Completed tabulation in the United States of tests of 24 airfoils at high Mach numbers

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June 1945 as
Advance Confidential Report L5E21


COMPLETE TABULATION IN TE UNITED STATES

OF TESTS OF 24 AIRFOILS AT HIGH MACH NUMBERS

(Derived from Interrupted Work at Guidonia, Italy

in the 1.31- by 1.74-Foot High-Speed Tunnel)

By Antonio Ferri


Langley Memorial Aeronautical Laboratory
Langley Fielc, Va.


WASHINGTON


'ACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of
advance research results to an authorized group requiring them for the war effort. They were pre-
viously held under a security status but are now unclassified. Some of these reports were not tech-
nically edited. All. have been reproduced without change In order to expedite general distribution.


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DOCUMENTS DEPARTMENT


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AACR No. L5E21





NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS
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WARllTIME REPORT

ORIGINALLY ISSUED


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NACA ACR No. L5E21

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS


ADVANCE COM'-,.TDEUTI AL REPORT

COMPLETED TABULATION IN THE UNITED STATES

OF TESTS OF 24 AIRFOILS AT HIGH MACH NUMBERS

(Derived from Interrupted Work at Guidonia, Italy

in the 1.51- by 1.7L-Foot High-Speed Tunnel)

By Antonio Ferri


SUMMARY

Two-dimensional data for 24 airfoil sections tested
in the 1.51- by 1.74-foot high-speed tunnel at Guidonia,
Italy, are presented. The test Mach numbers ranged
from 0.40 to 0.94 and the test Reynolds numbers from 530,000
to 420,000. The results indicate that thickness ratio is
the dominating shape parameter at very high Mach numbers
and that important aerodynamic advantages are to be gained
by using the thinnest possible sections.

The results of preliminary tests made to investigate
the effects of jet boundaries, Reynolds number, and
humidity at very high speeds are also presented. It was
found that the jet-boundary effects became very large at
high Mach numbers when models large with respect to the
tunnel height were used. In the absence of suitable
correction factors for large models it was considered
essential to use models small enough to make the jet-
boundary effects negligible. It was indicated that the
data presented for the 2L airfoils tested are essentially
free from jet-boundary and humidity effects.


INTRODUCTION


The rapid increase in airplane speeds during
the past 5 years has greatly accentuated the need for
experimental data in the subsonic Mach number range
above 0.7. Experimental aerodynamic data in this speed
range, however, are still very scarce. There are two
principal reasons for the lack of data. First, the
experimental equipment required to obtain data at high







NACA ACR No. L5E21


sr-es on models of significant size is extremely costly
'., ojnctruct and operate. Second, the problems of tech-
nique involved in obtaining data at these speeds are very
complex and are not yet fully understood. The tunnel-
wall-effect phenomena occurring at very high Mach numbers
with the presence of shock waves become so complex that
there see:ns little hope at present of obtaining correc-
tions for these effects by analytical methods.

The principal purpose of this report is to present
aerodynamic data for 19 related airfoils and for 5
miscellaneous airfoils at Mach numbers in the range 0.40
to 0.9L. The data were obtained on models of 1.575-inch
and 1.565-inch chord in the 1.51- by 1.74-foot high-speed
tunnel at Guidonia, Italy. Before the presentation of
the test results, a description is given of the equipment
used and the findings of preliminary tests made in an
attempt to develop a suitable testing technique and to
determine the isolated effects of such experimental varia-
bles as Reynolds number, ratio of the size of the model
to the size of the tunnel, and humidity.

The results presented herein represent the completed
part of a broad high-speed research program at Guidonia,
which was interrupted by the war.


I. EFFECTS OF REYNOLDS INURPBER, JET BOUNDARIES, AND

HUMIDITY IN TESTS OF AIRFOILS AT HIGH SPEEDS


A systematic study of the effects of Reynolds number,
air-stream boundaries, and humidity at high speeds was
made prior to the main part of the present investigation.
It is not certain, of course, that these are the only
factors affecting the results, but they are considered
the most important.


WIND TUNNEL


All the tests were made in the high-speed tunnel at
Guidonia (reference 1), a single-return tunnel that could
function at a pressure below atmospheric. The pressure
in the test section of the tunnel could be varied
from 1.0 atmosphere to 0.1 atmosphere. The tunnel had a


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NACA ACR No. L5E21


system of refrigeration by which the temperature at low
speeds could be held constant at as low a value as
150 Centigrade. The temperature of the air as it left
the compressor was very variable, depending on the
velocity and the pressure of the jet.

The tunnel was Dowered by a 3000-horsepower fourteen-
stage axial-flow compressor, which could produce a
velocity ranging from 0.4 to 2.9 times the speed of sound
when one minimum retangular section of the jet 1.31 by
1.74 feet in size was used. In tests at subsonic speeds
the test section of the jet was kept constant at these
dimensions.

