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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

REPORT No. 824

SUMMARY OF AIRFOIL DATA By IRA H. ABBOTT, ALBERT E.

VON

DOENHOFF,

and LOUIS S. STIVERS, Jr.

1945

AERONAUTIC SYMBOLS 1. FUNDAMENTAL AND DERIVED UNITS 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

2.0

: Uppe~ sJ-f'a;e _0. " .

/;6

1.2

rV r-o-:

II

.8

\

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~

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surface

~r

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--The ory o Experim enf

.4

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ns FIGURE 7.-Compa rison of theoretical and experimental preS3ure distributio 66(215}-216, a= 0.6 airfoil. c, = 0.23.

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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(b) Type of camber. 8.-Effect of amount and type. of cambN' on pressure distribntion at design lift.

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

(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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o Upper limit of low-drag range o Lower limIt of low-drag range

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(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.

~ ~

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F,GURE 42.-LiCi and drag characteristics of the NACA (,1(420)-422 airfoil at

-/.2

-.8

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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

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lnl

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Section lift coefficient, c[

FIGURE 49.-Lift and drag characteristics of an NACA 65(223)-'422 (modified) airfoil with standard roughness applied to the leading edge. ~ .....

42

REPOR'f NO. 824-NATIONAL ADVISORY COMMITTEE FOR AEHONAUTICS I

1

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Single flagged symbols are for 60° simulated split flap

. 1

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Air-foil thickness) percent of chord

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~

f..o

e'i =0.

.~ .24

-- 1--'->-

(5

l,..-

0

0

(b)

~

~ .24

:;>-

.24

..

.26

__ V v.

J--.....

NACA 24-series

.22

V

.24

.22

.26 1---

0

.26

--t--o--- r--...

V f-o-

~

() .28

~

Q.

~

\\)

~ l.tSI

V

t::

.~

""

() \\) It)

I

z>::l o

z>-

~V

() ()

.:::

Qo l'-' 11>0

III

:~

§

~

I~

£

--

./

;/

J

~

"" ,. - - - -=..-~-::.-;:,""',;:.J~:o::'""""'t__r,;­ -~-~ .......~, ......

.---.

t:"'

>-

V

Flap-hinge location o I

~m g

I

02

1.2

>1

c

o

a:: a::....

.§

~

I

:4tr.l

~

tr.l

.8

"'l

g >-

tr.l :tl

o

~c:j ..., .... c

.4t Hinge-location 2

m

(b)

(a)

~--.I63--1 (a) Flap configuration.

-

o

10

20

-----

30

Flap deflection, dfJ de9 (b) Maximum lift characteristics.

FIGURE 55.-FJap configuration and maximum lift coefficients for the NACA 63,4-420 airfoil with a O.25-airfoil-chord hinged slotted flap. R=6Xl()6.

...

,-

40

50

47

SUMMARY OF AIRFOIL DATA

~--=/~ Flap retracted

I.

.1

1d 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

..... ····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'

-

S 1.0

I

_J

17

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 win1

-------

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
>'=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-
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-


.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.v/V=PR/4

- - - - - - - - - - -------- ------- -----

~

1.0

""~

o NACA a=O.fJ

mean line lie

C

""-.,

'"

!> .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-

~

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-
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'-
-: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

~ ~'-
: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 >-3 ..... o Z > t"' > i;;1

~

.....

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

~

> l'J

~

o Z > '::i >-l

.....

(")

,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

J•. 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-
-

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

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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

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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 . C) -


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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

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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 _____________________________ .. _________ _

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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)

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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,

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1/

n

Power, absolute coefficient Op=

6/ V 5 Speed-power coefficiellt= -V ~nj Efficiency Revolutions per second, rps

pn

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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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