REPORT No. 492
TESTS OF 16 RELATED AIRFOILS AT HIGH SPEEDS
By JOHN STACK and
ALBERT
SUMMARY
In order to proti
information thut rnighi lad to the
devebpmeni of better propeller 8e4%i07w,
13 relaied eymmetrics.! airfoih haoe been tested in tha N.A.CA. highSpeedwind tunnd for a study oj the e$ect of thi&ne88form
on th aerodynamicchuracteri.stti.
The thicknas~orm variables stwdid were tb value of
the maximum thtiknee8, the podion along the chord ai
which the muximum thtikne88occur8, and the value of th
leading-edgeradiw8. A 8y8temof equatbn8 wimwsed to
dt$na the airfoilform so thutfair projil.e3havingq8temaiti clum.gtxwould be obtai~d. The bm”c thicknw form
h VW nearly thi? same as that Gh08~ for the reeent
invadigation of a lurge numbm of retied airfvil.ain the
variabkd.endy wind tunnel (NA.CA.
Tezhniuz.1Report No. 400).
The tests were cundwcted.through the low angle-ofattack rangefor speeh aim.ding from 36 percent of that
of 8owndto 81@t1y in a’.cem of the epeed at whicha eomprew?ibi?tiy burble, or breaikihm of fiw, omurs. The
corresponding Reynolde Number range ie 360,000 to
?’60,000. Became the ReyiwL_i2Number for the teet8 ti
somewhat lower thun that & iohich mo8t propeUer8 operate, and much lower than thd at which aiqq?.anewings
operaie, tlw dui!u are not directly applicubb to muny
practical problems, hd it ia probalh thui 8ome of the relatti 81wwn,particularly the relative eJe& of the 8hape
clmnge8m a$eded by compra%-?riliiy,are valid & mwch
higher vaLutxof tlu R.qvnoi2hNumber. The reeuh obtained were applied to the &@n of three camberedairfti
which were te#ed m part of this invedigation.
The principal fa&r8 a$ecting the choice of propellm
8ectiom are low drag at low and moderate lift toe-8
and a late comprewi.bili.tyburble,thut%, low drag8at high
8peed8. COnwZ&g thae factor8, the rti
indicate
that the maximum thickne#8sho?dd be sm.al!and locuted
at approximdely 40 percent of the chord afi of the leading
edge. Sd
variutti from the nomnal valwa for the
leading-edge radim are 8h0wnto have wmz.?.l
e$ect on the
aerodynamti characterietim. A cornpankwnwith timil.ar
tC8t8of comm07dyWW.ipropeller 8ec3%.7M
lMkzltt% that
& high speeck one of the cumbered airfo-ih tested, the
N’,A.O.A. 2/.09-$4, h 8Upt7iW. The rt%uh d80 indicate thd 8om@furth?r improvement in ai?’fd 8hape8
for higlwpeed applicaiiom may be apected.
E.
VON
DOmTHOFF
INTRODUCTION
Experimental investigations of the relationship between airfoil shapes and airfoil aerodynamic characteristics have generally been made at some particular
dynamic soale, or Reynolds Number, and usually ut
relatively low speeds. Because the forces on an airfoil
are afle@d by air compressibility, the speed at which
teats are made may become an important parameter in
the application of the results. It has been shown that
the speed of flow expressed in terms of the speed of wave
propagation, or the speed of sound, in the fluid is an
index of the extent to which the flow is affected by compressibili~.
Thus, the ratio of the flow velooity to the
velocity of sound, V/Ve, is a parameter indicative of
flow pattern similarity in relation to compressibility
effecti just M the Reynolds Number is an index of the
effects of viscosity.
Therefore, if the speed at which
the full-scale airfoil normally operates is greatly in excess of the speed at which the model was tested, the
test remlta maybe subject to a correction for the effects
of compressibility.
The importance of the compressibility effect cannot
be disregarded for many modern applications. Previous
airfoil tests over wide speed ranges (see reference 1)
indicated that for speeds in excess of 300 miles per hour
the compressibility effect on the airfoil characteristics
may be large. It is therefore necessaxy to investigate
the relationship between airfoil shape and the aerodynamic characteristics at high speeds for such applications as the design of propekwaj diving bombem,
and high-speed racing airplanes.
The aerodynamic characteristics of airfoils may be
considered as being dependent on the thiclmess-tochord ratio (hereinafter referred to as the “thiclmess”),
the thiclmess distribution, and the mean-line shape.
The present investigation was made to study the effects
of changw in the thiolmeas and the thickness distribution on the aerodynamic
charaeterikks
of airfoils,
partictiarly at high speeds, and to provide additional
information for the study of compressibility phenomens. This information should lead to the design of
better propeller sections.
The effects of these changes
were determined by tests over a wide speed range of 13
symmetrksd airfoils having systematic changea of threti
variables.
These variables are, for a iixed chord
339
,.,.
‘ 1’
. ..—— —..- ...- ..-—.
.
-—A
.
.
.
. .
.
340
REPORT
NATIONAL
ADVISORY
length, the maggtude of the mtium
thicknwa, the
position of the msximum thicknw,
and the radius of
the led.i.ng edge.
Three cambered airfoils were also
tested as a prelhnimuy step in the investigation of the
effects of mean-ke
shape on the aerodynamic characteristic at l@h speeds.
The tests consisted of the measurement of the lift,
drag, and moment about the quartar+hord axis of the
models for a range of speeds extending from about 35
percent of the speed of sound to speeds slightiy in
excess of the speed at which the breakdown of flow
corresponding to the compressibility burble occurred.
The tests were conducted in the N.A.C.A. high-speed
wind tunnel during 1932-33.