The jet was enclosed between two straight, parallel
side walls, which were perpendicular to the axis of the
model. The jet was not restrained by top and bottom
walls. (See fig. 1.) The effuser A-A was shaped in
such a way as to give a uniform flow at the plane a-a.
This uniform flow was attained in a series of preliminary
tests by increasing the length of the parallel-sided
effuser until satisfactory flow distribution was obtained.
The diffuser 3--L ," placed in a position to give uniform
flow arnd to e '..i--.i e the vibrations that tended to occur.
With the d'iffu3.- -'pe and location finally determined,
the veloc::ty W.aSs constant along the plane b-b in the
test' se,:;-L:.n of the tunnel even at the highest speeds.
By varying the position and the dimensions of the diffuser
a stable .end uificrm flow could be obtained even in the
Mach nin.itEr rd I.& approaching and exceeding the speed of
sound (I'.ach n... t-:-s of 0.9 to 1.2). The present test
program incluo 3.d lie.itsusreients made at Mach numbers up
to 0.94. Informr'- _'on on the shape and location of the
diffuser has been lost; therefore, the exact dimensions
of this setup are not available.

The velocity and the TMach number were determined
from a tunnel calibration basid on measurements of the
total pressure in the larce section of the tunnel ahead
of the entrance cone sn.d .n 'r.-rs..c-emtLents of the static
pressure at the wali neor tL ..-it of the entrance cone.
In order to check the e''.c-rity ensureded in this manner,
pitot-static cubes vfere ii?,t.i.lled at the top and bottom
of the jet just downrt-~enz of the exit of the entrance
cone. These tube.? -. q,:-lli-tative indication of the
jet-bcun-dary interf- .:wre L.'t "s. s hen the velocities
measured by these tubes WLtr appreciably different from
the velocity indicated by the entrance-cone pressure


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calibration, it was usually fund that the interference
effects were so large that they appreciably altered the
aerodyrna.Tic characteristics of the test models. No .ata
were taken when this condition existed.


EFFECT OF REYNGOLDS NTJIBER AND AIR-STREM BOUNDkARIES


Experimental methods.- In the study of Reynolds
number effects at high speed, preliminary tests were
made first on cylinders and spheres of various dimensions
(reference 2). An analogous series of preliminary tests
was then made for airfoils. l:,odels of airfoils of con-
stant profile bit of varying chord were tested.

For the study of the effect of the air-stream
boundaries, tests were made with varying ratio of model
chord to tunnel height over a range of Miach numbers.
The ratios used were: 0.0755, 0.09~2, 0.115, and 0.151.
The Reynolds number at each M1ach number was held approxi-
mately constant by varying the density.

Test models.- A profile was chosen having an arc
for the upper surface and a straight line for the lower
surface because this profile could be exactly reproduced
in various sizes. The rnoer surface could be made by
use of a lathe and the lower surface could be formed by
use of a shaper. The leading edge and the trailing edge
were sharp. The maximum thickness chosen was 8 percent,
Lnd the profile was designated C-8 (fig. 2). Four models
were constructed with such a profile; three with chords
of 1.575, 1.969, and 2.362 inches (L, 5, and 6 cm) for
force tests and one with a chord of 3.15 inches (8 cm)
for detenrining the pressure distribution along the pro-
file.

Tests and results.- At Mach numbers of 0.4, 0.5,
0.6, 0.7, 0.F, and 0.9, the lift coefficient, the drag
coefficient, and the pitching-moment coefficient about
the quarter-chord point of the airfoil were determined
for the three profiles having chords of 1.575, 1.969,
and 2.562 inches. All the models were tested at two
Reynolds numbers: approximately 250,000 and 840,000.
The model with the 1.575-inch chord was also tested at a
Reynolds number of 150,000. For the profile having a
chord of 3.15 inches, pressure readings were made at
angles of attack between -5.5 and 5..50 for Mach numbers


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NACA ACR No. L5E21


of approximately 0.7, 0.8, and 0.9. Values of lift and
of pitching moment were obtained from the pressure distri-
butions. Force-test results are shown in figures 3 to S.
In figures 9 to 11 the results of pressure measurements
are presented. Figure 12 shows the results obtained from
integration of the pressure diagrams compared with the
results obtained by use of the balance.

Reynolds number effects.- The results of the pre-
liminary tests of cylinders and spheres showed that for
the range of Reynolds numbers covered in the tests the
effect of Reynolds number decreased as the velocity
increased. At Mach numbers close to 1.0 there was vir-
tually no Reynolds number effect. In the airfoil tests
the importance of Reynolds number was considerable at
low Mach numbers and the effect of Reynolds number was
noted up to the critical Mach numbers at which the phe-
nomenon of shock began to appear (figs. 5 to 6). For
supercritical Mach numbers, the effect of Reynolds number
became less until it virtually disappeared for Mach num-
bers very near 1.0. In this range the formation of shock
waves seems to control the aerodynamic phenomena and the
development of the boundary layer. The boundary-layer
thickness probably depends to a large extent on the angle
of deviation of the air as it passes through the shock
wave. The friction drag is a reduced nart of the total
drag and, therefore, the Reynolds number effect is small.
The Reynolds number, however, could have an effect on
the characteristics of the shock wave itself through its
action on the boundary layer, but such an effect is not
indicated. In general, these airfoil test results con-
firmed the results of the sphere tests. Large-scale
tunnel tests made at the Deutsche Versuchsanstalt fur
Luftfahrt (the DVL) in Germany and flight tests made at
various times showed similar results.

