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NATIONAL ADVISORY COMMITTEE FOP AERONAUTICS
TECHNICAL MEKIVANIUM 1240
AIRFOIL MEASUREMENTS IN THE DVL EIGH-SPEED
WIND TUNNEL (2.7-METER DIAMETER)*
By B. GOthert
The present report is a brief summary of the investigations on
symmetrical and cambered airfoils in the DVL high-speed wind tunnel.
In the light of measurements of wings of different aspect ratio with
equal profile it is shown that the effect of the aspect ratio on the
increase in lift with rising Mach number expected on the basis of
calculations is closely confirmed by the measurements. Several recent
experiments on a wing with the small aspect ratio of b2/F = 1.15 are
discussed, where the lift disclosed no disturbances within the test
range, that is, up to angles of attack of a = S and Mach numbers of
M = 0.9, and the drag (at ca = 0) starts to increase at a much
higher Mach number than for a wing with the same profile but greater
The airfoils tested lt the DVL high-speed tunnel are represented
in figure 1. The tests primarily involved a series of symmetrical
*J'Profilmessungen in DVL-Hochgeechwindigkeitswindkanal (2,7-meter
Durchmeeser)." Eilienthal-Gesellschaft fur Luftfahrtforschung,
Berioht 156, pp. 5-16.
'The notation for the profile used in figure 1, which is normal
practice in the IDL, is exemplified on the.NACA airfoil 1 30 12 1.1 40:
Depth of camber, percent . f/l 1
Distance of maximnn camber from the leading edge,
percent . . x = 30
Thickness ratio, percent . .. d = 12
osae radius, percent . . p/ 1.1
Backward position of maximum thickness from the nose,
percent . ....... ... xd/ = 40
The addedlettere NACA indicate that the contour of the NACA systemiga-
tion is maintained.
G NACA TM 1240
standard NACA airfoils with thickness ratios ranging between
d/l = 0.06 and d/i = 0.18 (reference 1). In addition three
symmetrical profiles having thickness ratios of 9, 1.2, and 15 percent
with maximum thickness moved backward were investigated; the tests,
however, have not yet been correlated because of their use for
different purposes and the long delay between tests (reference 2).
So far only one profile with 2-percent camber and normal thickness
distribution has been investigated at the request of the Messer-
schmitt Co. (reference 3). A greater number of profiles of various
camber are ready to.be tested. .(In the meant-me three more cambered
profiles were investigated up to January 1943.)
On the previously enumerated profiles the pressure distribution
was measured in the center section of the rectangular wings fitted
with end plates and the drag was computed from measurements of
momentum loss behind the model wings. The wing chord of all these
models was 500 and 350 millimeters,respectively, so that the
Reynolds number even at the lowest Mach number of the tests,
(M = 0.30), with Remin =2.2 )x 100 was still considerably above
the critical value for the boundary-layer reversal on flat plates.
In addition a number of profiles with thickness ratio up to
d/l = 0.50 and chords of I = 60 millinetere and los vere touted so
as to obtain a preliminary insight into the effects of such profiles
on the drag at high Mach numbers, especially with respect to
II. RESULTS OF TESTS ON PROFILES AT HIGH SUBSONIC SPEEDS
1. Lift of Syametrical Profiles
The value aca/a governing the lift at high airspeeds was
determined for symmetrical profiles of varying thickness from DVL
tests and plotted against the Mach number in figure 2. The
theoretical curve for thepift increase according to Prandtl's
approximation ratio 1/ i M, is included for comparison. In
the pre subnonic range, that Is, up to the critical Mach
number, M*, at which the velocity of sound sl reached or exceeded locally,
the test curves of thin profiles up to d/l = 12 percent manifest
an increase in the aca/6a value which is in good agreement with
Prandtl's calculations. Only on the thickest profile with
d/l = 18 percent does the lift increase disappear with rising
Mach number, obviously as the result of the more unfavorable
development of the boundary layer on thick profiles.
