NATIONAL
ADVISORY COMMITTEE
FOR AERONAUTICS
REPORT
SUMMARY
.._vll#11_!
"_
No.
824
OF AIRFOIL
DATA
H. ABBOTT, ALBERT E. YON DOENHOFF
;
and
LOUIS
S.
STIYERS,
Jr.
t_,-_ G,
}-
¸
1945
_/i<
._-= -::_
:: : __:._._
[
' ..........
(:;L_ %
i<
|
:
For sale by the Superintendent
of Doeunxents,
U.S.
Go,, i_ment
Printing Ofnce. Washington
25.D.C.
Price tlJ0
i,"
o
REPORT
SUMMARY
By IRA
H.
and
Langley
OF AIRFOIL
ABBOTT,
ALBERT
LOUIS
Memorial
Langley
q
No. 824
E. VON DOENHOFF
S. STIVERS,
Aeronautical
Field,
DATA
Jr.
Laboratory
Va.
I
National
Advisory
tteadquarter_',
Created
by
of the problems
March
2, 1929.
1500
_]. BRII:;GS,
Bureau
Hampshire
Avenue
Ph.
D.,
Vice
C.
Chairman,
Sc.
HUNSA_,'ER,
Director,
D.,
G.
]tENR'¢
H.
ARNOLD,
Army
_rlI,I,IAM
So.
D.,
Smithsonian
General,
A.
National
AUBREY
Vice
Chairnmn,
Executive
Committee,
W.
BURI)EN,
States
Army,
War
Department.
Assistant
Secretary
Comnianding
FITCH,
Naval
of
Commerce
WILLIAM
OLIVER
of
BUSH,
Sc.
1).,
F.
1 ). E(:HOLS,
Mat6rM,
War
Director,
D.
Ph.D.,
Major
of
General,
and
Scientific
Ulfiversity,
United
Army,
Army
EDWARD
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E.
R.
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J.
So.
D.,
_V. I,EWIS,
LL.
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CONTENTS
Page
SUMMARY
..............................
INTRODUCTION
SYMBOLS
...................
...................................
HISTORICAL
DEVELOPMENT
DESCRIPTION
OF AIRFOILS
Method
of
Distributions
NACA
Four-Digit
NACA
Series
:
Five-Digit
NACA
1-Series
6-Series
NACA
Airfoils
CONSIDERATIONS
of
Rapid
Numerical
derivation
Coefficients
of
Numerical
of
Numerical
Description
Sources
Drag
on
pressure
..................
__
.....
distribution
......
................
.........
.............
calculation
..............
examples
Data
practical
Two-dimensional
Three-dimensional
.......
of Smooth
Drag
characteristics
in
Drag
characteristics
outside
Airfoils
low-drag
..........
range
low-drag
...........
range
.................
22
22
22
...............
24
methods
slipstream
and
Smooth
Airfoils
24
vibration_
29
30
..................
30
...............
37
Rough
Airfoils
data
...........
Three-dimensional
airplane
..............
......
data
37
37
.................
Position
5
High-Lift
Devices
.................
Lateral-Control
Devices
.....................
43
43
Leading-Edge
Interference
..................
49
50
...............
51
8
APPLICATION
Moment
Selection
CONCLUSIONS
WING
of
of
DESIGN
Section
Root
Data
Section
39
................
43
...............
51
..................
51
of Tip Section
.................
.................................
10
APPENDIX--_IETHODS
Two-DIMENSIONAL
12
Description
13
13
Symbols
.....................
Measurement
of Lift
14
14
Measurement
Tunnel-Wall
14
Correction
14
Comparison
OF OBTAINING
Low-TuRBULENCE
of Tunnels
of Drag
Corrections
for
Blocking
with
52
52
DATA
IN THE LANGLEY
TUNNELS
.........
..................
....
54
55
.....................
..................
...............
at
High
56
57
Lifts
........
59
............
59
REFERENCES
.........................
TABLES .........................
SUPPLEMENTARY
54
54
__
Experiment
60
64
DATA :
16
I--Basic
II--Data
Thickness
for Mean
16
III--Airfoil
Ordinates
16
IV--Predicted
18
.......
40
Center
Air Intakes
............................
TO
:
...................
of Aerodynamic
Application
Selection
.....
38
5
Pitching
Airfoils
...........
Unconservative
16
........
18
21
drag
construction
data
of
.....
..........................
.........................
data
Characteristics
Two-dimensional
characteristics
5
5
15
...............
Lift
on
transition
Effects
of propeller
Characteristics
of
5
5
drag
.....................
roughness
waviness
5
14
Airfoils
....................
Characteristics
fixed
with
14
...............
around
CHARACTERISTICS
of
distributions
distributions
calculation
of Flow
EXPERIMENTAL
thickness
Lift .................
Methods
with
Drag
8
...................
examples
Zero
Drag
Lift
on
irregularities
4
5
8
pressure
examples
Methods
of
of
of
Effect
of camber
Critical
Mach
Number
Moment
...............
ratio
4
7
7
.............
aspect
of surface
Airfoils--Continued
of section
3
7
...................
estimation
Effect
of Smooth
of type
Permissible
Permissible
5
6
.....................
Distributions
Effective
6
system
...........
distributions
Methods
Angle
.................
............
................
7-Series
2
5
..............
Characteristics
Effects
5
system
distributions
Numbering
Thickness
Pressure
.........
..............
Airfoils
lines
THEORETICAL
Airfoils
...................
Nunabering
Thickness
Drag
CHARACTERISTICS--Continued
1
5
system
...............
distributions
..............
lines
Mean
............
...................
Airfoils
1
Thickness
.....................
Numbering
Thickness
NACA
and
systeni
.................
distributions
...............
lines
Mean
Lines
Airfoils
Series
Numbering
Thickness
EXPERIMENTAL
3
system
.................
distributions
...............
lines_
Mean
........................
Combining
Mean
.............................
Numbering
Thickness
Mean
.....................
Page
1
V--Aerodynamic
Sections
Critical
Forms
..............
Lines ................
69
89
....................
Mach
Characteristics
...........................
99
Numbers
...............
of
Various
113
Airfoil
129
iil
REPORT
SUMMARY
By IRA H.
ABBOTT,
ALBERT E.
No.
824
OF AIRFOIL
VON
SUMMARY
ReceT_t airfoil
data for both flight and wind-tunnel
tests have
been collected and correlated
insofar
as possible.
The flight
data consist largely of drag measurements
made by the wakesurvey method.
Most of the data on airfoil section characteristics were obtained in the Langley two-dimensional
low-turbulence
pressure
tunnel.
Detail data necessary for the application
o]
NACA
6-series
airfoils
to wing design are presented
in supplementary
figures, together with recent data for the NACA
00-,
1_-, 2_-, _-,
and 230-series
airfoils.
The general
methods
used to derive the basic thickness
forms for NACA
6- and
7-series airfoils and their corresponding
pressure
distributions
are presented.
Data and methods are given for rapidly obtaining the approximate
pressure
distributions
.for NACA
fourdigit, five-digit,
6-, and 7-series airfoils.
The report includes
an analysis
of 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
of sub:face condition
on the lift and drag characteristics
are at
least as large as the effects of the airfoil shape and must be
considered
in airfoil selection and the prediction
of wing characteristics.
Airfoils
permitting
extensive
laminar
flow, such as
the NACA
6-series airfoils,
have much lower drag coe_icients
at high speed and cruising
lift coeficients
than earlier types of
airfoils if, and only if, the wing surfaces are suy_ciently
smooth
and fair.
The NACA
6-series
airfoils
also have favorable
critical-speed
characteristics
and do not appear
to present
unusual
problems
associated
with the application
of high-lift
and lateral-control
devices.
DATA
and Lovls
DOENHOFF,
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 NACA
6-series
airfoils.
The general
methods
used to derive the basic tki_kness forms for NACA
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
characteristics
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
figuces 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 follo_'ing
headings:
I--Basic
Thickness
Forms
II--Data
for Mean Lines
III--Airfoil
Ordinates
IV--Predicted
Critical Mach Numbers
V--Aerodynamic
Sections
Characteristics
These
supplementary
data for the airfoils.
figures
and
of
tables
Various
present
Airfoil
the
basic
SYMBOLS
INTRODUCTION
•A considerable
amount
of airfoil
data
A
has been accumulated
from tests in the Langley
two-dimensional
tunnels.
Data
have also been obtained
from
low-turbulence
tests both
An,
B,
a
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 airfoil 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
them insofar
as possible.
b
b_
bIo
C,
CDL
0
_5¥ 1
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,
basic 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 caused
by flap deflection
1
REPORT
chord
aileron
¢
Ca
Ca
Cdmi
n
cf_
¢fo
cf
ratio
h
h,
k
L
M
M.
typical
OL
P
pressure
of aileron
lift
coefficient
hinge-moment
(q_c_)
coefficient
surface
z
at
z p
Ol
A(_ o
A5
P.
P
Ol lo
on upper
Aot o
Oti
_.TE
and lower
surfaces
of airfoil
pb/2V
qo
R
Re,
S
pressure
coefficient
(_)
free-stream
velocity
inlet velocity
local velocity
increment
of local vdocity
increment
of local velocity
type of load distribution
At"
AVa
qV
of transition
distance
mean-line
ordinate
perpendicular
to chord
ordinate
of lower surface
ordinate
ordinate
complex
complex
angle of
of symmetrical
thickness
distribution
of upper surface
variable
in circle plane
variable
in near-circle
plane
attack
section
aileron
effectiveness
flap or aileron deflection;
down
flap deflection,
inboard
flap deflection,
outboard
airfoil parameter
(6--0)
value of e at trailing
edge
1)y additional
velocity
ratio
correspon(ling
to thi('kness
t,
velocity
ratio
corresponding
to thi(,l_ness
t2
distance
mean-line
along chord
abscissa
of
of
lift
ratio
turbulence
{ Tip
\Root
chord "_
chord/
factor
{Effective
\
Test
¢
angular
coordinate
airfoil parameter
_o
average
value
of z
determining
of _b (21r£2_
of types
in 1929
to
deflection
complex
variable
in airfoil plane
angular
coordinate
of z' ; also, angle
is slope of mean line
The development
mon use was started
caused
ratio
to increment
value
of
angle of zero lift
section
angle of attack
increment
of section
angle of attack
section
angle
of attack
corresponding
lift coefficient
taper
T
parameter,
angle of attack
at a constant
HISTORICAL
first airfoil thickn(.ss
ratio
second airfoil thickness
ratio
tl
t:
V
0
coefficient
pb/2V
free-stream
static
pressure
helix angle of wing tip
free-stream
dynamic
pressure
Reynolds
number
critical
Reynolds
mmfl)er
PO
(")
points
position
change
in section
aileron
deflection
coefficient
center
point
(_L_oP°)
q
critical
pressure
coetficient
resultant
pressure
coefficient;
difference
between
local ul)per- and lower-surface
pressure
coefficients
local static pressure;
also, angular
velocity
in roll in
Per
xc
hinge-moment
drag
loss of total pressure
free-stream
total pressure
section
aileron hinge moment
exit height
constant
lift
Mach number
critical
Mach number
Ho
x
of upper
Ol o
D
AH
OU,
aileron
design section
lift coefficient
moment
coefficient
about aerodynamic
moment
coefficient
about quarter-chord
section
normal-force
coefficient
Cn
surface
Y
Yc
yL
yt
Yv
inboard
outboard
hinge-moment
parameter
section
lift coefficient
Cmc/4
of lower
flap
flap
ACH_
c,
abscissa
chordwise
chord,
chord,
AERONAUTICS
XL
(x),,
increment
constant
Cma.
FOR
abscissa
_eu
l
COMMITTEE,
Xu
section
el
ADVISORY
section drag coefficient
minimum
section
drag coefficient
CH
V_
824--NATIONAL
chord
flap-chord
c
N'O.
design
is positive
of which
tangent
Reynohls
number'_
Reyimldsnumber
]
radial
coordinate
of z
¢ d_)
DEVELOPMENT
of NACA
airfoils
with a systenmtic
now in con>
investigation
of a family of airfoils
in the Langley
variable-density
tmmel.
Airfoils
of this family
were designated
by numbers
having
fore" 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
se(,tions
having
higher
maximum
lift
coefficients
and lower minimum
drag co(,flieients
than those
of sections
developed
before
that
time.
The investigation
also provided
infornmtion
on the changes
in aerodynamic
characteristics
resulting
from wtriations
of geometry
of the
mean line and thickness
ratio
(reference
1).
SU_/IMARY
The
include
investigation
was extended
in references
2 and
airfoils
with
the same
thickness
distribution
with positions
airfoil.
These
of the
airfoils
maximum
camber
were designated
five digits,
such as the NACA
of this family showed
favorable
except
for a large sudden
loss in
Although
these investigations
limited
number
of airfoils
with
far forward
by numbers
OF
3 to
but
on the
having
23012 airfoil.
Some airfoils
aerodynamic
characteristics
lift at the stall.
were extended
to include
a
varied
thickness
distribu-
tions (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 fiat 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 ah'foils 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 test
equipment
with
very
low airstream
turbulence.
This work was greatly
encouraged
by
the experiments
of Jones
(reference
7), who demonstrated
the possibility
of obtaining
extensive
laminar
layers in flight
at relatively_
large
R_l,,,_u_l_
,_u,,,_,s.l"_
TT,_..._._.;_,._._._jwith
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 adequate
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 NACA
16-series
(reference
10)
AIRFOIL
3
DATA
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
NACA
2- to 5-series sections
(reference
11).
Experience
with
these sections
showed
that none of the approximate
methods
tried
was sufficiently
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 comparatively
large
values
of the Reynolds
number
if the airfoil surfaces
were
smfficiently
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 design lift coefficient
when smooth,
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 _hickness
forms were derived
by
new and improved
methods
described
herein
in the section
"Methods
of Derivatinn
of Thick-noss
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
sections
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
METHOD
The
OF
COMBINING
cambered
MEAN
airfoil
OF
LINES
sections
AIRFOILS
AND
THICKNESS
of all NACA
DISTRIBUTIONS
families
con-
sidered
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
airfoils.
figures
by the
methods
described
for each
family
of
4
REPORT
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
Y
• 10
t
0
Ou(a'_
_'_.
'
1;I
Chord
hne
/
',
I
"uc(_L, VL)
',,
Ioli
Rodius
"(meon-h'me
_
t,hrocgh
5/ope
end
o£
Of" _5
yJ
(_)
O
• 005
• 05
• 25
.50
• 75
1.00
.01324
.0383l
.080_]
•08593
.0445fi
tan
• C0200
• 012£;4
.03580
.04412
.03580
0
FOR
sin 0
8
DERIVATION
OF
cos 0
0. 31932
.18422
.00979
0
-. 06979
• 18744
•06996
0
--. 06996
O. 94765
•98288
•99756
1.00000
•99756
0
• Thickness
distribution
b Ordinates
of the mean
• Slope of radius
through
obtained
from ordinates
line, 0.8 of the ordinate
end of chord.
of the NACA
for cq=l.0.
FIOURE
The process
for combining
a mean line
distribution
to obtain
the desired cambered
65,3-018
1.--Method
of combining
and a thickness
airfoil section
is
line connecting
the leading
and trailing
edges.
Ordinates
of
tim canibered
airfoil are obtained
by laying off the thickness
distribution
perpendicular
to tile mean line•
Tile abscissas,
ordinates,
and slopes of the mean line are designated
as x_,
y_, and tan 6, respectively.
If xv and yv represent,
tively,
the abscissa
and ordinate
of a typical
point
upper
surface
of the airfoil and y_ is the ordinate
THE
NACA
65,3-818,
yt sin 0
Yt cos 0
0
0
.00423
.00706
.00565
0
--.00311
0
respecof the
of tlle
at chordx_:ise position
x,
given
by the following
yv:Y_+yt
Tlle corresponding
nates are
expressions
x,.=x+y_
YE=--Y_--yt
sin 0
cos
COS
8
8
sin 0
cos 0
AIRFOIL
_u
yu
0
XL
•00077
•04294
• 24435
•50000
• 75311
1. 00000
O
• 01455
• 05029
• 11653
• 13O05
• 08025
0
0
• 00923
• 05706
• 25565
.50000
• 74689
1.00000
yL
0
--.01055
--.02501
--.04493
--.04181
--.00865
0
mean
lines
and
basic
thickness
forms•
of the leading-edge
point.
Because
tim 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
througli
tlle end of tlle chord for such mean lines is
usually
taken
as tlle slope
of the niean
line at x--0.005.
c
This
procedure
is justified
by the nulnner
in wllicll
the slope
increases
to tlle theoretically
infinite
vahle as x/c approaches
0. Tlle slope increases
slowly until vel T snmll values of x/c
are reached.
Large vahles
of tlle slope are tllus limited
to
vahles of x/c very close to 0 and may be neglected
in practical
airfoil design.
Tables of ordinates
are included
in the supplenlentary
data
for all airfoils for wtlicll standard
characteristics
are presented
FOUR-DIGIT-SERIES
AIRFOILS
(1)
(2)
cos 0
for tlle
a=l.O
0
.01255
.03765
-08073
•08593
-04445
NACA
Xv=X--yt
yu=yc.yt
YL=YO-Yt
airfoil.
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 straigllt
symmetrical
tllickness
distribution
the upper-surface
coordinates
are
relations:
8
0
1.00
0
0
_ s_n
s/n
c,boFd)
CALCULATIONS
y¢
(b)
r
chord
percent
SAMPLE
zu=x-y
xc=z+y
-
lower-surface
coordi-
(3)
(4)
The center for the leading-edge
radius is found by drawing
a line through
tlle end of tlle chord at tlie leading
edge with
the slope equal to the slope of the mean line at tllat point
and laying off a distance
from the leading edge along tllis line
equal to the leading-edge
radius.
Tliis method
of construction causes tile cambered
airfoils to project
sliglitly
forward
Numbering
NACA
airfoils
system.--The
of tlle fonr-(ligit
on tlle airfoil
geometry.
Tile
inaxilmml
value of the mean-line
cllord.
lea(ling
tentlls
nunlbering
system
for the
series (reference
1) is based
first
integer
indicates
the
ordinate
y_ in percent
of tlle
Tlle second integer
indicates
the (listance
from
edge to the location
of tim maxinuml
camber
of the cllord.
The last two integers
indicate
the
in
tlle
airfoil ttlickness
in percent
of the cllord.
Thus,
tlle NACA
2415 airfoil has 2-percent
camber
at 0.4 of ttle chord from tlle
leading
edge and is 15 percent
thick.
Tim first two integers
taken together
define tile mean line,
for example,
the NACA
24 mean line.
The synllnetrical
airfoil sections
representing
tlle thickness
distribution
for a
family
of airfoils
are designated
by zeros for tile first two
integers,
as in the case of tlle NACA
0015 airfoil.
SUMMARY
OF
Thickness
distributions.--Data
for the NACA 0006, 0008,
0009,
0010,
0012,
0015,
0018,
0021,
and
0024
thickness
distributions
are presented
in the supplementary
figures.
Ordinates
for intermediate
thicknesses
may
be obtained
correctly
by scaling
the tabulated
ordinates
in proportion
to
the thickness
ratio
(reference
1).
The leading-edge
radius
varies
as the square
of the
thickness
ratio.
Values
of
(v/l') 2, which is equivalent
to the low-speed
pressure
distribution,
and of r/I" are also presented.
These
data
were
obtained
by Theodorsen's
method
(reference
9).
Values
of
the velocity
increments
Ava/I" induced
by changing
angle of
attack
(see section
"Rapid
Estimation
of Pressure
Distributions")
are also presented
for an additional
lift coefficient
of
approximately
unity.
Values
of the velocity
ratio
v/V for
intermediate
thickness
ratios
may
be obtained
approximately
by linear scaling of the velocity
increments
obtained
from the tabulated
values
of v/V for the nearest
thickness
ratio; thns,
tl
Values of the velocity-increment
for intermediate
thicknesses
Mean
lines.--Data
ratio hva/V
by interpolation.
for the NACA
(5)
1
may
be obtained
62, 63, 64, 65, 66, and 67
mean
lines are
presented
in the supplementary
figures.
The data presented
include
the mean-line
ordinates
y_, the
slope
dyJdx,
the design
lift coefficient
c, and
the corresponding
design
angle of attack
a,, the moment
coefficient
C,n_,,,, the resultant
pressure
coefficient
PR, and the velocity
ratio
Av/V.
The
theoretical
aerodynamic
characteristics
were obtained
from thin-airfoil
theory.
All tabulated
values
for each mean line, accordingly,
vary linearly
with the maximum
ordinate
y_, and
data
for similar
mean
lines with
different
amounts
of camber
within
the usual range may be
Obtained
simply
by scaling
the tabulated
values.
Data
for the NACA
22 mean line may thus be obtained
by multiplying the data for the NACA 62 mean line by the ratio 2:6,
and for the NACA 44 mean line by multiplying
the data for
the NACA
64 mean line by the ratio 4:6.
NACA
FIVE-DIGIT-SERIES
AIRFOIL
DATA
Thickness
distributions.--The
thickness
distributions
airfoils of the NACA
five-digit
series are the same
for airfoils of the NACA
four-digit
series.
Mean lines.--Data
for the NACA
210, 220, 230,
for
as those
240,
and
250 mean lines are presented
in the supplementary
figures
in the same form as for the mean lines given herein
for the
four-digit
series.
All tabulated
values
for each mean
line
vary linearly
with the maximum
lift coefficient.
Thus,
data for
may be obtained
by multiplying
mean line by the ratio 4:2 and
by multiplying
the ratio 6 :2.
the
data
NACA
Numbering
for
the design
mean
line
the data for the NACA
for the NACA
640 mean
the
1-SERIES
system.--The
ordinate
or with
the NACA
430
NACA
240
mean
line
230
line
by
AIRFOILS
NACA
1-series
airfoils
are
des-
ignated
by
a five-digit
number--as,
for example,
the
NACA
16-212
section.
The
first integer
represents
the
series
designation.
The second
integer
indicates
the distance
in tenths
of the chord
from the leading
edge to the
position" of minimum
pressure
for the symmetrical
section
at zero lift.
The first number
following
the dash indicates
the amount
of camber
coefficient
in tenths,
indicate
the thickness
expressed
in terms
of the
and the last two numbers
in percent
of the chord.
design lift
together
The com-
monly
used sections
of this family have minimum
pressure
at 0.6 of the chord from the leading
edge and are usually
referred
to as the NACA
16-series
sections.
Thickness
distributions.--Data
for the NACA
16-006,
16-009,
16-012,
16-015,
16-018,
and
16-021
thickness
distributions
(reference
10) are presented
in the supplementary figures.
These data are similar in form to the data for
those
airfoils
intermediate
manner.
of the NACA
thickness
ratios
four-digit
series,
may be obtained
and data
for
in the same
Mean lines.--The
NACA
16-series
airfoils
as commonly
used
are cambered
with a mean line of the uniform-load
type (a=l.0),
which is described
under
the section
for the
NACA
6-series
airfoils
that follows.
If any
mean line is used, this fact should
be stated
designation.
NACA 6-S_.RIESAIRFOILS
other
type of
in the airfoil
AIRFOILS
Numbering
Numbering
system.--The
numbering
system
for airfoils of
the NACA
five-digit
series is based on a combination
of
theoretical
aerodynamic
characteristics
and geometric
characteristics
(references
2 and 3).
The first integer
indicates
the amount
of camber
in terms of the relative
magnitude
of
the design lift coefficient;
the design lift coefficient
in tenths
is thus three-halves
of the first integer.
The second and third
integers
together
indicate
the distance
from the leading
edge
to the location
of the maximum
camber;
this distance
in
percent
of the chord is one-half
the number
represented
by
these
integers.
The last two integers
indicate
the airfoil
thickness
in percent
of the chord.
The NACA
23012 airfoil
thus has a design
lift coefficient
of 0.3, has its maximum
camber
at 15 percent
of the chord, aml has a thickness
ratio
of 12 percent.
918392--51----2
5
system.--The
NACA
6-series
airfoils
are
usu-
ally designated
by a six-digit
number
together
with a statement
showing
the type of mean line used.
For example,
in the designation
NACA
65,3-218,
a=0.5,
the
"6"
{s
the
series
designation.
The "5"
denotes
the chordwise
position
of minimum
pressure
in tenths
of the chord beifind
the leading
edge for the basic symmetrical
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 favorable
pressure
gradients
exist on both surfaces.
The "2" following
the dash gives the design
lift coefficient
in tenths.
The last two digits indicate
the airfoil thickness
in percent
of the chord.
The designati0n
"a=0.5"
shows
the type of mean line used.
When
tion is not given,
it is understood
mean line (a= 1.0) has been used.
the mean-line
designathat
the uniform-load
REPORT NO. 824--NATIONAL
6
ADVISORY COMMITTEE
When the mean line used is obtained
1)y combining
than
one mean
line, the design
lift coefficient
used
designation
is the
of the mean lines
the
statement
algebraic
sum of the design lift coefficients
used, and the mean lines are described
in
following
having
the
number
as in the following
(a=0.5,
65,3-2181a=1.0
NACA
Airfoils
more
in the
a thickness
cli=0.3
' c,_=--0.11
distribution
obtained
ease:
FOR AEHONAUTICS
NACA
65(3_s)-(1.5)(16.5),
Some early
experimental
sertion
of the letter
"x"
a=0.5
airfoils
are
immediately
as in the designation
66,2x-115.
Thickness
distributions.--Data
designated
preceding
for available
by the inthe hyphen
NACA
6-series
thickness
forms
are
presented
in
the
supplementary
figures.
These data are comparable
with the sinfilar
data
for airfoils of the NACA
four-digit
series, except
that ordinates for intermediate
thicknesses
may not be correctly
ob-
t
by linearly
increasing
or deereasing
the ordinates
of one of the originally
derived
thickness
distributions
are designated
as in the follow-
tained
by scaling
thickness
ratio.
ing example:
a factor
will, however,
produce
shapes
satisfactorily
approximating
members
of the family
if the change
in thickness
ratio
is small.
Values
of v/V and hvdV
for intermediate
thickness
ratios
may be approximated
as described
for the
NACA
65(318)-217,
a=0.5
The significance
of all of the numbers
except
those in the
parentheses
is the same as before.
The first number
and the
last two numbers
enclosed
in the parentheses
denote,
respectively,
the low-drag
range
and the thickness
the chord of the originally
derived
thickness
The more recent
NACA
6-series
airfoils
members
between
of thickness
the conformal
families
having
transformations
in percent
distribution.
are derived
of
as
a simple
relationship
for airfoils of different
thickness
ratios
but having
minimum
pressure
at the same
ehordwise
position.
These
airfoils
are distinguished
from
the earlier individually
derived
airfoils
by writing
the number indicating
the low-drag
range as a subscript
; for example,
NACA
653-218,
a=0.5
For NACA
6-series
airfoils having
than 0.12 of the chord, the subscript
a tlfickness
ratio
number
indicating
low-drag
range should be less than unity.
a fractional
number,
a subscript
of unity
Rather
than
was originally
less
the
Ordinates
for the basic thickness
distributions
designated
by
a subscript
are slightly
different
from those for the corresponding
individually
derived
thickness
distributions.
As
before,
if the ordinates
of the basic thidkness
distribution
have been changed
by a factor, the low-drag
range and thickness ratio of the original
thickness
distribution
are enclosed
in parentheses
as follows:
NACA
If, however,
the
having
a thickness
65(a_8)-217,
a=0.5
ordinates
of a basic thickness
distribution
ratio less than 0.12 of the chord have been
changed
by a factor,
the number
indicating
the
range
is eliminated
and only the original
thickness
enclosed
in parentheses
as follows:
NACA
NACA
four-digit
series.
Mean lines.--The
mean
NACA
from
6-series
the
low-drag
ratio
is
65c10)-211
If the design lift coefficient
in tenths or the airfoil thickness
in percent
of chord
are not whole
integers,
the numbers
giving these quantities
are usually enclosed
in parentheses
as
in the following
designation:
airfoils
leading
ordinates
proportional
to the
of changing
the ordinates
by
lines
produce
edge
commonly
a uniform
to the
point
used
with
chordwise
-=a
c
and
the
loading
a linearly
de-
creasing
load
from this point
to the trailing
edge.
Data
for NACA
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 presented
in the
supplementary
figures.
the following
formula,
the original
expression
reference
11 :
The ordinates
wlfich represents
for mean-line
Y¢--c--2r(a+l)Cq ll_la[l(a
use
em-
ployed
for these airfoils.
Since tt, is usage is not consistent
with the previous
definition
of a number
indicating
the lowdrag range,
the designations
of airfoil sections
having
a thickness ratio less than 0.12 of the chord are now given without
such a number.
As an example,
an NACA
6-series
airfoil
having
a thickness
ratio
of 0.10 of the chord would
be
designated:
NACA
65-210
the tabulated
This method
61(l--X)
:log_
were computed
a simplification
ordinates
given
by
of
in
x)-"log_la_X
2 log. (1--
;+g-h
x)+14
(1--c/--4x'_"
1(a_;)2
_
c}
(6)
where
g=--l--a • 1
The
h=l_
al
ideal
angle
lift coefficient
[ a2 (1 _log,
[ 21 (l_a)2
log.
of attack
is given
(1--a)
are
-- _1 (1--a)2]
a: correst)onding
--
]b
+g
to the
design
eli
27r (a+
data
1) + 1]
by
(?l t =
The
a-
presented
for
1)
a design
lift
coefficient
c,
equal
to unity.
All tabulated
values
vary
directly
with
the design
lift coefficient.
Corresponding
data for similar
mean lines with other design lift coefficients
may accordingly
be obtained
simply
by multiplying
the tabulated
values
by
the
desired
hi order
Usually
distance
design lift coeffieicnt.
to camber
NACA
6-series
used having
vahles
from the leading
airfoils,
mean
lines
are
of a equal to or greater
than the
edge to the location
of nfinimum
pressure
for the selected
thickness
distrilmtion
at. zero lift.
For special
purposes,
load
distrihutions
other
than
those
corresponding
to the simple mean lines may be obtaiz_ed
1)y
combining
two or more types of mean line having
positive
or
negative
values
of the design lift coefficient.
The geometric
SUMMARY
and aerodynamic
characteristics
obtained
by algebraic
addition
nent mean lines.
NACA
of such combinations
of the values for the
7-SERIES
Numbering
system.--The
nated by a number
of the
The
first
number
"7"
,nay be
compo-
AIRFOIL
DA'I_A
serial
7
letter
airfoils
viously
"B."
Mean
are obtained
by
described
mean
lines
used
for
the
NACA
7-series
combining
two or more of the
lines.
A list of the thickness
predis-
AIRFOILS
NACA
following
NACA
OF
7-series airfoils
type (reference
tributions
and mean lines used to form these airfoils
is presented
in table I.
The basic thickness
distribution
is given
a designation
similar to those of the final cambered
airfoils.
For
example,
the
basic
thickness
distribution
for
the
are desig12):
747A315
indicates
the
series
number.
NACA
747A315 and 747A415 airfoils is given the designation
NACA 747A015 even though
minimum
pressure
occurs at 0.4c
on both upper and lower surfaces
at zero lift.
Combination
of this thickness
distribution
with the mean lines listed in
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
table I for the NACA
747A315
distribution
to the desired type
Thickness
distributions.--Data
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
series thickness
distributions
are presented
in the supplementary
figures.
These
thickness
distributions
are individually
derived
and do not form thickness
families.
The
thickness
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
Z©
airfoil changes
the pressure
as shown in figure 2.
for available
NACA
7-
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 thinn(,r
or thicker
the method
thickness
distributions
may be approximated
of equation
(5).
If the change
in thickness
is small, tabulated
values
with reasonable
accuracy.
of Ava/V
may
be applied
by
ratio
directly
m
/.8
/'_
u/ ,per
/"
12
/
NHCA
sur'foce)
basle
747A{215
"r,5/c,k'rvess
_
_,
d/t_tribu//on
M
_
\\
\
.6
.4
0
./
.2
.3
.d
.5
.C
.7
.8
lift coefficient
and
._
L0
x_e'
FIGURE
2.--Theoretical
pressure
distribution
for the
NACA
TABLE
747A315
airfoil
section
I.--ANALYSIS
OF
at
the
design
AIRFOIL
Mean-line
Airfoil
Basic
the
NACA
747A015
basic
thickness
distribution.
DERIVATION
combination
I
_
I
thickness
form
a=0
a =0.1
designation
747A315
........
747A415
........
The
numbers
I 747A015
747A015
]
in the
a =0.2
a =0.3
a =0.4
a =0.5
a=0.6
a =0.7
......................
.......................
.......................................
various
columns
headed
"Mean-line
combination"
I
indicate
.763
the magnitude
.............
of the design
lift
coefficient
used.
a=0.8
a =0.9
a=l.0
REPORT
8
THEORETICAL
NO.
824--NATIONAL
ADVISORY
this
CONSIDERATIONS
PRESSURE
The
pressure
FOR
circle
AERONAUTICS
in complex
coordinates
distribution
also
exerts
(7)
where
z
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
tllan 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 NACA
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
complex
variable
in circle
angular
coordinate
of z
a
basic
_0
constant
This
length
cir('le
curve
by
Theodorsen
in reference
9.
Figure
3 shows
the significance
of the various
phases
of the
process.
The circle about which the flow is originally,
calculated
its center at the origin and a radius of ae ¢°. The equation
has
of
plane
considered
determining
true
circular
usually
radius
is transformed
unity
of circle
into
an
arbitrary,
ahnost
the relation
z>-= e (_-¢0)+i(0-_)
(8)
Z
the
equation
of the
ahnost
circular
Z _=
developed
by
schematically
is
z = ae ¢o+_*
DISTRIBUTIONS
A knowledge
of the pressure
distribution
over an airfoil is
desirable
for structural
design
and for estimation
of the
critical
Mach number
and moment
coefficient
if tests are not
available.
COMMITTEE
gee+
curve
is
(9)
io
where
z'
complex
ae_
radial
0
angular
In
order
variable
in near-circle
coordinate
of z'
coordinate
for
the
plane
of z'
transformation
(8)
to be
conformal,
it
is
necessary
that
the quantity
(0--_b) (given
the symbol
--_)
be the conjugate
function
of (_b--_0) ; that is, if _ is represented
by a Fom'ie," series of the form
Z%_
I_21?t ?
_=_,
A,
sin 7_--_
1
then
(4_--¢0)
is given
B_ cos n4,
l
by
the relaLion
1
1
This relationship
indicates
that, if tile flmction
e(¢) is given,
(_b--¢0) can be calculated
as a function
of q_. Means
of
performing
this calculation
arc presented
in reference
13.
The
transformation
relating
the ahnost
circular
curve
to
the airfoil shape is
a(-2
a 2
_=z'-l-z,
(10)
Z'-plone
where
_" is the comph,x
coordinates
of tile airfoil
parts of i', respectively.
rclatio,s
The veh)city
and e is given
v
V--_
FIGURE
k
3.--Transformations
used
to
derive
airfoils
find
calculate
pressure
distributions.
variable
in the airfoil
plane.
The
x and y ave the real and imaginary
These coordinates
are given by the
x=2a
cosh
_b cos 0
Ill)
y=2a
sinh
4, sin 0
(12)
distril)ution
in terms of the airfoil 1)arameters
exaetiy
for perfect fluid tlow by the expression
[sin
(sinh2_
(ao+4,)+sin
(ao+_r_:)]
+ sin'20) _(1--d¢
e_°
) +(-d_
(13)
) _
SUMMARY
OF
AIRFOIL
9
DATA
where
v
local velocity
V
free-stream
ao
section
¢0
average
er_
over surface
of airfoil
velocity
angle of attack
value of ¢ (lf02_
value of e at trailing
_d_b)
edge
The basic symmetrical
shapes were derived by assuming
suitable values of dedo as a function of 4_. These vahws were
chosen on the basis of previous experience and are subject to
the conditions that
0_4, =0
and de/dr_ at 4 is equal to ded4) at --q_. These conditions
are necessary
for obtaining
closed symmetrieal
shapes.
de
Values of _(¢) were obtained
simply by integrating
d4_d4.
Values of ¢(4) were found by obtaining the conjugate of the
curve of e(¢) and adding a value _0 sufficient to make _e
value of _ equal to zero at ¢=7r.
This condition assures a
sharp trailing-edge
shape.
Inasmuch as small changes in the velocity distribution at any
de
point of the surface are approximately
proportional
to 1-t-d_
(see reference 14), the initially assumed values of de/deo were
altered by a process of successive approximations
until the
desired type of velocity distribution was obtained.
After the
final values of _ and e were obtained, the ordinates of the basic
thickness
distribution
were computed
by equations
(11)
and (12).
When these computations
were made, it appeared that there
was an optimum value of the leading-edge radius dependent
upon the airfoil thickness
and the position of minimum
pressure.
If the leading-edge
radius was too small, a premature peak in the pressure distribution
occurred in the
immediate
vicinity of the leading edge as the angle of attack
was increased.
If the leading-edge
radius was too large, a
premature
peak occurred a few percent of the chord behind the
leading
edge.
With the correct leading-edge
radius, the
pressure
distribution
became nearly flat over the forward
portion of the airfoil before the normal leading-edge
peak
formed at the higher lift coefficients.
Curves of the parameters ¢, e, d_/dep, de/dep plotted against
_ for the NACA
643-018 airfoil section are given in figure 4.
Experience has shown that, when the thickness ratio of an
originally derived basic form was increased merely by multiplying all the ordinates by a constant factor, an unnecessarily
large decrease in the critical speed of the resulting section
occurred.
Reducing the thickness ratio in a similar manner
caused an unnecessarily
large decrease in the low-drag range.
For this reason, each of the earlier NACA 6-series sections was
individually
derived.
It was later found that it was possible
-./6
0
FIGURE 4.--Variation
2
3z
W
¢_, roc//bns
of airfoi! parameters
section
¢, e, _,
5
d_ with tb for the NACA
basic thickness
6
643-018
PTr
air
foil
form.
to derive basic airfoil parameters
¢ and e that could be
multiplied
by a constant factor to obtain airfoils of various
thickness ratios, without having the aforementioned
limitations in the resulting
sections.
Each of the more recent
families of NACA 6-series airfoils, in which numerical
subscripts are used in the designation, having minimum pressure
at a given chordwise position was obtained by scaling up and
down the basic values of the airfoil parameters
_band e.
Theoretical
pressure
distributions(indicated
bY(v)
_)
for a family of NACA 65-series airfoils covering a range of
thickness ratios are given in figure 5 (a). This figure shows
the typical increase in the magnitude of the favorable pressure
gradient, increase in maximum velocity over the surface, and
increase in the relative pressure recovery over the rear portion
of the airfoil with increase in thickness ratio.
Figure 5 (b)
shows the pressure distribution
for a series of basic thickness
forms having a thickness ratio of 0.15 and having mininmm
pressure at various chordwise positions.
The value of the
minimum
pressure coefficient is seen to decrease and the
magnitude
of the pressure Fecovery over the rear portion of
the airfoil to increase with the rearward movement
of the
point of minimum pressure.
10
REPORT
NO.
824--NATION
_L
ADVISORY
COMMITTEE
FOR
AERONAUTICS
Z8
........
_,'_CA CSe O/5----
N_CAC_ 0/8 ___
NAC_65,-OZJ
rv'AC_ 642-015
EO
/6
(?)'
/.2
IVAC_ G6_ 015
%
.8
A<ACA 67,,/
NAC_ E,5_-02;
.4
0'5
(a)
0
.Z
...4
6
.8
LO
0
.2
4
_1_
(a) Variation
with thickness.
FIGURE 5.--Tbcorctical
(b) Variation
pressure
The pressure
distribution
for one of the basic
thickness
distributions
at various lift coefficients
distributions
for some basic symmetrical
symmetrical
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
fiat 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 leading
edge.
Rapid
estimation
of pressure
distributions.--In
the discussion
that follows, the term "pressure
distribution"
is used
to signify the distribution
of the sbltic pressures
on the upper
z]O
LO
NACA
with position of minimum
pressure.
6-series airfoils at zero lift.
and lower surfaces
of the airfoil along
"load distribution"
is used to signify
tli_ chord of tim normal
force resulting
the chord.
The term
the distribution
along
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 tile previous
section.
Although
this method
is
not unduly
laborious,
the computations
required
are too
long to permit
quick and easy calculations
of airfoils.
The need for a simple methotl
for large numbers
of quickly obt'lining
pressure
distributions
with engineering
accuracy
has led to
the
development
of a methotl
(reference
15) combining
features
of thinand
thick-airfoil
theory.
This
simple
method
makes
use of previously
calculated
characteristics
of a limited
number
of mean lines and thickness
distributions
the tllin airfoil,
or (if the thin _lirfoil 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 snmll angles of attack,
is substantially
equ.fl to a lift coefficient
c_, which
is designated
the ideal
or design
lift coefficient.
If, moreover,
the camber
of the
mean line is changed
by multiplying
tile mean-line
ordinates
by a constant
factor,
the resulting
load distribution,
tim
ideal or design _lngle of attack
_ and the design lift coelticient
c _ may be obtained
sinll)ly by multiplying
the original
Wthles
by the same fi_ctor.
The cllar_lcteristics
of a large number
of
mean lines are presented
in both graphical
and tabular
form
in the supplementary
figures.
The lo_ld-distribution
data
are presented
both
in the form of the resultant
pressure
coefficient
Pn and in the form of the corresponding
velocityincrement
ratios A_/V.
For positive
design
lift coefficients,
30
_C
LO
k
.8
that
may be combinetl
to form large mlmbers
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
aml
(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
5O
FIGURE 6.--Theoretical
.6
_1_
pressure
distribution for the NACA
coefficients.
652-015 airfoil
at several
lift
these
velocity-increment
ratios
are
positive
on
the
upper
SUl_IMARY
OF
surface
and negative
on the lower surface;
the opposite
is
true for negative
design
lift coefficients.
The second load distribution,
which results
from changing
the angle of attack,
is designated
herein thc "additional
load
distribution"
and tile corresponding
lift coefficient
is designated
the "additional
lift coefficient."
This additional
load
distribution
contributes
no moment
about
the quarter-chord
point and, according
to thin-airfoil
theory,
is independent
of
the airfoil geometry
except
for angle of attack.
The additional
load distribution
obtained
from thin-airfoil
theory
is
of limited
practical
application,
however,
because
this simple
theory
leads to infinite
values of the velocity
at the leading
edge.
This difficulty
is obviated
by the exact thick-airfoil
theory
(reference
9) which also shows that the additional
load
distribution
is neither
completely
independent
of the airfoil
shape
nor exactly
a linear
function
i_f the lift coefficient.
For this reason,
the additional
load distribution
has been
calculated
by the methods
of reference
9 for each of the thickness distributions
presented
in the supplementary
figures.
These
data are presented
in the form of velocity-increment
ratios
Ava/V corresponding
to an additional
lift coefficient
of
approximately
unity.
For positive
additional
lift coefficients,
these
velocity-increment
ratios
are positive
on the
upper
surfaces
and
negative
on the lower
surfaces;
the
opposite
is true for negative
additional
lift coefficients.
In addition
to the pressure
distributions
associated
with
these two load distributions,
another
pressure
distribution
exists which is associated
with the basic symmetrical
thickness form or thickness
distribution
of the airfoil.
This pressure
distribution
has
been
calculated
by
the methods
described
in the previous
section
for the condition
of zero
lift
and
is presented
which
is equivalent
coefficient
S, and
local velocity
ratio
corresponding
points
thickness
form.
in the
supplementary
as
at low Much
numbers
to the pressure
as the local velocity
ratio
v/V.
This
is always
positive
and is the same for
on the
The velocity
distribution
to be composed
of three
ponents
as follows:
upper
and
distribution
of the mean
lower
surfaces
DATA
11
The values
of v/V and of Av/V in equation
(14) should,
of course,
correspond
to the airfoil
geometry.
Methods
of obtaining
the proper
values of these ratios from the values
tabulated
in the supplementary
figures are presented
in the
previous
section
"Description
of Airfoils."
When the
distribution
approximately
ratio AvdV has the value of zero, the resulting
of the pressure
coefficient
S will correspond
to the pressure
distribution
of the airfoil
section
at the design lift coefficient
cz_ 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 ct will be found to be greater
than cu by an amount
dependent
on the thickness
ratio
of
the basic thickness
form.