Effect of air-stream boundaries.- The jet-boundary
effects for the ratios of chord to jet height of 0.0755
to 0.115 covered in these tests appear to be negligible.
Essentially equivalent results were obtained at a given
Reynolds number for all values of the ratios employed
in the tests. For a larger jet-boundary effect, a test
was made of the model with a chord of 3.15 inches for
which the ratio of the chord of the model to the height
of the air stream (0.151) is twice that normally used in
the tests. From the results of integration (fig. 12)
the values obtained for CL and Cmc/A are seen to


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NACA ACR C No. L5E21


coincide at high Mach numbers with the values found by
the force tests. This agreement indicates that the
boundaries of the air stream probably aid not interfere
appreciably with the distribution of the pressures. For
a I'ch number of 0.9' the effect of the air-stream
boundaries is important for the model of 3.15-inch chord
but is not important for the models of 1.575- and
1.969-inch chord. For higher Mach numbers the boundaries
also affected the results obtained with the two smaller
models.

It is interesting to note that the phenomenon of
choking of the air strewn, which occurs in closed-throat
wind tunnels at high speeds (reference 5). did not occur
in the tunnel in which the present tests were made. For
example, for model C-6, which had a chord of 3.15 inches,
it is estimated that choking in a closed-throat tunnel
would occur at a Mach number of 0.88 or lower. The
choking Mach number for the 2.552-inch-chord model is
estimated to be 0.90 or lower. These choking Moach num-
bers were calculated from one-dimensional theory for the
zero-lift condition. They are therefore somewhat higher
than the choking Ma-ch numbers that would actually be
obtained, especially for angles of attack other than that
for zero lift. In the present tests it was possible to
obtain data for these models at Mach numbers as high
as 0.94, and the results of the jet-boundary-effect tests
indicate that the data are essentially free from tunnel-
wall effects at this Mach number.


EFFECT OF HUMIDITY ArD CONDEIISATION


The air becomes very cold in the expansion that
occurs in the tunnel at high speeds. (The process is
very nearly aciaoatic.) Total condensation may occur in
the whole jet at high seeds if the dew point is passed.
Even if condensation does not occur in the jet, there is
a possibility of its occurring in the low pressure
regions over the test model where an additional expansion
and temperature drop occur. Very low local temperatures,
which are usually smaller than the local dew point, are
found at high subsonic speeds; local condensation there-
fore could occur and could produce a "condensation shock"
or a localized region in which condensation occurs.


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NACA ACR No. L5E21


Condensation complicates and modifies the flow over
the body because it alters the values of the temperature,
the pressure, and the speed in the air stream and, hence,
modifies the values of the resultant aerodynamic forces.
A complete examination of the effects of the phenomenon
of condensation shock is very complicated. The variables
involved include the value of the local humidity, the
speed of the condensation, the possibility of the exist-
ence of supersaturated air, and the scale of the model.

The condensation process is not instantaneous but
requires a finite time and its beginning may depend on
such factors as the nuclei of condensation. (The super-
saturated air may sometimes exist for a time at a tem-
Derature much lower than the critical.) If the tests are
made at small scale, the air can pass through the low
temperature region in so short a time that appreciable
condensation does not occur. Condensation is therefore
less likely to occur in small-scale tests than in large-
scale tests. In flight, for example, when appreciable
relative humidity is present, condensation normally
occurs and is easily seen on propellers and wings in
high-speed dives. Since the characteristics of the con-
densation vary with scale, it would appear to be practi-
cally impossible to simulate full-scale conditions in
tests in which small models are employed. The problem is
further complicated because the degrees of supersaturation
existing in the tests in a wind tunnel may be different
from in flight and the beginning of the condensation
depends on certain variable conditions of the air. The
condensation characteristics of different wind tunnels,
even with the same setuo, have in several instances been
noted to be widely different. In the subsonic tunnel of
the Aerodynamische Versuchsanstalt (the AVA) at Gottingen,
for example, it is normally necessary to dry the air
before it converges in the test section to prevent con-
densation; however, in the Langley 24-inch high-spted
tunnel, which has a comparable entrance-cone shape and
which operates under similar conditions, it is not nec-
essary to dry the air, and complete condensation seldom
occurs for relative humidities below 60 percent.

All the test data obtained up to the present time
tend to indicate that even for large-scale models the
effects of humidity are of secondary importance provided
that the percentage of humidity is low. In the Guidonia
high-speed tunnel previously described, it was very dif-
ficult to study humidity effects because of an automatic


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8 CONFTDENTTAL IThCA ACR No. L5E21


drying up of the air which took place. A small quantity
of water '.as removed from the tunnel air by the pump which
was used to evacuate the tunnel to the low initial ores-
sure. The condensation that occurred when the tunnel was
started was believed to cause water to collect behind the
test section and to adhere to the tunnel walls. As a
result of this automatic water removal, fog did not occur
in lhe test section even at supersonic velocities and no
air-crying equipment was necessary. Because the humidity
be'rame less during the progress of a test in this tunnel,
it was impossible to give precise results as to the effect
of humidity, but the general indication of the data that
have been obtained was that Ehe humidity effects were not
appreciable, at least not for the small-scale models
tested.

