theory of wing sections including a summary of airfoil data

THEORY OF WING SECTIONS

Including a Summary of Airfoil Data

By IRA H. ABBOTTDIRECTOR OF AERONAUTICAL AND SPACE RESEARCH NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

and ALBERT E. VON DOENHOFF

RESEARCH ENGINEER. NASA

DOVER PUBLICATIONS, INC. NEW YORK

Copyright ' ~949, 1959 by Ira H. Abbott and Albert E. von Doenhoff. All rights reserved under Pan American and Inter national Copyright Conventions.

Published in Canada by General Publishing Com pany, Ltd., 30 Lesmill Road, Don Mills, Toronto, Ontario.

This Dover edition, first published in 1959. is an unabridged and corrected republication of the first edition fint published in 1949 by the McGraw-Hill Book Company, Inc. This Dover edition includes a new Preface by the authors.

Stand4,-d Book. Number: 486-60586-8

Library 01 Congress Catalog Card Number: 60-1601Manufactured in the United States of America Dover Publications, Inc. ISO Varlek Street New York, N. Y. 10014

PREFACE TO DOVER EDITIONThe new edition of this book originally published in 1949 results from the continuing demand for a concise compilation of 'the sub sonic aerodynamic characteristics of modern NACA wing sections together with a description of their geometry and associated theory. These wing sections, or their derivatives, continue to be the most commonly used ones for airplanes designed for both subsonic and supersonic speeds, and for application to helicopter rotor blades, propeller blades, and high performance fans. A number of errors in the original version have been corrected in the present publication. The authors are pleased to acknowledge their debt to the many readers who called attention to these errors. Since original publication many new contributions have been made to the understanding of the boundary layer, the methods of boundary-layer control, and the effects of compressibility at super critical speeds. Proper treatment of each of these subjects would require a book in itself. Inasmuch as these subjects are only peripherally involved with the main material of this book, and could not, in any ease, be treated adequately in this volume, it was considered best to expedite republication by foregoing extensive revision.

IRA H.CHEVY CHASE, MD.ALBERT

ABBOTT

E. VON DOENHOFF

June, 1958

v

PREFACEIn preparing this book an attempt has been made to present concisely the most important and useful results of research on the aerodynamics of wing sections at suberitical speeds. The theoretical and experimental results included are those found by the authors to be the most useful. Alternative theoretical approaches to the problem and many experimental data have been rigorously excluded to keep the book at a reasonable length. This exclusion of many interesting approaches to the problem prevents any claim to complete coverage of the subject but should permit easier use of the remaining material. The book is intended to serve as a reference for engineers, but it should also be useful to students as a supplementary text. To a large extent, these two uses are not compatible in that they require different arrange ments and developments of the material. Consideration has' been given to the needs of students and engineers with a limited background in theoretical aerodynamics and mathematics. A knowledge of differential and integral calculus and of elementary mechanics is presupposed. Care has been taken in the theoretical developments to state the assumptions and to review briefly the elementary principles involved. An attempt has been made to keep the mathematics as simple as is consistent with the difficulties of the problems treated. The material, presented is largely the result of research conducted by the National Advisory Committee for Aeronautics over the last several years. Although the authors have been privileged to participate in this research, their contributions have been no greater than those of other members of the research team. The authors wish to acknowledge es pecially the contributions of Eastman N. Jacobs, who inspired and directed much of the research. The authors are pleased to acknowledge the im portant contributions of Theodore Theodorsen, I. E. Garrick, H. Julian Allen, Robert M. Pinkerton, John Stack, Robert 1'. Jones, and the many others whose names appear in the list of references. The authors also wish to acknowledge the contributions to the attainment of low-turbulence air streams made by Dr. Hugh L. Dryden and his former coworkers at the National Bureau of Standards, and to express their appreciation for the in spiration and support of the late Dr. George W. Lewis.

IRA H.ALBERTCHEVY CHASE, ~{D.

ABBOTT

E.