The pressure
distribution
will usually
be desired
at some
specified
lift coefficient
not corresponding
to ca.
For this
purpose
the ratio AvdV must be assigned
some
value
obtained
by multiplying
the tabulated
value of this ratio by a
factor
y(a].
For a first approximation
this factor
may be
assigned
the value
f(_) =c,-c,,
corresponding
line
to
form
of the
the velocity
disat zero angle of
NACA
the
design
2.O
sc*_face_
/
1.2
..-o--
-'oN
\
.8
-o
.4
vV± _)2
a = 06
load
" (3) The distribution
corresponding
to the additional
load
distribution
associated
with angle of attack
The velocity-increment
ratios At,/V and ht,,/V corresponding to components
(2) and (3) are added
to the velocity
ratio
corresponding
to component
(1) to obtain
the total
velocity
at one point,
from which the pressure
coefficient
S
is obtained;
thus,
S_(v±A
t7612/5]-216,
Upper
to
(15)
where c_ is the lift coefficient
for which the pressure
distribution is desired.
If greater
accuracy
is desired,
the value of
dr(a) may
be adjusted
by trial
and error
to produce
tim
actual
desired
lift coefficient
as determined
by integration
of the pressure-distribution
diagram.
Although
tiffs method
of superposition
of velocities
has
inadequate
theoretical
justification,
experience
has shown
that
the results
obtained
are adequate
for engineering
use.
In fact,
the results
of even the first approximations
agre6
well widL experimeh_al
dat_ and are adequate
for at least
preliminary
consideration
and selection
of airfoils.
A comparison
of a first-approximation
theoretical
pressure
distribution with an experimental
distribution
is shown in figure 7.
about the airfoil is thus considered
separate
and independent
com-
(1) The distribution
corresponding
tribution
over the basic
thickness
attack
(2) The
distribution
figures
AIRFOIL
Theory
Exp er,).en
/
(14)
When this formula
is used, values of the ratios corresponding
to one value of x are added together
and the resulting
value
of the pressure
coefficient
S is assigned
to the airfoil surface
at the same value of x.
0
.2
.4
.8
.8
LO
_/c
FIGURE 7.--Comparison
of theoretical and experimental pressure distributions
66(215)-216, a = 0 6 airfoil, c_ = 0.23.
for tile NAC A
REPORT NO. 824--NATIONAL
12
Some
discrepancy
naturally
occurs
between
the
ADVISORY COMMITTEE
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
is low.
Numerical
examples.--The
following
numerical
examples
are included
to illustrate
the method
of obtaining
the firstapproximation
pressure
distributions:
Example
1: Find the pressure
coefficient
x=0.50
oll the upper
and lower surfaces
S at the
of the
station
NACA
653-418 airfoil at a lift coefficient
of 0.2.
From
the description
of the NACA
6-series
airfoils,
determined
that this airfoil is obtained
by combining
FOR AERONAUTICS
The supplementary
figures give a value of 1.182 for v/V
atx=0.25
for the NACA
652-015 basic thickness
form.
The
desired
value
of v/V is obtained
by applying
formula
(5)
as follows:
14
V=(1.182-1) 15 +1
=1.170
From
the supplementary
figures
the following
values
of
5v_/V are obtained
at x = 0.25 for the following
basic thickness
foI'm s:
it is
the
NACA
65a-018
basic thickness
form with the a=l.0
type
mean line cambered
to a design lift coefficient
of 0.4.
The
following
data are obtained
from the supplenumtary
figures
for this thickness
form and mean line at x=0.50:
Thickness
form
NACA
6,52
015
............
NACA
651
012
.................
....
desired
equation
value
of A_',/V is computed
as follows
by use of
(15):
AVa
-V =(0.157)
(0.2--0.4)
at
_25
0.290
282
.
By interpolation
the value
of A_a/V of 0.287
may
be
assigned
to the 14-percent-thick
form.
The desired
value of
Av_/V is then computed
as follows
by use of equation
(15):
AVa=(0 287)
V
"
=0.115
The
?_
(0.6--0.2)
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 multiltlying
the
tabulated
value by the design lift coefficient.
Thus,
= --0.031
A/;
Tile
desired
tabulated
description
value
of Av/V
is obtained
by:nmltiplying
vahlc by the design lift coefficient
of Ill(' NACA
6-series_airfoils.
A'b'
V = (0.250)
as stated
Thus,
-v=
the
in the
(0.4)
(0.333)
(0.2)
=-0.067
Substituting
the foregoing
values of S as follows:
For
the upper
values
in equation
(14) gives
the
surface
=0.100
S=
Substituting
vahws of S:
For
the
upl)cr
these
values
in equation
(14) gives
the following
S= (1.235+
0.100--
the
lower
the lower
(1.235--
0.100_-0.031)
2
-=1.360
Examl)h,
2:Fin(1
the t)rcssu,'e
('oetti(;i(,nt
N a! the station
x=-0.25
on the
llt)])er
altd lower
Slll'faces
of the NACA
(i5(2L,,) 214, a=-0.5 airfoil at a lift (,o(,tli(,imtt of 0.(i.
The airfoil designation
shows that this airfoil was ol)laincd
by cmnl)ining
a thickness
form obtain(,d
|)y multilllying
Ilw
ordinates
of Ill(, NACA
652 015 form 1)y the factor
14/15
with the a=0.5
type mean
line (,aml)ered
to a design
lift
coefficient
of 0.2.
k
(1.170--
0.067--
2
0.115)
----0.976
surface
S=
2
surface
S=
0.031 )2
= 1.700
For
0.067-_- 0.115)
-----1.828
For
surface
(1.170q-
Example
3: Find the pressure
x=0.30
on the upper and htwcr
airfoil at a lift coefficient
of 0.5.
coefficient
S at tim station
surfaces
of the NACA
2412
The description
of airfoils
of the NACA
four-digit
series
shows that tit(, necessary
data may be found fi'om the NACA
0012 tlfickncss
form and 64 lnt.q(.u line in the supph,mentary
tigures.
From
these
tigurcs
lit(, folh)wing
At x=0.30
Y
V---l.162
At x=0.30
data
are obtained:
SUMMARY
For the
NACA
64 mean
line
OF
AIRFOIL
at x=0.30
A?)
at
the
NACA
64 mean
9
line
c4=0.76
The values
of Av/V
geometry
are obtained
by the factor
2/6 as
airfoils ; thus,
and c_ corresponding
to the airfoil
by multiplying
the foregoing
values
explained
in the description
of these
Av
2
=0.087
ch=
(0.76)(
value
of Ava/V is obtained
Av_ _ (0.239)
V--
lift
coefficient
is to separate
(0.5--
lower surface is decreased.
This
for various
amounts
of camber.
the
pressures
on
from
equation
(15)
effect
is shown
in figure
8 (a)
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
shows that
2)
----0.253
The desired
as follows:
design
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
V=0.-60
For
the
13
DATA
the load near
the leading
edge.
Figure
8 (b)
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/c 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.
0.253)
CRITICAL
MACH
NUMBER
=0.059
Substituting
the proper
values of S as follows:
For
the
upper
values
ill equation
(14)
gives
the
surface
S= (1.162+0.087+0.059)
of the low-speed
pressure
coefficient
S is known either
mentally
or from
theoretical
methods,
the critical
2
the
lower
surface
S=
experiMach
number
may be predicted
approximately
by the Von K_irmfin
method
(reference
19).
A curve relating
the critical
Much
number
and the low-speed
pressure
coefficient
S has been
cmcmaued
flulu the eq tlgt uLuhb
of 1 (fl el l:_ltt;e
_u and included
in
=1.712
For
The critical
speed is defined
as the free-stream
speed at
which the velocity
at any point along the sm'face of the airfoil reaches
the local velocity
of sound.
If the maximum
value
(I. i 6z -- O.08] -- o. obu)
the supplementary
figures.
These
numbers
are useful
for preliminary
=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
predicted
critical
considerations
absence
of test data and appear
to correspond
fairly well to
the Math
numbers
at which
the local velocity
of sound is
reached
in the high-critical-speed
range
of lift coefficient.
This criterion
does not, however,
appear to predict
accurately
£8
--
2.4
Upper
surf
oce
I
|
NACA 652-0/5
/i.aCl_ 65r015
.._.m cA 65_-0/5
!
zo
/
./VJOA
65z-_/5
.A/ACA 65s415
._(4
L6
•
f....L-_
/VAC,4 65_-415,
15E6/5
a=0.3
A/ACA 65_-2/5
I
ZE
A'ACA 65c4/5
.
,vAc_
, a=05
65_-4/5
/
.8
,/
<:%
/V4C,4 65E4/5,
.4
A_C_
0
._
.6
.8
ZO
ZO
_r/c
(a) Amount
of camber.
FIGURE 8.--Effect
of amount
and type of camber
Maeh
in the
on pressure
distribution
at design
lift,
65E4/5
c_:07
REPORT NO. 824--NATIONAL
14
ADVISORY COM:MITTEE
the Mach
numbers
at which large changes
ill airfoil
charactcristies
occur, especially
when sharp pressure
peaks
exist
at the leading
edge.
A discussion
of the characteristics
of
airfoil sections
at supercritical
Math
numbers
is beyond
the
scope of this report.
For convenience,
curves
of predicted
critical
Math
number plotted
against
the low-speed
section
lift coemcient
have
been included
in the supplementary
figures for a number
of
airfoils.
High-speed
lift coefficients
may
be obtained
by
multiplying
tire low-speed
lift coefficient
by the
factor
1
• The critical
Math
numbers
have been predicted
_/1--M 2
front theoretical
pressure
distributions.
For airfoils
of the
NACA
four- and five-digit
series an(l 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 maxilnum
critical
Maeh
number
decreases
rapidly
as the thickness
is increased.
The effect
of camber
is to lower the maximum
critical
Maeh number
and to shift the range of high critical
Maeh numbers
in 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
NACA
6-series
seetions
have
considerably
higher
maximum
critical
Math
numbers
than
NACA
24-, 44-, and 230-series
airfoils
of
corresponding
tlfiekness
ratios.
MOMENT
NACA
moment
required
FOR AERONAUTICS
64 mean
line in tlle
coefficient
for this
value is then
sut)plementary
mean
line is
4
= --0.105
ANGLE
Methods
of
OF
ZERO
of
moment
linearly
with the design lift coefficient
ordinates.
These theoretical
vahles
of the
airfoil
° when
c,=l.0.
Tilt'
=1.52
airfoil shows
that
the (h,sign
is 0.2.
Froin
the dala
on
Substituting
in equation
(16)
desired
value
of
a_ is then
or
are
at0= 1
°
.52--
= --3.0
Examlih,
2: Fin(I
NACA 2415 airfoil.
(0.5)
(16) gives
the
The
descrilition
of
shows tlmt tile required
(57.3)
(0.5)
27r
°
theoreti('al
angh,
lift
the
=0.25
°
(().76)('_-)
--0.253
= --0.028
and
monwnt
('oeffi('icnt
quarter-chord
point for the NACA 4415 airfoil.
From
tim
description
of the
NACA
four-digit
airfoils,
the required
data is found to be presented
from
equation
(16)
al)out
the
a,0=0.25
series
for the
lift
for the
by multiplying
the corresllonding
values
for the NACA
64
mean line (see supplementary
tigures)
by a factor
2/6; then
c_=
theoretical
of zero
the NACA
four-digit-series
airfoils
values of a_ and cq may be obtained
c,,,c,,= (-0.1:_9) (o.2)
L
design
The tabulated
values
of a_ may
be scaled
linearly
with
design
lift coefficient
or with the mean-line
ordinates.
Although
these theoretical
angles of zero lift may be useful
in prelimiimry
design,
they
should
not be used
without
experimental
verification
for such purposes
as establishing
the washout
of a wing.
lgumerieM
examples.--The
inethod
of computing
az 0 is
illustrated
in the following
exainph,s:
Example
1: Find
the theorctical
angle of zero lift of the
NACA 65.2--515, a=0.5
airfoil.
Tiffs airfoil
number
indicates
a design
lift coefficient
of
0.5.
Data
for the NACA
a=0.5
mean
line indicate
that
ae(.ordingly
the
or
the
NACA a--0.5
type mean line inch,led
in the SUl)l)MIwniary
tigures,
the value of c,,_; 4 is --0.139
for a design lift ('oeffi('ient
of 1.0.
The
desired
vahw
of the nmment
('ocfli('icnt
is
2: Find
ideal
57.3
21r ch
alo=ai--
coefficients
sufficiently
accurate
for preliininary
considerations,
but experimental
values
shouht
be used for stability
and control
calculations.
Numerical
examples.--The
following
nmnerical
examples
illustrate
the nwtlm(ts
of calculating
the moIne,_t
coefficients:
Exainple
1: Find the theoretical
moment
eoefiicient
about
the
qimrter-chord
point
for the
NACA
652 215,
a=0.5
airfoil.
ExaInl)le
the
angle of attack
o_ corresponding
to the design lift coefficient
c_ are included
among
the data for the various
mean lines
presented
in the supplementary
figures.
The approximate
values
of the angle of zero lift may
be obtained
front the
data
by using
the theoretical
value of the lift-curve
slope
for thin airfoils,
27r per radian.
The value of a: 0 in degrees
is then
a_=3.04
may be approximated
directly
from the values presented
in
the supplementary
figures for the various
mean lines.
These
values
were obtained
front thin-airfoil
theory
aim may
be
The designation
(.oellicient
of tiffs
LIFT
calculation.--Values
COEFFICIENTS
of calculation.--Theoretical
scaled up or down
with the mean-line
The
The
Cmc/4= (-0"157)
c_= (3.04)
Methods
figures.
--0.1_7.
= --2.0
(57.3)(0.253)
2rr
°
SUMS,IARY
DESCRIPTION
Perfect-fluid
airfoil contour
theory
smoothly
OF
FLOW
AROUND
OF
AIRFOILS
postulates
that
tile flow follow
tile
at all angles of attack
with no loss
AIRFOIL
DATA
5
lower surfaces.
If the region
of laminar
separation
occurs immediately
downstream
of minimum
pressure
(reference
20) and
flow is extensive,
from the location
the flow returns
to
of energy.
Consequently,
perfect-fluid
theory
itself
gives
no information
concerning
the profile drag or the maximum
lift of airfoil sections.
The explanation
of these pllenomena
the surface
almost
immediately
at flight Reynolds
numbers
as a turbulent
boundary
layer.
This turbulent
boundary
layer
extends
to the trailing
edge.
If the surfaces
are not
is found
from
a consideration
of the effects
of viscosity,
which are of primary
importance
in a thin region
near tile
surface
of the airfoil called the boundary
layer.
sufficiently
smooth
and fair, if the air stream
is turbulent,
or perhaps
if the Reynolds
number
is sufficiently
large, transition
from laminar
to turbulent
flow may occur anywhere
upstream
of the calculated
laminar
separation
point.
For low and moderate
lift coefficients
where inappreciable
Boundary
layers
in general
are of two types,
namely,
laminar
and turbulent.
The flow in the laminar
layer
is
smooth
and free from any eddying
motion.
The flow in the
turbulent
layer is characterized
by the presence
of a large
number
of relatively
small eddies.
Because
the eddies in the
turbulent
layer produce
a transfer
of momentum
from the
relatively
fast-moving
outer parts of the boundary
layer to
tile portions
closer to the surface,
the distribution
of average
velocity
is characterized
by relatively
higher velocities
near
the surface
and a greater
total boundary-layer
thickness
in
a turbulent
developed
tion
than
boundary
layer
under
otherwise
is therefore
for laminar
higher
flow.
than in a laminar
boundary
layer
identical
conditions.
Skin fricfor
turbulent
boundary-layer
flow
When the pressures
along the airfoil surface
are increasing
in the direction
of flow, a general deceleration
takes place.
At
the outer limits of the boundary
layer this deceleration
takes
place in accordance
with Bernoulli's
law.
Closer to tile surface, no such simple law can be given because
of the action
of the viscous
forces within
the boundary
layer.
In general,
however,
the relative
loss of speed is somewhat
greater
for
particles
of fluid within
the boundary
layer than for those at
the outer
limits
of the layer
because
the reduced
kinetic
energy
against
of the boundary-layer
the adverse
pressure
air limits
its ability
to flow
gradient.
If the rise in pressure
is sufficiently
great, portions
of the fluid within the boundary
layer may actually
have their direction
of motion
reversed
and may start moving
upstream.
When this reverse
occurs,
the flow in the boundary
layer
is said to be "separated."
Because
of the increased
interchange
of momentum
from
different
parts
of the layer,
turbulent
boundal T layers
are
nmch
more resistant
to separation
than
are laminar
layers.
Laminar
boundary
layers can only exist for a relatively
short
distance
in a region in which
the pressure
increases
in the
direction
of flow.
Formulas
for calculating
many
of the
boundary-layer
characteristics
are given in references
20 to 22.
After
laminar
separation
occurs,
the
flow may
either
leave the surface
permanently
or reattach
itself in the form
of a turbulent
boundary
layer.
Not much is known concerning the factors
controlling
this phenomenon.
Laminar
separation
on wings is usually
not permanent
at flight values of
the Reynolds
number
except
when it occurs near the leading
edge under conditions
corresponding
to maximum
lift.
The
size of the locally
separated
region
that is formed
when the
laminar
boundary
layer separates
and the flow returns
to the
surface
decreases
with
increasing
Reynolds
number
at a
given
angle of attack.
The flow over aerodynamically
smooth
airfoils at low and
moderate
lift coefficients
is characterized
by laminar
layers from the leading
edge back to approximately
tion of the first minimum-pressure
point
on both
boundary
the locaupper and
separation
occurs,
the airfoil profile drag is largely
skin friction
and the value
of the drag coefficient
mainly
on the relative
amounts
of laminar
and
flow.
If the location
of transition
drag coefficient
may be calculated
from boundary-layer
theory
by
references
23 and 24.
caused by
depends
turbulent
is known
or assumed,
the
with reasonable
accuracy
use of the
methods
of
As the lift coefficient
of the airfoil is increased
by changing
the angle of attack,
the resulting
application
of the additional
type of lift distribution
upstream
on the upper
moves
the minimum-pressure
surface,
and the possible
point
extent
of
laminar
flow is thus reduced.
The resulting
greater
proportion of turbulent
flow, together
with the larger average velocity of flow over the surfaces,
causes the drag to increase
with
lift coefficient.
In
the
forward
variation
pressure
case
of many
of the
older
types
of
airfoils,
this
movement
of transition
is gradual
and the resulting
of drag with lift coefficient
occurs smoothly.
The
distributions
for NACA
6-series
airfoils are such as
to cause transition
to move forward
suddenly
at the end of
the low-drag
range
of lift coetlicients.
A sharp increase
in
drag coefficient
to the value corresponding
to a forward
location of transition
on the upper surface results.
Such sudden
shifts in transition
give the typical
drag curve for these airfoils with a "sag"
or "bucket"
in the low-drag
range.
The
same characteristic
is shown
to a smaller
degree by some of
the earlier
airfoils such as the NACA
23015 when tested
in
a low-turbulence
stream.
At high lift coefficients,
a large part of the drag is contributed by pressure
or form drag resulting
from separation
of
the flow from the surface.
The flow over the upper surface is
characterized
by a negative
pressure
peak near the leading
edge, which
causes
laminar
separation.
The onset
of turbulence
causes the flow to return
to the surface as a turbulent
boundary
layer.
High Reynolds
numbers
are favorable
to
the development
of turbulence
and aid in this process.
If
the lift coefficient
is sufficiently
high or if the reestablishment of flow following
laminar
separation
is unduly
delayed
by low Reynolds
numbers,
the tm'bulent
layer
will separate
from the surface
near the trailing
edge and will cause large
drag increases.
The eventual
loss in lift with increasing
angle
of attack
may result
either
from relatively
sudden
permanent
separation
of the laminar
boundary
layer near
the leading
edge or from progressive
forward
movement
of
turbulent
separation.
Under
the latter
condition,
the flow
over a relatively
large portion of the surface may be separated
prior to maximum
lift.
A more extended
discussion
of the
flow conditions
associated
with maximum
lift is given
in
reference
5.
16
REPORT
EXPERIMENTAL
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
CHARACTERISTICS
SOURCES
from
NO.
OF
DATA
The primary
source of the wind-tunnel
tests in the Langley
two-dimensional
data presented
low-turbulence
is
pressure
tunnel
(TDT).
The methods
used to obtain
and
correct
the data are summarized
in the appendix.
Design
data
obtained
from
tests
of 2-foot-chord
models
in this
tunnel
are presented
Some wind-tunnel
NACA
wind tunnels.
is indicated
and
were conventional
Most
of the
the
in the supplementary
figures.
data presented
were obtained
in other
In each case, the source
of tlle data
testing
techniques
and corrections
unless otherwise
indicated.
flight
data
consist
of drag
used
measurements
made
by the wake-survey
method
on either the airplane
wing or a
"glove"
fitted
over the wing as the test spe(,imen.
Whenevcr the measurements
were obtained
for a glove, this fact
is indicated
in the presentation
of the data.
All data obtained
at high
speeds
have been reduced
to coeffii'ient
form by
compressible-flow
methods
In
the case of all
such
NACA
flight data, precautions
have been taken
to ensure
that
the results
presented
are not invalidated
by cross
flows of low-energy
air into or out of the survey
plane.
DRAG
CHARACTERISTICS
OF
SMOOTH
AIRFOILS
Drag characteristics
in low-drag
range.--The
value of the
drag coefficient
in the low-drag
range
for slnooth
airfoils
is
mainly
a function
of the Reynolds
number
and the relative
extent
of the laminar
layt,r and is moth, rately affected
by the
airfoil thickness
ratio and eamber.
The effee.t on minimum
drag of the position
of minimum
l)l'essure
which detel'mines
the possible
extent
of laminar
flow is shown
in figure 9 for
some
NACA
6-series
airfoils.
The
data
show
a regular
decrease
nfinimum
c .0/_
in drag
pressure.
o AIA(A 63:-215
A,'ACA 6d_-215
....
¢, ,'¢AC4 65_-L_15
.Oi,P
with
rearward
inovenlent
of
_ NACA
v NA_
'
i
i
merits
of airfoil sections
at flight Reynt>hls
enecs 25 and 26).
The variation
of minimum
drag coefiieient
....
f
I
"
:
r ¸--
0
A
. t_
_
cambcr
is
1
-q
-_
i
.%.0/2 --
"
with
(refer-
_
J I
ul?6 ......
mmfl)ers
in figure 11 for a number
of smooth
18-percent-thick
6-series airfoils.
These data show very little change
i
dY6_-2/5
C7,1-L_15
number for several
for a flat plate.
tested was a practical-construction
model.
It may be noted
that the drag coefficient
for the NACA
65_-418 airfoil at low
Reynohls
numbers
is substantially
higher
than
that of the
NACA 0012, whereas
at high Reynolds
mm_bers
the opposite
is the ease.
The higher
drag of the NACA
65a-418
airfoil
section
at low Reynohts
numbers
is caused
by a relatively
extensive
region
of laminar
separation
downstream
of the
point
of minimum
pressure.
This region
decreases
in size
with increasing
Reynohts
nunfl)er.
These data illustrate
the
inadequacy
of low Reynohls
number
test data either to estinlatc the full-s('ale
characteristics
or to detel'mil_e
the relative
shown
NACA
-----
k_
_
coefficient
FIGURE 10.--Variation of minimuln section drag coefficient with Reynohls
airfoils, togelher with laminar and turbtflent skin-friction
coefficients
65-series
66--,_eri_
v 653-8/8
OC:
t_
r_
t_
b
•_
o
i
_ .008
2
.3
Po5/t/Dn
"-"
of
.z
m/nlrnurn
.5
.6
pr-essuFe,
.7
.8
x_/e
._.
FIGURE 9.--Variation
of ndnimum drag coefficient with position of minimum
l)ressIIre for
s/nne N A C A 6-series airfoils of the same camber aml thickness.
R = 6 X 10%
v
_____
The variation
of minimmn
drag (,oeflieient
with Reynohls
number
for sevt,ral airfoils
is shown in figure 10.
The th'ag
coelii('ieId, gelwrally
decreases
with iucreasing
Reynohls
numi)er up to Rt,ynolds
numbers
of the order
of 20X 10t
Above
this Reynohts
mmfl)er
tht_ drag coefficient
of the NACA
65(4o.1)-420 airfoil
remained
substantially
constant
up to a
RcynohIs
munbt,
drag coefli('icnt
may
L
be i'aused
.....
r of n.early 40)< 105
The earlier
ine|'ease in
shown
by,the
NACA
66(2x15)-116
airfoil
by sm'face
irregularities
because
the specimen
___---.
>_--
._ .0_
i
0
2
Des/on
FIGURE
ll.--Variation
6-series
of itliniinllnI
airfoil
sections
.4
Ii'ft
sechb_
section
of
18-percent
drag
.6
coefT;c_e_
eoeffieielfl
thickness
with
ratio.
.8
¢_;
camber
R
=
for
9
X
several
10_.
NACA
SUM_IARY
OF
in nfinimum
drag coefficient
with increase
in camber.
A
large amount
of systematic
data is included
in figure 12 to
show the variation
of minimum
drag coefficient
with thickness ratio for a number
of NACA
airfoil sections
ranging
in
thickness
from 6 percent
to 24 percent
of the chord.
The
minimum
drag coefficient
is seen to increase
with increase
in
thickness
ratio for each airfoil series.
This increase,
however, is greater
for the NACA
four- and five-digit-series
airfoils (fig. 12 (a))
12 (b) to 12 (e)).
than
.o/o ___
t
the
NACA
6-series
airfoils
(figs.
.__
17ou_, _
• 012 -- ._moot_,
L!
for
l-
.......
y2
2_
I--"
Ser-I'em
o
m oo]
/4
(__._-.
+ z4, (4-_),'#
004
44
----
_
[
v 230 (5-d,g#) I
0/2
----
- __--6--
"-_-
_ 00,
_"
.g
q
17
DATA
The data presented
in the supplementary
figures for the
NACA
6-series
thickness
forms
show that
the range
of lift
coefficients
for low drag varies markedly
with airfoil thickhess.
It has been possible
to design
airfoils
of 12-percent
thickness
with a total theoretical
low-drag
range of lift coefficients of 0.2.
This theoretical
range
increases
by approximately
0.2 for each 3-percent
increase
of airfoil
thickness.
Figure
13 shows that the theoretical
extent
of the low-drag
range
is approximately
realized
at a Reynolds
number
of
9X10%
Figure
13 also shows a characteristic
tendency
for
the drag to increase
to some extent
toward
the upper end of
the low-drag
range
for moderately
cambered
airfoils,
particularly
for the thicker
airfoils.
All data for the NACA
6-series
airfoils
show a decrease
in the extent of thelow-drag
range with increasing
Reynolds
number.
Extrapolation
of
the rate of decrease
observed
at Reynolds
numbers
below
9 X 10 _ would indicate
a vanishingly
small low-drag
range at
flight values of the Reynolds
number.
Tests
of a carefully
constructed
model
of the NACA
65(,2,-420
airfoil showed,
however,
that
the rate of reduction
of the low-drag
range
with increasing
Reynolds
number
decreased
markedly
at
Reynolds
numbers
above 9_ 10 _ (fig. 14).
These data indi-cate that
the extent
of the low-drag
range
of this airfoil is
reduced
number
ct i
oO
o
.2
a
.4
v
.6
..-0
AIRFOIL
to about one-half
of 35X10%
the theoretical
.032
0
<<.OlZ
o IVACA
_] IVACA
0 NAC,4
z_ AIACA
.028
__. - -_
C:)
k_
qJ
....
.OOd
+
-[
•02d
i
84,-412
84_-d15
6%-418
64,-,¢21
\
I I I I I
I
I
d
o O--cJ ./
<:> .2 -A .4_
b .oo4
at a Reynolds
I
(b)
.0
value
•_-. 020
.0
(5
__.
_
i
o .016
I
!
b
.0/2
.....
0
" - k'-
"_
._ .012
0
C/i
oO
--
,_"
.4---
v
.6
%. 008
.004
(d)
012
.o08
0
-/.6
._
I
.004
_
I
0
d-
_
+
_
>----e_
8
/17-fell
o
o
0
.2
_
.4
I
12
I_
20
24
/h,,c/_f_ess,
pe_ce, _t <;i o_'o,,<I
Z8
-.8
-.4
Section
lift
0
.d
coefficient,
.8
L2
L6
e,
FIGURE 13.--Drag characteristics of some NACA 64-series airfoil sections of various thick.
nesses, cambered to a design lift coefficient of 0.4. R = 9 X 10_; TDT tests 682, 733, 735,
and 691.
c,,
I
-1.2
,.72
(a) NACA four- and five-digit series.
(b) NACA 63-series.
(c) NACA 64-series.
(d) NACA 65-series.
(e) NACA 66-series.
FIGURE 12.--Variation
of minimum
section drag coefficient with airfoil thickness ratio for
several NACA airfoil sections of different cambers in both smooth and rough conditions.
R = 6X 10_.
The values
of the lift coefficient
for which
obtained
are determined
largely
by the amount
The lift coefficient
at the center of the low-drag
low drag is
of camber.
range corre-
sponds
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.)
REPORT
N',O. S2-t--NATIONAL
ADVISO'RY
COMMITTEE)
FOR AERONAUTICS
-4
I
4
-.&
I
0
4
8
12
/6'
Reyno
(a)
Variation
of upper
and
lower
FIGURE
20
ds
limits
2d
flute,
of
14.--Yariation
bet-,
low-drag
range
of low-drag
i
28
3Z×/O
/._q
_
with
range
Reynolds
with
number
for
the
NACA
:8
65142D-420
airfoil.
T I)T
tests
3(X1, 312,
and
L6
329.
'
Drag
characteristics
of the
z_ /V,IC,4 G5_-6'18
7 A/ACA _5,3-_1_
---
:4
O
.4
.8
12
5_chbn
hf! co_ffJk_k_?t, q
(b) Section drag characteristics at various Reynolds numbers.
number.
Reynolds
o '_;424 _5,,-018
o AAC4 _5_-ZI8
.028
-LZ_
FI
in
I
low-drag
lift
outside
the
range
coefficient.
foils,
for
low-drag
For
the
range
is moth,
continue.
for
which
(See
the
already
lift
at
the
drag
high,
rapidly
anti
coefficient
rate,
fig.
lift
at
this
15.)
the
range.--At
increases
symmetrical
which
not
low-drag
drag
For
upper
upl)er
rate
highly
end
of
coefficient
end
increase
low-<'ambered
the
high
the
with
of
of
the
increase
eaml)ered
the
air-
end
does
sections,
low-drag
range
shows
a continued
cambered
with
is
rapid
increase.
Comparison
load
mean
load
farther
is
of
line
favorable
for
o
-I.o"
.Fw, U_E
hess
-1.2
15.--Drag
with
for
many
large
-.8
-.4
Sectlon
characlcrislics
various
0
.4
I/fl coeff/c/erTf_
of some
amounts
NACA
of carol)or.
A'
=
65-series
6 X
airfoil
106; T I)T
8
L2
1.6
to
c,
tests
163,
be
and
sections
of
18
percent
314,802,
813,
thickand
at
high
appears
The
location
that
parture
used
appears
of the
with
low-drag
by
the
I)e
a function
and
the
for
caused
distribution
approximate
the
by
of
lift
mean
for
methods
type
thickness.
in
the
the
13, from
to shift
line
the
basic
The
when
are
combined
thickness
previously
is
above
obtained
line
lift
shift
coefficient
mean
form
describe(1.
parison
line
three
NACA
drag
for
the
than
for
the
of
center
coefficients
the
exdesign
associated
The
of
the
This
normal
of
at
the
high
the
Reynohls
effect
is too
in sldn
effect
flow
lift
supplementary
variation
with
the
line
increasing
scale
turbulent
leading
of section
6-series
airfoils
NACA
large
friction
of
Reynolds
following
laminar
to
6-series
the
coefficients
high-speed
earlier
than
high
NACA
the
the
6-series
17.
anti
of
have
lift,
this
of
of
lift
coeffi-
camber.
values
('oeflicient,
generally
airfoils.
coeffimargin
lift
maxinmm
the
of
The
lower
of
range
higher
sections
NACA
range
choice
values
and
substantially
flight,
suitable
show
At
the
the
through
sections
ratio•
is
in
com
23012
in figure
sections
by
NACA
presented
section
cruising
28).
characteristics.--A
of the
6-series
23012
(refiwenee
drag
is
maintained
for
lift-drag
on
ehara('teristies
be
NACA
the
edge
drag
NACA
useful
however,
drag
the
usually
cients
velocity
the
corresponding
may
with
according
of
cients
partly
the
be
of type
de-
effect
the
near
Effects
This
wlfich
the
in
with
carry
mean
f#10.
variation
of
to higher
This
mean
some
theory.
airfoil
thickness.
increase
shows
thin-airfoil
in figure
is seen
airfoil
the
range
simple
range
eoetticient
velocity
low-drag
by
is shown
increasing
increments
to
27)
thM:ness
plained
the
to
(refert,nee
airfoil
lift
of
predietcd
given
in drag
coefficients.
onset
coefficients
airfoils
by
the
drag
27).
the
a uniformto
uniform-load
reference
for
to
on
separation
from
lift
cambered
the
low
and
of
airfoils
that
reductions
accounted
number
shows
16
show
m_mher
airfoils
for
obtaining
(fig.
Data
figures
for
data
forward
coefficients
•OO#
data
with
lower
SUMMARY
OF
AIRFOIL
19
DATA
I
I
-
i
i
)
I
i
\/
_
j
i
!
I
I
i
%
" i ....
I.....
i
qo
v
I'
I"
I"
i•
k
20
REPORT
NO.
824--NATIONAL
ADVISORY
COMS]ITTEE
FOR
AERONAUTICS
q5
"1"_'o
'lu_./o./,,/dooo
4ua_o.w
SUMMARY
OF
Effective aspect ratio.--The
combination
of high drags at
high lift coefficients, low drags at moderate lift coefficients,
and the nonregular
variation
of drag with lift coefficient
shown by the NACA 6-series airfoils may lead to paradoxical results when the span-efficiency concept (reference 29)
is used for the calculation
of airplane performance.
In the
usual application
of this concept, the airplane drag characteristics are approximated
by a curve of the type
C_-_ CDL=o-]-kCL _
I
.0_
o
(17)
It should be noted, however, that although equation (17)
provides
a reasonably
satisfactory
approximation
to the
drag of the airplane with NACA 23018 sections, such is not
the case for the airplane with the NACA 653-418 section.
The most important
reason for using high aspect ratios on
large airplanes is to reduce the drag at cruising lift coefficients
and to obtain high maximum values of the lift-drag ratio.
For the two wings considered,
the maximum
value of this
ratio is appreciably
higher for the airplane
with NACA
653-418 sections (19.8 as compared
with 18.5) despite the
fact that this airplane shows the lower effective aspect ratio.
Figure
18 (b) shows a similar comparison
with similar
results for two airplanes of aspect ratio 8 and NACA 2415
and 652-415 airfoils.
It is accordingly
concluded that the
effective, aspect ratio is not a satisfactory
criterion for use in
airfoil selection.
.O2
I
I
t
I
I
I
I
I
./0
--
m
I
I
IVACA G53-418
w_ny_ _
effective
aspect
rot/b,
AIACA 2,.7018 wt½g_ _
I effective
osl_ecf
rob'o,
.08
I
830
.
I
i/
I
I
65z-415
IVACtl Z415
I
I
I
I
wing;
I
o.tpecf
wln_, .aspect
A!ACA 65_-41E w_n_
effective
ospect
NACA 8415 w_77g_ _
I effeeh've
aspect
I
,
•
qa
I
r-oho,
r-alia,
8
8
rot]o,
6.97
robo,
7 416
__
I/
"_
•
z/
it
/'
c2.O7
,4/r-plane
.
/
06o
,"
7"
t_
t_<<,:
.o4
I
.06
¢
i'i/
I
/v_g{'lt
[]
_
.07
.o3
o
.07
9.29
i"
._ .06 ._
I
--JF
.09
(JO
r_
|
65_-418
w_bg; ospec/
rohb,
I0.-/Vt4Ct4 23018
w/n_,, aspect
f'of/o,
I0
....
.07--
I
/VACA
D
21
DATA
0.0150 to the wing drag coefficients.
The resulting
drag
coefficients have been approximated
by two curves corresponding to equation
(17) and matched to the drag curves
at lift coefficients of 0.2 and 1.0. These two curves correspond to effective aspect ratios of 9.29 for the airplane with
NACA 23018 sections and of 8.30 for the airplane with
NACA 653-418 sections
and illustrate
the typical
large
reduction
in the effective aspect ratio obtained
with such
sections.
This curve is usually matched to the actual drag characteristics at a rather low and at a moderately
high value of the
lift coefficient (reference 30).
The application
of this concept to two hypothetical
airplanes with NACA 230- and 65-series sections, respectively,
is illustrated
in figure 18 (a).
The wing drags of the airplanes have been calculated
by adding the induced drags
corresponding
to an aspect ratio of 10 with elliptical loading
to the profile-drag
coefficients of the NACA 23018 and
653-418 airfoils.
These sections are considered
representative of average wing sections for a large airplane of this
aspect ratio.
Ordinate scales are given in figure 18 (a),for
the wing drag and for the total airplane drag coefficients
obtained
by adding
a representative
constant
value of
./0
AIRYOIL
_ .04 %
o :o.oo63+ o.o4z_ c_,. _P/
,_,L:_,=,'_n
.0/
.02
o
/ S
-
.0/
.o,
/
.2
.4
Lift
(a) NACA
18.--Comparison
/
o
0
FiGurE
/
.6
.8
coefficient,
finite
aspect-ratio
drag
/
L2
I
0
.2
CL
65a-418 and 23018 wings of aspect
of
1.0
characteristics
.4
L/T/
ratio 10.
for
(b) NACA
two
types
to the
section
of
airfoils
drag
obtained
coefficients.
by
adding
the
.6
.8
coeffi'c/en_
drag
corresponding
L2
_z
65m-415and 2t15 wings of aspect
induced
1.0
ratio 8.
to
an
elliptical
span
loading
22
REPORT
EFFECT
Permissible
drag increments
31).
Although
shown
to result
OF
SURFACE
N_O.
824--N_ATIONTAL
IRREGULARITIES
roughness.--Previous
ON
work
ADVISO'RY
DRAG
has
shown
large
resulting
from surface
roughness
(reference
a large part
of these
drag increments
was
from forward
movement
of transition,
sub-
stantial
drag increments
resulted
from surface roughness
in
the region of turbulent
flow.
It is accordingly
important
to
maintain
smooth
surfaces
even when
extensive
laminar
flow cannot be expected,
but the gains that may be expected
from maintaining
smooth
surfaces
are greater
for NACA
6or 7-series airfoils
when extensive
laminar
flOWS are possible.
No accurate
method
of specifying
the surface
condition
necessary
for extensive
laminar
flow at high Reynolds
numbers has been developed,
although
some general
conclusions
have been reached.
It may be presumed
that
for a given
Reynolds
number
and chordwise
position,
the size of the
pernlissible
roughness
will vary directly
with the chord
of
the airfoil.
It is known,
at one extreme,
that
the surfaces
do not have
to be polished
or optically
smooth.
Such
polishing
or waxing
has shown
no improvement
in tests in
the Langley
two-dimensional
low-turbulence
tunnels
when
applied
to satisfactorily
sanded surfaces.
Polishing
or waxing
a surface
that is not aerodynamically
smooth
will, of course,
result
in improvement
and such finishes
may be of considerable practical
value because
deterioration
of the finish may
be easily seen and possibly
postponed.
Large models having
chord
lengths
of 5 to 8 feet tested
in the Langley
twodimensional
low-turbulence
tunnels
are usually
finished
by
santling in tile chordwise
direction
with No. 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
i'ougher
surface
texture
should
be considered
as a possible
source
of
transition,
although
slightly
rougher
surfaces
have appeared
to produce
satisfactory
results in some cases.
Wind-tunnel
experience
in testing
NACA 6-st,ries sections
and data
of reference
32 show
that
small
protuberances
extending
above
the general
surface
level of an otherwise
satisfactory
surface
are more likely to cause transition
than
sinall
del)ressions.
Dust
particles,
for examph,,
are more
effective
than small scratches
in producing
transition
if the
nmtt, l'ial at the edges of the seratcht,s
is not forced above the
general
surface
level.
Dust
particles
adhering
to the oil
h,ft on airfoil surfaces
1)y fingerprints
may be expected
to
cause transition
at high Reynohls
numl)t,i's.
Transition
spreads
from an individual
disturt)ance
with an
incluth,tl
angle of al)out
15 ° (references
31 and 33).
A few
s('altercd
spc('ks,
especially
near the h, ading edge, will cause
the flow to l)e largely
turbulent.
This fact Inakes necessary
an extrenlcly
thorough
inspection
if low drags
are to be
i'ealiz_,d.
SI)ecks
suiticit, nily
large
to cause
premature
trallsition
on full-size wings can I)e felt by hand.
The insl)ectioll
procedurt,
used
in the Langley
two-dimensional
low-tul'bulencc
tunnels
is to feel the t,ntire surface by hand
aft(,r which the surface is thoroughly
wiped with a dry cloth.
It has been noticed that transition
resulting
froin individual
COMMIITTEE
FOR
AERONAUTICS
small sharp
protuberances,
in contrast
to waves,
tends
to
occur
at the protuberance.
Transition
caused
by surface
waviness
appears
to approach
the wave gradually
as the
Reynolds
number
or wave
size is increased.
The height
of a small cylindrical
protuberance
necessary
to cause transition when located al_ 5_,percent
of the chord
with its axis
normal
to the suTfface is shown in figure 19.
These data were
•
_.050
__
\
_.030
] I.o,o
c
I
2
3
d
W/mg
FmURE
19.--Variation
protuberance
ameter
with
symmetrical
70 percent
obtained
with
necessary
axis normal
6-series
wing
5
Reynolds
number
to cause
premature
to wing surface
and
airfoil
section
lOxlO"
8
nurnD_F,
R
of the minimum
transition.
is located
of 15-percent
f
©
}_egmo./o's
height
Protuberance
at 5 percent
chord
thickness
and
with
of a cylindrical
has 0.035-inch
diof a 90-inch-chord
minimum
pressure
at
chord.
at rather
low values
of the
Reynolds
number
and
show a large
decrease
in allowable
height
with increase
in
Reynohls
nunfiier.
This
effect
of Reynolds
munl)er
on
permissit)h'
surface
roughness
is also evidt,nt
in figure 20,
in which a sharp incrt,ase
in drag at a Reynohls
numt)er
of
approxiInately
20X106
occurs
for the model painted
with
canmullage
lacquer.
The niagnitude
of the favorable
gradient
appears
to have a
small effect on the permissible
surface
I'oughnt'ss
for laminar
flow.
Figure
21 shows
that
the roughness
1)ecoInes more
important
at the extremities
of the low-drag
range
wliere
the favorable
pressure
gradient
is rciluced
on one surface.
The effect of increasing
the Reynolds
nuinber
for a sui'facc
of inarginal
snloothness,
which has an effect similar
to increasing
the surface roughness
for a given Reynohls
number,
is to reduce
rapidly
the extent
of the low-drag
range
and
then
to increase
tlie minimum
drag
cocfficient
(fig. 21).
The data of figure 21 were specially
chosen
to show
this
effect.
In nmst cases,
the effect of Reynohls
numt)er
predominates
over the effect of decreasing
the magnitude
of the
favorable
pressure
gratlient
to such an extent
that the
effect is the eliinination
of the low-drag
range (refereuce
Permissible
waviness.---More
difficulty
is generally
counteretl
in reducing
the waviness
to perInissil)h,
values
the maintenan('e
of laminar
flow than
in obtainillg
the
quired
surface
sInoothness.
In
of the
required
freetlom
fronl
ilifficult than that of tile rt, quired
addition,
surface
surface
only
34).
cnfor
re-
the specification
waviness
is more
smoothness.