Tests to study the effects of humidity have been
conducted in the 8.?6-fjot high-speed tunnel of the DVL
in Gernany using an N.CA 0015-64 airfoil section with
a 1.64-foot chord. In this wind tunnel the amount of
condensation existing in the test section can be con-
trolled by varying the cooling of the tunnel and thus
regulating the temperature of the air in the test section.
For very high values of relative humidity, it is necessary
to eliminate the cooling entirely in order to raise the
temperature enough to avoid condensation. The results of
the humidity-effect investigation in the DVL tunnel dem-
onstrated that, even for the relatively large-scale model
employed, the humidity effects were of secondary impor-
tance when the relative humidity was small.

In order to indicate the conditions under which con-
densation might occur in flight, figure 13 is presented
showing the local Mach number as a function of the flight
Mach number for which the conditions required for satura-
tion are reached. (hdiabatic expansion of the air from
its static condition to the conditions corresponding to
local Mach number is assumed.) Also shown in figure 13
are the values of maximum local Mach number that are
attained locally on two typical airfoils. The data cal-
culated for the NACA 25015 airfoil (unpublished) were
obtained from tests made in the Langley 2L-inch high-
speed tunnel. The data for uhe NACA 0015-64 airfoil were
obtained from the DVL tests mentioned previously. Fig-
ure 15 indicates that, even for very low values of the
relative humidity, local ,ach numbers are obtained at
which condensation is possible when the flight Mach num-
ber is 0.6 or greater.


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NACA ACR No. L5E21


The discussion in the preceding paragraphs has shown
that humidity effects are likely to be most pronounced
under large-scale conditions. Systematic tests to deter-
mine humidity effects could best be made in a large-scale
wind tunnel in which the temperature of the circulating
air could be varied by regulating the cooling. The tests
in such a wind tunnel could be made at various periods in
order to cover a wide range of relative humidities. Fig-
ure 14 has been prepared to indicate the conditions for
saturation in the test section of a wind tunnel for three
values of relative humidity and for various temperatures
of the air in the entrance cone of the wind tunnel where
the airspeed is low. Also shown in figure 14 is a com-
parison of the maximum local Mach numbers of the NACA 23015
and 0015-64 airfoils as functions of the stream Mach num-
ber to determine at wnat Mach number the conditions for
saturation are locally reached. The figure shows that,
for high relative humidity, it is necessary to have a
high temperature of the tunnel air stream in order to
eliminate condensation in the test section. It is also
shown that, even if condensation is eliminated in the
test section, the necessary conditions for the formation
of local condensation over the test model will normally
be attained.


COMPARISON OF TEST RESULTS FROM VARIOUS*

'IND TUNNELS AND FROM FLIGHT


Airfoil tests.- For a thorough examination of the
accuracy .nd significance of the test results obtained
in a given wind tunnel, it is essential that the results
be compared with those obtained in other wind tunnels
and in free flight on models of similar orofile. As a
step in this direction, tests were conducted on the
NACA 0015-64 airfoil in both the Guidonia 1.51- by
1.74-foot rectangular high-speed tunnel and in the
DVL 8.86-foot-diameter high-speed tunnel, which has
closed circular walls. The model used had a rectangular
plan form enclosed between two end plates. The chord of
the model was 1.658 feet (50 cm), the span was L.5 feet,
and the end plates were 25.6 by 43.2 inches. The ratio
of the model chord to the tunnel diameter was 0.185.
With this setup, the choking Mach number was about 0.86,
which is considerably higher than the choking Mach number
that would have been obtained with the model completely


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NACA ACR No. L5E21


spanning the tunnel jet. The data obtained in these
tests consisted of pressure distributions and wake sur-
ve ys.

The test conditions were adjusted to produce an
equivalent relative humidity of the air of 20 percent at
sea level. The Reynolds number varied with the Mach num-
ber from about 5,800,000 to 6, .00,000 in the high-speed
range of the tests.

The model tested at Guidonia had the same profile
but was of much smaller scale, the model chord being
1.575 inches (4 cm) and the ratio of model chord to tun-
nel depth being 0.0755. The relative humidity in the
Guidonia tests was always very low. The Reynolds num-
bers were, of course, very much lbwer than those of. the
DVL tests and varied around a value of about 500,000.
Force measurements of lift, drag, and moment were made
in the Guidonia tests; pressure-distribi.tion and wake-
drag measurements were made in the DVL tests. The
results obtained are compared in figures 15 to 17.
Figure 18 shows pressure-distribution measurements made
at the DVL for one angle of attack, a = -0.250. It may
be noted that the results from the tvo tunnels are at
variance, especially at high speeds. This lack of agree-
n,-nt indicates that the testing technique and the pro-
portions of the testing system are of great importance
in high-speed wind-tunnel work.

