The characteristics of 78 related airfoil sections from tests in the variable-density wind tunnel

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REPORT No. 460
THE CHARACTERISTICS OF
78 RELATED AIRFOIL SECTIONS FROM TESTS
IN THE VARIABLE-DENSITY WIND TUNNEL
By EASTMAN N. JACOBS, KENNETH E. WARD
and ROBERT M. PINKERTON
Langley Memorial Aeronautical Laboratory
REPRINT OF REPORT No. 460, ORIGINALLY PUBLISHED NOVEMBER 1933
27077 0-36-1 1
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
NAVY BUILDING, WASHINGTON, D.C.
(An independent Government establishment, created by act of Congress approved March 3,1915, for the supervision and direction of theselentific
study of the problems of flight. Its membership was increased to 15 by act approved March 2, 1929 (Public, No. 908, 70th Congress). It eonsista
of members who are appointed by the President, all of whom serve se, such without compensation.)
JOSEPH S. AMEs, Ph.D., Chairman,
President, Johns Hopkins University, Baltimore, Md.
DAVID W. TAYLOR, D. Eng., Vice Chairman,
Washington, D.C.
CHARLES G. ABBOT, Sc.D.,
Secretary, Smithsonian Institution, Washington, D.C.
LYMAN J. BRIGGS, Ph.D.,
Director, Bureau of Standards, Washington, D.C.
ARTHUR B. COOK, Captain, United States Navy,
Assistant Chief, Bureau of Aeronautics, Navy Department, Washington, D.C.
WILLIAM F. DURAND, Ph.D.,
Professor Emeritus of Mechanical Engineering, Stanford University, California.
BENJAMIN D. FOULOIS, Major General, United States Army,
Chief of Air Corps, War Department, Washington, D.C.
HARRY F. GUGGENHEIM, M.A.,
Port Washington, Long Island, New York.
ERNEST J. KING, Rear Admiral, United States Navy,
Chief, Bureau of Aeronautics, Navy Department, Washington, D.C.
CHARLES A. LINDBERGH, LL.D.,
New York City.
WILLIAM P. MACCRACKEN, Jr., Ph.B.,
Washington, D.C.
CHARLES F. MARVIN, Sc.D.,
Chief, United States Weather Bureau, Washington, D.C.
HENRY C. PRATT, Brigadier General, United States Army.
Chief, Mat€riel Division, Air Corps, Wright Field, Dayton, Ohio.
EDWARD P. WARNER, M.S.,
Editor "Aviation," New York City.
ORVILLE WRIGHT, Sc.D.,
Dayton, Ohio.
GEORGE W. LEWIs, Director of Aeronautical Research.
JOHN F. VICTORY, Secretary.
HENRY J. E. REID, Engineer in Charge, Langley Memorial Aeronautical Laboratory, Langley Field, Va.
JOHN J. IDE, Technical Assistant in Europe, Paris, Franed.
EXECUTIVE COMMITTEE
JOSEPH S. AMEs, Chairman.
DAVID W. TAYLOR, Vice Chairman.
CHARLES G. ABBOT. WILLIAM P. MACCRACKEN, Jr.
LYMAN J. BRIGGS. CHARLES F. MARVIN.
ARTHUR B. COOK. HENRY C. PRATT.
BENJAMIN D. Fo ULOIS. EDWARD P. WARNER.
ERNEST J. KING. ORVILLE WRIGHT.
CHARLES A. LINDBERGH.
JOHN F. VICTORY, Secretary.