DESCRIPTION
OF AIRFOILS
..g
the
The variables herein considered as determmm
thickness form are the mtiurn
thickmw, the position of the maximum thickness, and the radius of the
leading edge expressed in terms of the chord.
These
10–
-+—
COMMITTED
FOR
AERONAUTICS
DESIGN
NUMBERS
0006-63
0012-63
0009-63
0009-62
0008-64
0009-65
0009-66
0009-03
0009-33
0009-93
0009-06
0009-35
0009-34
2209-34
2409-34
4409-34
In the design numbers given above, the fhwt group of
four digits gives the oamber and thiclmess designation
and has the same significance as the airfoil design
numbers given in reference 1; that is, the tit
digit
indicates the mean camber in percent of the ohord;
the second, the position of the camber in tenths of the
chord aft of the leading edge; and the last two give the
mtium
thiclmw
in percent of the chord.
The
group of digits following the dash designate the thickness distribution.
The first digit designates the le&diqg-edge radius and the second digit gives the position
+——+
N. A.C.A. 0020-63
+ N. A.C.A. 0020
_
‘~
‘~+
~+>+
o
~+”+
-lo
0
1‘+---+.-+——=—————
20
30
10
50
40
.---”
+~
1
;0
1
70
~GUBEL—Ba.40tbfrkn~ dfstrfbtrtfonfor afrfollnkstai h the hfghuIEE3wfnd tmuml (N.A.Cl.A.IW2H3)mmfarnfly
afrfotls
(NAO.A.
parameters detwmhing
the thiclmess form so expressed as ratios to the chord will throughout this report be referred to simply as “thickness”,
“position
of mtium
thiclmes”,
and ‘%ading+dge
radius.”
Arbitrary values of these three variables were so chosen
as to provide systematic variations over the entire
probable useful rnnge of forms.
The resulting airfoil
forms were defied by means of a system of equations
to insure fairnm of the prcdi.les, and the coefficients
of’ the various terms of the equations were determined
born conditions imposed by the assumed values of
the independent variables.
The basic form is shown
in figure 1. On the same figure the basic thickness
distribution used in the investigation in reference 2 is
also shown. The leading-edge radius, the slope at the
tail, the maximum thiclmess, the trailing+dge
ordinate, and the position of the m&mum
thickness were
made the wne as those of the basic form given in
reference 2, which has been designated the “NA.C.A.
0020 “ airfoil.
Range of forms.-The
range of forms investigated
is shown by the airfoil design numbers in the following
table:
W
referenm
,?
1
80
90
100
wftb MO thloknws dktrlbution for N.A.O.A.
2).
of the maximum thickness in tenths of the chord nft
of the leading edge.
The significance of the leading-edge radius designation is given below-:
O designates sharp leading edge.
3 d@rnatea
one-fourth
normal leading-edge
radius.
6 designates normal leading-edge radius (the
lerding+xlge radius used in reference 2).
9 designates three times normal leading-edge
radius or greater.
The leading-edge radius of the blunt-nosed
airfoil
used in this investigation is three ties
the nornml
value.
Thus, the N.A.C.A.
0009-64 is a 9 percent thick
symmetxioal airfoil hwing a normal leading-edge radius
and its maximum th.iclmess 40 percent of the chord
aft of the leading edge. The N.A.C.A. 2409-34 airfoil has a mtium
mean camber of 2 percent located
at 40 percent of the chord, and is 9 percent thick.
The leading-edge radius is one-fourth of the normal
value and the mtium
thickness is located at 40 percent of the chord aft of the leading edge.
TESTS
OF
16 RELATED
AISFOIM
The range of thickness ratios tested in this investigation was small because it was considered necessary
to show only how relations already found for the tiect
of thickness variation at low speeds are affected by
compressibility, and also because the airfoils chosen for
high-speed application will of necessity be relatively
thin. The value 09 of the maximum thiclmeag ratio
of the airfoils designed for the study of variables
other than the maximum thiclmeas was chosen because it is representative of the thiclmess range from
which airfoil sections for propellers would probably
be chosen. The airfoil profiles are shown in iigure 2,
and the ordinates are given in table I.
Derivation of new thickness forms.-The
airfoil
forms tested in this investigation have been defined
Two equations were used rather
by two equations.
than a single equation, because a single-equation
system led to shape differences aft of the position of
maximum thiclmcss when the leading-edge radius was
changed and also led to revenmls of curvature unless a
very great number of terms were used.
If the chord is taken as the z axis from O to 1, the
ordinates y from the leading edge to the position of
maximum thicluwas are given by an equation of the
form
*y-~
Jz+u@+@+u&
(1)
The ordinates horn the position of maximum thickness
aft are given by an equation of the form
(~)
*y=&+
&(l–z)-t-dJl
-@+dJl–~)8
The coefficients of the equation for the forward
portion are determined horn the following conditions:
(a) Maximum thickness
x=m
y= 0.1 (where m is the location of the
maximum thicknaw in terms of
the chord measured from the
leading edge)
9.0
.
dx
(b) Lending-edge radius
The leading-edge radius is derived from equation (1) and is $.
Values
of
~
chosen
to
radii
are
GW6-63
AT
—
HI(3H
341
SPEEDS
.—
.
-—
_
..
0012-63
W09-63/
.—
CW9-62
b09-64
0009-65
0009-66
0009-03
m9-33/
●
om9-93c
.—
<
0009-05
0009-35
~
.—.
~
cxlo9-34
give certain desired leading-edge
shown in the following table:
sharp __...