Tile
prot)h,m
is not linfite(l
inerely
to finding the nlinimuln
waw'
size that will cause transition
undt,r given eon(litions
t)ecause
the Immbt, r of waves
and the shapt,
of the waw,s
require
consideration.
SUMMARY
¢°/6'
I
'
i .o/z[
I
[
OF
AIRFOIL
23
DATA
--_-
!
! i i
I
I J I i
:
Og
i'
_
OE
t
t
8
f
I
12
.016
I
/5
I
I
20
2_
Z8
.72
Reynolds
36
40
number,
R
44
4_
52
.....
60×10 _
i
o/2
i I
I
_
55
--
.006
(
-.9--
!
t 004
_
_-
ibl
I
0
4
8
16
20
Smooth
_,
.0/_-
I
-o
.012
"_0
-o
-v
IRI
]
15.3 x I0 _
/49
]
248
34(?
}
_46
J
i
I
Smoolh
I
I
I
i
with
1
Reynolds
I
TDT
camouflage
number
l
test
I
I
J
I
uv,,'?hI
t
.008
(b
,d
FIGURE
21.--Drag
characteristics
0
.d
.8
1.2
fiechbn //ffcoeff/c/e,g/,q
of
TDT
NACA
tests
65(4:1)-4.'20
300
and
airfoil
for
LO
two
surface
!
20
conditions.
486.
If the wave is sufficiently
large to affect the pressure
distribution
,in such a manner
that laminar
separation
is
encountered,
there is little doubt that such a wave will cause
premature
transition
at all useful Reynolds numbers.
A relation between the dimensions
of a wave and the pressure
distribution
may be found by the method of reference 35.
The size of the wave required to reverse the favorable pressure gradient
increases with the pressure gradient.
Large
negative
pressure gradients
would therefore
appear to be
favorable
for wavy surfaces.
Experimental
results have
shown this conclusion to be qualitatively
correct.
Little information
is available on waves too small to cause
36
t
ZO
4W
48
I
5Zx/O
°
328.
after painting;
for a 60-inch-chord
I
enomel
cur
off camoo,_loge
uv Ch b/ode
28
3E
number,
19
unimproved
cond/h'om
Synthet;c
ol/ _,oecks
! ....
i
I
24
Reynolds
condition;
(b) Lacquer
of drag coefficient
-
I
/2
(a)
FIGURE 20.--Variation
i i
I
O
<
TDT
test 461.
nmdel of the NACA
65(m)-420 airfoil for two surface conditions.
laminar separation or even reversal of the pressure gradient.
Data for an airfoil section having a relatively long wave on
the upper surface are given in figure 22. Marked increases
in the drag corresponding
to a rapid forward movement
of
the transition
point were not noticeable
below a Reynolds
number of 44X l0 _. On the other hand, transition has been
caused at comparatively
low Reynolds numbers by a series
of small waves with a wave height of the order of a few tenthousandths
of an inch and a wave length of the order of
2 inches on the same 60-inch-chord
model.
For the types of wave usually encountered
on practicalconstruction
wings, the test of rocking a straightedge
over
the surface in a chordwise direction is a fairly satisfactory
criterion.
The straightedge
should rock snmothly without
jarring or clicking.
The straightedge
test will not show the
existence of waves that leave the surface convex, such as the
wave of figure 22 and the series of small waves previously
mentioned.
Tests of a large number of practical-construction
models, however,
have shown
that those models which
passed the straightedge
test were sufficiently free of small
waves to permit low drags to be obtained at flight values of
the Reynolds number.
It is not feasible to specify construction
tolerances on airfoil ordinates
with sufficient accuracy
to ensure adequate
freedom
from waviness.
If care is taken to obtain fair
surfaces, normal
serious alteration
tolerances
may be used
of the drag characteristics.
without
causing
24
REPORT
NO.
8241NATIONAL
..(enfer
ADVISORY
COMMITTEE
FOR
AERONAUTICS
of wove
.005"
,.--4-
i_
_
60"
Oepor/ure
f/orr/
olT-fo/I
fOIr
surfooe
I
C "008
I
i_•oo8
0
.004
.g.oo_
0
4
8
/2
/d
ZO
2#
28
Win_
FIGURE
22.--Exlx,
rimental
curve
showing
variation
of drag
coefficient
with
Reynolds
number
roughness
capable
of producing
transition
is nearly
as great
as that caused
by much
larger
grain
roughness
when
the
roughness
is confined
to the leading
edge.
The degree
of
roughness
has a much larger effect on the drag at high lift
coefficients.
If the roughness
is sufiiciently
large to cause
transition
at all Reynohls
numbers
considered,
the drag of
the airfoil with roughness
only at the h,ading
edge decreases
with increasing
Reynolds
number
(fig. l0 and reference
36).
The effect of fixing transition
by means
of a roughness
strip of carborundum
of 0.01 I-inch grain is shown in figure 24.
The minimum
drag
increases
progressively
with
forward
movement
of the roughness
strip.
The effect on the drag
at high lift coefficients
is not progressive;
the drag increases
rapidly
when the roughness
is at the leading
edge.
Figure
25
shows that the drag coeiilcients
for the NACA
65(223)_ 422
and 63(420)
422 airfoils
were nearly
the same tllroughout
most of the lift range
when the extent
of laminar
flow was
limited
to 0.30c.
All recent airfoil data obtained
in the Langley
two-dimensional low-turbulence
pressure
tunnel
iiwlude
results
with
roughened
h,ading
edge, and these data are included
in the
supph, mentary
figures.
Tests with roughened
leading
edge
were formerly
made
only for a limited
numi)er
of airfoil
sections,
especially
those
having
large
thickness
ratios
(reference
37).
The siandard
roughness
seh,eted
for 24-inchchord
models
consists
of 0.011-inch
(,arl)orundum
grains
k
that
likely
to
be encountered
in
service
as
for
tim
NACA
40
44.
48
E2 x I 06
t_
65(4m-420
airfoil
section
with
a small
is shown in figure 12. These data
of the minimum
drag
coefficients
airfoils
are less than
the vahles
amount
of
surface
waviness.
Drag
with practical-construction
methods.
The section
drag coefficients
of several airplane
wings have 1)een measured
in flight by the wake-survey
method
(reference
38), and a
numher
of practical-construction
wing sections
have been
tested
in
tin,
Langley
two-dimensional
low-turbulence
pressure
tunnel
at flight
vahws
of the Reynohls
number.
Flight
data obtained
by the NACA
(reference
38) are summarized
in figure 26 and some data obtained
by the Consolidated Vultee Aircraft
Corporation
are presented
in figure 27.
Data
obtained
in
the
Langh,y
two-dimensional
lowturl)ulence
pressure
tunnel
for typical
practical-construction
sections
are presented
in figures 28 to 32.
Figure
33 presents
a comparison
of the drag eoetficients
obtained
in this wind
tmmel
for a model
of the NACA
0012 section, and in flight
for the same model
mounted
on an airplane.
For this case,
the wind-tunnel
and flight data agree to within
the experierl'or.
All
were
care
a
show that the magnitudes
for the NACA
6-sm'ies
for the NACA
fourand
five-digit-series
airfoils.
The rate of increase
of drag with
thickness
is greater
for the airfoils
in the rough
condition
than in the smooth
('ondition.
nlental
applied
to the airfoil surface at the h,ading edge over a surface
length of 0.08c measured
from the leading
edge on 1)oth surfaces.
The grains are thinly
spremt to cover 5 to l0 percent
of this area.
This standm'd
roughness
is consideral)ly
more
severe t llml that caused
by the usual manufacturing
irregularities
or deterioration
in service
but is considerably
less
than
36
number,
result
of accumulation
of ice or mud or damage
in military
combat.
The variation
of minimum
drag coefficient
with thickness
ratio for a mlmber
of NACA
airfoils with standard
roughness
Drag with fixed transition.---If
the airfoil surface
is sufficiently rough to cause transition
near the leading
edge, large
drag increases
are to be expected.
Figure
23 shows that,
although
the degree of roughness
has some effect, the increment in minimum
drag coefficient
caused
by the smallest
severe
32
Reynolds
wings
for
wllich
flight
data
carefully
finished
to produce
was taken
to reduce
surface
are
presented
smooth
waviness
in figure
26
surfaces.
Great
to a minimum
for all the sections
except
tile NACA
2414.5,
the N-22,
the
Republic
S 3,13, and the NACA
27-212.
Curvature-gage
nwasurenwnts
of surface
waviness
for some of these airfoils
are l)resented
ing to the
These
data
lamifmr
smooth
in reference
38.
Surface conditions
corresponddata
of figure
27 are described
in the figure.
show
that
the
sections
permitting
extensive
flow had substantially
than the other sections.
lower
drag
coefficients
when
SUMMARY
OF
AIRFOIL
DATA
25
%
%
%
%
%
%
I"
26
REPORT
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
%
%
(5
k
%
SUMMARY
OF
AIRFOIL
27
DATA
,32x/06
\
-'NACA
24
,
_
,_--¢_p_b/,c s-s,/}"-_
66,2-2(14.z)
2414.5"__--NACA
NACA
8
35-215
I
._"
NACA
27-212-
", I rq
x
"RepubDb
S-3,13
Q,I
'
"N-22
I
0
ff.O06
I
,dbhb g-3,/3--.
"_-_
/V-22.
.-_-
I
/_/
//,I/"
',,,
"'NAOA
,_L
3_/
/
35-2/5
"'A,AC,_
6_,2-2(_4.7)
//I
"_.oo,_
-_.Repub/,'c
I
i
"NA CA 2 7-2/2
/
I
D
.16
0
.32
Sechon
I/f/
.48
.64
coefficien_
ez
.96
.80
FIC,L'RE 26.--Comparison
of section drag coefficients obtained in flight on various
Tests of NACA 27-212 and 35-215 sections made on gloves.
FIGURE 25.--Drag
characteristics
of two NACA
6-series
roughness at 0.30c. R=26X10_.
airfoils
with
airfoils.
0.011-inch-grain
The wind-tunnel
tests of practical-construction
wing sections as delivered
by the manufacturer
showed
minimum
drag coefficients
of the order of 0.0070 to 0.0080 in nearly
all
cases regardless
of the airfoil
section
used (figs. 28 to 32).
Such values
may be regarded
as typical
for good current
construction
practice.
Finishing
the sections
to produce
smooth
surfaces
always produced
substantial
drag reductions
although
considerable
waviness
usually
remained.
None of
the sections
tested had fair surfaces
at the front spar.
Unless
special care is taken to produce
fair surfaces
at the front spar,
the resulting
wave may be expected
to cause transition
either
at the spar
location
or a short
distance
behind
it.
One
practical-construction
specimen
tested
with smooth
surfaces
maintained
relatively
low drags
up to Reynolds
numbers
of approximately
30X10 ° (NACA
66(2x15)-116
airfoil
of
fig. 10).
This specimen
had no spar forward
of about
35
percent
chord from the leading edge and no spanwise
stiffeners
forward
of the spars.
This type of construction
resulted
in
unusually
fair surfaces
and is being used on some modern
high-performance
airplanes.
A comparison
of the effect of airfoil section
on the minimum drag with practical-construction
surfaces
is very difficult because
the quality
of the surface
has more
effect on
the drag than the type
parison
can be obtained
of section.
from pairs
Probably
of models
the best comconstructed
at
L7
I
2
Lift
F]ov_
the
.3
coefhcler%
.4
C_
.5
.6
27.--Consolidated-Vultee
flight measurements
of the effect of wing surface condition
on drag of an NACA 66(215)-1(14.5) wing section.
same
time
by
the
same
manufacturers.
Data
for such
pairs of models are presented
in figures 30 to 32.
The results
indicate
that
as long as current
construction
practices
are
used the type of section
has relatively
little effect at flight
values of the Reynolds
number
for military
airplanes.
28
REPORT N O . 8 2 4-NATIONAL
ADVISORY COMMITTEE FOR AERONAUTICS
--3F
012
G
c
x
$ 008
c,
&8 004
6
4' A '
<
$
1;
' ' 'A ' ' '
ik
2L
Reynolds number,
2;
R
3L
3Lcxld6
FIGURE28.-Drag scale effect on 100-inch-chord practical-construction model of the
N A C A 65(216)-3(16.5) (approx.) airfoil section. c1=0.2 (approx.).
,016
Reynolds number,
R
FIGURE
%.-Variation of drag coefficient with Reynolds number for the N A C A 23016 airfoil
section together with laminar and turbulent skin-friction coefficients for a flat plate.
Q
-Y
.
C ,012
.a,
.u
\
<
016
3
8 ,008
+
--.
5
?F
&
012
i,
z
C
Q
;",004
8 009
CI
a,
8
v,
6
$ 004
0
-.2
0
.2
.4
.6
Section lift coefficient, c,
.8
1.0
FIGURE30.-Drag characteristics of the NACA 65(216)-417 (approu.) and KAC-4 23015
(approx.) airfoil sections built by practicalconstruetim methods by the same manufacturer. R=10.23XW.
i
i,
8
0
8
16
20
Reynolds number,
12
R
24
28
32x10'
F I G L R31.-Scale
E
effect on drag of the N A C A 66(215)-116 and N A C A 23016 airfoil sections
built by practical-construction methods by the same manufacturer and tested as received.
F I G C R32.-Drag
E
scale effect for a model of the S A C A BS-series airfoil section. 15.2i percent
thick, and the Davis airfoil section, 18.Z percent thick, hriilt by practical-construction
methods by the same manufacturer. ci=O.4G (appros.).
Reynolds number, f?
FIGL-RE
33.-Comparison
of drag coefficients measured in flight and wind tunnel for the
iYAC.4 0012 airfoil section at zero lift.
SUMMARY
OF
AIRFOIL
29
DATA
.016"
IIIIIIIIIIII111.11
-- 0
.2.0lg
(opprox.)_i?h de-icer O08e on upper
5urfoce
ond O/Oc on lower
surfoce
-- a NACA Z30/5
(opprox.)
with die-leer
removed
0 NACA 65(216)-215, o=g28 w/lh 0075e
de-icer"
-- Z_ NACA 85{2/d)-2/5
G=(2.8 _/lh de-icer /-emoved
--
N_CA
23015
I
_ Q=O.WO
]_
l
(229__
_ °r
0
_ .00_
_
004
O
©
W
8
12
FIGURE 34.--Effect
Important
savings
Reynolds
numbers
by
extensive
ing from
16
of de-leers
20
at high
even if
Drag increments
resultflow have been shown
to be important
(reference
31). The effects of surface roughness
on the variation
of drag with Reynolds
number
are shown
in figure 29, in which the favorable
scale effect usually expected
at high Reynolds
numbers
scale effect may be compared
was not realized.
with that shown
This type
of
for the NACA
63(420)-422
airfoil with rough
leading
edge
smooth
surfaces
(fig. 10).
Drag
increments
but otherwise
obtained
in
flight
layer
resulting
from roughness
with fixed transition
are
in the
presented
28
32
mumber, R
on the drag of two practical-construction
in drag
may
be obtained
keeping
the surfaces
smooth
laminar
flow is not realized.
surface roughness
in turbulent
Zd
Reynolds
turbulent
boundary
in reference
39.
The effect of the application
of de-icers to the leading
edge
of two smooth
airfoils
is shown
in figure 34.
The de-icer
"boots"
were installed
in both cases by the manufacturer
to
36
40
4W
airfoil sections with relatively
48
smooth
52x106
surfaces.
represent
good
typical
installations.
The minimum
drag
coefficients
for both sections
with de-icers
installed
were of
the order of 0.0070 at high Reynolds
numbers.
Effects
of propeller
slipstream
and airplane
vibration.Very few data are available
on the effect of propeller
slipstream
on transition
or airfoil drag; the data that are available do not show consistent
results.
This inconsistency
may
result
from variations
in lift coefficient,
surface
condition,
air-stream
turbulence,
propeller
advance-diameter
ratio, and
number
of blades.
Tests
in the Langley
8-foot high-speed
tunnel
indicated
transition
occurring
from 5 to 10 percent
of
the chord from the leading edge (reference
40). Drag measurements made in the Langley
19-foot pressure
tunnel
(fig. 35)
indicated
only moderate
drag increments
resulting
from
a
windmilling
propeller.
Although
the data of figure 35 may
not be very accurate
because
of the difficulty
of making
wake surveys
in the slipstream,
these data seem to preclude
very large drag increments
such as would result
from movement of the transition
to a position
close to the leading
edge.
These data also seem to be confirmed
by recent NACA flight
data (fig. 36), which show transition
as far back as 20 percent
_xlO6
_---7
,Left wing
section
,/-L in s//ps_reom
oucs[de
sl/pxfreom
0
E
A/rfo,/sechons
RoOf, /VACA 88(2x15;-0/8
Tzp, N_OA 87, /-(/.3)/5
Folio,
Aspecf
0
5.98
I
Propeller
o Propeller
z_ Propeller
L '&
.GO
o f?/ght
wing seclior_
ou'l side
slipstfeom
/ eft wln9 secfionL
in sh;osfreom
f
tip rod/us--_
w/bdmH//h_
removed
I
£
0
[3
Pow6f"
on
<
0
Power
off
M
o
.20
Cg
_.
-<
_--o
--
\
%_
k
(5
Z
6
OJstonce
FIGURE
plane
35.--The
from
effect
tests
of
of a model
918392--51--3
propeller
in the
5
from
operation
Langley
4
3
mode/
on
19-foot
renter
section
pressure
drag
Z
hne_
I
coefficient
tunnel.
0
0
.I
f/
of
CL=
a fighter-type
0.10;
R=3.TX
air106.
FIGURE
36.--Flight
measurements
.Z
Secton
of
outside
lift
transition
the
.3
.4
coeff/c/em/;
on
slipstream.
an
NACA
.5
.6
c,
66-series
wing
within
and
3O
REPORT
:NO.
8 2 4--;N'ATION'AL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
Q
of the
chord
in the
slipstream.
Other
unpublished
NACA
flight data on transition
oil an S-3,14.6
airfoil in the slipstream
indicated
that
laminar
flow occurred
as far back
as 0.2c.
Even less data are available
on the effects of vibration
on
transition.
Tests
in the Langley
8-foot high-speed
tunnel
(reference
40) showed
negligible
effects,
but the range
of
frequencies
tested may not have been sufficientlywide.
Some
unpublished
flight
data
showed
small but consistent
rearward movements
of transition
outside
the slipstream
when
the propellers
were feathered.
This effect was noticed
even
when the propeller
on the opposite
side of the airplane
from
the survey
plane was feathered
and was accordingly
attributed to vibration.
Recent
tests in the Ames full-scale
tunnel showed premature
adverse
measured
by tlle wake-survey
strut vibrated.
scale effect on drag coefficients
method
when a model-support
LIFT CHARACTERISTICS
OF SMOOTH AIRFOILS
Two-dimensional
data.--As
explained
in the section "Angle
of Zero Lift,"
tile angle of zero lift of an airfoil is largely
determined
by the camber.
Thin-airfoil
theory
provides
a
means for computing
the angle of zero lift from the mean-line
data presented
in the supplementary
figures.
Tile
agreement
between
the calculated
and the experimental
angle of
zero lift depends
on the type of mean line used.
Comparison
of the experimental
values of the angle of zero lift obtained
from the supplementary
figures
and the theoretical
values
taken
from the mean-line
data shows that the agreement
is
good except
for the uniform-load
type
(a----1.0) mean line.
The angles of zero lift for this type mean line generally
have
values
more
positive
than
those
predicted.
The
experimental
values of the angles of zero lift for a number
of NACA
four- and five-digit
and NACA 6-series
airfoils are presented
in figure 37. The airfoil thickness
appears
to have little effect
on the value of the angle of zero lift regardless
of the airfoil
series.
For tile NACA four-digit-series
airfoils, the angles of
zero lift are approximately
0.93 of the
airfoil theory;
for tile NACA 230-series
approximately
1.08; and for the NACA
uniform-load
0.74.
type
mean
line,
this
value given by thinairfoils,
this factor is
6-series
airfoils with
factor
is approximately
The lift-curve
slopes
(fig. 38) for airfoils
tested
in the
Langley
two-dimensional
low-turbulence
pressure
tunnel
are
higher
than those previously
obtained
in the tests reported
in reference
8.
It is not clear whether
this difference
in slope
is caused
by the difference
in air-stream
turbulence
or by
the differences
in test methods,
since
the section
data of
reference
8 were inferred
from tests of models of aspect ratio 6.
The present
values of the lift-curve
slope were measured
for
a Reynohls
number
of 6XI06 and at values of the lift coefficient
aplJroximately
equal
to the
design
lift
coefficient
of the
airfoil
section.
For the NACA
6-series
airfoils
this
lift coeffi-
cient is approximately
in the center
of the low-drag
range.
For airfoils having
thicknesses
in the range from 6 to 10 percent, the NACA
four-and
five-digit
series and the NACA
64-series
airfoil sections
have values
of lift-curve
slope very
close to the value for thin airfoils
(27r per radian
or 0.110 per
degree).
Variation
in Reynolds
number
between
3 X 106 and
9X 106 and variations
in airfoil camber
up to 4 percent
chord
appear
to have no systematic
effect on values of lift-curve
slope.
Tile
airfoil
thickness
and
the type
of thickness
distribution
appear
to be the primary
variables.
For the
NACA
fourand five-digit-series
airfoil
sections,
the liftcurve
slope
decreases
with
increase
in airfoil
thickness
For the NACA
6-series
airfoil
sections,
however,
the liftcurve slope increases
with increase
in thickness
and forward
movement
of the position
of minimum
pressure
of the basic
thickness
form at zero lift.
Some NACA
6-series
airfoils
show jogs in the lift curve
at the end of the low-drag
range, especially
at low Reynolds
numbers.
This jog becomes
more pronounced
with increase
of camber
or thickness
and with rearward
movement
of tile
position
of minimum
pressure
on tile basic thickness
form.
This jog decreases
rapidly
in severity
with increasing
Reynolds number,
becomes
merely
a change
in lift-curve
slope,
and
is practically
nonexistent
at a Reynolds
number
of
9 X 106 for most airfoils that would be considered
for practical
application.
This jog may be a consideration
in the selection
of airfoils
for small
low-speed
airplanes.
An analysis
of
the flow conditions
leading
to tiffs jog is presented
in reference 28.
The
variation
of maximum
lift coefficient
with
airfoil
thickness
ratio
at
a Reynolds
number
of 6X 106 is shown
in
figure 39 for a number
of NACA airfoil sections.
The airfoils
for which data are presented
in this figure have a range
of
thickness
ratio
from 6 to 24 percent
and cambers
up to
4 percent
chord.
From
the data for the NACA
four- and
five-digit-series
airfoil
sections
(fig. 39 (a)), the maximum
lift coefficients
for the plain airfoils appear
to be the greatest
for a thickness
of 12 percent.
In general,
the rate of change
of maximum
lift coefficient
with
thickness
ratio
appears
to be greatest
percent.
The
for airfoils
having
a thickness
data
for the
NACA
6-series
less than
12
airfoils
(figs.
39 (b) to 39 (e)) also show a rapid increase
in maximum
lift
coefficient
with
increasing
thickness
ratio
for
thickness
ratios
of less than
12 percent.
For NACA
6-series
airfoil
sections
cambered
to give a design lift coefficient
of not more
than
0,2, the optimum
thickness
ratio
for maximum
lift
coefficient
appears
to be between
12 and 15 percent,
excep!
for the airfoils
having
the position
of minimum
pressure
at
60 percent
chord.
The optimunl
thickness
ratio
for the
NACA
66-series
sections
cambered
for a design
lift coefficient of not more than 0.2 appears
to be 15 percent
or greater
SUMMARY
__
-4-%.
<9
Set-leg
--
AIRFOIL
DATA
31
__
_
0
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--
44J_-230
{5-d/git
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h
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fh/ckr?ess,
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IZ
per-cenf
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of
four- and five-digit
20
c,6o_d
Z4
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series.
(b) NAOA
63-series.
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Airfoil
24
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percenf
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of
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chord
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64-series.
-6
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-8
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4
8
/2
A_rfo/l thickness, percenf
16
ZO
of chord
24
(e)NACA66-series.
FIaURZ 37.--Measured
section angles of zero lift for a number
of NACA
airfoil sections of various thicknesses
and camber.
R=6XI(_.
24
32
REPORT
t
i
I
F, ogqed
I
NO.
I
l
symbols
8 2 4--1_TATIONAL
l
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[
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ADVISORY
COMMITTEE
FOR
AERONAUTICS
I
condition
.-Smooth
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-- ---'._--t_
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Q.. ./0
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.....
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Ioool
c,)
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o
0
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(a)
(j
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(b)
{ _',z_o _,5-d,19,/j
8
-_ ,_
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A/_/'o/'
12
/.4
16
ih/_kness, percent
(a) N'AOA four- and five-digit
22
,8
20
of chord
24
0
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V
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12
14
16
A/rfo// fh,cknes% percent
6
(b) NACA
series.
/8
of chord
22
20
24
C_-series.
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th/ckness,
16
percent
(c) NACA
,8
20
of chord
22
.o_
24
/6
8
A/rfo//
th/ckness,
(d) NACA
64-series.
/8
percent
of
20
22
24
cho,_d
65-series.
¢J
./2
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A/rfo//
'_
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16
percent
18
chord
of
20
22
2d
(e) NACA66-series.
FIGURE 38.--Variation
The
available
data
of lift-curve slope with airfoil thickness
indicate
that
a thickness
ratio
of
12
of NACA
NACA
airfoil sections
6-series
in both the smooth
sections
increase
and rough
with
conditions,
R=6)<10 _.
increasing
camber
lift
(fig. 39 (b) to 39 (e)).
The addition
of camber
to the symmetrical
airfoils
causes the greatest
increments
of maximum
lift coefficient
for airfoil
thickness
ratios
varying
from 6 to
in position
of minimum
pressure
on the basic thickness
form
for airfoils
having
thickness
ratios
of 6, 18, or 21 percent.
The maximum
lift coefficients
corresponding
to intermediate
thickness
ratios
increase
with forward
movement
of the
12 percent.
The
effectiveness
of camber
as a means
of
increasing
the maximum
lift coefficient
generally
decreases
as the airfoil
thickness
increases
beyond
12 or 15 percent.
The available
data indicate
that
the combination
of a 12-
position
having
The
percent-thick
lift coefficient
coefficient.
percent
or less is optimum
for airfoils
having
coefficient
of 0.4.
The maxinmm
lift coefficient
is least sensitive
[
ratio and camber for a number
a design
to variations
of minimum
pressure,
particularly
for tltose airfoils
design lift coefficients
of 0.2 or h,ss.
maximum
lift coefficients
of modcratcly
cambered
section
and a mean line cambered
for a design
of 0.4 yiehls
the
highest
maximum
lift
SUMMARY
OF
AIRFOIL
DATA
1
J.8
33
28
"
'
oO
o .2
"i--
,..-2.4
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v
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splff flop
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kJ
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0
4
Airfoil
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I£
16
fh_c/rness,
per-cemt
(a) NACA
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J
bolh/
-]
of
ZO
chord
8
/h/cA-hess,
0
Z4
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/2
percent
(b) NACA
four- and five-digit series.
/6
of
Z4
ZO
chord
63-series.
I
2.8
2.8
_.-Z4
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Rough
Smooth
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A_-fo/I
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Rough
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1
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16
per-cent
of
.4
24
ZO
chord
Rough
Smooth
(dl
0
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8
12
15
th/c/rmess,
perce_t
of
_0
c/_ord
Z4
(d) NAOA6,5-series.
(e) NAOA64series.
t
2.8
_o0
0
Isimulated
split
flop
deflected
60 °--
.2
_'_.4
_0
-_
.Z
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_20
o
t_
Alr-_off with
sp/i/ flop
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off-foil
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(_
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Airfoil
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FIGURE 39.--Variation
of maximum
section
lift eoe_eient
with
I
I
8
/g
16
fhiclr_ess,
percemf
airfoil thickness
of
ZO
c/_ord
24
66-series.
ratio and camber for several
roughness,
R=fXIO_.
NACA
airfoil sections
with and without
simulated
split
flaps and standard
34
REPORT
:NO.
824--NATIONAL
ADVISORY
The variation
of maximum
lift with type of mean line is
shown
in figure 40 for one 6-series
thickness
distribution.
No systematic
data are available
for mean lines with values
of a less than 0.5.
It should be noted, however,
that airfoils
such as the NACA
230-series
sections
with the maximum
camber
Airfoil
far forward
sections
with
show
large
values
of maximum
lift.
maximum
camber
far forward
and with
lhickness
ratios
of 6 to 12 percent
usually
stall
leading
edge with large
sudden
losses in lift.
A
sirable
gradual
stall is obtained
when the location
mum camber
is farther
back, as for the NACA
24-,
6-series
sections
with
normal
types
from the
more deof maxi44-, and
of camber.
2.O
f
0
Reyno/ds
number
o _OxlO_
c_ 9.0
.2
.4
Type
.6
of
combeG
.8
1.0
a
FIGURE 40.--Variation
of maximum
lift coefficient with type of camber for some NACA
653-418 airfoil sections from tests in the Langley two-dimensional
low-turbulence
pressure
tunnel.
A comparison
of the maximum
64-series
airfoil sections
cambered
of 0.4 with those of the NACA
approximately
0.15
AERONAUTICS
to 0.20.
The
scale
effect
on the
NACA
00- and 14-series
airfoils
having
thickness
ratios
less than
0.12c is very small.
The scale-effect
data for the NACA
6-series
airfoils
(figs.
41 (c) to 41 (f)) do not show an entirely
systcmatic
variation.
In general,
the scale
effect
is favorable
for these
airfoil
sections.
For the NACA
63- and 64-series
airfoils
with
small camber,
the increase
in maximum
lift coefficient
with
increase
in Reynolds
number
is generally
small for thickness
ratios of less than 12 percent
but is somewhat
larger for the
thicker
sections.
The character
of the scale effect for the
NACA
65- and 66-series
airfoil sections
is similar to that for
the NACA
63- and 64-series
airfoils
but the trends
are not
so well defined.
In most cases the scale effect for NACA
The values of the maximum
lift coefficient
presented
were
obtained
for steady
conditions.
The maximum
lift coefficient may be higher
when the angle of attack
is increasing.
Such
a condition
might
occur
during
gusts
and
landing
maneuvers.
(See reference
41.)
The systematic
investigation
of NACA
6-series
airfoils
included
tests of the airfoils
with a simulated
split flap deflected 60 ° . It was believed
that these tests would
serve as
q)
0
.8
FOR
6-series
airfoil sections
cambered
for a design lift coefficient
of 0.4 or 0.6 does not vary much with airfoil thickness
ratio.
The data of figure 42 show that the maximum
lift coefficient
for the NACA
63(420)-422
airfoil continues
to increase
with
Reynolds
number,
at least
up to a Reynolds
number
of
26X 106.
_/.8
(9
CO
O)
COMMITTEE
lift coefficients
of NACA
for a design lift coefficient
44- and 230-series
sections
(fig. 39) shows
that
the maximum
lift coefficients
of the
NACA
64-series
airfoils
are as high or higher
than those of
the NACA
44-series
sections
in all cases.
The NACA 230series airfoil
sections
have maximum
lift coefficients
somcwhat higher
than those of the NACA
64-series
sections.
The scale effect on the maximum
lift coefficient
of a large
number
of NACA
airfoil
sections
for Reynolds
numbers
from
3X10 _ to 9X108
is shown
in figure 41.
The scale
effect for the NACA
24-, 44-, and 230-series
airfoils
(figs.
41 (a) and 41 (b)) having thickness
ratios from 12 to 24 percent
is favorable
and nearly
independent
of the airfoil thickness.
Increasing
the Reynolds
number
from
3X106
to 9X106
results
in an increase
in the maximum
lift coefficient
of
an indication
of the effectiveness
of more powerful
types
of
trailing-edge
high-lift
devices although
sufficient data to verify
this assumption
have not been obtained.
The maximum
lift
coefficients
for a large
number
of NACA
airfoil
sections
obtained
from tests with the simulated
split flap are presented
in figure 39.
The data for the NACA 00- and 14-series airfoils equipped
with split flap for thickness
ratios from 6 to 12 percent
show
a considerable
increase
in maximum
lift coefficient
with increase in thickness
ratio.
Corresponding
data for the NACA
44-series
airfoils with thickness
ratios h'om 12 to 24 percent
show very
thickness.
little
For
variation
in maximum
NACA
6-series
airfoils
lift coefficient
equipped
with
with
split
flaps the maximum
lift coefficients
increase
rapidly
with
increasing
thickness
over a range of thickness
ratio, the range
beginning
at thickness
ratios between
6 and 9 percent,
depending upon the camber.
The upper limit of this range for the
symmetrical
NACA
64- and 65-series
airfoils
appears
to be
greater
than 21 percent
and for the NACA 63- and 66-series
airfoils, approximately
18 percent.
Between
thickness
ratios
of 6 and 9 percent
the values of maximum
lift coefficient
for
the symmetrical
NACA
6-series
airfoils
are essentially
the
same regardless
of thickness
ratio and position
of minimum
pressure
on the basic thickness
form.
The maximum
lift
coefficient
decreases
with rearward
movement
of minimum
pressure
18 percent.
for the airfoils
having
thickness
ratios
between
9 and
SUMMARY
OF
.AIRFOIL
35
DATA
I I
IVACA
L2
14-5er/es
(Z-d/g
f]
i -_
/c
/.2
"/
.8
/_m
(a)
CW
f T/_CA
Z l-ser_es
_7._
.._
IVACAOO-ser/e.s(d-d/q/t)
.8
-___._
/.P
5yrnbo/.£
z.o
!-dig/i)
/.5
with
flogs
oorresp.ond
to
c.:O._,
___ -o
and
0.6
ezi=0.6
"o
/f
---'-_-% _'-:_
-{
1.2
X
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c,,:o.4 _,,_0.0
o-
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u
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Cb
1.6
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Cli
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(c)
...._,...t
_
I. C
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"-'_- _ >"
_""_--_-_
!
(d)
f
I. _?
04
end
0.6
e,_ : O.4
16:
1.8
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"-o
c_ :0.2
L2
L6
.8
LZ
"..o
i.
4
8
A,7-foil
12
I_
ZO
thickness,
pea'cent
of
L2
24
chord
Z8
?2
0
4
8
Airfoil
(a) NAOA tou_-di_it series,
(e) NACA &'l-serieso
(e) NACA 6_series,
Fleisll_
: 0
41.--Vuriation
of maximum
section lift coefficient
I_
thickness_
I_
20
28
?g
airfoil sections of different
cambers.
percent
of
24
cMord
(b) N.&O.& four- and. fiTe,-di6it _erie&
(d) NACA 64-series.
(f) NAOA 66-series,
with airfoil thickness
ratio at several
Reynolds
numbers
for a number
of NACA
36
REPORT
NO.
824--NATIO:N'AL
ADVISORY
COMMITTEE
:FOR
AERONAUTICS
r
%
(
i
i
"-2
I
!
"b
I
i
i
f15
_S_S_S
.........
--_
o_--
k_
t
/
i_
%
N
=
%
c_
_
%
P._ _uq/o/jjaoo
%
Eo_p
eo
LIo/(oa
"N
T
S
.<
Z
_ e
ego
4
i-
(3
g _
c_
iii'
i
i
%
%
Y
k
SUMMARY
Substantial
increments
in maximum
lift
increase
in camber
are shown for the NACA
of moderate
split flaps.
percent
and
AIRFOIL
lift coefficient
is affected
very
For thickness
ratios
greater
lift coefficients
of the NACA
little by
than
15
63- and
37
DATA
2.O
coefficient
with
6-series
airfoils
thickness
ratios
(10 to 15 percent
chord)
with
For the airfoils
having
thickness
ratios
of 6
for the airfoils having
thickness
ratios of 18 or 21
percent,
the maximum
a change
in camber.
percent,
the maximum
64-series
equipped
maximum
OF
/.6
q)
z2
airfoils cambered
for a design lift coefficient
of 0.4
with split flaps are greater
than the corresponding
lift coefficients
of the NACA
44-series
airfoils.
o O.OOP r-oughness
o
.00_I r-ouqhness
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
tile maximum-lift
data
for
three-dimensional
wings
are compared
with
section
data,
account
should
be taken
of the span lc.ad distribution
over
the wing.
The predicted
maximum
lift coefficient
for the
wing will be somewhat
lower than the maximum
lift coefficients of the
the spanwise
sections
used because
of the
distribution
of lift coefficient.
amounts
to about 4 to 7 percent
an aspect
ratio of 6.
Maximum-lift
data
obtained
nonuniformity
of
The difference
for a rectangular
from
tests
wing
of a number
with
of
wings and airplane
models in the Langley
19-foot
pressure
tunnel
are presented
in table II.
Although
section
data at
tlle Reynolds
numbers
necessary
to permit
a detailed
comparison
are 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
configurations.
LIFT CHARACTERISTICS
OF ROUGH
AIRFOILS
Two-dimensional
data.--Most
recent
airfoil
tests,
especially of airfoils with the {hicker 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
0.20c from the leading
edge have
little
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 lift-curve
slope, particularly
for the thicker
airfoils having
the position
of minimum
pressure
far back.
These data are for a Reynolds
number
of 6 >( 106.
Maximum-
918392--51----4
1_
0
4
_
.O/ /Smoofhr-Oughness
8
/2
Revno/ds
/6
number,
2(7
24x/8"
}:1
FIGURE 43.--Effects of Reynolds number on maximum section lift coefficient c_...
NACA 63(420)-422 airfoil with roughened and smooth leading edge.
lift-coefficient
data
at
a Reynolds
number
of 6X106
of the
for
a
large number
of NACA
airfoil sections
with standard
roughness are presented
in figures 39 and 41:
The variation
of
maximum
lift coefficient
with thickness
for the NACA
fourand 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 NACA
00-series
airfoils
of
6 percent
thickness.
For a given thickness
15 percent,
the values
of maximum
lift
ratio greater
than
coefficient
for the
four- and five-digit-series
airfoils are substantially
Much less variation
in maximum
lift coefficient
the same.
with thick-
ness 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 abfoils
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 a rearward
movement
of the position
of minimum
pressure.
Except
for the NACA
44-series
airfoils of 12 to 15 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
for the plain airfoils
the
same
as those
observed
38
REPORT
NO.824--NATIONAL
ADVISORY
COMMITTEE
FORAERONAUTICS
i
/.6
_1.2
--
/
--
"\
b
/
_.8_
o
(
AS do/ivened
by shop,
d
_
i
/
As rich'repealby shop,
/'
tt
m As delivered
by shop,
._..zl
-0
t_st 468
520
Fsnol TDT
condition,
TDT
lest
/
o
test
Fl:_ol TOT
condition
TDT
test
498
464
TOT test
test 494
523
FiY_olcondition,
TOT
o
/
/
(b)
(a)
=4
-8
8
0
15
(a) NAOA
24
-8
(c)_/
0
5echbn
2412.
FIGURE 44.--Lift characteristics
8
ongle
15
of o/tock,
(b) NACi
2415.
_
24
deq.
-8
of the NACA 23012, 2412, and 2415 airfoil sections as affected by normal
0
8
model inaccuracies.
24
15
(c) NACA
23012.
R=9X106
(approx.).
.72
The maximum
lift coefficient
may be lowered
by failure
to
maintain
the true airfoil contour
near the leading
edge, but
no systematic
data on this effect have been obtained.
Examples
of this effect that were accidentally
encountered
are
presented
in figure 44, in which lift characteristics
are given
for accurate
and slightly
inaccurate
models.
The
model
inaccuracies
were so small that they were not found previous
to the tests.
Three-dimensional
data.--Tests
of several
airplanes
in the
I
Langley
full-scale
tunnel
(reference
42) show that many factors besides
the airfoil sections
affect the maximmn
lift coefficient
of airplanes.
Such
factors
as roughncss,
leakage,
leading-edge
air intakes,
armament
installations,
nacelles,
and fuselages
make it difficult
to correlate
the airplane
maximum
lift with
the airfoils
used,
even when
the flaps are
retracted.
The various
flap configurations
used make such
a correlation
even more difficult
when the flaps are deflected.
q_
k)
._)"
When
lowest
.--
the flaps
maximum
were retracted,
lift coefficients
both the highest
obtained
in recent
and the
tests of
airplanes
and complete
mock-ups
of conventional
configurations in the Langley
full-scale
tunnel
were those
obtained
with NACA
6-series
airfoils.
Results
obtained
from tests of a model of an airplane
in
.Z
0
/
i
_ . Z<:<_.'c'/
pFC_UFe
(L
0I
I
,
ci
tunne/)
the Langley
19-foot
pressure
tunnel
and of the airplane
in
the Langley
full-scale
tunnel
are presented
in figure
45.
Both tests were made at approximately
the same Reynolds
number.
The results
show that the airplane
in the service
condition
had a maximum
lift coefficient
more
than
0.2
rocjlc_ty ?-u,mPTe
I)
f, iIl-_ccale
lower
:_ /
FIOUliE 45.--The
O
effects
J
U
/Y
/5
of surface conditions on the lift characteristics
airplane.
R=2.SX106.
ZO
Zd
of a fighter-type
than
slope.
Some
was obtained
that
of the
model,
as well
as a lower
lift-curve
improvement
in the airplane
lift characteristics
by scaling leaks.
These results
show that air-
plane lift characteristics
reproduced
on large-scale
are strongly
affected
smooth
models.
by
details
not
SUMMARY
_2
OF
AIRFOIL
39
DATA
J
;0
i
0
A,'olur_o/tr-onsi/l'On
o
7r-m?s/h'on
f/xod
2
i!
-4
ot.
IOe
I
---
0
4
8
Anqle
of
/2
o/toch_
_
/6
deg
20
24
_¢
8
Angle
12
of o;/och,
16
ZO
v(, dec3
24
28
FIGURE 46.--The effect on the lift characteristics
of fixing the transition
on a model in the
Langley 19-foot pressure tunnel.
R=2.7XlO 6. (Model with Davis airfoil sections.)
FIGURE 47.--The effect on the lift characteristics
Langley 19-foot pressure tunnel.
R=2.TX106.
Lift characteristics
obtained
in the Langley
19-foot pressure tunnel
for two airplane
models in the smooth
condition
and with transition
fixed at the front spar are presented
in
figures 46 and 47.
In both cases, the lift-curve
slope was decreased
throughout
most of the lift range with fixed transition.
The maximum
lift coefficient
was decreased
in one
case but was increased
in the other case.
drag coefficient
at high lift coefficients.
The resulting
drag
coefficients
may be excessive
at cruising
lift coefficients
for
heavily
loaded,
high-altitude
airplanes.
Airfoil sections
that
have suitable
characteristics
when smooth
but have excessive
drag
coefficients
when
rough
sponding
to cruising
or climbing
uneonservative.
The decision
UNCONSERVATIVE
as to whether
of fixing the transition on a model in the
(Model with NACA airfoil sections.)
at lift
coefficients
correconditions
are classified
as
a given
airfoil
section
is conserv-
AIRFOILS
The attempt
to obtain low drags, especially
for long-range
airplanes,
leads to high wing loadings
together
with relatively
low span loadings.
This tendency
results
in wings of high
aspect
ratio that
require
large
spar
depths
for structural
efficiency.
The large
spar depths
require
the use of thick
root sections.
This trend
to thick root sections
has been encouraged
by
the relatively
small increase
in drag coefficient
with thickness
ratio of smooth
airfoils
(fig. 12).
Unfortunately,
airplane
wings are not usually
constructed
with smooth
surfaces
and,
in any case, the surfaces
cannot be relied upon to stay smooth
under
all service
conditions.
The effect of roughening
the
leading
edges of thick airfoils is to cause large increases
in the
ative will depend
upon the power
and the wing loading
of
the airplane.
The decision
may be affected
by expected
service
and operating
conditions.
For example,
the ability
of a multiengine
airplane
to fly with one or more engines inoperative
in icing conditions
or after
suffering
damage
in
combat
may be a consideration.
As an aid in judging
whether
the sections
are conservative,
the lift coefficient
corresponding
to a drag coefficient
of 0.02
was determined
from the supplementary
figures for a large
number
of NACA
airfoil
sections
with roughened
leading
edges.
