.222 -2.801 -2.320 -1. 798 -1. 267 -.75L -.282 .089 .278
0
L. E. radius: 1.000 Slope of radius through L. E,: 0.168
Lower surface
----I
0 1.124 1.356 1. 702 2.324 3.245 3.959 4.555 .5,504 6.223 6;764 7.152 7.396 7.498 7.427 7.168 6.720 6.118 5.403 4.600 3.744 2.858 1. 977 . 1.144 .428
0
0 .5 .75 1. 25 2.50 5.00 7.50 10 15 20 25 , 30 '35 40 45 50 55 60 65 70 75 80 85 90 95 100
UJ
q ~ ~
?d ~
oI"%j :> ..... ~
6.... t"' t:::1
~
:>
0 -1.124 -1.356 -1.702 -2.324 -3.245 -3.959 -4.555 -5.504 -6.223 -6.764 -7.152 -7.396 -7.498 -7.427 -7.168 -6.720 -6.118 -5.403 -4.600 -3.744 -2.858 -1.977. -1.144 ~.428
0
L. E. radius: 1.505
---
.....
o --:r
NACA 652-41 5
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
Upper surface
Upper surface
Lower surface
-----------0 1.170 1.422 1.805 2.506 3.557 4.380 5.069 6.175 1. 018 '7.·658 8.123 8. 426 8.569 8.522 '8.271 7.815 7.189 6.433 5.572 4.638 3.653 2.649 1. 660 .744 0
0 -1.070 -1.282 -1.591 -2.134 -2.925 -3.532 -4.035 -4.829 -5.426 -5.868 -6.179 ,-6.366 -6.427 -6.332 -6.065 -5.625 -5.047 -4.373 -3.628 -3.848 -2.061 -1.303 -.626 -.112 0
0 .594 .855 1. 368 2.635 5.152 7.658 10.159 15.152 ·20.137 25.118 30.096 35.073 40.048 45.024 50.000 54.979 59.961 64.947 69.938 74.935 79.937 84.945 89.960 94.980 100.000
Lower surface Upper surface
I
Lower surface
---0
i I
I
L. E. radius: 1.505 Slope of radius through L. E.: 0.084
.313 .542 1.016 2.231 4.697 7.184 9.682 14.697 19.726 24.764 29.807 34.854 39.903 44.953 50.000 55.043 60.079 65.106 70.124 75.131 80.126 85.109 90.080 95.040 100.000
0 .687 .958 1.484 2.769 5.303 7.816 10.318 15.303 20.274 25.236 30.193 35.146 40.097 45.047 50.000 54.957 59.921 64.894 69.876 74.869 79.874 84.891 89.920 94.960 100.000
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
0 -1.008 -1.200 -1.472 -1.936 -2.599 -3.098 -3.510 -4.150 -4.625 -4.970 -5.205 -5.335 -5.355 -5.237 -4.962 -4.530 -3.976 -3.342 -2.654 -1.952 -1.263 -.628 -.107 .206 0
.----
0 .245 .464 .927 2.126 4.574 7.0.14 9. .149 14.568 19.611 24.671 29.743 34.825 39.916 45.019 50.152 55.262 60.307 65.314 70.294 75.253 80.199 85.137 90.077 95.027 100.000
L. E. radius: 1.505 Slope of radius thl"Ough L. E.: 0.168
--- --- ---0 0 .755 1.233 1.036 1. 520 1.573 1.965 2.812 2.874 5.426 4.099 5.122 7.946 5.985 10.451 15.432 7.383 8. 459 20.389 25.329 9.280 30.257 9.883 10.280 35.175 10.470 40.084 44.981 10.423 49.848 10.106 54.738 9.501 59.693 8.672 64.686 7.684 69.706 6.573 74.747 5.387 4.157 . 79.801 84.863 2.930 89.923 1. 755 94.973 .715 100.000 0
0 -.957 -1.132 -1.377 -1. 776 -2.335 -2.746 -3.081 -3.591 -3.963 -4.232 -4.411 -4.508 -4.526 -4.431 -4.226 -3.929 -3.548 -3.104 -2.609 -2.083 -1.545 -1.014 -.527 -.139 0
Upper snrface
Upper surface
Lower surface
Station
,
0 .50 .75 1.25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0 1. 337 1.608 2.014 2.751 3.866 4.733 5.457 6.606 7.476 8.129 8. 595 8. 886 8. 999 8. 901 8.568 8. 008 7.267 6.395 5.426 4.396 3.338 2.295 1. 319 .490 0
0 .50 .75 1. 25 2.5 5.0 7.5 10 15 20 25 30 35. 40 45 50 55 60 65 70 75 80 85 90 95 100
0 -1.337 -1.608 -2.014 -2.751 -3.866 -4.733 -5.457 -6.606 -7.476 -8.129 -8.595 -8. 886 -8. 999 -8. 901 -8. 568 -8.008 -7.267 -6.395 -5.426 -4.396 -3.338 -2.295 -1.319 -.490 0
00
Lower surface
Ordinate Station Ordinate
._-- ---- ---- ----
---- --- --- ----
Station Ordinate Station Ordinate 0 1. 208 1. 480 1.900 2.680 3.863 4.794 5.578 6.842 7.809 8.550 9.093 9.455 9.639 9.617 9.374 8.910 8.260 7.462 6.542 5.532 4.447 3.320 2.175 1.058 0
NACA 653-21 8
Station Ordinate Station Ordinate
Station Ordinate Station Ordinate
Station Ordinate Station Ordinate 0 .406 .645 1.132 2.365 4.848 7.342 9.841 14.848 19.863 24.882 29.904 34.927 39.952 44.976 50.000 55.021 60.039 65.053 70.062 75.065 80.063 85.055 90.040 95.020 100.000
a=0.5
[Stations and ordinates given in percent of airfoil chord]
.......
o
NACA 653-01 8
NACA 652-41 5
NACA 652-21 5
,
0 .388 .625 1.110 2.340 4.819 7.311 9.809 14.818 19.885 24.858 29.884 34.912 39.942 44.972 50.000 55.026 60.047 65.063 70.073 75.077 80.074 85.063 90.046 95.023 100.000
0 1.382 1.673 2.116 2.932 4.178 5.153 5.971 7.276 8.270 9.023 9.566 9.916 10. 070 9.996 9.671 9.103 8.338 7.425 6.398 5.290 4.133 2.967 1.835 .805 0
0 .612 .875 1.390 2.660 5.181 7.689 10.191 15.182 20.165 25.142 30.116 35.088 40.058 45.028 50.000 54.974 59.953 64.937 69.927 74.923 79.926 84.937 89.954 94.977 100.000
0 -1.282 -1.533 -1.902 -2.560 -3.546 -4.305 -4.937 -5.930 -6.676 -7.233 -7.622 -7.856 -7.928 -7.806 -7.465 -6.913 -6.196 -5.36.5 -4.454 -3.500 -2.541 -1.621 -.801 -.173 0
!:C t'l "d
o
l:C >-3
Z
o
00
t-:> ~
~
:>-
....o>-3 Z
:>-
L. E. radins: 1.96 Slope of radius through L. E.: 0.084
L. E. radius: 1.96
I
L. E. radius: 1.505 Slope of radius through L. E.: 0.233
t"'
:>I:)
-< ....