_ . . . . . ______________________
(J=
mmnd_...-_
. . . . . . . . . . . . . . -------.--
.................................------------- !69 ~=
.514246
------
Ttuw tlnmn&---------------------------------
(c)
Radius of curvature at the point of maximum
thickness
Radius of curvature at z = m,
‘=~~(1
(1–m)’
–m) –o.588
FIGURE2—Akfd PIWflk
* Tha N.A.O.A. WY&94
Mu ban wViOUS&referredto as the N.A.O.A.204and
the N.A.O.A. 203S4, as the N.A.C.A. 216.
34!2
REPORT
NATIONAL
ADVISOBY
(this value is derived from the equation for the
after portion of the airfoil and is the same for
both equations at r= m).
The conditions that were taken to determine the
coefficients for the equation for the after portion are:
(a) Masimum thickness
~=yn,
y=o.1
$=0
(b) Ordinate at trailing edge
X=1
y=c4=Jo.oo2
[c) Trailing-edge angle
@=d,=f(m)
dx
The values of dl as a function of m, which were chosen
to avoid reversals of curvature, are given in the foUowing table:
X=1
m
F
dl
a2
Cm&
::
.5
.6
.316
.465
.iCO
Substitution
of the coefficients derived from the
foregoing conditions in equations (1) and (2) gives
equations for symmetrical airfoils 20 percent thick.
These coefficients are given in table IL
The airfoil ordinates for any other thickness are
determined by multiplying the ordinates derived from
the above equations by ~,
n~
where t is the airfoil thick-
expressed as a fraction of the chord.
The leading-
[1
it’.
edge radius for any- thickness is given by ~
~
Derivation of cambered airfoils.-The
three cambered airfoils were derived by combining one of the
best thiclmess forms, the 0009-34, with certain meanline forms chosen fi-om reference 2. The mean lines
chosen have the 2200, 2400, and 4400 forms.
The
methods of combining the thiclmess distiution
with
the mean-line forms are given in detail in reference 2.
APPARATUS
AND METHOD
Apparatus,-A
complete description of the highspeed wind tunnel and a detailed account bf the
method of conducting teds are given in reference 1.
The models used for this investigation were of 2-inch
chord .ud were made of steel. The method of constructing the airfoils is described in reference 3.
Method of testing.-The
teds consisted of the measurement of the lift, drqg, moment, and dynamic pressure for several speeds in the range *fig
from 35
percent of the speed of sound to speeds slightly in
excess of that at which the compressibility
burble
occurs. The corresponding Reynolds Number range
is from 350,000 to 750,000. The angle~f-attack
range
for the tests of the symmetriod airfoils extended horn
COMMI’ITE E FOR
AJIEONAUTICS
– 4° to 4°. The additional tests required to determino
the mtium
lift coe5cients would have unnecesmmi.ly
prolonged the testing program because inferior airfoils
for high-speed applications can be detected by their
earlier compressibility burble. The tests on the three
cambered airfoils were conducted
through the low
angle-f-attack
rmge, and one of the three which
showed promise as a practical propeller section was
chosen for tests throughout the complete angle-ofattack range. The order of the tests was arranged, as
far as practicable, so that the tests to determine the
effects of a single variable were made consecutively.
RESULTS
The
tmt results are presentad graphically in figures 3
to 18. Each figure presents completi data for one
airfoil for the range of angle of attack tested. Eaoh
curve shows the variation of one of the coe5cien ta
In the prewith V/Vc for a given angle of attack.
sentation of the momentioefficient
data the origin of
the axes for each angle of attack has been raised above
that for the previous angle of ~ttack, so that the
moment curve for any angle may be easily distrn.@shed.
The data presented in figures 3 to 18 were crossplotted in @gures 19 to 34 to show the aerodynamic
characteristics of the airfoils in the usual form. Figures
35 to 38 show the effect of the important shape vmiablea on the aerodynamic characteristics.
A compmison of the cambered airfoils is given in figures 39 and 40.
PRECISION
The
various
factors contributing to inaccuracy in
these experiments may, in general, be classified under
two divisiom.
The fit consists of systematic and the
second, of accidental errors. A detailed discussion of
the probable systematic errors is given in reference 1.
The.accidental errors are shown by the scattering of
the points on the curves and by differences between
original and check tests of the 0009–63 and 0009–66
airfoils. Errore in the angle of attick maybe as large
as %0, owing partly to errors in mounting the airfoils
md partly to dissymmetry of the symmetrical airfoih.
The balance and static-plate calibrations made before
md after the tests checked to within 1.6 percent. Inncmracies arising from other sources are within +0.006
for the lift coeflkient, +0.0006 for the drag coefficient,
md +0.002 for the moment coefficient.
The errors in
the results of the 0009-66 airfoil may be huger than
the above-mentioned
values because a special correction was applied to these data to account for the large
tiymrnetry
of this airfoil.
DISCUSSION
The data have been analyzed to show primarily the
~ffects of shape changes on airfoil aerodynamic chwwczristics at high speeds in order to provide information
TESTS
OF
16 RELATED
.8
.12
.6
./0
AIRFOILS
AT HIGH
343
SPEEDS
Angle of attock
x-2°
o 0°
+ 2°
n 4°
0°
*.
d.4
*.
~
$.08
+
k
0,
:G
$.2
al
8
*
,.
40
$
:.-. /
.;_. ,
g _.,
:
--f
$
-.2
$
-.40
.2
.4
.6
.8
0
.2
.4
.6
v/v=
FI13WEE
%—Effwtofcompressiblfkyon the aa’odgnamfochnmot.ainticsofthe NA.O& (033+safrfoil.
Angle of
X-2”
+ 2“
ottack
o 0°
o 4°
v/v=
FIQIJRE4.-EITwt ofmmpmsslbllkyon the wcdmo
obarnc.tuietfuofthe N.A,O_L fQ12-133
alrfoll.
