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SPRESSURE DISTRIBUTIONS ON A HEMISPHERECYLINDER AT SUPERSONIC AND HYPERSONIC

MACH NUMBERS

ByA. L. Baer

S..VKF, Ri ,, ,nc.

It August16

ARNOLD ENGINEERING

DEVELOPMENT CENTER

AIR FORCE SYSTEMS COMMAND

u S AAF

A ED C-TNI-61-o6

RESSUTJRE DITRIBTIO NS ON A HEMISPHERE

CYLINDER AT SUPERSONIC AND HYPERSONIC

MACH NUMBERS

By

A. L. Baer

VKF, ARO, Inc.

August 1961

ARO Project No. 300116

Contract No. AF 40(600)-800 S/A 24(61-73)

Program Area 750A, AFSC Project No. 8952, Task No. 89512

AEDC-TN-61.96

ABSTRACT

Pressure distribution tests at supersonic and hypersonicspeeds were conducted in the von Karman Gas Dynamics Facili-ty (VKF), Arnold Center, Air Force Systems Command onAGARD Model E, a hemisphere cylinder configuration.

Various experimental data concerning the aerodynamiccharacteristics of blunt nosed bodies are available; however,relatively few sources present findings over a wide Mach num-ber range. The present investigations, stimulated by the needfor applicable experimental data to compare with the predictionsof various theories, were conducted at Mach numbers 2 through8 over a Reynolds number range from 0.17 x 10 6 to 0.51 x 106

per inch.

This report presents a comparison of experimental resultswith available theoretical predictions of pressure distributions,pressure drag, shock wave shapes, and bow shock wave detach-ment distances.

3

AEDC-TN-61-96

CONTENTS

Page

ABSTRACT .................................... 3NOMENCLATURE ........... ....................... ... 7INTRODUCTION ................................ 9APPARATUS

Wind Tunnels ................... ..................... 9Model .................... ........................ 10Instrumentation and PrecisiQn of Results ............ ... 11

TEST PROCEDURE ..................................... .. 11RESULTS AND DISCUSSION

Nose Pressure Distributions ...... .............. .. 12Pressure Distributions along the Cylinder .......... ... 13Pressure Drag .............. .................... .. 14Shock Wave Shape ........... ................... ... 14Bow Shock Wave Detachment Distance ............. ... 15

CONCLUDING REMARKS .......... .................. ... 15REFERENCES .............. ....................... ... 16

TABLES

1. Variation of px/p, with Hemispherical No"-e Angle 0 . . . . 19

2. Variation of px/p with Distance Downstream of the

Shoulder Point ............ ..................... 19

3. Comparison of Experimental Pressure Drag Coefficientsto Modified Newtonian Pressure Drag Coefficients ...... 20

4. Experimental Shock Wave Shape Coordinates ......... .. 20

ILLUSTRATIONS

Figure

1. Tunnel A, a 40 by 40-in. Supersonic Wind Tunnel . . 21

2. Tunnel B, a 50-in. -Diam Hypersonic Wind Tunnel 22

3. Model Geometry ..... ................... 23

4. AGARD Model E .......... .................. ... 24

5

A E DC-TN'-61-96

Figure Page

5. Selected Flow Patternsa. M. = 5.06, Re/in. = 0.51 x 1 0 6. . . . . . . . 25b. M. = 4.03, Re/in. = 0.44x 106. . . . . . . . 26

6. A Comparison of Experimental Pressure Distributionsover the Hemispherical Nose with TheoreticalPredictions ............ ..................... ... 27

7. Experimental and Theoretical Pressure Distributionsalong Cylindrical Body ........ ................ ... 29

8. Experimental Pressure Drag Coefficients Comparedwith Theoretical Predictions ..... ............. ... 31

9. A comparison of Experimental and Theoretical ShockWave Shapes .. ....................................... 32

10. Experimental Shock Wave Detachment DistancesCompared with Theoretical Predictions .......... ... 34

6

A EDC-TN-61 -96

NOMENCLATURE

1

CDp Pressure drag coefficient, f0 Cp d(r/ro)2

Cp Pressure coefficient, PXP•

C pmax Pressure coefficient at stagnation point

d Model diameter, in.