U2
NACA 653-41 8 [Stations and ordinates given in percent of airfoil chord] Upper surface station_I Ordinate . 0
.278 .503 .973 2.181 4.639 7.123 9.619 14.636 19.671 24.716 29.768 34.825 39.884 44.943 50.000 55.051 60.094 65.126 70.146 75.154 80.147 85.127 90.092 95.046 100.000
0 1. 418 1. 729 2.20jJ 3.104 4.481 5.566 6.478 7.942 9.061 9.914 10.536 Hi 244 11.140 11.091 10.774 10.1£8 9.408 8.454 7.368 6.183 4.927 3.63"8 2.300 1.120 0
Lower surface
Statio~1 Ordina~ 0
.722 .997 1.527 2.819 5.361 7.877 10.381 15.364 20.329 25.284 30.232 35.175 40.116 45.057 50.000 54.949 59.906 64.874 69.854 74.846 79.853 84.873 89.908 94.954 100.000
I
0 -1.218 -1. 449 -1. 781 -2.360 -3.217 -3.870 -4.410 -5.250 -5.877 -6.334 -6.648 -6.824 -6.856 -6.711 -6.362 -5.818 -5.124 -4.334 -3.480 -2.603 -1. 743 -.946 -.282 .144 0
L. E. radius: 1.96 Slope of radius through L. E.: 0.168
NACA 653-61 8
NACA 653-41 8 a = 0.5
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord] Upper surface
Lower surface
0 1. 440 1. 766 2.271 3.233 4.715 5.891 6.882 8.482 9.709 10.643 11.325 11. 770 11. 970 11. 897 11. 506 10.788 9.820 8.674 7.397 6.038 4.636 3.247 1. 930 .777 0
0
l:g~{
1. 632 2.943 5.507 8.034 10.541 15.519 20.467 25.396 30.309 35.211 40.101 44.978 49.818 .14.687 59.636 64.628 69.653 74.702 79.768 84.841 89.911 94.970 100.000
0 -1.164 -1.378 -1. 683 -2.197 -2.951 -3.515 -3.978 -4.690 -5.213 -5.595 -5.853 -5.998 -6.026 -5.905 -5.626 -5.216 -4.696 -4.094 -3.433 -2.734 -2.024 -1. 331 -.702 -.201 0
L. E. radius: 1.96 Slope of radius through L. E.: 0.233
Lower surface
----------- - -
---- ------ - - .197 .411 .868 2.057 4.493 6.966 9.459 14.481 19.533 24.604 29.691 34.789 39.899 45.022 50.182 55.313 60.364 65.372 70.347 75.298 80.232 85.159 90.089 95.030 100.000
Upper surface
Station Ordinate Station Ordinate
Station Ordinate Station Ordinate 0
NACA 653-61 8 a = 0.5
!
0 .172 .385 .839 2.026 4.462 6.936 9.431 14.455 19.506 24.574 29.652 34.738 39.826 44.915 50.000 55.077 60.141 65.189 iO.219
75.230 80.220 85.189 90.138 95.068 100.000
0 1.446 1.776 2.293 3.268 4.776 5.971 6.978 8.602 9.848 10.803 11.504 11. 972 12.210 12.186 11.877 11.293 10.479 9.482 8.338 7.075 5.719 4.306 2.863 1. 433 0
0
.828 1. li5 1. 661 2.974 5.538 8. 064 10.569 15.545 20.494 25.426 30.348 35.262 40.174 45.085 50.000 54.923 59.859 64.811 69.781 74.770 79.780 84.811 89.862 94.932 100.000
0 -1.146 -1.356 -1.651 -2.152 -2.880 -3.427 -3.876 -4.564 -5.072 -5,433 -5.672 -5.792 -5.784 -5.616 -5.259 -4.723 -4.053 -3.302 -2.506 -1. 705 -.943 -.268 .239 .463 0
L. E. radius: 1.96 Slope of radius through L. E.: 0.253
[Stations and ordinates given in percent of airfoil chord] Upper surface
Lower surface
Station Ordinate Station Ordinate
--_.- ----- - - - - - 0
.059 .256 .689 1.846 4.248 6.706 9.194 14.225 19.301 24.407 29.537 34.684 39.849 45.034 50.273 55.468 60.546 65.557 70.519 75.445 80.347 85.239 90.133 95.046 100.000
0 1. 469 1. 821 2.375 3.449 5.115 6.448 7.575 9.404 10.815 11.893 12.687 13.209 13.456 13.395 12.9i4
12.173 11. 090 9.806 8.374 6.851 5.279 3.720 2.233 .920 0
0 .941 1. 244 1.811 3.154 5.752 8.294 10.806 15.775 20.699 25.593 30.463 35.316 40.151 44.966 49.727 54.532 59.454 64.443 69.481 74.555 79.653 84.761 89.867 94.954 100.000
0 -1.055 -1.239 -1.493 -1.895 -2.469 -2.884 -3.219 -3.716 -4.071 -4.321 -4.479 -4.551 -4.540 -4.407 -4.154 -3.815 -3.404 -2.936 -2.428 -1.895 -1.361 -.846 -.391 -.056 0
L. E. radius: 1.96 Slope of radius through L. E.: 0.349
o
l:C
NACA 654.021
~
[Stations and ordinates given in percent of airfoil chord] /
Upper surface
Lower surface
- - - - - - - - - - _._--
.50 .75 1. 25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0 1.522 1.838 2.301 3.154 4.472 5.498 6.352 7.700 8.720 9.487 10036 10.375 10499 10.366 9.952 9.277 8.390 7.360 6.224 5.024 3.800 2.598 1.484 .546 0
L. E. radius: 2.50
0
.50
.75 1.25 2.5 5.0 7.5 10 15 20 25 30 35 40 45
50 55 60 65 70
i5 80 85 90 95 100
o
~ ~ H
>-3 >-3 t'l M .."
Station Ordinate Station Ordinate 0
(")
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 -9.91\2 -9.277 -8.390 -7.360 -6.224 -5024 -3.800 -2.598 -1.484 -.546 0
o
l:C
:>t'l l:C
o
Z
:>q >-3 ....
(")
U2
I
NACA 654-221
NACA 654-421
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinateS" given in percent of airfoil chord]
Upper surface
Lower surface
Station Ordinate Station Ordinate 0
.372 .608 1.090 2.314 4.791 7.280 9.778 14.787 19.808 24.834 29.865 34.898 39.932 44.967 50.000 55.030 60.054 65.072 70.084 75.088 80.084 85.072 90.052 95.026 100.000
0 1.567 1. 902 '2.402 3.335 4.783 5.918 6.865 8.370 9.514 10.381 11.007 11.404 11. 570 11.461 11. 055 10.372 9.461 8.390 7.195 5.918 4.595 3.270 2.000 .861 0
0 .628 .892 1.410 2.684 5.209 7.720 10.222 15.213 20.192 25.166 30.135 35.102 40.068 45.033 50.000 54.970 59.946 64.928 69.916 74.912 79.916 84.928 89.948 94.974 100.000
0 -1.467 -1.762 -2.188 -2.963 -4.151
------
0 .247 .468 .933 2.135 4.582 7.062 9.557 14.575 19.616 24.668 29.729 34. 796 39.865 44.934 50.000 55.059 60.108 65.145 70.168 7.5.176 80.167 85.143 90.104 95.051 100.000
I
I
=g:~~~
I
=U~i
I
-7.024 -9.063 -9.344 -9.428 I -9.271 -8.849 -8.182 -7.319 -6.330 -5.251 -4.128 -3.003 ' -1.924 -c. 966 -.229 0
L. E. radius: 2.50 Slope of radius through L. E.: 0.084
--- - - -
0 1.601 1.956 2.493 3.505 5.085 6.329 7.371 9.034 10.304 11.271 11. 976 12.433 12.640 12.556 12.158 11.467 10.531 9.419 8.166 6.811 5.388 3.940 2.514 1.176 0
0 .753 1.032 1. 567 2.865 5.417 7.938 10.443 15.425 20.384 2.5.332 30.271 &5.204 40.135 45.066 50.000 54.911 59.892 64.855 69.832 74.824 79.833 84.857 89.896 94.949 100.000
--
-
[Stations and ordinates given in percent of airfoil chord]
lStati~ns
and ordinates given in percent airfoil chord]
Upper surface
Lower surface
0
I
---- --- --- - - 0 .424 .666 1.157 2.395 4.884 7.379 9.878 14.884 19.895 24.909 29.925 34.943 39.962 44.981 50.000 55. 019 60.036 65.051 70.061 75.066 80.065 85.058 90.043 95.022 100.000