Angle of
x -2”
+2”
FIGURE
5.—Effwtofcompresdbllltyon,themrodynamfccbnmoterfstfuofthe N.A.O.A.IMXW3a!rfoil.
15111-3&23
aftodr
0 o“
04”
.8
1.0
I
I
,
1
is”~+
Profile
Afwnent
‘a
-drag
coefficient,
.1 .1 .1
.
.
.
coef ficlent,
C+
.1 .(
.
.
II
I
I
I
C&
Momentl coejffkjen~, C.*
Al
0
n
$’
b
b
.
Q
.
OF
TIWH
16 RFILATEID AIRFOILS
AT
HIGH
345
SPEEDS
1.
Angle
P -4”
of aifack
X -2.80°
0 0.55”
+ 2.25°
.04°
u
*.
..&
.U
&
t
%
:.-. I
:J.
-J
.5-1
~Q
;-.1
o
u -.1
~
-.
G --l
$
-.
0
.2
.4
.6
.8
0
.2
v/v=
.4
.6
.8
.2
o
.4
v/v=
FIGURE
9.—Eflwt of com~blllty
.6
.8
1.0
.8
I.O
v/vc
on tbe fierdgmwnfo@lmraot@rfstIu
of the N.&O.A. lX03+J3
afrfofL
.6
Angle of attack
~ -20
b -4°
0 0°
+ 2“
❑ 4“
.4
0
~z
,9.
4
-.
%
d -.
*-
j.
J -.
.U
~ -.
t!
~
.4
o
u -.
-.2
:
$
-.4
0
.2
.6
.8
o
V7K
.2
.4
.6
.8
v/vc
fiGURE10.-EfIed of comptibflfty
.8
on the rumxlmo
v/v.
abarackristicaof tbe N&O.A. @3BCc3
afrfoii
-
.12
.6
~.lo
Arl@_eJf
b
*LS
*- .4
.8
b
“$.2
a
o
u
.$0
4
-.2
0
c
.~.m
c1
z
<
Q
~ .06
J-.
b
o
*- -. I
+-m
Q
2
%.
~-.l
L1
~-.l
$.02
0
u -./
oft%
x
0“
+2°04”
I
:
-.4
g
0
O
2
.4
v/n
.6
.8
0
2
.4
Vp=
.6
.8
0
2
.4
.6
v/Pz
fif3URElL—Effeclof wIO@wdMlftyon tbe naodgnam[o obamoteristiu of the N.A.O.A.IDW33afrfofL
— ——-.. _.— —.. _
346
REPORT
NATIONAL
ADVISORY
COMbfTPTE E FOR
AERONAUTICS
.8
A77$0of atfafa~
.6
o 0°
+ 2*
~.4
%.$
b
$.2
a
4“
$
$0
4
-.2
-.4
.6
02
L
o
.8
Vjv.
Fmum
12-lMOzt
of
1
I
.2
I
I
1
I
.6
1
I4
-8
V;F%
comwfdbllfty on the wrufmmmfo ~CS
Of the N. A.OA.
MXW3
P&fOfl.
App$
of
0;$
00°
+ 2°
n 4“
L?
%-.
I
$-. /
&
y;
-h
~_.J
$
0
.2
.4
.6
Vflc
FIGURE [email protected] of wmfmsdhflity
.8
on the
@mO
Ohamcteristks
of the N.A.O.& WOH!.5
F&foil.
.12
.6
H
& ‘0
n
<
g)g$
Ofl Ot;cgf
o
+ 2“
-F-kt—lNttttHt
+=7-P-lW-H—Hu+
llll&llllllllfll
W-H++-t
II
IEEEi--tq
0
-.2
&
v~=
.8
0
2
.4
Vfl=
.6
.8
FIQURE14.-Effect of mmpm@bIlftyon the eerc@mernfocfmmckMcs of the N.A.O.A.fW9+%okfoil.
0“
n 4“
,8
/.0
TESTS OF 16 RELATED
AJRFOILS
to be used in developing better propeller sections. Because the Reynolds Number for the teats k somewhat
lower than that at which most propellers operata, the
data are not directly applicable to many propeller
problems, but it is probable that some of the relations
shown, particularly the relative effect of the shape
~QUEE
AT
HIGH
347
SPEEDS
creases uniformly with the thickness ratio of the airfoils at speeds below that of the compressibility burble.
hcreasing
the thic.lamss of em airfoil causes the compreasibility burble to occur at progressively
lower
speeds.
The proiile-drag coefficients for a lift coefficient of 0.4 show, in general, the same changes as the
16.—Effectof comprmfbility on tbe aerodyrdunfoclkuncterktlcaof the N.&O.A. CKIXX+I
MoD.
changes as affected by compressibility,
are valid
much higher values of the Reynolds Number.
PROFILE
at
DRAG
The effects of compressibility
on proii.le dr-ag are
substantially in agreement with the results shown in
reference 1 and therefore are not discussed in detail.
The changes in the drag coefficients are small until’ a
minimum profile-drag coefficients, except for a slight
decrease in the profile-drag coefficient with increase of
speed over the lower end of the speed range.
Figure
35 also shows that the speed at which the rapid rise
in the drag coefficient or the compressibility burble
occurs, decreases as the lift is increased.
Effect of maximum
thickness
position.-Curve9
showing the variation of the minimum profile-drag co-
Angle
~-zo
of
+ 2°
attcxk
o 0°
II4°
C?
*.
~ -.1
..
$-.1
QJ
0-. /
u
%--/
&.