VON DOENHOFF

July, 1949

vii

CONTENTSPREFACE TO DOVER EDITION . . . . . . . . . . . . PREFACE. . . . . . . . . . . . . . . . . . . . . . .1. THE SIGNIFICANCE OF WING-SECTION CHARACTERISTICS . . Symbols. The Forces on Wings. Effect of Aspect Ratio. Application of Section Data to Monoplane Wings: a. Basic Concepts of Lifting-line T~eory. b. Solutions for Linear Lift Curves. c. Generalized Solution. Applicability of Section Data.

v vii

1

2. SIMPLE TWO-DIMENSIONAL FLOWSSymbols. Introduction. Concept of a Perfect Fluid. Equations of Motion. Description of Flow Patterns. Simple Two-dimensional Flows: a. Uniform Stream. b. Sources and Sinks. c. Doublets. d. Circular Cylinder in a Uniform Stream. e. Vortex. f. Circular Cylinder with Circulation. 3. THEORY OF WING SECTIONS OF FINITE THICI{NESSSymbols.

31

.

46

Introduetiou. Complex Variables. Conformal Transformations. Transformation of a Circle into & Wmg Section. Flow about Arbitrary Wing SeetiODS. Empirical Modification of the Theory. Design of Wing Sections.

4. THEORY OF

TJIIN

WING SECTIONS . . . . . . . . . . . .

~.

64

Symbols. Basic Concepts. Angle of Zero Lift and Pitching Moment. De sign of Mean Lines. Engineering ApplicatioD8 of Section Theory.

5. THE EFFECTS OF VISCOSITY . . . . . . . . . . . . . .Symbols. Concept of Reynolds Number and Boundary Layer. Flow around Wmg Sections. Characteristics of the Laminar Layer. Laminar Skin Frietion. Momentum Relation. Laminar Separation. Turbulent Flow in Pipes. Turbulent Skin Friction. Calculation of Thickness of the Turbulent Layer. Turbulent Separation. Transition from Laminar to Turbulent Flow. Calculation of Profile Drag. Effect of Mach Number on Skin Friction.

80

6. FAMILIES OF WING SECTIONSSymbols. IDtroduction. Method of Combining Mean Lines and Thickness Distributions. NACA F~igit Wing Sections: a. Thickness Distributions. b. Mean Lines. c. Numbering System. d. Approximate Theoretical Characteristics. NACA Five-digit Wing Sections: a. Thickness Distribu tions. b. Mean Lines. c. Numbering System. d. Approximate Theoretical Characteristics. Modified NACA Four- and Five-digit Series Wing Sections. N ACA l-Series Wing Sections: Q. Thickness Distributions. b. Mean Lines.

III

ix

x

CONTENTS

c. Numbering System. d. Approximate Theoretical Characteristics. NACA 6-Series Wing Sections: G. Thickness Distributions. b. Mean Lines. c. Numbering System. d. Approximate Theoretical Characteristics. NACA 7-8eries Wing Sections. Special Combinations of Thickness and Camber.

7. EXPERIMENTAL CHARACTERISTICS OF WING SECTIONS .Symbols. Introduction. Standard Aerodynamic Characteristics. Lift Characteristics: 4. Angle of Zero Lift. b. Lift-curve Slope. c. ~faximum Lift. d. Effect of Surface Condition on Lift Characteristics. Drag Charac teristics: G. Minimum Drag of Smooth Wing Sections. b. Variation of Profile Drag with Lift Coefficient. c. Effect of Surface Irregularities on Drag Characteristics. d. Unconservative Wing Sections. Pitching moment Charncteristics. 8. HIGH-LIFT DEVICES . Symbols. Introduction. Plain Flaps. Split Flaps. Slotted Flaps: 4. De scription of Slotted Flaps. b. Single-slotted Flaps. c. Extemal-airfoil Flaps. d. Double-slotted Flaps. Leading-edge High-lift Devices:a. Slats. b. Slots. c. Leading-edge Flape. Boundary-layer Control. The Chordwise Load Distribution ovcr Flapped 'Ving Sections.9. EFFECTS OF COMPRESSIBILITY AT SUBSONIC SPEEDS . . . .Symbols.. Introduction. Steady Flow through a Stream Tube: 4. Adiabatic