The variation
of this critical lift coefficient
with airfoil thickness
ratio and camber
is shown in figure 48.
These
data show that, in general,
the lift coefficient
at which
the
drag coefficient
is 0.02 decreases
with rearward
movement
of
40
REPORT
NO.
824--NATIONAL
ADVISORY
COMEMITTEE
FOR
AERONAUTICS
position
of minimum
pressure.
The
thickness
ratio
for
which this lift coefficient
is a maximum
usually
lies between
12 and 15 percent;
variations
in thickness
ratio
from this
optimum
range generally
cause rather
sharp decreases
in the
critical
lift coefficient.
The
addition
of camber
to the
symmetrical
airfoils usually
causes an increase
in the critical
lift coefficient
except for the very thick sections,
in which case
increasing
the camber becomes
relatively
ineffectual
and may
be actually
harmful.
All the data of figure 48 correspond
to
a Reynolds
number
of 6X106.
As shown in figure 49, the
drag coefficient
at flight values of the Reynolds
number
may
be considerably
lower than the drag coefficient
at a Reynolds
number
of 6X 106 if the roughness
is confined
to the leading
edge.
PITCHING
MOMENT
The variation
of the quarter-chord
pitching-moment
coefficient at zero angle of attack
with airfoil thickness
ratio and
camber
is presented
in figure 50 for several
NACA
airfoil
sections.
The quarter-chord
pitching-moment
coefficients
of
the
NACA
four- and five-digit-series
airfoils
become
less
negative
with increasing
airfoil thickness.
Almost
no variation in quarter-chord
pitching-moment
coefficient
with airfoil thickness
ratio or position
of minimum
pressure
is shown
by the NACA 6-series airfoil sections.
As might be expected,
increasing
the amount
of camber
causes an almost
uniform
negative
increase
in the pitching-moment
coefficient.
As discussed
previously,
the pitching
moment
of an airfoil
section
is primarily
a function
of its camber,
and thin-airfoil
theory
provides
a means for estimating
the pitching
moment
from
the mean-line
data
presented
in the supplementary
figures.
A comparison
of the experimental
cient and theoretical
values for the mean
in figure 51.
The experimental
cients for NACA
6-series airfoils
load type
theoretical
lines with
coefficients
LO
0
4
8
12
Airfoil
(a)
FIGVnE
48.-Variation
thickness
Rffi6X106.
and
camber
16
#h/ckness,
NACA
four-
and
(b)
NACA
63-series.
(e)
NACA
64-series.
(d)
NACA
65-series.
(e) NACA.
66-series.
of the
lift
coefficient
for a number
20
percen/
five-digit
airfoil
28
32
sections
to a drag
with
values of the moment
coefficambered
with the uniform-
mean line are usually
about
three-quarters
of the
values (figs. 50 and 51).
Airfoils employing
mean
values of a less than unity, however,
have moment
somewhat
more negative
than those indicated
by
theory.
The use of a mean line having
a value of a less than
unity,
therefore,
brings
about
only a slight
reduction
in
pitching-moment
coefficient
for a given design lift coefficient
when compared
with
the value obtained
with a uniformload type mean line.
The experimental
moment
coefficients
for the NACA
24-, 44-, and 230-series
airfoils are also less
negative
than those indicated
by theory but the agreement
is closer than for airfoils having
the uniform-load
type mean
line.
The pitching-moment
data for the airfoils
equipped
with
simulated
split flaps deflected
60 ° (fig. 50) indicate
that the
value of the quarter-chord
pitching-moment
coefficient
becomes more
negative
with increasing
thickness
for all the
ah'foils tested.
For the thicker
NACA
6-series sections
the
chord
series.
corresponding
of NACA
24
of
moment
coeffilines is presented
coefficient
roughened
of 0.02
leading
with
edges.
magnitude
movement
of the moment
of the position
coefficient
increases
with
of minimum
pressure.
rearward
SUMMARY
OF
AIRFOIL
DATA
41
%
I
I
!
!
REPORT
42
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR AERONAUTICS
0
CO
O
C_ -.2
q)
I
(b!
_ all
_ -_S-
e
0
I_
A it" fo/I fh,,'ol_n_mj
(a)
NACA
four
and
five-digit
(b)
serif.
24
_o
percent
of
z_
chr_,4
blACA63-seri_s.
I
!
i
'
"
o
'
"",
o 0 -El .f
---+-
1
I
'
I
zx
I
.4
I
2
E
--
I
i
I
G
_
.....
i
._ -./
CO
"_
=
:Lk,
.cj
2
:_7 _ +_, o ,
r
"¢--
t,_
f ,io
0
C
..__.____
O0
©
___
.?
_xt
.,d_
__
_
---T--
--
_..3
'
_
i
."1_{3
]
-'_0
4
8
12
ti_icHmems>
AiPfoil
(c)
16
pel-r_mf
2o
of
4
o
L'8
Lw
8
IZ
thichness_
Al'rfoi/
chor-d
(d)
NACA64-series.
IG
per-ce_f
NACA
'
of
20
cho_-d
airfoil
sections
" 2_
Z8
65-series.
I
__
]
oO
- b .z
A
.':7
24
/1,'r'fo,
"1
t'_/c'tw_es'%
(e) NACA
F_(iullE
50.--Variation
of sect
ion
quarter-chord
pitching-moment
coefficient
(measured
at
an
angle
R=6X10_,
percenf
of
28
chord
66-series.
of attack
of 0 a) with
airfoil
thickness
ratio
for
several
NACA
of different
cam
her,
SUMMARY
OF
/
AIRFOIL
increasing
opposite
/
thickness.
For
the
appears
to be the case.
/
_5
HIGH-LIFT
/
-./2
6_3-61 _
_./
a-05,,,,
_ -.08
a=GS,,
7
o'"
--6,ga- 41_ 0=0.5,,'
.-654-42/
,-65o-415
-#3.
4-420
6_ 4-,_go. a:a_ i/.6_(2/:_)_z/8
/
(3
_d
/
7
0
FIGURE
t
"" "'6"6(21_)-21
d--230/2
_ a-O.6
I
-.02
-.O_Z
-.06
-.OB
-.10
-.Ig
Theore//co/
rnomenf
coefficl'en/
for _I_
rneon /i77e obou f quor/erchord'po/7_f
51.--Comparison
of
theoretical
and
NACA
POSITION
The
center
section
o/_:._-24z_
'_ -.04
variation
of
corresponding
OF
measured
airfoils.
pitching-moment
-.14
oirfoil
coefficients
-.16
for
some
R=6X10_.
AERODYNAMIC
CENTER
chordwise
position
of the aerodynamic
to a Reynolds
number
of 6X 106 for a
large
number
of NACA
airfoils
is presented
in figure
52.
From
the data
given
in the supplementary
figures
there
appears
to be no systematic
variation
of chordwise
position
of aerodynamic
center
with Reynolds
number.
The data
for the NACA 00- and 14-series
airfoils,
presented
for thickness ratios
less than
12 percent,
show that
the chordwise
position
of the aerodynamic
center
is at the quarter-chord
point
and does not vary
with airfoil
thickness.
For the
NACA
24-, 44-, and 230-series
airfoils
with thickness
ratios
ranging
from 12 to 24 percent,
the chordwise
position
of the
aerodynamic
center
is ahead of the quarter-chord
point and
moves forward
with increase
in thickness
ratio.
The chordwise
the quarter-chord
moves
rearward
in accordance
6-series
airfoils,
the
DEVICES
airfoils equipped
53.
These
data
show that the maximum
lift coefficient
increases
less rapidly
with flap deflection
for the more highly
cambered
section.
Lift characteristics
of three NACA 6-series
airfoils with split
flaps are presented
in reference
44 and figure 54.
The maximum-lift
increments
for the 12-percent-thick
sections
were
only about three-fourths
of that increment
for the 16-percentthick section.
The maximum
lift coefficient
for the thicker
/
/
654-42/,
NACA
Lift characteristics
for two NACA 6-series
with plain
flaps
are presented
in figure
65_-6/8-"
_
43
DATA
position
of the aerodynamic
center is behind
point
for the NACA
6-series
ah'foils
and
with increase
in airfoil thickness,
which
is
with
the trends
indicated
by perfect-fluid
theory.
There
appears
to be no systematic
variation
chordwise
position
of the aerodynamic
center with camber
position
of minimum
pressure
on the basic thickness
form
these airfoils.
with
flap deflected
is about
the same
as that
obtained
for the NACA
23012 airfoil
in the now obgolete
Langley
variable-density
tunnel
(reference
45) and in the Langley
7- by 10-foot tunnel
(reference
46).
Tests
of a number
of slotted
flaps on NACA
6-series
airfoils (supplementary
figures and reference
47) indicate
that
the design
parameters
necessary
to obtain
high maximum
lifts are essentially
similar
to those
for the NACA
230series sections
(references
48 and 49).
Lift data
obtained
for typical
hinged
single slotted
0.25c flaps (fig. 55 (a)) on
the NACA
63,4-420
airfoil
are presented
in figure 55 (b).
A maximum
lift coefficient
of approximately
2.95 was obtained
for one of the flaps.
Lift
characteristics
for the
NACA
653-118
airfoil
fitted
with
a double
slotted
flap
(reference
47 and fig. 56 (a)) are presented
in figure 56 (b).
A maximum
lift coefficient
of 3.28 was obtained.
It may
be concluded
that
no special
difficulties
exist in obtaining
high maximum
lift coefficients
with slotted flaps on moderately
thick NACA
6-series
sections.
Tests of airplanes
in the Langley
full-scale
tunnel (reference
42) have shown
that
expected
increments
of maximum
lift
coefficient
are obtained
for split flaps (fig. 57) but not for
slotted
flaps (fig. 58).
This failure
to obtain
the expected
maximum-lift
increments
with slotted flaps may be attributed
to inaccuracies
of flap contour
and location,
roughness
near
the flap leading
edge, leakage,
interference
from flap supports, and deflection
of flap and lip under load.
LATERAL-CONTROL
An adequate
discussion
DEVICES
of lateral-control
devices
is outside
of
or
for
the scope of this report.
The following
brief discussion
is
therefore
limited
to considerations
of effects of airfoil shape
on aileron characteristics.
The data of reference
43 show important
forward
movements of the aerodynamic
center with increasing
trailing-edge
angle for a given airfoil thickness.
For the NACA 24-, 44-,
and
230-series
airfoils
(fig. 52) the
effect
of increasing
trailing-edge
angle is apparently
greater
than
the effect of
The effect of airfoil shape on aileron effectiveness
may be
inferred
from the data of figure 59 and reference
50.
The
section
aileron
effectiveness
parameter
Aa0/Aa is plotted
against
the aileron-chord
ratio cJc for a number
of airfoils
of different
type
in figure
59.
Also shown
in this figure
are the theoretical
values
of the parameter
for thin airfoils.
REPORT
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
.22
26
.24
28
4
8
Airfo//
/2
/8
fh/ckness,
(a) NACA
(c) NACA
Fmul_
L
52.--Variation
of section
20
percent
of
24
chord
28
32
240
4
8
12
16
20
24
A/r£oi/ ÷hickness, /oercenf of chord
four- and five-digit series.
64.series.
ch0rdwise position of the aerodynamic
(b) NAOA
(d) NACA
(e)NAOA
center
with airfoil thickness
ratio for several
NACA
28
_-se_les.
65.series.
66-se,
rles.
airfoil sections of different
cambers.
Rffi6Xl0 I.
32
SUMMARY
/VACA
OF AIRFOIL
DATA
45
66(215)-216-.
..4,_4"
/
//S"
J
I)_ -4
.:.:;';"
i ,_' 11
P if
/¢
(opprox.)
o
NACA
NACA
o
0
NACA
NACA
66(2/5J-2/6
23012
G.Ox/Oe
3.5
"from f'ef.. 45)
-20
0
20
def/ecfionj
Flop
40
6:,
60
66(215)-216 air-
data show no large consistent
trends of aileron-effectivevariation
with airfoil section
for a wide range of thickdistributiotls
and thickness
ratios.
In order to evaluate
aileron characteristics
from section data, a method
of analysis
is necessary
that will lead to results
comparable
to the usual
curves
of stick force
against
helix angle pb/2V
for threedimensional
data.
The analysis
that
follows
is considered
suitable
for comparing
two-dimensional
data.
the
relative
merits
of ailerons
from
of the aileron
in angle of attack
eter 5cRa, which
from
neutral
and
from
is plotted
is the
the
neutral.
against
product
resulting
This
equivalent
the hinge-moment
of the aileron
increment
20
FIGURE 54.--Maximum
change
paramdeflection
of hinge-moment
lift coefficients
6.0
6.0
40
deflection,
60
6:: deg
for some NACA
split flaps.
,90
airfoils fitted
I00
with 0.20-airfoil-chord
coefficient
based on the wing chord.
This method
of analysis
takes
into
account
the
aileron
effectiveness,
the
hinge
moments,
and the possible
mechanical
advantage
between
the controls
and the ailerons.
The larger
the value of Aa 0
for a given value of the hinge-moment
parameter,
the more
advantageous
the combination
should
be for providing
a
large
value
tion
that
as
Two-dimensional
data
are presented
in the form of the
equivalent
change in section
angle of attack
Aao required
to
maintain
a constant
section
lift coefficient
for various
deflections
0
Flop
FIC,URE 53.--Maximum
lift coel_cients for the NACA 65,3-618 and NACA
foils fitted with 0.20-airfoil-chord plain flaps. R=6X10 _.
The
ness
ness
80
deg
(e:£)-
©_I-212
651-21-P
the
for a given
aileron
airplane
involves
rolls
operates
is not
an overestimation
of
attack
the
span
effects
of pb/2V
the
on
the
the method
dimensional
not
considered.
and
other
In
force.
a constant
entirely
of the
hinge-moment
of the ailerons
are
control
at
correct,
effect
possible
of
assumpcoefficient
however,
of changing
coefficient.
spite
The
lift
In
and
angle
addition,
three-dimensional
these
inaccuracies,
provides
a useful means
of comparing
characteristics
of different
ailerons.
the
two-
46
REPORT
NO.
824------NATIONAL
ADVISORY
\
I
COMMITTE'E
FOR
AERONAUTICS
SUMMARY
000-
OF
AIRFOIL
47
DATA
--_
• 781
r-efroc/ed
Flop
I
//,_
I
S
,..Flop
pofh
GrTd
-
I
1
I
of ogreemem/
pred/'c'e_
f_'_:_S_/7_S-
plvof
piVOT
TPom
U
.---"
to 45 ° deflect/on-'"
Flop
de_leefed
f_
_7._ o
I
I
1, '
o
_,._
de-fle-cfion
65 _
X
3.2
J
/
/
28
I
fneosLyr-ed
/
.2/z r/op)X_,\/
/-/0t9
I
/
.8
808
I
be/_veen
/
0
.2
.4
.6
ACL,. pr-edlcted
.8
LO
FIGURE 57.--Comparison
between measured values of the increments
to flap deflection
and values predicted
from two-dimensional
/
/
L2
in lift coefficients due
data.
Split flap.
2.4
/
I
LO
_d
:< 1.6
_
.8
i
_1o
/.2
._.
Vo
/
.8
.2
/
[
/
.4
0
i
.2
4
A£'_,,
FIGURE 58.--Comparison
between
to flap deflection and values
(b)
0
20
40
Flop
deflection,
60
6_
80
IO0
deg
(a) Flap configuration.
(b) Maximum lift characteristics.
FIGURE 56.--Flap
configuration
and maximum lift coefficients for the NACA
with a double slotted flap. R=6X10 _.
65_-118 airfoil
.6
p_ed/cfed
measured
predicted
.8
LO
LZ
values of the increments in lift coefficients
from two-dimensional
data.
Slotted flap.
due
48
REPORT
NO.
SUPPLEMENTARY
8 2 4--NATIONAL
INFORMATION
ADVISORY
COMMITTEE
REGARDING
FOR
TESTS
OF
AERONAUTICS
TWO-DIMENSIONAL
MODELS
Air-flow
Symbol
Basic
airfoil
Type
characteristics
Reference
of flap
T
M
R
o
+
NACA
0009 .........................................
................................
1.93
O. 08
NACA
0015 ............................................
do ............................
1.93
.10
1.4XIO 6
X
NACA
23012 ...............................................
do ...............................
1.60
.11
2.2X106
1.93
• 10
1.4X106
1.93
.11
1.4XlO
(1)
.17
2.5X108
do .............................
(1)
.18
5.3X106
do .............................
0)
.14
6.0XlO
6
.............................
0)
13.0XlO
6
.14
6.0XlO
_
.20
to
• 48
.09
8.0Xl08
2.8X10 _
to
6.8X10 _
1.2XlO 8
Plain
C]
NACA
66(2x15)-009
0
NACA
66-009 .......................................
Plain
A
NACA
63,4-4(17.8)
Internally
_7
NACA
b
NACA
p"
r,,
(approx.)
66(2x15)-216,
04,2-(1.4)
NACA
65,2-318
Plain,
............................
a=0.6
66(2x15)-I16,
NACA
..................................
a=0.6
................................
(13.5)
................................
(approx.)
..............................
NACA
63(420)-521
NACA
66(215)-216,
NACA
...................................
(approx.)
Plain
Internally
.............................
a=O.6 .................................
66(215)-014
straight
..........................
Plain
contour
..............
...............................
balanced
.................
balanced
(1)
...............
do ..........................
0)
do ..............................
0)
..........................
1.93
51 to 55
56
57, 48
58
6
59
59
59
59
l
60
61
6.0XlO _l
0
NACA
66(215)-216,
do ............................
(')
c_
NACA
652-415 .............................................
do .............................
0)
.13
6.0XlO_
[3-
NACA
653 418
do ..............................
(1)
.13
6.0X10
t
02
q
NACA
651-421 ............................................
do ..............................
(1)
.13
6.0XlO
6
62
(1)
.14
8.0XIO
6
0
i Approaching
a=0.6
.............................
.........................................
NACA
65o1_)-213 ....................................
NACA
745A317
(approx.)
.................................
do ..............................
(1)
.13
6.0XlO
8
NACA
64,3-013
(approx.)
...................................
do .............................
0)
.13
6.0XlO
6
NACA
64,3-1(15.5)
do ..............................
(1)
• 13
6.0XIO
6
(approx.)
Internally
................................
balanced
.................
62
1.00.
.8
,_o
"Theoretical
....
vl
-
o
"
q)
_
_.6
Th_oreticol-
,2-"
_
i li
"
"'Exloerimen¢ol
_
"
7
f#
Z
ss
_
s
!
i P"
(a)
0
./
._A ;/eron
(a)
59.--Variation
" //
,/
iii
FI6UEE
,'"
of
section
$ range
aileron
chord
from
0° to
.3
rot/G
.4
1
_//
0
.I
ca/e
.Z
A/le/'or)
10%
effeetiveness
chord
(b) ,_range
with
aileron
chord
ratio
for true-airfoil-contour
Gaps sealed;
el=0.
ailerons
without
exposed
overhang
(b)
.3
ro#/o,
from
balance
.d
male
0° to 20 °.
on
a
number
of
airfoil
sections.
SUMMARY
OF
AIRFOIL
49
DATA
1
Basic
Type
airfoil
Basic
ct
Type
_/)aileron
Air-flow
characteristics
•
AI
R
.....
NACA
NACA
NACA
0009
64,2-(1.4)
03.5)
66(215)-216,
a=0.6_
O
• 150
/
True
airfoil
2 Approaching
I
0.20cplain
0.187cplain
"100/
0.20c
1.93
(_)
I
plain
0.10
I .18
(')
I
6d,
2-(Lzl)
]
I
"33t
Reference
1.4X10 e
4-0X106
9.OXi0'
airfoil
/
I
I
64
I
Referenee
el
NACA66(215)
216,a=0.61
NACA
63,4-4(17.8)
(up-
63
- -
of aileron
prox.)
0.1OO
.450
I
I O.2Oc
" ---_-4
plain
0.20c with 0.43c!
hal balance
|
/
-[
inter----[
I
contour.
1.00.
I
N_O_
I
0009,
,..
.'
""
-.
,-N/_CA
(125)
-/ U"
/'
'_,,
O>
I
-2
-4l
dNeror?
-6
de2flec//om,
_ I---
_v-
/
c/eg,
/
._ /
"-
/2
.---_ "'"
/6 ..---- ----"
-8
-.0018
FIGURE
-.0016
=00141
-.0012
-.0010
A ¢=_,
FmtTI_E
section
60.--Variation
angle
of the aileron
airfoil sections.
of the
of attack
on
hinge-moment
required
the NACA
Gaps sealed.
=0008
parameter
to maintain
0009, NACA
:O00B
:00041
=0002
0
rad/ons
a constant
64,2-(1.4)(13.5),
with
section
and
the
lift
equivalent
coefficient
NACA
change
for
in
of the
of attack
the
NACA
and
66(215)-216,
to maintain
straight-sided
a=0.6
airfoil
parameter
Acg6
a constant
ailerons
sections.
with
section
on
Gaps
the
the
lift
NACA
equivalent
coefficient
63,4-4(17.8)
change
in
for deflection
(approx.)
sealed.
a=0.6
The
NACA
64,2-(1.4)(13.5)
airfoil
shows
appreciably
smaller values of AcH_ for a given value of Aao than the other
sections
presented.
No explanation
for this difference
can
be offered,
although
some of the difference
may result from
the slightly
smaller
chord of the flap for this combination.
The effects of using straight-sided
ailerons instead
of ailerons of true airfoil
contour
are shown
in figure 61 for two
NACA
6-series
airfoils.
One of the two combinations
for
was provided
with an
combination
was without
and
hinge-moment
required
deflection
66(215)-216,
contour
on three
airfoil
sections
are shown
in figure 60.
The characteristics
of the NACA 66 (215)-216,
a = 0.6 section
are essentially
the same as those for the NACA
0009 airfoil
within
the range
of deflection
for which data are available•
data
are available
whereas
the other
angle
of true-airfoil-contour
Ae_l
For the purpose
of evaluating
the effect of airfoil shape on
the aileron
characteristics,
it is desirable
to make the comparison
with unbalanced
ailerons
to avoid confusion.
Plots
of the parameters
for plain unbalanced
flaps of true airfoil
which
balance
61.--Variation
section
internal
balance•
This difference
prevents
any comparison
between
the two
combinations
but does not affect
comparison
of the two
contours
for each case.
For the NACA
66(215)-216,
a=0.6
airfoil,
the straight-sided
aileron has more desirable
characteristics
for the range of deflections
for which data are avail-
able•
It appears,
however,
that
the straight-sided
would be less advantageous
than the aileron of true
for positive
deflections
greater
than
12 °. In the
aileron
contour
case of
the
NACA
63,4-4(17.8)
(approx.)
airfoil,
the
straightsided aileron appears
to have no advantage
over the aileron
of true airfoil
contour.
The advantage
of using straightsided ailerons
appears
to depend markedly
oll the airfoil used
but sufficient
data are not available
to determine
the significant airfoil parameters.
Figure
62 shows that in one case
the effect of leading-edge
roughness
on the aileron characteristics is unfavorable.
LEADING-EDGEAIRINTAKES
The problem
of designing
satisfactory
leading-edge
air
intakes
is to maintain
the lift,
drag,
and
critical-speed
characteristics
of the sections
while providing
low intake
losses over a wide range of lift coefficients
and intake
velocity
ratios.
The data of reference
65 show that desirable
intake
and drag characteristics
can easily
be maintained
over a
rather
small range
of lift coefficients
for NACA
6-series
airfoils.
The data of reference
65 show that the intake
losses
increase
rapidly
at
moderately
high
lift
coefficients
for the
shapes
tested.
Unpublished
data
taken
at the
Langley
Laboratory
indicate
that
shapes
such as those
of reference
65 have low maximum
lift coefficients.
Recent
data show
50
REPORT
NO.
824--NATIONAL
ADVISORY
8
..#"
-/6 ....
of
/eod/bg
<_-Smoofh
edge--"
_ "--
._
"_
0
<
available to permit such desirable configurations
signed without experimental
development.
/
-4
Aileron
-8
-.0018:0016
-.0014
de{lection,
d_g'--
-.00/2:0010
12"_
=0008:0006
--.0004
--.0002
to be de-
INTERFERENCE
/
--
AERONAUTICS
loss in maximum lift coefficient
(fig. 63).
Some pressuredistribution
data for the air intakes shown in figure 63 indicate that the critical speed of the section has been lowered
only slightly and that falling pressures in the direction of
flow were maintained
for some distance from the leading
edge on both surfaces at lift coefficients near the design lift
coefficient
for the section.
Sufficient
information
is not
- --,-/2
4
---
FOR
that air-intake
shapes can be provided for such airfoil sections with desirable air-intake
characteristics
and without
_.
_
6
Roughness
COMMITTEE
0
ACH_ _ rodORS
FIGURE 62.--Variation
of the hinge-moment
parameter AeH6 with the equivalent change in
section angle of attack required to maintain a constant section lift coefficient for deflection
of the aileron on the NACA 64,2-(1.4)(13.5) airfoil section, smooth and with roughness at
the leading edge of the airfoil. (For description of aileron, see fig. 60.)
The main problem of interference
at low Math numbers is
considered to be that of avoiding boundary-layer
separation
resulting from rapid flow expansions caused by the addition
of induced velocities about bodies and the boundary-layer
accumulations
near intersections.
No recent
systmmatic
investigations
of interference
such as the investigation
of
reference 66 have been made.
Some tests have been made of airfoil sections with intersecting
flat plates (reference 67).
These configurations
may be considered to represent approximately
the condition
of a wing intersection
with a large flat-sided fuselage
In
/'Zt-hd/_7.)
24-I'nc/_
chord
/.6
1.4
/
-'o'/
h_,:o./8_.../[
/.2
_
-.
=
S
,
:_'1>
,
/
1.0
k.
7.
"
_
,
%=4
/
[
,
Co_flgsur'aflbn
-o P/o/k? o/7-fo//--n ZJuc/-ed mode/
(low flow)
00ueted
mode/
0
Secton
ong/e
FIGURE 63.--Lift
",. ,,,•
=.
.
V, he 1135
J
8
of offock,
R
30×10'
--
.2.4_
IG
_,
24
' he
.,i !
C
=4
deg
and flow characteristics of an NACA
7-series type airfoil section
=0.186
V,. h¢ =_186
(V'
f43"--
O
Secf/bn
with leading
0"-'_"_
.4
h'ft
l
.8
coefhc(enf,
edge air intake.
1.2
¢_
/.6
SUMMARY
OF
this case, the interference
may be considered to result from
the effect on the wing of the fully developed turbulent boundary layer on the fuselage or flat plate and the accumulation
of
boundary
layer in the intersection.
These tests showed
little interference
except in cases for which the boundary
layer on the airfoil alone was approaching
conditions
of
separation
such as were noted with the less conservative
airfoils at moderately
high lift coefficients.
Some scattered
data on the characteristics
of nacelles
mounted
on airfoils permitting
extensive laminar
flow are
presented
in references
68 to 70. The data appear to indicate that the interference problems for conservative
NACA
6-series sections are similar to those encountered
with other
types of airfoil.
The detail shapes for optimum interfering
bodies and fillets may, however,
be different for various
sections if local excessive expansions
in the ftow are to be
avoided.
Some lift and drag data for an airfoil with pusher-propellershaft housings are presented in reference 71. These results
indicate that protuberances
near the trailing edge of wings
should be carefully
designed to avoid unnecessary
drag
increments.
Another type of interference
of particular
importance
for
high-speed
airplanes results in the reduction
of the critical
Mach number of the combination
because of the addition of
the induced velocities associated with each body (reference
72).
This effect may be kept to a minimum by the use of
bodies with low induced velocities, by separation
of interfering bodies to the greatest possible extent, and by such
selection and arrangement
of combinations
that the points
of maximum induced velocity for each body do not coincide.
APPLICATION
TO
WING
DESIGN
Detail consideration
of the various factors affecting wing
design lies outside the scope of this report.
The following
discussion is therefore limited to some important
aerodynamic features that must be considered in the application
of
the data presented.
APPLICATION
OF SECTION
DATA
Wing characteristics
are usually predicted
from airfoilsection data by use of methods based on simple lifting-line
theory (references 73 to 76).
Application
of such methods
to wings of conventional
plan form without spanwise discontinuities
yields results of reasonable
engineering
accuracy
(reference
77), especially
with regard to such important
characteristics
as the angle of zero lift, the lift-curve
slope,
the pitching
moment,
and the drag.
Basically
similar
methods not requiring the assumption
of linear section lift
characteristics
(references
78 and 79) appear
capable
of
yielding results of greater accuracy,
especially at high lift
coefficients.
Further
refinement may be made by consideration of the chordwise distribution
of lift (reference 80).
Wings with large amounts of sweep require special consideration (reference 81).
AIRFOIL
51
DATA
The usual wing theory assumes that the resultant air force
and moment on any wing section are functions of only the
section lift coefficient (or angle of attack)
and the section
shape.
According
to this assumption,
the air forces and
moments on any section are not affected by adjacent sections
or other features
of the wing except as such sections or
features affect the lift distribution
and thus the local lift of
the section under consideration.
These assumptions
obviously are not valid near wing tips, near discontinuities
in
deflected flaps or ailerons, near disturbing
bodies, or for
wings with pronounced
sweep or sudden changes in plan
form, section, or twist. Under such circumstances,
cross flows
result in a breakdown
of the concept of two-dimensional
flow over the airfoil
sections.
In addition
to these
cross flows, induced effects exist that are equivalent
to a
change in camber.
Such effects are particularly
marked
near the wing tips for wings of normal plan form and for
wings of low aspect ratio or unusual plan form.
Liftingsurface theory (see, for example, reference 81) provides a
means for calculating
wing characteristics
more accurately
than the simple lifting-line theory.
Although span load distributions
calculated for wings with
discontinuities
such as are found with partial-span
flaps
(references
82 and 83) may be sufficiently
accurate
for
structural
design, such distributions
are not suitable
for
predicting
maximum-lift
and stalling characteristics.
Until
sufficient data are obtained to permit the prediction
of the
maximum-lift
and stalling
characteristics
of wings with
discontinuities,
these characteristics
may best be estimated
from previous results with similar wings or, in the case of
unusual configurations,
should be obtained by test.
The characteristics
of intermediate
wing sections must be
known/or
the application of wing tileory, but da_a for such
sections are seldom available.
Tests of a number of such
intermediate
sections obtained by several manufacturers
fol
wings formed by straight-line
fairing have indicated that the
characteristics
of such sections may be obtained with reasonable accuracy by interpolation
of the root and tip characteristics according to the thickness variation.
SELECTION
OF ROOT
SECTION
The characteristics
of a wing are affected to a large extent
by the root section.
In the case of tapered wings formed by
straight-line
fairing, the resulting nonlinear variation of section along the span causes the shapes of the sections to be
predominantly
affected by the root section over a large part
of the wing area.
The desirability
of having a thick wing
that provides space for housing fuel and equipment
and reduces structural
weight or permits large spans usually leads
to the selection of the thickest root section that is aerodynamically
feasible.
The comparatively
small variation
of
minimum
drag coefficient with thickness
ratio for smooth
airfoils in the normal range of thickness ratios and the maintenance of high lift coefficient for thick sections with flaps
deflected usually result in limitation
of thickness ratio by
characteristics
other than maximum lift and minimum drag.
52
REPORT
NO.
824--NATIONAL
ADVISORY
The critical Mach number
of the section is the most serious
limitation
of thickness
ratio for high-speed
airplanes.
It is
desirable
to select a root section with a critical Mach number
sufficiently
high to avoid serious drag increases
resulting
from
compressibility
effects at the highest
level-flight
speed of the
airplane,
allowance
being made for the increased
velocity
of
flow over the wing resulting
from interference
of bodies
and
slipstream.
Available
data
indicate
that
a small
margin
exists between
the critical Mach number
and the Mach number at which the drag increases
sharply.
increase,
it becomes
increasingly
difficult
sible to avoid the drag increases
resulting
ity
As airplane
speeds
and finally imposfrom compressibil-
effects by reduction
of the airfoil thickness
ratio.
In tile cases of airplanes
of such low speeds that compressi-
bility considerations
do not limit the thickness
less than about
0.20, tlle maximum
thickness
ratio
ratio
to values
is limited
by excessive
drag
coefficients
at moderate
and high lift
coefficients
with
the surfaces
rough.
In these
cases,
the
actual
surface conditions
expected
for the airplane
should be
considered
in selecting
the section.
Consideration
should
also be given to unusual
conditions
such as ice, mud,
and
damage
caused in military
combat,
especially
in the case of
multiengine
airplanes
for which
ability
to fly under
such
conditions
is desired
with one or more engines
inoperative.
In cases for which root sections
having
large thickness
ratios
are under consideration
to permit the use of high aspect ratios,
a realistic
appraisal
of the drag coefficients
of such sections
with the expected
surface
comtitions
at moderately
high lift
coefficients
will indicate
an optinmm
aspect
ratio
beyond
which corresponding
increases
in aspect ratio and root thickness ratio will result in reduced
perforinance.
Inboard
sections
of wings on conventional
airplanes
are
subject
to interference
effects and may be in the propeller
slipstream.
The wing surfaces
are likely to be roughened
by
access
doors,
landing-gear
retraction
wells,
and armament
installations.
Attainment
of extensive
laminar
flows is,
therefore,
less likely on the itlt)oard wing panels than on the
outboard
panels.
Unless
such effects
are minimized,
little
drag reduction
is to be expected
from the use of sections
permitting
extensive
laminar
flow.
Under
these conditions,
the use of sections
such as the NACA
63-series
will provide
advantages
if the
more
conservative
laminar
flow.
sections
than
are thick, because
those
permitting
SELECTION
such sections
are
more
extensive
OF TIP SECTION
In order to promote
desirable
stalling
characteristics,
the
tip section
should
have a high maximum
lift coefficient
and
a large
range
of angle of attack
between
zero and maximum
lift as compared
with the root
section.
It is also
desirable
that the tip section stall without
a large sudden
loss
in lift.
The attainment
of a high maximum
lift coefficient
is
often more difficult
at tile tip section
than at the root section
COMMITTEE
FOR
The selection
section
presents
can be given on
of camber
that
cates the design
its weight.
The
farther
forward
will,
cient
AERONAUTICS
of the optimum
type of camber
for the tip
problems
for which no categorical
answers
the basis of existing
data.
The use of a type
imposes
heavy
loads on the ailerons
compliof the lateral-control
system
and increases
use of a type of camber
that carries the lift
on the section
and thus relieves
the ailerons
however,
have
of the section
little
effect on the maximum
unless the maximum-camber
lift coeffiposition
is
well forward,
as for the NACA
230-series
sections.
In this
case a sudden
loss of lift at the stall may be expected.
The
effects on the camber
of modifications
to the airfoil contour
near the trailing
edge, which may be made in designing
the
ailerons,
should not be overlooked
in estimating
the characteristics
of the wing.
If the root sections
are at least
moderately
thick,
it is
usually
reduced
desirable
thickness
to select
a tip section
ratio.
This reduction
with
a somewhat
in thickness
ratio,
together
with the absence
of induced
velocities
from interfering bodies, gives a margin
in critical speed that permits
the
camber
of the tip section
to be increased.
This reduction
in
thickness
ratio will probably
be limited
by the loss in maximum lift coefficient
resulting
from too thin a section.
A small
amount
of aerodynamic
washout
may
also be
uscfnl as an aid La the avoidance
of tip stalling.
The permissible
amount
of washout
may not be limited
by the increase in induced
drag, which is small for 1 ° or 2 ° of washout
(reference
73).
The limiting
washout
may be that which
causes the tip section
to operate
outside
the low-drag
range
at the high-speed
lift coefficient.
This limitation
may be
so severe
as to require
some adjustment
of the camber
to
permit
Lhe use of any washout.
A change
in airfoil section
between
the root and tip may
be desirable
to obtain
favorable
stalling
characteristics
or
to take advantage
of the greater
extent
of laminar
flow that
may be possible
on the outboard
sections.
Thus,
such combinations
as an NACA
230-series
root section
with an NACA
44-series
tip section
or an NACA
63-series
root section
an NACA
65-series
tip section
may be desirable.
It should
be noted
that
the tip sections
may easily
with
be so
heavily
loaded
by the use of an unfavorable
plan form as to
cause tip stalling
with any reasonable
choice of section
and
washout.
Both
high
taper
ratios
and large
amounts
of
sweepback
are unfavorable
in this respect
and are particularly bad when used together,
because
the resulting
tip stall
promotes
longitudinal
instability
at the stall in addition
to
the usual lateral
instability.
CONCLUSIONS
for tapered
wings because
of the lower Reynolds
number
of
the tip section.
For wings with small
camber,
the most
effective
way of increasing
tile section
maximum
lift coefficient is to increase
the camber.
The amount
of camber
used
The following
conclusions
may be drawn
from the data
presented.
Most of the data, particularly
for the lift, drag,
and
pitching-moment
characteristics,
were
obtained
at
Reynolds
numbers
from 3 to 9 X 106.
1. Airfoil sections
permitting
extensive
laminar
flow, such
as the NACA
6- and 7-series
sections,
result
in substantial
will be limited
in most
cases by either
requirements
or by the requirement
that
low drag at the high-speed
lift coefficient.
reductions
in drag at high-speed
and cruising
lift coefficients
as compared
with other
sections
if, and only if, the wing
surfaces
are fair and smooth.
the
the
criticM-speed
section
have
SUMMARY
2. Experience
with full-size wings has shown that extensive
laminar
flows are obtainable
if the surface finish is as smooth
OF
as that provided
by sanding
in the chordwise
direction
with
No. 320 carborundum
paper
and if the surface
is free from
small
scattered
defects
and
specks.
Satisfactory
results
are usually obtained
if the surface is sufficiently
fair to permit
a straightedge
to be rocked smoothly
in the chordwise
direction without
jarring
or clicking.
3. For wings
of moderate
thickness
ratios
with surface
conditions
corresponding
to those
obtained
with
current
construction
methods,
minimum
drag
coefficients
of the
order of 0.0080 may be expected.
The values
of the minimum drag coefficient
for such wings depend
primarily
on
the surface
condition
rather
than
on the airfoil section.
4. Substantial
reductions
in drag
Reynolds
numbers
may
be obtained
wing surfaces,
even if extensive
laminar
coefficient
at
high
by smoothing
the
flow is not obtained.
5. The maximum
lift coefficients
for moderately
cambered
smooth
NACA
6-series
airfoils
with the uniform-load
type
of mean line are as high as those for NACA 24- and 44-series
airfoils.
The
NACA
230-series
airfoils
have
somewhat
higher
maximum
lift coefficients
for thickness
ratios
less
than 0.20.
AIRFOIL
DATA
53
9. The effect of leading-edge
roughness
is to decrease
the
lift-curve
slope, particularly
for the thicker
sections
having
the position
of minimum
pressure
far back.
10. Characteristics
of airfoil
sections
with
the expected
surface
conditions
must be known
or estimated
to provide
a
satisfactory
basis for the prediction
of the characteristics
of
practical-construction
wings
and
the selection
of airfoils
for such wings.
11. The NACA
6"-series airfoils
provide
higher
critical
Mach
numbers
for high-speed
and cruising
lift coefficients
than earlier
types
of sections
and have a reasonable
range
of lift coefficients
within
which high critical Mach numbers
may be obtained.
12. The NACA
6-series
sections
provide
lower predicted
critical
Mach
numbers
at moderately
high lift coefficients
than
the earlier types
of sections.
The limited
data available suggest,
however,
that the NACA 6-series sections
retain
satisfactory
lift characteristics
up to higher Mach
numbers
than the earlier sections.
13. The NACA
unusual
problems
6-series
airfoils
do not appear
with regard
to the application
to present
of ailerons.
14. Problems
associated
with the avoidance
of boundal Tlayer separation
caused
by interference
are expected
to be
similar
for conservative
NACA
6-series
sections
and other
6. The maximum
lift coefficients
of airfoils with flaps are
about
the same for moderately
thick NACA
6-series sections
as for the NACA
23012 section but appear
to be considerably
lower for thinner
NACA
6-series sections.
good airfoils.
and fillets may
sive expansions
7. The lift-curve
slopes for smooth
NACA
6-series
airfoils
are slightly
higher
than
for NACA
24-, 44-, and 230-series
airfoils
and usually
exceed
the theoretical
value
for thin
airfoils.
15. Satisfactory
leading-edge
air intakes
may be provided
for NACA
6-series sections,
but insufficient
information
exists
to allow such intakes
to be designed
without
experimental
development.
Detail
shapes for optimum
interfering
bodies
be different
for various
sections
if local excesin the flow are to be avoided.
8. Leading-edge
roughness
causes
large
reductions
in
maximum
lift coefficient
for both plain airfoils
and airfoils
equipped
with split flaps deflected
60 ° . The decrement
in
maximum
lift coefficient
resulting
from standard
roughness
is essentially
the same for the plain airfoils as for the airfoils
equipped
with the 60 ° split flaps.
LANGLEY
I_/_EMORIAL
NATIONAL
LANGLEY
J_kERONAUTICAL
.ADVISORY
:FIELD,
COMMITTEE
VA.,
March
LABORATORY,
FOR
5, 1945.
.AEROI_AUTICS,
APPENDIX
METHODS OF OBTAINING DATA IN THE LANGLEY TWO-DIMENSIONAL LOW-TURBULENCE TUNNELS
By MILTON M. KLEIN
DESCRIPTION
OF
TUNNELS
The Langley two-dimensional
low-turbulence
tunnels are
closed-throat
wind tunnels having rectangular
test sections
3 feet wide and 7_/ feet high and are designed to test models
completely
spanning
the width of the tunnel
in twodimensional
flow. The low-turbulence
level of these tunnels,
amounting to only a few hundredths
of 1 percent, is achieved
by tile large contraction
ratio in tile entrance
cone (approx.
20:1)
and by the introduction
of a number
of finewire small-mesh
turbulence-reducing
screens in the widest
part of tile entrance
cone.
The chord of models tested in
these tunnels is usually about 2 feet, although thecharacteristics at low lift coefficients of models having chords as large
as 8 feet may be determined.
The Langley two-dimensional
low-turbulence
tunnel operates at atmospheric
pressure and has a maximum speed of
approximately
155 miles per hour.
The Langley
twodimensional
low-turbulence
pressure tunnel operates at pressures up to 10 atmospheres absolute and has a maximum
speed of approximately
300 miles per hour at atmospheric
pressure.
Standard
airfoil tests in this tunnel arc made of
2-foot-chord
wooden models up to Reynolds
numbers
of
approximately
9 X 106 at a pressure of 4 atmospheres
absolute.
The lift and drag characteristics
of airfoils tested in these
tunnels are usually measured by methods other than the use
of balances.
The lift is evaluated from measurements
of the
pressure reactions on the floor and ceiling of the tunnel.
The
drag is obtained
fl'om measurements
of static and total
pressures in the wake.
Moments are usually measured by a
balance.
el
i
el
T
Creel4
a
B
c
ca
Cd p
Cd
T
Ct
54
t
coefficients
of potential
function
for a
symmetrical
body
fraction of chord from leading edge over
which dcsign load is uniform
dimensionless
constant
determining
width
of wake
chord
drag coefficient corrected
for tunnel-wall
effects
drag coefficient uncorrected
for tunnel-wall
effects
drag coefficient measured in tunnel
section lift coefficient corrected for tunnelwall effects
for tunnel-
design lift coefficient
lift coefficient measured in tunnel
moment
coefficient
about
quarter-chord
point corrected for tunnel-wall
effects
moment
coefficient
about
quarter-chord
point measured in tunnel
average of velocity readings of orifices on
floor and ceiling used to measure blocking
at high lifts
average value of F in low-lift range
potential function used to obtain n-factor
total pressure in front of ah.foil
total pressure in wake of airfoil
coefficient of loss of total pressure in the
Cmc/4
t
F
Fo
Y
Iio
HI
wake (H°_0H')
maximum value of II_
tunnel height
Hcm(lx
hT
K = cd'
Cd T
L
Lt
q0
true lift resulting from a point vortex
lift associated
with a point vortex
as
measured by integrating
manometers
upstream
limit of integration
of floor and
ceiling pressures
downstream
limit of integration
of floor
and ceiling pressures
resultant
pressure
coefficient;
difference
between local upper- and lower-surface
pressure coefficients
static pressure in the wake
free-stream
dynamic pressure
S
static-pressure
S,
static-pressure
m
n
PR
SYMBOLS
A1, A2, . . . A,
section lift coefficient uncorrected
wall effects
C lt
Pl
V
AV
coefficient
coefficient
(_)
in
the
distance along airfoil surface
velocity,
due to row of vortices,
point along tunnel walls
free-stream
velocity
increment
in free-stream
velocity
blocking
wake
at any
due
to
SUMMARY OF AIRFOIL DATA
!