4
0
2
.4
.6
.8
/.0
v/K
~amm 16.—Eff0Sof mmprcssfbilityon the aeiw.iymmnio
oharaotwktk of the N.A.O.A.fiai%31aIi%ll.
speed corresponding
to that of the compressibility
burble is reached; the drag coefficient then rapidly
increases.
lMect of thickness.-The
effects of thickness on the
minimum profile-drag coefficient and on the proiiledrag coefficient for a lift coefficient of 0.4 are shown in
figure 35. The minimum proiile-drag coefficient in-
efficient with speed, for airfoils having various positions
of the maximum thiclmess, axe given in @ure 35. The
N.A.C.A. 0009-04 has the lowest minimum profile dr8g
over the entire speed range, and also has the highest
speed for the comprwaibility burble.
Airfoils having
the position of mtium
thiclmess forward or aft o
the 40 percent location have progressively higher mini-
348
~POItT
NATIOh-AL
1.6
20
1.4
.18
12
./6
1.0
ADV160RY
COMMITTEE
FOR
AEROh-AUTICS
Angle of attack
x-2° o 0°
9-4”
+2 °a40a60
Q 10” A 12°
V 8°
./4
.j
~.
&
5.12
g
.
.
<“8
&
u
~.6
al
o
u
;.10
b
o
~ .~
al
:
k
.s .4
4
J
~.06
-2
P I
$-./
&
.04
0
0 for
~_,
-.
~
.02
-.2
0 for 2°
.
O
_.,
$
al
4°
fb
~“
_., O for -2°
-.4
0
.6
.2
.8
0
.6
.2
.8
0 fQr -4”
-o
2
FIcm3E 17.—Effect
of mmmedilftg
r
I
I
I
,
o-
&
n--
I +1
I
WI
~
w
* .4
.6
,8
1.0
Vfi
V%c
v+=
I
+-*
on the aemxlgnmniaohemc&Mcs
of the N.A.O.A.z4W-34aIr[oIf.
.16
. /4
Angle
P-4”
of az?ack
x-2°
o 0“
n 4“
i- 2°
.12
&
~.
c
u 10
~.
k
al
$.08
0!
Q
&
& .06
*
o
&
.04
.0.2
0
FIGCEE
l&–Effect 0[ mm~~
.2
.4
J5
.2
.8
v/vc
On tb tie
chnmddstks
of tb
.4
.6
v/vc
N.A.C.A. 44W alrfoll.
.8
1.0
M
Moment
coef, C.d
Pro fik-drag
coeffickn~
C=o
Angle of affack,
degrees, a
Moment
coef, C.,m
Profile-drag
coefficient
Anqk of affack,
dqrees,
a
CDO
w
I
Moment
Coef, C.OB
Profile-drag
caeffkien~
(&
Angle of affack,
degrees, d
Moment
coef, Cm&
Profile-drag
coeffitin~
C{O
Angle of of fock,
degrees, a
I
!7
Moment
coef, C.&
Moment
coefJCvOfl
,
Prof;le-dreg
coeffiden~
C=O
Angle of ofiock,
degrees, a
Profile-drag
coefffdenti
C=o
Angle of ai%’ock,
degrees, d
I
f!
E
I
I
Lib”.#?ll”A
g>
&
Q
I
I
I
I
I
M
Moment
coet, C.&
I
A
i
VTwFFFH
1
t
I
II
t
I
I
1
I
I
I
I
I
I
I
I
I
I
Moment
coefr Cm,&
I
.
Profile-drag
. coefficisn~
C?O
Angle of of fock,
degrees, a
Profile-dreg
. coeffkbn~
.
C..O
Angle of otfack,
degrees, d
w
%
Moment
coef, C.oB
.!
A
&
c1
k!
‘k
I
b)
b
>
0
%ofile-drug
. coe ffiaent,
C?e
Angle of oitock,
degrees, d
Moment
coef, C.Oh
Profile-drug
. coeffia~n~
C?O
..
Angle of attock,
degrees, d
—.
352
REPORT
NATIONAL
ADVISORY
mum profile drags and earlier compressibility burbles.
Prcdile-drag coefficient curves for a lift coefficient of
0.4 are also shown in figure 35. Differences in the
proiiledrag coefficient between the 20, 30, and 40 percent locations are very small at the lower speeds.
Airfoils having their maximum thicknesses located at 50
and 60 percent of the chord have the highest drag for
speeds up to approximately 65 percent of the speed of
sound.
At higher speeds the airfoil having the farthmt
forward location of the maximum thickness becomes
the poorest, due to the earlier compressibility burble.
Considering the speed range as a whole, the 40 percant
position seems to be the optimum.
Effect of leading-edge radius.-Figure
35 shows that
the effects of changes in the leading-edge radius on
minimum profile drag are negligible except for very
<-
COMMLT!CEE
FOR
AERONAUTICS
Examination of the effects of variations of the lending-edge radius for airfoils hav@
their maximum
thiclmes-s located at 50 percent of the chord shows w
slight increase in the minimum profde drag with
increase of the leading+dge
radius.
At higher lift
coefficients, there is a very laxge drag increase for the
sharp leading edge.
The airfoils having the leadingedge dmignations 3 and 6 show small ddlerences.
4
&
% Q<QJ o
O?
*Z
?
-4
.06
M55
$ ~1.03.04
* .Q
~.~
t?
u U.02
To
~J
R::
-.4
-.2
0
.2
..4
Lift coefficfen~
ckacMMiu
FIGURE8L—AerIYiYnamiO
.6
.8
Lift coefficient
/.0
C=
ofthe N.A.O.A. OUW-.34
dIfO~
radius.
Airfoils havlarge values of the leadingdge
ing variations of the leadingdge
radius from a sharp
leading edge to the normal leading-edge radius have
practically the same minimum profile drag over the
An increase of the leading-edge
entire speed range.
radius to three times the normal value causes a relatively large increase in drag at the lower speeds, as
well as an earlier compressibility burble.