M"" Free-stream Mach number

Po Stilling chamber pressure, psia

Px Local static pressure, psia

POO Free-stream static pressure, psia

qw Free-stream dynamic pressure, psia

r Orifice coordinate defined by Fig. 3, in.

ro Hemispherical nose radius, in.

R Shock wave coordinate defined by Fig. 3, in.

Re Reynolds number

To Stilling chamber temperature, °R

x Distance in axial direction measured from forwardstagnation point, in.

6 Detachment distance of bow shock wave, in.

8 Angular dimension on hemispherical nosemeasured with respect to the model axialcenterline, deg

y Ratio of specific heats for air

'7

A EDC-TN-61-96

INTRODUCTION

In support of present day trends toward blunted aerodynamic shapes

for supersonic and hypersonic speeds, various approximations have been

developed to describe the flow characteristics about bodies with blunted

leading edges. Certain theories are widely known and accepted for use

in the derivation of pressure distributions and pressure drag coefficients

over spheres and other blunt shapes, while other approximations deal

with shock wave shapes and bow shock wave detachment distances. There

is, however, a shortage of applicable experimental data which in turn

precludes a comparison of theoretical methods with empirical results to

determine which theoretical procedures best predict the characteristics

of blunt-nose bodies. A test program was initiated to provide experi-

mental data for comparison with theoretical predictions of pressure dis-

tributions, pressure drag, shock wave shapes, and bow shock wave

detachment distances as applied to the axisymmetric blunt body problem.

Tests were conducted on AGARD Model E in the VKF 40 by 40-inch

supersonic wind tunnel (Tunnel A) and in the 50-inch-diam hypersonic

tunnel (Tunnel B) at the Arnold Engineering Development Center. Pres-

sure distribution and bow shock wave shapes were obtained at Mach

numbers 2, 3, 4, 5, 6, and 8 at zero angle of attack. Reynolds numbers

for these tests varied from 0. 17 x 106 to 0. 51 x 106 per inch.

A comparison of experimental results of pressure distributions,

pressure drag, shock wave shapes, and bow shock wave detachment dis-

tances with the predictions of various theories are presented in this

report.

APPARATUS

WIND TUNNELS

The 40 by 40-in. tunnel (Tunnel A) shown in Fig. 1 is a continuous,

closed circuit, variable density, supersonic wind tunnel with a Mach

number range from 1. 5 to 6. Variations in Mach number are produced

with flexible plates which are automatically positioned at the desired

contour by electrically driven jack units. A complete description of

Tunnel A may be found in Ref. 1.

Manuscript released by author July 1961.

9

AEDC-TN-61-96

Tunnel B (Fig. 2) is an axisymmetric, continuous-flow, variabledensity, hypersonic wind tunnel with a 50-in. -diam test section.* Becauseof changes in boundary-layer thickness due to changing pressure level,the Mach 8 contoured nozzle produces an average test section Mach num-ber which varies from 8. 02 at a stagnation pressure of 100 psia to 8. 10 at800 psia. The centerline flow distribution is uniform within ±1 percentin Mach number, whereas off-center the flow is uniform to about ±0. 3 per-cent. There is a slight axial gradient on the order of'0. 01 Mach numberper foot.

The continuous tunnels at the von Karman Gas Dynamics Facilityare driven by a 100, 000-hp central compressor system arranged to pro-vide a total of nine stages of compression. For operation of Tunnel A,up to five stages of compression are utilized to provide a Reynolds num-ber range from 0.3 x 106 to 9.0 x 106 per ft at M, = 1. 5 and from0. 4 x 106 to 4. 3 x 106 at M= = 6. Variable densities are obtained at each

Mach number by introducing air from a 5300-cu-ft, 4000-psia storagesystem. Below Mach number 4, the tunnel is operated at stagnation tem-

peratures of approximately 100'F, whereas for tests at the higher Machnumbers, this temperature can be raised to a maximum of 300 0 F to

prevent test section air liquefaction. Supply air is processed throughlarge capacity, silica-gel driers to maintain an absolute humidity below

0. 0001 lb of water per lb of air (dew point of -35 0 F at atmosphericpressure).

Stagnation pressures up to approximately 800 psia are supplied to"Tunnel B by the compress.or system. A propane fired heater producesa maximum air temperature of 900'F, sufficient to prevent liquefaction

of the air in the test section.