0 .947 1.150 1. 447 1.986 2. 797 3.441 3.997 4.885 5.574 6.112 6.522 6.816 7.005 7.093 7.075 6.939 6.665 6.195 5.507 4.683 3.759 2.770 1.760 .792 0
0
.576 .834 1.343 2.605 5.116 7.621 10.122 15.116 20.105 25.091 30.075 35.057 40.038 45.019 50.000 54.981 59: 964 64.949 69.939 74.934 79.935 84.942 89.957 94.978 100.000
0 -.847 -1.010 -1.233 -1.614 -2.165 -2.593 -2.963 -3.539 -3.982 -4.322 -4. 578 -4.756 -4.863 -4.903 -4.869 -4.749 -4.523 -4.135 -3.563 -2.893 -2.167 -1.424 -.726 -.160 0
0 .456 .701 1.195 2.437 4.929 7.426 9.926 14.929 19.936 24.945 29.955 34.966 39.977 44.989 50.000 55.010 60.018 65.025 70.029 75.031 80.029 85.025 90.019 95.009 100.000
---- ------- - 0 .155 .363 .813 1. 992 4.414 6.880 9.371. 14.395 19.455 24.538 29.639 M.754 39.882 45.026 50.211 50.362 60.421 65.428 70.398 75.340 80.264 85.181 90.100 95.034 100 000
0 1. 620 1. 991 2.553 3.631 5.315 6.651 7.773 9.572 10.951 12.0nO 12.765 13.258 13.470 13.362 12.890 12.056 10.942 9.637 8.193 6.664 5.097 3.550 2.095 .833 0
0 .845 1.137 1.687 3.008 5.586 8.120 10.629 15.605 20.545 25.462 30.361 35.246 40.118 44.974 49.789 54.638 59.579 64.572 69.602 74.660 79.736 84.819 89.900 94.966 100.000
0 -1.344 -1.603 -1.965 -2.595 -3.551 -4.275 -4.869 -5.780 -6.455 -6.952 -7.293 -7.486 -7.526 -7.370 -7.010 -6.484 -5.818 -5.057 -4.229 -3.360 -2. 485 -1.634 -.867 -.257 0
-
I
Station Ordinate Station Ordinate I
- - - ---- - - - 0 1.184 1.418 1. 755 2.378 3.292 4.007 4.626 5.605 6.362 6.950 7.395 7.706 7.909 7.997 7.957 7.780 7.425 6.832 5.970 4.966 3.849 2.72.3 1. 587 .597 0
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 80 85 90 95 100
0 -1.184 -1. 418 -1. 755 -2.378 -3.292 -4.007 -4.626 -5.605 -6.362 -6.950 -7.395 -7.706 -7.909 -7.997 -7.957 -7.780 -7.425 -6.832 -5.970 -4.966 -3.849 -2.723 -1.587 -.597 0
Jâ&#x20AC;˘. E. radius: 1.575
Ordinate Station Ordinate
0 .544 .799 1.305 2.563 5.071 7.574 10.074 15.071 20.064 25.055 30.045 35.034 40.023 45.011 50.000' 54.990 59.982 64.975 69.971 74.969 79.971 84.975 89.981 94.991 100.000
0 1. 537 1.864 2.374 3.358 4.866 6.066 7.060 8.665 9.885 10.815 11.494 11.939 12.140 12.056 11.672 11.015 10.126 9.060 7.861 6.563 5.200 3.813 2.441 1.150 0
Upper surface
0 1. 230 1. 484 1.858 2.560 3.604 4.428 5.140 6.276 7.156 7.844 8.366 8. 736 8.980 9.092 9.060 8.875 8. 496 7.862 6.941 5.860 4.644 3.395 2.103 .913 0
-
--
0 .599 .860 1. 372 2.638 5.154 7.660 10.162 15.155 20.140 25.121 30.100 35.076 40.051 45.026 50.000 54.975 59.952 64.938 69.919 74.913 79.915 84.925 89.945 94.972 100.000
NACA 66(21 5)-41 6
a=0.6
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord] , I
Station Ordiuate Station Ordinate I
.401 .640 1.128 2.362 4.846 7.340 9.838 14. 845 19.860 24.879 29.900 34.924 39.949 44.974 50.000 55.025 60.048 65.067 70.081 75.087 80.08.5 85.075 90.055 95.028 100.000
0 -i,337 -1.584 -1.946 -2.614 -3.602 -4.370 -4.992 -5.973 -6.701 -7.235 -7.606 -7.819 -7.856 -7.676 -7.260 -6.635 -5.842 -4.940 -3.973 -2.983 -2.016 -'-1.121 -.373 .114 0
L. E. radius: 2.27 Slope of radius through L. E.: 0.168
NACA 66(215)-21 6
Lower surface
------ ------0
0 .742 1. 018 1. 550 2.848 5.397 7.917 10.421 15.404 20.366 25.316 30.258 35.195 40.129 45.063 50.000 54.944 59.897 64.862 69.840 74.833 79.841 84.864 89.902 94.951 100.000
Ul
c::1 ~ ~
~
"'i
---I
0 1. 073 1. 300 1. 642 2.261 3.186 3.906 4.508 5.472 6.206 6.761 7.161 7.418 7.534 7.480' 7.242 6.820 6.246 5.558 4.779 3.942 3.065 2.181 1. 326 .557 0
o
0 -1.130 -1.344 -1.644 -2.188 -2.972 I -3.580 -4.106 -4.930 I -5.564 -6.054 ' -6.422 I -6.676 -6.8.18
=~:~;
I
=~:~8i
I
=~:g;g
I
-2.049 -1.069 -.281 0
I
-6.685 -4.997
I,. E. radius: 1.575 Slope of radius through L. E.: 0.084 !
-
0 .258 .482 .950 2.152 4.603 7.083 9.579 4.596 19.634 24.684 29.742 34.805 39.871 44.937 50.000 5.5.056 60.103 65.138 70.160 75.167 80.159 85.136 90.098 95.049 100.000
I
-
I
L. E. radius: 0.893 Slope of radius through L. E.: 0.084
0 -1.023 -1. 230 -1. 534 -2.075 -2.870 -3.482 -3.992 -4.800 -5.410 -5.865 -6.189 -6.388 -6.462 -6.384 -6. 138 -5.724 -5.174 -4. 528 -3.807 -3.046 -2.269 -1.509 -.810 -.241 0
Lower surface
--
[Stations and ordinates given in percent of airfoil chord]
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 80 85 90 95 100
Station
L. E. radius: 2.50 Slope of radius through L. E.: 0.233
[Stations and ordinates given in percent of airfoil chord] Lower surface.
IOrdina~
L. E. radius: 1.311 Slope of radius through L. E.: 0.042
NACA 66(21 5)-21 6
Upper surface
Upper surface
Lower surface
Station Ordinate Sta:ion
NACA 66(21 5)-01 6
------Station Ordinate Station Ordinate
Lower surface
Station Ordinate Station Ordinate
-
NACA 66, 1-21 2
U ppcr surface
------------~
0 -I.-WI -1.676 -2.065 -2.761 i -3.821 -4.633 -5.303 -6.342 -7.120 -7.691 -8.088 -8.313 -8.356 -8.176 -7.746 -7.087 -6.247 -5.299 -4.278 -3.231 -2.204 -1.248 -.446 .088 0
L. E. radius: 2.50 Slope of radius through I,. E.: 0.168
NACA 65(421)-420
[Stations and ordinates given in percent of airfoil chord]
Upper surface
. Station Ordinate Station Ordinate
---- ------- - -
NACA 65(215)-114
a=0.5 [Stations and ordinates given in percent of airfoil chord]
Lower surface
Upper surface
NACA 654-421
Lower surface
Upper surface
-------Station Ordinate Station ~rdinatel 0 .371 .607 1. 091 2.317 4.794 7.284 9.781 14.788 19.806 24.832 29.862 34.897 39.936 44.978 50.023 55.073 60.141 65.191 70.198 75. 181 80.148 85.106 90.061 9.5.021 100.000
0 1.242 1. 501 1. 886 2.615 3.701 4.563 5.308 6.500 7.428 8.155 8.708 9.098 9.356 9.471 9.431 9.224 8.800 8.084 7.068 5.889 4.585 3.265 1. 937 .762 o
0 .629 .893 1.409 2.683 5.206 7.716 10.219 15.212 20.194 25.168 30.138 35.103 40.064 45.022 49.977 54.927 59.859 64.809 69.802 74.819 79.852 84.894 89. 939 94.979 100.000
I
0 -1. 112 -1.319 -'-I. 608 -2.127 -2.869
I
~3.441
-3.934 -4.702 -5.290 -5.741 -6.080 -6.312 -6.462 -6.523 -6.483 -6.336 -6.048 -5.574 -4.866 -4.037 -3.107 -2.177 -1.235 -.432 0
L. E. radius: 1.575 Slope of radius through L. E.: 0.110
,
!