E
REPORT No. 460
THE CHARACTERISTICS OF 78 RELATED AIRFOIL SECTIONS FROM TESTS IN THE
VARIABLE-DENSITY RIND TUNNEL
By EASTMAN N. JACOBS, KENNETH E. WARD, and ROBERT M. PINKERTON
REPRINT OF REPORT No. 460, ORIGINALLY PUBLISHED NOVEMBER 1939
SUMMARY ence 1) but, with the exception of the M-series and a
An investigation of a large group of related airfoils series of propeller sections, the airfoils have not been
was made in the N.A.C.A. variable-density wind tunnel systematically derived in such a way that the results
at a large value of the Reynolds Number. The tests were could be satisfactorily correlated.
made to provide data that may be directly employed for a The design of an efficient airplane entails the careful
rational choice of the most suitable airfoil section for a balancing of many conflicting requirements. This
given application. The variation of the aerodynamic statement is particularly true of the choice of the wing.
characteristics with variations in thickness and mean-line Without a knowledge of the variations of the aerody-
form were therefore systematically studied. namic characteristics of the airfoil sections with the
The related airfoil profiles for this investigation were variations of shape that affect the weight of the struc-
developed by combining certain profile thickness forms, ture, the designer cannot reach a satisfactory balance
obtained by varying the maximum thickness of a basic between the many conflicting requirements.
distribution, with certain mean lines, obtained by varying The purpose of the investigation reported herein was
the length and the position of the maximum mean-line to obtain the characteristics at a large value of the
ordinate. A number of values of these shape variables Reynolds Number of a wide variety of related airfoils.
were used to derive a family of airfoils. For the purposes The benefits of such a systematic investigation are
of this investigation the construction and tests were limited evident. The results will greatly facilitate the choice
to 68 airfoils of this family. In addition to these, several of the most satisfactory airfoil for a given application
supplementary airfoils have been, included in order to and should eliminate much routine airfoil testing.
study the effects of certain other changes in the form of the Finally, because the results may be correlated to
mean line and in the thickness distribution. indicate the trends of the aerodynamic characteristics
The results are presented in the standard ,graphic form with changes of shape, they may point the way to the
representing the airfoil characteristics for infinite aspect design of new shapes having better characteristics.
ratio and for aspect ratio 6. A table is also given by Airfoil profiles may be considered as made up of cer-
means of which the important characteristics of all the tain profile-thickness forms disposed about certain
airfoils may be conveniently compared. The variation of mean lines. The major shape variables then become
the aerodynamic characteristics with changes in shape is two, the thickness form and the mean-line form. The
shown by additional curves and tables. A comparison thickness form is of particular importance from a
is made, where possible, with thin-airfoil theory, a structural standpoint. On the other hand, the form of
summary of which is presented in an appendix. the mean line determines almost independently some
of the most important aerodynamic properties of the
INTRODUCTION airfoil section, e.g., the angle of zero lift and the
The forms of the airfoil sections that are in common pitching-moment characteristics.
use today are, directly or indirectly, the result of The related airfoil profiles for this investigation were
investigations made at Gottingen of a large number of derived by changing systematically these shape vari-
airfoils. Previously, airfoils such as the R.A.F. 15 ables. The symmetrical profiles were defined in terms
and the U.S.A. 27, developed from airfoil profiles of a basic thickness variation, symmetrical airfoils of
investigated in England, were widely used. All these varying thickness being obtained by the application
investigations, however, were made at low values of of factors to the basic ordinates. The cambered pro-
the Reynolds Number; therefore, the airfoils developed files were then developed by combining these thickness
may not be the optimum ones for full-scale application. forms with various mean lines. The mean lines were
More recently a number of airfoils have been tested in obtained by varying the camber and by varying the
the variable-density wind tunnel at values of the shape of the mean line to alter the position of the
Reynolds Number approaching those of flight (refer- maximum mean-line ordinate. The maximum ordinate
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
of the mean line 2s referred to throughout this report as the If the chord is taken along the x axis from 0 to 1,
camber of the airfoil and the position of the maximum
the ordinates y are given by an equation of the form
ordinate of the mean line as the position of the camber.
An airfoil, produced as described above, is designated by f y = ad ^x + ax + a2x2+ a3x' + a4x4
a number of four digits: the first indicates the camber in The equation was adjusted to give the desired shape
percent of the chord; the second, the position of the camber by imposing the following conditions to determine the
in tenths of the chord from the leading edge; and the last constants:
two, the maximum thickness in percent of the chord.