MODEL

The model (Figs. 3 and 4), designed and built by the VKF, consisted

of two sections: (1) a cylindrical body 5. 80 in. in diameter and 31. 55 in.

long, and (2) a hemispherical nose section of 2. 90-in. radius, 7. 60 in.

long. The overall model was 6. 75 body diameters or 39. 15 in. long.

The model was instrumented with 28 pressure orifices arrangedin a single ray along the body from the stagnation point. The hemi-

spherical portion of the nose section contained 10 orifices spaced atin-deg intervals from the stagnation orifice. Three additional orifices

on the nose section were equally spaced beginning at 1 in. from the

shoulder orifice. The pressure orifice arrangement on the cylindrical

10

AEDC-TN-61-96

body section began 0. 625 in. beyond the nose-body joint, and orificeswere equally spaced at 2-in. intervals to within approximately one-halfof a body diameter of the model base.

INSTRUMENTATION AND PRECISION OF RESULTS

Model pressures in Tunnel A were measured with a system of 15-,5-, and 1-psid transducers connected to orifices along the body in sucha manner as to give the desired sensitivity depending upon orifice loca-tion. These transducers will record pressures to a precision of approxi-mately 0. 1 percent of the rated capacity.

In Tunnel B, model pressures were measured with a sequential pres-sure switching system having nine synchronized valves, each valve beingconnected to a 5-psid transducer. To attain various ranges of instrumentsensitivity, seven-reference pressures which could be varied in approxi-mately 2-psia increments from a near vacuum were available. Eachtransducer was calibrated for a range of ±0. 3, ±0. 6, and ±1. 2 psid, andthese ranges, in conjunction with the seven reference pressures, wereautomatically selected to insure the best available precision of pressuremeasurement.

The pressure distribution data presented in this report are subjectto the following uncertainties based on repeatability of measurements:

Nominal M. Px/_P_

2 ±0. 0103 ±0. 0104 ±0. 0155 ±0. 0256 ±0. 0508 ±0. 050

TEST PROCEDURE

The conditions at which these tests were conducted are summarizedin the table on the following page:

,: 11

AEDC-TN-61-96

Nominal M®, Po, psia To, OR Rex 0- 6 , per inch

2 8.1 555 0.173 32.3 605 0.354 71.9 623 0.445. 150.7 655 0.516 174.5 683 0.37

174.8 738 0.338 650 1340 0. 22

All data presented were obtained at zero angle of attack and zero-deg roll angle.

Photographs to define the shock wave shape at supersonic Machnumbers were made with a double-pass schlieren system and a shadow-graph system which was utilized strictly for photographs of the noseregion (see Fig. 5). In Tunnel B, a conventional, short-range,divergent ray, spark shadowgraph system was used to record flowpatterns about the nose of the model.

RESULTS AND DISCUSSION

NOSE PRESSURE DISTRIBUTIONS

Pressure distributions over the hemispherical nose of AGARDModel E at all test Mach numbers, as given in Table 1, are presentedin Fig. 6 along with other M, = 6 data obtained in the VKF (Ref. 2)and certain results at Mach numbers 1. 97 and 3. 04 by Perkins andJorgensen as presented in Ref. 3. Theoretical comparisons to theexperimental data in the form Px/P 2 are afforded by the modified New-tonian approximation (Cp = Cpmax cos 2 0) and by the solutions of Van

Dyke and Gordon for a sphere with y = 1. 4 (Ref. 4). In addition, theexperimental results are compared with a prediction of the local pres-sure ratio obtained by the following empirical expression for localpressure coefficient (Ref. 3).

CP - 2 coS2 0 - 2 - Cpmax) o (1)

The modified Newtonian approximation has long been known to givesatisfactory predictions within certain restrictions, and, except forthe results at M., = 6 and 8, good agreement is shown here until thenose-cylinder junction is approached. The solution at the shoulder(0 = 90 deg) gives Px = p,, which is -generally valid only for the lower

12

A E DC-TN-61-96

Mach numbers. By matching the Newtonian approximation with thePrandtl-Meyer relation at the point on the surface where both the pres-sure and the pressure gradient given by the two formulas are equal, thepressure distribution may be predicted to the shoulder. For the presentcomparisons, this approach was used for M. = 6 and 8 and is in excellentagreement with the experimental results.