V"
local velocity at any point on airfoil surface
potential function for flow past a symmetrical body
distance
along chord or center
line of
tunnel
v
Y
variable
Yw
dy_
dx
z
Ol Io
O_ o
!
F
V_
*/b
W
A
of integration
(-_)
slope of surface
distribution
of symmetrical
iF
J----2_l°g
_rz
sinh 2hr
iF log sinh 7r
27r
- \
F strength
of a single vortex
z
variable
complex
OF
factor
)
(18)
hr tunnel
height
thickness
4-
.+
for tunnelm
section angle of attack measured in tunnel
strength of a single vortex
ratio of measured lift to actual lift for any
type of lift distribution
v-factor for additional-type
loading
v-factor for basic mean-line loading
_-factor applying to a point vortex
component of blocking factor dependent
on
shape of body
quantity
used for correcting effect of body
upon velocity measured by static-pressure
orifices
component of blocking
size of body
potential function
stream function
2hr
(x+iy)
.+
complex variable (x+iy)
angle of zero lift
section angle of attack corrected
wall effects
MEASUREMENT
The factor _ was obtained as follows: The image system
which gives only a tangential component of velocity along the
tunnel walls is made up of an infinite vertical row of vortices
of alternating
sign as shown in figure 64. If the sign of the
vortex at the origin is assumed to be positive, the complex
potential function/for
this image system is
where
distance perpendicular
to stream direction
ordinate
of symmetrical
thickness
distribution
distance perpendicular
to stream direction
from position of Hc_a_
Y
yt
OL 0
corrected indicated tunnel velocity
tunnel velocity measured by static-pressm'e
orifices
55
dependent
on
_
i7 u
hr
Upper"
x"-
"-_
_Pos///on
_volL.,,
of
n
po/mf
vorfex
x
l
Z_ o_vef"
•+
FIGURE
64.--Image
system
for
calculation
.,_,.
of _-factor
low-turbulence
_c_//--""
in
the
Langley
two-dimensional
tunnels.
The velocity u, due to the row of vortices,
along the tunnel walls where
hr
y=-_
is then obtained as
at any point
LIFT
1_
The lift carried by tile airfoil induces an equal and opposite
reaction upon the floor and ceiling of the tunnel.
The lift
may therefore be obtained by integrating
the pressure distribution along the floor and ceiling of the tunnel, the integration being accomplished
with an integrating
manometer.
Because the pressure field theoretically
extends to infinity in
both the upstream and the downstream directions, not all the
lift is included in the length over which tile integration
is
performed.
It is therefore necessary to apply a correction
factor _ that gives the ratio of the measured lift to the actual
lift for any lift distribution.
The calculation was performed
by first finding the correction
factor _ applying to a point
vortex and then determining
the weighted average of this
factor over the chord of the model.
7rX
u=2_ r sech hr
(19)
where x is the horizontal distance from the point on the wall
to the origin.
The resultant
pressure coefficient PR is then
given by
PR=_
2r
=h_
_x
sech hr
(20)
where V is the free-stream
velocity.
The lift manometers
integrate
the pressure distribution
along the floor and ceiling from the downstream
position n
to the upstream
position m (fig. 64).
For a point vortex
56
REPORT
located
a distance
x from
the tunnel,
the limits
The lift L' associated
the
integrating
:NO.
the origin
along
of integration
with a point
manometers,
the
become
vortex,
is given
L' =
824--:NATIONAL
ADVISORY
center
line
of
n--x
and m--x.
as measured
by
by
qoPR dx
(21)
COMMITTEE
FOR
The values
low-turbulence
AERO=NAUTICS
of _b and
pressure
for the Langley
tunnel
are given
_a
table for a model having
the _-factor
corresponding
(indicated
by the value
additional
type
two-dimensional
in the following
a chord length of 2 feet, where _b is
to the basic mean-line
loading
of a) and va is the _-factor
for the
of loading
as given
by
thin-airfoil
theory:
l--X.
where q0 is the free-stream
The true lift L resulting
dynamic
from the
L
pressure.
point vortex
is given
by
2q0r
a
yb
1.0
.8
.6
.4
.2
0
0.9347
.9342
.9336
.9330
.9325
.9322
=V
_o=0.9296
The
correction
factor
yz is then
In order
additional
calculated
1
_
n-z
_X
yields
2
_=_
Fe-'_/h_(e_'/hT--e'm/hr)7
tan-I
L 1_
the variation
type of lift
for the class
of _ with
distribution,
C additional
variations
in the
the value
of _ was relift distribution
given in
figure 6 of reference
74.
The value of _, for this case was
0.9304,
as compared
with 0.9296 for a thin airfoil.
Because
of the small variation
of _ with the type of additional
lift,
the value for thin-airfoil
additional
lift was used for all calculations.
The lift coefficient
of the model
in the tunnel
=_-I-zarJ,_ sech hr dx
which
to check
e-_/hre_(m+'__)/h_
(22)
-J
the Langley
two-dimensional
low-turbulence
tunne!s,
the orifices
in the floor and ceiling
of the tunnel
used to
measure
the lift extend
over a length
of approximately
13
feet.
A plot of _ against
x for the Langley
two-dimensional
low-turbulence
pressure
tunnel
is shown
in figure 65.
The
_-factor
for a given
lift distribution
is obtained
from
the
expression
uncorrected
for blocking
c{ is given in terms of the lift coefficien_ measured
in the tunnel
Czr and the design lift coefficient of the airfoil c_, by the following
expression:
In
(24)
c,__CZT__I/___I)
Z _
"qa
_V]a
Because
that the
Cl_
_ does not differ much from n_, it is not necessary
basic loading
or the design lift coefficient
be known
with great accuracy.
Because
of tunnel-wall
and other effects,
the lift distribution over the airfoil in the tunnel
does not agree exactly
with
the assumed
lift distribution.
Because
of the small variations of n with lift distribution,
errors caused
by this effect are
considered
negligible.
It can also be shown that errors caused
by neglecting
the effect of airfoil
thickness
on the distribution
of the lift reaction
along
the tunnel
walls are small.
z©
MEASUREMENT
OF
DRAG
The drag of an airfoil may be obtained
from observations
of the pressures
in the wake
(reference
84).
An approximation
to the drag is given by the loss in total pressure
of the
air in the wake of the airfoil.
The loss of total pressure
is
.8
.6
measured
by a rake of total-pressure
tubes
in the wake.
When
the total pressures
in front of the airfoil
and in the
wake
are represented
by H0 and //1, respectively,
the drag
.4
coefficient
obtained
from
loss of total
pressure
cd r is
.2
Ca7,--"f,_w_k_HJyw
-2
D/sfonce
FIGURE
65.--Lift
-/
0
I
downs/reom
efficiency
factor
from
v# for
center
2
reference
a point vortex situated
line of the tunnel.
3
4t
po/nf
5
/r_ funn_,/_
at various
positions
6
where
the
H_
x_ ff
along
coefficient
of loss of total
pressure
(25)
in the
wake
(Ho--HI"_
\
qo
/
SU_IMARY
y_
distance
perpendicular
to stream
direction
from
OF
AIRFOIL
57
DATA
position
x,
of H_ma _
/./
If the static
pressure
in the wake is represented
by
the true drag coefficient
uncorrected
for blocking
ca' may
shown
to be (reference
84)
Pl,
be
.8
'
fwo '
dY c
--_:_..
(26)
.6 ---
where
The
$1 is the
static-pressure
assumption
is made
coefficient
that
the
in the wake
variation
Ho--p_
q0
pressure
of total
across the wake can be represented
by a normal
probability
curve.
The drag coefficient
Cd' is then easily obtainable
from
measurements
of CaT by means of a factor K, the ratio of cd'
to c_r, which depends
only on S_ and the maximum
value of
He.
If the
the equation
maximum
value of Hc is represented
of the normal
probability
curve is
_
_..
by
cjKc_,7
--H,
=
_
14/QA'e dP,p/h
I qol I
_ ,_fO//c
pressuro
.,4
30
.I
.8
.4
.3
.5
.C
.7
.8
.9
°. with
S_ as a parameter.
1.0
H_ax,
FIGURE 66.--Plot
The
potential
given by
_(Bvoy
of Kas
a function of He
function
w
for
a
symmetrical
body
is
A_
where
B
width
of the
y_=By_
is a dimensionless
wake.
is used,
constant
that
If a convenient
the
ratio
determines
variable
of integration
K is
c
C t
t'a
K_
w=Vz+_+¢+
the
2
1_
is independent
been
assuming
coefficient
ments
with
ment
_'_
of the
evaluated
_/_HH_
width
(1--_/1----_)
of QT, H¢_,
and
$1 as parameter
of this problem
of the
for various
S_ to be constant
Cd' may thus be
S_.
is given
is given
TUNNEL-WALL
dY
(27)
across
obtained
A plot
wake.
values
The
of H¢_,x
the wake.
from tunnel
quantity
and
S_ by
of K as a function
in figure 66.
A parallel
in reference
85.
AV-- A1 _2
--_rr2 _
of H_,_
(30)
1
treatwhere
the
term
reference
86.
For convenience
AV may be written
CORRECTIONS
in free-stream
velocity
caused by the
effect) is obtained
from consideration
(29)
This operation
is equivalent
to replacing
the body by a circle
of which the doublet
strength
is 2rA1; the term A_/z represents the disturbance
to the free-stream
flow.
The total
induced
velocity
at the center
of the body
due to all the
images is expressed
in reference
86 as
The drag
measure-
In two-dimensional
flow, the tunnel
walls may be conveniently considered
as having
two distinct
effects upon the flow
over a model in a tunnel:
(1) an increase
in the free-stream
velocity
in the neighborhood
of the model
because
of a
constriction
of the flow and
(2) a distortion
of the lift
distribution
from the induced
curvature
of the flow.
The increase
walls (blocking
(28)
w---- Vz-4-_
--._Hcmax,)-_,
K has
+_
where
V is the free-stream
velocity
and the coefficients
A_,
A_, . . . are complex.
If the tunnel
height
is large compared
to the size of the body, powers
of 1/z greater
than
1
may be neglected
and
Cd T
and
...
tunnel
of an
infinite
vertical
row of images
of a symmetrical
body
as
given in reference
86; the images represent
the effect of the
tunnel
walls.
A,
is the
in tunnel
same
as
calculations,
AV
V =Aa
the
term_
the
kt2V
expression
of
of
(31)
where
71"
2 //
C "_2
(32)
A
16A1
: c-_-V
(33)
The factor
a depends
only on the size of the body and is
easily calculated.
The factor A depends
on the shape of the
body and is more difficult
to calculate.
For bodies such as
REPORT
58
NO.
8 2 4--NATIONAL
ADVISORY
spending
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
COMMITTEE
fcy
(34)
where
v is the
dyt/dx is the
the ordinate
velocity
at any point
slope of the
is yr.
airfoil
on the
surface
airfoil
at any
surface
point
AERONAUTICS
of
the
by
be replaced
f
dz----2i
. . ....
t_J/h
of
67.--Sketch
to obtain
this
for derivation
consider
the
flow past
symmetrical
body
asshown
in figure
67.
The
function
for this flow is given by equation
(28).
tiating
and
multiplying
equation
dw
A
Z _z=
The
depend
residues,
line
Z2
about
only on the
is given by
Zn
--A,/z
fc z_ ewdz
curve
and,
from
the
theory
the path
of integration,
"-t-d-Y}
dx dx, and
Z
will
dz = z dw
= (x÷ iy) (d_ + i de)
_ is the
potential
tion.
On the
surface
.!;
Since
equal
points
vanish.
the body
numerical
of
the
The
function
of the
and ¢ is the
body
de-=0,
dz=fc x d++i fc
z -_dw
term
and
lower
surfaces,
y dq_ will have
equal
for A= c_VV
gives
Kx)
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 exists
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 thick-
orifices
to the midchord
indicated
tunnel
velocity
mately
0.002.
In order to calculate
stream
func-
so that
y d,
(35)
is symmetrical,
the term
x de will have
values but opposite
signs at corresponding
upper
solving
d_b by v ds, replac-
point of the model.
The
V' could then be written
corrected
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 approxi-
d_w
dz---- --27riA,
dz
d_o
where
upper
of
but
z -_
the
direction)
replacing
cV
V'=
fc
over
and
ness 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 h and a factor ( which depended
upon
the size of the model and the distance
from the static-pressure
nA,
"'"
a dosed
term
a
potential
Differen-
z gives
2A2
VZ-z'
integral
(28) by
surfaces,
y de
,_,orly ,,/,
lnlegr'ohor7
of A-factor.
expression,
integration
,f
of which
A,=--_
ds
lower
y d4_ (counterclockwise
_.j0
In order
an
and
or
and
ing ds by
FIGURE
upper
therefore,
z _
Reversing
I,
points
dep may
surface;
expression
FOR
and
I;x
values
dq_ will
at
corre-
the effect
of the
tunnel
lift distril)ution,
a comparison
is made of the
of a given airfoil in a tunnel
and in free air
thin-airfoil
theory.
It is assumed
that the
in the tunnel correspond
most closely to those
the additional
lift in the tunnel
and in free
(reference
87).
On this basis the following
derived
(reference
87), in which the primed
to the coefficients
measured
in the tunnel:
c_= [1-- 2A(a÷
_) -- a]c_'
walls
upon
the
lift distribution
on the basis of
flow conditions
in free air when
air are the same
corrections
quantities
are
refer
(37)
SUMMARY
4 ffCme
_0----(l+¢)a0'-_
14t
OF
t
dc_'/dao'
¢aZo
(38)
!
c_c/_= [1-- 2A(¢+
_)]c_¢/4'-_
a_
4(7Cmc/4
In the foregoing
equations,
the terms
dc//dao
are usually
negligible
for 2-foot-chord
models
two-dimensional
low-turbulence
tunnels.
(39)
t
), aaZo, and acz'/4
cd= [1 --2A (_-_ _)] c_'
BLOCKING
AT
HIGH
from unity in the high-lift
range for any aix foil tested
in the
tunnel;
this variation
indicates
a change
in blocking
at high
lifts.
A plot of FIFo against
angle of attack s0' 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 a0' up to
12°; but for values of a0' greater
than 12 °, FIFo increases
and
the increase
is particularly
noticeable
at and over the stall.
/.20_
/'/_
(40)
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.
FOR
59
DATA
in the Langley
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
speed.
The correction
to the drag coefficient
is therefore
given by the
following
relation:
CORRECTION
AIRFOIL
-16
-12
-8
-4
0
Geornefr-/c
FmURE
88.--Additional
blocking
4
ongTIc
factor
for the
at the
NAC._
of
8
/2
c_ttoo/_,
tunnel
6,t3-418
walls
_,
plotted
/8
28
Z4
_/_9
against
angle
of attack
airfoil.
A theoretical
comparison
was made of the blocking
factor
Aa 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
Aa and the change
in F to be unique
for chord lengths
up
to 50 inches in that different
bodies having
the same blocking
factor
Aa gave approximately
the same
value
of F.
For
chords up to 50 inches,
the relationship
is
AV
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 v_ake
upon the free-stream
velocity.
Since the wake effect shows
up primarily
in the drag,
the increase
in blocking
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 lowenergy
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
AV/V is the true
blocking.
The foregoing
correction
increment
relation
to the blocking
in tunnel
velocity
due to
was adopted
to obtain
the
F
in the range of lifts where F0 ) 1.
Considerable
uncertainty
exists
regarding
the
correct
numerical
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
COMPARISON
A check of the validity
been made
in reference
curves
for models
having
height,
uncorrected
and
has therefore
WITH
not been attempted.
EXPERIMENT
of the tunnel-wall
corrections
has
87, which
gives lift and moment
various
ratios
of chord to tunnel
corrected
for tunnel-wall
effects.
6O
REPORT
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
!
/.2
/
/
q.8
_.4
.v.
/
.0
/
/
/
J
-.4
/Io
-.8
Airfoil
I-Airfoil
c_
_24
A
Pressure
d/str/butiom,
/o
A
Imleqrahh_
ter,
TDT test momorne,
640
z
AL"fo/I
B
Pressure
distribuhbn,
A/rfoll
B
ImlegrohDq
TDT test monometer_
6_55
I
J
-8
-15
0
8
/6
24
Sechbn
32
-Z4
-15"
onqle of ottock, a'o,deg
-8
(b)
(a) Comparison for airfoil A.
FIGURE 69.--Comparison
between
lifts obtained
0
from pressure-distribution
measurements
and lifts obtained
Comparison
IO
Z4
3,2
for airfoil B.
from reactions on the floor and ceiling of the tunnel.
o gO uncorrected
o 45
I
I
z_ 90' correcled
o 45
/.6
8
for" block/rag
I
I
I
for- blocA'img
I
/.2
/
.8
/
0
£
,,-"
/
",I
\
,% \
%
"I
o Bolonce
N InfegrOfln
t_..4
\
_ monometer_
-.8
-Z 4
-/6
FIGURE 70.--Comparisou
-8
__ech'on ongle
0
of o/to,-h,
8
/6
oto, dec]
between
lifts obtahmd from balance measurements
reactions on the floor and ceiling of the tunnel.
24
and
from
0
.I
.2
3
4
.5
.6
.7
.8
.9
x/c
FIGURE 71.--Comparisonbetween correctedand uncorrectedpressuredistributions
fortwo
chord sizesof a symmetrical NACA
6*series
airfoil
of 15-percent
thickness,a0=0°.
L,
SUMMARY
The
general
the
agreement
method
A comparison
cal
derived
factor
factors
obtained
In
been
floor
and
two
airfoils
87 between
and
88.
the
the
theoreti-
experimentally
The
to be in good
13.
theoretical
agreement
cor-
with
of
with
those
ceiling
n-factor
has
obtained
also
results
been
values
a check
those
chord
the
shows
checked
70.
made
been
lengths
in good
angle
The
agreement
for
tunnel-wall
both
6-series
air-
in figure
against
between
models
lift
of correcting
NACA
plotted
the
the
verifies
71,
chordcorrected
the
method
of
corrections.
REFERENCES
I. Jacobs,
Eastman
N., Ward,
M.: The
Characteristics
Tests
in the
No. 460, 1933.
Kenneth
E.,
of 78 Related
Variable-Density
and Pinkerton,
Robert
Airfoil
Sections
from
Wind
Tunnel.
NACA
Rep.
2. Jacobs,
Eastman
N., and Pinkerton,
Robert
M.: Tests
in the
Variable-Density
Wind Tunnel
of Related
Airfoils Having
the
Maximum
Camber
Unusually
Far
Forward.
NACA
Rep.
No. 537, 1935.
3. Jacobs,
Eastman
Harry:
Tests
Variable-Density
of
N., Pinkerton,
Robert
M.,
Related
Forward-Camber
Wind
Tunnel.
NACA
4. Stack,
John,
and Von Doenhoff,
Albert
Airfoils at High Speeds.
NACA Rep.
Rep.
17.
18.
integrating-
of attack
are
16.
of
The
of
method
for
for
agreement.
the
15.
the
methods
comparison
87)
at zero
two
with
coefficients
x/c.
the
of the
(reference
disof
A comparison
that
by
pressure
integration
tunnel
are
in figure
distributions
making
the
has
pressure
position
pressure
in
69
a comparison
from
the
measurements
distributions
the
n-factor,
from
that
balance
Finally,
of two
obtained
obtained
in figure
manometer
which
values
lift
give
from
pressure
of the
pressures
given
lift
validity
and
Greenberg,
Airfoils
in the
No.
610,
26.
1937.
27.
5. Jacobs,
Eastman
N.,
and
Sherman,
Albert:
Airfoil
Section
Characteristics
as Affected
by Variations
of the Reynolds
Number.
NACA Rep. No. 586, 1937.
28.
Variable-Density
Wind
Tunnel.
NACA
Rep.
Aerodynamic
Tested
in the
No.
628,
7. Jones,
B. Melvill:
Flight
Experiments
on the Boundary
Jour. Aero. Sci., vol. 5, no. 3, Jan. 1938, pp. 81-94.
8. Jaeobs,
Eastman
N., and Abbott,
Ira H.:
Obtained
in the N.A.C.A.
Variable-Density
by Support
Interference
No. 669, 1939.
9. Theodorsen,
Shape.
10. Stack,
ibility
and
Theodore:
NACA Rep.
John:
Tests
Burble.
of
Airfoils
NACA
Rep.
Designed
Layer.
Airfoil Section
Data
Tunnel
as Affected
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Theory
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No. 411, 1931.
11. Jacobs,
Eastman
N.: Preliminary
and New
Methods
Adopted
Investigations.
NACA ACR,
918392--51--5
Other
1938.
Sections
NACA
of
Rep.
29.
30.
31.
32.
Arbitrary
33.
to Delay
the
Compress-
No. 763, 1943.
Report on Laminar-Flow
Airfoils
for Airfoil and Boundary-Layer
June 1939.
61
Albert E., and Stivers,
Louis S., Jr.: Aerodynamic
of the NACA
747A315
and 747A415
Airfoils
in the NACA
Two-Dimensional
Low-Turbulence
Pressure
Tunnel.
NACA CB No. L4125, 1944.
Naiman,
Irven:
Numerical
Evaluation
by Harmonic
Analysis
of the e-Function
of the Theodorsen
Arbitrary-Airfoil
Potential
Theory.
NACA ARR No. L5H18,
1945.
Theodorsen,
Theodore:
Airfoil-Contour
Modification
Based
on
e-Curve
Method
of Calculating
Pressure
Distribution.
NACA
ARR No. L4G05,
1944.
Allen,
H. Julian:
A Simplified
Method
for the Calculation
of
Airfoil
Pressure
Distribution.
NACA
TN
No.
708,
1939.
Munk,
Max M.: Elements
of the Wing Section
Theory
and of
the Wing Theory.
NACA Rep. No. 191, 1924.
Glauert,
H.: The
Elements
of Aerofoil
and Airscrew
Theory.
Cambridge
Univ. Press, 1926, pp. 87-93.
Theodorsen,
Theodore:
On the Theory
of Wing Sections
with
Particular
Reference
to the Lift Distribution.
NACA
Rep.
No. 383, 1931.
19. Von
K_rm_n,
Th.:
Compressibility
Effects
in Aerodynamics.
Jour. Aero. Sci., vol. 8, no. 9, July 1941, pp. 337-356.
20. Von Doenhoff,
Albert
E.: A Method
of Rapidly
Estimating
the
Position
of the Laminar
Separation
Point.
NACA
TN No.
671, 1938.
21. Jacobs,
E. N., and Von Doenhoff,
A. E.: Formulas
for Use in
Boundary-Layer
Calculations
on Low-Drag
Wings.
NACA
ACR, Aug. 1941.
22. Von Doenhoff,
Albert
E., and Tetervin,
Neah
Determination
of
General
Relations
for the Behavior
of Turbulent
Boundary
Layers.
NACA Rep. No. 772, 1943.
23. Squire,
H. B., and Young,
A. D.: The Calculation
of the Profile
Drag of Aerofoils.
R. & M. No. 1838, British
A. R. C., 1938.
24. Tetervin,
Neal:
A Method
for the Rapid Estimation
of Turbulent
Boundary-Layer
Thicknesses
for Calculating
Profile
Drag.
NACA
ACR No. L4G14,
1944.
25. Quinn, John H., Jr., and Tucker,
Warren
A. : Scale and Turbulence
Effects
on
the
Lift
and
Drag
Characteristics
of the
NACA 653-418, a= 1.0 Airfoil Section.
NACA ACR No. L4Hll,
1944.
E.: Tests of 16 Related
No. 492, 1934.
6. Pinkerton,
Robert
M.,
and
Greenberg,
Harry:
Characteristics
of a Large
Number
of Airfoils
DATA
12. Von Doenhoff,
Characteristics
from Tests
that
is valid.
14.
the
made
measuring
wise
shows
moments
(40))
reference
found
to check
tributions
in
in reference
of
were
curves
and
experimentally.
order
foils
corrected
lifts
(equation
corrections
rection
the
the
is made
correction
has
of
of correcting
OF AIRFOIL
34.
Tucker,
Warren
A., and Wallace,
Arthur
R.: Scale-Effect
Tests
in a Turbulent
Tunnel
of the NACA
653-418,
a-----1.0 Airfoil
Section
with 0.20-Airfoil-Chord
Split Flap.
NACA
ACR No.
L4122, 1944.
Davidson,
Milton,
and Turner,
Harold
R., Jr.: Effects of MeanLine Loading
on the Aerodynamic
Characteristics
of Some LowDrag Airfoils.
NACA
ACR
No. 3127, 1943.
Von Doenhoff,
Albert
E., and Tetervin,
Neal: Investigation
of
the Variation
of Lift Coefficient
with Reynolds
Number
at a
Moderate
Angle of Attack
on a Low-Drag
Airfoil.
NACA
CB, Nov. 1942.
Oswald, W. Bailey:
General
Formulas
and Charts
for the Calculation of Airplane
Performance.
NACA Rep. No. 408, 1932.
Millikan,
Clark B.: Aerodynamics
of the Airplane.
John
Wiley
& Sons, Inc., 1941, pp. 108-109.
Hood,
Manley
J.:
The
Effects
of Some
Common
Surface
Irregularities
on Wing Drag.
NACA TN No. 695, 1939.
Loftin,
Laurence
K., Jr.: Effects
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Types
of Surface
Roughness
on Boundary-Layer
Transition.
NACA
ACR No.
L5J29a,
1946.
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Alex C., Jr. : Transition
between
Laminar
and Turbulent
Flow by Transverse
Contamination.
NACA TN No. 891, 1943.
Braslow,
Albert L.: Investigation
of Effects of Various Camouflage
Paints and Painting
Procedures
on the Drag Characteristics
of
an NACA 65(_21)-420, a-----1.0 Airfoil Section.
NACA
CB No.
L4G17,
1944.
62
35.
REPORT
Jones,
Robert
T.,
Determining
NACA
Rep.
36.
Abbott,
Frank
T.,
of Roughness
Characteristics
L4H21,
37.
June
John
Zaloveik,
A.,
Effect
Hood,
and
of
A.
C.
A.
Abe,
parative
Flight
Abbott,
in
Langley
H.,
and
of
Various
Bogdonoff,
3120,
of an
Slotted
tion
734,
N.
of an
N.
1938.
of
of
Maximum
of
Airplanes.
of
with
S.,
in
tim
661,
Wind-Tunnel
23030
64.
with
Airfoils
668,
Rep.
with
of
a
NACA
No.
65.
Investigation
of
ACR
Ames,
of
an
Plain
No.
Mil(;on
N.
Flap
A.
and
C.
M.:
Ailerons
A.
Jr.:
0009
Three
68.
Analysis
of Avail-
wit, hour
Exposed
69.
Airfoil
Tabs.
with
NACA
a
TN
50-
70.
Plain
54.
Sears,
Plain
lliehard
Characteristics.
teristics
of
Flal).
Flap
and
B., Jr.,
of an
Flap
I.:
an
and Sears,
Richard
N. A. C. A. 0009
Three
and
N.
and
Tabs.
NACA
NACA
TN
No.
761,
1940.
Sears,
Richard
A. C. A. 0009
I.: Pressure-Dislribution
Airfoil
with
a 30-Perc(,nt-
Three
NACA
Tails.
Wind-Tunnel
I--Effect
NACA
I.: Pressure-Distribution
Airfoil
with
an 80-Percent-
lnvestigalion
of
0009
ARR,
Gap
on lhe
Airfoil
with
June
1941.
TN
of
No.
759,
1940.
71.
Ira
72.
73.
Control-Surface
Aerodynamic
Characa 30-Percent-Chord
NACA
of Ailerons
3F18,
and
at
1943.
Investigation
Contour
Plain
ACR
E.:
Flap
No.
on
3L20,
of
of
654-421
an
1943.
Aileron
True
Airfoil
Wind-Tunnel
XIV--NACA
Plain
a Low
EffecAirfoil
Sections.
Investigation
0009
Airfoil
Flap.
NACA
ARR
Drag
Wind-Tunnel
and Tabs
Airfoil.
July
Inveson the
NACA
Rep.
and
Ward,
Tests
a
Thick
Frank
T.,
Housings
No. 3K13,
Russell
of
of
G.,
Airfoils
Raymond
F.:
Wings.
on
and
and
NACA
W.,
Jr.:
NACA
on
for
H.:
the
30
Charac-
of
the
by
InvestiCombination.
Pusher-Propeller
Section.
NACA
572,
a
1943.
Estimation
Bodies.
NACA
of
ACR,
Critical
March
Characteristics
1936.
V.:
Rep.
of
Affected
3D27,
Airfoil
Ray
No.
Plates
Experimental
Data
and
Rhode,
R.
to the
Prediction
Wings.
No.
Determination
Rcp.
on
Wing-Nacelle
Streamline
C. A.
Wing--II.
Critically
65,3-018
Wright,
Flat
Nacelle
CB
Drag
Wing
A.
1935.
Low-Drag
Airfoil
Low-Drag
and
540,
of
N.
Measurements
a
a Typical
NACA
in the
Drag
on
Charles
Lift
on an
1943.
Leading
1942.
and
NACA
Frick,
Jr.:
Jacol)s,
Eastman
N.,
teristics
as Applied
Distribution
Lift
Low-Drag
and
the
Interference
No.
Nov.
Nacelle
Roughness.
Julian,
at
of Longitudinal
CB,
Some
Bomber
E.:
Rep.
Effects
NACA
Jr.:
Air
Combinations
NACA
Interference
C.,
Admitting
Kenneth
of 209
of a New Type
of
ACR,
July
1942.
Anderson,
for
A.: Preliminary
Tunnel
of Low-
1942
Tunnel.
H.:
Horton,
Elmer
Low-Turbulence
Suitable
N.,
of
Tapered
74.
No.
Ralph
W.:
Modifications
E.,
and
NACA
Airfoils.
Robinson,
Speeds
1940.
an
Chord
and
True
Balance
on the
Wind-Tunnel
XV--Various
653-418,
on
NACA
CB,
Sept.
1942.
Ellis,
Macon
C., Jr.:
Effects
Shaft
ACR
Airfoil
Internal
Investigation
Plain
Ailerons
Holtzclaw,
of Profile
ACR,
from
Macon
AI)bott,
Data.
Tests
0.20
Sealed
Double
Sections
Eastman
tI.
Test
ACR
Purser,
Paul
Characteristics.
Albert
in the
Fuselage
Allen,
on
1943.
1944.
of Ailerons
NACA
gation
NACA
No.
of
NACA
652-415,
and
Leading-Edge
Pressure-Distribu-
Flap
3G20,
1944.
teristics
1944.
No.
1943.
Von
Doenhoff,
Invcstigation
Ellis,
Wind-Tunnel
XIII--Various
0.30-Airfoil-Chord
20-Percent-Chord
803,
Abbott,
E.:
Wind-Tunnel
NACA
L4H12,
Representative
1939.
B., Jr.,
of an
No.
Low-Drag
Arrangements
D.:
Airfoil.
Variable-Density
Investi-
J.
a
Crane,
Robert
M., and
tigation
of the Effects
and
67.
L4E01,
B.,
a
3F29,
ARR,
Distribution
a Plain
Flap.
30-Percent-Chord
Riebe,
John
M.:
Characteristics.
on NACA
No.
NACA
B.: Pressure
a Slotted
and
ACR
]I--Ailerons
Aileron-Chord
Airfoil.
Richard
I.,
Control-Surface
Jacobs,
a
Albert
L.:
Wind-Tunnel
of
0.20-Airfoil-Chord
with
a
Investiga30-Percent-
Airfoil.
of Balanced-Aileron
Bird,
of
CB
Wind-Tunnel
VI--A
Vernard
NACA
66(215)-014
Edge.
Arrangemez_ts
Various
and
66,2-216
Braslow,
tiveness
of
1944.
Paul
E., and
Control-Surface
Drag-Airfoil
1939.
Stewart
Effectiveness
and
with
G.,
Moment
Characteristics.
with
Collection
4All,
Speeds.
with
0.60
ACR
Investi-
Wind-Tunnel
677,
Purser,
of
James
with
Invesof a
1942.
0015
Lockwood,
U'sed
M.:
H.
Low-
1939.
A.:
No.
Crandall,
Various
664,
Airfoil
Rep.
Wind-Tunnel
with
Thomas
NACA
G.,
A.:
Dcnaci,
No.
1939.
Flap.
No.
Hinge
Use
1938.
and
Airfoil.
Characteristics
Investi-
Investigation
Slotted
Variable-
1939.
No.
F.
ACR
NACA
of Control-Surface
66-009
Wind-Tunnel
V--The
the
March
Robert
B.:
Characteristics.
the
633,
L.,
Overhangs
Rogallo,
Sears,
of
on
No.
Clarence
NACA
NACA
Airfoil
A.:
and
Airfoil
23021
and
the
William
23012
NACA
on
Rep.
Gillis,
Contour
of
0.20-Airfl)il-
23012
Flap
Reduce
ARR,
Carl
J., and
Delano,
A. C. A. 23012
Airfoil
N.
NACA
62.
to
NACA
Modifications
Trailing-
of
No.
Thomas
Harris,
Balance.
Ames,
Milton
Investigation
Plain
618,
61.
1944.
A.
Rep.
a Double
A. C. A.
Rol)ert
Data
53.
Chord
C.
23021,
Harris,
and
Wcnzinger,
over an
NACA
of
Summary
Effects
Tests
A.
NACA
NACA
J.,
Plain
1942.
Various
Contour
63.
Wind-Tunnel
A. C. A.
Flaps.
Ames,
Milton
Investigation
Chord
No.
C.:
Airfoils
Rep.
60.
66.
Percent>Chord
52.
Rep.
1,4G10,
Thomas
23012,
59.
Com-
Characteristics
IIarry:
N.
Flap.
with
Flaps.
Slotted
Street,
A.
A.:
Investigation
No.
the
with
Edge
Milton
B., Jr.:
Churacteristics.
Richard
I., and Liddell,
of
Control-Surface
NACA
1939.
James
S.:
65,-212
NACA
and
Surface.
Investigation
of
1944.
CB
Harris,
M.:
J.,
Carl
Swanson,
L4130,
of
Section
Overhang
51.
C.
Split
ACR
1943.
Wenzinger,
able
A.
of
58.
Drag
Characteristics
Greenberg,
Flaps.
Carl
gation
57.
of Propellers
Flow
on
the
Tunnel
Wind-Tulmel
and
and
Oct.
]_ichard
Itarold
No.
Jr.:
Seylnour
Airfoil
Wenzinger,
of
N.
on
Thick
Separation.
Measurements
Full-Scale
NACA
J.,
Sizes
gation
50.
Si)lit
1944.
Pitching-Moment
Tunnel
Carl
Profile
NACA
Stalling
1945.
CB
Wing
Hoot.man,
Dingeldein,
on
and
Trailing
Control
Sears,
tion
AERONAUTICS
T., and
Ames,
Control-Surface
:Beveled
Chord
June
Investigation
Wind-Tunnel
Johnson,
F.,
Wind
Wenzinger,
of
and
829,
Flaps.
Ira
gation
49.
56.
Milton:
NACA
L4125,
ACR,
and
Airplane.
66,1-212,
Density
on
No.
Full-Scale
and
Flight.
A Flight
NACA
of an
NACA
Split
No.
Drag
No.
Conventional
M. Edward:
Effects
Extent
of Laminar
S.,
and
E.,
of
in
ARR
H.,
Felicien
Chord
48.
and
ACR
Jones,
Robert
tigation
of
Flap
Modifications
Drag
55.
Effects
Davidson,
Roughness
Critical
to
Clotaire:
Airfoil.
and
66(215)-216,
47.
The
the Lift
NACA
and
Obtained
Gaydos,
on
the
Lift
Paul
Fulhner,
H.,
Roughness
and
Harold
Purser,
as
Katzoff,
Maximum
Sweberg,
Plain
on
of
Flow.
Jr.:
Coefficients
NACA
27-212
Silverstcin,
Airfoils.
46.
Method
FOR
NACA
Surface
Manley
J.,
of Vibration
Edge
45.
R.,
Numbers
Airfoils.
Ira
Wood,
Fixed.
Lift
Coefficients
NACA
Rep.
No.
44.
Harold
Profile-Drag
and
Measurements
43.
Graphical
COMMITTEE
1942.
A.:
John
the
42.
Abbott,
Low-Drag
Airfoils
L4E31,
1944.
N.
41.
N.,
CB,
Transition
40.
Turner,
ADVISORY
Two-Dimensional
of Extreme
Leading-Edge
Airfoils
to
Indicate
Those
Zalovcik,
the
A
in
High
Reynolds
of Three
Thick
Eastman
NACA
39.
Doris:
Distribution
1941.
and
824--:N'ATIO/_AL
1944.
Jacobs,
and
No.
Cohen,
Jr.,
at
Investigation
Low-Drag
38.
and
Pressure
No. 722,
NO.
of
Airfoil
Air
No.
631,
Section
CharacForces
and
Their
1938.
of
SUMMARY
75.
Soul_, H. A., and Anderson,
R. F.: Design Charts
Relating
Stalling
of Tapered
Wings.
NACA Rep. No. 703, 1940.
76.
Harmon,
Sidney
M.: Additional
Design
Charts
Relating
to the
Stalling
of Tapered
Wings.
NACA ARR,
Jan. 1943.
Anderson,
Raymond
F.: The Experimental
and Calculated
Characteristics
of 22 Tapered
Wings.
NACA Rep. No. 627, 1938.
Tani, Itiro: A Simple Method
of Calculating
the Induced
Velocity
of a Monoplane
Wing.
Rep. No. 111 (Vol. IX, 3), Aero. Res.
Inst.,
Tokyo
Imperial
Univ., Aug. 1934.
Sherman,
Albert:
A Simple
Method
of Obtaining
Span
Load
Distributions.
NACA
TN No. 732, 1939.
77.
78.
79.
80.
81.
82.
to the
Jones,
Robert
T.: Correction
of the Lifting-Line
Theory
for the
Effect of the Chord.
NACA
TN No. 817, 1941.
Cohen,
Doris:
Theoretical
Distribution
of Load
over a SweptBack Wing.
NACA
ARR, Oct. 1942.
Pearson,
H. A.: Span Load Distribution
for Tapered
Wings with
Partial-Span
Flaps.
NACA Rep. No. 585, 1937.
OF AIRFOIL
83.
84.
85.
86.
87.
88.
63
DATA
Pearson,
Henry
A., and Anderson,
Raymond
F.: Calculation
of
the Aerodynamic
Characteristics
of Tapered
Wings with PartialSpan Flaps.
NACA
Rep. No. 665, 1939.
The Cambridge
University
Aeronautics
Laboratory:
The Measurement of Profile Drag by the Pitot-Traverse
Method.
R. & M.
No. 1688, British
A. R. C., 1936.
Silverstein,
A., and Katzoff,
S.: A Simplified
Method for Determining Wing Profile Drag in Flight.
Jour. Aero. Sci., vol. 7, no. 7,
May 1940, pp. 295-301.
Glauert,
H.: Wind
Tunnel
Interference
on Wings,
Bodies
and
Air, crews.
R. & M. No. 1566, British
A. R. C., 1933.
Allen, H. Julian,
and Vincenti,
Walter
G.: Interference
in a TwoDimensional-Flow
Wind Tunnel
with the Consideration
of the
Effect of Compressibility.
NACA Rep. No. 782, 1944.
Fage, A. : On the Two-Dimensional
Flow past a Body of Symmetrical
Cross-Section
Mounted
in a Channel
of Finite
Breadth.
R. & M. No.
1223,
British
A. R. C., 1929.
_4
REPORT
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
SUMMARY
OFAIRFOIL
DATA
65
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66
NO.
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COMMITTE_
FOR
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69
DATA
DATA
FORMS
Page
70
NACA
641-012
.......................................
70
NACA
642-015
........................................
79
......................................
70
NACA
643-018
.......................................
80
0010
..........................................
71
NACA
644-021
..........................................
80
NACA
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.......................................
71
NACA
65,2-016
.......................................
80
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....................................
71
NACA
65,2-023
.........................................
81
NACA
0018
.........................................
72
NACA
65,3-018
.........................................
81
NACA
0021
......................................
72
NACA
65-006
...........................................
81
NACA
0024
...........................................
72
NACA
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82
NACA
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73
NACA
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........................................
82
NACA
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.......................................
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NACA
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82
NACA
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........................................
73
NACA
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NACA
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NACA
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NACA
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..........................................
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NACA
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NACA
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.........................................
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NACA
63,4-020
75
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66,1-012
..........................................
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...........................................
75
NACA
66,2-015
..........................................
84
NACA
63-009
.........................................
75
NACA
66,2-018
..........................................
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NACA
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..........................................
76
NACA
66-006
...........................................
85
NACA
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........................................
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NACA
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...........................................
85
NACA
632-015
.........................................
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NACA
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...........................................
86
NACA
633-018
......................................
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NACA
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...........................................
86
NACA
634-021
.........................................
77
NACA
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..........................................
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NACA
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.........................................
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NACA
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NACA
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..........................................
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NACA
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...........................................
78
NACA
664-021
..........................................
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64-009
............................................
78
NACA
67,1-015
..........................................
88
NACA
64-010
...........................................
79
NACA
747A015
..........................................
88
NACA
0006
...........................................
NACA
0008
NACA
0009
NACA
918392-
..........................................
.........................................
51.---6
..........................................
Page
79
83
87
70
REPORT
NO.
8
2 4----NATIONAL
ADVISORY
COMMITTEE
:FOR
AERONAUTICS
2.0
NACA
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c)
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1.252
1. 209
1. 176
1.126
1. 087
1. 037
• 984
.933
0
4.501
4.352
3.971
3.423
2.748
1.967
1.086
.605
.095
radius:
vl V
AvJ
V
c)
0
.5
1.25
2.5
12 fr----
(r/I')2
Y
(percent
c
0.595
1,700
1.283
.963
.692
.560
.479
.380
.318
.273
.239
.188
.15I
.120
.095
.070
.046
.030
0
SUMMARY
OF
AIRFOIL
71
DATA
2.0
NACA[0010
x
(percent
1.6
c)
y
(percent
0
.8
NACA
0010
c)
FORM
(v/V)_
0
.5
1.25
2.5
5.0
7.5
10
15
20
25
30
40
50
6O
70
80
90
95
I00
1.2
BASIC:THICKNESS
1. 578
2.178
2. 962
3.500
3. 902
4. 455
4. 782
4.952
5.002
4.837
4. 412
3. 803
3.053
2.187
1. 207
• 672
.105
v/V
avdV
0
0
.712
1.061
1. 237
1. 325
1. 341
1.341
1,341
1.329
1.309
1.284
1.237
1.190
1.138
1.094
1. 040
.960
• 925
•844
1.030
1.112
1.151
1.158
1.158
1.158
1.153
1.144
1.133
1.112
1. 091
1. 067
1.046
1. 020
.980
.962
2. 372
1. 618
1.255
.955
.690
• 559
.479
.380
.318
.273
• 239
• 188
.150
• 119
.094
.069
.045
.030
0
.4
L. E. radius:
1.10 percent
c
f
NACA
1.6
(percent
c)
Y
(percent
0
.5
I. 25
2.5
5.0
7.5
1O
15
20
25
30
40
50
6O
70
80
9O
95
100
/.2
.8
NACA
00/2
.4
ff
L. E. radius:
0012
BASIC
THICKNESS
(v/V) 2
c)
0
0
1.894
2.615
3.555
4.200
4.683
5.345
5.738
5,941
6. 002
5. 803
5. 294
4. 563
3. 664
2.623
1.448
.807
.126
.640
1. OlO
1. 241
1.378
1".402
1. 411
1.411
1.399
1.378
1. 350
1. 288
1.228
1. 166
1. 109
1. 044
• 956
.996
O
1.58 percent
c
NACA
BASIC
FORM
vlV
Av d V
O
.800
1• 005
1. 114
1,174
1.184
1.188
1.188
1. 183
1.174
1.162
1.135
1.108
1. 080
1. 053
1. 022
.978
• 952
O
1. 988
1. 475
1.199
• 934
.685
.558
.479
.381
.319
.273
.249
.187
.149
.118
.092
.068
• 044
.029
0
I
jl
j
o
0015
TRICKNESS
FORM
I.G
z
(percent
c)
Y
(percent
c)
(vl I')_
vl V
Avol V
O
• 739
.966
1. 112
1. 204
1. 224
1. 233
1• 233
1. 229
1. 218
1.204
1. 170
1. 131
1.098
1.064
1. 024
.972
• 934
O
1.600
1.312
1. 112
.900
.675
.557
• 479
.381
.320
• 274
.239
.185
• 146
• 115
• 090
• 065
• 041
• 027
0
"-....
