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CASE
_
FILE
f_
!"_ V
NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
L
2
TECHNICAL
No.
AERODYNAMIC
1546
CHAI_CTER._TICS
AT
By W.
NOTE
F.
MACH
Lindsey,
Langley
OF
NUMBERS
D.
24
BETWEEN
B. Stevenson,
Aeronautical
Langley
Field,
Laboratory
Va.
1948
16-SERIES
0.3
and
Washington
September
NACA
AND
Bernard
AIRFOILS
0.8
N.
Daley
NATIONAL
AERODYNAMIC
F.
C0_[ITYEE
TECHNICAL
N_fE
CHARACTERISTICS
OF
AT
By W.
ADVISORY
MACH
Lindsey,
NUMBERS
D.
B.
NO.
FOR
AERONAUTICS
1546
24 NACA
BETWEEN
16-SERIES
0.3
Stevenson,
AND
and
AIRFOILS
0.8
Bernard
N.
Daley
SUMMARY
An investigation
has been conducted
to determine
the aerodynamic
characteristics
of a group
of NACA
16-series
airfoils
releted
in camber
and thickness
over a Mach number
range from 0.3 to approximately
0.8.
The results
obtained
from the present
Invest_gation
were
combined
with
the data of 12 NACA 16-serles
airfoils
obtained
under the same con-ditions
and previously
reported
in NACA Rep.
No. 76-_.
currently
available
force-test
data for NACA 16--serles
obtained
under
the same test conditions
in the Langley
speed
tunnel
are
All the
airfoils
2h-inch
high-
I)
use
presented.
IBTRODUCTION
The
NACA
16-series
airfoils
were
derived
(referen0e
for
at high speeds,
particularly
for propeller
applications.
The variations
in design
camber
and thickness
ratio,
covered
in referenze
l, were not
of sufficient
scope to meet all the requiremsnts
of propeller
design.
A test program
was formulated,
therefore,
whereby
the aerodynamic
characteristics
would be obtained
for some of the airfoils
of
reference
1 over an extended
angular
range,
as well as for 12 additional
airfoils
of the same series.
The results
of this investig_tlon
combined
with the data of ref3rencs
1 are presented
herein
uncorrected
for tunnel-wall
constriction
effects.
The magnitude
of the constriction
effect
on Mach number
at supercritical
speeds
is approximately
2 percent
of the uncorrected
value and does not affect
the validity
of the conclusions.
SYMBOLS
c_
c_
cz i
anglo
section
design
of atSack,
llft
section
degrees
coefficient
lift
coefficient
(incompressible
potential
flow)
2
NACATN No. 1546
c Zo
section
lift coefficient
at
M = 0
(experimental
were obtained
by extrapolating
from
M = 0.3
by Glauert's
method)
cd
section
drag
c c/4
section
axis
pltchlng-moment
Z/d
lift-drag
M
stream
Mcr
critical
Mach
is attained
Poma x
maximum
t/c
thlckness-chord
x
airfoil
Y
airfoil
ordinate,
camber
line
to
values
M = 0
coefficient
coefficient
about
quarter-chord
ratio
Mach
number
number;
locally
Mach number
at which
as on airfoil
incompressible
ratio,
station,
pressure
of
sound
coefficient
percent
fractions
of
fractions
APPARAI"UB
speed
AND
chord
of
chord
measured
normal
to
TESTS
Force
measurements
of lift, drag, and pitching
moment
were made
in the Langley
24-inch
high-speed
tunnel
(described
in reference
2)
on a series
of airfoils
having
NACA 16-series
profiles.
The thicknesschord
ratios
of the airfoils
tested
ranged
from 6 to 30 percent
and the
design
lift coefficients
ranged
from 0 to 1.0.
The specific
airfoils
for which
force meaeurem_nte
were made in this investigation
are given
in table
I and are differentiated
from those airfoils
reported
in
reference
1.
The models
were made of duralumin
and had a chord Of 5 inches.
Each model
spanned
the 24-inch
test section
and passed
through
holes
cut in flexible
brass
end plates
that preserved
the contour
of the
tunnel
walls.
The holes were the same shape as, but elightly
larger
than,
the model.
The ends of the model were secured
in a balance
of
the type described
in reference
3.
angles
range
The llft, drag,
and pitching-moment
coefficients
were measured
at
of attack
corresponding
at low Mach numbers
to a llft-coefficient
from 0 to approximately
1.O.
