effect of blockage ratio on drag and pressure distributions for bodies
TRANSCRIPT
11
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NASA TECHNICAL NOTE
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NASA TN D-7331
EFFECT OF BLOCKAGE RATIO ON DRAG
AND PRESSURE DISTRIBUTIONS FOR BODIES
OF REVOLUTION AT TRANSONIC SPEEDS
by Lana M. Couch and Cuyler IV. Brooks, Jr.
Langley Research Center
Hampton, Va. 23665
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTON, D.C. • NOVEMBER 1973
https://ntrs.nasa.gov/search.jsp?R=19740001903 2018-04-02T19:02:15+00:00Z
, , /_ i _
1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.
NASA TN D-7331
5. Report Date
November 19734. Title and Subtitle
EFFECT OF BLOCKAGE RATIO ON DRAG AND PRESSURE
DISTRIBUTIONS FOR BODIES OF REVOLUTION AT
TRANSONIC SPEEDS
7. Author(s)
Lana M. Couch and Cuyler W. Brooks, Jr.
9. Performing Organization Name and Address
NASA Langley Research Center
Hampton, Va. 23665
12, Sponsoring Agency Name and Address
National Aeronautics and Space Administration
Washington, D.C. 20546
6. Performing Organization Code
8. Performing Organization Report No.
L-8449
10. Work Unit No.
501-06-09-01
'11. Contract or Grant No.
13. Type of Report and Period Covered
Technical Note
14. Sponsoring Agency Code
15. Supplementary Notes
16. Abstract
Experimental data were obtained in two wind tunnels for 13 models over a Mach
number range from 0.70 to 1.02. Effects of increasing test-section blockage ratio in the
transonic region near a Mach number of 1.0 included change in the shape of the drag curves,
premature drag creep (i.e., transonic creep), delayed drag divergence, and a positive incre-
ment of pressures on the model afterbodies. Effects of wall interference were apparent in
the data even for a change in blockage ratio from a very low 0.000343 to an even lower
0.000170. Therefore, models having values of blockage ratio of 0.0003 - an order of
magnitude below the previously considered "safe" value of 0.0050 - had significant errors
in the drag-coefficient values obtained at speeds near a Mach number of 1.0. Furthermore,
the flow relief afforded by slots or perforations in test-section walls - designed according
to previously accepted criteria for interference-free subsonic flow - does not appear to be
sufficient to avoid significant interference of the walls with the model flow field for Mach
numbers very close to 1.0.
t7. Key Words (Suggested by Authoris))
Transonic wall interference
Drag
Facilities
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Unclassified
18. Distribution Statement
Unclassified - Unlimited
20. Security Classif. (of this page)
Unclassified
21. No. of Pages
109
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i
EFFECT OF BLOCKAGE RATIO ON DRAG AND PRESSURE DISTRIBUTIONS
FOR BODIES OF REVOLUTION AT TRANSONIC SPEEDS
By Lana M. Couch and Cuyler W. Brooks, Jr,
Langley Research Center
SUMMARY
In an attempt to determine the severity of wind-tunnel wall interference under near-
sonic test conditions, aerodynamic force and pressure measurements were obtained at
zero normal force for 13 bodies of revolution over a Mach number range from 0.70
to 1.02.
Three specific effects on the drag data occurred near a Mach number of 1.0 as a
result of increasing the test-section blockage ratio for a given model profile:
i. The shape of the drag curves changed from a relatively rapid increase to a very
gradual increase in drag with increasing Mach number. This change occurred for
increases in test-section blockage ratio above approximately 0.0010. The shape of
the drag-coefficient curves, obtained at values of test-section blockage ratio less than
0.0010, is relatively insensitive to changes in blockage ratio.
2. Increasing the blockage ratio above approximately 0.0003 produced a premature,
positive deviation, or transonic creep, of the drag curve from the trend of the subsonic
data. Since the Mach number at the initiation of transonic creep agrees with the calcu-
lated Mach number for choked flow in a solid-wall tunnel, transonic creep may be the
first indication of significant wind-tunnel wall interference near a Mach number of 1.0.
3. The occurrence of drag divergence was delayed by approximately 0.013 in Mach
number because of an increase in blockage ratio from 0.0002 to 0.0010. For blockage
ratios greater than 0.0010, the drag-divergence Mach number was essentially constant.
Therefore, near a Mach number of 1.0 increasing the blockage ratio delays the occurrence
of drag divergence - the result that would be expected because of an effective decrease in
the free-stream Mach number at the model.
There was only one obvious effect of wall interference on the model surface-
pressure distributions obtained for a given model shape at different values of blockage
ratio. For Mach numbers greater than approximately 0.96, a region of supersonic flow
existed around the models. An increase in the value of blockage ratio for Mach numbers
greater than 0.96 caused a positive increment of pressure to occur on the model. The
effect on the drag data of this pressure-drag increment coincided quite well with the
change in shape of the drag curves.
The results of this investigation indicated that models having values of test-section
blockage ratio of 0.0003 - an order of magnitude below the previously considered "safe"
value of 0.0050 - had significant errors due to wall interference in the drag-coefficient
values obtained near a Mach number of 1.0. Furthermore, the flow relief afforded by
slots or perforations in test-section walls - designed according to previously accepted
criteria for interference-free subsonic flow - does not appear to be sufficient to avoid
significant interference of the walls with the model flow field for Mach numbers very
close to 1.0.
INTRODUCTION
In the past, numerous experimental investigations have been conducted in transonic
wind tunnels to determine the drag of both complete aircraft configurations and various
aircraft components at high subsonic and transonic Mach numbers. For these investi-
gations, data obtained at test-section blockage ratios of 0.0050 or less were generally
considered to be free of wall-induced blockage effects. However, the advent of the super-
critical design concept and the effort to develop a near-sonic transport have placed
renewed emphasis on accurate drag measurements in the near-sonic speed range (Mach
numbers of 0.95 to 1.0). As a result of this increased emphasis, it was believed that the
severity of wind-tunnel wall interference should be reexamined at near-sonic Mach num-
bers. Therefore, geometrically similar bodies of revolution were tested in two wind
tunnels and in flight under the same conditions. The model-to-wind-tunnel blockage ratios
were 0.0028 and 0.000684. A comparison of the results obtained in the flight test and
wind-tunnel test, at a blockage ratio of 0.0028 (ref. 1), indicated differences in drag char-
acteristics of sufficient magnitude to cause concern about the validity of drag data obtained
in the wind tunnel near a Mach number of 1.0. This discrepancy was believed to be the
result of wall interference due to test-section blockage in the wind tunnel. To investigate
this result further, bodies of revolution which provided a systematic variation in blockage
ratio from 0.00017 to 0.0043 were tested in the Langley 16-foot transonic tunnel and the
Langley 8-foot transonic pressure tunnel to assess the extent of wall interference effects
near'a Mach number of 1.0. The significant variables included in the investigation were
Mach number and model diameter and length.
SYMBOLS
Values are given in both SI and U.S. Customary Units. The measurements and calcu-
lations were made in U.S. Customary Units.
2
A local cross-sectional area of model
d2A
dx 2
Amax
A s
C D
CD ,b
Cp
Cp,b
Cp,sonic
d
K
iref
M
NRe
P
q_
reference area, maximum cross-sectional area of model
cross-sectional area of sting
drag coefficient at zero normal force, adjusted to a condition of free-stream
static pressure at model base, Dragq_Amax
base-drag coefficient
pressure coefficient
base-pressure coefficient
pressure coefficient corresponding to
maximum diameter of model
M = 1.0 local flow
curvature constant in model profile equations
length of model
reference length of model (length to body closure)
free-stream Mach number
Reynolds number based on model length
model surface pressure
model base pressure
free-stream static pressure
free-stream dynamic pressure
R radius of model
longitudinal center-line distance from model nose
X m longitudinal center-line distance from model nose to maximum diameter
of model
(7 standard deviation of variable
APPARATUS
Model Description
The five model shapes investigated in the wind-tunnel tests were (I) the blunt-nose
supercritical body of type A, (2) the blunt-nose, finned body of type B, (3) the blunt-nose,
supercritical body of type C, (4) the blunt-nose, supercritical body of type D, and (5) the
pointed-nose body of type E. Sketches of all models are shown in figure I; the letters
indicate the profile type and the numbers are coded to the diameters - as indicated in
the following table:
Configurationnumber
code
1
2
3
4
5
6
cm
6.35
8.99
12.70
15.70
22.25
27.08
Diameter
in.
2.50
3.54
5.00
6.18
8.76
10.66
Pertinent dimensions of all models and stings are listed in table I, and model coordinates
are listed in table II.
Generally, the models had machined metal noses and were otherwise constructed of
wood with fiber-glass-covered surfaces, or they were made totally of aluminum. The
models were turned on a lathe to obtain the required profiles within a tolerance of
+0.0025 cm (+0.001 in.) in radius. Although the models were generally smooth, deviations
in the radius of the models may have been as much as ±0.0127 cm (+0.005 in.) due to
warping or shrinking of the wood. These deviations were well within the limits for hydrau-
lic smoothness for the test conditions and model sizes of this investigation. (See ref. 2.)
4
The surface-pressure orifices were constructed of metal tubing with 0.076-cm(0.030-in.) inside diameter, installed flush with andperpendicular to the model surface.Onelongitudinal row of pressure orifices was installed in each model, and eachmodelwas tested with the orifices in the sameorientation in roll. The locations of all surface-
pressure orifices are listed in table III.
Type A.- The profile of the blunt-nose, supercritical body of type A is defined by
the following equations:
For 0 < x < Xm=lref =lre f'
A,,/' x _ = K x\iref ) - A (l_ef_
Xm < x <0.990and for lref = lref
Xm 1where = -. The profile is symmetrical fore and aft of the point of maximum diam-
lre f 2eter, except for truncation at the base to accept the sting. Three models of this profile,
having maximum diameters of 8.99, 12.70, and 15.70 cm (3.54, 5.00, and 6.18 in., respec-
tively) and a fineness ratio (i/d) of approximately 9.0, were investigated.
Type B.- The profile of the blunt-nose, finned body of type B was identical to the
type A profile, except that the aft 12.7 cm (5.0 in.) of the body were modified. The cross-
sectional area distribution of the body including the four 3-percent-thick delta biconvex
fins was equivalent to the cross-sectional area distribution of the A-3 body. One model
of this profile having a 12.70-cm diameter (5.00 in.) was investigated in the wind tunnels
and in a flight test (ref. I).
Type C.- The profile of the blunt-nose, supercritical body of type C is defined by
the following equations:
X < XmFor 0 <=lref - lref,
K x '
\lref)
5
and for Xm < x <0.990,iref - iref -
A,,fx _= K\ire f] Amax
Xm 1.0 Xmwhere - The profile for 0 _-< x _<_ is identical to that of type A;
lref 1.0 + (2/_)" lref lref
however, aft of the location of the maximum diameter, the profile has a constant second
derivative in the area distribution. The model is truncated at the base to accept the sting
and to give a ratio of base diameter to maximum diameter equivalent to that of the type A
models. Consequently, the type C models have a fineness ratio (l/d) of approximately
9.5 - a value slightly larger than the fineness ratio of the type A models. Five models
of this type, having maximum diameters of 8.99, 12.70, 15.70, 22.25, and 27.08 cm (3.54,
5.00, 6.18, 8.76, and 10.66 in., respectively), were investigated in the wind tunnels.