124

188

247

Law. b. Velocity of Sound. c. Bernoulli's Equation for Compressible Flow. d. Cross-sectional Areas and Pressures in a Stream Tube. e. Relations for a Normal Shook. First-order Compressibility Effects: G. Glauert-Prandtl Rule. b. Effect of Mach Number on the Pressure Coefficient. Flow' about Wing Sections at IIigh Speed: 4. Flow at Subcritical Mach Numbers. b. Flow at Supercritieal ~{ach Numbers.. Experimental Wing Characteris tics at High Speeds: 4. Lift Characteristics. b. Drag Characteristics. c. Moment Characteristics. Wmgs for High-speed Applications.REFERENCESAPPE~DIX

300 309

I. Basic Thickness Forms.

II. Mean Lines . . .

382406449

I I I. Airfoil Ordinates IV. Aerodynamic Chnracteristies of \Ying SectionsINDJ4~X

.

CHAPTER 1 THE SIGNIFICANCE O:F WING-SECTION CHARACTERISTICS1.1. Symbols.AAn

CD Co, CLCL ma x CAl CJI oe D E E G H

JL L. L, M

8V X,"a

a.Go

ac

bC

c

c'Cd Cd,

c,

Cl elCI.

Cl max

c.C.

c....Cc

aspect ratio coefficients of the Fourier series for the span-load distribution drag coefficient induced dra.g'"coefficient lift coefficient maximum lift coefficient pitching-moment coefficient pitching-moment coefficient about the aerodynamic center drag Jonesi' edge-velocity factor, equals ratio of the semi perimeter of the plan form of the wing under consideration to the span of the wing a factor (see Fig. 13) a factor (see Fig. 14) a factor (see Fig. 15) a factor (see Fig. 9) lift " additional" loading coefficient U basic" loading coefficient pitching moment wing area speed longitudinal distance between the aerodynamic center of the root section and the aerodynamic center of the wing, positive to the rear wing lift-curve slope effective section lift-curve slope, 40/ E section lift-curve slope aerodynamic center wing span wing chord mean geometric chord, 8/b mean aerodynamic chord section drag coefficient section induced-drag coefficient section lift coefficient local U additional" section lift coefficient for a wing lift coefficient equal to unity local U basic" section lift coefficient section maximum lift coefficient section-moment coefficient section-moment coefficient about the aerodynamic center root chord tip chord

1

2d. section drag


f a factor (see Fig. 8) k a spanwise station l section lift Z. " additional" section lift It ",basic" section lift m seetion moment r an even number of stations used in the Fourier analysis of the span-load distribution u a factor (see Fig. 10) v a factor (see Fig. 11) tD a factor (see Fig. ~) ~ projected distance in the plane of symmetry from the wing reference point to the aerodynamic center of the wing section, measured parallel to the chord of the root section, positive to the rear 71 distance alang the span ~ projected distance in the plane of symmetry from the wing reference point to the aerodynamic center of the wing section measured perpendicu1U' to the root chord, positive upward ex angle of attack act section angle of attack a. effective angle. of attack eli angle of downwash section angle of attack for zero lift a ... angle of zero lift of the root section a. wing ang1e of attack measured from the chord of the root section 0. + il/l

=

f(x

+ iy)

:2q,2 + i:~ = /:"r(x + iy) == f'(z) uX ..u~t

and

(j2cP + ~.a2;p = JJl1J (X +.) = - f"( z ) ~ iJ 2 ay2 ~y y

48adding, we have


ax2

02/ax)dx=

+ (o(j)loll)dy] + i [(iJ~/iJx)dx + (iJ1/I/iJy)dyJd.x+ i dy

dz

In order for dw/dz to have a definite meaning, it is necessary that the value of du: 'dz be independent of the manner with which dz approaches zero. If dy is assumed to be zero, the value of the differential quotient dw/dz is o

~

A."..

o

o ... ..,C

e

o

0_

...,

20

-

.-

-

a 0.1 0.2 6 O.L. " 0.6

Q

0

~ I

1& 8 12 16 20 .Airtoll thlckaess. percent of chord

(cJ

NACA 6~- serles.