These
data were obtained
for a Mach
_ACA TN _o. 1!96
number
number
range
range
3
from 0.3
extended
to approximately
0.8.
The c?rresponding
Reynolds
approximately
from 0.85 × lO 6 to 2 x lO 6.
Drag
coefficients
for several
of the airfoils
were obtained
by the wakesurvey
method.
The wake--survey
measurements
were generally
limited
to an angle of attack
of 0 ° or the design
angle.
Critical
Mach numbers
at low angles
of attack
were estimated
by
means
of small
total-pressure
tubes mounted
on the upper
surface
of
the airfoils.
The tubes were generally
located
at the 75-percent-chord
station
and 2 to 3 percent
chord above
the airfoil
surface.
The Mach
number
at which
the measured
total pressure
decreased
approximately
0.02 percent
was taken as an estimate
of the critical
Mach number.
NACA
16-SERIES
AIRF01I_
The NACA 16-series
airfoils
are designated
by a five-digit
number
(except
for the case in which
the design
lift coefficient
is
equal
to or more than 1.0).
The first digit represents
the series
classification.
The second
digit
indicates
at design
conditions
the
distance
in tenths
of chord from the leading
edge to the position
of
mln[mum
pressure.
The third digit,
first digit
following
the dash,
indicates
the amount
of camber
expressed
in terms of design
llft
coefficient
in tenths.
The last two digits
together
express
the
thickness
in percent
chord.
The
thickness
distribution
of
the
NACA
16-series
airfoils
was
developed
(reference
i) to produce
a shape having
very low induced
velocities
and thus having
high critical
Mach numbers.
The ordinates
for the basic or symmetrical
profile
of the NACA 16-serles
airfoils
can be obtained
from the following
equations:
_I
= O'Ol-tc ( 0"989665xlI/2
-
0"239290xi
- O'O_lO00x12
-
0"559400x13_
s_nd
where
to the
y
is
camber
the ordinate
line and
x
in fractions
of
is the station
the chord measured
normal
in fractions
of the chord.
4
NACATN No. 1546
Subscripts I and 2 pertain to the region ahead of and behind the
maximumthickness location, respectively
Ifor example, xI _ 0.5
and
r_ >
5)
The
leading-edge
radius
L.E.
The
ordinates
The
for
camber
expressed
radius
= 0.0048972C_)
a 9-percent-thick
llne
for
the
in percentage
airfoil
NACA
are
16-series
of
the
chord
2
presented
airfoils
was
in
table
where
the
Yc
is
station
The
in
the
= _0.079577czi_
mean-llne
fractions
ordinates
and
of
slopes
I OgeX
ordinate
the
of
-
loge(l
in fractions
II.
derived
(reference
l) to have essentially
a uniform
chordwlse
loading.
camber
line, designated
the
a = 1
mean line in reference
4,
expressed
in equation
form as
dx
dYo
is
This
can be
- x_
of
chord
and
x
is
chord.
the
camber
line
for
NACA
16-series
airfoils
are presented
in table II.
It may be noted
that the slope
of the leading-edge
radius
as given
in table II differs
from that given
in the corresponding
table of reference
1.
Since
the slope of the
leadlng-edge
radius
is determined
by the slope of the camber
line, the
value
specified
for the leading-edge
radius
depends
upon the chordwise
station
x
at which
the
specified
in reference
1
and fairing
difficulties
of highly
cambered
thick
camber-line
slope is obtained.
The slope
corresponded
to the 0-percent-chord
station
were later encountered
at the leading
edge
airfoils.
The slope specified
in table II
corresponds
to the 0._-percent-chord
station.
The leading-edge
radius
must be as specified
but the slope of the leading-edge
radius
does not
appear
to be rigidly
fixed,
probably
as a result
of the approximations
made
in determining
the extremities
of the camber
line.
(See
reference
1.)
NACA _W No.
1_6
5
PRECISION
The errors
to which
accidental
andsystematic.
the
data were subject
can be classified
The accid@ntal
errors
arose
from
as
inaccuracies
in model
installation,
in calibrations
of alr stream
and
balance,
and in the reduction
of the test records.
The accidental
errors
evaluated
from an inspection
of the test data are as follows:
c Z
............................
cd
+0.005
.............................
/9.0005
Cmc/_ .............................
_,
deg
from
+0.oo2
.............................