Type D.- The profile of the blunt-nose, supercritical body of type D is defined by the
following equations:
X (: XmFor 0 <=lre f - lref'
Xm xand for <_ -< 1.052,
Iref iref
/l_e f/ [(v/2)(x - Xm_A" x =Ccos_ l__efLX_ _
where Xm_ 1.0 and C
Iref 1'2( 1 A-_a;\) +1"0
( lm;C = (A s - Amax) lref - x
is a function of the base area and is defined by
Therefore, the actual base is slightly larger than As, and the actual length of the model
is slightly less that that predicted by the equations in order to provide clearance for the
sting. Three models of this type, having maximum diameters of 6.35, 8.99, and 15.70 cm
(2.50, 3.54, and 6.18 in., respectively), were investigated in the wind tunnels.
Type E.- The pointed-nose model of type E has a modified Sears-Haack profile, as
given in reference 3. This model has a maximum diameter of 12.70 cm (5.00 in.), a
i ¸ / H / _ •
fineness ratio I/d of approximately 9, and Iref/d of 12.0. The free-flight model of
reference 3 also had a fineness ratio iref/d of 12.0, but the maximum diameter was
25.4 cm (i0.0 in.) and there was no simulated sting-type support.
Stings
All tests were made with models sting supported through an access hole at the
model base, except for the model which was tested in flight. The model support stings,
except for configuration C-6, were scaled to approximately the model size and were
designed in accordance with the criteria of reference 4 in order to minimize the effects
of sting interference on the flow over the aft end of the model. This reference specifies
the minimum length of straight_-sting section aft of the model base and the maximum angle
of the sting flare. The ratio of cylindrical sting length to sting diameter for configura-
tion C-6 was smaller than desirable. Pertinent dimensions and flare angles of the stings
are presented in table I.
Wind Tunnels
This investigation was conducted in the Langley 16-foot transonic tunnel and the
Langley 8-foot transonic pressure tunnel. The 16-foot transonic tunnel (TT), which has
a nominally 4-percent-open, slotted, octagonal test section, as shown in figure 2, is an
atmospheric wind tunnel with continuous air exchange. This wind tunnel has continuously
variable airspeed through a Mach number range from 0 to 1.30. Test-section plenum
suction is used for speeds above a Mach number of 1.10. In order to eliminate any lon-
gitudinal static-pressure gradients that might occur along the center line, the test-
section wall divergence is adjusted. These adjustments are based on the results of the
wind-tunnel calibration. The average distance from center line to wall is 2.37 m
(93.31 in.), and the cross-sectional area is 18.50 m 2 (199.15 ft2).
The 8-foot transonic pressure tunnel (TPT) has a Maeh number range from 0
to 1.30. The test section is 2.16 m square (85.2 in. square) with filleted corners so that
the total cross-sectional area is 4.52 m 2 (48.70 ft2). The top and bottom walls have four
slots each, as shown in figure 3(a). The sidewalls are normally flat and solid; but for
this investigation, a set of wooden fairings was installed in an attempt to reduce the wall
interference effects. Two sidewall fairing strips were mounted in the streamwise direc-
tion on each wall, as shown in figure 3(b). The cross-sectional area of these fairings is
constant through the test section, except in the vicinity of the model being tested, where
they are contoured to account for 40 percent of the model cress-sectional area (i.e., the
cross-sectional area of the fairing decreases in the vicinity of the model). Forward of
the test section the fairings taper smoothly into the wall of the entrance nozzle. Down-
stream of the model, the fairings are contoured to represent 40 percent of the cross-
/i i
sectional area of the support sting and are tapered to near zero thickness in the vicinity
of the large tunnel sting. The maximum cross-sectional area of the fairings is approx-
imately 0.27 percent of the cross-sectional area of the test section.
Configuration C-3 was also tested in the 8-foot transonic tunnel at the Calspan
Corporation (TT CAL).
Test Conditions
All models v_ere tested at zero normal force over the Mach number range from
0.70 to 1.02. Close spacing of test points at Mach numbers between 0.90 and 1.02 gen-
erally was maintained in order to improve the definition of the drag-divergence region.
Boundary-layer transition was fixed according to the criteria of reference 5 on all models
at about 2 percent of the model length downstream of the nose. The 0.25-cm-wide
(0.10-in.) boundary-layer transition strip consisted of grit sparsely distributed in a thin
film of lacquer. Grit size determined from criteria of reference 6 for all configurations
is included in the following table:
C onfigu ration
A-2
A-3
A-4
B-3
C-2
C-3
C-4
C-5
C-6
D-I
D-2
D-4
E-3
Grit number
180
120
120
120
180
120
120
120
120
180
180
120
120
am
Grit height
0.0064
.0102
.0102
.0102
.0064
.0102
.0102
.0102
.0102
.0064
.0064
.0102
.0102
in.
0.0025
.004
.004
.004
.0025
.004
.004
.004
.004
.0025
.OO25
.004
.004
In the 16-foot transonic tunnel, the test Reynolds numbers varied from 11.48 x 106
to 13.7.8 x 106 per meter" (3.5 x 106 to 4.2 × 106 per foot) for each model and the stag-
nation temperature varied between 310.93 K and 355.37 K (I00 ° F and 180 ° F). During
the iavestigation data were generally taken at dewpoint temperatures of about 269.26 K
(25 ° F); however, data were taken in two separate runs on the same model at dewpoint
temperatures of approximately 269.26 K and 283.15 K (25 ° F and 50 ° F). In comparing
these two runs, no effects of condensation could be observed in the pressure distributions
or the force data.
8
•'.. •i. "• /•" . • .
! •
Tests in the 8-foot transonic pressure tunnel were conducted at a Reynolds number
of 13.12 × 106 per meter (4.0 x 106 per foot). The stagnation temperature was held
constant at 322.04 K (120 ° F) with the airstream dried to a dewpoint temperature less
than 272.04 K (30 ° F) to avoid condensation effects.
Comparisons of the Reynolds numbers, based on model length, at which each model
was tested in the various facilities are shown in figure 4.
Instrumentation
Aerodynamic forces were measured with internal six-component strain-gage bal-
ances. The model surface pressures were measured with 34.47-kN/m 2 (5.0-psi) and
6.90-kN/m 2 (1.0-psi) differential pressure transducers in the 16-foot and 8-foot tunnels,
respectively. The transducer was mounted inside the model in a scanning unit, which
was capable of scanning 48 orifices with a dwell time per orifice selected to insure that
each pressure had settled out. The base pressures and any nose orifice that would be
subjected to near-stagnation conditions were measured on individual pressure transducers
located outside the test section. Free-stream static and stagnation pressures were meas-
ured on precision mercury manometers. The stagnation temperature was measured with
a platinum resistance thermometer in the 16-foot tunnel and with a thermocouple in the
8-foot tunnel.
Accuracy and Corrections
iAccuracies of the various parameters obtained in the wind-tunnel tests were deter-
mined by the root-sum-square method for combining errors from independent sources.
This method was described and used in reference i. The standard deviations at a Mach
number of 1.0 of the parameters of interest in the Langley 16-foot transonic tunnel and
8-foot transonic pressure tunnel are presented in the following table:
Parameter
M ..o....°°...°..°.....
CD .....................
Cp ....................
P_, kN/m 2
q_, kN/m 2
p, kN/m 2
Pb' kN/m2
(psi) .............
(psi) .............
(psi) ...........
(psi) .............
Standard deviation (i_)
0.002
0.001
0.001
0.007 (0.001)
0.138 (0.02)
0.014 (0.002)
0.007 (0.001)
, - • • . "4
Root-mean-square deviations are included in reference 7 for the data obtained in the
8-foot transonic tunnel at the Calspan Corporation (formerly Cornell Aeronautical
Laboratory, Inc.) and are comparable with the values presented above.
The values of drag coefficient were corrected for a base-drag coefficient computed
over the total base area. No buoyancy corrections were made to the data.
The effect of the sidewall fairings on the test-section calibration in the 8-foot tran-
sonic pressure tunnel cannot be determined, since each fairing is designed to be tested
with its corresponding model installed.
PRESENTATION OF RESULTS
Figure
Data obtained for finned model (configuration B-3) in
wind-tunnel and flight tests ........................... 5
Variation of drag coefficient with Mach number for the6various configurations .............................
Variation of base-pressure coefficient with Mach number for the
various configurations ............................. 7
Variation of drag-coefficient increment with Mach number ........... 8
Variation of drag-coefficient increment with Mach number for models of
comparable blockage ratio ........................... 9
Variation of drag-coefficient increment with blockage ratio at discrete
Mach numbers .................................. I0
Variation of drag-divergence Mach number with blockage ratio ......... 11
Variation of transonic creep Mach number with blockage ratio ......... 12
Pressure-coefficient distributions obtained for type A confi_drations ...... 13
Pressure-coefficient distributions obtained for configuration B-3 ........ 14
Pressure-coefficient distributions obtained for type C configurations ...... 15
Pressure-coefficient distributions obtained for type D configurations ...... 16
Pressure-coefficient distributions obtained for configuration E-3 ........ 17
Comparison of drag-coefficient increments obtained from both
force-balance and pressure integration ..................... 18
DIS CUSSION
Effects of Blockage Ratio on Drag
Drag coefficients.- A comparison of the variation of drag coefficient with Mach num-
ber obtained for the finned model (type B) in both wind-tunnel and flight tests is presented
10
r ¸
r
k -
in figure 5(a). The flight data are reported in reference i. The same model-sting com-
bination was tested in the 16-foot and 8-foot tunnels; the ratios of model to test-section
blockage for these tests were 9.000684 and 0.0028, respectively. The model used in the
flight test was identical to the wind-tunnel model, except that the sting was not present.
Since there was essentially no variation of axial-force coefficient over an angle-of-attack
range in the wind-tunnel data (ref. I), the axial-force coefficients from the flight test can
be compared with the drag coefficients obtained in the wind tunnel. The subsonic drag-
coefficient levels obtained in the wind tunnel agree quite well through a Mach number of
approximately 0.95, although the wind-tunnel data indicate a lower drag-coefficient level
than that of the flight data. In general the shapes of the drag curves obtained for the
model in the 16-foot tunnel (blockage ratio of 0.000684) and in flight are very similar.
The model in the 8-foot tunnel (blockage ratio of 0.0028) shows sizable differences in both
the shape and magnitude of the drag curves near M -- 1.0. These differences were
believed to be the result of wind-tunnel wall interference.
The variation of base-drag coefficient with Mach number obtained for the finned
model (configuration B-3) in both wind-tunnel and flight tests is presented in figure 5(a)
and on an expanded drag-coefficient scale in figure 5(b). The base-drag coefficients
obtained in the three tests are in good agreement throughout the Mach number range. In
figure 5(b) the expanded drag scale shows that although the trends of the data are similar
at Mach numbers below 0.95 and above 1.00, some differences occur in the levels of the
three sets of data. The main differences observed in the data can be attributed not only
to the lack of a sting in the flight test, but also to the differences in the Reynolds numbers,
since the curves tend to converge near M = 1.0 as do the Reynolds numbers (fig. 4 and
ref. i).
In order to further explore the effects of increasing the blockage of the test section,
a systematic investigation was made in the Langley 16-foot and 8-foot transonic wind
tunnels. The model-to-test-section blockage ratio varied from 0.00017 to 0.0043 in the
investigation.