(1) Maximum ordinate 0.1 at 0.3 chord
Thus the N.A.C.A. 2315 airfoil has a maximum camber
of 2 percent of the chord at a position 0.3 of the chord x=0.3 y=0.1
from the leading edge, and a maximum thickness of 15 dy/dx = 0
percent of the chord; the N.A.C.A. 0012 airfoil is a (2)Ordinate at trailing edge
symmetrical airfoil having a maximum thickness of 12
percent of the chord. x=1 y=0.002
In addition to the systematic series of airfoils, (3)Trailing-edge angle
several supplementary airfoils have been included in
x=1 dy/dx= —0.234
order to study the effects of a few changes in the form
of the mean line and in the thickness distribution. (4) Nose shape

Preliminary results which have been published in- X=0.1 y = 0.078
clude those for 12 symmetrical N.A.C.A. airfoils, the
00 series (reference 2) and other sections having differ- The following equation satisfying approximately the
above-mentioned conditions represents a profile having
ent nose shapes (reference 3); and those for 42 cam-
bered airfoils, the 43 and 63 series (reference 4), the 45 a thickness of approximately 20 percent of the chord.
and 65 series (reference 5), the 44 and 64 series (refer- t y = 0.29690.1/ — 0.12600x — 0.35160x2+ 028430x3
ence 6), and the 24 series (reference 7). — 0.10150x4
. / - ^^olo^° a - N. A. C. A. family
t_e
r
O ^e
+ Clark Y
o Gdtt. 398
/0 ./; .2 .4 .5 .6 .7 .8 .9 /.O
±v = 0.29690 Arx_- 0.12600 x -0.35160x' +0.28430 x' -0.10150x'
Basic ordinates of N.A.C.A. family airfoils (percent of chord)
Ord____.I O 1 31-157 4.3581 55..90261 7.000110.80511&9091 9.6031 9.002110.003149.0721 8.823107 .sod 17d u, 184.872192.413101.344 1 1 0. 210
L.E. radius, 4.40.
FIGURE I. Thickness variation
The tests were made in the variable-density wind This equation was taken to define the basic section.
tunnel of the National Advisory Committee for Aero- The basic profile and a table of ordinates are given in
nautics during the period from April 1931 to February figure 1. Points obtained by removing the camber
1932. from the Gottingen 398 and the Clark Y sections, and
DESCRIPTION OF AIRFOILS applying a factor to the ordinates of the resulting
Well-known airfoils of a certain class including the thickness curves to bring them to the same maximum
Gottingen 398 and the Clark Y, which have proved to thickness, are plotted on the above figure for com-
be efficient, are nearly alike when -their camber is parison. Sections having any desired maximum thick-
removed (mean line straightened) and they are reduced ness were obtained by multiplying the basic ordinates
to the same maximum thickness. A thickness variation by the proper factor; that is
similar to that of these airfoils was therefore chosen for
the development of the N.A.C.A. airfoils. An equation ±y, =6-t (0.29690.1/x-0.12600x-0.35160x2
defining the shape was used as a method of producing
fair profiles. +0,28430e-0.10150x')
CHARACTERISTICS OF AIRFOIL SECTIONS FROM TESTS IN VARIABLE-DENSITY WIND TUNNEL
where t is the maximum thickness. The leading-edge and
radius is found to be yr=(1 p)2 [(1-2P)+2Px-el
a
=' .Iota
r` 2 0 20 ae) (aft of maximum ordinate)
When the mean lines of certain airfoils in common The method of combining the thickness forms with
use were reduced to the same maximum ordinate and the mean-line forms is best described by means of the
compared it was found that their shapes were quite diagram in figure 2. The line joining the extremities
different. It was observed, however, that the range of the mean line is chosen as the chord. Referring to
of shapes could be well covered by assuming some
the diagram, the ordinate yt of the thickness form is
simple shape and varying the maximum ordinate and
measured along the perpendicular to the mean line
its position along the chord. The mean line was, from a point on the mean line at the station along the
therefore, arbitrarily defined by two parabolic equa-
chord corresponding to the value of x for which yt
tions of the form was'computed. The resulting upper and lower surface
yo= be+ bx+ b2 X2
i points are then designated: -
where the leading end of the mean line is at the origin
Stations x„ and x,
and the trailing end is on the x axis at x=1. The
Ordinates y„ and yt
values of the constants for both equations were then
expressed in terms of the above variables; namely, where the subscripts u and l refer to upper and lower
(1)Mean-line extremities surfaces, respectively. In addition to these symbols,
the symbol 0 is employed to designate the angle be-
X=0 y^=0
tween the tangent to the mean line and the x axis.