The largest
systematic
leakage
of air through
+0.i
error
to whlch
the data were
subject
the (3/64
inch) gaps at the Junctures
arose
of
airfoils
and tun_lel wall.
The corrections
were first determined
by
tests
on an NACA 0012 airfoil
with
v_r_ous
end gaps; these
corrections
were applied
to the data of reference
1.
Tests
to determine
the correction
were extended
for the present
Investigation
to include
not only
airfoils
of various
thlckness-chord
ratios
but also a large angle-ofatteck
range.
The tests of the NACA
16-series
airfoils
cambered
for a
design
l_ft coefflc_ent
of 0.3 and having
thickness-chord
ratios
from
6 to 21 percent
were made.
The angle-of-attack
r_nge
corresponded
to
the range presented
herein
for those airfoils.
Investigation
of the end-leakage
effects
showed
that the correction
to drag coeff_clent
depended
not only on Much number
and lift coefficient
but also on thlckmess-chord
ratio.
The investigation
further
indicated
that camber
mdght have an effect
on the angle-of-attack
correction
since the tests on the cambered
airfoils
showed
only a
shift
in angle of zero lift (see also fig. l0 of reference
2); whereas
the tests on a sy_mmtrical
airfoil
(reference
l) indicated
that the
correction
was a function
of lift coeff_clent.
The maximum
difference
between
NACA
the
two
corrections
The corrections
for end
16-series
airfoils
were
d_d
not
exceed
0.3 °.
leakage
as determined
considered
to be more
by the tests on
reliable
than those
used in reference
1 because
of the greater
renge of the test.
The
corrections
were applied
not only to the 12 _ddltion_l
eIrfoils
but
also to the 12 airfoils
reported
_n reference
1.
Differences
in the
aerodynamic
characteristics
for airfoils
_n th_s paper emd _n
reference
1 are primarily
a result
of the change
in the end-leakage
corrections.
A comparison
of dr_
coefficients
obtained
from force-test
data corrected
for end leakage
At low design
llft coefficients
the d_fferences
from wake surveys
is sho_1 in figure
are approximately
and
1.
of
6
NACATN No. 1546
the samemagnitude as the accidental errors.
At high design llft
coefficients
the differences increase and thereby indicate that the
applied leakage correction mlght be too small in that lift-coefflcient
range. The wake--survey drag coefficients,
however, do not increase
as rapidly with design lift
coefficient as would be expected,
especially at high values of czi.
The remaining systematic errors associated with these data arise
from wlnd-tunnel wall interference.
The correction for this effect
as determined by the method of reference 5 maYbe subject to error at
supercritlcal
Mach numbers. The msthod, however, should give an
estimate of the magnitude of the errors Involved. An estimate of
the error can be obtained from figure 2 which shows a comparison
between basic aerodynamic data for the NACA16-309 airfoil
corrected
and uncorrected for tunnel-wall effects.
An examination of figure 2
Indicates that the correction _s generally small and, therefore, has
not been applied to the results presented herein. A further examination _ndicates that at the highest Machnumbers the correction
appears to have the greatest effect on Machnumber. Thus, in the
application of the data in a design problem, the approximately
2-percent correction for Machnumber could have a large effect.
The choking phenomenonIs an additional effect of tunnel walls
that enters
into the problem
of w_nd-tunnel
testing
at high subsonic
Mach numbers.
At the choking
Mach numbers
sonic velocities
extend
from model
to tunnel
wall,
and the static
pressure
is lower behlnd
the
model
than In the undisturbed
region
upstream
of the model;
thus, large
gradients
in static
pressure
cen be produced.
The resulting
flow past
the model
is unlike
any free-air
condition,
and data obtained
at and
near
choking
Mach munbers
are, therefore,
of questionable
value.
Data
near
the choking
Mach number
_re, consequently,
omitted
from this paper
with
the exception
of a few conditions
shown In flgure
3.
The arrows
at the zero-lift
axes (fig.
3) show the one-dimenslonal
theoretical
choklngMach
number
at design
condltlons
for each of the airfoils
_n_d
indicate
how closely
these basic date approach
the choking
speed.
The
data at the higher
angles
of attack
generally
do not approach
their
respective
choking
Mach numbers
as closely
as do the data near design
conditions.
RESULTS
The variation
at constant
angles
tested
constitutes
in figure
3.