NACA TM 1240
After exceeding the critical Mach number M, that is, as soon
as the sonic velocity is locally exceeded at the profile and
compresIibility shock occurs, the premises of the Prandtl law
are no longer complied with, hence no agreement is to be expected
between the experimental and theoretical curve. While in this
range the lift increase for thin profiles up to d/1 = 12 percent
increases at first, and then shows no marked decrease until after
substantially exceeding the critical Mach number, the lift on
the thick profiles of d/l = 15 percent and 18 percent decreases
as soon as the critical Mach number is exceeded and finally drops
to zero at about M = 0.83. This dissimilar behavior of the lift
on thin and thick profiles in the supercritical range of Mach numbers
can be explained from the pressure-distribution records by the
dissimilar development of the compressibility shocks.
On studying the range of Mach numbers on a profile with
compressibility shock occurring only on the suction side (fig. 3),
it is seen that this shock has already- moved much farther toward
the trailing edge on the thin profile than on the thick profileV
this causes the earlier manifested lift increase on the thin
profile and the lift decrease on the thick profile, as seen by
a comparison with the pressure distribution curve at small Mach
number indicated by thin lines.
If at further rise in Mach number the pressure side also happens
to cane into the range of the compressibility shock (fig. 4), these
shocks develop on suction and pressure side near the trailing edge
of thin profiles at sufficiently high subsonic Mach numbers, so that
a large lifting surface remains, which however is substantially less
compared to the pressure distribution without pressure-side compressi-
bility shock. On the thick profile, on the other hand, the suction-
side compressibility shock lags behind in its rearward movement, so
that for the lifting surface at the forward part of the profile there
is a corresponding negative lifting surface at the rear part of the
profile and the lift therefore drops to zero or even negative values
in spite of the positive angle of attack of the profile.
The formation of the cited pressure distributions also affords a
possibility of estimating the lift distribution on profiles at higher
Mach numbers than correspond to the measured range. As the pressure
distribution of the thin profile in figure 4 indicates, at M = 0.88
the compressibility shocks on suction and pressure side have already
travelled close to the trailing edge so that on this profile no
further fundamental change in lift is to be expected. This is
readily seen by a comparison with the pressure distribution of an
airfoil at a supersonic speed, as represented in figure 5 according
to a measurement by Ferri (reference 4). The pressure distribution
NACA TM 1240
at supersonic velocity resembles in the low-pressure variation as
well as in the position of the compressibility shock the pressure
distribution on the thin profile. Accordingly it is to be presumed
that the curves for the lift increase in figure 2 may not be
extrapolated to zero for the thin profiles, but that the lift is
actually maintained throughout even at further approach to sonic
velocity. Several tests in the DTL high-speed tunnel are available
which show that the lift at the very high Mach number of M = 0.90
does not continue to drop steeply but rather starts again to rise
to higher lift coefficients. For the same reason it is to be
expected that on the thick airfoils a rise in Mach number beyond
the test range will be accompanied by a lift increase to rational
values, because the suction-side compressibility shock will travel
to the trailing edge even on the thick airfoil' at sufficiently high
subsonic Mach numbers and so cancel the overlap in the pressure-
2. Lift of Cambered Airfoils
Only one cambered airfoil with 2-percent depth of camber and
13-percent thickness ratio has been tested, althoucl a large
number of cambered model wings had been prepared for testing.
Aside frmn the lift increase 6cW/0& and the drag which are
similar to those on symmetrical airfoils of equal thickness ratio,
an unusual result of these measurements was the sudden displacement
of the angle of attack for zero lift at high Mach numbers (fig. 6).
While up to M = 0.8 the angle for zero lift of the cambered airfoil
was located at mo = -1.50, it rose to %o = 20, or changed by
about 3.50 when the Mach number increased to M = 0.86. Thus
a wing must be given a 3.50 higher setting in this range, if lift
conditions similar to those at small Mach numbers are to be reached.
This displacement of zero angle of attack is also attributable to
a particular formation on the pressure side of the compressibility
shock that suddenly moves in direction of the wing trailing edge
in the 0.8 to 0.86 Mach number range (figs. 7 and 8).