X=1 y'=0
This angle is given by
(2) Maximum ordinate of mean line
6 = tan-1 dx
x=p (position of maximum ordinate)
y Oa lxa. ya B=Ion-' dx
./0- 9 yt
v Mean /ins
P1
Chord
p ^ x
Or /xt, yt/ x„ = x - y, sine Yu ' Y + yt cos B
-./OL Rodius fhrough end of chord xt = x + y, sin a yt = yt - yt cos e
/.00
Sample calculations for derivation of N.A.C.A. 6821
z v, ue tan a sin v aos a y, sine y. cos a z, v. x, m
00.01250 00.03314 00.00489 10..3480303030 0..3357719430 0..9932387450 00.01186 00.03094 ....0...0.0.0.8.4.......0..0.3..6.8.3. 00.01438 -00.02805
.3000 .10503 .06000 0 0 1 0 .10503 .30000. .16503 .30000 -.04503
1.am ..002792818 0.04898 --..1077134437 --..1067839277 ..9989676321 --..000053875 ..0007291086 1..0800053875 ..012281683 ..9599946135 --..00231087
Slope of radius through and of chord.
FIGURE 2.-Method of calculating ordinates of N.A.C.A. cambered airfoils.
yo=m(maximum ordinate) The following formulas for calculating the ordinates
dye/dx = 0 may now be derived from the diagram:
xa=x-y, sin 6
The resulting equations defining the mean line then ya=y,+y, cos 0
became xl=x+yt sin 0
yt=yr-y, cos 0
Mpyr = 2 I2Px - el Sample calculations are given in figure 2. The center
for the leading-edge radius is placed on the tangent to
(forward of maximum ordinate) the mean line at the leading edge.
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
A family of related airfoils was derived in the manner models, which are made of duralumin, have a chord
described. Seven values of the maximum thickness, of 5 inches and a span of 30 inches. They were con-
0.06, 0.09, 0.12, 0.15, 0.18, 0.21, and 0.25; four values structed from the computed ordinates by the method
of the camber, 0.00, 0.02, 0.04, and 0.06; and six values
described in reference 8.
of the position of the camber, 0.2, 0.3, 0.4, 0.5, 0.6, and
Routine measurements of lift, drag, and pitching
0.7 were used to derive the related sections of this moment about a point on the chord one quarter of the
family. The profiles of the airfoils derived are shown chord behind its forward end were made at a Reynolds
collectively in figure 3.
Number of approximately 3,000,000 (tank pressure,
For the purposes of this investigation the construc-
tion and tests were limited to 68 of the airfoils. Tables approximately 20 atmospheres). Groups of airfoils
were first tested to study the variations with thickness,
of ordinates at the standard stations are given in the
figures presenting the aerodynamic characteristics. each group containing airfoils of different thicknesses
These ordinates were obtained graphically from the but having the same mean line. Finally, all airfoils
computed ordinates for all but the symmetrical sec- having a thickness of 12 percent of the chord were
^-----
06 2206 2306 2406 2,506 2606 2706
-GX09 2209 2309 2409 2509 2609 2709
001Z- '— 2212_ 2312 ^2412 2612 -^2712
O55 2215 X315 2615 -^
0-018 2218' ^_2318 C_24^18 8' ^ 2618 2918
LC -^ ^ _.^1 '^-2421 -^
^4206 4306 4406 4506 4606 4706
0025
4209 4309 4409 4509 4609 4709
9212 4312 4412 4512 4612 4712
4215 4315 4415 4515 4615 4715
4218 4318 4418 4518 4618 4718
4221 4321 4421 4521 4621 9721
620—6 6306 6406 6506 6606 6706
6209 6309 6409 6509 6609 6709
6212 6312 6412 6512 6612 6712
6218 6318 6418 6518 6618 ^-6718
6221 6321 6421 6521 6621 6721
F—E 3.—N.A.C.A. sWoll pmffiw.