_n aerodyn_zHc
characteristics
with Mach
of attack
for each of the NACA 16-series
the basic data for the investigation
_nd
numbers
airfoils
is presented
NACATN No. 1546
7
The data of figure 3 were cross-plotted to show the effects of
variation of thickness-chord ratio and camber or design lift
coefficient on the aerodynamic characteristics.
The cross-plotted results
are showrl _n figures h to 9.
The effect
lift
coefficient
and l_-percent
respectively.
airfoil
having
figure 14.
of csmber on the variation of llft-drag
ratio with
for airfoils
of 6-percent, 9--percent, 12-percent,
thickness is presented In figures i_ ii, 12, a_ 13,
The effect of thickness on lift-drag
ratio for cP_mbered
a design lift
coefficient of 0.3 is presented in
The theoretically
derived maxlmnmnegative pressure coefficients
(reference 4) for NACA16-series airfoils
are presented in figure 15.
Figtu'e 16 permits the max_mumnegativepressure coefficients
in an
_ncompresslble or low-speed flow to be transcribed to critical
Ms_ch
numbers in accordance with yon Ka_rm_n-Tsien'sreletion (reference 6).
A comparison between the theoretically
derived and the experln_ntally
determined critical
Machnumbers is given in figure 17. The n_sured
critical
Machnumbers at several stations on an tultwlsted propeller
tip are compared in figure 18 with the values estimated from twodimensional flow.
A comparison is madein figure 19 between the critical
Maeh
number and the Machnumber for llft break and maximumllft-drag
ratio.
The effects of thickness and camberon the Machnumbers for llft
bresk
and drag rise are presented in figure 20.
A tabulation of the airfoils
investigated and the figure numbers
containing the pertinent test data are given in table I.
DISCUSSION
Subcritical
Lift.-The
NACA16-series airfoils
at the design angle of attack
of 0° and at low Machnumbers do not produce experimental lift
coefficients of the samevalue as the design lift
coefficients.
The difference can be attributed primarily to viscosity in the real flow and
its modifying effect on the theoretically
predicted influence of the
camber line, especially over the rear of the model.
At low Machnumbers and at an angle of attack of 0°, figures 4
to 9 showedthat the experimental llft
coefficients decreased from
85 percent of the'design lift
coefficient for airfoils
of 6-percent
thickness to 38 percent of the design lift
coefficient
for airfoils
of 21-percent thickness.
The variation with thickness for airfoils
between 6--percent and 21-percent thickness can be approximated by
8
NACATN No. 1546
the relation
-c_ = i00 - <t)l. 35 (_ii
c _i
values in percent).
C_mbered
\
airfoils
(flgs.
attack
of the
__c_i = O.1
and
0.5__
having
a
thickness
of
30 percent
chord
7 and 9) produced
negative
lift coefficients
at an angle of
of 0 °.
These
negative
lift coefficients
were about -20 percent
design
llft coefficient.
The negative
llft coefficients
of the 30--percent-thick
airfoils
were
produced
as a result
of either
separation
on the upper
surface
of the airfoil
or a greater
chordwise
extent
of separation
on the upper
surface
than on the lower and less curved
surface.
The separation
effects
were
illustrated
by an unpublished
investigation
of the flow
past thick
airfoils.
The llft characteristics
of many of the airfoils
(figs.
4 to 9)
at angles
of attack
between
2° and 8 ° exhibited
a break or region
of
reduced
slopes
over an angular
range of 2 ° to 3° . At angles
of attack
beyond
this region
of reduced
slope,
the slopes
increased
but generally
did not reach the values
produced
near an angle of attack
of 0 °.
Figures
4 to 9 illustrated
that the break became
more pronounced
as
either
the design
lift coefficient
or the thickness-chord
ratio was
increased.
The thdckness-chord
than camber.
(Compare
figs. _
ratio,
however,
to 6 with
figs.
had a greater
7 to 9.)
effect
The forward
movement
of the center
of pressure
and the rapid
increase
in drag, which
occurred
simultaneously
with
the break in the
llft curve,
indicated
that transition
moved rapidly
forward
or that
laminar
separation
occurred.