3. Neutral Stability Point of Symmetrical Profiles
The neutral stability point which owing to the symmetry of the.
profile in this instance also indicates the position of the applied
moment was computed for the series of NACA airfoils of varying thick-
ness from the pressure-distribution measurements over a range of
small lift coefficients. According to figure 9 the curves for the
varyingly thick profiles are so staggered at small and medium velocities
that for thick profiles the neutral stability point lies nearer to
NACA TM 1241 5
the leading edge. This is due to the boundary layer which thickens
more on the suction than on the pressure side and therefore reduces the
lift at the trailing edge in accord with the effective jet boundary
at the edge of the boundary layer. This decrease in lift caused
by the one-sided thickening of the boundary layer is naturally
so much greater as the profile is thicker.
At increasing Mach number all neutral-point curves shift toward
the wing leading edge, the shift being greater for the thicker profiles.
This also is explainable by means of the boundary layer, since with
rising Mach number the pressures governing the boundary-layer
development increase and thus the same effect is produced as by a
further thickening of the profile.
After exceeding the critical Mach number, that is, after locally
exceeding the velocity of sound the curves of the thin airfoils with
6"to 12-percent thickness ratio bend sharply in direction of the
tail-heavy neutral stability-point positions, while the curves of the
thick profiles continue to rise in the old direction. This dissimilar
behavior in the range of the ccmpresslbility shocks is already evident
front the previously discussed pressure-distribution curves in this
speed range (figs. 3 and 4). Owing to the dissimilar compressibility-
shock position on the pressure and suction side of thick airfoils
it results in overlap in the pressure distribution which as a result
of the downwash shifts the applied moment forward. This overlap
cancels out on the thin airfoils especially at high Mach numbers.
On the contrary, the pressure distributions disclose that the applied
moment travels in direction of the wing center as in pure subsonic
4. Drag of Symmetrical Profiles
The drag of the symmetrical profiles with different thickness
ratios explored in the high-speed tunnel is plotted against the
Mach number in figure 10 for symmetrical air flow. There is no
change in drag coefficient up to the critical Mach number, that is,
in the subsonic range, but after a certain increase in Mach number
beyond the critical,the well known steep-drag rise occurs. The
amount of the drag rise covered on an average by these tests is up
to drag coefficients (referred to frontal area) of around 0.4.
In the pure subsonic range the drag coefficient of the profiles
tested is practically constant, although the Reynolds number of the
tests increases with increasing Mach number. This observation was
made on the symmetrical NACA airfoils as well as on other tests on
different models. In the evaluation of these curves
NACA TM 1240
It should be remembered that the Reynolds number effect leading to
a drag decrement is opposed by the effect of compressibility on
increasing the velocities which acts in the sense of a drag increase.
Calculations for predicting the drag curve at subcritical Mach numbers
have up to the present not given the complete equality of these two
mutually counteracting influences; it must not be forgotten that these
approximation processes considered only the Reynolds number and
the apparently increased profile thickness, but not the compressi-
bility in the formation of the boundary layer. By this camission no
provision is made, for example, for the fact that substantial
temperature differences occur within the boundary layer which, for
instance, at the point where locally the velocity of sound is
exactly reached, already amounts to about 450 C. So when the
boundary-layer laws obtained for incompressible flow are applied
to compressible flow the difference between measurement and
preliminary calculation is, in view of this omitted temperature
gradient, not surprising.
Incidental to the steep drag increase the question arises as to
what values the drag will attain at further increasing Mach number.
From numerous measurements in the high-speed tunnel it was found
that the drag coefficient based on frontal area appears to )end
toward a terminal value of the order of magnitude of cv = 1.2 at
high Mach numbers, so that this value may serve as reference point
for an extrapolation of the drag coefficients beyond the test range.
This value is confirmed satisfactorily by the measurements on
thick eymmetrical airfoils of small chord represented in figure 11,
and whose thickness ratio had been raised to 50 percent in view of
propeller root profiles. The profile chord of these wings ranged
between 36 and 60 millimeters, the span was about 500 millimeters.