Upper surface
Lower surface
- - -- - - - - - - - - Station' Ordinate Station Ordinate - - - ._-- - - - - - - 0 0 .303 1.268 1.541 .532 1.008 1. 952 2.225 2.734 4.693 3.910 7.180 4.843 9.677 5.649 14.691 6.942 19.720 7.948 24.757 8.736 29.801 9.336 34.848 9.765 39.898 10.050 44.949 10.187 50.000 10.163 55.050 9.970 60.096 9.566 65.135 8.891 70.161 7.912 75.174 6.753 80.170 5.437 85.150 4.065 90.111 . 2.617 95.056 1. 226 100.000 0
0 .697 .968 1.492 2.775 5.307 7.820 10.323 15.309 20.280 25.243 30.199 35.152 40.102 45.051 50.000 54.950 59.904 64.865 69.839 74.826 79.830 84.850 89.889 94.944 100.000
>......
::0 "1
o
......
t-<
t::I
~ >-
0 -1.068 -1.261 -1.524 -1.990 -2.646 -3.147 -3.581 -4.250 -4.764 -5.156 -5.448 -5.645 -5.766 -5.807 -:;.751 -5.590 -5.282 -4.771 -4.024 -3.173 -2.253 -1.373 -.549 .038 0
L. E. radius: 1.575 Slope of radius through L. E,: 0.168 I--'
o eo
NACA 66-006
. NACA 66-009
[Stations and ordinates given in percent of airfoil chord] Upper surface
Upper surface
Lower surface
---- - - - - - - - - - 0
.50 .75 1.25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
.461 .554 .693 .918 1.257 1.524 1. 752 2.119 :2.401 2.618 2.782 2.899 2.971 3.000 2.985 2.925 2.815 2.611 2.316 1.953 1. 543 1.107 .665 .262 0
0 .50 .75 1. 25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
----
----
I
Ordinate Station Ordinate
-----------0 .50 .75 1.25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0 -.461 -.554 -.693 -.918· -1. 257 -1.524 -1..752 -2.119 -2.401 -2.618 -2.782 -2.899 -2.971 -3.000 -2.985 -2.925 -2.815 -2.611 -2.316 -1.953 -1.543 -1.107 -.665 -.262 0
L. E. radius: 0.223 ,
Station
0 .687 .824 1.030 1.368 1.880 2.283 2.626 3.178 3.601 3.927 4.173 4.348 4.457 4.499 4.475 4.381 4.204 3.882 3.428 2.877 2.263 1.611 .961 .374 0
0 .50 .75 1. 25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0 -.687 -.824 -1.030 -1.368 -1.880 -2.283 -2.626 -3.178 -3.601 -3.927 -4.173 -4.348 -4.457 -4.499 -4.475 -4.381 -4.204 -3.882 -3.428 -2.877 -2.263 -1.611 -.961 -.374 0
,....
NACA 66-209
NACA 66-21 0
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates giv('n in percNlt of "irfoil chord]
[S(at.lons and ordinall'" p:iven ill IJl'rcent of airfoil chord]
Upper surface
Lower sui-face
-------
Station Ordinate Station Ordinate 0
[Stations and ordinates given in percent oC airfoil chord]
,.....
NACA 66-206
Upper surface
Lower surface
Station Ordinate Station Ordinate
---- - - - ---- - - - 0 .461 .707 1.202 2.447 4.941 7.439 9.939 14.942 19.947 24.954 29.962 34.971 39.981 44.990 50.000 55.009 60.018 65.026 70.031 75.034 80.034 85.031 90.023 95.012 100.000
0 .509 .622 -.798 1.102 1.572 1. 947 2.268 2.791 3.196. 3.513 3.754 3.929 4.042 4.095 4.088 4.020 3.886 3.641 3.288 2.848 2.3.39 1.780 1.182 .578 0
0 .539 .793 1.2982.553 5.059 7.561 10.061 15.058 20.053 25.046 30.038 35.029 40.019 45.010 50.000 54.991 59.982 64.974 69.969 74.966 79.996 84.969 89.977 94.988 100.000
Rtation
Ordinate Station Ordinate
-.409 -.482
-.584
I I
I
-.148 .054 0
0 .442 .686 1.179 2.420 4.912 7.409 9.908 14.912 19.921 24.931 29.944 34.957 39.971 44.986 50.000 55.014 60.027 65.038 70.046 75.050 80.050 85.044 90.034 95.018 100.000
0 .735 .892 1. 135 I. 552 2.194 2.705 3.141 3.850 4.39R 4.821 5.145 5.378 5.528 5.594 5.578 5.476 5.275 4.912 4.400 3.772 3.058 2.283 1.477 .690 0
0 .558 .814 1.321 2.580 .<;.088 7.591 10.092 15.088
20.079 25.069 30.056 35.043 40.029 45.014 50.000 54.986 59.973 64.962 69.954 74.950 79.950 84.956 89.965 94.982 100.000
0 -.635 -.752 -.921 -1.180 -1.562 -1.857 -2.107 -2.504 -2.804 -3.031 -3.201 -3.318 -3.386 -3.404 -3.372 -3.286 -3.133 -2.852 -2.456 -1.982 -1.466 -.937 -.443 -.058 0
I
Lower surface
Station Ordinate
~~:~~I~rdinat~
0 .436 .679 1.171 2.412 4.902 7.399 9.898 14.90:l 19.912 24.924 29.937 :)4.952 :l9.968 44. P84 50.000 55.016 60.030 65.042 70.051 75.056 80.055 85.049 90.037 95.019 100.000
0 .564 .821 l.:l2<J 2.588 5.098 7.6!)] 10.102 15.097 20.088 25.076 30.063 35.048 40.032 45.016 50.000 .54.984 59.970 64.()58 69.949 74.944 79.945 84.951 89.963 94.981 100.000
- - - - - - ---- - - - -
__ 0
-.730. -.940 -1.099 -1.234 -1.445 -1.604 -1.i23 -1.81f) -1.8R9 -1.900 -1.905 -1.882 -1.830 -1.744 -1.581 -1.344 -1.058 -.747 -.434
Upper surface
Lower surface
0 .806 .980 I. 245 1.099 2.40\ 2.958 3.432 4.202 4.796 5.257 5.608 5.862 6.024 IL095 6.074 5.960 5.n6 5.132 4.759 4.071 3.289 2.445 1. 570 .724 0
o
I
0 -.706 -.840 -1.031 -1.327 -I. 769 -2.ll0 -2.389 -2.8.'\6 -:1.204 -3.467 -3.664 -3.802 -3.082 -3.905 -3.R68 -1.770 -3.594 -1.272 -2.815 -2.281 -1.697 -1.099 -.536 -.092 0
::0 M
"C
o
::0 >-:3
Z
9
00
... t>:>
~>
>-:3 .... o
Z
L. E. radius: 0.530
I
-----
- -
-
L. E. radius: 0.530 Slope of radius through L. E.: 0.084
L. E. radius: 0.223 Slope of radius through L. E.: 0.084
L. E. radius: 0.662 Slope of radius through L. E.: 0.Og4 ----_._-
~------.
> t"' > C) <! ....