The differences in the drag-coefficient values at
low Mach numbers are probably due to the difference in
Reynolds numbers. The largest differences between the
results from the two tunnels ure in the crag and pitching-
moment coefficients at high f.ach numbers. The abrupt
changes in the coefficients from the DVL tests at Mach
numbers in the vicinity of 0.8 arc probably associated
with the phenomenon of choking, and the results obtained
in this range are therefore considered extremely ques-
tionable. Because of the much smaller relative size of
the model in the Guidonia tests and also because of the
fact that the jet was not restrained by top and bottom
walls, similar effects did not 3ccur. Further tests were
made at the DVL tunnel of a smaller model of the same
profile having a chord of 1.148 feet, the model-chord to
tunnel-dianeter ratio being 0.15. The results obtained
with the smaller model are shown in figure 16. It will
be noted that the rate of drag rise past the critical
speed is appreciably less than with the larger model and


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NACA ACR ITo. L5E21


thus is in better agreement with the results of the
Guidonia tests.

Free-flight tesus were in the general research pro-
gram at Guidonia, but they were interrupted by the w-vr.
The few flight tests made, however, indicated that the
drag-coefficient curves had about the same slpe's at
supercritical speeds as wsre obtained in the Guidonia
wind-tunnel tests.

Bomb tests.- additional comparisons between high-
speed winTd-5unnel and flight data were obtained in tests
of an airplane bomb of conventional shap_. The approxi-
mate shape of the bo.mb is indicated in figures 1i and 20,
v,hicli show the results of the tests. The bomb .'as
launched in flight at an altitude of 59.5.00 feet, and
its trajectory as a function of ti'me w-;s recorded v.ith a
phototheodolite. The sceed, the [Ki.ch tLnum/er, the accel-
eration, and the drag. coefficient :were obtained from the
trajectory data. A one-third scale rmodel ft this bomb
was tested in the PVL C .6-foot-d.iLmeter high-speed tun-
nel (the ratio of bomb diameter to tunnel diameter
was 0.01'55, much lower than that normally; used). A one-
tenth scale model cf the sane bomb was tested in the
3Giidonia 1.31- by 1.74-foot rCectangular high-speed tun-
nel using a ratio of model diameter to air-streamn height
of abbut 0.071L. Sii;ilar tests were .mcie in a .jiid tun-
nel at the AV,\~ in Coctir.gen, which has a partly free air
stream similar to that at SuiLonia but 47 inches high.
The size of the model used in these tests is int known,
but it is believed that the ratio of model diameter to
tunnel air-stre- i height was considerably higher than
that used in the tests in the other wind tun..Iels. The
results shown in figI Lr 19 indicate reasonably ,Dod
agreement in the frnn of the drag curves obtained. As
might be expected. how.Jever, the drag-coefficiert valLes
obtained at very high i:ach numbers in the closed DVL tun-
nel are higher than those found at Guio-nia in the
relatively unrestricted jet. The results obtained in a
subsequent launching Df the bomb, with reinforcements to
the tail structure, in flight: tests at the DVL are shovn
in figure 20.


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NCCA aCR No. L5E21


CONCLUSIONS


The following conclusions were drawn from the investi-
gati-on of the effects of ieynolds number, air-stream
boundaries, and humidity in tests of airfoils at high
speeds:

1. It has been shown that the ratio of tunnel height
to model size, the form of the test section, and the
testing technique have a very great bearing on the
results obtained at subsonic Mach numbers above 0.7.

2. Reynolds number effects were of secondary -mpor-
tance at very high Mach numbers for the range investi-
gated.

3. In the absence of suitable correction factors,
the only safe experimental technique consists in keeping
the scale of the model small enough so tnat the correc-
tions required are negligible.

I. In a closed air stream, the model must be small
enough that the highest desired test M1acn number is below
the choking Mach number ?f the tunnel, at which the
effects of the tunnel walls on the flow over the model
become extremely large.

5. By use of a jet which is not restrained by top
an. bottom walls the maximum rMdch number that can be used
for a given value of the ratio of jet height to model
chord is appreciably higher than the value that can be
obtained in a closed jet.

6. The considerations of condensation phenomena that
have been discussed have brought out the fact that the
conditions under which condensation occurs depend on many
variables and that only with great difficulty could
flight conditions be simulated in wind-tunnel tests in
which small-scale models are used. Vyind-tunnel tests
should be conducted with low values of the relative
humidity, because under such conditions the effects of
condensation are known t) be negligibly small.


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TACA ACR No. L5E21


rT7. T r"7' .ErT ,''c IP. ?!L ATPFf .1IG ; T1 T T T'A'T-.

il"E'qP" 'AM~IF'F 03T 1 O1.0 0 c 1.


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Tr.enty-four profiles vwc-re tested' in th.e 1 .51 .y
1 .7!.-foo t hi 'ih-s peed tun.tel at ui.'._crna with the ,-rtly
free te"t sect ion rr-vious'ly ScrTibd. T-r ever-r r r C-
file the ift, the Crs. ,, nm. ch ,s ,tchic n- ,i"c:t 5t t the
uairter-c!,ord jcintc. re v .neasuAred bL,'c Le CI th tree-
como:r eni .sent- l l.Lic b al ni; 'escrl e in r. fer.en
Tn extre: -ities cf tie models wIere Et":.ed at t-e balance
suppoCrts 3!and tihe models "ere .: Lcl:ed durinr tihe tcsts to
verify that the aerod;*,nrmo: c lo r s .'.*:LC r. c bend thi.em
appreciably. AT tih tests ,e,.. r-e- pc r.td vi th t.e :no'.cel
inverted. Fr.r some models, the tests were rer, _,ted later
when the static atmospheric con.'i-ti.ns v..re c.cio-lEtely
different and '.:ith different hu.-iditli s in the test sec-
tion. (The values of tha -elat '.ve humidity v.ere sli'-.'vs
lo";.) The differences i: L-e rE.su'.lts o-ts r.ed '-Ere not
cppreciabl. .