.
With increase in lift, at lower speeds, the airfoil
having a sharp leading edge has the highest proiile drag
due to the rapid drag increase with angle of attack.
As the speed is increased the drag of the N.A.C.A.
0009–93 becomes greater, because of its earlier comThe 0009–33 has the lowest proiile
pressibility burble.
drag. The quarter normal leading+dge
radius is
therefore the optimum value for the range of angle of
attack tested.
C’
FI13UEE3Z-Aerodmmmh obnobxktlcs Ofthe N.A.O.A. ZK&34alrfoU.
IJFr
The lift coefficients for symmetrical airfoils in the
usual working range can be expressed in the following
manner:
C.= ~~a
where =(
‘CL
tie lift~me
slope) depends on tl;e shape
of the airfoil and the flow parameters.
For speeds
below that of the compreasibi.lit.y burble it has been
shown theoretically in references 4 and 5 that, as n
tirst approximation,
the effect of compressibility
on
lift is to increase ‘C’
~
with
the factor
7.32“
J%
has been substantiated experimentally for
speeds below that at which the compressibility burble
This
factor
—
!2
.. —.—. —.—— ..- —
A-.
354
RDPORT
I
NATIONAL
#
I
Minimum
CO MMITTEE
ADVTSORY
170R AERONAUTICS
I
Profile
I
profile
drag
.12
t
dreg
1
[
fo;
CL= 0.4
I
I
I
Vor\ “ofion wi fh thickness
I
N.A. C.A. OO12-63.-
R. A. C.A. 0012 -63..J
I
.08
.08
I
N. A.C.A.
~. --0009-63
.- I N. A.C. A.
0009-63—
/
/ //
.04
/ Ij
/>
$
,12
I
I
_ IUA.C.A. _
,0006-63
_
_
_
__
_
—
~
.04
-- .-IV.A.C. A. _
0006-63
/
0
:
al
.G
t
I
Voriofion
I
I
N. A.C.A. 0009-62 --
5.08
Q)
2
b
Q .~
k
6
z
Q.
/
.
to
9
0 d’
.
~
%
w ifh position
I
‘- ‘N. A.C.A.
0009-63
of znoximum
fhickne
I
Ss
~-A.c-A.
I
i
N. A. C. A.0009-t
/ -’]N. A.C.A.
, . N. A.C. A. — .08$
-. ‘0009-64
u
11
0
flr+m >-
I ~/1 I
t
!
I
r.
I
%
0$
,
“..
<
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I
=
i
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t
i
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‘hi. A.c. A.
I%A.C.A. 0009 -03--0009-63
1
t
.08
.04
,
rud;us
I
!
f- ;-IV. A.C.A. _
.08
/
,
8
i
N. A.C.A. 0009 -93-,
,
t
N.A. C.A. 0009-03.,
I
i
edge
t
.04
I
n
o
.4
.2
-8
.6
v/&
0
1.0
.2
.4
.6
/. o
.8
v/q
Fmm
W.-Effect C4compmsdbffftyon proflk drag.
.24
.24
A
A.C.A.
/ \-‘-N.OCW6-63
.20
.16
.20
_
.16
I
dci.
d C=
a
/ 7
dd
/
.12
/
e
-- --N. A.C.A.
OLW9-63
/
~
\
_
/
.12
N. A.C. A
0009-63
---w *
N. A. C.A.’---* —
0009-64
‘
---
.08
I
1
‘-IV. A.C.A. _
0012-63
.08
<
N. A.C.A.
0~9-65
.04
1
o
.2
.4
.6
v/~
.—
~13CRE 33.-El7ect
ofmmpmsibflfty on Ufbcmrmdop
.8
1.0
0
1.2
Varfntfon
wftbtbicknem.
,
#
.2
.8
.4
1.0
1
i..?
Vj$q
FKIUEE
37.-Effeat of mmpresslbflf on llfkarve sfopo. Varlatlonwith @t[on
ofmaznom thhknms.
TESTS
OF
16 RELATED
AIRFOILS
Considering first the airfoils having the mtium
thickness located at 30 percent of the chord, it is
apparent that the sharp leading edge is definitely bad.
Variations of the leading-edge radius, provided that
the leading edge is rounded, have apparently negligible
—
effect on ~
at lower speeds, in agreement
with the
results of reference 2. It is to be noted that the bluntnosed airfoil, the N. A.C.A. 0009–93, shows a very
dCL
dCL
rapid rise in ~
at high speeds.
This rapid rise in ~
is also shown by the 0009-62 airfoil, which has its
maximum thickness well forward.
It should also be
noted that the compressibility burble tends to occur
progressively
at lower speeds as the leading-edge
radius is increased.
Similimity of the eflects of increasing leading-edge
radius to the effeciw of increasing thickness n@ht have
.24
AT
355
SP1313DS
trend of the effects of camber particularly at l@h
speeds, a few airfoils having certain camber variations
and one of the best thicknew forms have been tested.
Selection of thiokness form.—The choice of the best
form for the thickness distribution was made principally on the basis of low drag and late compressibility
burble.
Within the lift-coefficient range investigated,
the tests of symmetrical airfoils indicate that, for an
airfoil of medium thickmss, the maximum thickness
should be located at 40 percent of the chord aft of the
leading edge and the leading-dge radius should be onequarter of the normal value.
Thus, the 34-thickness
distribution would seem to be the beat. The N.A.C.A.
0009-34 and three cambered airfoils having this thickness distribution were therefore built and tested.
A
comparison of the N.A.C.A.
0009+4
and N.A.C.A.