Ul
o
NACA 661-012
N·ACA 661-212
NACA 662-015
NACA 662-215
NACA 662-415
::0
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates ~iven in percent of airfoil chord]
[Stations and ordinates given in percent. of airfoil chord]
[Stations and ordinaws given in percent of ",iI'foil chord]
(")
Upper surface
Upper surface
Lower surfilCe
Station Ordinate Station Ordinate
- - - - - - - - - ----0 .5 .75 1.25 2.5 5.0 i.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0 0 .906 .5 .75 1. 087 1. 358 1.25 1.808 2.5 2.496 5.0 3.037 7.5 3.496 10 4.234 15 4.801 20 5.238 25 5.568 30 5.803 ' 35 5.947 40 45 6.000 5.965 50 5.836 55 5.588 60 5.139 65 4.515 70 3.767 75 2.944 80 2.083 85 1. 234 90 .474 95 0 100
L. E. radius: 0.952 ----
-
--
0 -.906 -1.087 -1.358 -1.808 -2.496 -3.037 -3.496 -4.234 -4.801 -5.238 -5.568 -5.803 -5.947 -6.000 -5.965 -5.836 -5.588 -5.139 -4.515 -3.767 -2.944 -2.083 -1.234 474
0.
I
1
_J
Lower surface
Upper surface
Upper surface
Lower surface
Station Ordinate Station Ordinate
Station Ordinate Statiou Ordinate
--- - - - - - - -
- - - - - - - ---- - - -
0 .424 .666 1.156 2.395 4.883 7.379 9.878 14.883 19.894 24.908 29.925 34.943 39.962 44.981 50.000 55.019 60.036 65.051 70.061 75.066 80.065 85.057 90.043 95.022 100.000
0 .953 1.154 1.462 1.991 2.809 3.459 4.011 4.095 5.596 6.132 6.539 6.833 7.018 7.095 7.068 6.931 6.659 6.169 5.487 4.661 3.739 2.755 1. 750 .789 0
0 .576 .834 1. 344 2.605 5.117 7.621 10.122 15.117 20.106 25.092 30.075 3.5.057 40.038 45.019 50.000 54.981 59.964 64.949 69.939 74.934 79.935 84.943 89.957 94.978 100.000
0
-.853
-1.014 -1.248 -1.619 -2.177 -2.611 -2.977 -3.559 -4.004 -4.342 -4.595 -4.773 -4.876 -4.905 -4.862 -4.741 .-4.517 -4.109 -3.543 -2.871 -2.1-17 -1.409 -.716 -.157 0
I
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 80 85 90 95 100
0 1.122 1. 343 1.675 2.235 3.100 3.781 4.358 5.286 5.995 6.543 6.956 7.250 7.430 7.495 7.4.<;0 7.283 6.959 6.372 5.576 4.632 3.598 2.530 1. 489 .566 0
0 .5 .75 1. 2,5 2.5 5.0 7.5 10 15 20 2.<; 30 35 40 45 .<;0 55 60 65 70 75 80 85 90 ·95 100
Station
-5.99.5 -6.543 -6.956 -7.250 -7.430 -7.495 -7.450
=~:~
-6.372 -5.576 -4.632 -3.598 -2.530 -1.489 -.566 0
Sta~ion I~rdinate
Upper surface I
0
.·103 .646 1.134 2.370 4.855 7.349 9.848 14.854 19.868 24.886 29.906 34.929 39.952 44.976 50.000 55.023 60.045 65.063 70.075 75.081 80.079 85.070 90.052 95.026 100.000
I
I
I
I
0 1.168 1.409 1.778 2.417 3.413 4.202 4.872 5.957 6.790 7.437 7.927 8.280 8. .<;01 8.590 8.551 8.378 8.030 7.402 6.547 5.526 4.393 3.202 2.005 .881 0
0 .594 .854 1. 366 2.630 5.145 7.651 10.152 15.146 20.132 25.114 30.094 35.071 40.048 45.024 50.000 54.977 59.955 64.937 69.925 74.919 79.921 84.930 89.948 94.974 100.000
-?058 -1.269 564 -2.045 -1. -2.781 -3.354 -3.838· -4.6ll -5.198 -5.647 -5.983 -6.220 -6.359 -6.400 -6.347 -6.188 -5.888 -5.342 -4.603 -3.736 -2.801 -1.856 -.9il -.249 0
I
1
I I
Lower surface
Station Ordinate Station Ordinate -----
0 -1.122 -1.343 -1.675 -2.235 -3.100
=!:m -5.286
Ordinate
Lower surface
0 .314 .544 1.019 2.241 4.711 7.199 9.696 14.709 19.736 24.771 29.812 34.857 39.904 44.952 50.000 55.046 60.090 65.126 70.1.<;0 75.162 80.1.<;9 85.139 90.104 95.053 100.000
--------0 1. 206 1.467 1.873 2.592 3.718 4.617 5.381 6.624 7.581 8.329 8.897 9.309 9.571 9.685 9.656 9.173 9.100 8.431 7.518 6.419 5.187 3.872 2.519 1.196 0
0 .686 .956 1.481 2.759 5.289 7.801 10.304 15.291 20.264 25.229 30.188 35.143 40.096 45.048 50.000 54.954 59.910 64.874 69.850 74.838 79.841 84.861 89.896 94.947 100.000
0 -1.006 -1.187 -1.445 -1.848 -2.454 -2.921 -3.313 -3.932 -4.397 -4.749 -5.009 -5.189 -5.287 -5.305 -5.244 -5.093 -4.816 -4.311 -3.630 -2.839 -2.003 -1.180 -.451 .068 0
I
L. E. radius: 0.952 Slope of radius through L. E.: 0.084
L. E. radius: 1.435 . Slope of radius throngh L. E.: 0.084
L. E. radius: 1.435 I
I
L. E. radius: 1.435 SlopeofradiusthroughL. E.: 0.168 ---
---
----
><l
o
~
~ ....
>-:3 >-:3 M M "1
g > M
::0
o Z > q >-:3
H
(")
Ul
NACA 663-018 i Stations and
ordinat~s
given in percent of airfoil chord]
Upper surface
._-----Rtation
Lower surface
Ordinate Station Ordinate
----- ---- - - - - - - 0 .5 .7S
1.25 2.5 .>.0 7.5 10 15 20 25 30 35 40
4.> 50
5, liO Ii.> 70 75 80 85 90 9.> 100
0 1.323 1.571 1.952 2.li4Ii a. f)yO 4.513 5.210 Ii. :3:1a 7.188 7.M8 8.346 8. 701 8.918 8. 998 8.942 8.733 8.323 7.580
0 .5 .7ii 1.25
2..> 5.0 7.5 10 15 20 2.> 30 35 40
45 50 55
60 fi.1)
H. fi97
70
5.451 4.201i 2.934 1. 714 .646 0
75 80 85 90 9.> 100
0 -1.323 -1.571 -1.952 -2.li4fi -a.liYO -4.513 -5.210 -1i.3a3 -7.188 -7.848 -8.346 -8.701 -8.918 -8.998 -8.942 -8.733 -8.323 -7.580 -Ii. 597 -5.451 -4.206 -2.934 -1.714 -.646 0
L. E. radius: 1.9.55
NACA 663-218
NACA 663-41 8
NACA 664-021
[Stations an(l ordinates given inpcrccnt of airfoil chord]
{ Stations and ordinates !!ivcn in percent of airfoil chord)
{Stations and ordinates given in percent 01 airfoil chord]
Upper surface
Lower surface
Upper surface
Rtation Ordinate Station Ordinate
- - - --- ---- - 0 .389 .628 1.115 2.346 4.827 7.320 9.818 14.825 19.M1 24.863 29.887 34.914 39.942 44.971 50.000 55.028 60.054 65.075 70.089
0 1-368 1.636 2.054 2.828 4.002 4.933 5.724 7.004 1.982 8.742 9.317 9.731 9.989 10.093 10.045 9.828 9.394 8.610 7..>68 {;.345 75.095 80.093 5.001 85.081 3.606 90.060 2.230 9.>.030 . .961 100.000 0
0 0 .611 -1.268 .872 ·-1.496 1.38S -1.840 2.654 -2.456 5.173 -3.370 7.680 -4.085 10.182 -4.690 15.175 -5.658 20.159 -6.390 25.137 -6.952 30.113 -7.3iS 35.086 -7.fi71 40.0OR -7.847 45.029 -7.903 50.000 -7.839 54.972 -7.638 59.946 -7.252 64.925 -6.550 -.>.624 69.911 74.905 -4.51\5 7l'.907 -3.409 84.919 -2.260 ' 89.940 -1.19fi -.329 94.970 100.000 0
E. radiu" 1.955 Slope of radius through L. K: 0.084
1,.