The wings were mounted on an adjustable central spindle, the drag
at zero setting was determined by means of a thin wire extending
forward at the model. These measurements also show within measuring
accuracy the nearly constant drag coefficient up to the critical
HI. COgREIATION O THE PROFILE MEASUEMEW S IN THE
DVL fIGB-&EEED TUNNEL WIT THE MEASUREMRNS IN THE
IAMBE WIND TUHEL OF THE DVL
The measurements in the DVL high-speed tunnel generally cover a
speed range of from 100 meters per pecand to about 90 percent of the
NACA TM 121L0
velocity of sound. At the lowest airspeed compressibility usually
has such a small effect that the test data in this range are
directly comparable with the measurements in low-speed wind tunnels.
The series of symmetrical NACA airfoil sections, for which an
abstract from the high-speed measurement is given in the present
report, was also tested in the large tunnel of the VIW (5 x 7 meters)
at low speeds (reference 5). The data from both tes-ss a'e
compared in figures 12 and 14. For the comparison the tests from the
high-speed tunnel were extrapolated to the Mach number of M = 0.2
corresponding to the speed in the larGe tunnel which lavolved no
difficulties in view of the flatness of the curves in this range
of Mach numbers. he Reynolds number in both wind-tunnel tests
was Re = 2.7 x 10o. The agreement between the measurements in
both tunnels is unusually good. The discrepancies in drag and
in moment about the quarter-chord point range within measuring
Only for the lift increase aca/Lm do the hfgh-speed measurements
systematically exceed those of the large tuLnol by about 5 percent.
This difference is probably due to the fact that normal wings with
aspect ratio b2/F = 5 were used in the la'te tunnel, while the vrinCs
in the high-speed tunnel were fitted with end plates. In the
conversion of the angle of attack with the end-plate measurements
to two-dimensional flow, it is concei 'ble that the simple equations
employed for taking the end plate into account, according to 0. Schrenk,
still contain certain inaccuracies.
IV. EFFECT OF ASPECT RATIO ON THE AERODYNAMIC
COEFFICIENTS OF RECTANGULAR WINGS
The previously reported test data were obtained, as a rule,
from pressure-distribution measurements in the center section of
rectangular wings, hence reproduce the profile characteristics for
two-dimensional flow in good approximation. The drag measurements
on the small wings of large thickness with their comparatively large
aspect ratios, b /F = 10 or more, form the only exception.
1. Effect of Aspect Ratio
In the pure subsonic range it is of importance to know whether
the aspect ratio acts in accord with the theoretical calculations
(reference 6) on the rise in the lift increase 2ca/ & with
increasing Mach number. According to these calculations the lift
NACA TM 1240
increases at constant angle of attack of the wing only in two-
dimensional flow in the ratio 1/\/1 M, while for finite aspect
ratio the rise is smaller and disappears altogether in the extreme
case of very small aspect ratios.
On the basis of later measurements on wings with the easn profile
NACA 00012 1.130 with three different aspect ratios (b2/F = w
from pressure-distribution moasuremento, and b2/F = 6 and 1.15 from
force measurements) this question regarding the lift increase could be
answered to the extent that the toot data are in satisfactory agreement
with the calculations. On the wing with very small aspect ratio in
particular, b2/p = 1.15, the rise of the ca/&a values with
increasing Mach number is extremely small (fig. 15).
According to the cited theoretical investigations this diminished
rise in Bca/ a for small aspect rati? is attributable to the fact
that, while the lift belonging to the effective angle of attack of
the wing increases in accord with calculations for two-dimensional
flow with the Prandtl factor 1/Vl M, the induced downwash angle
at the wing also increases as a result of the increased lift and
so reduces the lift by way of the effective angle of attack. This
reduced lift increase is therefore so much greater as the downwash
effect is greater, that is, as the aspect ratio becomes smaller.
For the very same reason this reduction disappears completely when
as for infinite aspect ratio the downwash is infinitely small.
The measurements for b2/F = and b2/F = 6 show no substantial
differences in their fundamental distribution even in the supercritical
range of Mach numbers, as for instance, the temporary marked rise in
lift after exceeding the velocity of sound followed by a marked drop
as a result of the pressure-distribution overlap. On the wing with
aspect ratio b2/ = 6, which was measured up to M = 0.90, it is
noted again that the lift characteristic aca/)m at very high
Mach numbers of M = 0.90 no longer decreases but begins to rise
again with further increase in Mach number.