O
.5
1, 25
2.5
5.0
7.5
lO
15
20
25
30
4O
5O
6O
7O
8O
9O
95
100
/.8
.8
NACA
00/5
.4
f
1
L. E. radius:
1---------
0
I
.2
.4
.6
.v/c
.8
/.0
2.48
0
0
2. 367
3.268
4. 443
5. 250
5. 853
6. 682
7.172
7. 427
7. 502
7. 254
6. 617
5. 704
4.580
3.279
1. 810
1.008
.158
.546
• 933
1.237
1. 450
1. 498
1. 520
1. 520
1. 510
1.484
1. 450
1. 369
1. 279
1. 206
1.132
1. 049
•945
.872
0
percentc
t
_,//'
72
REPORT
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
2.O
NACA
x
(percent
/.6
(percent
.5
1.25
2. 5
5. 0
7.5
l0
15
20
25
30
40
50
60
70
80
90
95
100
__4
.8
I
----
NACA
0018
BASIC
THICKNESS
y
c)
0
/.2
0018
FORM
(vl I ")
c)
v
I."
AvJ
V
o
0
2.841
3.922
5. 332
6.300
7. 024
8.018
8.606
8.912
9. 003
8. 705
7. 941
6.845
5.496
3.935
2. 172
1.210
.189
• 465
• 857
1.217
1. 507
1. 598
1. 628
1.633
1.625
1. 592
1. 556
1.453
1.331
1. 246
1. 153
1. 051
.933
.836
0
.682
• 926
1.103
1. 228
1.264
1.276
1. 278
1. 275
1. 262
1. 247
1.205
1. 154
1.116
1.074
1.025
• 966
• 914
0
1. 342
1.178
1. 028
.861
• 662
• 555
• 479
• 381
.320
• 274
• 238
• 184
.144
.113
.087
.063
• 039
.025
0
0
.4
"----4-------..__..__..___._._
L.
E.
radius:
3.56
percent
c
1
0
NACA
/6
0021
x
Y
(percent
c)
FORM
vl v
Av./V
c)
0
.5
1.25
2.5
5
7.5
10
15
20
25
30
40
50
60
70
80
9O
95
lOO
.8
THICKNESS
(v/_r)..
(percent
O
_2
BASIC
3.315
4. 576
6. 221
7. 35O
8. 195
9. 354
10. 040
10. 397
10. 504
10. 156
9. 265
7. 986
6. 412
4. 591
2. 534
1. 412
• 221
0
0
.397
• 787
1. 182
1.543
1. 682
1. 734
1. 756
• 630
• 887
1. 087
1.242
1.297
1.317
1. 325
1. 320
1. 306
1. 290
1. 240
1. 178
1. 133
1. 085
1.027
• 957
• 895
0
1. 742
1. 706
1. 664
1. ,5,38
1. 388
1. 284
1. 177
1.055
.916
.801
0
1.167
1. 065
• 946
•818
• 648
• 550
• 478
• 381
• 320
• 274
• 238
.183
.142
.Ill
• 084
• 061
• 0,37
• 023
0
.4
L.
E.
radius:
4.85
percent
c
0
I
NACA
\
L5
x
c)
.8
5.229
7.109
8.400
9.365
I0.691
11.475
11,883
12. 004
11.607
10. 588
9.127
7.328
5. 247
2.896
1.613
.252
70
8O
9O
95
100
0024
.4
L.E.
._
.6
x/c
I
.8
LO
radius:
6.33percent
THICKNESS
FORM
(vl V )'
c)
.... _:isg-
50
60
ICACA
(percent
0
.5
1.25
2.5
5.0
7.5
10
15
20
25
30
40
ZE
BASIC
Y
(percent
0
0
0024
c
v/V
0
0
.335
.719
1. 130
1 548
1. 748
1. 833
1.888
1. 871
1. 822
1. 777
1. 631
1. 450
1. 325
1.203
1. 065
.891
• 773
0
.579
.848
I. 063
1. 244
1. 322
1.354
1.374
1.368
1,350
1.333
1.277
1.204
1.151
1.097
1.032
.944
.879
0
At'./1"
1. 050
.964
.870
.771
• (_32
.542
.476
• 383
• 321
.274
• 238
• 181
• 140
• 109
• 082
.059
• 0:15
• 022
0
SUMMARY
OF
AIRFOIL
DATA
73
2.0
NACA
/.8
(percel)
Y
(percent
0
i. 25
2.5
5.0
7.5
10
15
2O
30
40
5O
6O
70
8O
9O
95
100
/.2
f_
.8
16-006
NACA
t c)
16-006
BASIC
THICKNESS
2
(v/V)
c)
0
1. 059
1. 085
1. 097
1.105
1.108
1.112
1.116
1. I23
1.132
1.137
1.141
1.132
1.104
1. 035
.962
0
0
• 646
.903
1. 255
1. 516
1. 729
2. 067
2. 332
2. 709
2, 927
3.000
2.917
2. 635
2. 099
1. 259
• 707
• 060
FORM
v/v
Avo/V
0
1. 029
1. 042
1. 047
1. 051
1. 053
1.055
I. 057
1. 060
1. 064
1. 066
1. 068
1,064
1. 051
1. 017
•981
0
5. 471
1. 376
.980
•689
• 557
• 476
•379
.319
.244
.196
.160
.130
.104
.077
• 049
•032
0
.4
L. E. radius:
0.176 percent
e
0
NACA
16-009 BASIC
THICKNESS
FORM
/.6
(percent
0
1.25
2.5
5.0
7.5
10
15
2O
30
40
50
60
70
80
9O
95
1O0
1.2
f
,8
NACA
c)
16-009
Y
(percent
(v/V)
c)
O
.969
1. 354
1. 882
2. 274
2. 593
3.101
3.498
4.063
4. 391
- 4. 500
4. 376
3. 952
3.149
1. 888
1. 061
•090
vlV
0
1. 042
1.109
1.139
1.152
1.158
1.168
1.177
1.190
1. 202
i. 211
1. 214
1. 206
1.156
1. 043
.939
0
Av./V
0
1. 021
1. 053
1. 067
1. 073
1.076
1.081
1.085
1. 091
1.096
1.100
1.106
1.099
1.075
1.022
.969
0
3. 644
1. 330
.964
•684
•554
• 475
•378
.319
.245
.197
• 160
• 131
.103
.076
• 047
.030
0
.4
L. E. radius:
J
0.396
percent
c
i
0
NACA
/,6
x
(percent
/,2
0
1.25
2.5
5.0
7.5
I0
15
20
30
40
50
60
70
8O
90
95
1O0
f11-_
(
\
.8
NACA
18-012
.6
..,--,._.__
0
L. E. radius:
>
_-..,...,.,.__
.2
i
.6
.4
z/v
J
.,9
c)
1,0
y
(percent
16-012 BASIC
c)
0
1. 292
1. 805
2. 509
3.032
3.457
4.135
4.664
5.417
5. 855
6. 000
•5. 835
5. 269
4.199
2. 517
1.415
.120
0.703 percent
c
THICKNESS
FORM
(vlV)2
vlV
Avd V
0
1.002
1.109
1.173
1.197
1. 208
1. 223
1. 237
1. 257
1.271
1.286
1.293
1.275
1.203
1.051
.908
0
0
1. 001
1. 053
1. 083
1. 094
1. 099
1. 106
1. 112
1. 121
1. 128
1. 134
1. 137
1.129
1. 097
1. 025
• 953
0
2.624
1. 268
• 942
.677
.551
.473
.378
•319
.245
.197
.161
.131
.102
.075
.045
.027
0
74
REPORT
NO.
82
4--NATION_AL
ADVISORY
COMMIT-TEE
FOR
AERONAUTICS
'20
NACA
1.6
16-015
x
_
/.2
_.__
.8
.....
I ......
........
m
.d
: ....
NACA
_
16-015
c)
0
1.25
2. 5
5. 0
7.5
10
15
20
30
40
50
60
70
80
90
95
100
..---._
--
THICKNESS
FORM
y
(percent
.______.
BASIC
(percent
.
c)
r V
(vlV)2
0
1. 615
2. 257
3. 137
3.790
4.322
5. 168
5. 830
6. 772
7. 318
7. 500
7. 293
6. 587
5. 248
3. 147
1. 768
.150
0
0
.956
1.105
1. 200
1. 239
1. 256
1. 278
1. 297
1. 327
1. 349
1. 364
1. 374
1. 348
I. 254
1. 053
.875
0
• 978
1. 051
1. 095
1. 113
1. 121
1. 130
1. 139
1. 152
1. 161
1. 168
1. 172
1. 161
1.120
1. 026
• 935
0
Avd
V
2. 041
1. 209
• 916
• 668
• 547
• 471
• 377
• 318
• 245
• 197
• 161
• 131
• 102
• 074
• 043
.025
0
.
L.
E.
radius:
1.lO0
percent
c
f
NACA
16-018
BASIC
THICKNESS
FORM
/.6
(percent
m
NACA
c)
(percent
0
i. 25
2.5
5.0
7.5
10
15
20
30
40
50
6O
70
8O
9O
95
1O0
/2
.8
x
16-0/8
y
c)
v
(v/V)2
0
1. 938
2. 708
3. 764
4.548
5. 186
6. 202
6. 996
8. 126
8. 782
9.000
8. 752
7.904
6. 298
3. 776
2.122
• 180
V
0
0
• 903
1. o_
1. 217
1.271
I. 302
1. 332
I. 357
I. 399
1. 426
1. 447
1. 452
1. 421
1. 306
1. 051
• 837
0
.950
1. 045
1.103
1.128
1. 141
1.154
1.165
1. 183
1.194
1.2(}3
1. 205
1. 192
I. 143
1. O25
• 915
O
Ava/V
1. 744
1. 140
• 883
.657
.541
.468
• 376
• 318
• 245
• 1(}8
• 162
.131
. 102
• 073
• 042
• 024
0
.4
..____--f
L.
E.
radius:
1.584
percent
c
J
NACA
16-021
BASIC
THICKNESS
FORM
/.8
J
x
J
H
%X
-
(percent
--
Y
c)
(v/!/)2
(percent
vl V
Av ./V
c)
----J
/
/
0
1.25
2.5
5.0
7.5
10
15
2O
30
40
5O
.8
NACA
.4
__
f
.......
J
70
80
9(1
95
100
16-021
_.r
I
I_
J
I
0
0
2. 261
3. 159
4. 391
5. 306
6. 050
7. 236
8. 162
9. 480
10. 246
10.500
10. 211
9. 221
7.348
4. 405
2. 476
• 210
.2
.6
J
J
.8
lO
L.
E.
radius:
2.156
percent
c
0
O
• 826
1. 062
1. 221
1. 295
1. 342
1.39I
1. 419
1. 474
1. 506
1. 535
1. 536
I. 495
I. 361
1. 039
• 80I
0
• 909
1. 031
1. 105
1.138
1.159
1.179
1.191
1. 214
1. 227
1. 239
1. 239
1.2Z_
I, 166
1. 019
• 895
0
1. 574
1. 069
• 828
• 640
• 534
• 463
• 374
• 317
• 245
• 198
• 162
• 131
• 102
• 072
• 041
• 023
0
SUMMARY
OF
AIRFOIL
DATA
75
NACA
2.O
.....
c,
I:
I
A4(upper
x
(percent
I surfoce)I
c)
0
/.6
\
NACA _3, 4-020
L. E. radius:
/F
y
(percent
BASIC
c)
3.16 percent
TIIICKNESS
(v/V)2
0
1. 714
2. 081
2. 638
3.606
4. 947
5.964
6.800
8. 090
9. 006
9. 630
9. 955
9. 978
9. 765
9. 366
8. 819
8. 143
7. 351
6. 464
5. 496
4. 466
3. 401
2. 342
1.348
• 501
0
.5
• 75
1.25
2.5
5.0
7.5
1O
15
20
25
30
35
40
45
5O
55
60
65
7O
75
8O
85
9O
95
16O
/<
63,4-020
FORM
v/V
J',v,/V
0
0
•444
•605
•820
1. 080
I. 277
1. 383
1.456
1. 551
l• 614
1.659
1.689
1.630
1.567
1.500
1.433
1.362
1.288
1.213
1.137
1.059
• 978
• 896
• 811
• 728
• 651
• 666
• 778
• 906
I. 039
1.130
1.176
1.207
1. 245
1. 270
1. 288
1. 300
1. 277
1. 252
l. 225
1.197
1.167
1.135
1.101
1. O66
l. 029
• 989
• 947
• 901
• 853
• 807
1. 395
1. 280
1. 201
1. 072
• 846
• 645
• 543
• 475
• 386
• 330
• 289
• 257
• 219
• 192
• 169
• 148
• 128
• 112
• 097
• 084
• 071
• 059
• 046
• 036
• 023
0
e
/
_J
NACA
x
(percent
/.6
c)
0
f--cz
=.0.3
(upper
.5
• 75
1.25
2.5
5
7.5
10
15
20
25
30
35
40
45
5O
55
6O
65
70
75
80
85
9O
95
16O
surface)
is
-b
"
"_.0,3
qower
sur£oce)
%
_
.8
6.3-006
NACA
.4
f
L. E.
radius:
63-006
Y
(percent
x
(percent
./
s
.c,
=.08(upper
0
surfoce)
.5
• 75
I. 25
2.5
5
7.5
10
15
2O
25
3O
35
4O
45
5O
55
6O
65
7O
75
8O
85
9O
95
16O
/.2
....
.08
(/o_er surface)
.,9
_ACA 63-009
.4
fl
_
O
---..,...._
_
I
.z
.6
.4
x/v
c)
.8
10
L. E. radius:
THICKNESS
(vl V) _
c)
0
6
• 503
• 609
• 771
1. 057
1.462
I. 766
2. OlO
2. 386
2. 656
2. 841
2. 954
3. O6O
2. 971
2. 877
2. 723
2. 517
2. 267
1. 982
1. 670
1. 342
1. 008
.683
• 383
• 138
O
• 973
1.050
1.080
1. llO
1. 130
1. 142
1. 149
1. 159
1. 165
1. 170
1. 174
1. 170
1. 164
1. 151
1. 137
1. 118
1.096
1. 074
1. 046
1.020
•994
• 965
•936
• 910
• 886
0,297 percent
NACA
/.6
BASIC
vl V
AVal V
O
• 986
1.025
l. 039
1. 054
1.063
l. 069
1• 072
1.077
1. 079
1. 082
1.084
1.082
1.079
1.073
1.066
I. 057
1. 047
I. 036
1.023
1.010
• 997
• 982
• 967
• 954
• 941
4. 483
2. ll0
1. 778
1. 399
• 981
• 692
• 562
• 484
• 384
• 321
• 279
• 245
• 218
• 196
• 176
• 158
• 141
• 125
• 111
• 098
• 085
• 073
• 060
• 047
• 032
0
c
63-009
Y
(percent
FORM
BASIC
THICKNESS
(v/V)
c)
2
FORM
v/v
0
0
0
• 749
• 906
1.151
1. 582
2.196
2. 655
3.024
3.591
3.997
4. 275
4. 442
4. 500
4. 447
4.296
4. 056
3. 739
3. 358
2. 928
2. 458
1. 966
1. 471
.990
• 550
• 196
0
•885
l. 002
1.051
l. 130
l. 180
I. 205
1. 221
1.241
1.255
1.264
1.269
1.265
1. 255
1.235
1. 208
1.175
1. 141
1. 104
1. 065
1. 025
•984
•942
.903
• 868
• 838
• 941
1. 001
1. 025
1. 063
1. 086
1. 098
1.105
1.114
1.120
1.124
1.126
1.125
1.120
1.111
1.099
1. 084
I. 068
1.051
1.032
1.012
•992
•971
•950
•932
.915
0.631 percent
c
Av./
V
3.058
1.889
1.647
1. 339
• 961
•689
•560
•484
•386
•324
•281
•248
• 220
• 196
• 175
• 156
• 140
• 124
.16O
•095
•082
•069
•057
•044
• 030
0
76
REPORT
2O
/.6
NO.
8 2
4--_N'ATIONAL
ADVISORY
:!ltt T!i]
/.2
.8
.4
COMMITTEE
FOR
AERONAUTICS
NACA
63-010
c)
(percent
x
0
,)
(v/l')_
FORM
Avo/V
0
0
.829
1. 004
1. 275
1. 756
2. 440
2. 950
3. 362
3.994
4. 445
.841
.978
1. 037
1. 131
1.193
1.223
1. 245
1. 270
1. 285
1. 296
1. 302
1. 299
1. 286
1. 262
1. 231
1.11,13
I. 154
1.113
1. 069
1. 025
.979
.935
.893
• 853
.822
.917
• 989
1. 018
1. O63
1. 092
1. 106
1. 116
1.1'27
1. 134
1. 138
I. 141
I. 140
1. 134
1.123
1. 110
1. 092
1. 074
1. 055
1. 034
1.012
• 989
• 967
.945
.924
• 907
4. 753
4. 938
5.01_)
4.938
4. 766
4.496
4. 140
3. 715
3. 234
2. 712
2.166
1.618
1. 088
. (')04
• 214
0
radius:
v/V
0
.5
• 75
1.25
2.5
5.0
7.5
10
15
2O
25
30
35
4O
45
5O
55
6O
65
7O
75
80
85
9O
95
16O
E.
TtIICKNESS
y
(percent
L.
BASIC
0.770
percent
NACA
e
63_-012
x
2. 775
1. 825
1. 603
1.316
.952
• 687
.560
.484
.386
.325
• 282
.248
.220
• 196
• 175
• 156
• 139
• 123
.108
• 094
.081
• 069
• 056
• 043
• 030
0
BASIC
THICKNESS
FORM
y
(percent
c)
(percent
e)
(v/V)2
v/V
AV,,IV
.........................
/.6'
i._
O
]
.8
,'VACA
._
23_-U/2
,
--
0
0
0
.985
1.194
1.519
2.102
2. 925
3. 542
4. 039
4. 799
5. 342
5. 712
5. 931t
6. 000
5. 92O
5. 7O4
5.37O
4. (,135
4.42O
3.84(I
3. 210
2. 55(;
1. ,(}(}2
I. 274
.7(17
.250
0
.7,50
.925
1. 005
1. 129
1. 217
1. 261
1.2194
1. 330
I. 349
1. 3112
1. 371)
1. 3116
I. 348
1.317
1. 2711
1.22(`}
I. 181
I. 131
I. 076
1. I)2t
• !,169
.920
.871
.826
• 791
• 866
• 962
1. 003
1. 063
1.103
1. 123
1. 138
1. 153
1.161
1.167
1.170
1. 109
1.16t
I. 148
1.130
1.109
1.1187
l. 0{;3
1. (137
1. Ol 1
• 984
• 959
.933
• 909
• 889
• 5
.75
1.25
2. 5
5
7. 5
lO
15
20
25
31)
35
40
45
5O
55
6O
65
7O
75
80
85
90
95
16O
J
I
2.
1.
1.
1.
336
695
513
266
.933
. (k_2
.559
.484
.387
.326
.283
.249
.221
.196
.174
. 1.55
. 137
.121
.11t6
.091
.07(`t
.067
.055
.042
.029
0
f
L
E
ral
us
1 087
percent
NACA
(`)32
x
015
BASIC
Y
(percent
c)
/8
(percent
THICKNESS
FORM
(v/1,')_
c)
v
V
Avo/V
I ....
0
_4
L.
.4
.6
.8
LO
E.
radius:
• 822
• 938
1. 105
I. 244
1. 315
1.3ti0
1.415
1. 446
,1. 467
1. 481
1. 475
1. 446
1. 401
1. 345
1. 281
1. 22(}
1. 155
I. 085
1. 019
• 953
. 894
. 839
• 789
• 7._10
4. 721
3. 934
3. 119
2. 310
1. 541
.852
• 300
0
1.594
i)crccnt
0
• 6O0
6. 108
5. 453
100
.Z
0
0
I. 204
1. 462
1. 878
2. 610
3. 648
4. 427
5. 055
6.011
6. 693
7. 155
7. 421
7. 5(',0
7. 386
7. 009
6. 665
.5
• 75
1.25
2.5
5
7.5
10
15
2O
25
30
35
40
45
5O
55
6O
65
7O
75
80
85
_)
95
L2
0
e
c
. 775
1. 918
1. 513
.907
.969
1. 051
1. 115
1. 371`I
1. 182
. (,}03
.674
1. 147
1. 166
.557
.484
1.
1.
I.
[.
1.
1.
.388
.330
.286
.251
.222
.196
190
202
211
217
214
202
1. 184
1. 160
1. 132
1.105
1.075
1. 042
1. 009
• 976
• 946
• 916
• 888
.866
.174
.153
.135
. 118
.11)2
. 088
. 07(i
. 063
• I)51
. 039
. 026
0
SUMMARY
Z.O
I
=. 32
OF
AIRFOIL
DATA
77
NACA
i
x
(percent
c)
y
(percent
0
/.6
BASIC
_/ower
purl'ace)
.8
N40A
63_-018
.4
/
/
THICKNESS
FORM
(v/V)2
v]
AvdV
0
0
• 441
• 700
• 848
1.065
1. 260
1. 360
1. 424
1. 500
1. 547
1. 570
1. 598
1. 585
1. 550
1. 490
1.411
I. 330
I. 252
1.170
1. 087
1. 009
.933
• 868
.807
• 753
• 712
.664
•837
.921
1. 032
1. 122
1. 166
1. 193
1. 225
1. 244
1. 257
1.26_
1. 259
1. 245
1. 221
1. 188
1.1,53
1. 119
1. 082
1. 043
1. 004
• 966
.932
• 898
• 868
• 844
1. 639
1. 361
1.258
1. 105
•871
.663
• 553
.484
• 390
.333
• 289
• 253
• 223
• 197
• 173
• 152
.133
• 115
• 099
• 084
• 072
•059
• 048
• 036
.024
0
--
/
/
c)
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
.5
• 75
1.25
2.5
5
7.5
I0
15
2O
25
3O
35
40
45
50
55
6O
65
7O
75
8O
85
9O
95
100
1.2
":3Z
633-018
surface)
L. E, radius:
2.120 percent
c
oi
NACA
/
_
\_
x
(percent
surface)
.'e z = .38/upper
c)
634-021
y
(percent
BASIC
c)
THICKNESS
FORM
(v/V)2
v/V
Ar./V
/.6
.._
/i-t
0
'
"..,\;
/.2
.8
i
/
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
4.16O
3.054
2.021
1.113
• 392
0
,5
.75
I. 25
2.5
5
7.5
10
15
2O
25
30
35
40
45
,5O
55
6O
65
7O
75
8O
85
9O
95
100
0
0
• 275
.564
•725
1,010
1. 260
1. 394
1. 487
1. 592
1. 655
1. 698
1. 721
1. 709
1. 654
1. 578
1. 479
1. 380
1. 281
1.180
1. 084
• 994
.911
• 839
• 774
• 721
•676
.524
• 751
• 851
1. 005
1.122
1.181
1.219
1. 262
1. 286
1. 303
1. 312
I. 307
1. 286
I. 250
1. 216
1.175
1.132
1,086
1. 041
• 997
• 954
.916
.880
• 849
• 822
1. 430
1. 236
1.156
1. 034
• 842
• 653
• 550
• 484
•392
• 335
• 291
•255
• 225
• 198
.173
.150
• 130
• 112
• 096
• 081
.068
•057
.046
• 035
.023
0
/
/
L. E. radius:
2,650 percent
NACA
c
64,2-015
BASIC
TIIICKNESS
FORM
I
.e
/
I%.
: 20
7owe,-
/.6
S
z =.ZO
{upper
surface)
z
(percent
0
.5
• 75
1.25
2.5
5.0
7.5
10
15
20
25
30
35
4O
45
5O
55
6O
65
7O
75
8O
85
9O
95
16O
//
/
/.Z
//(-..
/
surface)
.8
--
/VAOA
54
2-015
--
.4
..._..._l
--
/
If
/
__1
0
.Z
.4
Y
(percent
(v/V)_
c)
0
1. 216
1. 453
1. 829
2. 538
3.514
4.243
4. 838
5. 781
6. 454
6,067
7. 307
7. 481
7. 480
7. 268
6.8,50
6.311
5. 670
4. 944
4.158
3. 338
2. 506
1. 698
• 96l
• 351
0
/
.6
w/e
c)
.8
LO
L. E. radius:
1.65 percent
c
v/V
0
6
.710
.825
• 962
1.122
1. 234
1. 288
1. 323
1. 371
1. 401
1. 422
1. 441
l. 458
1. 471
1. 432
1. 366
1. 299
1. 234
1.16_
I. 102
1. 039
.973
• 910
• 849
.791
.739
• 843
• 908
•981
!. 059
1,111
1,135
1,150
1. 171
1.184
1,192
1.200
1. 207
1.213
I. 197
1. 169
1.140
1.111
1. 081
1. 050
1.019
• 986
• 954
• 921
• 889
.860
AvdV
1. 936
1. 500
1. 359
1.161
.911
.678
• 553
• 477
• 383
• 325
• 285
• 253
• 227
• 202
• 175
.156
• 137
• 122
• 102
• 086
• 080
• 071
• 656
•039
.027
0
78
REPORT
NO.
824--NATIONtAL
ADVISORY
CO'MMIT'TEE
:FOR
AERONAUTICS
NACA
2O
32
(percent
64-006
Y
c)
(percent
....
el=.02
(upper
.8
L.
E.
radius:
0
.997
1.o29
1.o42
1,o53
1.o58
1.o62
1.065
1.071
1.074
1.077
1.079
1.081
1.082
1.077
1.069
1.060
1.050
1.039
1.027
4, 623
2.175
1,780
1.418
•982
•692
.560
.483
.385
.321
.279
,246
,220
•198
•178
.158
.142
•126
.112
•098
1.014
1.000
.985
.969
.085
.072
.060
.047
0.256
percent
radius:
(vlV)
',
I.-.
.......
g..o {uppersu_fooe)
l"-=06 lower
_"_
[
.8
64-002
---
L
""
NA CA
I
I
• 955
1. 008
1. 041
1. 062
1. 073
1.08()
1. ()g6
1. (}93
1. 099
1. 103
1. 107
1. It)9
1.111
1. 105
1. 091
1. 078
1. O64
1.0_)
1. 034
1. 016
• 997
• 978
• 958
• 937
• 916
0.455
percent
4
.d
.8
L.
/.o
E.
Y
TIIICKNESS
(v/V)2
0
FORM
v
V
0
0
O
• 739
.892
1.128
1.533
2, 109
2. 543
2.898
3.455
3.868
4. 170
4. 373
4. 479
4.490
.872
• 990
1. 075
1. 131
1.166
1.186
I. 200
1. 221
1. 236
1. 246
1. 255
1.262
.934
.995
1.037
1.0(_{
1.080
1.089
1.095
1.105
1.112
1. 116
1•120
1.123
1.126
1. lit;
1.1_
1. 088
1. 072
1.055
1.036
1.016
.996
.975
• 952
.930
.907
1. 267
1. 246
1. 217
1. 183
1. 149
1. 112
1. 073
1. O33
• 992
• 950
• 907
.865
• 822
4. 364
4. 136
3.
3.
3.
2.
2.
1.
1.
826
452
026
561
069
564
069
• 611
• 227
0.579
544
994
686
367
• 969
• 688
• 560
,480
• 385
.323
• 279
• 246
• 220
• 198
• 176
• 158
• 141
• 125
• ll0
• 096
• 083
• 071
• 059
• 046
• 031
Avo/V
c)
0
radius:
3.
1.
1.
1.
c
BASIC
(percent
95
100
.2'
Av_IV
0
75
8O
85
90
0
vlV
.912
1,016
1.084
1.127
1,152
1.167
1.179
1.195
1.208
1.217
1.2125
1.230
1.235
I. 22(}
1.191
1.163
1.133
1.102
1.069
1.033
,995
•957
•918
.878
.839
.5
• 75
1.25
2.5
5.0
7.5
10
15
20
25
30
35
40
45
5O
55
6O
65
7O
surroco)l_
2
0
0
l
FORM
• 658
• 794
1. 005
1. 365
1. 875
2, 259
2, 574
3.069
3.437
3. 704
3.8_A
3.979
3. 9(}2
:{,8M3
3. 6M4
3,411
3. (181
2. 704
2.291
1. 854
1. 404
• 961
• 550
• 206
0
x
c)
TItICKNESS
c)
NACJ64-009
(percent
.031
0
0
55
9O
65
7O
75
80
85
9O
95
19O
E.
BASIC
Y
(percent
.9_3
• 936
c
64-008
.5
.75
1.25
2.5
5.0
7.5
1O
15
20
25
30
35
4O
45
L.
Av ol V
.995
1.058
1,085
1. 108
1. 119
1.128
1. 134
1. 146
1. 154
1.160
1.164
1. 168
1. 171
1,160
1.143
1.124
1.102
1. 079
1. 054
1. 028
1.000
• 970
.939
• 908
• 876
0
i
V
O
z
c)
v
(v/V)
c)
NACA
(l)erqcnt
FORM
.494
• 596
.754
1.024
1.405
1.692
1.928
2,298
2.572
2. 772
2.907
2.98l
2,995
2.919
2. 775
2. 575
2.331
2.0_)
1. 740
1.412
1.072
.737
.423
.157
0
•5
.75
1.25
2.5
5.0
7.5
10
15
20
25
30
35
40
45
5O
55
6O
6,5
7O
75
80
85
9O
95
100
surfoce)
THICKNESS
0
0
L2
BASIC
l)erccnt
c
3.130
1. 905
1. 637
1•340
.963
• 686
• 560
• 479
• 383
• 323
.281
• 248
• 221
.198
• 176
.158
• 140
• 125
• 109
• 095
• 082
• 070
• 057
• 044
• 030
0
SUMMARY
OF
AIRFOIL
79
DATA
NACA
20
(percent
c)
64-010
Y
(percent
0
_
(Upp@r
=.08
NACA
.5
.75
1.25
2.5
5
7.5
10
15
20
25
30
35
40
45
50
55
60
65
7O
75
80
85
90
95
16O
su/-fooe)
64-0/0
.4
L. E. radius:
c)
THICKNESS
(vlV)2
c)
FORM
v/V
AVo/V
0
0
0
• 820
• 989
1.250
1. 701
2. 343
2. 826
3.221
3.842
4. 302
4. 639
4• 864
4. 980
4.988
4. 843
4. 586
4. 238
3.820
3.345
2. 827
2.281
1. 722
1. 176
• 671
• 248
0
• 834
• 962
I. 061
1.130
1.181
1. 206
1. 221
1. 245
1. 262
1. 275
1. 286
1.295
1. 300
1.279
I. 241
1. 201
1.161
1.120
1. 080
I. 036
.990
• 944
.900
• 850
• 805
• 913
• 981
1. 030
1.063
1. 087
1. 098
1. 105
1. 116
1• 19-3
1. 129
1. 134
1. 138
1. 140
1. 131
1. 114
1.096
1.077
1.058
1.039
1.018
• 995
• 972
• 949
• 922
•897
0.720
percent
NACA
x
(percent
BASIC
c
641-012
Y
(percent
2. 815
1.817
1. 586
1.313
• 957
• 684
• 559
• 480
• 386
• 325
• 280
• 246
• 220
• 199
• 176
• 158
• 139
• 124
• 109
• 095
• 081
• 069
• 057
• 044
• 030
0
BASIC
THICKNESS
(v/V)_
c)
FORM
vlV
Av,/V
/.6
0
.et =./2
(upper
.5
• 75
1.25
2.5
5.0
7.5
10
15
2O
25
30
35
40
46
.5O
55
6O
65
70
75
80
85
9O
95
19O
xclrfcloe)
__------/.2
(lower
surface
l
":/2
.8
• NAOA
G4_-012
.4
........,.,__
El
radius:
x
(percent
1.6
.-re
=._2
(upper
,5
• 75
1.25
2.5
5.0
7.5
10
15
20
25
30
35
40
45
5O
55
6O
65
70
75
8O
85
9O
95
16O
,t
/
.8
NAOA
64z-0/5
.4
i
o
.4
_e
.6
i
i
.8
c)
0
surface)
/
I,E
0
• 750
• 885
1. 020
1.129
1. 204
1. 240
1.264
1.296
1.320
1.338
1.351
1.362
1.372
1.335
I. 289
1.243
1. 195
1. 144
1.091
1.037
• 981
• 928
.874
•825
• 775
•866
• 941
1. Ol0
1. 063
I. 097
I. 114
1. 124
1. 139
1. 149
1 156
1. 162
1. 167
1. 171
1. 156
1. 136
1. 115
1.093
1.070
1.044
1. 018
• 990
• 963
• 935
.908
• 880
1.040 percent
NACA
_
0
• 978
1.179
1. 490
2. 035
2. 810
3.394
3.871
4. 620
5.173
5. 576
5. 844
5. 978
5.981
5. 798
5. 480
5.056
4. 548
3. 974
3.350
2. 695
2. 029
1. 382
• 786
• 288
0
2. 379
1.663
1.508
1.271
•943
• 685
•559
•482
•388
•328
.281
•247
• 221
• 199
• 177
• 158
• 138
• 122
• 103
• 088
•074
• 063
• 052
• 045
• 028
0
i
L. E.
i
0
r
LO
L. E. radius:
c
645 015 BASIC
Y
(percent
c)
(vlV)2
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
0. 810
6. 266
5.620
4. 895
4.113
3.296
2. 472
1.677
• 950
• 346
0
1.590 percent
THICKNESS
o
•670
• 762
•896
1.113
1.231 _
i. 284
1.323
1.375
1.410
1.434
1.454
1.470
1,485
1. 420
1.365
1. 300
1.233
1. 167
1. 101
1.033
• 967
• 902
•841
• 785
• 730
c
FORM
dv
O
.819
•873
• 947
I. 0_5
1.109
1.133
1.150
1.172
1.187
1.198
1.206
1.213
1.218
1. 195
1. 168
1. 140
1. 110
1.080
1.049
1. 010
.983
• 950
• 917
• 886
• 855
av./V
1. 939
1.476
1. 354
1. 188
• 916
• 670
• 559
• 482
• 389
• 326
• 285
• 250
• 225
• 202
• 179
• 158
• 135
• 121
• 105
• 090
• 078
.065
• 054
• 041
• 031
0
80
REPORT
:NO.
8 2
4--:NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
NACA
x
(percent
(uppe:
_cz=.3Z
....
surfoce)
,-
%
NACA
G4_-016
.4
/
L.
E.
radius:
2.208
:r
(percent
. _:-v_=.
44
[upper
c)
.B
G%-021
o
• 546
• 705
• 862
1. 079
1. 244
1. 327
1. 380
1.4,50
1. 497
1. ,N_5
I. 562
1. 585
• 739
• 840
• 920
1. 039
1.115
l. 152
1.175
1. 204
1. 224
1. 239
1. 250
1. 259
1. 265
1. 232
1.198
1. 164
1. 128
1. 091
1. 053
1.014
• 976
.937
.901
.864
.8;/4
BASIC
TIIICKNESS
(v/1
c)
--
I
I
0
1.046
1. 985
2.517
3. 485
4.871
5.915
6. 769
8. 108
9, 01.15
9. 807
10.269
10.481
IlL 431
I 0. 030
9. 404
8. 607
7. 678
6, 649
5. M9
4. 416
3. 287
2. 213
I. 245
.449
0
.5
• 75
1.25
2.5
5.0
7.5
l0
15
20
25
30
35
40
45
50
55
5O
65
70
75
80
85
9O
95
1(10
L8
N4CA
0
1. 646
1.3(')0
1.269
1.128
• 904
• 669
• 558
• 486
•391
• 331
• 288
• 255
• 228
.200
• 177
.154
• 134
.117
• 102
• 088
• 074
• 063
.051
• 039
• 027
0
c
644-021
y
(1)ercent
_v,/V
V
(v/l')_
1.600
1. 518
1. 436
1. 354
1. 272
1.190
|. 109
1. 028
.952
.879
• 812
• 747
• 695
percent
0
i
FORM
FORM
"':
v
I:
At,,/I"
surface)
L6
.....
THICKNESS
v
c)
NA('A
//
BASIC
0
1. 428
1. 720
2. 177
3.005
4. 186
5. 076
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. 8&_
I.951
1.101
• 400
0
.5
• 75
1.25
2.5
5.0
7.5
10
15
2O
25
30
35
40
45
5O
55
6(1
65
7O
75
8O
85
9O
95
I0O
_\
]
y
(percent
0
/7"_\
.
c)
6t3-018
.4
L.
E.
radius:
I
2.8_4
percent
NACA
0
0
.462
• 5O3
• 759
1. 010
1. 248
1. 358
1.43l
1. 527
1. 593
1. 654
I. 681
I. 712
I. 71)9
I. 607
I. 507
I. 406
1. 307
1. 209
1.112
1. 029
• 932
• 851
.778
.711
.653
• 680
• 776
• 871
1. 005
1. 117
1. 165
1. 196
1. 236
1. 262
1.2Sl
1. 297
1.3[)_
1.3O7
1. 268
1. 228
1. 186
1.143
l. 099
1. 458
1. 274
1. 203
1. 084
.878
,665
.557
48(;
.395
.335
.29:1
.251)
.232
.202
,17g
.155
.134
. 111
.099
1.1155
1.010
. !)65
• 923
.084
.07l
.059
.047
• 882
• 844
• _(18
.036
.022
0
c
65,2-016
BASIC
THICKNESS
FORM
l
_
,
..'-
__ e z =. 20
%
surfoce)
(upper
(percent
c)
(percent
Y
(v/132
c)
v/l"
_v./V
/.6-0
L2
.8
_.
55
(_)
65
71)
75
8O
85
90
95
100
NACA 65,_:-0/6
.4
I
O
0
1.2O2
l. 423
1. 796
2. 507
3.54;I
4. 316
4. 954
5. 958
6. 701
7. 252
7. 645
7. 892
7. 995
7. (,)38
7.672
7. 184
6, 495
5. 647
4. 713
3, 7;18
2.75(,)
1.817
• 982
.340
.5
.75
1.25
2.5
5.0
7.5
10
15
20
25
3(}
35
40
45
59
.2
.4
L.
.6
.8
1.0
E.
0
radius:
1.704
0
0
.5O0
.69O
.842
1. 068
1. 217
1. 287
1. 328
1.37!1
1. 409
1. 433
1. 453
I. 469
1.4_4
1. 4117
1.4!}I
1. 421
1. 328
l. 235
I. 147
1. O56
.970
.886
.816
.769
.748
. 831
• 918
1. 033
1. 103
1. ]34
1.152
1.174
1. 187
1.1 (.17
1.2(15
1. 212
1.21_
l. 224
1. 221
1. 192
I. 152
1. III
1.071
1. 028
.985
.733
pereont
c
• 941
• !)03
• 877
.856
1. 959
1. 650
1. 500
1. 275
. 9211
• 689
• 545
.48O
.39(1
.325
285
255
225
200
180
160
1411
125
ll0
995
(180
O66
.05O
.049
.025
0
SUMMARY
OF
AIRFOIL
81
DATA
NACA
x
(percent
f
/.
/.6
er
urfo
e)
y
(percent
0
Z
/.2
.8
/
BASIC
c)
THICKNESS
(v/V)2
O
1. 664
2. 040
2. 628
3. 715
5. 300
6. 478
7. 433
8. 889
9. 917
10. 648
ll. 142
ll. 423
11. 499
11. 361
10. 949
10. 179
9. 108
7. 848
6. 461
5. 015
3.618
2. 345
1. 258
• 439
0
.5
• 75
1.25
2.5
5.0
7.5
10
15
2O
25
30
35
4O
45
5O
55
60
65
7O
75
8O
85
9O
95
16O
?>
.4
c)
05,2-023
O
.400
.500
• 682
• 943
1.232
1. 375
1.467
1,577
1.628
1. 655
1. 677
1. 694
1. 708
1. 716
1. 712
1. 606
I. 428
I. 274
1.135
I. 003
• 893
.803
• 732
• 682
• 651
FORM
v/V
AvJV
0
• 632
• 707
• 826
• 971
1. 110
1.173
1. 211
1. 256
1.276
1. 286
1. 295
1. 302
1. 307
1.310
1. 308
1. 267
1. 195
1.129
1. 065
1.6Ol
• 945
• 896
• 856
• 826
• 807
1. 414
1. 161
1. 084
• 967
• 811
• 633
• 539
• 479
• 380
• 324
• 281
• 247
• 229
• 198
• 178
• 161
• 147
• 110
• 096
•093
•080
•053
•035
•022
•018
0
_.-_...__
.........--
/
/
L. E. radius:
2.955 percent
c
.,../
NACA
x
(percent
c)
y
(percent
0
.4
_--.---..._.__
/I
/
BASIC
c)
THICKNESS
(v/V)_
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
6.45O
5. 486
4.456
3.390
2. 325
1. 324
• 492
0
.5
• 75
1.25
2.5
5.0
7.5
10
15
2O
25
3O
35
40
45
5O
55
60
65
7O
75
8O
85
90
95
16o
IV4CA65,3-©/8
65, 3-018
FORM
v/V"
0
0
• 650
• 750
• 872
1.020
1. 179
1. 263
1.320
1.393
1. 439
1. 473
1. 502
1. 526
1. 546
1. 562
1. 513
1. 433
1. 348
1. 258
1. 169
1. 079
• 992
• 905
• 818
• 738
• 658
• 806
• 866
• 934
1. el0
1.086
1. 124
1. 149
1. 180
1.200
1. 214
1.226
1. 235
1. 243
1. 250
1.230
1.197
1. 161
1.122
1.081
1. 039
.996
• 951
• 904
.859
.811
Avo/V
1. 750
1. 387
1. 268
1.108
•890
• 677
.568
• 489
•395
•334
• 292
• 260
• 232
• 209
• 186
• 165
• 142
• 123
• 107
• 093
.080
.066
• 054
•040
• 024
0
/
/
L. E. radius:
1.92 percent
NACA
%
(per_ntc)
e
65-006
Y
(percent
BASIC
THICKNESS
(v/V)2
c)
FORM
v/V
Av./V
1.6
0
.....
.5
• 75
1. 25
2.5
5.0
7.5
10
15
2O
25
30
35
40
45
50
55
6O
65
70
75
80
85
9O
95
100
surfoce]
ez:.O/(upper
L2
.-0
....
:01
(/o,,_r
s_,-foc4
_
.8
IVACA
55-006
.4--
L. E. radius:
.4
.6
ale
.8
1.0
0
0
1.044
1.055
1.063
1.081
1.16O
1. 112
1. 120
1. 134
1. 143
1• 149
1.155
1. 159
1.163
1.166
1.165
1. 145
1. 124
1.16O
1.073
1.044
1.013
.981
• 944
• 902
• 858
• 476
• 574
• 717
• 956
1.310
1.589
1.824
2.197
2. 482
2. 697
2. 852
2. 952
2.998
2.983
2.900
2. 741
2. 518
2. 246
1.935
1.594
1.233
• 865
• 510
• 195
0
0.240 percent
c
O
1. 022
1.027
1.031
1.040
1,049
l• 055
1.058
1.065
1.069
1.072
1. 075
1.077
1.078
1.080
1.079
1. 070
1. 060
1. 049
1.036
1. 022
1.006
• 990
.972
.950
• 926
4.815
2. 110
1. 780
1.390
• 965
• 695
• 560
.474
.381
.322
.281
• 247
• 220
• 198
• 178
• 160
• 144
.128
• 114
.100
• 086
•074
.060
•046
.031
0
82
REPORT
NO.