..0~

..,.. ....~

eo

-6

ro4

.s.0

-4I;.

--.ll ~

...c

..:tt

.. ~

A.

-2~4~

..0 .p 0

5

110

.,;,.

......

V

A..

0

n

0

~

'"

i

i ~

20

Ja. 8 12 16 A1rfoil tblckn percent(d) BACA

or

20 chord

24

65- eerie

airfoil eectiooa or various thicknesees and cambers. R, 6 X lOS.

128


those obtained in flight. Application of these wing-section data to the prediction of the characteristics of wings of finite span depends on the adequacy of three-dimensional \V~g theory. These data are not applicable at high speeds where compressibility effects become important. 7.3. Standard Aerodynamic Characteristics. The resultant force on a "ring section can be specified by t"90 components of force perpendicular and parallel to the air stream (the lift and drag, respectively) and by a moment in the plane of these t\VO forces (the pitching moment). These forces are functions of the angle of attack of the section. The standard method of presenting the characteristics of 'ling Sections is by means of plots of the lift, drag, and moment coefficients against angle of attack or, alternately, plots of angle of attack, drag, and moment coefficients against lift coefficient. Plots of wing-section characteristics are presented in Appendix IV for a wide range of shape parameters. On the left-hand side of each plot, the lift coefficient and the moment coefficient about the quarter-chord point are plotted against the angle of attack. On the right-hand side of each plot the drag coefficient and moment coefficient about the aerodynamic center are plotted against the lift coefficient. In most cases, the data indicated in the following table are presented.Surface condition Split flap deflection degrees Reynolds number, millions

Charneteristie

Left-hand side Lift tift Lift Moment~Io~ent

. . . .

I4Iift...........

.

Smooth Rough Smooth Rough Smooth SmoothRight-hand side

0 0 60 600 60

3,6,9 6 6 6 3,6,9 6

Drag Drag Moment

. . .

Smooth Rough" Smooth

0 0 0

3,6,9 6 3,6,9

*O.011-ineh amin carborundum lipread tbinJy to cover 5 to 10 per cent of the area from the leadinc ede to 0.0& alung boUa surfaces of a IleCtion wit.h a chOld of 24 inchee.

7.4:. Lift Characteristics. 4. Angle of Zero lift. As indicated in Chap. 4, the angle of zero lift of a wing section is largely determined by the camber. The theory of wing sections provides a means for computing the angle of zero lift from the mean-line data presented in Appendix II. The agreement between the calculated and the experimental angles of zero lift

EXPERIMENTAL CHARACTERISTICS OF WING SECTIONS

129

depends on the type of mean line used. Comparison of the theoretical data given in Appendix II 'lith the experimental data of Appendix IV shows that the agreement is good except for the uniform-load type (a = 1) of mean line. The angles of zero lift for this type of mean line are generally closer to 0 degrees than predicted. The experimental values of the angles of zero lift for a number of NACA four.. and five-digit and NACA C)-series wing sections are presented in Fig. 56. The thickness ratio of the wing section appears to have little effect on the angle of zero lift regardless of the type of thickness distribu

-3_ -6..c

tID

....oo

'-t

~

; -4II

'-'4

ol(.)

6

v

A..

oQ

e

u

-.

C)

v

-.