From this general trend for b2/F-- anl t2/F = 6
the test curve of the wing with b2/F = 1.15 differs in noticeable
manner, to the extent that this wing neither exhibits a greater
increase nor a marked decrease in the ca/4c curve in the
supercritical range of Mach numbers.
NACA TM 1240
2. Wing With Aspect Ratio b2/F = 1.15
(IACA airfoil section 00012 1.130)e
The wing designed with the NACA airfoil section 00012 1.130
had a chord of I = 0.35 meters. It was supported at wirn center
by a single balance support which transmitted the lift and drag of the
model wing at a 450 angle obliquely to the balance. The moment was
measured on a separate balance over a synmetrical moment arm.
Lift: Figure 16 shows the lift coefficient ca plotted against
the angle of attack a for several Mach numbers. In contrast to all
profile measurements known so far, no disturbances of any kind were
observed throughout the entire range of Mach numbers up to M = 0.91,
notwithstanding the fact that the angle of attack was raised up to
a = 8, save that the highest Mach number M = 0.91 at high a
no longer fieldss the slight deflection of the lift curve in direction
of higher ca, but on the contrary, a slight deflection in the
opposite sense, that is, toward lover ca However, it is to be
noted that the lift coefficient as a result of the small aspect ratio
at o = 8 mounts to little more than ca, 0.2.
Schlieren observations made contemporary with the force measure-
ments Indicated that at M = 0.82 severe compressibility shocks
occurred even at zero angle of attack. According to the Bchlieren
photographs the location of the compressibility shocks on the
pressure side was a little nearer to the trailing edge than on the
suction side, so that the overlap observed on the profile in
two-dimensional flow and the loss in lift produced by it, was
largely canceled out.
The small effect of the Mach number on the rise of the lift curves
ca = f(a) is more accurately represented in figure 17 on the variation
of the lift increase bca/aa with respect to the Mach number.
cai'ba increases very little, in fact, a little less even than the
Moment: In figure 18 the moment coefficient referred to the
1/4 chord of the wings is plotted against the lift coerficient c,
for several Mach numbers. According to it the moment curves are
not rectilinear any more oven at low speeds, and this oscillating
variation is considerably simplified at increasing Mach number.
2These measurements are to be published as a separate report
in the near future.
NACA TM 1240
But disoontinuous moment Jumps as on wings in two-dimensional
flow are completely absent.
Another unusual fact is that the moment curves with rising
Mach number turn considerably in the unstable sense, which
corresponds to a shift of the neutral stability point toward the
leading edge (fig. 19). Even at low speeds the neutral stability
point, which owing to the synmetrical ring profile is also
identical with the center of pressure, lies about 18 percent
ahead of the 1/4 point, that is, only about 7 percent aft of
the wing leading edge. This forward position is explained by the
fact that owing to the small aspect ratio of the wing the stream
lines are considerably curved compared to the wing chord which at
the tip especially leads to greater negative lift and even loss
o lift. Since at high Mach numbers for the model wing with
/F = 1.15 there corresponds a comparable wing in incompressible
flow with a smaller aspect ratio, the further forward shift of
the neutral stability point with increasing Mach number is readily
understood, even though the magnitude of this travel was, at first,
surprising. For example, the neutral point lies already at the nose
when M 0.76 is reached; at still higher M it and with it the
center of pressure lies even ahead of the wing leading edge.
A comparison with Winter's tests on wings of small aspect
ratios (reference 7) indicated that a wing with b2/F = 1 and
12.7-percent thickness ratio corresponding to the previously
reported measurements likewise exhibited a very forwardly located
neutral stability point, which was determined as being less than
10 percent behind the leading edge.
Drag: The drag of the wing with b2/F = 1.15 in symmetrical
flow is plotted against the Mach number in figure 20, along with
the corresponding drag curves of the rectangular wing with b2/F = 6
and of a wing with 350 positive sweepback and b2/ = 6. All wings
had the same NACA 00012 1.130 profile. The drag increase on the
wing with b2/P = 1.15 is considerably delayed relative to the
rectangular wing and starts only a little earlier than on the wing
with 350 positive angle of sweepback. The reduction from b2/F 6
to b/F = 1.15 therefore causes the same delay in drag increase
at high Mach numbers, as obtained for b2/F = 6 with a 300 positive
The cause of this beneficial drag action of the wing with small
aspect ratio is likely to be found in a transition to three-
dimensional flow as a result of the small aspect ratio. At the
wing tips, whose range of influence in this particular case amounts
to a considerable portion of the total wing area, a flow occurs which
NACA TM 1240
is rather comparable to an axially symmetrical than to a two-dimensional
flow, and as a consequence exhibits the more favorable characteristics
of a three-dimensional flow.