All the models v.'ere mnde i.f -roll. -rl' Ced steel end
had chord:..3 cf 1 .75 inch.-.s for th -ic.: 'e.r "s tic~ c rcf r-
c- nt or .r,:-oter Tn order 'o r:'~'ert exc:s-s i v: ten'ii. ,
the rmoccls vi th t-ic-.:nCss rating of l'sE th-a3 per.nt
hvd chlords of I .ar.' In-ches

Tl-e 'crefil L-P of -nmall model, s.lori ,L rre.s rnd
exactly W, :ith the profile d.sir:ed. Fr u.-.-sc c. e.cu-
racv, ther -roi'cre an onpical device E'3 constu:td iNt": t
per'.nitttd photo,'ap;in,, v' t exLtrc.re "i cisi cr the true
sccti.or of ea.Sch mo.,del ( n 3 .re-a-' ., ncr aCscid sc'l- e L ;-'or
each model two end sections v'cre U. -Oap.ed and Th3
trie n;rofile v's projected on che :h' o tc.rjph to nrov'dc
the desired cno:-orison. B'cu.s -the ar -f.oil were con-
structed by riachine, -he .ronf"il.e s'-pe _did not v.ry a ;ross
the model soan. This fact ."as corfi -r-f d br su:permir:-;oosir.p
drwi'-.'ins of the t:'.o cr,: sections. It v es 'e-r filed that
the surLi'ace V.w s c.dequ".tcly cnc).t Ly r mL, v r.ir there t n-
gential illLuminated surface r'.nder .'reat ma.'nification.

Figure 21 shows tlje specifid .:hc.pes of the profiles
tested. In figure 22 the cattua.l shp.-E cf the proIiles
tested are compared with the specific. e.] shapes. In crder


CO 1.r'TDEINTIiL


*n 71 T 'rrAT







~ ACA CR ;:o. L5Z21


that the diffeo:enca between the actual aid thi specified
prt?1 les say be cleq4lz seen, the ordin.- te scale used in
ft -ure 2d ha3 been eiilar.:ed. Trvble T sh)ws the ordinates
of t-Phe orfiles tested.

1.11 the terts wcie o-erformed at an sa.roiximately
constant ReynDldcs nui:ber varying in the rare from 5LC,000
to a2C,032'. i'he density, and consequently the eynmolds
n'u7her, i-d to be kept low for the thinner airfuils in
nrder to oreve:-t excessive loadc.


.ATRFl'rL TESTED


The profiles listed in the fcllcvwing table vere
tested:


I -- -- -- 5 :'---



iiACA 0012-6L 2 .
IA A I 1OC-6L' 5 "N:

PT '

:'ACA 'o,5-6L 5 .I.
(L,. Cer:
-AA 00o3-gL 5 I '.s.
(c, per
:hcA C0012-. L U.S.I
10 pe

I' 6 lFer(
;IACA 0009-t.6 5 1; TO




Q 1 per
;ACA 2506 1 2A
,I (,' perc
t;- CA 2512 6 E I


rf -'" i


I "I-ference


A. 515 6




III
2L 1 67
::.F. 1 7


cent thick)
U. P.3 2
cent thick)

recent thick)
iCA Ml
cent thick)
:n C006T

A 2509


cent thick)
rTH69?


(a)


aDevelcoped at Zurich '.i-versity.


Fr T T :T7 : T~I


C:0C.) ID-I'ETIAL









NACA ACR ;o. L5E21


RESULTS


In figures 23 to 46 the results of the tests of the
2l. airfoils are shown in the form of the usual coefii-
cients: CL and CD are plotted against the test i,.scl
number at ths same angles of attack, and Cmc. /L is
plotted against the P.!ach number at r.slues cf CL -orre-
spanding to the given angles of attack. Figures lh7 to 70
show a, CD, and Cm-/. plotted against the corre-
sponding CL for ecch airfoil rt the- samr ;."Szh n,.Lmbers.
In figure 71 the anrle of zero lifL is pitted against
Mach number for representative i.irfoils of t-ie group.
Figure 72 gives th3 r.:eximum lift-irag ratio (L/D)mnax
a for (L/E)max, and CL for (L 'max as funztio.ns
of Mach niurber for all the airfcils tested. Figures 75
and 7 present CDmi. and (L/D)max as functions of the
maximum percentage thickness for all the airfoils at
various Mach numbers, and figures 75 and 76 show C.in
and (L/D)jmx plotted against .n.ach number for several
groups of airfoils havin- the same maximum thickness.