The methods of Ref. 4 which, for a sphere, results in the "Newtonian

plus centrifugal" analytic approach of Busemann, also show excellentagreement with experimental points. These predictions, as stated byVan Dyke and Gordon, do not extend to 0 = 60 deg where the Newtoniantheory plus centrifugal force effects results in the pressure at the sur-face being zero (Px = 1 - 4/3 sin2 0).

It should be noted that the solutions presented in Ref. 4 were obtained

for what herein are called nominal Mach numbers. These solutions were

used strictly as given by shifting the ordinate to correspond with the theo-

retical Px/P. depending on the calibrated Mach number. Also, the pre-.

dictions for M. = 8. 10 required an interpolation between Mach numbers 6and 10, which apparently was satisfactory.

To obtain the empirical expression given in Ref. 3 for the pressure

distribution, the assumption was made that the expansion of the flow

over the hemisphere is similar to that predicted by Newtonian theory

but differs from theory by an amount which varies approximately as*

the cosine of the angle 0. The approximation provides results which*

agree well with experimental findings but, like the Newtonian theory at

high Mach numbers, is inadequate as the shoulder is approached.

PRESSURE DISTRIBUTIONS ALONG THE CYLINDER

Table 2 gives the experimental pressure distributions along the

cylindrical body, and these results are compared with the theoretical

methods of Love (Ref. 5) in Fig. 7. The method of Ref. 5 for M>I 1may be taken as a modification of blast wave theory since the blast wave

pressure decay laws were utilized. Love 1. Ls suggested the use of the

experimental shoulder pressure to bring th predicted pressure distribu-

tions into closer agreement with experimental values. This was done for

all test Mach numbers with the difference between the purely theoretical

and the "theoretical plus experimental" approaches being shown for

Ma = 6. 02. It is interesting to note that for M. = 8. 10 the shoulder pres-

sure was exactly as predicted by Love, and modifications were not needed.

13

E- DC-TN-61-96

The approximate solutions, based on blast analogy, of inviscid,hypersonic flows about simple slender bodies as suggested by J. Luka-siewicz in Ref. 6 were also used for pressure distribution comparisonsat M. = 5.06, 6.02, and 8. 10. To use the methods of Ref. 6 (y = 1.4),one must know, in addition to M,, the drag coefficient which definesthe flow field. For the comparisons shown, the drag coefficients used

were the experimentally determined values of CDp at the appropriate

Mach numbers. Here one should note that the second approximation

for the pressure distribution (axisymmetric flow) given by Ref. 6

greatly improves the predictions afforded by the first approximation,

and although deficiencies exist near the shoulder region, agreement

with experimental data improves in the aft region of the body.

PRESSURE DRAG

A comparison between experimental pressure drag coefficients andvalues determined with the modified Newtonian approximation are pre-

sented in Table 3 and shown in Fig. 8. The theoretical values are

slightly higher than the experimental results as would be expected sincethe modified Newtonian pressure distributions presented in Fig. 6 are

higher than the experimental results; specifically for 6 values between'

20 and 60 deg where the section loading is high as opposed to beyond

60 deg. Here the local surface slope is small and will not result in an

appreciable change in pressure drag even though there exists in some

cases large differences between the theoretical predictions and experi-

mental results (see Fig. 6, M. = 6. 03 and 8. 10).

It was shown in Ref. 3 that the pressure distributions follow closely

an empirical relation (see Eq. 1) which results in the expression,2 Cpmax - ICD 2 3 . Pressure drag values determined in this manner

agree well with-the majority of the ,2xperimental data presented in Fig. 8.

SHOCK WAVE SHAPE

The experimental shock wave shape coordinates given in Table 4

were obtained from scaling schlieren photographs similar to Fig. 5a.

Figure 9 presents a comparison between these experimental shock wave

shapes and the theoretical shapes obtained by the methods of Ref. 11.

Excellent agreement with experimental results is shown for Mach num-

bers 1. 99, 3, and 4.03, whereas small deviations exist for the higher

Mach numbers. The first and second approximations for shock wave

14

A ED C-TN-61-96

shape as given by blast analogy (Ref. 6) are included for comparisonsat Mach numbers 5. 06 and 6. 03. Here one should note that although theexperimental shock wave is displaced from the body more than predictedby blast analogy, the second approximation affords predictions of shockwave slope.