The variation of drag coefficient with Mach number for each of the models tested is
presented in figure 6. Data obtained from the five type C models - three of which were
tested in two different facilities - are presented in figure 6(a). Effects similar to those
observed for configuration B-3 are apparent when comparing the data on a model tested
both in the 16-foot tunnel (the lower blockage ratio case) and in the 8-foot tunnel (the higher
blockage ratio case). As the blockage ratio is increased, the drag divergence is delayed
and the drag curve has a much less rapid rise. Furthermore, the models (configura-
tions C-5 and C-6) which have relatively large blockage ratios in the 16-foot tunnel exhibit
drag characteristics similar to those observed for the large blockage ratio cases in the
smaller tunnel. The data obtained for the type D models (fig.6(b)) also show the same
ii
effects due to increase in blockage ratio. A comparison of the data obtained for the
smallest model tested (configuration D-l), which had a blockage ratio of only 0.00017 in
the 16-foot tunnel and 0.00070 in the 8-foot tunnel, shows effects similar to those observed
for the comparison of larger blockage ratio models. The pointed-nose model (configura-
tion E-3) shows the same relative drag characteristics for the two blockage ratio cases
as the blunt-nose models. Flight data for the RM-10 (ref. 3), which was geometrically
similar to configuration E-3 for the forward three-quarters of the model, are also pre-
sented in figure 6(d). The flight model was different from the wind-tunnel model in that
it had no similar base, since the afterbody was faired into the tail boom. Also, as stated
in reference 3, the error in the drag coefficient is ±0.009 at M = 1.0 and the error in the
Mach number is no worse than +0.01. Unfortunately, the magnitude of the possible errors
in the flight data precludes any firm conclusions based on the comparison with the wind-
tunnel data.
The variation of base-pressure coefficients with Mach numbers for each model
tested is presented in figure 7. In general, the base-pressure data obtained for each of
the models in the 16-foot and 8-foot tunnels are in fairly good agreement, considering the
differences in Reynolds numbers. The only difference which may be attributable to wall
interference in the base pressures is that the Mach number at which the maximum value
of the base pressure occurs increases slightly with increase in blockage ratio - an effect
comparable to the delay in the drag divergence with increase in blockage ratio, as will be
shown in figure 11.
Drag-coefficient increments.- The variations of drag-coefficient increment with
Mach number are compared for models within a geometrically similar profile type and
are presented in figure 8 with expanded scales to show the data trends more clearly.
These drag coefficients have been adjusted to an arbitrary common level by subtracting
the value of the drag coefficient at M = 0.90 for each model. The delay in the drag diver
gence and the change in shape of the drag curves with increasing blockage ratio are quite
apparent at these values of blockage ratio whether comparing flight and wind-tunnel data
(fig. 8(a)), data from different wind tunnels (figs. 8(c) and (d)), or data for various values
of blockage ratio from one wind tunnel (figs. 8(b) and (c)).
It should be noted that for models tested at values of blockage ratio less than approx-
imately 0.0010, the shapes of the drag-coefficient curves within a profile type are essen-
tially the same near M = 1.0 (except for some creep in the curves). At first glance, this
appears to be encouraging for successful application of a fairly simple correction to data
obtained for models tested at blockage ratios less than 0.0010. However, in an 8-foot tun-
nel a limit of 0.0010 in blockage ratio would require that a body of revolution have a diam-
eter no greater than 7.62 cm (3.00 in.).
12
: i:i
Since the same model-sting combinations were tested in two different wind tunnels
at different blockage ratios and the differences in the drag data still were present, it can
be assumed that the drag differences were not due to model support interference.
For models tested at blockage ratios of 0.0028 (figs. 8(a) and (b)) and 0.00311
(fig. 8(c)), the shape of the drag curve appears to be somewhat erratic, having a bump or
increase near a Mach number of 1. The phenomenon is apparently real since it occurred
on three different models and in two different wind tunnels. The bump did not occur in
the data of models tested at smaller blockage ratios nor did it occur in the data of config-
uration D-4 (fig. 8(d)), which was tested at a blockage ratio of 0.0043 in the 8-foot tunnel.
Data obtained from geometrically similar models (type C), which have comparable
blockage ratios in different wind tunnels, are presented in figure 9. The variations of the
drag-coefficient increment with Mach number for the models tested at comparable block-
age ratios are nearly identical throughout the Mach number range from 0.90 to 1.01. This
agreement indicates that the discrepancies observed for the models tested at various
blockage ratios apparently result from effects of wall interference due to model blockage
of the test sections. Since models tested at similar unit Reynolds numbers and at com-
parable blockage ratios in different size test sections have different model Reynolds num-
bers, this agreement also indicated that there were no significant Reynolds number effects.
The variation of incremental drag coefficient with blockage ratio at which a model
was tested is presented in figure 10. Each faired line and its symbol represent the data
obtained at one Mach number for models tested at several blockage ratios. The data
obtained for all the profile types tested show similar variations of drag coefficient with
blockage ratio. Since the data being compared were obtained for models which were geo-
metrically similar in profile, the drag-coefficient levels should have been the same except
for very small differences in this Mach number range due to model Reynolds numbers.
For Mach numbers of 0.99 and higher, the data obtained at the low blockage ratios show
fairly large drag-coefficient increments. However, as the blockage ratio increases, the
drag-coefficient increments decrease, and models tested at blockage ratios greater than
approximately 0.0010 show only a very small, nearly constant increase in drag increment.
A value of blockage ratio of 0.0050 generally has been considered to be sufficiently low to
avoid significant effects of wall interference. However, it should be noted in figure 10(b)
that a model such as type B tested at a blockage ratio of 0.0028 (approximately one-half of
the previously accepted "safe" value) at a Mach number of 1.00 yielded a drag-coefficient
value which was 0.057 lower than the flight value. Furthermore, at a blockage ratio of
0.00068 and a Mach number of 1.00 the wind-tunnel drag coefficient was still 0.042 lower
than the flight value.
The data obtained for type B at the three values of blockage ratio indicate the gen-
eral trend of drag coefficient with blockage ratio; however, no data were obtained for this
13
i ¸¸ : i • •
model which could show the trend as zero blockage ratio is approached in the wind tunnel.
It does appear from the type D data in figure 10(d) that obtaining data near M = 1.0
which are free of significant effects of wall interference would require extremely small
models permitting only meager instrumentation.
Drag-divergence Mach number.- The variation of drag-divergence Mach number
with blockage ratio of the four types of geometrically similar models is presented in fig-
ure 11. Drag-divergence Mach number is defined as the free-stream Mach number at
which the direction of the tangent vector to the curve of drag coefficient plotted against
Mach number is changing most rapidly with distance along the curve, that is, the Mach
number at which the radius of curvature is a minimum. The drag-divergence Mach num-
ber increased by approximately 0.013 (from M = 0.980 to 0.993) for an increase in block-
age ratio from about 0.0002 to 0.0010. For values of blockage ratio greater than 0.0010,
the drag-divergence Mach numbers for types A, C, and D remain approximately constant.
Only three values of blockage ratio were tested for type B, and the curve is not well
defined. The trend of increasing drag-divergence Mach number with increasing blockage
ratio is opposite from the result that would be expected for subsonic flow in which the
test-section walls are too closed (i.e., an increase in the effective free-stream Mach
number at the model causing a premature rise in drag). In contrast, near M = 1.0 the
results are more like those that would be expected for subsonic flow in which the test-
section walls are too open (i.e., a decrease in the effective free-stream Mach number at
the model accompanied by the delay in the drag rise).
Transonic-creep Mach number.- The variation of transonic-creep Mach number
with blockage ratio is presented in figure 12. The experimental wind-tunnel data, repre-
sented by the symbols, were obtained by determining the Mach number at which the drag
curve begins to deviate consistently by 0.0010 or more in drag coefficient from a straight
line passed through the subsonic data (i.e., 0.70 < M = 0.92). The curve in figure 12 is
faired through the free-stream Mach numbers that would correspond to choked flow at the
point of minimum cross-sectional area of the test section due to the presence of each
model. This calculation assumes that the walls are solid and neglects the relieving effects
of the slots. The free-stream Mach number is calculated for each value of blockage ratio
by using the stream-tube area relations of continuous, one-dimensional flow. By com-
paring figures 12 and 11, it appears that for blockage ratios less than 0.0003 the transonic
creep is masked by the beginning of the drag-divergence region. The agreement of the
Mach numbers at the initiation of creep in the drag curves with the calculated Mach num-
bers for choked flow in a solid-wall tunnel indicates that the creep results from the inter-
ference of the wall with the rapid lateral growth of the model flow field as a Mach number
of unity is approached. Consequently, the transonic creep may be the first indication of
significant wind-tunnel wall interference near M = 1.0. Therefore, the flow relief
afforded by slots or perforations - designed according to previously accepted criteria
14
for interference-free subsonic flow (for example, ref. 8) - does not appear to be sufficient
to avoid significant interference of the walls with the model flow field for Mach numbers
very close to 1.0.
Effect of Blockage Ratio on Pressure Distributions
Surface-pressure-coefficient distributions are presented for all models in figures 13
to 17. Pressure data were obtained in both the 16-foot and 8-foot transonic tunnels at the
Langley Research Center and also in the 8-foot transonic tunnel at the Calspan Corporation
for configuration C-3. The pressure coefficients are plotted against the center-line dis-
tance from the model nose which is nondimensionalized by the reference length of the
particular model. Pressure data are presented for each model at all test conditions in
each facility; unfortunately, no pressure data were obtained in the flight test.
For Mach numbers below approximately 0.96, the general trend of the pressure
distributions obtained for the model types A and C (figs. 13 and 15) is a smooth distribution
consisting of a rapid expansion around the nose, a rather flat distribution over the mid-
section of the model, and a fairly rapid compression to the base. The pressure distribu-
tions obtained for the models of types B and D (figs. 14 and 16) are quite similar to the
distributions obtained for types A and C. The pressure distributions of the type D models
generally show a small region of overexpansion around the nose and have a more gradual
compression to the base which begins nearer the longitudinal midpoint of the model than
do the compression regions for types A and C. The pressure distributions obtained for
the same model tested at two different blockage ratios show good agreement, provided
that the local flow around the model is substantially subsonic. However, for Mach num-
bers greater than approximately 0.96, a supersonic region develops around the model. As
the free-stream Mach number is increased toward unity, a discrepancy begins to appear
in the data obtained for the same model tested at identical free-stream conditions but at
two different blockage ratios. Comparlson of the pressure distributions for the two
values of blockage ratio shows a positive increment of pressures on the moclel tested at
the larger value of blockage ratio. The affected region typically maintains a constant size
and tends to move downstream on the model as the free-stream Mach number is increased.
(See configuration C-2 in figs. 15(c) and (d).) The location of the region of increased sur-
face pressures in conjunction with the geometry of the model determines the extent and
direction of the interference effect on the drag coefficient. Increments in pressure drag
that result from these differences in the pressure distributions obtained for configura-
tion C-2, at two different blockage ratios (figs. 15(a) to (d)), correspond quite well with the
trend of the differences observed between the two sets of drag data obtained for this con-
figuration (fig. 6(a)). The correspondence between the interference effects in the pressure
and drag measurements obtained from M = 0.90 to 1.02 was typical of the data obtained
15
for models tested at various blockage ratios, as canbe seen for three configurations in
figure 18. Therefore, in the transonic Machnumber region, the interference of the wallwith the model flow field apparently producesanadditional pressure increment, thus
altering the value of the drag coefficient.