----.
_.~~prr su~ace.
Lower surface
------------Station Ordinate Station Ordinate ---- - - - - - - - - - 0 .280 .509 '.981 2.194 4.656 7.140 9.636 14.651 19.683 24.726 29.775 34.829 39.885 44.943 50.000 55.056 60.107 65.149 70.178 75.191 80.185 85.162 90.120 95.060 100.000
0 1.405 1.692 2.147 3.000 4.306 5.347 6.231 7.669 8.773 9.633 10.287 10.759 11. U59 11.188 11.148 10. 923 10.464 9.639 8.539 7.238 5.794 4.276 2.744 1.275 0
0 .720 .991 L 519 2.806 5.344 7.860 10.364 15.349 20.317 25.274 30.225 35.171 40.115 45.057 50.000 54.944 59.893 64.851 69.822 74.809 79.815 84.838 89.880 94.940 100.000
0 -1.205 -1.412 -l. 719 -2.256 -3.042 -3.651 -4.163 -4.977 -5.589 -6.0sa -6.399 -6.639 -6.775 -6.808 -6.736 -6.543 -6.180 -5.519 -4.651 -3.658 -2.610 -1.584 -.676 -.011 0
L. E. radius: 1.955 Slope of radius through L. E.: 0.168
--
J
I,ower surface
Station Ordinate Station Ordinate -------- - - -
---
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 80 85 90 95 100
/
0 1. 525 1.804 2.240 3.045 4.269 5.233 6.052 7.369 8.376 9.153 9. 738 10.154 10.407 10.500 10.434 10.186 9.692 8. 793 7.610 6.251 4.796 3.324 1.924 .717 0
0 .5
.75 l.25 2.5 5.0 7.5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0 -1. 52.5 -1.804 -2.240 -3.045 -4.269 -5.283 -6.052 -7.369 -8.376 -9.1sa -9. 738 -10.154 -10.407 -10.500 -10.434 -10.186 -9.692 -8. 793 -7.610 -6.251 -4.796 -3.324 -1.924 -.717 0
rJl
d ~ ~
L. E. radius: 2.550
I
_ ..
-
~
-
>-<
o
"1
~
NACA 664-221
NACA 67,1-215
NACA 747A315
NACA747A415
{Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
(Stations and ordinates given in percent of airfoil chord]
[Stations and ordinates given in percent of airfoil chord]
Up""r surfa~-e
Lower surface
Upper surface
------Station Ordinaw Station Ordinat<'
- - - _._- ---- - - - 0 .372 1. 570 .610 • • 1.8ti9 I. 095 2.342 2.323 3. 221i 4.S00 4.580 7.291 5.ti53 9.788 6.51i5 14.797 8.039 19.815 9.170 24.MO 10.047 29.869 10.709 34.900 11.183 39.933 11.478 44.967 11. 595 50.000 H.lm 55.032 11.281 60.063 HI. 763 55.087 9.823 70.103 8. 581 75.109 7.145 80.106 5.091 3.99(; 85.092 90.067 2.440 9.1.034 1.032 100.000 0 ()
0 .628 .890 1.405 2.li77 5.200
7.709 10.212 15.20:1 20.185 25. HiO 30.131 35.100 40.01i7 45.0:3:! 50.0110 54.968 59. 937 64.913 69.897 74.891 79.894 84.908 89.933 94.966 100.000
---- ------- - -
-1.470 -1.729 -2.128 -2.854 -3.948 -4.805 -5. sal -li.ti9a -7.578 -8. 2m -8.7Ii5 -9.123 -9.336 -9.405 -9.:331 -9.091 -8.621 -7.763 -6.6.17 -5.355 -3.999 -2.(150 -1.406 -.400 0
L. g. radius: 2.550 Rlopu of radius through L. K: 0.084 --
.402 .642 1. 128 2.361 4.848 7.344 9.845 14.854 19.869 24.887 29.908 34.930 :39. 95:1 44.976 50.000 55.024 f~l. 047 65.068 70.086 75.098 80.100 85.092 90.071 95.037 100.000
0 1.213 1. 460 1.867 2.577 3.557 4.321 4.947 5.954 5.7:l5 7.348 7.825 8.185 8.430 8.570 8. f>OO 8.516 8.302 7.935 7.3?:! 6.515 5.335 :l.999 2.5:l7 L 103 0
Upper surface Lower surface ------Station Ordinate Station Ordinate
-------
Station Ordinate Station Ordinate 0
II
I
Lower surface
Ii
.598 .858 1.372 2.639 5.1.52 7.656 10.155 15.146 20.131 25. 113 30.092 35.070 40.047 45.024 50.000 54.976 59.953 64.932 69.914 74.902 79.900 M.908 89.929 94.963 100.000
0 -1.11:1 -1-320 -1.553 -2.205 -2.925 -3.473 -3.913 -4.608 -5.143 -5.558 -5.881 -6.125 -6.288 -6.380 -0.394 -6.326 -6.160 -5.875 -5.429 -4.725 -3.743 -2.65.1 -1. 5Q.1 -.471 0
0 .229 .449 .911 2.109 4.564 7.05.1 9.558 14.599 19. 668 24.758 29.867 35.001 40.200 45.375 50.447 55.463 60.435 65.366 70.241 75.130 80.073 85.0~8
90.016 95.004 100.000
L. K radius: 1.52:3 Rlope of radius through L. E.: 0.084 -
- - - - ---- - - - ---0 1.30.> 1. 599 2.065 2.935 4.264 5.2l'6 6.140 7.497 8.503 9.242 9.731 9.982 9.962 9.572 8.964 8. 206 7.324 6.365 5.354 4.336 3.295 2.257 1.289 .481 0
0
.771 1.051 1.589 2.891 5.436 7.947 10.442 15.401 20.332 25.242 30.133 34.999 39.800 44.625 49.553 54.sa7 59.565 64.6:34 69.759 74.870 79.927 84.962 89.984 94.996 100.000
0 -1.031 -1.207 -1.473 -1.927 -2.518 -2.952 -3.304 -3.M3 -4.247 -4.546 -4.773 -4.926 -5.020 -5.040 -5.014 -4.930 -4.772 -4.509 -4.ll0 -.3.502 -2.743 -1.915 -1.097 -.405 0
L. E. radius: 1.544 Slope of radiUS through L. E.: 0.232 -
.-
-
Upper surface
::d "1
o>-< ~
t;
Lower surface
~
;...