0009-34 airfoils (figs. 23 and 31) shows that, except for
the elightiy earlier compressibility
burble of the
I
I
I
I
HIGH
k40ximum thickness
0.3 c
from leading edge
Moximum ihickness
0.5c.
from leading edge
.20 I ~--- .: N. A.C. A.
0009-93
.16
~zl
dd
N. A.C. A. 0009 -63,,
.12 -
_
00Q9-35
0“
h 1
,)
y
-
; N. A.C.A.
I
,
MA. C.A. 0009 -33,,
/
“
/
/
/
. 14.A. C.A.--Z
0009-05
.08
~
1
‘- “:-N.A.C.A
0009-65
IAL
/
<
.04
0
.2
.4
FmtmE
.6
v/K
.8
&%-Effmtof mm-llltg
1.0
on IMt+m’veSJOW
been expected because of the higher induced velocities
over the forward portion of the airfoil caused by such
form changes.
Results of the tasts of airfoils with
various leading-edge
radii ha~~
their mtium
thickness located at 50 percent of the chord are in
substantial agreement with the results obtained from
the tests with the airfoils having their mtium
thicliness located at 30 percent of the chord, except that the
compressibility burble shown by the airfoil having the
normal leading-edge radius occurs at the l@her speed.
TJHTS
0
OF CAMBERED AIRFOIIS
A detailed study of camber variations has not’been
attempted as part of this investigation.
However, in
order to study the application of the data obtained
from the symmetrical airfoil tests as well as to devalop,
if possible, by means of a few tests, a more efficient
practical propeller section and to indicate the general
.2
.4
.6
v/~
.8
1.0
1.2
Variationwith kading+ige mdhm.
N. A.C.A.
0009–34 airfoil, there is practically
no
difference in the minimum proiile drag of these airfoils.
At moderate lift coefficients the profile drag of the
N.A.C.A.
0009–34 decreases slightly with increasing
speed, whereas the proiile drag of the N.A.C.A.
0009-64 increases.
Because of thie difference, which
may be attributed to the more gradual compressibility
burble of the N.A.C.A. 0009-64, the N.A.C.A. 0009-34
has a lower proiile drag over part of the speed range.
As at minimum drag, however, the N. A.C.A. 0009–34
hss the earlier compressibility
burble.
From this
comparison it is apparent that the general superiority
of either of these airfoils is difficult to establish.
This
comparison shows, however, that the shift of the
maximum ordinate horn the normal to the 40 percent
location causea much greater improvement than can be
obtained from small changes in the leading-edge radius.
Future tests to study camber effects should probably
OF
TESTS
16 RELATED
AJRFOIM
effects of compresIMects of compressibility,-The
sibility on the lift and drag of the cambered airfoils
are similar to those previously discussed for the symmetrical airfoils.
Some comprmsibility effects occur on
cambered airfoils that are not shown by the symmetrical
airfoils.
As the speed corresponding to the compressibility burble is exceeded, the angle of zero lift a% sud-
-------
9C9
—-—
3R9
AT
HIGH
357
SPDEIDS
practically constant.
men
tie speed is hcreased
nbov~ that at which the compressibility burble occurs,
the lift coefficient decreases rapidly and the negative
moment coefficient increasea rapidly; consequently,
there is a large and rapid rearwaxd movement of the
center of premure.
The magnitude of the change in
the moment coefficient over the low-speed part of the
N.A. C. A. 2409-34
-.:Z’
1
1
o
I
I
.4
I
I
I
.8
FIWJEE
I
-.4
40.-(Xmpari?an of 309,
denly tends toward zero. An effective displacement of
the lift curve occurs.
Over the lower portion of the speed range the negative moment coefficient increases with increase of speed.
The relative amount of the increase is approximately
the same as the increaae in the lift coefficient.
The
location of the center of pressure, therefore, remains
I
I
.4----3E9,
~\
.8-
I
I
.4
I
I
0
I
I
.4
1==1
.8
I
J-.2
1.2
u
and NA.O.A. 24W31rdrfofls.
range is suiliciently large to warrant full-scale studies
to obtain information for the design of wings for diving
bombem.
Comparison of cambered airfoils,-A
comparison of
the N.A.C.A. 2409-34 airfoil with the 3C9 and 3R9
airfoils
is given in figure 40. The data for the 3C9 and
3R9 have been interpolated from the results presented
.—
..— -
..—.
358
RDPORT
NATIONAL
ADVISORY
COMMITTEE
reference 1. At the lower speeds the N.A.C.A.
2409-34 has the lowest minimum drag, the lowest
maximum lift, and therefore the smallest useful angular
. range.
As the speed is increased above sii-tenths of
the speed of sound the N.A.CA. 2409-34 airfoil becomes
superior to both the 3C9 and the 3R9 airfoils, because
of the larger compressibility effect on the C and R airfoils.
It is probable that the low~eed
mtium
lift of the
NL.C.A.
2409-34 could be increased by increasing the
lending-edge radius.
Because the effect of the leadingedge radius on profile drag is small, it would seem that
the 2409-04 airfoil section might ba better for applications requiring n section to operate over a considerable
range of the lift coefficient.
In the development of
cambered airfoils, of which the three tested form a
preliminmy step, the effects of shape variations on the
maximum lift will be more thoroughly investigated,
particularly at the lower speeds.
ADRONAU’PICS
3. The optimum vrdues of the lewling~dge radius lie
between 0.22 percent and 0.89 percent of the chord for
airfoils of 9 percent thiclmess.
4. At high speeds the N.A.C.A. 2409-34 airfoil is
superior to the commonly used propeller sections.
The
results indicate that some further improvement may bo
expected.
in
LANGLEY
MEMORLU
AERONAUTICAL
REFERENCES
1. Stack, John: The N. AC.A. High-Speed Wind Tunnel and
Tests of Six Propeller Sections. T.R. No. 403, N. A. C. A.,
1933.