Since
compressibility
has the same effect
on adverse
pressure
gradients
as increases
in thickness,
this
assumption
is further
substantiated
by the effect
of compressibility
on the breaks
in the curves
inasmuch
as increases
in the Mach number
of
the flow generally
tended
to
aerodynamic
characteristics.
near
Figure
design
emphasize
4 shows at a Mach number
angle of attack
generally
the
abruptness
of
the
change
of 0.30 that the lift-curve
increased
with design
lift
in
slope
coefficient
for 9-percent-thdck
airfoils.
For thicker
airfoils,
the
change
in lift-curve
slope with design
lift coefficient
became
very
small.
Increasing
the thlckness-chord
ratio of an airfoil
of given
design
llft coefficient,
however,
resulted
in a decrease
in liftcurve
slope.
Pitching-moment
coefficients.-Thln-alrfoll
theory
(su_m_rlzed
reference
h) has shown that the effect
of increasing
the camber
of
in
airfoils
having
approxlmatelyuniform
chord loading,
such as the
NACA 16-eeries,
is to produce
a large increase
in the negative
pitchingmoment
coefficient.
The theory
has also shown that the effect
of angle
NACA TN No. 1546
of
attack
design
is
lift
9
independent
of
coefficient
camber
would
have
and,
no
therefore,
effect
on
increasing
_c_,"
The
the
data
in figures
4 to 6 are in agreement
with the thln--airfoil
theory.
Increases
in thickness-chord
ratio
(especially
above 12 percent),
however,
produced
a forward
movement
of the center
of pressure
and
positive
increase
in
_
(figs.
7 to 9).
T_is
effect
of
a
thickness
_z
is probably
a result
of the adverse
effect
of viscosity
on the loading
near
the trailing
edge of the thicker
airfoils.
The effect
of compressibility
was to produce
a large rearward
movement
of the center
of
pressure
without
noticeably
affecting
_--_.
3c_
Dry.The drag data presented
in the form of polars
indicate
that
the change
in minimum
drag coefficient
with design
lift coefficient
is
small
at low Mach numbers
for thlckness-chord
ratios
of 9 percent
(fig.
4).
This change
increases
with
thickness
(figs.
5 and 6), but
at a sufficiently
slow rate that for airfoils
of 15--percent
thickness
at low Mach numbers
the maximum
lift-drag
ratio
increases
with design
lift.
(See also figs. I0 to 13.)
Increases
in Mach number
above a
value
of approximately
0.60 caused
the maximum
llft-drag
ratio
to
occur
at progressively
lower llft coefficients
and at lower design
coefficients
(figs.
I0 to 13).
This effect,
illustrated
by figures 10(c) to 10(f) aml figures
ll(c) to ll(f),
is a result
of an
increase
lift and
in induced
velocities
associated
is the normally
expected
effect
with an increase
of compressibility.
in
lift
design
The maximLua lift-drag
ratio
for a given airfoil
at low Mach
numbers
(figs.
i0 to 13) generally
occurred
at a lift coefficient
approxdmatel_
0.i to 0.2 greater
than the design
value.
Pressuredistribution
data (unpublished)
has shown at low Mach numbers
that
the shape of the pressure
distribution
for an NACA 16--212
an angle
of attack
of 2 ° corresponded
more
closely
to the
or design
distribution
than did the distribution
obtained
Consequently,
in that speed range
the airfoil
more efficient
at an angle of attack
slightly
ar_le
of attack
of 0 °.
airfoil
at
theoretical
at 0 °.
could be expected
greater
than the
to be
design
The general
decrease
in the lift-drag
ratio with
increases
in
tblckness-chord
ratio shown _in figure
14 results
from the observed
and expected
increase
in drag coefficient
and some decrease
in lift
coefficient.
As the Mach number
increased,
the effect
of thlckn_ea
on lift-dra_
ratio was magnified
in accordance
with the usual effects
of compressibility
on the aerodynamic
characteristics.
i0
NACATN No. i_46
Critical
The
critical
undisturbed
Mach
stream
number
at which
Mach
is
sonic
that
Number
value
velocities
of
the
are
Mach
attained
number
of
the
locally
within
the flow field.
Experimental
investigations
in two-dlmensional
flows
have shown that the adverse
effects
of compressibility,
such as
the drop in llft coefficient,
rapid rise in drag coefficient,
and
abrupt
changes
in moment
coefficient,
do not occur until
the critical
Mach number
has been reached
or exceeded.
The Mach number
at which
abrupt
changes
in aerodynamic
characteristics
occur
in a two-dimenslonal
flow cannot
at present
be reliably
predicted.