Surface-pressure-coefficient distributions obtainedfor configuration E-3, thepointed-nosemodel, in the 16-foot and 8-foot transonic tunnels at Langley andin the flighttest of the RM-10 (ref. 3) are presented in figure 17. The data obtainedin the wind tunnelsagree fairly well through a Machnumber of approximately 0.95; at higher Machnumbers,discrepancies similar to those observedfor the blunt-nose modelsbegin to appear. Theeffects of wall interference on the pressure distributions are the same for the pointed-nosemodel as for the blunt-nose models. The distributions obtainedfor the RM-10 in theflight test generally showonly fair agreementwith the wind-tunnel data over the similarportion of the models and, as expected,no agreementnear the back where the models weredifferent. These results are not surprising, since the estimated maximum inaccuraciesin the pressure coefficients from the flight test were stated in reference 3 to be =_0.04atM = 0.75 to ±0.02 at M = 0.95 and to +0.004 at M = 1.27. Therefore, no firm conclu-
sions can be drawn by comparing the pressures measured in the flight test with those
measured in the wind-tunnel test.
Pressure coefficients, calculated for configuration E-3 by the program of refer-
ence 9, are indicated by the faired lines in figure 17. The comparison of this theory with
the experimental data shows good agreement through a Mach number of 0.997, which was
unexpected since this is a subsonic theory.
CONCLUSIONS
The results of this investigation of bodies of revolution confirm that drag-coefficient
values obtained at transonic flow conditions near a Mach number of 1.0 in wind tunnels are
affected by wall interference with the model flow field.
There were three specific effects on the drag data that occurred near a Mach num-
ber of 1.0 as a result of increasing the test-section blockage ratio for a given model
profile:
i. The shape of the drag curves changed from a relatively rapid increase to a very
gradual increase in drag with increasing Mach number. This change occurred for
increases in test-section blockage ratio above approximately 0.0010. The shape of the
drag-coefficient curves, obtained at values of test-section blockage ratio less than 0.0010,
was relatively insensitive to changes in blockage ratio.
2. Increasing the blockage ratio above approximately 0.0003 produced a premature,
positive deviation, or transonic creep, of the drag curve from the trend of the subsonic data
16
Since the Mach number at the initiation of transonic creep agrees with the calculated
Mach number for choked flow in a solid-wall tunnel, transonic creep may be the first
indication of significant wind-tunnel wall interference near a Mach number of 1.0.
3. The occurrence of drag divergence was delayed by approximately 0.013 in Mach
number due to an increase in blockage ratio from 0.0002 to 0.0010. For blockage ratios
greater than 0.0010, the drag-divergence Mach number was essentially constant. There-
fore, near a Mach number of 1.0, increasing the blockage ratio delays the occurrence of
drag divergence - the result that would be expected due to an effective decrease in the
free-stream Mach number at the model.
There was only one obvious effect of wall interference on the model surface-
pressure distributions obtained for a given model shape at different values of blockage
ratio. For Mach numbers greater than approximately 0.96, a region of supersonic flow
existed around the models. An increase in the value of blockage ratio for Mach numbers
greater than 0.96 caused a positive increment of pressure to occur on the model. The
effect on the drag data of this pressure-drag increment coincided quite well with the
change in shape of the drag curves.
The results of this investigation indicated that models having values of test-section
blockage ratio of 0.0003 - an order of magnitude below the previously considered "safe"
value of 0.0050 - had significant errors due to wall interference in the drag-coefficient
values obtained near a Mach number of 1.0. Furthermore, the flow relief afforded by
slots or perforations in test-section walls - designed according to previously accepted
criteria for interference-free subsonic flow - does not appear to be sufficient to avoid
significant interference of the walls with the model flow field for Mach numbers very
close to 1.0.
Langley Research Center,
National Aeronautics and Space Administration,
Hampton, Va., July 2, 1973.
17
i_ ..... _ i
L
REFERENCES
I. Usry, J. W.; and Wallace, John W.: Drag of a Supercritical Body of Revolution in
Free Flight at Transonic Speeds and Comparison With Wind-Tunnel Data. NASA
TN D-6580, 1971.
2. Schlichting, Hermann (J. Kestin, transl.): Boundary Layer Theory. Fourth ed.,
McGraw-Hill Book Co., Inc., c.1960.
3. Thompson, Jim Rogers: Measurements of the Drag and Pressure Distribution on a Body
of Revolution Throughout Transition From Subsonic to Supersonic Speeds. NACA
RM L9J27, 1950.
4. Cahn, Maurice S.: An Experimental Investigation of Sting-Support Effects on Drag and
a Comparison With Jet Effects at Transonic Speeds. NACA Rep. 1353, 1958.
(Supersedes NACA RM L56FI8a.)
5. Braslow, Albert L.; and Knox, Eugene C.: Simplified Method for Determination of
Critical Height of Distributed Roughness Particles for Boundary-Layer Transition
at Mach Numbers From 0 to 5. NACA TN 4363, 1958.
6. Braslow, Albert L.; Hicks, Raymond M.; and Harris, Roy V., Jr.: Use of Grit-Type
Boundary-Layer-Transition Trips on Wind-Tunnel Models. NASA TN D-3579, 1966.
7. Chudyk, D.W." Transonic Wind Tunnel Tests of Several NASA Bodies of Revolution.
Rep. No. AA-4018-W-5 (Contract No. NAS 1-10649), Cornell Aeronaut. Lab., Inc.,
Jan./Mar. 1971. (Available as NASA CR-I12069.)
8. Goethert, Bernhard H.: Transonic Wind Tunnel Testing. AGARDograph No. 49,
Pergamon Press, 1961.
9. Hess, J. L.; and Smith, A. M.O.: Calculation of Potential Flow About Arbitrary Bodies.
Progress in Aeronautical Sciences, Vol. 8, D. K_chemann, ed., Pergamon Press,
Ltd., c.1967, pp. 1-138.
18
_'i_:!_ i i__
/
TABLE I.- MODEL DESCRIPTION
Configuration
A-2
A-3
A-4
B-3
C-2
C-3
C-4
C-5
C-6
D-I
D-2
D-4
E-3
Maximum Length Reference Basediameter length diameter
cm in. cm in. cm in. cm in. 16 ft TT
8.99 3.54 80.85 31.83 81.64 32.14 2.29 0.90 .......
12.70 5.00 114.30 45.00 115.45 45.45 3.18 1.25 .......
15.70 6.18 141.22 55.60 142.72 56.19 4.14 1.63 .......
12.70 5.00 114.30 45.00 115.45 45.45 3.18 1.25 0.000684
8.99 3.54 85.34 33.60 81.64 32.14 2.29 .90 .000343
12.70 5.00 120.65 47.50 115.45 45.45 3.18 1.25 .000684
15.70 6.18 149.10 58.70 142.72 56.19 4.11 1.62 .00104
22.25 8.76 210.24 82.77 202.03 79.54 6.35 2.50 .00210
27.08 10.66 257.02 I 101.19 245.95 96.83 7.06 2.78 .00311
6.35 2.50 60.58 23.85 57.73 22.73 1.78 .70 .000170
8.99 3.54 85.85 33.80 81.64 32.14 2.29 .90 .000343
15.70 6.18 150.22 59.14 142.72 56.19 4.14 1.63 .......
12.70 5.00 137.62 54.18 152.40 60.00 3.18 1.25 .000684
CylindricalBlockage Sting sting
ratio diamete r length
8 ft TPT cm in. cm ] in.
m
0.00140 1.78 0.70 21.59 / 8.50
.00280 2.54 1.00 35.31 13.90
.00430 3.51 1.38 43.94 17.30
.00280 2.54 1.00 34.93 13.75
.00140 1.78 .70 17.02 6.70
.00280 2.54 1.00 22.56 8.88
.00430 3.51 1.38 25.63 10.09
....... 5.72 2.25 44.20 17.40
....... 5.72 2.25 25.76 10.14
.000698 1.27 .50 17.78 7.00
.00140 1.78 .70 17.02 6.70
.00430 3.51 1.38 35.05 13.80
.00280 2.54 1.00 28.50 11.22
Included
angle ofsting flare,
deg
6
6
6
6
6
6
6
8
8
6
6
6
6
i ¸ : •
i• ,
x//lref
0
.002
.004
.005
.006
.0075
.008
.010
.0120
.0125
.0140
.0160
.0180
.0200
.0250
.0400
.0500
.0600
.0750
.0800
.1000
.1200
.1400
.1500
.1600
.1800
.2000
.2400
.2500
.28OO
.3000
.3200
.3500
.4000
.4500
TABLE II.- NONDIMENSIONAL MODEL COORDINATES
R//lref
Type A
0
.00696
.00946
.01134
.01291
.01422
.01539
.01645
.01742
.01832
.01916
.02556
.03005
.03357
.03648
.03894
.04108
.04295
.04460
.04607
,04855
.05052
.05207
.05412
Type B
0
.00696
.00946
.O1134
.01291
.01422
.01539
.01645
.01742
.01832
.01916
.02556
.03005
.03357
.03648
.03894
.04108
.04295
.04460
.04607
.04855
.05052
.05207
.05412
Type C
0
.00696
.00946
.01134
.01291
.01422
.01539
.01645
.01742
.01832
.01916
.02556
.03005
.03357
.03648
.03894
.04108
.04295
.04460
.04607
.04855
.05052
.05207
.05412
Type D
0
.OO713
.00969
.01159
.01316
.01450
.01570
.01678
.01777
.O1868
.01954
.02604
.03060
.03416
.03709
.O3958
.04172
.04360
.04525
.04671
.04915
.05108
.05256
.05443
Type E
0
.00232
.00298
.00428
.00722
.0121
.0161
.0197
.0259
.0309
.0347
.0374
.0393
.0406
.0414
2O
i ¸ : •
TABLE II.- NONDIMENSIONAL MODEL COORDINATES - Concluded