2. Jacobs, Eastman N., Ward, Kenneth E., and Pinkertonj
Robert M.: The Charactetilm
of 78 Related Afrfoil
Sections from Teats in the Variable-Density Wind Tunrml.
TX. No. 460, N. A. C.A., 1933.
3. Jacobs, Eastman N., and Abbott, Ira H.: The N. A,C.A.
Variabl&Density Wind Tunnel. T.R. No. 416, N. A. C. A.,
1932.
4. Ackemt, J.: ~er Luftkr&fte bei seh gromen @schwindigkeiten insbesondere bei ebenen %rtimungen. Helvetioa
Physics Acts, VOL I, lk3CiCdUS Quintus, 1928, pp. 301-322.
5. Glauert. H.: The Effect of Commemibfitv on the Lift of rin
Aero;oil. R. & M. No. 1135, British A.-R.C., 1928.
The principal factors tiecting the choice of propeller
sections are low drag at low and moderate lift coefficients and a late compressibility burble; that is, low
drags at high speeds.
Considering these factors, these
re.dts indicate:
1. The airfoil thickness should be small.
2. The best position for the m&nmm
thickness is
approximately 40 percent of the chord aft of the lea~~
edge.
TABLE
I
OF lfRFOIZS
Zma-34
TT11
7
Im2-m
Km-a
ma-m
MB-m
MIJ-?s
Uwa-a
!M?J-34
:%%
.07m
. 15XJ
. LYm
.2033
.3X0
.40xl
.EOxl
:%%
.Xml
:=
LOXO
Lmm
Ol!u 0.0144
. .0!236
. Olm
.030!4 .M71
o
1.
01=
.0181
.0214
.Ozm
.M71
.0!M9
.mia
.Ww
.0r70
:R%
. OEM
. M74
. mfl
.MM
Iadfng+dge
radfus---
.mm
.042s .ml
.0476
.M41
.M7’9
.mm
.W
.Ca7
.04m
.M33
.W
.M39
.M41
.0u2
.0331
.m7a
. 014s
.M31
.mu
.OW
.03W
.02?8
J3&
.OW
.mm
.015s
.mm
-—
slorJ9=-
andof
chord..-_.
0
t
0
)
1 01s9
.M37
. a317
. m74
.0410
.0144
.04m
.0441
.0415
. m74
:%2
. Om
.m
.M5i
.Om
.Cm?3
LOlm
: &l&
o
a 0133
.0177
)
)
o
L02L2 am
.m74
.m.5z
.0340
.
mm”mmoam
:$%:8%.m70 .0144
olm
.U3%9.ols4
:%3
.W26 .0255
.0S9 .fG13
.Ozm
.M78
.0245
.ml
.03m
.fu!?5
.aEa
.Cm8
.Cc85
.0397
.0437
.0f60
.Om
.mm
.0s.9
X&J
:8$%
.0227
.M23
.Cm!3
.Om
.0440
.W.m
.0fz3
.0395
f333
.Wn
.m77
.Olm .0149 .ml
.m
.m
.m
.m
arm
.0376
.0U2
.0a3
.W9
.fmc
.042Q
. ....
)
Lam
.0114
.0166
.O?m
0.0117
. Olm
. 02s1
.m134
%%
.0341
xi?
.W&2
:~m .~ .Of@l .mm .Wm
.W
.Ws .043%
.W .WM :04m .0W3 .0160 :&%!
.04m.03m.0354.m64 .Ofm .0S3
N-& .02m.Oi?-9.oz8 .0393
.om .Gml .fIm .0315 :%$
.oms .0111 .0111 .0111 . Olm . Olm
.ml
.m
.M31 .Olm
.m
.m
--t—l—.CIl?3
.m
.m
.rrm
.m
44M-34
XQ2-35 Km-3
Lower
I%E
o
0.0125
LABORATORY,
NATIONAL ADVISORY COIJMI~EE
FOR AERONAUTICS,
LANGLEY FIELD, VA., April 28, 19S4.
CONCLUSIONS
ORDINATES
FOR
%%
. mlo
%%
.023S
. Olss
.0102
.mm
. Olw
.CmN
-R
–.CE3m
–.olm
-:
-.
-.
–. Olst
–. m
–. mm
–. Ore-5
-.0249
-. Cm3
–. 0161
-. w
-. ma
–. m
.mn
y&
-. Wo
-. mm
-, mfa
–,
-.
-,
-.
-,
-.
.mz
—..
I
+
o
it
o
t
)
I
qlo
w
w
m
mm
-. mm
-, mm
–. 0137
–. 01F3
–. 0183
-.0212
–. 0Z31
–. m47
-. 02bo
–. w
–. frzzl
–. Ols$
-. ola7
–. mm
–. w
-. CKm
-. Olzz
–. 0147
.M2a
.mz2
-: M70
0373
–. 0B4
-. Olw
%’f!&
‘2/10
m43
lKQ6
mm
m18
m14
m
TESm
OF
16 RELATED
AIRFOILS
TABLE
COEFFICIENTS
BneIoekfoUfDdgm no.
AT
HIGH
II
FOR FORM
EQUATIONS
Cceflidentsforqu8tIon (I)
1
Q
41
al
Cc8fi3dentsfor eqnetIon(2)
I
T
m
~
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . 0.2.WKO a 21S337 –2 Q31w :*?
~
. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . .. . . . . . . . . . . . . . . .2WXU –. W6U32 –. 643310
–. 24&W
. 17m34 –.2W17
~-------------------------------------------------.m
~-------------------------------------------------.X@3m –. 310275 . 3417w –.32182u
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