There
is, however,
the generalization
that the _ch
number
for the force break
is equal to or greater
than the critical
Mach
number.
Thus,
as a first step in the hlgh-speed
application
of
airfoils,
the critical
Mach numbers
should
be known.
The theoretical
critical
Mach nu_er
of a body can be estimated
from the maxlmLun theoretical
negative
pressure
coefficient
(fig. 15
and reference
_) by using
some method
of estimating
the effect
of
compressibility
on the pressure
coefficient
(fig.
16).
The maximum
negative
pressure
coefficient
may also be obtained
from the following
empirical
equation
(within
_2 percent
for design
llft coefficients
from 0 to 1 and thlckness-chord
ratios
from 6 to 21 percent
chord):
--Pomax
=
o
c _i
o
+oo
) c
In order
to evaluate
the applicability
of the theoretical
critical
Mach numbers,
the theoretical
values
obtained
from figures
15 and 16
were compared
in figure
17(a) with the critical
Mach number
estimated
from total--pressure
measurements
near the surface
of the airfoils.
A
further
comparison
was made in figure
17(b) between
theoretical
critical
Mach numbers
(obtained
from the methods
of reference
h and fig. 16) and
the critical
measurements.
Mach numbers
determined
The experimental
lift
from pressure-distribution
coefficients
were extrapolated
from
M = 0.3
to
M = 0
by Glauert's
relation
given in reference
7.
The comparisons
presented
illustrated
that for NACA 16-series
airfoils
the critical
Mach numbers
obtained
from the several
specified
sources
were
in reasonably
good agreement.
The effects
of thickness-chord
ratio
(fig. l_c))
and design
llft
coefficient
(fig. l_d))
on the variations
in critical
Mach number
with
the low-_peed
(incompressible)
lift coefficient
were similar
to
and independent
of each other.
Increases
in either
variable
increased
the angle-of-attack
or lift-coefficient
range of ktgh critical
Mach
numbers
but were accompanied
by a reduction
in the maxlmAm
value of
the critical
Mach number.
NACATN No. !546
ii
Investigations in three-dim_nslonal flows have shown a del_y in the
onset of the adverse effects from those predicted by two-dimensional
tests or by section critical
Machnumbers. The results of one threedimensional investigation are presented in figure 18. Pressuredistribution
measurementswere madein the Langley 24-inch hlgh-speed
tunnel on an untwisted propeller blade having NACA16-series airfoil
sections.
The untwisted propeller blade could also be considered to
represent a semispan of an untwisted tapered wing having an aspect
ratio of 6.7. The results, su_nm_rizedin flgtu_e 18 for an angle of
attack of 0°, showed that the critical
Mach number for the outer
stations was delayed _pproximately 0.05 beyond the value estimated
from two-dlmensional data. A delay of approximately 0.04 was obtained
as far inboard as the 50-percent-semispan station.
A more extensive
investigation of the variation of the relieving effects with aspect
ratio (unpublished) is in general agreement with this result.
Supercrltical
AirpL_ue high speeds are now in a range for which propellers
would be forced to operate at supercritical
speeds. The critical
Mach
number of an airfoil
section is not an adequate index of section performance at supercritlcal
speeds, and since no usable criterions are
yet available to design optimum sections for supercrit!cal
operation,
the supercritical-speed
performance of available airfoil
sections must
be investigated experimentally.
The data presented in figure 3 for
airfoils
of various thickness-chord ratios and cambers offer a good
opportunity for studying the supercritlcal
characteristics
of
NACA16-series airfoils.
The adverse effects of compressibility,
which occur on airfoil
characteristics
at constant angles of attack
as the Mach number is increased above the critical,
are evidenced by
a steep increase in drag, sudden decrease in lift,
and abrupt ch._n_e
in pitching moment(fig. 3). These conditions have previously been
referred to as shock stalling or compressibility
stalling and more
recently have been called force breaks. For this discussion, the lift
break is defined as the point at which the rate of change of llft
coefficient wlth Machnumber is 0 or slightly negativ%whereas the
drag rise is determined as the point at which the rate of change of
drag coefficient with Machnumber is O.1; both conditions are
determined for constant angles of attack.