X/iref I R/lref
Type A Type B Type C Type D Type E
0.4800
.5000
.5200
.5500
.6000
.6500
.6800
.7000
.7200
.7500
.7600
.8000
.8200
.8400
.8500
.8600
.8800
.9000
.9030
.9200
.9400
.9600
.9700
.98OO
.9900
1.0000
1.0100
1.0200
1.0300
1.0400
1.0450
1.0532
0.05497
.0550O
.05497
.05412
.05207
.05052
0.05497
.05500
.05497
.05412
.05207
.05052
0.05497
.05500
.05497
.05413
.05213
.05065
0.05500
.05495
.05483
.05358
.05107
.04934
.04855
.04607
.04460
.04295
.04108
.O3894
.03648
.03357
.03005
.02556
.02271
.01916
.01422
.O4855
.04607
.04460
.04295
.04108
.03894
.03602
.03178
.02650
.02047
.01745
.01511
.01422
.O4881
.04658
.04530
.04390
.04235
.04066
.03879
.03673
.03444
.03186
.03044
.02892
.02728
.02549
.02354
.02136
.01888
.01596
.01423
.04725
.04481
.04344
.04196
.04037
.03867
.03683
.03484
.03268
.03032
.02906
.02773
.02632
.02483
.02323
.02150
.01962
.01753
.01642
.01423
0.0417
.0413
.0402
.0384
.0356
.0313
.0253
.0185
.0113
.0104
21
k
" ) i •
b_
TABLE Ill.- NONDIMENSIONAL PRESSURE-ORIFICE LOCATIONS
Pressure i
orifice Configuration Configuration Configuration
A-2 1 A-3 A-4
1 0 ..... 0
2 .0311 ..... .0178
3 .0467 0.0297 .0257
4 .0622 .0396 .0356
5 .0778 .0594 .0446
6 .0933 .0891 .0534
.1089 .1069 .0623
8 ,1245 .1287 .0712
9 .1556 .1485 .0801
10 .1867 .1683 .0890
11 .2178 ..... .0979
12 .2489 .2079 .1067
13 .2800 .2475 1246
14 .3111 .2970 1424
15 .3422 .3465 1780
16 .3734 .3960 .2136
17 .4045 .4455 .2492
18 .4356 .4950 .2848
19 .4667 .5445 .3203
20 .4978 .5940 .3559
21 .5269 .6435 .3916
22 .5600 .6831 .4272
23 .5911 .7227 .4626
24 .6223 .7623 .4984
25 .6534 .8019 .5339
26 .6845 .8217 .5695
27 .7156 .6415 .6051
28 .7467 .8613 .6408
29 .7778 .8811 .6764
30 .8089 .9009 .7119
31 .6400 .9207 .7475
32 .6556 .9405 .7631
33 .8712 .9603 .8187
34 .8667 .8543
35 .9023 .8721
36 .9176 .6900
37 .9334 .8988
38 ,9489 .9077
39 .9645 .9166
40 .9255
41 .9344
42 .9433
43 .9522
44 .9611
45 .9700
46
47
48
X/lref
:onfigur ation I : on f __nfi_llr a-tion
B-3 C-2 _ _ C-3 C-4
O0o9 66. l-0. o:o-o8;.0311 I .0196 .0176
I
.0196 .0467 I .0297 .0267I
.0297 .0622 .0396 .0356
,0396 .0776 .0594 .0445
.0594 .0933 .0691 .0534
.0891 .1089 .1089 .0623
.1089 .i245 .1287 .0712
.1287 .1556 .1485 .0801
.1485 .1867 .1683 .0890
.1683 .2178 .1881 .0979
.1981 .2489 .2079 .1068
.2079 .2800 .2475 .1246
.2475 .3111 .2970 .1424
.2970 .3423 .3465 .1780
.3465 .3734 .3960 .2136
.3960 .4045 .4455 .2492
.4455 .4356 .4950 .2846
.4950 .4667 .5445 .3204
.6445 .4978 .5940 .3560
.5940 .5289 .6435 .3916
.6435 .5600 .6831 .4272
.6831 .5912 .7227 .4628
.7227 .6223 .7623 .4984
.7623 .6534 .8019 .5339
.8019 .6845 .8217 .5695
.8217 .7156 .6415 .6051
.8415 .7467 .8613 .6407
.8613 .7778 ,8811 .6763
.8811 .8090 .9009 .7119
.9009 .8401 .9207 .7475
.9207 .8556 .9405 .7831
.9405 .8712 .9603 .8187
.9603 .8867 .9801 .6543
.9801 .9023 .9999 .6721
.9179 1.0197 .8899
.9334 1.0395 .9077
.9490 .9255
.9645 .9433
.9956 .9611
1.0112 .9789
1.0268 .9678
.9967
1.0056
1.0145
1.0234
1.0323
Configurat_ion] Configuration Configuration
C -5_ C -6 D-Io o--.0089 .0089 0.0175,0219
.0178 I ,0178
.0267
.0356
.0445
.0534
.0623
.0712
.0801
.0890
.0979
.1068
.1246
.1424
.1780
.2136
.2492
.2848
.3204
.3560
.3916
.4272
.4628
.4984
.5339
.5695
.6051
.6407
.6763
.7119
.7475
.7831
.8187
.8543
.8721
.8899
.0967
.O356
.0445
.0534
.0623
.0712
.0801
.0890
.0979
.1066
.1246
.1494
.1780
.2136
.2492
.2848
.3204
•3560
•3916
.4272
.4628
.4984
.5339
.5695
.6051
.6407
.6763
.7119
.7475
.7831
.6187
.8543
.8721
.6899
.9077 .9077
.9255 .9265
.9433 ,9433
.9611 ,9611
.9789 .9789
.9878 i .9878J
.9967 .9967
1.0145 1.0056
1.0234 1.0234
1.0323 1.0323
.0329
.0438
.0548
.0657
.0876
.1095
,1314
.1534
.1753
.1972
.2191
.2410
.2629
.2848
.3067
.3505
.3943
.4382
.4820
.5256
.5696
.6134
.6572
.7010
.7449
.7666
.7887
.8106
.8325
.8544
.6763
.8982
.9201
.9420
.9596
.9771
.9946
1.0121
1.0297
0.014
.0311
,0467
.0622
.0778
.0933
.1089
.1245
.1556
.1867
.2176
.2489
.2800
.3111
.3423
.3734
.4045
.4356
.4667
.4978
.5289
.5600
.5912
.6223
.6534
.6845
.7156
.7779
.8090
.6245
.6401
.8556
.8712
.8868
.9023
.9179
.9334
.9645
.9956
1.0266
1.0517
1.0517
.0979
.1067
.1246
.1424
.1780
.2136
.2492
.2848
.3204
.3560
.3916
.4272
.4628
.4984
.5339
.5695
.6051
.6407
.6763
.7119
.7475
.7831
.8187
.6543
.8721
.6899
.9077
.9255
.9433
.9611
.9789
.9876
.9967
1.0056
1.0145
1.0234
1.0323
_onfiguration ]
E-3
0.0050
.0130
.0250
.0500
.0750
.1000
.1500
.2000
.2500
.3000
.3500
.4000
.4500
.5000
.5500
.6000
.6500
.7000
.7500
.8OOO
.8500
.8750
H:
c_ c
A 2 80.85,31.83}
8.99 c_____3. 541
A 5 114.30 12.70 _._
(45.001 (5.00)
15.70_ 141.22(55.601 (6.181
B 3 114.30 12.70 ____
(45.00) 15.00l
o
___ -=
C 2 85.34 8.99 _
(33.60) (3.54}
c 3 120.65 12.7o C_._147.5m (5.oo)
C 4 149.10 15.70(58.70} (6.18}
f
C 5 210./4 22.25(82.77) (8.76)
fC 6 257.02 27.08 k._
(I01.19) (10.66)
ZCc]
E 3 137.62 !2.7054.18) (5.00)
D 1 60.58 6.35 (
123.85) (2.50)
D 2 85.85 8.99 _
(33.80) (3.54)
D 4 150.22 15.70(59.14) (6.18)
Figure 1.- Model sketches. (Dimensions are given in centimeters (inches).)
boOo
• /
Slots
Body of revolution
Movable circular-arc
support strut
Cross-sectional view of test section showing location of eight slots
Region ofmodel installation
Total slot openingI
Ipercent of wall perimeter)____.,. 4, ill 16
\\
Slot configuration
Figure 2.- Test-section configuration o£ Langley 16-foot transonic tunnel.
24
Movable circular-arc support strut
.Body of revolution
_--Diffuser entrance flap
Cross-sectional view of test section showing location of eight slots
Total slot opening
(percent of
wall perimeter)----'-
._-Region of model installation-_i
2
i
5 10
/.---J
\
Slot configuration
(a) Distribution and shape of slots.
Figure 3.- Test-section configuration of Langley 8-foot transonic pressure tunnel.
25
b_
Flow
_X/--I ndented to_' match model
cross-sectional
ar ea
distribution jFairings
""-- Fairings
Test section - top view
\ Fairings_
_--Fairings % \"\Model
Photograph of sidewall fairing strip installed in the test section
Test section - end view
Location of sidewal fairing strips
(b) Installation of sidewall fairing strips in test section.
Figure 3.- Concluded.
Conf.No
A-2
A-3
20 x 106 A-4
16
12-
Re
8
d
Oy-Conf.
slo.
C-2
C-3
C-4
C-5
C-6
36 Io
28
-- Z
24
20
NRe ._
16 Ib
12 --
8
]6 Ft. 8 Ft.-_ TPT
16 Ft. 8 Ft.
TT TPT
< - _ >
-- - -v- (
Type C
8 Ft.TT-CAL
0.7 .8 .9 l.O 1.1
M
Conf. 16 Ft, 8Ft.No.
IT TPI
3-3 o -
E-3 -
__ _( _A---- - ----
q
q
Flignt
I
C -_-_- Types B and E ' 1
Conf. 16 Ft. 8Ft.No. TT TPl
D-I o
D--2 ......
D-4
..... C_] _
.7 ,8
5:]
FType D
[[.9 1.0
M
Figure 4.- Variation of NRe with M for the various models.
27
.28
.... 16 Ft. _"
---o--- 8Ft. TPT
,_ Flight , reference1
.24
.2O
.16
CD
• 12
(
.08
.Oa
CD.b )
-. 0468
4S<>
I
!
I
76 .84 .92 1.00 1.08M
(a) Variation of CD and CD, b with M.
CD.b
-.Ola
-.012
-.010
E-. 008
-. 006 -
---o---I6 FI TT
cG 8 Ft. "i-PT
Flight reference 1 )
IJ
0_.- _
,--/ 0<-©
<0
0
_Oc bO,<>
-.004. 68 76 .84 M .92 1.00
I
1.08
(b) Variation of CD, b with M (expanded CD, b scale).
Figure 5.- Data obtained for finned model (configuration B-3) in wind-tunnel
and flight tests.
28
• 16
• 12
08
CD
08
04
• 04
• 04
04
Configuration C-2
/'I,V
Configuration C-3
C fig ration C-4
i I I Ii t I ti I It
I t
Configuration C-5
"I'/IIi
Configuration 0-6
Conf. ].6 Ft. 8 Ft. 8 Ft. TTNo. TT TPT CAL
C-2 _ -- ,oC-3 ---m-- - ,m _,_--
C-4 ---O--- - _ -
C-5
C-6
-- -=
.90¥
/
_4 _- _
0.80 .85 .95 1.00 1.05
(a) Type C.
Figure 6.- Variation of CD with M for the various configurations.
29
¢oo
.16
•12
.08
•04
0
CD.08
.04
Configuration
Configu ration
Conf. 16Ft. 8 Ft.No. TT TPT
D-1 + ---_t_----D-2 _ ---_ ....D-4 ----_---
........... )_,..... E---::___q,;._ ___ :z._-q_
_% ............ _:_:_ >--c .--_ >_:_
I
/
/
.08
•04
0•80
Configuration
....... •-t .............
•85 .90 .95M
(b) Type #.
Figure 6.- Continued.
i1.O0 1.05
• 16
Conf•No.
A-2
A-3A-4
8 Ft. TPT
• 12
.08
• 04
0
CD
.08
.04
.08
.04
(c) Type A.
CD
.24
20
• 16
• 12
.08
I
.04 --
O.80
Configuration E-3
• 85
16Ft. "iT
---,,_---- 8 Ft. TPT---¢<--- Flight -eference 3 )
k----Z
L/
/
/i
/
• 90 .95 1. O0 l. 05M
(d) Type E.
Figure 6.- Concluded.
31
.24
Conf. 16 Ft. 8 Ft. 8 Ft. --No. TT TPT CAL
C-2 _ ---,o- - -C-3 _ --=a .... -_-
C-4 _ ---9-- -C-5 _--C-6
.2O
• 16
• 12
.08
.04
0
.08
04
CP,b 0
.08
.04
.08
• 04
.O8
.04
080 .85
Figure 7.- Variation of
.90 .95 1.00 1.05
(a) Type C.
Cp, b with M for the various configurations.
32
"j.20
• 16
• 12
.08Configuration D-1
Conf 16Ft. 8 Ft.No. TT TP[
D-1 + .... : ....D-2 _ --- © ....
D-4 .... _ ....
n\
Cp,o
.04
.08
.04
.08
Configuration )-2[
ConfigurationI[:)-4
.04
8C • 85 .90 .95M
I1.O0 1,05
(b) Type D.
Figure 7.- Continued.