It can be observed from the test results that:

The lift-coefficient curve as a function of Mach
number presents a ma:-irrmun and later a minirmum value.
The Mach numbers at these values can be defined as the
first and the second critical iM.ach nur.bers f-r the lift.
The M:ach number at .which the drag-2oeffic'rent curve
abruptly bends upward is defined herein Gs the critIcal
Mach number for the drag. It will be noted that the
critical Mach numbers as defined herein ire different
for the lift and for the drag drt.. The critical ach
nu-mbers used, furthorrore, do not n-cessarily correspond
to the streak '.:sch number Et wviich local sonic velocity
is reached.

The rate of drag rise past the crnit'-cil '.':h nurbcr
increases as the lift coefficient, th; anr-le jf ottclk,
and the thickness ratio are increased.

The first critic-. :Mach n.u.ber for CL and the
critical Mach n-umber for CD for each airfoil is lowered
with the increase in angle of attack.


CONFIDENTIAL


CO:i-IDEi]TIAL









NACA ACR No. L5E2l


For each series of airfoils at the same angles of
attack, these critical Mach numbers decrease as the
thickness increases.

The critical Mach numbers at the same thinness and
the same angle of attack are much lower for the cambered
profiles than for the symmetrical profiles tested at the
same angle of attack. At equal thickness and equal
camber, the critical Mach numbers are higher where the
maximum thickness was at the LO-percent-chord station
than where it was at the 50-percent-chord station.

Above the critical Mach numbers, the drag increases
and the lift decreases very rapidly; for a profile with
a larger thickness and sharper curvature, the increase
in drag and the decrease in lift is sharper.

These general phenomena agree vjith results of other
laboratories. (See, for example, reference L.)

Lift.- At subsonic Mach numbers the increase in lift
coefficient with Mach number follows approximately the
theoretical relation 1 especially for the low

thickn-jess ratios. After the first critical Mach number
is reached, the lift coefficient decreases very rapidly
until it reaches a minimum at the second critical Mach
number when it again starts to increase. This second
critical Mach number is lowered with the decrease in the
first critical Mach number. Airfoils with larger camber
had greater decreases in lift. For these airfoils,
generally, the angle of attack fr zero lift changed
greatly and tended toward positive values (fig. 71). At
the hi* hest test Mach numbers all the wings functioned
in a manner very similar to symrr.etrical profiles. This
phenomenon agrees with the fact th&t the value of the
angle of zero lift for an unsy.rnrLrical profile changes
sign and becomes considerably reduced in magnitude in
passing from a subsonic to a supersonic velocity.

The lift-curve slope dCL/da increases up to the
first critical Mach number after which there is a con-
siderable decrease up tn the second critical Mach number.
(See figs. 57 to 70.) The second critical Mach number
is greatly affected by the value of the maximum per-
contage thickness. For the lover thicknesses tested,


CONFIDENTIAL


COF 0 TF DEFTI AL








NACA ACR V:o. L5E21


the second critical '.Mach number was reached only at the
maxinumr speed of th_ test.

'Morent.- The carve of pitching-.:noment coeffic-i.nt
against Alach number has a fairly regular form (figs. 35
to 46). Generally, the value of Cm/i remains constant
up to the first critical Mach nurrber and then tends to
decrease. For the larger thickness ratios there is Tn
increase in Crnci, at the first critical ; Pech number,
and it appears thet the center of pressure rm.oves forward.
Vihen the Mach number is increased beyond the critical
value, C,. decreases antil it re.cehes a n.ini:mu and
then tcnds to increase.

The center of pressure moves ap-reciably at low
values of Cy for profiles of large csrber. For sym-
metrical profiles the -artations of C c/1 t low values
of CL are small, especially if the maximum thickness
is about .40 percent of the chord.

Drsg and lift-draF ratio.- The value of (L/D)max
decreased rapidly beyond the first critical Mach number
for the lift and continued to decrease until the second
critical Mach number was reached. It then varied very
slo'wlyv with further increase in Msch nurrber (fiT 72).
The larger thicknesses suffer more pronounced relative
changes in (L/D)max. The ongle of attack and the lift
coefficient corresponding to the (L'D)ra. (fig. 72)
decrease as far as the second critical point and then
begin to increase rapidly. The variations are -aprecisbly
influenced b', the value of maxi'Tmum thickness, ratio asnd
by the mean camber.

.n order to empha-ize the importance of rraximum per-
centage thickness on the values of CD3n and (T./D),my,
figures 75 and 7 v.ere prepared to show the values of
these factors as f-nction of m].ximum rers;ntaseo t..i-2kness
at constant Mo.ch number f)r eech series considered. These
figures sn.o, that the? offe't cf the .ma.irmun percento..e
thickness beccmes greater Es the iTL:h nu-rber increases
for all profiles tested. For ?.nch numbers around 0.W,
the effects of thickness ratio are very larce. At lo'v
test speeds, for example, when the m3xirium thickness is


COtF I DEFTIAL


CONF0'I DEITIAL








NACA ACR No. L5E21


varied from 6 to 12 percent, CD increases about
30 percent; at Mach numbers around 0.8 or greater, the
increase becomes 200 to 00 percent. The r-tio
of the values of (L/D)nax for the ;ACA 0006-31 airfoil
to those for the NACA 0012-34 airfoil changes from
about 1.18 at a Mach number of 0.65 to 4.5 at a Mach
nur.ber of 0.85 and to 2.2 at a Mach number of 0.94. It
is also interesting to compare the aerodynamic character-
istics of various profiles at equal maximum percentage
thicknesses. (See figs. 75 and 76.)