BOW SHOCK WAVE DETACHMENT DISTANCE

Bow shock wave detachment distances at all test Mach numbers wereobtained from measurements of photographs similar to Fig. 5b and are

.presented in Fig. 10. The methods of Ref. 11, which were used for pre-dicting shock wave shapes show excellent agreement with empirical

bow shock wave detachment distances. The theory presented i--. Ref. 4also gives satisfactory results. All of these theoretical predictions,excluding Ref. 12, for Mach numbers above 4 predict detachment dis-

tances greater than experimentally determined values.

CONCLUDING REMARKS

Tests were conducted at -Mach numbers 2 through 8 at zero angleof attack to obtain pressure distribution and optical data on AGARDModel E for comparison with theoretical predictions of pressure distrib-

ution, pressure drag coefficients, shock wave shapes, and bow shock

wave detachment distances. .The results of these investigations indicatethat:

1. Excellent agreement with theory in the shoulder region wasobtained at Mach numbers above 5 by matching the Newtonian

app- oximation with the Prandtl-Meyer relation at the point

on the surface where the pressure gradient and pressure

given by the two relationships are equal.

2. The modified Newtonian approximation generally overestimated

the pressure distribution but when modified by an empiricalrelation from Ref. 3 agreed well with experimental results.

3. Pressure distributions over a hemisphere can be closely

predicted by the methods of Ref. 4 for e less than 40 deg.

4. Along the cylindrical body downstream of the hemisphericalnose, the methods presented by Ref. 5 do not give satisfactorypredictions of the pressure distribution.

15

AEOC-TN-61-96

5. Pressure drag coefficients for a hemisphere are overestimatedusing the modified Newtonian approximation but agree wellwith an empirical relation given in Ref. 3.

6. The methods of Ref. 11 afford a good prediction of shockwave shapes for the hemisphere-cylinder model.

7. References .11 and 4 give a good approximation of bowshock wave detachment distances.

REFERENCES

1. Schueler, C. J. and Strike, W. T. "Calibration of a 40-InchContinuous Flow Tunnel at Mach Numbers 1. 5 to 6."AEDC-TN-59-136, November 1959.

2. VKF-AEDC Investigations of a Spherically Blunted Cone at

Mach Number 6.

3. Perkins, E. W. and Jorgensen, L. H. "Investigation of the

Drag of Various Axially Symmetric Nose Shapes of FinenessRatio 3 for Mach Numbers from 1. 24 to 3. 67."NACA-RM-A52H28, November 1952.

4. Van Dyke, M. D. and Gordon, H. D. "Supersonic Flow Past aFamily of Blunt Axisymmetric Bodies. " NASA Technical

Report R-l, 1959.

5. Love, E. S. "Prediction of Inviscid Induced Pressures from

Round Leading Edge Blunting at Hypersonic Speeds."ARS Journal, Vol. 29, October 1959, pp. 792- 794.

6. Lukasiewicz, J. "Hypersonic Flow-Blast Analogy.

AEDC-TR-61-4, June 1961.

7. Sommer, S. C. and Stark, J. A. "The Effect of Bluntness on theDrag of Spherically Tipped Truncated Cones of FinenessRatio 3 at Mach Numbers 1. 2 to 7.4." NACA-RM-A52B13,April 1952.

8. Chauvin, L. T. "Pressure Distribution and Pressure Drag for a

Hemispherical Nose at Mach Numbers 2. 05, 2. 54, and 3. 04."NACA-RM-L52K06, December 1952.

9. Hunt, G. K. "Supersonic Wind Tunnel Study of Reducing the Dragof a Bluff Body at Incidence by. Means of a Spike."

RAE Report No. AERO 2606, May 1958.

16

AEDC-TN-61-96

10. Beecham, L. J. "The Hemispherical, Differential Pressure Yaw-meter at Supersonic Speeds. " RAE Technical Note No.

AERO 2687, June 1960.

11. Love, E. S. "A Re-examination of the Use of Simple Concepts forPredicting the Shape and Location of Detached Shock Waves.

NACA-TN-4170, December 1957.

12. Stollery, J. L. and Maull, D. J. "A Note on Shock DetachmentDistance. " Journal of the Royal Aeronautical Society.Vol. 64, .June 1960, p. 357.