Station Ordinate Station Ordinate
- - - - ---- - - - - - - 0
0 .183 l.318 .398 1.622 .852 2.106 2.041 3.01ti 4.487 4.4ll 6.972 5.488 9.476 6.390 14.521 7.827 19.1'98 8.897 24.698 9.687 29.818 10.216 34.964 10.497 40.176 10.499 45.364 10.121 50.447 9.516 55.474 8.753 60.454 7.859 65.393 6.878 70.273 5.838 75.164 4.78.1 80.107 3.692 85.066 2 592 90.037 1. 546 . 95.015 1 .639 100.000 0
0 .817 1.102 1.648 2.959 5.513 8.028 10.524 15.479 20.402 25.302 :lO.182 35.036 39.824 44.636 49.5.13 54.526 59.546 64.607 69.727 74.8.16 79.893 84.934 89.963 94.985 100.000
0
-.994 -1.160 -1.406 -1. 822 -2.349 -2.730 -3.038 -3.501 -3.845 -4.095 -4.286 -4.411 -4.485 -4.493 -4.462 -4.381 -4.215 -3.992 -3.622 -3.053 -2.344 -1.578 -.&38 -.247 0
L. E. radius: 1.544 Slope of radius through L. E.: 0.274
I
I I ....-
-
113
SUMMARY OF AIRFOIL DATA
IV-PREDICTED CRITICAL MACH NUMBERS Page
Critical Mach number chart___ _ __ ___ __ _ __ ___ _ ___ __ __ _ __ _ __ Variation of critical Mach number with low-speed section lift coefficient: For the NACA 0006,0009, and 0012 airfoil sections_ _____ For several N ACA 14-series airfoil sections of various thicknesses ________________________________ .. __ __ _ __ For several N ACA 24-series airfoil sections of various thicknesses_ __ ___ ___________ __ ______ _ __ ___ __ _ _____ _ For several N ACA 44-series airfoil sections of various thicknesses __________________ . _ _ __ _ __ _ __ __ _ __ __ __ __ For several N ACA 230-series airfoil sections of various thicknesses________________________________________ For several N ACA 63-series airfoil sections of various thicknesses, cambered for various design lift coefficients_ _ For several N ACA 63-series symmetrical a~rfoil sections of various thicknesses .. _ _ _ __ __ __ __ _ _ __ __ _ __ __ _ __ __ __ _ __ . For several N ACA 63-series airfoil sections of various thicknesses, cambered for a design lift coefficient of 0.2_ _ _ _ __ For several NACA 63-series airfoil sections of various thicknesses, cambered for a design lift coefficient of 0.4 ____ . _ For two N ACA 63-series airfoil sections of different thicknesses, cambered for a design lift coefficient of 0.6_ __ _ __ For several N ACA 64-series symmetrical airfoil sections of various thicknesses_ ___ __ __ _ __ __ _ __ _ __ _ __ __ __ _ __ __ __ For several N ACA 64-series airfoil sections of various thicknesses, cambered for a design lift coefficient of O. L __ " __ For several N ACA 64-series airfoil sections of various thicknesses, cambered for a design lift coefficient of 0.2 __ .. ___ For several NACA 64-series airfoil sections of various thicknesses, cambered for a design lift coefficient of 0.4_ __ __ _ For two N ACA 64-series airfoil sections of different thicknesses, cambered for a design lift coefficient of 0.6. __ . __
114
115 115
Page
Variation of critical Mach number with low-spced section lift coefficient-Con tin ued For sever.al N ACA 65-series symmetrical airfoil sections of various thicknesses .. ____________________________ ____ For several N ACA 65-series airfoil sections with a thickness ratio of 0.18 and cambered for various design lift coefficients ______________________________________ ~-
116 116 117 117 118 118 119 119, 120 120 121 121 122
For several N ACA 65-series airfoil sections of various thicknesses, cambered for a design lift coefficient of 0.2__ ____ For several N ACA 65-series airfoil sections of various thicknesses, cambered for a design lift coefficient of 0.4_ _____ For several N ACA 65-series airfoil sections with mean line of the type a=0.5 and cambered for a design lift coefficient of 0.4 _____________________ .. ___ '. ~ _________ ____ For two NACA 65-series airfoil sections of different thicknesses, cambered for a design lift coefficient of 0.6_ _____ For two N ACA 65-series airfoil sections with mean line of the type a=0.5, with different thicknesses, and c8.!llbered for a design lift coefficient of 0.6 _ _ _______________ ____ For several N ACA 66-series symmetrical airfoil sections of various thicknesses _____ " ___________________________ For several N ACA 66-series airfoil sections of various thicknesses, cambered for a design lift coefficient of 0.2_ .. __ . __ For two N ACA 66-series airfoil sections of different thicknesses, cambered for a design lift coefficient of 0.4 ___ .. __ For several N ACA 66-series airfoil sections with a thickness ratio of 0.16 and cambered for various design lift coefficients_ _ __ ______________________________ __ ____ For several NACA 6-seri,cs airfoil sections with different positions of minimum pressure and various thicknesses, cambered for various design lift coefficients____________ For two N ACA 7-series airfoil sections with a thickness ratio of 0.15 and cambered for different design lift coefficients_ _
122 123 123 124 124 125
125 126 126 127 127
128 128
114
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 1.0
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SUMMARY OF AIRFOIL DATA
129
V-AERODYNAMIC CHARACTERISTICS OF VARIOUS AIRFOIL SECTIONS J:'age
N ACA 0006 _____. ____________________________________. ____ NACA 0009 ____ .______________________________ c ________ •• _ NACA 1408 ________ .. __ .. __ . ______________________________ NACA 1410_____________________________________________ NACA 1412 _________ .. ________________ __________________ N ACA 2412_ ______ __ _________ ________ ___________________ N ACA 2415 _____ . _________ . ______________________________ N ACA 2418 ___ ~ ___ ______________________________________ N ACA 2421._ _____ ________ ___ _______________ ____ __ ______ N ACA 2424__ _____ ______________________ ____ ______ ______ N ACA 4412 _________________________________ c _ _ _ _ _ _ _ _ __ _ NACA 4415 ________________________ .. ______ ______________ NACA 4418 ______________________ . _____ - ____ .____ _____ __ N ACA 4421. _______________________________________ ____ _ N ACA 4424. _________ ._ __________________________________ N ACA 23012 .. ______ ________ __________ ___________________ N ACA 23015 ___________________________ - ________ " . _- - ___ NACA 23018 _________________________________________ .__ NACA 23021. _______ ._ ________ ___ __ ______ ___ __ ___ ______ _ _ N ACA23024 _____________ - - ___ - ____ -____ - ___ - _- - ____ - - - __ N ACA 63,4-420--- ______________________ - ___ - _- - ____ - ___ N ACA 63,4-420 with 0.25e slotted flap (a) Configuration _________________ - - - __ - - - .. - - -- - -- --. (b) Aerodynamic characteristics with hinge location 1_ _ __ (c) Aerodynamic characteristics with hinge location 2_ _ _ _ NACA 63,4-420, a=0.3_ .. ____________________________ ~____ NACA 63(420)-422 ____________________ . -- _______ - ---- ---NACA 63(420)-517 __________________________ - _- - - _- - - - - _NACA 63-006 ____________________ . _________ .____________ NACA 63-009 _________________________________ - - _______ NACA 63.:..206 __________ . ___________ .. ____________________ .NACA 63-209 ____________________ ~ _____ . ______ - -- --- ---NACA 63-210 __________________ ._ _______________________ N ACA 63 1-012 ________________________ - - - _- - - - - -- - - - - .. - NACA 63 1-212 _______________________________ - - - __ -.--_'. N ACA 63 1-412 ______ . ____ .. ___ . ___ - ___ - - - __ - - - - - - -. - - - - - -. N ACA 63 2-015 ____ .. ____ c _. ____________ - ____ - - - - - _ - - - - - - NACA 632-215 ___ ~ ____ ._________ ._ - ________ .. _______ .. _____ NACA 63 2-415 ____ .___________ . ____________ ----------.-N ACA 632-615 ___________________ - ___ - - - __ .. - _- - - - - - - - - - NACA 63 a-018_______________________ ___________________ N ACA 633-218 _____ . _________ - ___ - ___ - - - - - - - - - - - - - - - - - - N ACA 632-418 ________________________ - ______ - - - _- - - - - - N ACA 633-618 __________ . _'" _- ___ - ___ - - - - - - - -. - - - - - - - - - N ACA 634-021. __________ - __ - .. __ - - - - .. - - - -- - - - - - - - - - - - - - N ACA 63r 221. ____ .. _________ - ___ - - _- - - - - - - - - - - - - - - - - - - N ACA 634-421 _______ .. _______ - _.. _- - _- - - -.