~ 8 12 16 Alrton thicknes.. percentFIG.

or

20 chord

(e) MACA 66- .eries.56. (Cond1ldal)

tion or camber. For the NACA four-digit series wing sections, the angles of zero lift are approximately 0.93 of the value given by the theory of thin wing sections. For the NACA 23o-serics wing sections, this factor is approximately 1.08; and for the X.\Cl\ f.)-~(~r ies sections with the uniform load type of mean line, this factor is approximately 0.74. b. L~Jt-curve Slope. Lift-curve slopes fOI" a number of NACA four- and five-digit series and KACA fJ-8Cri~ wing ~~t.jons are plotted against thick ness ratio in Fig. 57. These values of the lift-curve slope were measured for a Reynolds number of 6 million at vulues of the lift coefficient approxi mately equal to the design lift coefficient of the wing sections. This lift coefficient is approximately in the center of the low-drag range for the NACA f>-Series wing sections. In the range of thickness-ratios from (i to 10 per cent, the NACA four and five-digit series and the XAC.-\ 64-series wing sections have values of the lift-curve slope very close to the value given by the theory of thin wing sections (2... per radian, or 0.110 per degree). Variation of Reynolds Dum

130

THEORY OF WING SECTIONSP1a~d .~bola 1ndlcat~

roUSb

condltl~n

~

, a. c t

..

.12

..o

.10

...

.,

r--' . -

...

-.iii

-- --:t t--

-.e

t-~ 1 -

Berl

.. ~- ~

--20

-~ ~1~

c'\

"'8aIootb~~

:J

...

E .~ :s.068hal

eA

EI

at(4

00'

I

--.

-.: ~

4 1g1t)

Bogp-

"

230 (5 4181t)22

10 12 14 16 18 Alrtoll thickneas. percent or choreNaCA tour- and f'lve-d1s1t aerie

-33

"I

0

.lIa..12~

r 8lllooth_

J

'0

-

III

I

I

.Iw-- ~I'

,

-1.1

.!t- -

--

-~ ~-,

--~--4

~O

\..acuabeO00.2 40.~

.08

vo.

,,

8

12 14 Alr1"o11 thlcknes.. percen1i 10

I

I

I

O

16 18 chord

20

22

(b)

.ACIl " - rlea.

..

.a

.12~.)

.. I..10

~r

~~

1'f - --

....~ -~

r- 1.1

~

---, r -

......

vre:-~- ~........J.~

I t

1\

I - T RouP

.,

aU

t ...

e

C 1

.08

5

,

e O.~ A o. '9 o.

e

0

0.1

I8(0)

I Ior16chord

10 12 14 Alrtoll. thicknesa. percerat

18

20

22

lACA 6l,- .eriea.

FrG. 51. Variation of lift-eurve slope 1Ifith arfoil thickness ratio and camber for a


131

na...d31;;0 "1..

-Jllbo11 indicate rouF condition

14

.;

.... -I2t s.

8' ...

~J

.,

4~

~J

,.I

r .ootbI

4tpo--

1'--1 tt--

1--

De

10

-., I-I"

J

.....J.,4~

1"-_

-~

'1E>

\ Roup

:I 064

...

I

08

06

V

o.~ o. o.

0

,

I

120 22

8

10 12 AlrtoU tb1c1cne percent or chord (d J MACA 65- n

11A

i

.

.12~.)

'r 8IIIooth~.),~~

rf

8'

.10

... ~

J~~.)- t-_

.s-=i.

/,

e~

....

to)

II

cl

l

r'\, - -'

t

e

E)

A

0 0.2

r--Roup

0.420

~~22

I I6810 Alrtoll12

thiem....

.008

e~ ~

',-

J.,

~

.-.eFIG.70

~ .,...

.

~

a; rw:...

-

--.1,.

-.~

~r.;)

III

-1.2

-.8

-.4

"o~l_ 1U~ coer~~ol.at.

0

.8

o~

1.2

L'

(b) Section drag characteristics at various Reynolds numbers. Variation of low-drag range with Reynolds number for the NAC_4 65(421)-420 airfoil.

156


mean line with data for sections cambered to carry the load farther forward shows that the uniform-load mean line is favorable for obtaining low-drag coefficients at high lift coefficients (Fig. 72). Data for many of the wing sections given in Appendix IV show large reductions of drag with increasing Reynolds number at high lift coefficients.