8 2 4--NATIONtAL
ADA'ISORY
COMMITq'EE
FOR
AERONAETICS
NACA
2.O-x
(percent
65-008
y
c)
04 /ow,r
4/ACA 65-008
-4
FORM
v/ V
AVJ
V
0
0
.627
.756
.945
1.267
1. 745
2.118
2.432
2.931
3.312
3.599
3.805
3.938
3.998
3.974
3.857
11._8
3.337
2.971
2. 553
2.096
1. 617
1.13l
.0(_
.252
0
.978
1.010
1.043
1.086
1.125
1.145
1.158
1.178
1.192
1.203
1.210
1.217
1.222
1.226
1.222
1.193
1.1C_3
1.130
1.094
1.055
1.014
.971
.923
.873
.817
.989
1.005
1.021
1.042
1.061
1.070
1.076
1.085
1.092
1.097
1.100
1.103
1.105
1.107
1.105
1.092
1.078
1.0_3
1.046
1.027
1.1107
19_5
.961
.934
•904
3.695
2. 010
1. 696
1. 340
.956
• 689
.560
.477
• 382
• 323
.281
• 248
.221
• 199
.178
• 160
.145
.128
• 113
.098
.084
.072
.059
.044
.031
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
SUr_OC_)
(_p_r
_104
_
I
0
TIIICKNESS
(v/ V)2
c)
(percent
0
1.6
BASIC
._l_____
__t-------
L.
E.
radius:
0.434
percent
NACA
x
(percent
/.6"
c)
65-009
y
(percent
0
.8
NACA
65-009
TIIICKNESS
FORM
(vlV)2
c)
v/v
avo/ V
O
0
.700
.845
1. 058
1. 421
1. 961
2.383
2. 736
',1.299
3. 727
4. 050
4. 282
4.431
4. 496
4. 469
4. 336
4.086
"1. 743
3. :/28
2. 850
2.1/42
1. 805
1. 200
.738
.280
0
• 945
• 985
1. 037
1. 089
1. 134
1. 159
1. 177
.972
.992
1. 018
1. 044
1. 065
1. 077
1. 085
1. (195
1, 1()3
1. 109
1.113
1.116
1. 119
1. 122
1. 118
1.11)5
1.11_9
1. (170
1. 050
1. 029
1. 006
• 981
. (,t55
.925
.893
• 5
.75
1.25
2. 5
5.0
7. 5
10
15
20
25
30
35
40
45
,_X)
55
60
65
70
75
80
85
90
95
100
_upper surface)
=.00
BASIC
0
0
l e[
c
1. 200
1. 216
1. 229
1,238
1. 246
1. 252
1. 258
1.2f10
1. 220
1. 185
1. 145
1. 103
1,059
1. 013
• 963
.912
.856
.797
3.
1.
1.
1.
270
962
655
315
.950
• 687
• 500
.477
.382
.323
• 280
.24S
• 220
198
178
160
144
128
111
.097
• 084
• 071
.059
• 044
.030
0
I
L.
E.
radius:
0.552
pcrecnt
c
NACA65-010
.T
q
--.08
(upper
i
/lower
surfoce_
_
.8
--
0
--
NACA
65-010
6O
65
70
75
8O
85
9O
95
100
-
f__.._..
1
--
_
---.____
_
.2
.4
•6"
,_i_
(1)crccnt
.5
• ;5
1.25
2.5
5. 0
7.5
10
15
20
25
30
35
40
45
,5O
55
/.8
l:O 0
c)
0
surface)
o
•4
Y
(t)ercent
/.5
.8
LO
L.
E.
BASIC
radius:
0.687
TIIICKNESS
FORM
(r/1 ")2
c)
r/V
0
0
0
.772
.932
1. 169
1. 574
2. 177
2. 647
3. 041)
3. 666
4. 143
4. 503
4. 760
4. 924
4.996
4. 003
4. 812
4. 530
4. 146
3. 682
3. 156
2. ,584
1. 987
1. 385
• 810
• 1106
0
.911
.0(10
1. 025
1. 085
1. 143
• 954
• 980
1. 012
1. 042
1. 069
1. 085
1. 094
1.1110
l. ll4
1.121
1. 126
1. 130
1. 133
1. 136
I. 133
1.115
1. 990
I. 076
I. 055
I. 031
1. 005
.979
.950
• 919
• 8!44
perccnt
1. 177
1. 197
I. 224
1. 242
1. 257
I. 268
1. 277
1.2_4
1. 290
1.2_4
I.244
1. _02
1.1 r_
1. 112
1. 002
1. Ol I
.95_;
.9(_1
.844
.781
c
avo/ V
2. 96)7
1.9ll
1.614
1. 292
• 932
• 679
• 558
• 480
• 321
.2_0
• 248
.222
.199
• 17!)
.160
.141
.126
• 11()
• ()07
• 082
.070
• 058
• 045
.03O
0
SUMMARY
OF
AIRYOIL
83:
DATA
NACA
x
(percent
c)
y
(percent
0
/.6
........
¢z :-12
{upper
.5
• 75
1. 25
2.5
5.0
7.5
10
15
2O
25
30
35
40
45
50
55
6O
65
7O
75
8O
85
9O
95
100
surfoce)
/.2
--:/2 'lo..e,-s.,-:ooe)
.8
NACA
G5C012
..4
f
lJ
L. E. radius:
651-012
BASIC
c)
THICKNESS
(v/V)2-
FORM
vl V
Av_l V
0
o
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
.848
•935
1. 000
1. 082
1.162
1. 201
1.232
1.268
I.295
1,316
1.332
1. 343
1. 350
1. 357
1. 343
1. 295
1. 243
1. 188
1.134
1. 073
1. 010
• 949
• 884
.819
.748
• 021
.967
1.000
1.040
1.078
1.096
1.110
1. 126
1. 138
1. 147
1.154
1. 159
1. 162
1. 165
1. 159
1. 138
1. 115
1. 090
1. 065
1. 036
1. 005
• 974
.940
.905
•865
1.6O0 percent
2. 444
1. 776
I. 465
1.200
• 931
• 702
.568
• 480
.389
.326
.282
.251
.223
• 204
.188
• 169
.145
.127
•111
.094
• 074
• 062
• 049
• 038
• 025
0
e
0
NACA
x
(percent
.......
cz =.22
[Upper
c)
6,_2-015
y
(percent
BASIC
c)
THICKNESS
(v/V)2
FORM
v/V
2xvJV
surfoce)
/.6
0
O,,f
/.2
--.Z2
.8
[/ower
surfoce)
/
--
NACA
0
1.124
1. 356
I. 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
.5
•75
1.25
2.5
5.0
7.5
10
15
2O
25
3O
35
40
45
5O
55
6O
65
7O
75
8O
85
9O
95
16O
652-0/5
f
j
L. E. radius:
1.505 percent
NACA
-x,
,---
c:.32/upper
x
(percent
surface)
\
c)
0
G
/2
I
S-
J
"--:32
/
.5
.75
1.25
2.5
5.0
7.5
10
15
2O
25
30
35
4O
45
5O
55
6O
65
70
75
8O
85
9O
95
100
""C,
flower
_urfoce)
.8
NACA8#:0/8
.4
f.___-----
/
f
.2
.4
.6
xle
.8
0
• 654
• 817
.939
1. 063
1.184
1. 241
1. 281
1. 336
1. 374
1. 397
1. 418
1. 438
1.452
1. 464
I. 433
1. 369
1. 297
1. 228
1.151
1. 077
I, 002
•924
•846
.773
•697
.809
.904
•969
1. 031
l. 088
1.114
1.132
1.186
1.172
1.182
1.191
1.199
1. 205
1. 210
1.197
1.170
1.139
1.108
1. 073
1. 038
1. 001
•961
.920
.879
.835
2.038
1. 720
1. 390
I. 156
•920
• 682
• 563
• 487
• 393
• 334
.290
• 255
• 227
• 203
• 184
.160
•143
.127
•109
•096
•078
•068
.052
• 038
• 026
0
....-----
I
s
0
f
ZO
L. E. radius:
c
65a-018
y
(percent
BASIC
c)
(v/V)_
0
l, 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
1.96 percent
THICKNESS
e
FORM
v/v
0
0
• 625
• 702
• 817
1. 020
1.192
1. 275
1. 329
1.402
1. 452
1. 488
1.515
1. 539
1. 561
1. 578
1. 526
1.440
1.353
1. 262
l. 170
1. 076
• 985
• 896
• 813
• 730
• 657
.791
.838
.904
1. 010
1. 092
1.129
1.153
1.184
1. 205
1. 220
1.231
1. 241
1. 249
1. 256
1. 235
1.200
1.163
1.123
1. 082
1. 037
.992
.947
.902
.854
.811
Avo/V
1. 746
1. 437
1. 302
1.123
•858
•650
•542
•474
•385
•327
•285
•251
•225
•203
• 182
• 157
• 137
• 118
• 104
•087
•074
•062
.050
•039
•026
0
84
REPORT
:NO.
8 2 4--NATIO:NAL
ADVISORY
COMMITTEE
I
I
i
(percent
J
/.0
,=.44
(upper
//
.4
/
'.44 ('lower surface)
\
!I
UACA
c)
(percent
BASIC
THICKNESS
\
654-0ZI
J
E.
y
c)
FORM
radius:
2.50
percent
vl V
(v/V)2
0
1. 522
1. 838
2. 301
3.154
4. 472
5. 498
6. 352
7. 700
8. 720
9. 487
10. 036
10. 375
10. 499
10. 366
9. 952
9. 277
8. 390
7. 360
6. 224
5. 024
3.800
2. 598
1. 484
• 546
.5
• 75
1.25
2.5
5.0
7.5
10
15
2O
25
3O
35
40
45
5O
55
6O
65
7O
75
8O
85
9O
95
100
f
J
x
0
surface)
J
/
654-021
l
\
.,9
AERONAUTICS
NACA
2. O
/.2
:FOR
V
AV.I
0
• 514
• 607
• 740
• 960
1. 186
I. 293
1.371
I. 469
1. 533
1. 580
l. 621
1. 654
1.680
1. 700
1. 633
1. 508
1. 397
1. 286
1. 177
1. 073
• 970
• 872
• 778
• 694
• 616
• 717
• 779
• 860
• 980
1. 089
I. 137
1. 171
1. 212
1. 238
1. 257
1. 273
1. 531
1. 333
1. 215
1. 062
• 838
• 649
• 544
• 478
.388
• 330
.289
255
229
206
184
158
139
120
101
0
1.
1.
l.
1.
1.
1.
1.
1.
1.
286
296
304
278
228
182
134
085
036
• 985
• 934
• 882
• 833
• 785
• 087
• 073
• 058
• 047
• 035
• 020
0
c
J
jJ
0
NACA
66,1-012
97
BASIC
TI{ICKNESS
FORM
Y
(percent
c)
c)
(percent
(vl V) 2
AVa/ V
vl V
4
/.6
fuppet-
12
="
lq
]
0
surfoce}
1,2
_
__
.8
NAC4
6_/-012--
.4
_
__i
0
0
0
.900
1. 083
I. 343
1.803
2. 484
3.019
3. 482
4. 214
4. 779
5.218
5. 550
5. 786
5. 934
5. 998
5. 972
5. 844
5. 594
5. 165
4. &35
3.789
2. 964
2. 008
1. 244
• 477
0
• 854
• 902
.964
1. 069
1. 138
1. 175
I. 201
1. 237
1. 257
1. 272
1. 284
1.29;t
1. 302
1. 309
1,313
1. 320
1. 327
1. 297
1. 221
1. 143
1. 001
• 974
• 885
• 792
• 701
.924
.950
.982
1. 034
1. 067
1. 084
1. O96
1. 112
1. 121
1. 128
1. 133
1. 137
1. 141
1. 144
1. 146
1. 149
1. 152
1. 139
1. 105
1. 069
1. 030
.987
.941
.890
.837
.5
.75
1.25
2.5
5.0
7.5
10
15
2O
25
30
35
40
45
50
55
60
65
7O
75
80
85
9O
95
100
jj
L.
E.
radius:
0.893
percent
2.
1.
1.
1.
555
780
540
247
.925
.673
• 552
• 474
• 381
• 319
.280
• 248
• 220
• 195
.176
.161
• 144
• 130
• 117
.099,
.083
• 069
• 053
• 04l
• 028
0
c
0
:NACA
c,
=.20
(upper
surface)
(percent
c)
66,2-015
(percent
Y
BASIC
TIIICKNESS
FORM
(vl V)n
c)
vl V
. Avo/V
1.6------
J
0
J
/2
'""._0
...... (lower
-%
surface)
\
.B
- NACA 6_g-015
.4
L.
0
.2
.4
.5
.8
0
1.110
1. 329
1. 645
2.229
3.086
3.757
4.337
5.255
5.964
6. 516
6. 933
7. Z_0
7.415
7. 495
7.46O
7. 294
6.961
6. 405
5. 597
4. 652
3.616
2. 545
1. 488
.560
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
1.0
E.
radius:
1.384
percent
c
0
0
• 700
• 870
• 940
1. 048
1.154
1. 210
1. 244
1. 290
1.323
1. 342
1. 359
1. 374
1. 387
1. 397
1. 407
1.415
1.42|
1. 372
1. 267
1.162
1. 057
• 9,5,3
.848
• 743
• 640
• 837
• 933
• 970
1. 024
1. 074
1.10O
1.115
1.136
1.150
1.158
1.166
1. 172
1. 178
1.182
1.186
1.190
1. 192
1.171
1.126
1. 078
1. 028
• 976
• 921
• 862
.800
2. 085
1. 703
1. 382
1.156
• 898
• 656
.547
• 473
• 382
• 323
• 283
• 248
• 222
• 199
• 179
• 161
• 145
• 131
• 122
• 102
.080
.066
.050
• 037
• 025
0
SUMMARY
OF
AIRFOIL
85
DATA
NACA
!
J
.-" vz: .22
x
(percent
[upper
surfoce}
\
\-
.8
\
L. E. radius:
x
(percent
/.cz,.OI
i.
_----
c)
{upper
_/ower
Surfoce}
surfoce)
_-.
.8
NACA 60-006
.4
-- ----------....______
x
(percent
16
c)
0
.5
• 75
1.25
2.5
5.0
7.5
10
15
2O
25
30
35
40
45
5O
55
6O
65
7O
75
8O
85
9O
95
19O
I
/upper
surface)
\
.8
--
---
NACA
66-008
..4
i
/
.2
.4
.6
_/c
I
.B
r
I.O
c)
• 461
• 554
• 693
• 918
1. 257
1. 524
I. 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
01223 percent
NACA
c_: 03
0
0
• 590
.740
• 918
1. 084
1. 217
1. 285
1. 325
1. 373
1. 401
1. 422
1. 440
1. 456
1. 468
1. 478
1. 488
1. 497
I. 502
I. 442
1. 314
1.185
1. 059
•936
.817
• 700
• 594
• 768
• 860
• 958
1. 041
1.103
1.134
1,151
1.172
1.184
1.192
1. 200
1. 207
1. 212
1. 216
1. 220
1. 224
1. 226
1. 201
1. 140
I. 089
1. 029
• 967
• 904
• 837
• 771
1. 659
1.317
1. 209
1. 091
• 867
.665
.544
•469
1379
•323
•282
•251
•224
.2Ol
•181
• 162
• 146
• 134
.102
• 089
• 078
• 064
.052
.041
• 027
0
BASIC
0
L. E. radius:
o
,.D
Av°l V
c
66-006
y
(percent
.5
• 75
1.25
2.5
5.0
7.5
10
15
2O
25
30
35
40
45
50
55
6O
65
7O
75
80
85
9O
95
100
('i
,.'Ol
vl V
(vl I_)_
c)
2.30 percent
0
/0
FORM
j
NACA
Z2
THICKNESS
f
J
o
BASIC
0
1. 438
1. 730
2.180
2. 938
3.984
4.804
5. 486
6, 541
7. 342
7.957
8. 419
8,741
8. 933
8. 998
8. 934
8. 719
8.316
7. 629
6. 657
5. 523
4.296
3. 027
1. 789
•672
0
.5
• 75
1.25
2.5
5.0
7.5
10
15
20
25
30
35
40
45
50
55
60
65
7O
75
80
85
9O
95
100
.4
_i
Y
(percent
0
Z8
t2
c)
66,2-018
L. E. radius:
66_)8
y
(percent
THICKNESS
FORM
(vll')_
vlV
AvUV
0
1. 052
1. 057
1. 062
1. 071
1. 086
1. 098
1. 107
1. 119
1. 128
1. 133
1. 138
1. 142
1. 145
1. 148
1. 151
1. 153
1.1,55
1. 154
1. 118
1. 081
I. O40
•996
•948
•890
.822
0
i. 026
1. 028
1. 031
1. 035
1. 042
1. 048
1. 052
1. 058
1. 062
1. 064
1. 067
1. 069
1. 070
I. 071
1. 073
1. 074
1. 075
1. 074
1. 057
1. 040
1. 020
•008
•974
•943
•907
4. 941
2.500
2. 020
1. 500
• 967
.695
.554
.474
.379
• 320
• 278
• 245
• 219
• 197
• 178
• 161
• 145
• 130
• 116
• 102
•089
.075
•061
.047
.030
0
c
BASIC
c)
THICKNESS
(v/V)
FORM
2
v/V
Av.I V
3. 794
2. 220
1. 825
1. 388
.949
• 689
• 552
• 474
• 379
• 321
• 278
• 246
• 220
• 198
• 178
• 161
• 145
• 130
• 115
• lO1
• 087
• 073
.058
• 045
• 029
0
0
0
0
• 610
.735
• 919
1. 219
1. 673
2. 031
2. 335
2. 826
3. 201
3.490
3.709
3.865
3.962
4.6O0
3.078
3. 896
3. 740
3.459
3.062
2. 574
2. 027
1. 447
•864
•338
0
•968
1. 023
1. 046
1. O78
1.107
1.128
1.141
1.158
1.171
1.178
1.186
1.191
]. 196
1. 201
1. 205
I. 208
1. 213
1. 202
1.1'56
1. 103
I. 048
• 980
• 926
• 855
• 768
•984
1. 011
1. 023
1. 038
1. 052
1. 062
1. 068
I. 076
1. 082
1. 085
1. 089
1. 091
1. 094
1. 096
1. 098
1. 099
I. 101
1. 096
1. 075
1. 050
I. 024
• 994
• 962
• 925
• 876
0.411 percent
c
86
REPORT
NO.
824--N-ATION1ATJ,
AD_ISORY
COMMITTEE
FOR
AERONAUTICS
NACA
x
(percent
O
.5
• 75
1.25
2.5
5.0
7.5
10
15
2O
25
30
35
40
45
50
55
6O
65
70
75
8O
85
9O
95
16O
1.6
/e
/G
z =.05
/upper"
c)
surface)
/
/.2
.8
NACA 56-009
.4
66-009
y
(percent
BASIC
c)
THICKNESS
FORM
vlV
(v/V)
AvolV
0
0
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
• 930
.999
1.036
1.079
1.119
1.142
1.159
1.178
1.190
1. 201
1. 210
1. 217
1. 221
1. 228
1. 232
1. 237
1. 240
i. 230
1. 172
1.113
i. 050
• 985
•915
• 839
•747
• 964
• 999
1.018
1. 039
1. 058
1.069
1. 077
1. 085
1.091
1,096
1.100
1.103
1.105
1.108
1.110
1.112
1.114
1.109
1.083
1.055
1. 025
.992
•957
•916
•864
3. 352
2.16O
1.750
1. 340
• 940
• 686
• 552
• 473
• 379
• 323
• 280
.246
• 220
• 197
• 178
• 161
• 145
• 130
• 116
• 100
• 085
•071
• 057
•043
•028
0
f
_
_
_________I
L. E.
I
radius:
0.530 percent
NACA
x
(percent
c)
0
,q
=.07
(upper
.5
• 75
I. 25
2.5
5.0
7.5
10
15
2O
25
30
35
4O
45
5O
55
6O
65
70
75
80
85
90
95
16O
surface)
/.Z
"f_'_'---
"-:0
7
_/ower
surface)
(
\
.8
\
\
NACA
56-0/0
.4
L. E. radius:
Y
(percent
"1
(percent
,.G
=.IZ
(upper"
sut'foce)
0
/
,o
.5
• 75
1.25
2.5
5
7.5
10
15
2O
25
30
35
40
45
50
55
6O
65
7O
75
8O
85
9O
95
100
\
I----
\
"<
\
NACA 561-012
f
___.._,I
0
.Z
-4
c)
.5
.8
/.0
L. E. radius:
BASIC
THICKNESS
vlV
(vl V)_
c)
FORM
0
0
0
• 759
• 913
1.141
1.516
2. 087
2. 536
2.917
3. 530
4. 001
4. 363
4. 636
4. 832
4. 953
5.000
4. 971
4. 865
4. 665
4. 302
3. 787
3.176
2. 494
I. 773
1.054
• 408
0
• 896
• 972
1.023
1.078
1.125
1.154
1.174
1.198
1.215
1. 226
1,236
1. 243
1. 249
1. 255
1. 261
1• 265
1,270
1.250
1. 190
1• 121
I, 052
• 979
.904
• 821
• 729
• 947
• 986
1. O11
1.038
1. 061
1.074
1.084
1. 095
1. 102
1.107
1.112
1. 115
1. 118
1.120
1.123
1.125
1.127
1. 118
1.091
1.059
1.026
• 989
• 951
.906
• 854
0.602 percent
NAGA
/.6
66-010
c
BASIC
THICKNESS
FORM
vlV
(vl V)
c)
0
0
0
• 906
1. 087
1.358
1• 8O8
2. 496
3.037
3.496
4. 234
4. 801
5. 238
5. 568
5.803
5. 947
6.000
5. 965
5. 836
5. 588
5.139
4. 515
3. 767
2. 944
2. 083
1.234
• 474
0
.800
.915
•980
1.073
1.138
1.177
1.204
1.237
1. 259
1.275
1.287
1.297
1. 303
1.311
1.318
1.323
1.331
1.302
1.221
1.139
1. 053
• 968
• 879
• 788
• 687
• 894
•957
• 990
1.036
1.067
1.085
1. 097
1. 112
1. 122
1. 129
1.134
1. 139
1.142
1. 145
1. 148
1.150
I. 154
1. 141
1.105
1. 067
1.026
• 984
• 938
• 888
• 829
0.952 percent
3. 002
2.012
1.686
1.296
• 931
• 682
• 551
• 473
• 379
• 322
• 279
.246
• 220
• 198
• 178
• 161
• 146
• 130
• 114
• 099
• 085
• 070
• 056
• 043
• 027
0
c
66r012
Y
(percent
,_vd V
e
Av,IV
2. 569
1.847
1.575
1.237
•913
• 674
• 549
• 473
• 380
• 323
• 280
• 246
.221
.197
• 176
• 162
• 147
• 132
• 113
• 098
• 084
• 069
• 053
• 040
• 031
0
SUMMARY
OF
AIRFOIL
87
DATA
NACA
x
(percent
....
Cz=.2
(upper
?
/z--._-E2_/ower
\
surfoce)
/
\
NACA
G02-015
•
.4
p
f
/
L. E.
radius:
I
Cz=.3
x
(percent
surfoce)
(upper
c)
1.435 percent
NACA
.. ......
BASIC
e)
66_-018
y
(percent
THICKNESS
(v/V)
0
1.122
1.343
1.675
2.235
3.100
3. 781
4. 358
5. 286
5. 995
6. 543
6. 956
7. 250
7. 430
7. 495
7. 450
7. 283
6. 959
6. 372
5. 576
4. 632
3. 598
2. 530
1.489
• 566
0
.5
• 75
1.25
2.5
5
7.5
10
15
20
25
30
35
40
45
50
55
60
65
7O
75
80
85
90
95
100
_urfoce)
.f
.8
y
(percent
0
/.6
LZ
c)
662-015
FORM
_
v/V
AV./V
0
0
• 760
• 840
.929
1. 055
1.163
I. 208
I. 242
1.288
1.317
1.340
1.356
1. 370
1.380
1.391
1.401
1.411
1.420
1.367
1.260
1.156
1.053
• 949
• 847
• 744
• 639
• 872
.916
• 964
1. 027
1. 078
1. 099
1.114
1.134
1.148
1.158
1.164
1.170
1.175
1.179
1.184
1.188
1.192
1.169
1.122
1. 075
1. 026
•974
•920
•863
• 799
2.139
1. 652
1:431
1.172
•895
• 663
• 547
•473
• 381
• 322
• 280
.248
• 222
• 200
• 180
• 163
• 146
• 131
• 113
• 096
• 080
• 065
• 051
• 039
• 025
0
c
BASIC
e)
THICKNESS
FORM
(v/V)
v/V
Av=/V
L6
0
/
/
L.2
.8
",5,
?
i/
'lower
---:3
/
\
surfoc_
NACA
-O/B
0
1.323
1. 571
1. 052
2. 646
3.69O
4.513
5. 210
6. 333
7.188
7.848
8.346
8.701
8.918
8.998
8.942
8.733
8.323
7. 580
6. 597
5. 451
4. 206
2. 934
1. 714
• 646
0
.5
• 75
1.25
2•5
5
7.5
lO
15
2O
25
30
35
40
45
50
55
60
65
70
75
8O
85
9O
95
100
\
/
>-
0
0
• 650
• 735
• 850
1. 005
1.154
1. 234
1. 285
1. 350
1. 393
1. 423
1. 445
1. 464
1. 481
1. 496
1. 509
1. 522
1. 534
1. 438
1.302
1.172
1. 045
• 922
• 803
• 692
.587
• 806
• 857
• 897
1. 002
1. 074
1.111
1.134
1.162
1.180
1.193
1. 202
1. 210
1. 217
1. 223
1. 228
1. 234
1. 238
1.199
1.141
I. 083
1. 022
• 950
• 896
• 832
• 766
1_. 773
1. 456
1.312
1.121
•858
• 649
• 545
• 472
•381
•323
• 282
• 250
• 223
• 201
• 181
.163
• 147
• 131
• 114
• 095
• 077
• 061
• 048
•037
• 022
0
/
/
_/
L. E. radius:
1.955 percent
NACA
c
664-021
BASIC
THICKNESS
FORM
:
(upper
/
o/
//
....:4
2
surfoce)
f/ovver
x
(percent
/
0
surfoce)
\
//i
/
NACA
884-0£'1
/
0
c)
.6'
.5
• 75
1.25
2.5
5
7.5
10
15
2O
25
30
35
4O
45
5O
55
6O
65
70
75
80
85
9O
95
100
\
/
/
•8
LO
L. E. radius:
y
(percent
c)
(v/V)2
0
1. 525
1. 804
2. 240
3.045
4. 269
5. 233
6. 052
7. 369
8. 376
9.153
9. 738
10.154
10. 407
10.500
10. 434
10.186
9. 692
8. 793
7. 610
6. 251
4. 796
3. 324
I. 924
• 717
0
2.550 percent
c
v/V
AVo/V
0
0
• 580
.635
• 755
•952
1.143
1. 246
1.318
1.405
1. 459
1. 499
1. 528
1,551
1.574
1.594
1. 611
1. 629
1. 648
1. 508
1. 335
1.176
I. 031
• 891
• 763
• 648
• 539
• 761
• 797
• 869
•976
1.069
1.116
1.148
1.185
1. 208
1. 224
1. 236
1. 245
1.255
1. 263
1. 269
I. 276
1. 284
1.228
1.155
1.084
1.015
• 944
• 873
• 805
• 734
1. 547
1. 314
1. 218
1. 054
• 828
• 635
• 542
• 472
• 381
.324
.283
•251
• 224
• 202
• 183
• 165
• 148
• 132
.I14
•093
.073
•058
• 046
.034
• 020
0
88
REPORT
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
2.0
AERONAUTICS
NACA
67,1-015
x
y
(percent
e z
=./2
(upper
0
/.2
,'0
/
__..._------
_..__.-----._
/-.
\
"--,/z (/ower _urfocd
/
c)
FORM
v/V
(v/v)
\
\
.8
O
1. 167
1. 394
1. 764
2. 395
3. 245
3. 900
4. 433
5. 283
5. 940
6. 454
6. 854
7. 155
7.359
7. 475
7. 497
7. 421
7. 231
6.9O5
"6. 402
5. 621
4.540
3.327
2. 021
• 788
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
8O
85
9O
95
100
/
f_
(percent
TItICKNESS
AvJ
V
surfoce)
i
/.6
c)
BASIC
NACA 67,1-015
.4
f
0
• 650
• 970
1. 059
1.140
1. 209
1. 239
1. 259
1.285
1. 304
1. 318
1. 330
I. 34l
1. 351
I. 360
1. 368
1. 375
1. 381
1. 388
1. 390
1. 321
1.176
1.018
• 864
• 712
• 570
• 806
• 985
1. 029
1. 068
1.100
1.113
1.122
1.134
1.142
1. 148
1.153
1.158
1.162
1.166
1.170
1.173
1.175
1.178
1.179
1.149
1. 084
1. 009
• 930
• 844
• 755
2.042
I. 560
I. 370
1.152
.906
• 667
• 548
• 470
• 370
•312
• 276
• 248
• 221
• 201
• 180
• 160
O
• 142
• 124
• 111
• 108
• 094
• 071
• 060
• 045
• 025
0
/jl
L.
E.
radius:
1.523
percent
NACA
.-
e,_ =.22
_pper
surfoee)
747A015
z
c)
(percent
0
/.2
y
/,
" ":22
(lower
sur face)
.%
/
.8
NACA
747A0/5
.4
f
/f
/
-.-------_,_____.__
.2
L
iii
I
.4
_/_
,
c)
.8
1.0
L.
E.
FORM
radius:
1.544
percent
v/V
0
• 660
• 799
• 942
1,100
1. 201
1. 259
I. 295
1. 339
1.36(.}
1.39(}
1.4(}9
1. 423
1. 435
I. 391
1. 348
1,306
1. 265
1. 221
1.178
1.115
I. 027
• 938
• 852
• 774
• 703
/
.6
THICKNESS
(v/V)2
0
1. 199
1. 435
1. 801
2. 462
3.419
4. 143
4. 743
5. 684
6. 384
6. 898
7. 253
7. 454
7. 494
7.316
7. 003
6. 584
6. 064
5.449
4. 738
3. 921
3. 020
2. 086
1. 193
• 443
0
.5
• 75
1.25
2.5
5
7.5
10
15
2O
25
30
35
40
45
,5O
55
60
65
70
75
80
85
9O
95
100
,-O
BASIC
y
(percent
/
c.
c
O
• 812
• 894
• 971
1. 049
1. 096
1.122
1.138
1.156
•
1.170
1.179
1.187
1.193
1.198
1.179
1.161
1.143
1.125
1.105
1. 085
1. 056
1,013
• 969
• 923
• 880
• 838
Av_/V"
2. 028
1. 680
1.5()0
1. 325
• 990
• 695
• 551
• 465
• 383
• 324
• 283
• 252
.224
• 199
• 176
• 156
• 138
• 122
• 108
• 093
• 079
• 065
• 052
• 040
• 02g
• 018
SUMMARY
II--DATA
OF
FOR
NACA
mean
line
62 ................................
Page
90
NACA
mean
line
63 ................................
90
NACA
mean
line
64 ..................................
90
NACA
mean
line
65 ..................................
91
NACA
mean
line
66 .................................
NACA
mean
line
NACA
mean
NACA
mean
NACA
mean
NACA
mean
NACA
mean
AIRFOIL
MEAN
89
DATA
LINES
Page
NACA
mean
line
a_
NACA
NACA
mean
mean
line
line
a:
0.1 ..................................
a:0.2
...............................
94
94
NACA
NACA
mean
line
a:0.3
................................
94
91
67 ............................
91
NACA
mean
mean
line
line
a:0.4
a=0.5
...............................
..............................
95
95
line
210 .................................
92
NACA
mean
line
a:0.6
.............................
95
line
220 .................................
92
NACA
line
230 .....................................
92
NACA
mean
mean
line
line
a:0.7
a_0.8
..........................
.................................
96
96
line
240 ....................................
93
NACA
mean
line
a=0.9
.............................
96
line
250 .....................................
93
NACA
mean
line
a=
0 ....................................
1.0 .................................
93
97
90
REPORT
3O
NO.
824--NATIONAL
I
l
ADVISORY
COMMITTEE
FOR
AERONAUTICS
1
NACA
2..O
ezi=0.90
z
(percent
&
c)
0
1.25
2.5
/.0
I
I
NACA
Y_.2
c
--
meo
i
62
1/770
i
Y ¢
(percent
dy
c)
eli=0.80
ai=l.60
dy
0
1.25
2.5
5.0
7.5
10
15
20
25
;10
40
50
60
70
80
9O
95
100
.2
c
(percent
c_cl4
= --0.113
ddx
MEAN
9?
c)
o
62
PR
0. 6OOO0
56250
52,5011
45(}90
37500
30000
15OOO
0
--. 00938
--. 01875
--. 0375O
--. 05625
--. 0759O
--. 09375
--. 11250
--. 13125
--. 14062
--. 15000
• 726
1. 406
2. 625
3. 656
4. 500
5. 625
6.09O
5.977
5. 906
5. 625
5. 156
4.50O
3. 656
2. 625
1. 406
• 727
0
NACA
(percent
LINE
a_=2.8i
0
5,0
7,5
10
15
2O
25
30
40
5O
60
70
80
90
95
100
MEAN
Av/V=
PR/4
0
0
• 371
• 258
• 328
• 682
031
314
503
651
802
530
273
113
• 951
• 843
• 74I
• 635
• 525
• 377
• 261
1.
1.
1.
1.
1.
1.
1.
1.
0
LINE
63
°
c,c14
• 376
• 413
• 451
• 383
• 318
• 279
238
• 211
• 185
• 159
• 131
• 094
• 065
0
=--0,134
c/dx
PR
AvlV=PR/4
c)
O
0. 40000
• 38333
• 36067
• 33333
• 30000
• 26667
• 20000
• 13333
• 00667
0
--. 02449
--. 04898
--. 07347
--. 0979O
--. 12245
--. 14694
--. 15918
--. 17143
• 489
• 958
1. 833
2. 625
3. 333
4.59O
5. 333
5. 833
6. 6O0
5, 878
5. 510
4. N98
4. 041
2, 939
1. 592
• 827
0
NACA
MEAN
0
0
• 389
• 553
• 788
• 940
1. I)66
1. 221)
1. 259
I. 233
1,160
• 949
• 8,50
• 762
• 673
• 560
• 406
.291
0
LINE
• 097
• 138
• 197
• 235
• 207
• 305
.315
• 368
• 290
• 237
• 213
• 19l
• 168
• 140
• 102
• 073
0
64
2..O
cli=0.76
x
(percent
c)
_c
(percent
LO
0
1.25
2.5
5.0
7.5
1O
15
20
25
30
40
5O
6O
70
8O
9O
95
10O
y_
c
0
• 369
• 726
1. 406
2. 039
2. 625
3. 656
4. 560
5.156
5. 625
6. 09O
5. 833
5. 333
4. 500
3. 333
1. 833
• 958
0
ai=0.74
c)
°
dy
cm c/4 = --6.157
PR
c/dx
O. 30000
.29062
.28125
.26250
,24375
• 2259O
.18750
.15O00
.1125o
.0759O
0
--. 03;133
--.06(_7
--. I(W_)(}
--. 13333
--. 16067
--• 183:13
--. 201_H)
0
• 257
• 391
• 546
.668
• 748
.87l
• 966
l. 030
1. 040
• 9(39
• 910
• 827
• 7,5(}
• 635
• 466
• 334
0
AV/V=
PR/4
0
• 064
• 098
• 137
• 167
• 187
.218
• 242
• 258
• 260
• 250
• 228
• 207
• 188
• 15O
.117
• 084
0
SUMMARY
OF
AIRFOIL
91
DATA
3.O
NACA
clt=0.75
MEAN
ai=0
LINE
°
65
¢me/4=
--0.187
2.O
(percentx
c)
0
1.25
2.5
5.0
7.5
10
15
20
25
3O
/.0
------_...,..,._
/
"\
0
Yc.Z
100
PR
0. 24000
• 23400
• 22800
• 21600
.20400
.19200
.16800
.14400
• 12000
• 09690
.04800
0
--. 04800
--. 09600
--. 14400
--. 19200
--. 21600
--. 24000
• 296
.585
1. 140
1. 665
2.160
3.060
3. 840
4.500
5. 040
5. 760
6. 000
5. 760
5. 040
3. 840
2. 160
1• 140
0
70
8O
9O
95
dy c/d.v
C)
0
40
5O
6O
N,#C,4 55
rneon
//_e
(percentY _
O
AV/V=
PR/4
0
.205
.294
• 413
.502
.571
.679
.760
.824
• 872
.932
• 951
• 932
• 872
• 760
• 571
.413
0
• 051
• 074
.103
.126
• 143
.170
.190
.206
• 218
• 233
• 238
• 233
.218
.190
.143
.103
0
C
/f
O
/
NACA
MEAN
LINE
66
2.0
csi=0.76
p_
X
(percent
/.0
f
0
1.25
2.5
5.0
7.5
10
15
20
25
30
40
5O
6O
70
80
90
95
100
/J
/
\
/
/
0
Ye
c)
2
C
Ye
(percent
at=--0.74
c)
0
°
Cmcl_=
dy ddz
Pn
0. 20000
19583
19167
18333
• 247
• 490
.958
1. 406
1• 833
2. 625
3. 333
3. 958
4. 500
5. 333
5. 833
6. 000
5. 625
4. 500
2. 625
1. 406
0
--0.222
0
15000
13333
11667
10000
06667
• 03333
0
--.
--.
07500
15000
--.
--.
--.
22500
26250
30000
0
.135
•244
•334
.408
.466
•557
.635
•700
.75O
•827
.910
.999
1.040
.966
• 748
.546
0
17500
16667
Av/V'=PR/4
• 034
• 061
• 084
• 102
• 117
• 139
.159
.175
.188
.207
.228
.250
• 260
• 242
• 187
• 137
0
/I
2.O
NAGA
p_
eli=0.80
f
/.0
/
z
(percent
i
0
1.25
2.5
5
.212
,421
.827
1.217
1.592
2.290
2.939
3.520
4.041
4.898
5.510
5.878
6.000
5.333
3.333
1.833
0
2O
25
30
40
50
60
70
80
9O
95
100
Y_
T
._______.-------"
i
0
I
.__
.6"
.8
ZO
ye
(percent
0
7.5
10
15
NACA 07
mean hive
c)
MEAN
LINE
ai=--l.60
c)
dy
°
67
c_¢/4=
--0.266
_/dx
0. 17143
• 16837
• 16531
• 15918
• 15306
• 14694
• 13469
• 12245
• 11020
• 09796
• 07347
• 04898
.02449
0
--. 13333
--. 26667
--. 33333
--. 40000
P_
0
• 137
• 195
• 29t
• 356
• 406
• 483
• 560
•616
• 673
• 762
• 850
• 949
1. 160
1.259
1.066
.788
0
Av/V=PR/4
0
.034
• 049
.073
.089
.102
.121
.140
.154
.168
.191
.213
.237
.290
.315
.267
• 197
0
92
REPORT
NO,
8
2 4--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
3O
NACA
cti=0.
30
MEAN
ai=2.
LINE
09 °
210
cm c/4=
-0.006
2O
I
x
(percent
i
c)
Y _
(percent
dy ddx
c)
Av/V=
PR
PR/4
!
i
!
!
0
1.25
2.5
5.0
7.5
10
15
i
i
/.0
i
iI
---_c----!
o
i
]
¢,
0
0. 59613
• 36236
.18504
--. O0018
• 596
.928
1.114
• 345
• 391
• 305
.195
• 156
.122
781
626
489
408
348
1. 087
1. 058
• 999
• 9411
• 881
• 823
.7{)5
• 588
.470
• 353
.2;15
.I18
• 059
0
_0
25
3O
4O
50
6O
7O
8O
9O
95
100
0
0
1. 381
565
221
--.
• 102
.087
• 075
• 061
• 049
• 040
• 032
.025
• 016
• 011
302
242
• 198
• 160
• 128
• 098
• 065
• 044
01175
0
0
L
NACA
czi=0.
]
x
......
i
(percent
c)
30
yc
(percent
MEAN
ai=l.
86 °
dy
c)
LINE
220
grad4
= --0.
c/dx
Pn
010
AV/V=
P_¢/4
i
____
0
1.25
2.5
5.0
7.5
10
15
20
25
30
40
50
60
70
80
90
95
100
NACA 220
!
I
, meon
line
]
Y_.£
12
.442
.793
1,257
1. 479
1. 535
I. 463
1. 377
1. 291
1. 2115
1. 033
.861
.68(,}
.516
.344
.172
.086
0
!
2O
0. 39270
• 31541
• 24618
• 1;1192
• 04994
.6O024
0
--.
NACA
C_i=0.30
l_r
0
01722
MEAN
_i=
LINE
1.65 °
0
• 822
1. 003
• 988
• _)0
• 81)1
• 615
• 465
• 378
• 320
• 253
• 2O5
• 169
• 135
• 19O
• 064
• 040
0
• 206
• 251
• 247
• 225
• 2(X)
• 154
• 116
• 095
• 082
._)3
• 051
• 642
• 034
• 625
.016
.010
0
230
C._14=--0.014
__
x
(percent
i
c)
y,
(percent
c)
PR
dyo/dx
AV/V=
Pn/4
/0-i
i
i
i
NACA
f_eor]
Y--£
(,
230
line
2
I
r
.2
.4
.8
LO
0
1.25
2.5
5.0
7.5
10
15
2O
25
30
40
5O
6O
70
80
9O
95
100
0
• 357
• 666
1. 155
1. 492
1. 701
1. 838
1. 767
1.656
1. 546
1.325
1. 104
• 883
• t)62
• 442
• 221
.110
0
0. 30508
• 26594
• 22929
• 16347
• 10762
• 06174
--. 00009
--. 02203
--.
0
02208
0
0
• 528
.132
•
•
•
•
•
•
•
•
.168
.198
.213
.215
.170
.130
.105
.09_)
673
791
853
859
678
519
419
361
• 274
• 217
.177
.069
.054
.044
• 144
• 105
,069
• 042
.036
.026
.017
.011
0
SUMMARY
OF
AIRFOIL
93
DATA
NACA
oi=0.30
x
(percent
L....
Y_
(percent
c)
0
1.25
2.5
5.0
7.5
10
15
20
25
30
40
50
6O
70
80
9O
95
100
l
,_i=1.45
c)
0
NACA
mean
250
h_e
I
0
1.25
2.5
5.0
7,5
10
15
20
25
30
40
5O
60
70
80
90
95
100
Y°
(percent
c)
f
/
0
918392--51--7
.4
.6
.8
10
.5
.75
1.25
2.5
• 6.0
7.5
10
15
20
25
_0
35
4O
45
5O
55
60
65
70
75
8O
85
9O
95
100
dy ddx
PR
377
491
625
718
750
677
• 566
•477
•410
.304
• 234
• 186
• 150
• 110
.071
• 047
MEAN
LINE
°
cm_/_= --0.026
PR
0
LINE
a,:=4.,56 °
0
c)
.469
•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
dy ddx
........................