The drag rise as defined
is admittedly quite arbitrary because early increases in drag
resulting from effects of compressibility on the boundary layer are
neglected. The effect is such that in somecases, particularly
at
moderately h_gh _ugles of attack, the total increase in drag is large
before a rate of change of drag coefficient with Machnumber of 0.1
is attained (for example, see fig. _(d) at _ = 7.77o); any other
definition
of the drag rise, however, would be equally _bltrary.
In order to provide a comparison between the conditions at the
critical
speed and at the Machnumber of the lift
break, figure 19
12
NACATN No. 1546
has been prepared. It can be seen that at llft
coefficients near the
design condition, the Machnumber for lift break Is only slightly
greater than the critical
Machnumber; with increasing lift
coefficient, however, the lift--break Mach number exceeded the critical Mach
number
by
an
increasing
and drag rise for
fig. 20) decrease
for thickness-chord
increment.
The
Mach
numbers
of
llft
break
the various
NACA 16-series
airfoils
(presented
in
with increase
in thickness
from approximately
0.8
ratios
of 6 percent
to 0.7 for thlckness-chord
ratios
of 15 percent.
For applications
in which
numbers
will be encountered,
the thlckness-chord
confined
to the lower values
(that is, 9 percent
very high Mach
ratios
should
be
and less)
to assure
high
force--break
Mach numbers.
In addition
to the effect
of thickness,
figure
20 also shows that an increase
in camber
of the thinner
airfoil
sections
generally
decreases
the force-break
Mach numbers.
A more
significant
effect
of camber,
however,
is the fact that for moderate
llft coefficients,
the maxi_m_m force-break
Mach number
is obtained
with an airfoil
having
a design
camber
that is less than the value
corresponding
to the operating
lift coefficient.
The trend toward
decrease
in the optimum
camber
was expected
at speeds
near the lift
break
for these airfoils,
since other data (reference
8) have indicated
that the aerodynamic
characteristics
of cambered
sections
are
generally
inferior
to those of symmetrical
sections
at very high
supercritlcal
Mach numbers.
A related
inferiority
of the cambered
airfoils
is their change
in the angle of zero llft that occurs
at
high Mach numbers.
The change
is a function
of the airfoil
camber
or design
lift coefficient.
As a result,
the adverse
changes
angle
of attack
required
to maintain
a fixed llft coefficient
as the design
camber
was reduced.
Figure
19
the llft-break
as much as 0.3
in
decreased
shows
that the maximum
llft-drag
ratios
obtainable
at
conditions
generally
occur at section
lift coefficients
greater
than the design
llft coefficient.
In order
to
obtain
high values
of lift-drag
ratio at the highest
possible
Mach
number,
it therefore
appears
that airfoils
cambered
for llft coefficlents
less than the desired
operating
lift coefficient
(thus having
a higher
lift--break
Mach number)
would be preferable.
For the thinner
airfoils
in figures
i0
and
ll,the
higher
are shown
to
highest
Mach
be advantageous
at Mach
numbers
presented
(that
the
having
airfoils
only
slight
the highest
efficiencies.
shown
to maintain
the best
coefficient
range
higher
the
indicate
optimum
than
that,
design
lift
numbers
less
is, near the
camber
--(c_i
_
These airfoils
of
efficiency
over a
(c Z = 0 to 0.5)
design
cambered
which
coefficient.
airfoils
than
lift
0.i)_
c zi
0.7.
At the
break),
however,
are
shown
to
have
slight
camber
are also
large operating
lift--
extends
to values
Figures
i0
at higher
Mach numbers
than those
llft coefficient
may be less than
and
presented,
0.i.
much
ii also
the
NACATN No. 1546
13
CONCLUDING
R]_4AEKS
The results of the investigation of 24 NACA16-series airfoils
related in camberand thickness over a Machnumber range from 0.3 to
approximately 0.8 indicate the following conclusions, the validity of
which is not affected by neglecting tunnel-wall effects:
I. For camberedHACA16-series airfoils
at low Machnumbers M
and at an angle of attack of 0°, the ratio of the lift
coefficient
produced cz to the design llft
coefficient
czi was generally less
than unity and varied with airfoil thickness-chord
ratio
t/c
as
follows
(all
values
measured
in percent):
-cz i
= i00
-
2. The theoretical
method
of estimating
the critical
Mach number
provided
values
which were
in reasonably
good agreement
with
experiment.
In the lift-coefficient
range
for high critical
Mach
numbers,
the Mach number
for lift break was only slightly
greater
than the critical
Mach number.