028

.0240

4~IA

tcJ

.p

.....00

c G)

-

.020

is/l~HACA 6~-4l8"I

o ...'-t~

CD

.016

~

~

tQ

\ ~r\~

I

I

I

..... .p0C)

s: 0

.012

.~

~ .jl~

RACA

65,-218II

It)

.008

~. "t:>: ~~ ~. ~.~

:U

I

I CA

\

6 53-018,\

'"\i\

.~

V if?

\

1\

~~

I~ ~

d~J ':> ~ ~

.oa,.

.",,:

L

1.

~~

p~....

.7

-

~

~.~~

.... Li. ~

r 1M

J

RACA 6~-618JlACA

~\

).\

65.,-8J.8- W

0 ...........- ......- ............- ......- ...----......- .....----.....- .....- ............ o 1.2 .8 1.6 -1.2 -.8

-.4

Sectlon

~lrt

coefficient.

CI

FIG.71. Drag characteristics of some NACA. 65-seriea airfoil sections of 18 per cent thickness

with various amounts of camber. R, G X 10'.

This scale effect is too large to be accounted for by the normal variation of skin friction and appears to be associated with the effect of Reynolds number on the onset of turbulent flow following laminar separation near the leading edge.1M A comparison of the drag characteristics of the XACA 23012 and of three NACA 6-series wing sections is presented in Fig. 73. The drag for the N.~CA 6-series sections is substantially lower than for the NACA 23012 section in the range of lift coefficients corresponding to high-speed flight, and this margin may usually be maintained through the range of lift

EXPERIl.{ENTAL CHARACTERISTICS OF rVING SECTIONS

157

coefficients useful for cruising by suitable choice of camber. The NACA 6-series sections show the higher maximum values of the lift-drag ratio. At high values of the lift coefficient, however, the earlier NACA sections .generally have lower drag coefficients than the N ACA 6-series sections. c. Effect oj Surface Irregularities Oil Drag Characteristics. Numerous measurements of the effects of surface irregularities on the characteristics of wings have shown that the condition of the surface is one of the most important variables affecting the drag. Although a large part of the drag increment associated with surface roughness results from a forward move ment of transition, substantial drag increments result from surface rough ness in the region of turbulent flow." It is accordingly important to maintain smooth surfaces even when extensive laminar flow cannot be expected. The possible gains resulting from smooth surfaces are greater, however, for wing sections such as the XA(~A G-series than for sections where the extent of laminar flow is limited by a forward position of mini mum pressure, No accurate method of specifying the surface condition necessary for extensive laminar flow at high Reynolds numbers has been developed, although some general conclusions have been reached, It may be presumed that, for n given Reynolds number and chordwise location, the size of the permissible roughness will vary direct ly with the chord of the lying section. It is known, at one extreme, that the surfaces do not have to be polished or optically smooth. Such polishing or waxing hus shown no improvement in tesu,.3 in the Kf\CA two-dimensional low-turbulence tunnels when ap plied to satisfactorily sanded surfaces. Polishing or waxing a surface that is not aerodynamically smooth ,,;U, of course, result in improvement, and such finishes may be of considerable practical value be cause deterioration of the finish may be easily seen and possibly postponed. Large models having chord lengths of 5 to 8 feet tested in the NACA two-dimensional low-turbulence tunnels are usually finished by sanding in the ehordwise direction with Xo, 320 carborundum paper when an aerodynamically smooth surface is desired," Experience has shown the resulting finish to be satisfactory' at flight values of the Reynolds number. Any rougher surfuee texture should be considered as a possible source of transition, although slightly rougher surfaces have appeared to produce satisfactory results in some cases.. l.;oftin6S 8ho\\'00 that small protuberances extending above the general surface level of an otherwise satisfactory surface are more likely to cause transition Ulan are small depressions. Dust particles, for example, are more effective than small scratches in producing transition if the material at the edges of the scratches is not forced above the general surface level. Dust particles adhering to the oil left on wing surfaces by fingerprints may be expected to cause transition at high Reynolds numbers.