33
•24
.20
• 16 Co_figuration
Conf• 8Ft.No. TPT
A-2 -- p----A-3 ---;_ ....
A-4 - - -42---
• 12
.08
.04Configuration
...... _.__- ZY- ' "5
0
Cp,b
.08
• 04
Configuration A-4
\x
,>
.08
• 04
20
15
12
Cp,b
.08Configuration E-3
•O4
(c) Type A.
----o--- 15Ft. TT--_-- 8Ft./PT
\
080 .85 .90 .95 t. O0 1.05
(d) Type E.
Figure 7.- Concluded.
34
•• _ k,i ¸,
',___i_._,_i,_i_"•••' ' i_ :i _i _ '
CD
0
oo_
b--b---
\
\\ \
K
\
\
\
\
,I 1
\
0
00
cxDCr_
C_
C_d
CO
0 .v._
o0
0 ,-_c.)_ 0
0
1
g
00 0
06"=W0 0
0 00
0C_
0
I
35
.... ?
_:i ;i i/_ i _
.... iii;_ _
L
I--I--
O0 I----
On "_" O00_CO 0 r"_ C',,J _r
0_ rYm
. CX.I 0"_ '_t"t-- 0 I I I
0
\
\
\
\ \
l!
il
0
00
O0
C_
g.
C_
0
0-,
0
0I
O0
ol.-I
Cx.J
0"
0 0 0 0
06"=Wfl 3 _ 0 3
C_
0C_
C)
I"
36
- • • • .
. • . .: - ,
- .- . . ..
._> i ¸¸. •
i
.r
• 12
. I0
•08
0
,,• •06
0
I
.04
•02
.92
I_6Ft. TT
BlockageRatio
.00034
.00068.00104.00210.00311
i"
.94
8 Ft. TPT
Conf• BIockageNo. RatioC-2 .o .0014C-3 p .0028C-4 _ .0043C-5C-6
.96
M
/
.98
:
/ 1!
11tl
I//
/ f-
I. O0
/
J//I
/ /i1 I
/ /
//i
/
/
!
//
/ !
/
1.02
(c) Type C.
Figure 8.- Continued.
,k ¸ .
oo
12
16 Ft. TT
BlockageRatio
.00017
.00034
Conf.
NO.
D-1D-21:)-4
8 Ft. TPT
BlockageRatio
.00070
•00]40•00430
10
.08
oo',
:_ .06
(_3
I
C.D.04
• 02
///
It
II
I II
,/
/
i!/
1!
1/
zl
/
/
//
/!
/
_J
.92 •94 .96
M
(d) Type D.
Figure 8.- Concluded.
.98 1. O0 I. 02
Conf. BlockageNo. Ratio
.O4
0
°i. 02II
I
-. 02
z_ C-.5 .0021
c-3 .0o2t16 Ft. TT8Ft. TT -CAL
LI
O
I
.04 - -L.....!
O
_.. 02II
0 "_
-. 02.90
Conf. BlockageNo. Ratio
C-3 .0028
C-6 .0031
8 Ft. TPT
16 Ft. TT
• 94 .98 I. 02M
Figure 9.- Variation of drag-coefficient increment with
comparable blockage ratio.
M for models of
39
i : • •
0
• O5
Mach 8 Ft.No. TPT
.98 P
.99 P1.00 _>1.01 /_
o
E_0
I
r-_
.O4
•O3
• O2
.01
_k
<_
/
00 .0008 .0016 .0024 .0032 .0040
BIockage ratio
©
.0048
(a) Type A.
Figure i0.- Variation of drag-coefficient increment with blockage ratio at discrete Mach numbers.
,i
)
O0
c_ Z
0
0
_o '-4
°,,._
o
Tsa
06 GO"=W(]3 _
41
7
:\
! 4
• 12
.11
%\
• 10
\.09
• 08.07 _
v_°_o_ _
_"-" ..0405
.03
.02
.01
1\
\
\\
\
MachNo.
•980•985•990• 99.5
I. 000I. 010I. 020
16 Ft.
TT
o
[]©
8 Ft.TPT
P
P
\
\
\\
\\
\\
\
\\
_ --_---_:: =--::_
-.01.0008 • 0016 .0024
Blockage ratio
(c) Type C.
Figure 10.- Continued.
•0032 .0040 .0048
42
• _i : i!_ L •...... i iiil
i ¸¸ / ,
oO
C_
F
_L
0 0 0 0 CD 0 0
06"=W(l3 _ (I3
43
44
Jaqwnu q3eW a3uaQa^!p-6eJ(]
00m
,,..)0
t",m
k
bb
0r_
o,_
,.O
bO
Ibb
©
©0r-i
0,_,-4
I>I
,i.,-.I
(D
bb
_#00"
"o_l_a o_mtoolq ql_maoqtunu qo_IAI doa2o-o_uosu_a] 3o uo!l_a_A -'_I o_n_,;[
@00" _00" _00" 9100" 8000" 0_6"
I.O
[]
-IV3 - II "_.J8 vIdl q.-I8 []
II q-J 9[ o
e_ep le_UOW!Jadx3 - sloqLuXS
lauum, lleM-p!los _oj W po)loqo - aAJn3
"--_C-.,..,
,-...,
iqB!IJ
\\
\D
_6"
96"
_6"
O0"I
W
- _. -
il :, i _i:!:i/_:_ i ;
, "=7 • • L /-
i¸ :: C" : " :
• U_ ,i__, •
-2
Mach 8 Ft.No, TPT
•85 ,0.90.95 9.98
/ :iI • •
-1
2
-.1
-.2
-.I
0
.I
.2
-.2
-.]
2
46
0 .i .2 .3 .4 5 .6 .7 8 .9 1.0
xl I ref
(a) Configuration A-2; 0.85 < M < 0.98.
Figure 13.- Pressure-coefficient distributions obtained for type A configurations.
_iiiii _ : :!
"u _ _ , _ i_ . _
_ii_;: :i _i I:i_,':/
ii_ •
Cp
-.2
-.1
.1
.3
-.2
-.1
.1
.3
-.2
-.1
.3.2 .3 4 5 .6
x/I ref
.7 .8 9 1.0
(b) Configuration A-2; 0.991 < M < 1.011.
Figure 13.- Continued,
47
"_ _, _i _'
•_:I_II• •
-.i
.I
.2
.3
-.I
Math 8 Ft.No. TPT
• 85 ,O
.90 E3
.95.98
.3
Cp
.i
.2
.3
.i
I .2 3 .4 .5 .6 .7 .8 .9
X/Ire f
(c) Configuration A-3; 0.85 <_-M -< 0.98.
Figure 13.- Continued.
1.0
48
Math 8 Ft.
No. TPT
.991 ,0
1.0001.01].
] .2 .3 .4 .5 6 .7 .8xl I rel
(d)Configuration A-3; 0.991 _-<M _-<1.011.
Figure 13.- Continued.
10
49
i ¸
: !il i ¸ :
-.2
0
.i
.2
-.2
.I
Mach 8 Ft.No. TPT
• 85 ,0
• 9o p.95 <#.98
.2C
D
_2
_2
0 .l 2 .3 .4 .5 .6 7 .8 9 1.0x/
ref
(e) Configuration A-4; 0.85 _-<M -<0.98.
Figure 13.- Continued.
50
ii__i ::i_i!_
'9' i
• i _
i _i:_
-.2 --
=1
0
.1
.2 >
.3
-.2
=1
Cp 0 --
.1
3.2
.3
=2
-.1
0 --
1
g.2
.30
Math
NO.
.99
].00
1.01
3 J
b
8 Ft.TPT
,oP9
.1 .2 .3 .4 x/I .5ref
¢>
.[ [3
) ;
;>,
.E: 3
.8
(f) Configuration A-4; 0.99 -<M _-<1.01.
Figure 13.- Concluded.
1.0
51
Mach 16 Ft.
No. TT
• 699 0
• 800 []
CP
.3
0 ] .2 .3 .4 .5 .6 .7 .8 .9 1.0
X/Ire f
(a) 0.699 < M < 0.800
Figure 14.- Pressure-coefficient distributions obtained for configuration B-3.
52
:i
_ L _ . :
Cp
3
Mach 16 Ft. 8 Ft.
No. TT 1-PT
• 849 O ,C,
•900 []
.3 .4 5 6 .7
x/I ref
(b) 0.849 < M -< 0.900.
Figure 14.- Continued.
53
.2
Mach 16Ft.
No. TT
.9]9 0• 94O []
i _ "
=l
.1
-.2
-1
.1
.2
P
.3
.6
1.0
1.1
1.2
].3.3 .4 .5 .6 7
Xllre f
(C) 0.919 __-<M < 0.940.
Figure 14.- Continued.
54
+. .,
_ • i_I_I ,+il
, , +,_
/,'+ ,_/,+/ .
C
P
Mach ]6 Ft. 8 Ft.
No. [T TPT
• 950 O ,O
• 958 C] P
(d) 0.950 _ M _ 0.958.
Figure 14.- Continued.
8
55
_._.
-.2
-.I
.I
-.2
-.I
.i
.2
Mach 16 Ft. 8Ft.No. TT TPT
• 968 0 _3• 975 [] ,_
.3C
P
.4
.5
1.0
ii
1.2
1.3.3 .4 .5 6 .7
x/Iref
(e) 0.968 < M -< 0.975.
Figure 14.- Continued.
8 1.0
56
Mach 16 Ft.No. TT
• 979 O• 985
1
.l
C .20
3
i.I
1.2
1.3
(f) 0.979 =<M =<0.985.
Figure 14.- Continued.
57
x • • :
• i: ! ,/
L
-.2
CP
--.i
0
.i
n2
-.1
0
.i
.2
.3
Mach 16 Ft. 8 Ft.N0, TT TPT
• 990 0 ,0•994 [] ,E3
.4
.5
.6
.7
.8
1.0
1.1
1.2
1,3l 2 .3 .4 .5 6 .7
x/l rel
(g) 0.990 =<M =<0.994.
Figure 14.- Continued.
1.0
58
-.2
Mach ]6 Ft. 8 Ft.No. TT TPT
.999 0 ,01.010 0 ,3
=I
-.2
-.]
.3
CD
.z_
.5
.6
.8
1.0
l.l
1.2
1.30 i3 .4 .5 .6 7
xllref
(h) 0.999 _-<M -< 1.010.
Figure 14.- Concluded.
.8 .9 1.0
59
: "j
/'i _!,/ i _ L i
• ) _ii _
/
?
i.i !_ .il •
/
CP
-.2
-.l
.I
.2
-l
.l
Mach 16 Ft. 8Ft.No. IT TPT
•698 © P.8ol [] P.85o 0•901 z_ ,_
-.i
.l
.2
-.l
.l
2 0 .i .2 .3 4 5 .6 .7 8 .9 l.O i.I
x/I ref
(a) Configuration C-2; 0.698 =<M <_-0.901.
Figure 15,- Pressure-coefficient distributions obtained for type C configurations.
6O
k
• ::ii!__I:i:
,r
: i_ _'//! ::! y" •
CP
Mach 16 Ft. 8 Ft.
No. TT TPT
.921 0
.94o []• 960
.971 ./x
.2 .3 .4 .5 .6 .7 8 .0
Xllre f
(b) Configuration C-2; 0.99.1 _-<M _-<0.971.
Figure 15.- Continued.
61
CP
-.2
Macn 16Ft. 8Ft.