1. A brief survey of the airfoil measurements in the DML high-
speed tunnel is given in the light of several diagrams.
2. By measurements on wings of different aspect ratios it is
proved that in the pure subsonic range the aspect ratio affects the
rise of the lift as the theory stipulates. Thus the lift for wings
of infinite aspect ratio, for example, increases with 1 1 42,
while in the extreme case of vanishingly mall aspect ratio the
lift remains constant in spite of increasing Mach number.
3- High-speed measurements on a rectangular wing with b2/F = 1.15
disclosed that in the entire test range, that is, up to M = 0.90
and angles of attack up to a 80, no rough discontinuities in
lift and moment were observed. The drag rise at zero lift on this
wing compared to the wing of b2/F = 6 was shifted considerably
toward higher Mach numbers.
Knappe: Gbthert's drag curves showed no rise at small and
medium Mach numbers. But according to theoretical considerations a
linear increase above the Prandtl factor should occur, as definitely
observed in the Hoinkel tunnel. The reason that this effect did
not occur on G6thert's curves might be found in a superposition
of mutually opposing effects of Reynolds and Mach number. In the
measurements in the Heinkel high-speed tunnel the effect of the
Reynolds number was suppressed by turbulence edges." This is
also plainly observed on the position of the test points on part of
Helmbold. According to Gothert (JB. 1941, D9F, p. I. 684) it
is possible to correct the airspeed in the tunnel, even when
supersonic areas already occur at the profile. Promise is, of
course, that they do not yet reach the tunnel wall. But this
condition exists long before reaching the velocity of sound. In
this respect the free jet shows more favorable characteristics,
since on it the supersonic areas extending out from the profile
NACA TM 1240
are able to reach the jet boundary only when the jot leaves the
nozzle with sonic velocity. The corrective possibility which
in the tunnel rests on the measurement of the minimum pressure
at maximum speed at the tunnel wall and provides reference points
for the prediction of the intensity of the reflected dipole grid
by means of the Prandtl-Busemann law is, on the free jet, given
by the measurement of the greatest Jet expansion and the subsequent
determination of the reflected dipole grid. The correction possi-
bility therefore ends only at sonic velocity on the free jet.
Translated by J. Vanier
National Advisory Committee
NACA TM 1240
1. G6thert, B.: Profilmessungen im DTL-Hochgeschwindigkeitawindkanal
(2,7 m 0). FB 1490.
Gbthert, B.: Druckvertellunge- und Impulsverlustechaubilder fir
dae Profil NACA 0 00 06 1,1 30 bei hohen Unterschallgeschwin-
digkeiten. FB 1505/1.
FB 1505/2: dasselbe fur das Profil NACA 0 00 09 1,1 30,
FB 1505T3: daaselbe ftr dea Profil NACA 0 00 12 1,1 30,
FB 1505/4: dasselbe fOr das Profil NACA 0 00 15 1,1 30,
FB 1505/5: daeselbc flir das Profil NACA 0 00 18 1,1 30.
GCthert, B.: Hochgeechwindigkeitsuntereuchungen an symmetrischen
Profilen mit verachiedenen Dickenverbiltniseen im DVL-Hochgeechwin-
digkeitewindkanal (2,7 m 0) und Vergleich nit Meesungen in
anderen Windkaniilen. FB 1506.
2. Gothert, B./Richtor, G.: Messungen am Profil NACA 0015-64 Im
Hochgeschwindigkeitewindkanal der DV~ (2,7 m )), Druckvertellungs-
auwvertung. FB 1247.