With
increasin_
lift coefficients,
however,
the lift-break
Mach number
exceeded
the critical
Mach number
by an increasing
increment.
3. The design
camber
resulting
in best lift-_rag
r_t_o
for a
given
lift coefficient
decreased
abruptly
as the force-break
Mach
number
was approached
and exceeded.
For example,
the 6-percent-thick
airfoil
when cambered
for a design
llft coefficient
of 0.1 produoed
the best llft-drag
ratios
at a Mach number
of 0.80 and at all operating
lift
coefficients
for
which
a
comparison
fixed
4. The adverse
changes
in angle of
lift coefficient
decreased
as the
was
possible
attack
design
Langley
Aeronautical
Laboratory
National
Advisory
Com_/ttee
for Aeronautics
Langley
Field,
Va., December
19, 19_7
(c z = 0
to 0.5).
required
to maintain
camber
was reduced.
a
14
NACA_ No. 1546
REFERENCES
i.
Stack, John: Tests of Airfoils
Designed to Delay the Compressibility
Burble. NACARep. No. 763, 1943.
2. Stack, John, Lindsey, W. F., and Littell,
Robert E.: The
Compressibility Burble and the Effect of Compressibility on
Pressures and Forces Acting on an Airfoil.
NACARep. No. 646s
1938.
3. Stack, John: The N.A.C.A. High-Speed Wind Tunnel and Testa of Six
Propeller Sections. NACARep. No. 463, 1933.
4. Abbott, Ira H., yon Doenhoff, Albert E., and Stivers, Louis S., Jr.:
Summaryof Airfoil
Data. NACAACRNo. L5C05, 1945.
5. Allen, H. Julian, and Vincentl, Walter G. : The Wall Interference
in a Two-Dimsnsional-Flow Wind Tunnel with Consideration
of the
Effect
l
6.
yon
of
Compressibility.
NACA
Rep.
No.
782,
Karman,
Th. : Compressibility
Effects
Aero. Sci.,
vol. 8, no. 9, July 19hl,
in Aerodynamics.
pp. 337-356.
7. Glauert,
H.:
The Effect
of Compressibility
on
Aerofoil.
R. & M. No. 1135, British
A.R.C.,
Proc. Roy. Soc. (London),
ser. A, vol. llS,
1928, pp. 113--119.)
8.
19h4.
/
Ferrl,
Antonio:
Completed
Tabulation
Tests
of 24 Airfoils
at Hlgh Mach
Interrupted
High-Speed
Work at Guidonla,
Tunnel.)
NACA ACR
in the
Numbers.
Italy,
in
No. LSE21,
Jour.
the Lift of an
1927.
(Also,
no. 779, March
l,
United
States
of
(Derived
from
the 1.3119h9.
by
1.7h-_oot
NACA TN N0. 1546
15
,a
15 o.d
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16
NACA TN No. 1546
TABLE II
THICKNESS
DIS_IBUTION
AND _-LIRE
I%L_CA16-8_IES
EAII values
CKARACTERISTICS
FOR
AIRF01I_
in percent
chord]
Mean--line characteristics
Station
for
NACA 16-O09
c _I = 1.0 b
ordinate a
Ordinate
0
0
0
.6
1.25
.676
.969
2.5
5
7.5
i0
15
2.593
3 .i01
2O
3.498
25
30
40
50
60
7O
8O
9O
95
3.81Z
4 .O63
4.391
aValues
5.3%
3 .z_9
1.888
1.061
.090
Slope of L.E. radius
measured
hFor other design
characteristics
O
-.03227
-.06743
-. ii032
-.z7486
-.23432
-.62",'34
x 9)2
through
end of chord
from and perpendicular
other thl_knesses
.34771
.29195
.23432
.19993
.17486
.13804
.11O32
.08743
.06743
.03227
5.516
5.356
4.86z
3.982
2.587
Z .58O
0
3.952
= 0.3966(_
.40665
.93o
1.580
2.12o
2.587
3.36_
3.982
.479
.861
.5oo
4.3_
L.E. radius
0.6223_
.295
.535
1.35_
1.882
2.27%
i00
Slope
multiply
NACA
llft coefficients
by desired
value
= 0.4212c_i
to mean line;
16-009
ordinates
multiply
of
c zi.
mean--line
_SA/_
for
NACATN No. 1546
17
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0.30.
..,...-
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cd.
18
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