158


Transition spreads from an individual disturbance with an included angle of about 15 degrees. H 42 A few scattered specks, especially near the2.8

o

..

2.0e~-

I I

IDCA 6~-418D DCAt----

65,-418, a~.-

---.. =0.5 - r-.

r---

-~--

1.2I

~.

.8

r

II

r:'

'r

rJ) ~

~~~ ..........

;l~~

o

o

I

--4

.. ...'-t~

s a o

-.2

- .8

J

7 1

-rwlr

~...I

-

~

-

-

~

"(.;1

S o

-.~

~

= -.4-16-88tQ~lOD

I

0

aDS1. or attack.

a

~b(10.

deg

24

FIo.72. Comparison of the aerodynamic characteristics of the NACA 65,-418 and NAC_~ 66,-418, CI ==.0.5 airfoils. B, 9 X 10'.

leading edge, will cause the flow to be largely turbulent. This fact makes necessary an extremely thorough inspection if low drags are to be realized. Specks sufficiently large to cause premature transition can be felt by hand. The inspection procedure used in the N ACA two-dimensional low-turbulence


159

tunnels is to .feel the entire surface by hand, after which the surface is thoroughly wiped with a dry cloth.0J2

028

o

.2

...o ...'-4 '-4

. 1i:0

0-

td

G24020

.~ ~.....'r---.....-_.8 I

or-......._

1.0

.. _ + - - - t - _ t - - - t -......._+---I

.ou :: . a.ba 0012

8 0

rIIf /J

008AftL"T

..... .04

o 0

.

..1

....a.o. position

1;0

"" 80 011

-.2

Q

JUOA-'5,~8

-II IIICA 653-418,

=0.5.k

zlo .2'5

7/0

-.060

.267

-Qq1

I -.,-1.6-1.2-

I I-.8"etlon 11ft coeff1cient. FIG. 72. (Ccmcluded)

IJc& 1.2

-.J..

0

1.6

z.0

It has been noticed that transition caused by individual sharp pro tuberances, in contrast to waves, tends to occur at the protuberance. Transition caused by surface waviness appears to move gradually up stream toward the wave as the Reynolds number or wave size i~ increased. The height of a small cylindrical protuberance necessary to cause

160


transition when located at 5 per cent of the chord with its axis normal to the surface" is shown in Fig. 74. These data were obtained at rather low2.8T

I 1I

I

I I I II

II~""""~. Q~

EI lIACA .1IACA

e

DCA

o .: 1. 6

...

I--

6 lIACA 65~~5 9 DCA " 215)~,

8taJdaiid

!012 9 9 roupn... 9~~-l&J.~

I

I

I

Jl

x

106

6

I

.

9

nJ. L.

F~

I

... ....o.p

.... u

e:

,1. 2

"

.... ....... .po

4"1~

,

g

ao

.~

IJ'~

0

...j3.~

~

--. '9,[)

t

.Art

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Ih

~~J~

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~.

II

~

\,.I

60--6

o

--b.

,dI.

~

--

-

[ ~J~

for deflecfed flop

_nose.A~

I:lJ"~

/

I'V

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~

~

rr~

....~~

~ ~v

10-~1IIr'

lD'"~!o"""'"

-'

l--"""

o/6

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l-=== ~~I

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~

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1/ ......

l...oo"'~ ....~ ~t,I' .~

"

~ 'C

l/~ ~I-"""~I""'"~Io"""~~

L...;l~

..... ~I...oo"'~

l/~

"J" N''''

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L..--'~

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. ,

3.2

126. (Condtule4)

HIGH-LIFT DEVICESI I ',,..A) N.A.CA. 65., -/18A!A.aA./4/0~)

223

I l. --N.A.C.A.64-series (f

(~

_

FIG.

SecIiaIlhickness lf1fio, ~ lpercenf 127. Effect of thickness ratio and type of wing section on maximum lift with double.

4

8

/2

/6

20

slotted 1laps.

Ftpdud

line

~---------

. T 1 ' 5 c - - - - - - - - -....

(o)AIRFOL WITHRAP

c::Airfo7chord line~

XI12

,,;

r8~ ~

FIG.

128. Typical airfoil and flap configuration.

2243.2

THEORY OF WING SECTIONSDouble slottedflop wiIh fore tip .~ r---...... ...... ~I III

01t75cJ

2.8

r----... ~

~)----4)

2.4

.>---

~--

~_J.

---,---

~ 2.0

J ...

~

i.~

Plain wing section~

~ 1.6

~

/1..............

fA...............

:~

111.2~-p-' ......

)-_1

J

~

-

."'4

.8

--Smooth ---- Leading edge rough.4

':'2FIG.

129. Variation of minimum pressure for 80rne NACA tHeries wing aectiODS of 10 per cent tbiclmees and a design lift coefficient of 0.2 .. R, 6 X 10'..

Position ofmimil1lU71 pteSSIIe, % maximum section lift coefficient with position of

.3

.4

.5

.6

.7

FIXED AUXILIARY WING SECTION (AXED SLAT)