DTL-Industriebericht: Hochgeschwindigkeitasessungen am Heinkel-
Profil 0 00 12 0,715 36,6 im DVL-Hochgeschvindigkeitswindkanal
(2,7 m 0). Editor: B. G6thert. Cownissioned by Firma Ernet
Heinkel Flugzeugwerke G.m.b.H., Rostock.
Profile Me 2 35 13
(2,7 m 0). Editor:
A. G., Augeberg.
Hochgeschwindigkeitsaeasungen am Measerschmitt-
1,1 30 im DYL-Hochgeschwindigkeitevindkanal
B. G6thert. Ccmmissloned by Meeserechmitt-
4. Ferri, A.: Alcuni riBultati sperimentali riguardanti profile alari
provati alla galleria ultrasonora di Guidonia.
5. Doetech, H: Untersuchung der Profilreibe NACA 00 Im 5 x 7 m Windkanal
der DVI. FB 914.
6. Gothert, B.: Plane and Three Dimensional Flow at High Subsonic
Speeds. NACA TM 1105, 1946.
7. Winter, H.: Strbmungevorghnge an Platten und profilierten Korpern
bel kleinen Spannweiten. Forechung cuf dam Gebiete des
Ingenieurweeens, Bd. 6(1935), Ausg. A, p. 45, figure 16.
NACA TM 1240
U) I C
U a I II I -
it p I A
i) r r '
os i w
r>l ^ Si !> ^^
NACA TM 1240
,o L z ---z 1LIL
2 04 0.6 O0 Od
Figure 2.- Lift increase ca /Ax in two-dimensional flow plotted against
Mach number for symmetrical NACA airfoils of varying thickness (lift
coefficient ca 0).
NACA TM 1240
Figure 3.- Pressure distributions of profiles of varying thickness with
expressed compressibility shock on the suction side (pure subsonic flow
yet on the pressure side).
--N-4#J ao-1,7i H-i a,--f
? -- ^ T ^ Sonic velocity
--AW N --2.S- M a .-3f3
+ -- -- L*0B a *2S' 1- -- Mi a..-23'"
I 2 .4 I 1 .l 9 I i .4 .6 0 t.O
Figure 4.- Pressure distribution with compressibility shocks on suction
and pressure side.
NACA TM 1240
'22 VQ ._
Figure 5.- Pressure distribution at supersonic flow M
= 1.85 (according
1- I I I
,: Angle or attack for ca = O
attack at zero lift of a cambered profile at high Mach
Messerschmitt 2 35 13 1.1 30).
figure 7.- Pressure distribution on a cambered profile at Li = 0.80
and ,It = 0.84 (angle of attack ac. 0) (profile: Ivesserschmitt
2 35 13 1.1 30).
NACA TM 1210
Figure 8.- Pressure distribution on a cambered profile at M = 0.80
and M = 0.84 (a,. a 1.60). (Profile: Mlesserschmitt 2 35 13 1.1 30)
Figure 9.- Neutral stability point position c,-cm /ca for various trick
symmetrical NACA profiles plotted against Mach number (ca Z 0).
NACA TM 1240
S Profile drag coefficient c Thickness ratio
front -d/t n ft T
l06e- (referred to the frontal surface) i 87
\t?.07- ----------- -
Angle of attack a = 0
_.0 __ __
0.06 0 .....
Critical Mach number
0 Mach number
02 a.? 4 0f 0 .e 07 9S Ws o
Figure 10.- Profile drag coefficient c p for various thick symmetrical
IL..CA profiles plotted against IMach number (ca = 0).
NACA TM 1240
| _I j ....I _Y I/ ach number u
4 a 4J 44 u v 01 aas (
Figure 11.- Drag coefficient c at zero lift for thick symmetrical NACA
airfoils plotted against the Mach number (airfoil series 000 d/l 1.1 30).
Figure 12.- Profile drag coefficient cwp for profiles of different d/1
(NACA series 000 d/1 1.1 30 and 2 40 d/' 1.1 30) according to tests
in the high-speed tunnel and in the large tunnel. Reynolds number in both
cases: R = 2.7x 106; Mach number M 0.20; lift coefficient ca = 0.