No. TT TPT
• 976 O
.980 [] D•984 0 ©.990 A A
_ z A / A A A
----C
0 p, sonic _
.i
.2
-.l
.1
sonic
.2
9
-.1 0 )O(_@DOD oO _°_0 _COC,OO([ (: ODc_EL_
0 o_ _%_-C
0 p, sonic
.1
Qi
.20 .l 2 .3 .4 .5 .6 .7 .8 .9
X/Ire f
0
(
0
0
I1.0 1.1
(c) Configuration C-2; 0.976 _-<M < 0.990.
Figure 15.- Continued.
62
Mach 16 Ft. 8Ft.No. TT TPT
•995 0.999 [] P
1.010 O _>1.019 A
0c
P
.1
.2 .3 .4 .5 6 .7 .8 .9x/I rel
(d) Configuration C-2, 0.995 <-M < 1.019.
Figure 15.- Continued.
63
cp
-.2 _ I I
---C
_ p, sonic_
1
o _
1
2
-.1
0 _ ....... _'_<
.l
.2 >
Mach 16Ft. 8Ft. 8Ft. TTNo. TT TPT CAL
•697 © O,• 8O0 3 C,• 849 _ <_ Q
•900 zx .A
A
-.1
0
.1
_,E'=_.--@z'__ _-_ _E ,, _ _,a _
E]E
-1
0 .i .2 3 .4 .5 .6 .7 .8 .9xll re[
(e) Configuration C-3; 0.697 _-<M -<0.900.
Figure 15.- Continued.
c,
I10 l l
64
Mach 16 Ft. 8Ft. 8Ft. TT
No. TT TPT CAL
• 921 0
.940 []
.951 o _
.961 zx
.1
CP
2
(f) Configuration C-3; 0.921 -< M _-<0.961.
Figure 15.- Continued.
65
CP
-.2I
__ r--Cp, sonic
A0 _
A
A
Mach 16 Ft. 8Ft. 8Ft. TT
No. TT TDT CAL
•969 q
.977 D
.979 C _ #•985
Z
A A
A_
A
A
A2
C-- p, sonic-
---Cp, sonic
_/ __ _][]LJD[]] ] E E E L [] [] [] T][[][ ],r'l,
-I
30
.l[]
_E
[]
.2
- ]
0
_Cp, sonic
cJ_)o_ D_ c c c c c c c0
c
0
.1 o
CO0 D
OCD@(0 C
Do
)
0
.2 .3 .4 .5 .6 .7 .8
X/Ire I
.q
C
I1.0 I.i
(g) Configuration C-3; 0.969 _-<M -<_0.985.
Figure 15.- Continued.
66
L •
7, 'ii.
]i • ,_
-.2
-.1
.1
.2
.3
-:1
Cp 0
.i
I I
--C
t%
'_ --C
m p, sonic-
L E:_d_Dd
[]
rn
Mach 16 Ft. 8Ft. 8Ft. If
No. Ti- TPT CAL
•990 O ,O q
• 995 []
1.000 0 <_ Q
< z <>
L E q E E LEBnE3 E
HE3EU
3
[]
.3 N-
I4
0 .1 .2 .3 4 5 .6 .7 .8 .9 1.0x/I
ref
(h) Configuration C-3; 0.990 _-<M < 1.000.
Figure 15.- Continued.
1.1
67
[:'- , .':
_'/'/.L.i.i.
.2C
P
-.2
7- Cp, sonic-i
E]Z]L_
.I
.3
[]
C
- I p, sonlc
o
0.i
-6.2
[
NlachNo.
I. 008I. 020
] [
16 Ft. 8 Ft.TT TPT
o ,o[]
[
8Ft. TTCAL
n.
F- []
-q
[], [z1,
oo :_cC C C 0
E3E3
()
P
)
8
©
.3
.4
()
0 .1 .2 .3 .4 .5 .6 .7 .8
x/I ref
(i) Configuration C-3; 1.008 < M < 1.020.
Figure 15.- Continued.
.9 1.0 1.1
68
Mach 16 Ft. 8Ft.X]o. Fl TPT
•699 0.801 [].85_ © 9• 900 z_ .&
2
CP
3
.2
.3
-:I
.2 .3 .4 5 .6 .7 .8 .9
x/Ire f
(j) Configuration C-4; 0.699 _-<M -<_0.900.
Figure 15.- Continued.
1.0 1.1
69
Mach 16 Ft. 8Ft.
No. TT TPT
.921 0
• 941 []
•95o 0 S>
0
P
.i
.4 o .2 .3 .a .5 .6 .7 8
X/'re f
(k) Configuration C-4; 0.921 _<M -<_0.950.
Figure 15.- Continued.
1.0 1.1
7O
i ¸ i:: ¸ /
CP
0
Mach 16 Ft. 8Ft.
No. TT TPT
.961 O• 970 []
.976 _ _)
.2 .3 .4 5 .6 .7 .8 .9
X/Ire f
(1) Configuration C-4; 0.961 _-<M _-<0.976.
Figure 15.- Continued.
11
71
.; ': , t . " .
/ -
/
:;:_i I¸:¸• _
: <.i, i: ,_ : '_i
-.2
-.I
.I
.4
nl
0C
P
.3
.4
-t
.2
.3
1
Mach 16Ft. 8Ft.No. TT TPT
•981 O.9_ [].992 <} 9
.2 I 3 4 .5 .6 I 7 8 I 9
Xllre f
t.0 l.]
(m) Configuration C-4; 0.981 _-<M < 0.992.
Figure 15.- Continued.
72
i':/¸ / " // 'L
Mach 16 Ft. 8Ft.No. TT TPi-
• 995 ©1.000 [] E3].olo _ 9
!i :: !_:ii__
Cp
.2 .3 4 .5 .6 .7 .8 .9
xllre f
(n) Configuration C-4; 0.995 < M _-<1.010.
Figure 15.- Continued.
73
/
/
CP
-.2
=I
0
.i
.2
.3
.4
.I
.2
F
F
[][]
[]
3
00
0
Cp, sonic
[].nlZt []
Cp,sonic
]E] [] q
O0 DC
Mach 16Ft.No. TT
1.020 01.O99 []
E [] [][] E] [] 3_
0 o( ooDC
[]E]E []
oOC 0 0 DOG:pc D0
0C
[]
[]
[]
D
©0
.3
.4
.5.] .2 .3 .4 .5 .6 ,7 .8
x/Ire f
(o)Configuration C-4; 1.020 < M -_<1.099.
Figure 15.- Continued.
.9 1.0 I.I
74
2
-1
Mach 16Ft.No. TT
• 698 C• 802 []
E Fj 7
Dm DE F1E] E L:J U D" D LJ U E:]EDDE
E][]
[]
CD
0
o
.1
D
.2
O0 On Dr" Ooc 0_ DoG O
0©
0
.4
.5
.6
.I
.8
.9
1.0
1.1
1.2
1.32 .3 .4 .5 .6 .7 8 .9
x/I"ef
(p) Configuration C-5; 0.698 =<M < 0.802.
Figure 15.- Continued.
1.0 1.1
75
i •
_i i I _ •
• •'i
i• L
.I
Cp
.2
Math 16Ft.
No. IT
•850 ©
•901 []
(q) Configuration C-5; 0.850 _-<M < 0.901.
Figure 15.- Continued.
76
-.2
Mach 16 Ft.
No. TT
.921 0
.941 []
-.I
.2
-.I
.2
C0
.3
.4
.5
.6
.7
8
.9
1.0
Iii
L.2
1.3m2 3 m_ 5 16 17 m8
X/Ire f
.9 1.0 1.1
(r) Configuration C-5; 0.921 _-<M _-<0.941.
Figure 15,- Continued.
77
Math 16Ft.
Xlo. TT
.952 co•961
2
CD
.3
1.0
l.l
1.2
1.3
(s) Configuration C-5; 0.952 -<M -<0.961.
Figure 15.- Continued.
78
Mach I6 Ft.No. TT
.972 0
.977 []
[ 3
)
©
I
L
3
.6Ii .2 ,3 _ I5 .7
x/I ref
I
[
) SE
(t) Configuration C-5; 0.972 < M < 0.977.
Figure 15.- Continued.
3
I
]
)
9
)D
G
I
I
I
lIO 1.1
79
-.2! I I
--C
p, sonic
--.1 d___ E [] DE E
o 'g_
.2
-I
.2
CD
.3
[]
f--Cp, sonic-
J/ @_¢ o o o
©
Mach 16Ft,
No. TT
.982 O• 987 []
UdED EU L []q mD3 [] []
q
EE
O De 0 3 O0 )C Oc3 0 o )oc
3 E3
[]E
3C0
R
3
Eq
[]
L)0
©
.5
.8
3
.9 --
1.0
1.1
1.2
1.32 .3 .4 .5 .6 7 .8 9
X/Iref
(u) Configuration C-5; 0.982 _-<M <_-0.987.
Figure 15.- Continued.
Il0 ].l
80
! i i¸¸ _
_' , ; _,/i _ • _
i
0
.I
.2
Cp
.3
Mach 16 Ft.No. TT
.991 0•997 []
.8
.9
1.0
I.I
1.2
1.30 .1 .2 .3 .4 .5 .6 .7 .8 .9
X/Ire f
(v) Configuration C-5; 0.991 =<M <: 0.997.
Figure 15.- Continued.
1. I
81
-.2
Mad 16 Ft.
No, IT
1.000 0
1.012 Z
-.1
.2
=L
.2
CD
.3
.7
.8
.9
1.0
1.1
1.2
1.3.1 .2 .3 .4 .5 .6 7 .8 9
x/Iref
(w) Configuration C-5; 1.000 -<_M < 1.012.
Figure 15.- Continued.
L.0 l.l
82
.. . i _.
k ,
"'V .
CP
Mach 16Ft.No. TT
1.O22 O
I
I
I
I
I
I
I
I
I
i
I
I
I
I
I__ e-
l
I
I
i
I
I
I
I
I
__+_
.3
I
f.4 .5
x/Iref
C
II
I
I
i
.6 .7 .8
__
.9 1.0 1.1
(x) Configuration C-5; M = 1.022.
Figure 15.- Continued.
83
2
,i
. L
i__ ,"i __k_::
.1
Mach 16Ft.No. TT
.700 0• 8O2 []
1.0
I.I
2 .3 .4 .5 .6 .7 .8 9
X/Iref
(y) Configuration C-6; 0.700 < M -< 0,802.
Figure 15.- Continued.
LO ].1
84
: :>i:: i/:¸
:ii_, _._ _ i_
0
.l
-,2
.2
Cp
.3
Mach 15 Ft.No. TT
• 851 0• 902 []
.2 .3 .4 .5 .6 7 .8 .9
x/l ref
(z) Configuration C-6; 0.851 -<M -< 0.902.
Figure 15.- Continued.
85
p, ,Oli(
I
p, nJ,
0 .1 .2
I
_5i
I.4
Mach 16 Ft.
No. TT
922 1942 []
E
J
C
.5 .6 7
x/I ref
TTZ]-
I Fq
DIC)
©
C
k.8 .9 1.0
(aa)Configuration C-6; 0.922 <_-M -<_0.942.
Figure 15.- Continued.
86
j _ ,i,/_ ' _ .
C _i_:::i;/
¸%:.¸ <j_ : !
• /
-.2 --_
Cl,soric
[]0
.1 3_
-.2 •f -C
), SOl liC_
(
Co
0
)
.4
.6
.7
.8
]
.9
1,0
L1 --
1,2
q]
1.30 .l .2
.I
.2
CP
.3
Mach 16 Ft.No. TT
•052 0•961 []
_ -
_- 1'
C
o )
m
3 .4 5 .5
x/I ref
E D
O
E
(
.g
__ r
E
]D
_ E
L)
(
o
C _
i __ __
I1.0
(bb) Configuration C-6; 0.952 =<M < 0.961.