13. Serbin, Hyman. "Supersonic Flow around Blunt Bodies."Readers' Vorum, Journal of the Aeronautical Sciences,

Vol. 25, .No. 1, January.1958, p. 58.

17

4

AEDC-TN-61-96

TABLE 1VARIATION OF Px/P. WITH HEMISPHERICAL NOSE ANGLE 0

moo 1. 99 3. 00 4.03 5. 06 6.02 6.03 8. 10

Re/in. x10- 6 0. 17 0. 35 0.44 0. 51 0.33 0.37 0.22

Orifice Nose AngleeNo. d_ _ _

1 0 5.598 12.07 21.35 33.56 - 07.03 -.2 10 •.)233 1.63 20.5L 32.29 )j5.65 45.67 83.h5

3 20 5.006 10.55 18.50 28.87 - Lj.98• 3.03* 30 L.319 8.879 15.39 23.93 - 33.89 60.7h5 ho 3.5o8 7.075 12.09 18.70 - 2(.39 h6.61

6 50 2.7•9 5.21h 8.702 13.29 18.Uh 18.72 32.8L7 60 2.C73 3.6V6 5.911 8.909 12.52 12.52 21.518 70 1.L37 2.3h9 3.686 5.396 7.L28 7.56h 12.969 80 0.95).9 1.h09 2.135 3.051 L.237 4.252 7.23010 90 0.6282 0.8303 1.2381 1.698 2.262 2.3hi 3.823

TABLE 2VARIATION OF px/p0. WITH DISTANCE DOWNSTREAM OF THE SHOULDER POINT

M 1.99 3.00 4.03 5.06 6.021 6.03 8.10

Re/in. x10 0.17 0.35 0.44 0.51 0.33 0.37 0.22

Orifice x/dNo.

10 0,5X00 0.6282 0.8303 1.23; 1.698 2.262 2.3h1 3.82311 0.672L 0.6929 0.8072 1.159 1.516 2.022 2.035 3.27712 0.8hL8 0.7503 0.82Ul .?? 1.L52 - - 3.06613 1.0173. 0.7919 0.8L52 1.113 1.386 1.916 1.87h -1L 1.L182 0.8359 0.8623 1.020 1.251 1.729 1.703 2.50515 1.7630 0.8760- 0.8707 0.9892 1.193 - 1.605 2.2b716 2.1079 0.9111 0.8M09 0.9hL6 1.122 - 1.503 2.05217 2.Lý27 0.9075 0.8800 0.9257 1.061 1.333 1.386 1.89118 2.7975 - O.8706 - - - - 1.75L19 3.1b2L l.Olh 0.8681 0.8789 0.9535 1.169 1.219 1.65720 3.b872 1.0L2 0.8705 0.8707 0.9299 1.107 1.182 1.55721 3.832C - 0.8713 - - 1.065 - 1.07222 L.1768 1.015 0.8561 0.8621 0.8788 - - l.h0723 L.5217 1.038 0.8927 - - 1.37b2L i.F665 1.009 0.8898 0.859L 0.8765 1.039 1.12h 1.33625 5.2113 1.019 0.9008 0.8687 0.8677 1.019 1.117 1.28626 5.5562 1.031 0.931h 0.8899 0.8677 - 1.113 -27 5.9010 1.018 0.9127 0.8865 0.8595 1.015 1.i01 1.1l728 6.2L58 1.021 0.9200 0.8982 0.85L8 1.013 1.080 1.109

19

AE DC-TN-61-96

TABLE 3COMPARISON OF EXPERIMENTAL PRESSURE DRAG COEFFICIENTS

TO MODIFIED NEWTONIAN PRESSURE DRAG COEFFICIENTS

CDP

ModifiedMo 1/M2 Re/in. x10- 6 Experimental Newtonian

1.99 0.252 C.17 0.'PPR. 0.e2793.c0 0.111 0.35 0.8480 C.8779L.03 0.062C C.LL 0.6712 0.89685.06 C.0 192 c.5I o.87 48 0.90L (6.03 0.0275 C.37 0. 886t 0.90918.10 0.01C2 0.22 0.9000 C.9139