NACA TM 1240
DVL High-speed wind tunnel (2.7m 9)
Mach number M = 0.2
0 Large wind tunnel DVL (5 x 7m) (FB 914)
SThickness ratio d/t
0 ol 02 o.24
Figure 13.- Lift increase aca/ in two-dimensional flow on profiles of
different d/l (NACA series 000 d/l 1.1 30) according to measurements
in the high-speed tunnel (pressure distribution measurements) and in the
big tunnel (weighing).
DVL High-speed wind tunnel (2.7m )
Mach number M = 0.2 o
mt,4 > 0 (tail heavy)
O OY ..
Neutral stability point position bc /aca for profiles of different
d/l (NACA series 000 d/1 1.1 30) according to pressure distribution
measurements in the high-speed tunnel and weighing in the big tunnel.
NACA TM 1240
increase according to theory
I I I I I 1 Mach number N
o t s 4 oa as 1t
Figure 15.- Effect of aspect ratio A on the lift increase aca/ at high
Mach numbers in the zero lift range (NACA series 00012 1.1 30).
Figure 16.- Lift coefficient ca plotted against m for a rectangular wing of
A = 1.15 and NACA airfoil section 00012 1.30 at different Mach
NACA TM 1240
a Increase according to theory A = 1.15
am;---- ----- ---- --
Macn number M
IJ 44 45 41 S7 RI 40 to
Figure 17.- Lift increase ca /b, of a wing with A = 1.15 and of an airfoil
of the NACA series 00012 1.1 30 plotted against the Mach number at
Figure 18.- Moment coefficient CmL/4 plotted against lift coefficient ca
for a rectangular wing of A = 1.15 and for the profile NACA 00012 -
1.1 30 at different Mach numbers.
V- Leading edge of the profile
I I I
=_,_ -I I 1II_1L
Figure 19.- Neutral stability point acm/aca of a wing with A = 1.15 and
profile NACA 00012 1.1 30 plotted against Mach number at ca = 0
(cm > 0: tail heavy, referred to I /4 line).
I Mach number U
NACA TM 1240
:u -- -- -I
: Rectangular wing A =
-Rectangular wing A 1.15
Swept-back wing A = 6; q = 350 /
'I Mach nunter u
43 t* 4 IS 4o 41 #i to
Figure 20.- Drag coefficient cw at zero lift plotted against Mach number
for several model wings of different aspect ratios A and angle p ; profiles
of all models measured in flight direction are NACA 00012 1.1 30.
NACA TM 1240
From G6thert, B.: Hochgeechwindigkeltemeasungen
an einem Fligel kleiner Streckung. Zentrale fdr
viseenschaftlichee Berichtsweeen dea Luftfahrt-
forechung des Generalluftzeugmeisters (ZWB)
Berlin-Adllorhof, Forschungsbericht Nr. 1846,
figures 6 and 7.
NACA TM 1240 29
--- -4-I-- --
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f0 o .
.o 0 a
rtQ h- -
1 7 -- s ^ $---- c c
^^~~~~a s^a^ .S
a): o -fi-- ^ ^ :==o^ t
:r ; Q __ ^ __ __ __ __ __ __ ^ J c o
30 NACA TM 1240
-cJ --- -
oQ d o
\ -^ ^M ----- --
r ,- U
____ | l,
re Md -)
o o a
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S / a i v or
C P 43 4 s
to o o i
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m 0 ) 0 -
0 E-4E- I
0 -4 4 4'
\ E- q
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0 1 m 0 C
0 0 0 .. 0
0 0 4 0
-l q- .
-H I :s
$ O 0cc 0
S- 0 o l
0 0o o
S 0O 0
0 -0 0
P d P4-i 54
054 a 05 -. 0
0 0 00
$. ,-4 H
o o -
0 V 00
m x! 4
T4: *^ 1
>> 0 4
00 h t
S B *H
^ I'0 C
(D F -
co, b O i
O0 0 4
(D 0 0
CD +- aL
C m 0
0 ^ (D
0 c 0
S--1 H ..M
-l d 0
(U (D o
4. 0 -
t>* 0 4-
p co 0 0
P 0 -P0
m 0 o
*-0 0 0
c -P ;-
I3 1262I ur runu081
3 2208105 028 7