Figure 15.- Continued.
87
-.2
Mach 15 Ft.
No. TI
• 970 O• 976 []
.I
.I
-.2
-.l
.3
CP
.4
.7
8
.9
1.0
1.1
1.2
1.31 .2 .3 4 .5 .6 .7 .8 .g 1.0 ].1
x/I ref
(cc) Configuration C-6; 0.970 =<M _-<0.976.
Figure 15.- Continued.
88
Mach 16 Ft.'40. IT
.982 0
.988 []
.]
cP
2
7
8
.9
1.0
I.I
1.2
• i .2 3 .4 5 .6 .7 8 .9
X/Ire t
(dd) Configuration C-6; 0.982 < M _-<0.988.
Figure 15.- Continued.
l0 11
89
Mach 16 FLNo. TT
.992 0
.995 []
9O
.1 .2 .3 .4 .5 .6 .7 .8 .9
X/Iref
(ee) Configuration C-6; 0.992 _-<M < 0.995.
Figure 15.- Continued:
Mach 16Ft.No, ]-T
1.002 O].011 []
1
-.2
7
8
1.0
L.1
L2
.1 .2 .3 .4 .5 .6 .7 8 .9
x/I ref
(ff) Configuration C-6; 1.002 =<M -< 1.011.
Figure 15,- Continued.
91
H .2
_1
.1
.2
.3
CP
(DC OOC
----C
-- -- p, sonicC
0
©
Mach 16Ft.No. TT
1.02] o
0
(' oO o OOC 0
I
I
Io o _oo cDO U C: O Do
.4 w_.
.5
.6
r
I
.7
.8
o
C
oo
.... _ • _-__--
.9
1.O
1.1
1.2
1.30 1 .2 .3 4 .5 6 .7 .8 .9
x/lref
(gg) Configuration C-6; M = 1.021.
Figure 15.- Concluded.
l0 ]l
92
L
/,
i , i :/
ii
Mach
No.
• 697
• 799• 849
• 899
16 Ft.
TT
0
[]
<>z_
8Ft.
TPT
<>
0
CP
.i
--.i
.20 .i .2 .3 .4 .5 6 .7 .8 .9 1.0 1.1
Xllre f
(a) Configuration D-l; 0.697 < M < 0.899.
Figure 16.- Pressure-coefficient distributions obtained for type D configurations.
93
_" %1
-.2
-.l
.l
-.2
-.i
0
P
.i
-.2
-.l
.l
-.2
.2
Mach 16 Ft. 8 Ft.
No. TT TPT
.918 O
• 940 []
•949 <> <_• 959 A
.2 .3 .4 5 .6 i7 8
X/I ref
.9
(b)Configuration D-l; 0.918 -<_M < 0.959.
Figure 16.- Continued.
1.0 l.l
94
r
I
©B
©
_°
o
I
_°
ITA
I1^
Q
CO
i
_ ,_, _i_ _ _"; "_ i .... i_i_"
.... qi! ; i ¸ r _ : : ; :i I .
_ _ __ _ - • ; _i_:ii_ ,_;!_ii_,_i__i- _-
i
.i ?
• i
LL
"/ ' L"
f
x
-.2
-.1
_A
.1
5-.2
=1
C ,_,P
.i
--]p, sonic
[]-.I --
[]
Nlach
No.
• 989
• 995• 996
1.011
16 Ft.
TT
0
[]
©A
8 Ft.
TPT
<>.A
2L_,
.i
-.2
Cp, sonic
Cp, sonic
F _ [] [] [3 =3 3 EIDEDE3•[
^/N,
yq
:]_---
0
;PGOp,sonic
i .2 .3 ._ .5 .6 7 .8 .9xll
ref
(d) Configuration D-l; 0.989 =<M < 1.011.
Figure 16.- Continued.
DO ( )
[2E
F]F1
,4L
t>
<>9 ¸
E_
[3
O0
I1.0 1.1
96
• _i _i____ _ _,_
i _ _
_ ; ,'_ , -_ _ _i_
:i
_1
CP
0
Mach 16Ft. 8Ft.No. TT TPT
._o p
._8 p
.951 _ 9
.3
.2 3 4 .5 .6 .7
X/Ire f
8 .9 l.O 1.1
(e) Configuration D-2; 0.850 < M < 0.951.
Figure 16.- Continued.
97
• "i' _
" . , . - • •
98
cp
-.2
Mach ]6 Ft. 8 Ft.No. TT TPT
•970 ©
.976 E
•981 0
?0 _<_ p, sonic _
.1
'__ [
-_ Cp, sonic .... 40 -[!] ........
.1
.2
-.2
[]
1 b 0
_) ,._.O 0 )©q_- oOC 0 .0 ( 0_J'-C
p, sonic
0
1 I
• ] .2 3 .a .5 .6
X/Ire f
0 _ )0
D
.7 .8 .9
I
c-i
1.0 1.1
(f) Configuration D-2; 0.970 < M _-<0.981.
Figure 16.- Continued.
,_ _ii_ • -, "
! ,{__ii _i}i____!
• v -
i.... i_•/_;-.
i •ii•_!_ }
-.2
-.1
.2
.3
-.2
__;><>p,sonic
Y
3C
cO-- p,
Mach 16Ft. 8Ft.No. TT TPT
•984 ©• 990 [] P.995 0 ©
sonic - E_
-.2
0
C 3
G_
) o,DO0(r_) OCn _@0_
° Das_q:_t°Cp,somc
.2 .3 .a .5 .6 .7 .8 Q
X/I ref
(g) Configuration D-2; 0.984 -_ M _ 0.995.
Figure 16.- Continued.
c
o
I]0 I I
99
• k " •
y
:i_ i ,h _
ii _ i i
-.2
0 _
1
2
E_
2 --
]
.3
-.1 0
_D0 -- --
[
.2_
•3 0
.3
:l
po
3,scnicI
Ii
I
F-i
II
" i
]E 31 E]
_FIICP,
)
)
p, sonic
Mach 16Ft. 8Ft.No. TT TPT
•999 0 ,01.00] E]I. 0]9
3[ _J[ 1::] flz
4x/I ref
!
.6
sr n cs_: TjsE
D! © )
.7 8 .9
(h) Configuration D-2; 0.999 =<M < 1.019.
Figure 16.- Continued.
!
>
[3L_[]
1.1
lOO
-.2
-.1
[CI or
0
P p,
o
0
1
.2
-.2
-.1 _ -
0
.1
.20
.2
-.2
-.1
.1C
P
.2
-.2
Mach 8Ft.No. TPT
• 85 P.90 }:3
.95 ©
.98 A
i
tj
5; )
.2 .3 4 .5 6
Xllre f
.7 .8
s
(i) Configuration D-4; 0.85 _-<M _-<0.98.
Figure 16.- Continued.
1.0 11
101
-.2
Mach 8 Ft.
No. TP]
.985 Z• 99] 13
1.ooo _,1.01o
-.1
.1
.2
-.2
-.1
0
CP
.1
.2
-.2
-.]
2
-.2
-.1
.2.2 .3 .4 ,5 ,6 7 .8 0
xll rel
(j) Configuration D-4; 0.985 _-<M _-<1.010.
Figure 16.- Concluded.
1.0 1.]
102
CP
-.2
_l
.2
.3
-.2
.l
"4
.( '
/
0
/
r
]
/.
0 - _C
-q/
I
.2 5
.3 --
0 1 .2
.3
-.2
-.1
MacY
No,
• 698
• 800
•850
L
16 Ft. 8Ft. FligmTT IPI
0[]
]
5 .6
x/I ref
Theory Iref. 9_ ....
!
4_ " __
}S>
\
\
.8 .9 1.0
(a) 0.698 _-<M <_-0.850.
Figure 17.- Pressure-coefficient distributions obtained for configuration E-3.
103
_':.,i.: i_:I'_
L
-.2
-.1 _:iCp, sonic-
_<0 /,
Q-
.1/
.2 I
0
.3
-.2
._< _,--<
7
Mach 16 Ft. 8Ft. FlightNo. TT TPT
•901 O ,O Q•920 [].94o O
Theory (ref. 9) .....
\\
-.l --
Cp ..'I:: -_
0 _[]/
.I [/
I
[]I
I.2 I
.3
-.2
]_]"
\\
-.I
0
.i
!
.2 ©
6
.3o l
.f
.___ ___ _ __A_--L_-_-c_-_
I2 .3 .4 .5 6 17
x/l ref
(b) 0.901 =< M =<0.940.
Figure 17.- Continued.
.8
C
9 1.0
104
Mach 16Ft. 8Ft. FlightNo. TT TPT
950 0 ,_ Q.961 [].97] 0
Theory (ref. 9) ....
.3 .4 .5 .6 .7
x/I ref
(c) 0.950 < M < 0.971.
Figure 17.- Continued,
8 . 9¸ 1.0
105
Mach 16 Ft. 8Ft.
No. -_ TPT
.976 O
.981 [] El Theory (ref. gl ---
.986 Q
-.2 i i
__f -%,sonic_ ,-] < <>_ > __>/<
0 --I_" \v
f
.1<
//
.2 "_II
.3 7
-.2
p_l __j/Z
0
J
.1 j:i///
[].2 /
IIi
I
--Cp, sonic-
__ ---E
3
-.2
__ p,son_c_
-.1 )
.1
.2
.3
0 ,,,(
Y
//
®/III
©
0 l .2 .3 4 .5 .6 .7
x/I ref
",\\\
\
q,,
\\
\
\\,(
.8 .9 1.0
106
(d) 0.976 =<M =<0.986.
Figure 17.- Continued.
-.2
Mach 16 Ft. 8Ft.
No. TT TPT
• 99O 0
• 997 []
].ool © ©Theory (ref. 9) .....
4
-.2
-.1
C13
0
.3
-.2
=]
.2
.3.2 .3 .4 .5 .6
x/I ref
.7 .8 .9 1.0
(e) 0.990 =<M =<1.001.
Figure 17.- Continued.
107
_ _" iI, _ , _ _
-.2
_i
.I
.2
CP
.3
.4
[]
]
I
sonic
[
]
]
Mach 16Ft. 8Ft.No. TT TPT
1.011 0 PI. 021 [] ,_
LJ _ '
[] EE "I r, r
C ,E3 _-J _-
]
rl
j LJ
F:I
,[3[]
-.2
=1
0
.l
.2
--Cp,
/
©
sonicC
() ()
() ()
.3 0
108
.4.I .2 .3 .4 .5 .6
X/Ire f
(f) 1.011 < M < 1.021
Figure 17.- Concluded.
.7 .8 .9 1.0
c3)C.Dc"
(1)(,Dk_O
Ll..
OO
r'_
¢D
.08
.O7
.O6
.O5
.O4
.O3
F---
.02kl-
.01
0 2I
//
/
© C-2
[] C-3
<> C-4
//i
/////
z_Z]/
-.01. Ol 0 . Ol .02 . 03 . 04 .05 .06 .07
CD16 Ft. TT CD8 Ft. TPT) pressure integration
Figure 18.- Comparison of drag-coefficient increments obtained from both
force-balance and pressure integration•
/
.O8
.ASA-La.gley,1973 , L-8449 109
'k_• -_ I_ILI_I.•_•I_ _ill , • kii,!i k i i¸
J_xI_Iii__ _irl __¸I_ir____!_ivl!rL