The larger increments in C in occur for the pro-
files with larger camber, for which the critical Mach
number is lower. l.ith increase in the value of the maxi-
mum percentage thickness, the value of dCDin /dM
increases and even at very high Mach numbers this differ-
ence Oetween various profiles is considerable.

The profile shape has considerable effect on (L/D)max
(fig. 76); the unsymmetrical profiles have larger (L/D)max
values at low Mach numbers. ;:t nirher speeds, the symmet-
rical profiles with the maximum thickness at about 40 per-
cent of the chord had higher efficiencies than those with
the maximum thickness at 30 percent of the chord. The
difference between the various profile types is consid-
erable for low Mach numbers: however, it decreases with
increase in Mach number and is small for Mach numbers
around 0.94.


CO NC LUS TONS


The following conclusions may be drawn from the
results obtained from tests of 24 small-scale airfoils
in the Guid-nia high-speed tunnel:

1. At subsonic Mach numbers both the profile shape
and the thickness ratio had a large effect on the minimum
drag coefficient.

2. Reducing the thickness ratio, moving the point
of maximum thickness from 50 to 40 percent of the chord,
and reducing the camber all tended to increase the
critical Mach number.


COnlIDET TIAL


CONFIDENTIAL









NACA ACR No. L5E21


5. Airfoils of lsrge percentage thickness shcild n3t
be used at high I'ach nu.nbers because of the radical
adverse changes in their characteristics at supercritical
speeds.

1... "Then the critical speed was exceeded, the drug
coefficients increased rapidly. Abrupt decreases in lift
and changes in moment occurred at somewhat higher critical
Mach numbers.

c. The lift coefficient continued to decrease as the
speed was advanced beyond the first critical M3ach number
until a second critical .ch number vwas reached, bIeond
which the lift coefficient inorcessd in v.lue.

6. At very high s upercritical Yach n'iumrbers the
thickness rat o is the dr~inating variable, the drag
coefficient being almost directly proportional to the
thickness at a Tisch number of 0.9.4


rational Advisory Commnittee for Aeroneutiks
Langley Memorial Aeronautical Laboratory
Lanrgly Field, '.'s


C DNFIDE7TI AL


CO NFIDENTI A L







NACA ACR No. L5E21


REFERENCES

1. Ferri, Antonio: La galleria ultrasonora di Guidonia.
Atti di Guidonia No. 15, 1939. (Available in Air-
craft Engineering, vol.XII, no. 140, Oct. 1940,
pp 502-305.)
2. Ferri, Antonio: Influenza del numero di Reynolds ai
grand numeri di Mach. Atti di Guidonia
No. 67-68-69, 1942. (Available as R.T.P. Tr. No.1933,
British Ministry of Aircraft Production.)

3. Byrne, Robert W.: Experimental Constriction Effects
in High-Speed Wind Tunnels, NACA ACR No. L4L07a,
1914.
4. Ferri, Antonio: Investigations and Experiments in
the Guidonia Supersonic Wind Tunnel. NACA TM
No. 901, 1939.

5. Stack, John, and von Doenhoff, Albert E.: Tests of
16 Related Airfoils at High Speeds. NACA Rep.
No. 492, 1934.

6. Jacobs,Eastman N., Ward, Kenneth E., and Pinkerton,
Robert M.: The Characteristics of 78 Related Air-
foil Sections from Tests.in the Variable-Density
Wind Tunnel. NACA Rep. No. 460, 1933.

7. Jacobs, Eastman N., and Anderson, Raymond F.: Large-
Scale Aerodynamic Characteristics of Airfoils as
Tested in the Variable Density Wind Tunnel. NACA
Rep. No. 352, 1930.


CONFIDENTIAL


CONFIDENTIAL










NACA ACR No. L5E21


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NACA ACR No. L5E21


CONFIDENTIAL
Air fo// Reynolds number, R
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COMMITTEE FOR AERONAUTICS


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NACA ACR No. L5E21


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.4----- -

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NAIIOIAL ADYMISORY
OMM-ITTEE FOP AEROA utiK



74 CONFIDENTIAL
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Fi g. 4







NACA ACR No. L5E21


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NACA ACR No. L5E21


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Fig. 6







NACA ACR No. L5E21


,y9/e of" aC/aoc/, cc, dae


6-.-










I"- UNAL AI A'
-COMMITTE OR ARONAUTS
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Fig. 7







NACA ACR No. L5E21








--
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NATIONAL ADVISORY
COMMITTEE FOR AERONAuTICS




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Fig. 8a







NACA ACR No. L5E21


S6 .7 .8 .9 /0
tIc7 ane07ber1 A-1
Ie! rarv/ os -P/ties of //i/ coeff/ci/'en
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L5E21


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NACA ACR No. L5E21


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NACA ACR No. L5E21


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NATIONAL ADVISORY
I MMIFT FORI AERONAUTlCS
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NACA ACR No. L5E21


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NATIONAL ADVORY
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CONFIDENTIAL

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