tions. Two sets of trailing-edge ordinates are given. tested to study the variations with changes in the
Those inclosed by parentheses, which are given to mean line.
facilitate construction, represent ordinates to which RESULTS
the surfaces are faired. In the construction of the
The results are presented in the standard graphic
models the trailing edges were rounded off.
Three groups of supplementary airfoils were also form (figs. 4 to 80) as coefficients corrected after the
method of reference 8 to give airfoil characteristics for
constructed and tested. The derivation of these air-
infinite aspect ratio and aspect ratio 6. Where more
foils will be considered later with the discussion.
than one test has been used for the analysis, the infinite
APPARATUS AND, METHODS aspect ratio characteristics from the earlier test have
A description of the variable-density wind tunnel been indicated by additional points on the figure. Table
and the method of testing is given in reference 8. The I gives the important characteristics of all the.,airfoils.
CHARACTERISTICS OF AIRFOIL SECTIONS FROM TESTS IN VARIABLE-DENSITY WIND TUNNEL T
Lw0r. /2
.947 U i 00
- //..737077 yy Wp -/0
---2222...66476139 O P20e r c4e0n t 6o0f ch8-d0 100 •l0
y
.00/ .44 .09 36 v
-2.902 l
-a2. 2827 20 .40 G.OB 32
u0 -- ,/...8473032/23421 1.8 .36 ,uy .07. 28 .^O
1 -0 .40 L6 .32 8.06 24 0
L4 .26V% 0.05 20 w
28 0 .v
24 0 LD c. p. /.2V .24 ^. v04 16,
k K
40 20 °.03 12^
N 20^ CIE
0 16 y C .8 8u .16 0 .02 8 ^^
ol /2^l 60o ./2 O .0/ 4,^
u
g0 .4^ .0B 0 00
0 4u .2 .04 -4 0
m
oQv 0 0 ^-.z -8 a
Airfoil: N.A.C.A. 0006 R.N.:.^21Q000
--49 W.00 WPCSrzoheeresr:.re (e5sc tf"htexedl3td.e.0 dof"o.t Lmr. M.t)u:A2n.0nLV.8.e e Tl%D-ewo(s0fote...•l:/ slU ele.-Dc4f.f.)Te-: .36c 762t4..54 _-.'42 -..43 DACiaorftroerie.l-:cI N-t4e.A-d3.C 2t.o A .i n0f0i0n6ite asTpRees.cNt:t : -Vr o Li --//62
A0 ngl4e of 8., tac1k2, a1 6(d e2g0re e2s4) 28 32 ..4 2 L.i4ft c.o6e ff8ic ie1n0t , 1C.2 1.4
F--4.-N.A.C.A. 0000.W.H.
sta.Op'r. C.'r. Uc/u0
O O 0 v a
1251.420-1.961 U -C O
25711..5050534,9...605/5660/2069/-----31243....61059650166902/ U4 0 -/0O P20e r c4e0n t o6f0c ho8rd0
225044..340536--44..435063 h
43004.53052/4-4..355012 .44 .09 36 wl
D 657000332...-47'2436--233..74942763/ 20 .40 ^'.. 08 32 ag
SU 69001/..906676--1/..906676 1.8 .36 .gN,.07 ea
100!095)(A 5J
/L0.E0.Ro0d.:0.609 1.6 .32 0.06 24l
41 e U
28 1 C 1.4 .28- 0.05 20 w
1? c. p. /6 p
q 22040241/ 1/..02G 8 ..2204^8 vQ..0034 /2v
o /6D 6i LD .88u.160 .02 8'^
at /2^^Bi .680 .12 0 .0/ 4^k
w
8 0 /0, •4`1.08, 0 Op
° 4u 11 vi IC .2 .04 -4 0
.o
04 Airfoil: N.A.CA. 0009 R.N.:3,2/0,000 0 0 y -.2 "a ec
-4 cF SPirzees:. (5st-xn3d0.o"t m.):20V.8e /b.(bAalsfee:c /.-)6:6-83.25 -.2 ^°u -.3 Airfoil.• N.A. C. A. 0009 R. N.: 32/0,000
Where tesled:L.M.A.L. Test:VOT 746 Dote. /-6-32 Test: V.D.T. 746
-8 u Corrected for tunnel-wall effect. -.4 0 -.4 Corrected to inf)iVM aspect ratio
-6 -4 An0g le 4of o6ft ac1k2, a1 (6d e2g0re e2s4) 28 32 -4 0 .2 .L4ift c.o6e ff.ic8ie n1t0. C/l.2 14
Fla". 6.-N.A.C.A. 0000 MIMI.