~

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d

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~

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ao, deg

If}

24

NACA i412 ",Ving Section

APPE.VDIX I1T

473

.4

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.8

.8

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J

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IT

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t I I-.8N-~CA

I I

I ( I t I

Cz.8lZ

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/.6

1412 \\~g Section (Coiltin1ted)

4741.8


2.4

2.0 1.81.2

:R~

i

~

0.8

';J

0.1

a.1rZ

8 0.40

..: -0.1 II -0

,"

~

0

..

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Ii 8

...

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:8 -0.8-0.4

I

CI

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NACA 2408 Wing Section

APPENDIX IV

475.. ;~f-: H~':~ :V= ~:-T:~ ~'t~~ :~4~- :..1 i i'"

0.032 ........ ..

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::

r .aII

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4943.6


~2

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., deg

16

24

32

NACA 4421 '\\Ting Section

APPENDIX IV

495

,

I..

.6

.8

N.fi-+--Io-+--+-~I--+--t-+-I 1.0

A

II

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IA ~020 1--I.....- I -.......~........-I--60-~~-+-OO+- --t-........ ..foo-........--I-........-+-f--t~..............,...1'-1-1 .......

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r ."

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tttttttm_lm~ttttjjjj

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is

N ACA 4421 '\\Ting Section (ContinllM)

4963.6

THEORY OF lVING SECTIONS

3.2

2.8}

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24

.32


APPEJ.VDI4Y 1l'"

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c,

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1.6

NACA 63-006 'Ying Section (Continued)

510


32

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r~

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0

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de9

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24

32'

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_.

APPENDIX IV.D36

511

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t I I I I I I I I.8

I.e

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NACA 631-212 \ring Section (Continued)

522~6


Z

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NAca tiaA21U \\ mg

t;eCtiOll

(Continued)


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24

..32

NACA 64-006 Wing Section

APPENDIX IV

551

,

I

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NACA 64-006 Wing Section (Continued)

552


36

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NACA fl4-OO9 Wing Section

APPENDIX 11'

553

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___

1.6

554


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24

.JZ


APPBNDIX IV.D36

555

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J:'- .253 ....... 253

i a: c. POS ilion

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NACA MAOIO Wing Section (Continued)

596

THEORY OF WING ljECTION8

3.2

2.8i

2.4

b.2OC .lanal.ted .~t flap CSeneoted

JC106 ~ ....... V 8tan4aN roup2.0

V, 6

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x

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NACA 64A210 WIng Secuuii

APPENDIX IV

597

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5983.6 I


3.2

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! I I ! I i I I I ; I I I I i I I I 32 24

Secfion angle of' attack, et Ot deg

NACA 64A410 Wing Seet:.lD

APPENDI.J( IV

599

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theory of wing sections including a summary of airfoil data

Documents

new contributions

dover edition preface

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useful results of research

dover editionthe new

new preface

result of research

doenhoff research engineer