O: 75867
• 69212
• 60715
• 48892
• 36561
• 29028
• 23515
• 15508
• 09693
• 05156
• 01482
--. 01554
--. 04086
--. 06201
--. 07958
--. 09395
--. 10539
--. 11406
--.12OO3
--. 12329
--. 12371
--. 12099
--. 11455
--. 16301
--. 07958
Av] V= Pn]4
0
.281
• 369
• 477
.552
.592
• 624
• 610
• 547
• 470
• 346
• 255
• 107
• 154
• 119
• 076
• 05l
--• 03218
//e
(percent
•094
•123
.156
• 180
• 188
• 169
• 142
• 119
• 103
• 075
• 059
• 047
• 038
• 028
• 018
• 012
0
250
dy ddz
MEAN
AV[ V=PR/4
0
0
0. 21472
• 19920
• 18416
• 15562
• 12999
• 10458
• 06162
• 02674
--. 00007
--. 01880
•258
.498
• 922
1.277
1. 570
1.982
2.199
2.263
2•212
1. 931
1.609
1. 287
.965
.644
.322
.161
0
cq=l•0
0
c_c/4=--0.019
ai=1.26
0
c)
°
0
NACA
x
(percent
240
--. 02700
cq=0.30
c)
LINE
0. 25213
.22877
• 20625
• 16432
• 12653
• 09290
• 03810
--. 09OlO
--. 02169
.301
• 572
1. 035
1.397
1.671
1.991
2. 070
2. 018
1. 890
1. 620
1. 350
1•080
• 810
• 540
• 270
• 135
0
NACA
x
(percent
MEAN
• 070
• 092
• 119
• 138
• 148
• 156
• 153
• 137
• 117
•087
•064
•049
•038
•030
• 019
.013
0
a=O
cmd,
=--0.083
P ,_
1.000
1. 985
1.975
1.950
1.900
1,850
1. 800
1. 700
1. 600
I. 500
1. 400
1. 300
1. 200
1.100
1. (DO
.900
,800
.700
.609
.500
.400
.300
.200
.16O
0
At'/V=
P R/4
0. 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.
8
2
4--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
NACA
30
eli=l.0
x
(percent
Y c
(percent
c)
0
LO
30
35
40
45
50
55
60
65
-- -bA:iiii •
•
•
•
•
•
•
•
•
•
6. 291;
6. 029
5. 664
5.218
4. 706
4. 142
3. 541
5.910
2. 281
1. 652
1.1145
• 482
0
7O
75
80
85
9()
95
100
NACA
Cli=l.O
c)
0
!
i
i
_.--._____
(pcrecn
--.
--.
--.
--,
--.
--.
67479
59896
49366
38235
31067
25(157
16087
09981
0528l
01498
01617
94210
(111373
08168
09637
I08()0
--.
--.
--,
--.
--.
--.
--.
--.
11694
12;I07
15644
1269:1
12425
11781
I 0(12(1
0_258
MEAN
lANE
ai=4.17
z
(percent
cmc14=--0.086
AV/V=
t c)
°
.....................
0. 455
1,818
1.0
e=
1" _
0
,5
• 75
1.25
2.5
5. 0
7.5
10
15
20
25
311
35
40
45
5O
55
66
65
7(1
75
8O
85
9O
95
160
.2
.4
!
.0
.8
tO
0
Av[ V=PR/4
MEAN
LINE
°
(percent
• 391
• 365
• 339
.313
• 287
• 2(;0
.234
• 208
• 182
.1_)
• 130
. 11(4
• 078
• 1152
• 020
I. 5(13
l, 459
1.355
1.25/1
1. 146
1. 042
.938
.834
.7'2!I
.625
.521
.417
.3l: _I
.2(18
.104
0
0
a=0.3
Cm ¢/_ = --0.106
t'R
dy#d.r
c)
0. 417
1. O17
At,/I
"=
Pt¢14
c)
.....
l/me
1Ol
O76
059
I125
/1=--0,094
dy d dz
ai=3.84
.r
(percent
[ 177_on_!
•
•
•
•
a=().2
O. 69492
• 64047
• 57135
• 475!12
• 3761iI
• 314_7
• 26_03
• 19373
• 124(15
• (J6;145
• I)2030
--.OI41M
--. 04246
--. 06588
--. 0_522
--, 10101
--. 11359
--. 12317
--. 12O_i5
--. 1331i3
--. 13440
--. 13186
--. 12541
--. 11361
--. I)$94 l
• 414
• 581
• 882
1. E_O
2. 583
3,443
4. 169
5,317
6. 117
6. 572
6. 777
6. 789
6.646
6. 3T3
5. 994
5. 527
4. 98!1
4. 396
3. 762
3. 102
2. 431
1. 764
1. 119
• 518
0
el i=
__.....
• 429
• 404
• 379
• 354
• 328
• 303
• 278
• 253
• 227
• 202
• 177
• 152
• 126
1. 717
1. 616
1. 515
1. 414
1. 313
1. 212
l.lll
I. 010
• 91)9
• 808
• 707
• 606
• 505
• 404
• 3O3
• 2(15
• 101
0
0
.5
.75
1.25
2,5
5.0
7.5
l0
15
20
25
30
35
40
45
50
55
611
65
7O
75
811
85
91)
95
100
NACA
w
PR/4
ely o/dx
• 933
1. 608
2. 689
3.55l
4, 253
5. 261
5, 9115
6. 282
6. 449
6. 443
5,0
7.5
10
15
2O
25
°
a=0.1
PI_
c)
• 440
• 616
.75
1.25
2.5
LINE
ai=4.43
0
.5
MEAN
i......
0
• 389
• 5411
.832
1. 448
2. 458
3.2!)3
4,008
5. 172
6.1)52
6. 6M5
7. O72
7.175
7. 074
6. 816
6. 433
5. !14!)
5. 383
4. 753
4. (/711
3.368
2. 645
1. 924
1.22,1
• 57(/
0
0. 65536
• (_1524
.54158
• 45399
• 36344
• 30780
• 2O621
• 2O246
• 15068
• 111278
• 04_33
--. 002O5
--. 0:1710
--. ()6492
--. 0_746
--. 105(17
• 1201-1
• 1311!)
--, (3()1)1
--. 14365
--. 14500
--. 14279
--. 136;_;M
--. 12430
--. 09907
1
53_
1. 429
1. 319
1.2{)9
1. 099
• I)_;(,)
• _479
• 769
• 659
• 54!)
• 440
• 330
• 22{)
• 110
0
(1. ;:I_5
.357
.330
,302
.275
.247
.220
.192
. 165
. 137
. l l0
.082
.055
. O28
0
SUMMARY
OF AIRFOIL
DATA
95
NACA
MEAN
LINE
a=0.4
J.O
Czi=l.O
:_
(percent
c)
Y¢
(percent
ai=3.46
°
Cm
el4=
--0.121
dv _/dx
c)
PR
AV/V'= Pn/4
2.0
0
0
• 366
• 514
,784
1. 367
2. 330
3. 131
3.824
4.1968
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
.5
• 75
1.25
2.5
5.0
7.5
10
15
20
25
3O
35
40
45
5O
55
6O
65
7O
75
80
85
96
95
100
p_
/.0
Y.
T2
0. 61759
.57105
.51210
.43106
.34764
• 29671
.25892
.20185
.15682
.11733
.07988
.04136
--.00721
--.05321
--.08380
--.10734
--.12567
--.13962
--.14963
--.15589
--.15837
--.15(383
--.15062
--.13816
--.11138
1,429
0.357
1.310
1.190
1.07l
.952
•833
.714
.595
•476
.357
.238
.119
• 327
• 298
• 268
• 238
• 208
.179
• 149
• 119
• 089
• 060
• 030
0
ff
NACA
Cl,;= 1.0
(percent
N*C*
a=0.5
mean
line
c
c)
Y¢
(percent
0
0
.5
.75
1.25
2.5
5.0
7.5
10
15
20
25
3O
35
4O
45
50
55
60
65
70
75
80
85
90
95
100
• 345
.485
• 735
1.295
2. 205
2. 970
3. 630
4. 740
5.620
6. 310
6. 849
7. 215
7. 430
1 7. 490
7.350
6. 965
6. 405
5.725
4. 955
4,130
-3.265
2. 395
- 1. 535
.720
0
-
0
N.AC.4
a:O.6
medm
I/_e
-c-.g
f_
f
0
I
q
.z
.4
,6
.8
ZO
.5
• 75
1.25
2.5
5.0
7.5
10
15
20
25
30
35
40
45
50
55
_0
65
70
75
80
85
9O
95
100
Y"
(percent
"ai=3.04
°
era j4=
c)
'
--0.139
PR
MEAN
ai=2.58
0
,325
.455
• 695
1. 220
2•080
2•805
3.435
4.495
5,345
6. _15
6.570
6. 965
7,235
7.370
7.370
7. 220
6.880
6.275
5.505
4.£_0
3. 695
2.720
1. 755
.825
0
a=0.5
0.58195
•53855
.48360
• 10815
133070
.28365
• 24890
•19690
.15_50
.12180
.O9OOO
.05930
.02800
--.00630
--.05305
--•09765
--•12550
--.14570
--. 16015
--.16960
--•17435
--.17415
--.16850
--.15565
--. 12660
c .=1,0
c)
LINE
dyddx
c)
NACA
X
(percent
MEAN
LINE
°
dy ¢/dx
......................
0.54825
.50760
• 45615
.38555
.31325
.26950
.23730
.18935
• 15250
.12125
.09310
.00160
.04060
.014(15
--.01435
--.04700
--.09470
--.14015
--. 16595
--.18270
--.19225
--.19515
--.19095
--.17790
--.14550
1. 333
1. 200
1. 067
• 933
• 800
• 667
.533
• 400
• 267
• 133
0
_,v/"V= P n/4
0.333
• 300
• 267
• 233
• 200
• 167
• 133
• 100
• 067
• 033
0
a=0.6
e_,/4=--0,158
P
Av/V=
PM4
1.250
0.312
1.094
. 938
.781
.625
.469
.312
.156
0
• 273
• 234
• 195
.1,56
• 117
• 078
•039
0
96
REPORT
NO.
8
2 4--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
NACA
cti=l.O
X
(percent
O
LINE
a{=2.09
Yc
(percent
c)
MEAN
°
a=0.7
C_,14=--0.179
PR
c)
dy
0
.5
.75
1.25
2.5
5.0
7.5
10
15
21)
25
30
35
40
45
5O
711
75
80
85
90
95
100
O. 51620
.47795
• 42960
• 36325
• 29545
• 25450
• 22445
• 17995
.14595
.11740
• 09200
• 068411
.04570
Cl,:=
x
c)
1. 176
• 02315
0
--. 02455
--. 05185
--./)8475
--. 13650
--. 18511)
--. 20855
--. 21955
--. 21960
--. 21)725
--. 16985
NACA
(percent
V_PR/4
.....................
• 305
• 425
• 655
1.160
1. 955
2. 645
3. 240
4.245
5. 060
5. 715
6. 240
6.635
6. 925
7. 095
7. 155
7.090
6. 900
6. 565
6. 030
5. 205
4. 215
3. 140
2. 035
• 965
I)
55
60
65
At]
ddx
1.0
MEAN
Yc
(percent
ai=
dy
•
•
•
•
•
.980
• 784
.588
• 392
• 196
°
245
196
147
098
049
0
0
LINE
1.54
O. 294
a=0.8
c=,/4=
_/dx
-0.202
P R
Av/V=
PR/4
c)
0
• 287
.404
.616
1. 077
1. 841
.5
.75
1.25
2.5
5.6
7.5
10
15
20
25
30
35
40
45
50
55
6O
65
7O
75
80
85
99
95
100
0. 48535
.44925
• 40359
• 34104
.27718
.23868
• 2105O
.16892
• 13734
• lllOl
• 118775
2. 483
3.043
3. 985
4.748
5.367
5. 863
6. 248
6. 528
6. 709
6. 790
6. 770
6. 644
6. 405
6. 037
5. 514
4. 771
3. 683
2. 435
1.16;:;
O
--.
--.
--.
--.
--.
--.
--.
NACA
cq=l.0
z
(percent
c)
ye
(percent
0
0
.5
• 75
1.25
2.5
• 269
.379
• 577
1. 008
1. 720
2. 316
2. 835
3.707
4.410
4. 980
5. 435
5. 787
6.045
6. 212
6.290
6.279
6.178
5. 981
5.681
5.265
4.714
3.987
2. 984
1. 503
O
5. 0
7.5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
_o
85
99
95
100
1.
Ill
0.278
.06634
• 0461)1
• 0261::;
. O0620
--. 0143;:;
--. 03611
--. 06010
08790
12311
18412
23921
25583
24904
20385
MEAN
ai=0.9(}
c)
• 208
.139
• 069
.833
.556
.278
0
0
LINE
°
dyJdz
0.45482
• 42'0(;4
•37740
.31821
• 25786
.22153
• 19500
•15595
.12644
.10190
.08047
.I)6084
.04234
.02447
.00678
--.01111
--. 029t;5
--.04938
--. 071_1
--.09584:;
--.12605
--.16727
--. 252(_
--. 314{;3
--. 26086
a=0.9
Cm_/_ =-0.225
PR
I. 05;:;
AV/V=Px/4
O. 263
• 526
0
.132
0
SUMMARY
OF
AIRFOIL
97
DATA
,2.O
NACA
Czi=l.O
z
(percent
Y_
(percent
c)
0
.5
• 75
1.25
2.5
5.0
7.5
10
15
2O
25
30
35
40
45
50
55
6O
65
7O
75
8O
85
9O
95
100
a=LO
/_ e o /7 //he
NAC,_
Y_
C
f
f_-------.2
.4
.8
/.©
0
--
-
• 250
• 350
• 535
• 930
1. 580
2.120
2. 585
3.365
3. 980
4. 475
4. 860
5.150
5. 355
5. 475
5. 515
5.475
5, 355
5. 150
4. 860
4. 475
3. 980
3. 365
2. 585
1. 580
0
¢)
MEAN
LINE
oti_O °
dy_/dx
......................
O. 42120
• 38875
.34770
29155
23430
19995
17485
13805
11030
08745
06745
04925
03225
01595
0
--. 01595
--.03225
--.04925
--.06745
--. 08745
--. 11030
--. 13805
--. 17485
--.23430
......................
a=l.0
Creel4= --0.250
PR
AV/V= Pn/4
1.06O
0.250
SUMMARY
OF AIRFOIL
III--AIRFOIL
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
0006 ..............................................
0009 .............................................
1408 .............................................
1410 .............................................
1412 .............................................
2412 ............................................
2415 .............................................
2418 ............................................
2421 ............................................
2424 ............................................
4412 ..............................................
4415 ............................................
4418 ............................................
4421 .............................................
4424 ............................................
23012 ...........................................
23015 ............................................
23018 ............................................
23021 ............................................
23024 ............................................
Page
100
i00
i00
100
100
100
100
100
100
100
101
101
101
101
101
101
101
101
101
101
63,4-420
........................................
63,4-420,
a=0.3 ..................................
63(420)-422
.......................................
63(420)-517
........................................
63-006 ...........................................
63-009 ...........................................
63-206 ...........................................
63-209 ...........................................
63-210 ...........................................
63,-012 ...........................................
63,-212 ..........................................
63,-412 ..........................................
632-015 .........................................
632-215 ...........................................
632-415 ..........................................
632-615 ..........................................
633-018 ..........................................
633-218 ..........................................
633-418 ..........................................
633-618
.....................................
634-021 .........................................
634-221 ...........................................
634-421 .........................................
64-006 .....................................
102
102
102
102
102
102
102
102
102
102
103
103
103
103
103
103
103
103
103
103
104
104
104
104
64-009
64-108
64-110
............................................
........................................
..........................................
104
104
104
64-206
64-208
64-209
64-210
641-012
641-112
641-212
641-412
642-015
642-215
642-415
643-018
..........................................
............................................
.........................................
...........................................
..........................................
............................................
.........................................
..........................................
..........................................
.........................................
..........................................
.........................................
104
104
104
105
105
105
105
105
105
105
105
105
99
DATA
ORDINATES
Page
105
106
106
106
106
106
106
106
106
106
106
107
107
107
107
107
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
643-218 ..........................................
643-418 ..........................................
643-618 ...........................................
644-021 ..........................................
644-221 .............................................
644-421 ...........................................
65, 3-018 .......................................
65, 3-418, a=0.8 ..................................
65, 3-618 .......................................
65(216)-415,
a=0.5 ......
: ..........................
65-006 ...........................................
65-009 ...........................................
65-206 ...........................................
65-209 ...........................................
65-210 ............................................
65-410 ...........................................
NACA
NACA
651-012 ..........................................
651-212 ..........................................
107
107
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
651-212,
65,-412
652-015
652-215
652-415
65_-415,
653-018
653-218
653-418
653-418,
653-618
653-618,
654-021
654-221
654-421
654-421,
107
107
107
108
108
108
108
108
108
108
108
108
108
109
109
109
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
65_215)-114 ..........................................
65c_21)-420 ..........................................
66,1-212 ...........................................
66(215)-016
......................................
66(215)-216
......................................
66(215)-216,
a=0.6 ................................
66(215)-416
......................................
66-006 ...........................................
66-009 ...........................................
66-206 ...........................................
66-209 ...........................................
66-210 ...........................................
109
109
109
109
109
109
109
110
110
110
110
110
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
NACA
66,-012
66,-212
662-015
665-215
66r-415
663-018
663-218
663-418
664-021
664-221
67,1-215
747A315
747A415
110
110
110
110
110
111
111
111
111
111
111
111
111
a=0.6 ....................................
..........................................
..........................................
...........................................
..........................................
a=0.5 ...................................
..........................................
..........................................
..........................................
a=0.5 ....................................
..........................................
a=0.5 ....................................
..........................................
..........................................
..........................................
a=0.5 ....................................
..........................................
..........................................
..........................................
..........................................
..........................................
..........................................
..........................................
...........................................
...........................................
...........................................
..........................................
..........................................
...........................................
100
REPORT
NO.
824--NATIONAL
°
ADVISORY
COMMITTEE
FOR
AERONAUTICS
1
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DATA
101
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102
REPORT
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
IIIIIIIIIIIIIIIIIIIIII
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SU/V_MARY
OF
AIRFOIL
103
DATA
+_
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fllJl
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=+_
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104
REPORT
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONATJTICS
"B
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SUMMARY
OFAIRFOIL
DATA
105
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106
REPORT
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
SUMMARY
OFAIRFOIL
DATA
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108
REPORT
NO.
8 2 4--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
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109
DATA
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REPORT
NO.
824---NATIONAL
ADVISORY
COMMITTEE
:FOR AERONAUTICS
°l
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SUMMARY
OF
AIRFOIL
111
DATA
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SUMMARY
OFAIRFOIL
DATA
IV--PREDICTED
Critical
Mach
Variation
of
number
critical
chart
CRITICAL
Page
114
...............................
Much
number
with
low-speed
section
0009,
and
14-series
0012
airfoil
airfoil
sections
sections
of
lift
coefficient:
For
For
the NACA
0006,
several
NACA
thicknesses
For
NACA
thicknesses
several
NACA
several
NACA
several
several
various
For
For
several
nesses,
For
For
several
various
several
nesses,
For
several
nesses,
For
several
nesses,
For
two
nesses,
airfoil
230-series
NACA
sections
airfoil
63-series
cambered
NACA
thicknesses
NACA
for
airfoil
various
of
NACA
thicknesses
NACA
cambered
NACA
cambered
NACA
cambered
NACA
cambered
sections
design
airfoil
cambered
for a design
NACA
63-series
airfoil
for
a design
for
for
of
airfoil
sections
a design
64-series
airfoil
for
a design
nesses,
cambered
For several
NACA
For
two
For
nesses,
two
118
type
a design
120
nesses,
For two
airfoil
sections
lift
of various
coefficient
sections
lift
coefficient
lift
of
of
coefficient
of
different
of
of
thick-
0.1 ......
120
121
thick-
0.4 ......
several
122
lift
NACA
for
of 0.15
airfoil
with
and
of
a thickness
various
for
design
of various
of
with
lift
thick123
0.4 ......
mean
line
a design
lift
124
coeffi124
sections
of different
lift coefficient
sections
with
different
coefficient
thicknesses,
thick-
of 0.6 ......
mean
line
and
125
of
cambered
of 0.6 .....................
66-series
symmetrical
.................................
66-series
airfoil
125
airfoil
sections
of
126
sections
of various
thick-
lift coefficient
of 0.2 ......
sections
of different
thick-
126
for a design
lift coefficient
of 0.4 ......
66-series
airfoil
sections
with
a thickness
NACA
of
with
sections
0.16
and
cumbered
........................................
6-series
minimum
cambered
for
For two NACA
sections
123
cambered
for a design
NACA
66-series
airfoil
several
lift
122
sections
airfoil
65-series
nesses,
cambered
For several
NACA
For
airfoil
for a design
lift coefficient
65-series
airfoil
sections
NACA
thicknesses
positions
121
thick0.6 .......
several
various
section
for a design
lift coefficient
of 0.2 ......
65-series
airfoil
sections
of various
thick-
a = 0.5,
ratio
of
coefficients
thick-
0.2 ......
of various
coefficient
sections
of
of various
sections
lift
sections
airfoil
cambered
for a design
NACA
65-series
airfoil
for
For
0.6 .......
65-series
symmetrical
................................
65-series
NACA
the
119
of
low-speed
of the type
a=0.5
and cambered
cient
of 0.4 ..........................................
117
lift
coefficient
NACA
nesses,
cambered
several
NACA
For
airfoil
for
117
thick-
with
0.18
and
cambered
........................................
For
of
several
number
65-series
116
118
of various
NACA
For
various
_
NACA
thicknesses
ratio
of
coefficients
119
airfoil
a design
64-series
several
lift coefficient
of 0.4 ......
sections
of different
thick-
airfoil
a design
64-series
For
Mach
116
various
lift coefficients_
sections
64-series
symmetrical
.................................
64-series
several
various
various
for a design
lift coefficient
of 0.2 ......
63-series
airfoil
sections
of various
thick-
cambered
For
various
of
sections
63-series
symmetrical
..............................
63-series
nesses,
cambered
several
NACA
nesses,
For two
of
.........................................
thicknesses,
For
sections
........................................
thicknesses
For
44-series
Page
115
airfoil
........................................
thicknesses
For
24-series
NUMBERS
Variation
of critical
coefficient--Continued
115
........................................
several
For
......
various
MACH
113
various
7-series
cambered
for
pressure
for
design
lift
127
airfoil
design
airfoil
various
127
sections
and
with
various
different
thicknesses,
lift coefficients
............
sections
with
a thickness
different
design
lift
coefficients_
128
ratio
_
128
] |4
REPORT
:NO.824--1_TATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
1.0
.9
\
\
18
from
equo_/ons
(8] ond
(82] o£
meFerence
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2.2
Low-speed
Critical
pressure
Math
number
£_
ooeff/cZemf,
chart.
3.0
8
3.4
0.8
SUMMARY
OF AIRFOIL
115
DATA
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t.,
o
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0
N
%
c4
<
<
z
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b
%
%
116
REPORT
NO.
8 2 4--NATIONAL
ADVISORY
COMMITTEE
FOR
f
/'/,,/I
A" I /'I
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/
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/,,
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m
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%
SUMMARY
OF AIRFOIL
117
DATA
o
e_
p.
o)
N
g
%
o
%
°_
o
118
REPORT
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR AERONAUTICS
SUMMARY
OF
AIRFOIL
119
DATA
m,
.<_
ZN
_o
...,
%
120
REPORT
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
, III
AERONAUTICS
/
I
I
%
L
SUM1V£ARY
OF AIRFOIL
DATA
121
122
REPORT
NO.
8 2 4--NATIONAL
ADVISORY
CO:_IMITTEE
FOR
AERONAUTICS
o
SUMMAaV
OF AIRFOIL
123
DATA
o
o_
Z'S
=N
m
2_
e_
N
"a
a
.£
.._
".E
_g
_'_
-_ .,-,
124
REPORT
NO.
8 2 4--NATIONAL
ADVISORY
Ill
COMMITTEE
FOR
AERONAUTICS
l
.',+
I,/i
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.,
_
I
_V
SUMMARY
OF
AIRFOIL
DATA
]25
%
918392--51--9
126
REPORT
NO.
824--NATIONAL
ADVISORY
COMMITTEE
Z
I
+
---+
1
%
\
FOR
AERONAUTICS
SUMMARY
OF
AIRFOIL
DATA
127
128
REPORT
NO.
824--NATIONAL
ADVISORY
CO_IM;ITTEE
FOR
AERONAUTICS
z_
i
I"
I
I
ii
SUMiXIARY
V--AERODYNAMIC
OF
CHARACTERISTICS
AIRFOIL
129
DATA
OF
VARIOUS
AIRFOIL
SECTIONS
Fage
NACA
0006
...................................
131
NACA
6_3-418
.........................................
194
NACA
0009
....................................
132
NACA
643-618
.......................................
195
NACA
1408
.................................
133
NACA
644-021
......................................
196
NACA
1410
.................................
134
NACA
644-221
......................................
197
NACA
1412
...................
135
NACA
644-421
.......................................
198
NACA
2412
................................
136
NACA
65,3-018
NACA
2415
..................................
137
NACA
65,3-418,
NACA
2418
138
NACA
65,3-618
NACA
2421
................................
139
NACA
NACA
2424
............................
140
NACA
65,3-618
with
0.20c
65(216)-415,
a=0.5
NACA
4412
...................................
141
NACA
65-006
NACA
4415
.................................
142
NACA
65-009
...................................
205
NACA
4418
.....................................
143
NACA
65-206
...........................
206
NACA
4421
.............................
144
NACA
65-209
NACA
4424
..............................
145
NACA
65-210
NACA
23012
................................
146
NACA
65-410
................................
209
NACA23015
.....................................
147
NACA
65r012
............................
210
NACA
23018
..........................
148
NACA
651-212
NACA
23021
149
NACA
23024
150
NACA
651-212
characteristics)
NACA
C3,4-420
151
NACA
651-212,
NACA
63,4-420
NACA
651-412
...............................
NACA
65.o-015
....................
215
NACA
652
..................................
216
..........................
217"
(a)
(b)
• .......
.................................
...........................
........................
...............................
with
0.25c
slotted
flap
......................................
a=0.8
201
scaled
plain
........................
.......................
207
.................................
211
_ith
0.20c
.......................
a:0.6
1 ....
Aerodynamic
characteristics
with
hinge
location
2 ....
154
NACA
65..-415
155
156
NACA
652-415,
a=0.5
NACA
653
..............................
157
NACA
63(420)-517
NACA
63-006
NACA
63-009
NACA
............................
..............................
018
653-118
with
Configuration
(b)
63-206
...............................
160
NACA
Aerodynamic
characteristics
65z-218
..............................
NACA
63-209
............................
161
NACA
653
NACA
63
162
NACA
65z-418,
NACA
631-012
..................................
163
NACA
65z-618
NACA
631-212
..................................
164
NACA
653-618,
NACA
631-412
..............................
165
NACA
654-021
NACA
632-015
................................
166
NACA
654
NACA
632
..........................
167
NACA
654-421
NACA
632-415
...................................
168
NACA
654-421,
NACA
632-615
...................................
169
NACA
65(21_)-114
NACA
633
170
NACA
65(4211-420
NACA
633-218
.........................
171
NACA
66,1-212
NACA
_32-418
..............................
172
NACA
6"3-618
.................................
173
NACA
66,1-212
characteristics)
NACA
634
..............................
174
NACA
66(215)-016
NACA
634-221
..................................
175
NACA
66(215)-216
NACA
634-42l
..............................
176
NACA
66(215)
NACA
64-006
...............................
177
NACA
64
178
NACA
66(125)-216
characteristics)
NACA
64-108
...............................
179
NACA
66(215)-216,
NACA
64-110
.............................
180
NACA
66(215)-216,
NACA
64-206
...........................
181
flap
NACA
64-208
................................
182
NACA
NACA
64-209
64-210
.............................
............................
183
184
NACA
641-012
.......................
185
NACA641-l12
.........................
186
NACA
64_-212
...........................
187
NACA
641-412
...........................
188
NACA
642-015
..............................
189
NACA
642-215
..................................
190
NACA
642-415
....................................
191
NACA
643-018
.....................................
192
NACA
643-218
.....................................
193
009
................................
(a)
(b)
(c)
(d)
(e)
(f)
(g)
NACA
218
slotted
flap
220
...............
221
222
418 ...............................
o=0.5
223
.............
224
..................
a=0.5
225
.....................
226
....................................
227
221 ......................................
228
.................
a=0.5
229
...............................
230
..................................
231
............
232
...............................
with
233
0.20c
split
......................
flap
(lift
and
moment
234
...........
" ......................
235
...................................
216
Airfoil-flap
Flap
213
0.309c
double
..........................
159
021
moment
219
..........................
018 ..............................
and
....................
(a)
215
(lift
212
158
210 ...............................
flap
214
location
215
split
.............................
hinge
NACA
208
....................
with
a=0.3
....................
422 ................................
202
203
204
152
1 53
63,4-420,
63(420)
flap .............
...........................
.........................
characteristics
(e)
200
...........................
,Configuration
Aerodynamic
NACA
NACA
199
...............................
with
a=0.6
236
sealed
with
0.20c
..................................
plain
split
flap
flap
.............
(lift
and
237
moment
238
.........................
a=0.6
with
configuration
configuration
Aerodynamic
0.20c
239
0.30c
slotted
and
0.10c
plain
..................
240
.................................
characteristics.
Slotted
240
flap
retraeted___
241
Lift
and
deflected
moment
eharaeteristies.
22 ° _ ..........................
Slotted
flap
Lift
and
deflected
moment
eharaeterislies.
27 ° ..............................
Slotted
flap
Lift
and
deflected
moment
characteristies.
32 °_ ..............................
Slotted
flap
Lift
and
deflected
moinent
eharaet_eristies.
37 ° ...................................
Slotted
flap
66(215)-416
....................................
242
243
244
245
246
130
REPORT
NO.
8 2 4--NATIONAL
ADVISORY
COMMITTEE
FOR AERONAUTICS
].)age
NACA
NACA
NACA
NACA
NACA
66-006
66_)09
66-206
66-209
66-210
NACA
NACA
NACA
NACA
66,-012
661-212
662-015
662-215
...........................................
...........................................
...........................................
...........................................
...........................................
..........................................
..........................................
..........................................
...........................................
247
248
249
250
251
252
253
254
255
Page
NACA
NACA
NACA
NACA
NACA
NACA
662-415
663-018
66,_-218
663-418
66_-021
664-221
NACA
NACA
NACA
67,1-215
747A315
747A415
..........................................
.......................................
..........................................
........................................
........................................
...........
: ..........................
.........................................
...........................................
.............................................
256
257
258
259
260
261
262
263
264
SU_vIMARY
OF
AIRFOIL
131
DATA
NACA
0006
;=
I
Z
o
i
132
REPORT
NACA
NO.
8241NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
0009
t
I
I
I
i.
%
Z
i
i
I
g
i
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%
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f
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%
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...
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1•
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f
1"
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SUMMARY
OF
AIRFOIL
133
DATA
NACA
I
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i
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F_
1408
I
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[_
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i'
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I
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ai
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918392--50--10
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(¢ua!oACiaoo
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r,"
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o
134
REPORT
NACA
NO.
824--NATIONAL
ADVISORY
COM_IITTEE
FOR
AERONAUTICS
1410
%
I
__
7--
r
t-
t
-
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<11
co
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i.
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_
SUI_IMARY
OF
AIRFOIL
DATA
135
NACA
'
1 41 2
<3_
I! .........
=o
g
o
Z
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m
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g
o
N
*a %uwa/yjaoo
/.,z/I uo.q,_a_
136
REPORT
NACA
NO.
824--NATIONAL
ADVISORY
COI_IMITTEE
FOR
AERONAUTICS
241 2
c_
i
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SUM:2_IARY
OF
AIRYOIL
137
DATA
NACA
11
I
!
i
i
2415
i
i
{
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t_
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REPORT
NACA
241
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
8
I
%
I
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SUMMARY
OF
AIRFOIL
139
DATA
NACA
2421
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140
REPORT
NACA
1NO. 824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
2424
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OF
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141
DATA
NACA
441
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NACA
I
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
4415
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143
NACA
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144
REPORT
NACA
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
4421
%
i
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SUMMARY
OFAIRFOIL
DATA
145
NACA
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146
REPORT
NACA
2301
_TO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
2
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147
DATA
NACA
23015
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148
REPORT
NACA
NO.
8 2 4--2_TATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
23018
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OF
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149
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NACA
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NACA
-i
NO.
824--NATIONAL
ADVISORY
COMMITTEE
)'OR
AERONAUTICS
23024
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OF
AIRFOIL
151
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NACA
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152
REPORT
NACA
63,4-420
NO.
824--NATIONAL
with
ADVISORY
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FOR
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OF
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DATA
153
NACA
63,4-420
with
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154
REPORT
NACA
63,4-420
with
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
flap
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OF
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DATA
155
NACA
63,4-420,
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REPORT
NO.824--NATIONAL
ADVISORY
COM2_IITTEE
FORAERONAUTI
CS
NACA
63(420)-422
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SUMMARY
OF
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157
DATA
NACA
63(420)-517
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158
REPORT
NACA
NO.
8 2 4--NATIONAL
ADVISORY
COh_MITTEE
FOR
AERONAUTICS
63-006
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159
DATA
NACA
I
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63-009
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160
REPORT
NACA
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
63-206
I
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161
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NACA
%
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63-209
162
REPORT
NACA
63-21
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
0
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163
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NACA
63t-01
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164
REPORT
NACA
631-21
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824--NATIONAL
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FOR
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165
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NACA
631-41
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166
REPORT
NACA
632-01
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
5
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167
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NACA
632-21
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168
REPORT
NACA
632-41
[
NO.
8 2 4--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
5
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NACA
632-61
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170
REPORT
NACA
633-01
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824--NATIO_N:AL
ADVISORY
C'OMMITTEE
FOR
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8
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171
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633-218
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172
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NACA
633-41
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
8
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173
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174
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NACA
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
634-021
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175
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NACA
634-221
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176
REPORT
NACA
NO.
8241NATIONAL
ADVISORY
COMMITTEE
:FOR
AERONAUTICS
634-421
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177
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NACA
64-006
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NACA
NO.
8 2 4--:NATIONAL
ADVISORY
COMhIITTEE
1,_,q_ A l,:l_{ }N .\ U T I CS
64-009
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179
DATA
NACA
64-108
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NACA
N0.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
64-110
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182
REPORT
NACA
:NO.
824--::NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
64-208
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183
DATA
NACA
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184
REPORT
NACA
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
64-210
m
C
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%
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%
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OF
AIRFOIL
DATA
185
NACA
641-012
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186
REPORT
NACA
641-1
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
12
%
i
%
%
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OF
AIRFOIL
187
DATA
NACA
641-212
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188
REPORT
NACA
641-41
NO.
8 2 4--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
2
I
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SUMMARY
OF
AIRFOIL
189
DATA
NACA
642-01
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190
REPORT
642-21
NACA
N0.
8 2 4--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
5
%
-1-
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SUMMARY
OF
AIRFOIL
191
DATA
NACA
642-415
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192
REPORT
NACA
643-01
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
8
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OF
AIRFOIL
193
DATA
NACA
643-21
8
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194
REPORT
NACA
643-41
NO.
8 2 4--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
8
%
\J
%
%
'::b
%
%
SUMMARY
OF
AIRFOIL
195
DATA
NACA
I
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196
REPORT
NACA
NO.
824.--N_T'IONAL
ADVISORY
COMMITTEE
:FOR
AERONAUTICS
644-021
I
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OF
AIRFOIL
197
DATA
NACA
644-221
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198
REPORT
NACA
NO.
824---NATIONAL
ADVISORY
COMMITTEE
i
AERONAUTICS
644-421
•
m.
FOR
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SUMMARY
OF
AIRFOIL
199
DATA
NACA
65,3-01
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200
REPORT
NACA
65,3-418,
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
a =0.8
%
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?
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%
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OF
AIRFOIL
DATA
20]
NACA
65,3-618
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202
REPORT
NACA
ill
65,3-618
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
with flap
o
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OF
AIRFOIL
DATA
203
NACA
65(216)-415,
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%
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204
REPORT
NACA
NO.
8 2 4--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
65-006
"_-
(::b
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o4
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OF
AIRFOIL
DATA
205
NACA
I
65-009
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206
REPORT
NACA
NO.
8 2 4--1_ATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
65-206
I
I
I
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%
i
%
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SUMMARY
OF AIRFOIL
207
DATA
NACA
65-209
i
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1"
I"
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208
REPORT
NACA
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
65-210
I
%
/
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L"
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OF
AIRFOIL
209
DATA
NACA
i
65-410
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210
REPORT
NACA
651-01
N0.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
2
I
I
J
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%
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SUMMARY
OF
AIRFOIL
211
DATA
NACA
651-212
i
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212
REPORT
NACA
651-212
with
NO.
8 2 4--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
flap
%
%
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%
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SUMMARY
OF
AIRFOIL
213
DATA
NACA
•
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651-212,
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214
REPORT
NACA
:NO.
824--NATIONAL
ADVISORY
COMMITTEE
:FOR
AERONAUTICS
651-412
<-4
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SUMMARY
OF
AIRFOIL
DATA
215
NACA
652-01
5
%
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%
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216
REPORT
NACA
652-21
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
5
CO
1..^
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SUMMARY
OF
AIRFOIL
217
DATA
NACA
f
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652-41
I"
5
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218
REPORT
NACA
652-41
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
a = 0.5
5,
I
I
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SL_I_IARY
OF
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219
DATA
NACA
653-018
I
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220
REPORT
NACA
653-118
NO.
with
824--NATIONAL
flap
ADVISORY
COMMITTEE
FOR
AERONAUTICS
.
%
%
z
J
SUI_II_IARY
OF
AIRFOIL
221
DATA
NACA
%
%
653-11
8 with
flap
%
i
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%
oo
%
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918392--51--15
222
REPORT
NACA
NO.
8 2 4--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
653-218
%
%
I
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SUMMARY
OF
AIRFOIL
223
DATA
NACA
.....
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653-41
8
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REPORT N0. 824--NATIONAL
224
NACA
653-41
8,
ADVISORYCOMMITTEE FOR AERONAUTICS
a =0.5
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SUMMARY
OFAIRFOIL
DATA
225
NACA
653-618
!
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lu_uo_
226
REPORT
653-61
8,
NO.
824--NATION_:L
AD'VISORY
CO'MMITTEE
FOR
AERONAUTICS
a = 0.5
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q)
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OF
AIRFOIL
227
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NACA
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NACA
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
654-221
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SUMMARY
OF
AIRFOIL
229
DATA
NACA
654-421
(o
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REPORT
NACA
654-421,
NO.
8241NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
a = 0.5
%
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SUMMARY
0F
AIRFOIL
231
DATA
NACA
65(215)-1
14
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%
232
REPORT
NACA
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
65(421)-420
I
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OF
AIRFOIL
DATA
233
NACA
66,1
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ko
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234
REPORT 1krO.824--NATIONAL
NACA
66,1
-212
ADVISORYCOMMITTEE FOR AERONAUTICS
with flap
x
T,
_5
£
,<
rj
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%
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SUMMARY
OF
AIRFOIL
235
DATA
NACA
66(215)-01
6
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236
REPORT
NACA
66(21
i.
NO.
8 2 4--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
5)-216
!
%
%
%
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SUMMARY
OF
AIRFOIL
237
DATA
NACA
I
I
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with
flap
REPORT
238
NACA
66(21
5)-21
NO.
6 with
824--NATION!AL
ADVISORY
COMMITTEE
FOR
AERONAT2TICS
flap
.,d
oo
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SUMMARY
OF
AIRFOIL
239
DATA
NACA
_
J
66(21
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REPORT
240
NACA
66(21
5)-21
6,
N0.
a = 0.6
8 2 4--NATIONAL
with
ADVISORY
COMMITTEE
FOR
AERONAUTICS
flap
?,'_,','1",'_'1,° .... °
T
£
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%
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SUMMARY
OF
A]RVOIL
241
DATA
NACA
66(215)-21
6, a = 0.6
with
flap
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t
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IX;
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242
REPORT
66(21
5)-216,
NO.
a _-0.6
824--NATIONAL
with
ADVISORY
COMMITTEE
FOR
AERONAUTICS
flap
I
×:
%
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SUMMARY
OFAIRYOIL
DATA
NACA
[[
Jill
IJ
ir
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243
66(215)-216,
a = 0.6
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with
flap
244
REPORT
NACA
66(215)-216,
_0.
824--NATIONAL
a = 0.6
i: It
!
ADVISORY
with
CO_I51ITTEE
FOR
AERONAUTICS
flap
i
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SUMMARY
OFAIRFOIL
DATA
NACA
El
I
I
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245
O = 0.6
66(215)-216,
with
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7
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,
246
REPORT
NACA
NO.
8 2 4--NATIONAL
ADVISORY
COMI_IITTEE
FOR
AERONAUTICS
66(215)-416
l
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OF
AIRFOIL
DATA
247
NACA
66-006
I
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%
248
REPORT
NO.
824--NATIO_TAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
%
iI
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%
)
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7,
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SUMMARY
OF
AIRFOIL
249
DATA
NACA
I
66-206
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250
REPORT
NACA
I
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
66-209
i
t
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%
t
i
I
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%
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SUMMARY
OFAIRFOIL
DATA
251
NACA
_
66-210
m
I
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_£.A_L
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o_
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_uaodJ_o_
7ua_o/,1/
252
REPORT
NACA
661-01
N0.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
2
i l
I
I
%
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......
/I
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,
i
SUMMARY
OF
AIRFOIL
253
DATA
NACA
661-21
2
%
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%
%
%
c,I
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918392--51--17
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CuouJoDI
i •
254
REFORT
NACA
662-01
N0.
824--2_TATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
5
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%
%
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SUMMARY
OF
AIRFOIL
DATA
255
NACA
662-21
5
"--'4"----
(
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%
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I"
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25()
REPORT
NO.824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
NACA
662-415
I
•
_
I"
I*
I"
SUIVIIYIARY
OF
AIRFOIL
257
DATA
NACA
663-018
I
i
I
(b
?.
i
I
%
"8
r_
"6
-+
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%
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_.
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258
REPORT
NACA
663-21
N0.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
8
I
i
Ii
I
%
\
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SUMMARY
OF
AIRFOIL
DATA
259
NACA
663-418
II
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%
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p-.+--+---+---
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260
REPORT
NACA
:NO.
8 2 4--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
664-021
"%
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>
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%
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Cuo_uol41
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SUMMARY
OF
AIRFOIL
261
DATA
NACA
m_
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664-221
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262
REPORT
NACA
67,1
_TO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
-215
%
i
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I\
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%
I"
%
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SUiVZIVZARY
OF
AIRFOIL
263
DATA
NACA
747A315
i
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03
%
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%
t"
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264
REPORT
NACA
NO.
824--NATIONAL
ADVISORY
COMMITTEE
FOR
AERONAUTICS
747A415
I
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%%
Z
Positive
d/reetion_ ot axis and snslm (forces and momants_ are shown by arrows
Velocities
Moment about
Azis
F_
Symo
_1,
Dmigz_on
_xmt,ltel
'to II.zm)
lyml0oL
Veeii;natlon
Positive
din_/oa
8_o
Lo_/tud/nsL..__
I_rsL._.
NormAL ....
Absolute
coefficients
(rolling)
X
Y
X
Y
Z
Pitebin<_
yawim_.._I
i
AaSulsr
i I "_
L
M
N
_mX
Piteb.__.
X""* Y
Yaw ....
r
t
Angle of set of control
position),
8. (Indicate
of moment
(pit_)
D_ipstiou
surface
surface
(relstive
by proper
coe/_cient
Cr==on-_
_sw_)
4. PROPILLER
D
Diameter
p
Geometric
p/D
V'
Pitch ratio
Inflow velocity
V'.
Slipstream
T
Thrust,
absolute
coefficient
Cr='_---_
Q
Torque,
absolute
coefficient
Co=_
SYMBOLS
P
Power,
absolute
0.
Speed-power
coemcieut----
n
n
Efficiency
Revolutions
per second,
pitch
velocity
A
.
t mph----0.4470
1 mpsffi2.2369
raps
mph
ft-lb/sec
hp
rps
(&)
S. NUMEIglCAL RELATIONS
I hp----76.04
kg.m/s==550
I metric horsepowerm0.9863
_/p-_
1 lb--0.4536
kg
I kg==2.2046
I mi==1,609.35
lb
1 m=ffi3.2508
ft
re=ffiS,280
ft
to neutral
subscript.).