8
REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAIITICS
Sla Up'r. 20
/25.02..05 53 .2/ .58605./9554--21.6081954 vu to /Oo ./2
7//05.5 5 44..3.62480530----4435..532654805530 o O P20e r c4e0n to6f0c hor6d0 00 ./0-
20 5738-5.738
25 5.941-5.941
4300 65..060023--65.600032 .44 .09
50 5.294-5294
O 67004 3.656643--43..656643 2.0 .40 -08
t'w 899005 1 2..864024375 --- 21.66.4024736 /.8 .36 xN.07
a %00 (. ^)(-. p 6)
L. E. Rod.:1.58 C 1.6 .32 0.06
26 0v 0 /.4 .28C11 0U.05
24 0 20e.p. ,m vV.04
-0 40 L/ 1.01.20v 8^= .03
p /660
A .16 02
o O
12 80 ..6'.12 .0/
9 -/00 .4'.08 0
i
° 4 u .2 .04
o u
0 Qc Airfoil: N.A. C.A. 0012 R.N:3,230,000 0 0 u .2
-4 4 PSrizees.: (SsWfndO. o" tm.):20V7 .DI.(akt/es.e, 1c2.f-:3 608-3.41 -.2 -.3+u^
Where tested.• L.M.A.L. Test., V.D.T. 743
-8 u Corrected for funnel-wol/ effect. -.4 -.4
-8. -4 0An 4gle 8 of /o2fto c1h6, o :2 (d0e g2re4es 2) 6 32 ` -4 L.if4t c.o6e ffici8e n1t.. 0C ./.2 1.4
FI°URE 0.-N.A.C.A. 0012Oit 0.
Slo Up'r. L'w'r a 20
[205 2.3067-23067 NUl p 0/00 ./2
2.53.268-3268
5722//.5.05005 5 7674578...... 64/425742853203/------654 577...6.6.24/4578542132037 11 0 P2e0r 4ce0n t o6f0c ho8r0d 00 10
U0U 3456B970O00000 76543/......2678S52581070/004849-------736547/......2826755751080/0948402 2/.0B ...434460 `rCv.$ 0.00789
`o l/9 00 (/./.SO0B0)6-(-/.. 01050681 V
1.6 .32 0.06
L. E. ROd.:248 C
280 0 1.4 .260- u0.05
c. . .v
24 w0 20 42V .24•w^y.04
g20 40 ,.0 208 .113
L /
a0l //26 ^8600 ..86 wvou ..1126 a0 ..00/2
8,0100 .4v .08 .0
t
0 4v .2 .04 j-./
.g ul v
-4 0C. Airfoih . fAVm. e)0:02/.1/(.5Of t. /DRs.oeNtc.e:3.:)/,22: 0-6908,-03.0410 -.2O 0 y u-.23
-8 u Fo.•rL MtuAnnL.e lT-wesat:l lV eDf.fTe. c7t28 -,4 0-.4
-6 -4 0 4 6 12 16 20 24 28 32 4
Angle of ot/oc/r, of (degrees) Lift coefficient C
Flo- 7.-N.A.C.A. 0015 etrlall.