TABLE 4EXPERIMENTAL SHOCK WAVE SHAPE COORDINATES

M 1: i. 99 Mo=3 Mo=4. 03 Moo= 5. 06 M)= 6. 03

x/d R/d x/d R/d x/d R/d x/d R/d x/d R/d

0 0.505 0.352 0 0.315 0 C.20 0 0.1660.085 0.659 c.055 0.L86 0.0.5 0.L68 0.085 0.L27 0.085 0.3780.170 0.811 0.17C 0.607 0.170 0.r/3 0.170 0.516 0.170 0.5050.256 0.911 0.25L 0.698 0.25d 0.667 0.25L 0.602 0.25L o.58o0.339 1.O1L 0.339 C.785 0.339 0.72L 0.339 0.661 0.339 0.652C.L24 1.117 0.M2L c.855 C.L2L 0.809 0.024 0.729 C.L2L 0.7260.509 1.207 C.C09 0.921 0.509 0.850 0.509 0.791 0.509 0.796

-0.593 1.299 0.593 0.988 0.593 C.917 0.593 0.857 0.678 0.8830.678 1.396 0.67F 1.055 0.679 0.987 0.678 I 0.909 0.848 0.9710.763 1.77 0.763 1.116 0,848 1.081 0.8L8 0.996 1.017 1.065C.8!,8 1.559 0.8L8 1.179 1.017 1.168 1.017 1.091 1.187 1.1350.932 1.629 0.932 1.230 1.127 1.261 1.187 1.186 1.3"6 1.1981.017 1.721 1.017 1.266 1.356 1.T,2 1.356 1.250 1.526 1.2611.102 1.802 1.102 1.339 l."26 1.hhC 1.526 1.323 1.695 1.3331.187 1.870 1.187 1.393 1.695 1.513 1.695 1.L07 1.865 1.h051.272 1.91j 1.272 1.6 1.8 I. 1.i5F66 1.8F5 1.L82 2.03) !.L<81.356 2.01)t 2.35 1.h98 2.03K 1.67( 2.0Ch 1.530 I 2.20L 1.5321.526 2. 1,T 1. q24 1.593 2.20C i.Th8 2.20L 1.589 2.373 1.5881.(95 2.288 1.495 1.696 2.373 1.818 2.313 1.65L 2.5L3 1.6631.865 2.-32 1.8,5 1.786 2.563 1.8R3 2. 43 1.730 2.882 1.7862.03C 2.577 2.03) 1.791 2.8&2 2.022 2.F82. 1.839 3.221 1.8702.20L 2.(9- 2.206 1.963 3.221 2,1-1 3.221 1.950 3.560 1.9822.374 2.829 2.-43 2.063 3,560" 2.28F 3."' 0 2.063 3.899 2.0852.5L3 2.955 P.-1; 2.232 3.'.99 2.616i W.r99 2.182 L.238 2.17h2.713 3.061 3.C02 2.3?9 L.23F 2.531 h.238 2.282 L.577 2.2562.882 3.189 3.391 2.55L )1.577 2.6)9 b.517 2.375 h.916 2.3283.052 3.231 3.?30 2.7-0 L.916, 2.775 '.916 2.L8L 5.256 2.,'323.221 3.L32 ),.069 2.8"5 5.256 2.383 5.256 2.5"9 5.595 2.521

:z.Lo8 2.998 5.595 3.0c9 5.595 2.71b 5.931 2.595

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20

A ED C-TN-61-96

POINTr OF MODEL ROTATION 7 CAMERA PORT LOCATION

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21

AEDC-TN-6 1-96

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AEDC-TN-61-96

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AEDC-TN-61 -96

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29

AEDC-TN-61-96

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DEPARTMENT OF THE AIR FORCEHEADQUARTERS ARNOLD ENGINEERING DEVELOPMENT CENTER (AFMC)

ARNOLD AIR FORCE BASE TENNESSEE

MEMORANDUM FOR DTIC-OCQ 7 JUN 2028725 John J. Kingman RoadFort Bel;voir VA 22060-6218Attn: Larry Downing, 703-76-0011

FROM: AEDC/IN-STINFO251 First StreetArnold AFB TN 37389-2305

SUBJ: Change in Distribution Statement/Restrictions

1. The below listed Technical Report has been reviewed by the OPR and it hasbeen determine that there are no restrictions required on this report and should bemade available to the general public, Distribution Statement A:

AEDC-TN-61-96

2. Point of contact is the undersigned at DSN 340-7329 or Coin 931-454-7329.

J. .AMPBE I(L>AE Stinfo Off0 r