-. - - - - - - - - - - - - - NACA 64-006 ___________ --- _____ ---- --. ---------------NACA 64-'-009 ___________ .. - ________________ .. ___________ N ACA 64-108 ___ .... _.. __ . __ - _____ . _- ___ - - - - - - - - - - - - - - - - - - NACA 64-110 ____ . ____ ._. - __________ ---------.-----.----NACA 64-206 ____ .__________________ .. ______ ---' ---------NACA 64-208 ______________________ . --.----------------NACA 64-209 ____________________ - ___ -- -- - ---- - -- - -- -- -N ACA 64-210 ______ . ______ . __________________ - - - __ - - - - _N ACA 64 1-012 ____________________________ - _- - - - _- - - - - - N AC A 64 1-112 ________________________ - ___ - __ - - - _- - - - - - NACA·64 1-212 ____________________________________ - - - ___ N ACA 64 1-412 ___________________ - ___ - - - - - - - - - - - - - - - - - - N ACA 642-015 _______________________________ - - - __ - - - - - NACA 64 215 ________ "_________________________________ r NACA 642-415 ___________ . ___________________ ._____ -_ -- __ NACA 643-018 ___________________ . _____ ._________________ NACA 643-218_ .. ____________ ~_"_________________________
131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 158 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193
Page
NACA 643-418 ___ . ____ . ___ . ______________ . __ .. __________ NACA 643.-618 __________________ . __________________ . ___ N ACA 6~-021. ________________________ .. ______ . ___ _____ N ACA 64r 221. ____ . ____________________ . ___________ .... _ N ACA 64r 42L __________________ .. ___ . ____________ . ____ NACA 65,3-018..----. __________ .. _____________ . _ ___ __ ___ _ NACA 65,3-418, a o=0.8_ .. _.. ___________________ . ___________ NACA 65,3-618..-- _____________________________ ~ __ ______ NACA 65,:3-618 with 0.20e sealed plain flap_________________ NACA 65(216)-415, a=0.5________________ ________________ NACA 65-006 __________ . __________________ .____________ NACA 65-009 _____________ ... ___________ .. ________________ N ACA 65-206_ ________ _______________ ___________________ N ACA 65-209_ _____________ __ _________ ___ . ______ _______ N ACA 65-210 ____________ .. _____ ___ _____ ________ ____ ______ N ACA 65-410 ____ .. __. _____ . ______ .. _______________ _______ N ACA 65 1-012 ___ .. __ '_ __________ __________________ _______ NACA 651-212 _____ . _________________ .~_ ________ ________ NACA 65 1-212 with 0.20e split flap (lift and moment characteristics) _ ___ ______ ______________________________ NACA 65 1-212, a=0.6 ______________________ ._____________ NACA 651-412 _____________________________ .. __________ ._ NACA 65 2-015_ _ _ _________ ______________________________ NACA 652-215_ _ _ ____ ___________ ________ __ ______ ________ N A C A 65 r 415 ______________ . ____________________ _______ NACA 65 2-415, a=0.5 ____ .____________ __________________ N ACA 653-018_ _ _ ____________________________ ____ ____ ___ NACA 65:,-118 with 0.30ge double slotted flap (a) Configuration ____________ .. ______________________ (b) Aerodynamic characteristics_ _ ______ _____ ___ _______ N ACA 653.-218 _________________ " _________ - - ___ - __ - ____ - N ACA 65:,-418 ___ .. ___ .. ___ . _______________________ _______ N ACA 653-418, 0= 0.5_ ____________________________ _______ N ACA 6Sa-618 ______ ._ ___________ _ _ _ ______________ _______ NACA 65a-618, a=0.5 __________________________ ._________ N ACA 654-021. ___________________________ - ______ - ____ - _ N ACA 654-22L __ .. _ _______ _ _ _ ____________________ _______ N ACA 65 r 42 1. __________________________________ - ___ - - NACA 65c 421, a=0.5 _____ .. ______________ c_______________ NACA 65(216)-114 _________________ .. __ __ ______ _____ _______ N A C A 65 (421)-420 ____________________ - ___ - - _____ - - - - __ - - NACA 66,1-212-- _________________ ._____________________ NACA 66,1-212 with 0.20e split flap (lift and moment characteristics) __________________ . _____________ '__ - ___ - _ N ACA 66(215)-016 ______________________________________ . _ NACA 66(215)-216 _______________________________ - ____ -N ACA 66(215)-216 with 0.20e sealed plain flap_ _____ _ _ _ __ ___ N ACA 66(125)-216 with 0.20e split flap (lift and moment characteristics) _________________________ - _- __ -- - - - __ - -NACA 66(215)-216, a=0.6_________________________________ NACA 66(215)~216, a=0.6 with 0.30e slotted and 0.10c plain, flap (a) Airfoil-flap configuration _________________________ - _ (b) Flap configuration _____________ -_ --- -- _____ - - __ -- (c) Aerodynamic characteristics. Slotted flap retracted___ (d) Lift and moment characteristics. Slotted flap deflected 22° _ ~ _______ .. _________ _________ ____ ___ Slotted flap (e) Lift and moment characteristics. deflected 27°___________________________________ (f) Lift and moment characteristics. Slotted flap deflected 32° _____ ._____________________________ (g) Lift and moment characteristics. Slotted flap deflected 87°___________________________________ N ACA 66(215)-416 ______________________________ - - -_ -- - -
194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233' 234 235 236 237 238 239 240 240 241 242 243 244 245 246
130
REPORT NO. 824-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS Page
Page
NACA 66-006 _______________________ -.: _______________ - __ N ACA 66-009_ . ___________ .. _________ - _______ - ________ - __ NACA 66--206 ________________________________________ - __ NACA 66-209 ___________________________________.-- ___ - __ N ACA 66-210 _____________. _________________ .__ - _______ - __ N ACA 66 1-012 _____________________ - - - __ - - ___ - - - _ - - - _ - -NACA 66 1-212 ___________ -____________________________ _ NACA 662-015 ______________________ - - __ - - __ - - - - _- - - __ -NACA 66 215 ____________ . ____________________________._ r
247 248
249 250 251 252 253 254
'255
N ACA 662-415 __________________ "_ ________ _____ ______ _ NACA NACA N ACA N ACA N ACA N ACA NACA N ACA
663--018" ________________ .. _________ ~ ______ ._______ _ 663-218 _________________________________________ _ 663-418 _________________________________________ _ 664-021 _______ .. ______ .. ______________________ .. ___ _ 664-221 ___________________________________ .. _____ _ 67,1-215 _______________________________________ ~_ .. 747A315 ___________ . _________________ ._ ... _______ . 747 A415 _____________________________ .. _________ _
256 257 258
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Flop refere n ce lIne
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z Positive directions of axes and angles (forces and moments) are shown by arrows Moment about axis
Axis
Designation
LongitudinaL ______ LateraL _____________ N ormaL _____________
X Y
X Y
Z
Z
Rolling _______ Pitching. __ . __ Yawing. __ .___
Absolute coefficients of moment L M N 0,= qbS Om= qcS O"=qbS (rolling) (pitching) (yawing)
Angle
Velocities I
Force (parallel axis) Sym- to symbol Designation Symbol bol
L M N
Positive direction
Designation
Y----+Z Z----+X X---+Y
RoIL _______ PitclL ___ . __ Yaw ________
Linear Sym- (compobol nent along Angular axis)
'" I)
'"
p q
u
v
r
w
Angle of set of control surface (relative to neutral position), o. (Indicate surface by proper subscript.)
4. PROPELLER SYMBOLS
D P p/D
V' V. T
Q
Diameter Geometric pitch Pitch ratio Inflow velocity Slipstream velocity Thrust, absolute coefficient OT= Torque, absolute coefficient Oa=
p 0,
;D4
1/
n
Power, absolute coefficient Op=
6/ V 5 Speed-power coefficiellt= -V ~nj Efficiency Revolutions per second, rps
pn
~nr.
pn
Effective helix angle=tan- I (2
LF
5. NUMERICAL RELATIONS
1 hp=76.04 kg-m/s=550 ft-lb/sec 1 metric horsepower=O.9863 hp 1 mph=0.4470 mps 1 mps=2.2369 mph
fD6
pn
1 Ib=0.4536 leg 1 kg=2.2046 Ib 1 mi= 1,609.35 m=5,280 ft 1 m=3.2808 ft
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