AIAA-2002-4419

Wind tunnel Tests of a Missile Having Elliptic Cross Sectioned Body Daniel Levin* and Asher Sigal**

Faculty of Aerospace Engineering

Technion - Israel Institute of Technology, Haifa 32000, Israel

A model consisting of an elliptic cross-sectioned body and tail was tested at Mach numbers between 0.7 and 3.0. A matching model having a circular body was also tested for reference. The longitudinal stability derivatives of the configurations were obtained by fitting polynomials to the test data. The experimentally obtained data are compared with predictions, which include a new component buildup method, the Missile Datcom code, and a hybrid method. The present component buildup method agrees well with the test data, except for an overestimate of the normal-force curve slope and a slight deviation in the center of pressure location at the subsonic range. The Missile Datcom code yields good estimates in the supersonic range, but overestimates the normal-force curve slope for subsonic Mach numbers.

Nomenclature a =horizontal semi-axis of ellipse b =vertical semi-axis of ellipse Cm =pitching-moment coefficient Cmα

=pitching-moment curve slope CN =normal-force coefficient CNα

=normal-force curve slope CXo =forebody axial-force coefficient d =diameter of baseline (matching circular)

body E =ellipticity ratio, a/b M =Mach number r =radius of baseline body SR =reference area, (π/4)d2 xcp =center of pressure location with respect to

body tip. Greek α =angle of attack

Introduction

The first part of this two-part study, Ref. 1, describes analysis of a missile whose body has an elliptic cross section with ellipticity ratios of 1.25/0.8. Schematics of this missile, and that of a matching circular body missile are depicted in Fig. 1. * Head, Wind Tunnel Laboratory; Senior Member, AIAA. ** Adjunct Research Associate; Associate Fellow, AIAA; E-mail: AsherS@aerodyne.technion.ac.il Copyright © 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

The objectives of this part of the study were to test the two missiles at sub-, trans-, and supersonic Mach numbers, to obtain the longitudinal stability derivatives and to compare the experimentally obtained data with the predictions of Ref. 1.

The Experimental Investigation

Test Models A photograph of the test models is shown in Fig. 2. Both noses and centerbodies were machined of aluminum alloy. The afterbodies and the fins were made of steel, and soldering was used to assemble the tail units. The designation of the models C100-T Circular body and tail. E125-T “Oblate” elliptic body and tail. E080-T “Prolate” elliptic body and tail. Wind Tunnels and Tests The tests were carried out in the two high-speed wind tunnels of the Faculty of Aerospace Engineering of the Technion. The transonic facility is induction-driven, close cycle facility. The test section is 60 cm wide by 80 cm high. The floor and the ceiling are perforated. Mach number range is 0.4 to 1.13 and the stagnation pressure is atmospheric, yielding Reynolds numbers of about 0.08 to 0.15x106 per cm. The supersonic wind tunnel is a blow-down facility, having a flexible nozzle, which is operated by a single jack. The test section is 40 cm wide by 50 cm high. Mach number range is 1.6 to 3.5, and the matching Reynolds numbers are about 0.45 to 0.9x106 per cm. For details see Refs. 2 and 3. Two types of tests were performed: a) Transonic Mach number transients at a fixed nominal angle of attack of 3.0 deg.

AIAA Atmospheric Flight Mechanics Conference and Exhibit5-8 August 2002, Monterey, California

AIAA 2002-4419

Copyright © 2002 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

b) Polars, namely angle of attack sweeps at Mach numbers of 0.7, 0.9, 1.0, and 1.1 at the transonic tunnel and 1.8, 2.4, and 3.0 at the supersonic facility. Angle of attack varied between –5.0 and 15.0 deg.

Measurements and Data Processing Two six-component sting balances were used to measure the forces and moments acting on the models. Their measurement ranges match the estimated loads in the two wind tunnels. The estimated accuracy is 0.8% of the maximum loads in the two facilities. Base pressure was also measured to allow obtaining forebody axial-force coefficient. (Base drag contribution excluded.) Nonlinear calibration matrices were used to convert the measured signals to loads. The forces and moments were converted to coefficients using baseline diameter and cross section area as reference length and area, respectively. Reference points for moments are the centers of the models. Polynomials were fitted to the CN vs. α and Cm vs. CN curves. The coefficients of the linear terms are the normal-force curve slope and the center of pressure, respectively. Test Results I – Transients The longitudinal characteristics obtained from the transient tests are presented in the two parts of Fig. 3. The ratio CN/α is an approximation to the normal-force curve slope, and the ratio Cm/CN is an approximation to the center of pressure location, relative to the centers of the models. Generally, the approximate normal-force curve slope of configuration E125-T (“oblate”) is about 1.3 units larger than that of C100-T, (baseline) and the approximate center of pressure location is about 0.3 reference diameters more forward. The approximate normal-force curve slope of configuration E080-T (“prolate”) is smaller than that of the baseline by about 0.9 units in the subsonic range. At Mach numbers between 0.95 and 1.05, the two curves coincide. The approximate center of pressure location of missile E080-T is 0.2 reference diameters more aft than that of the baseline, except for M=0.95, where the curves touch each other. The trends of the variations of the transonic characteristics of the three configurations are similar. Test results II – Polars Sample of raw test data, for Mach number of 0.7, is presented in Fig. 4. The trends associated with body ellipticity are as expected. The stability derivatives were obtained as discussed before. They are presented in Fig. 5. Usually the curves are separated. Only in the near-sonic range the normal-force curve slopes of C100-T and E080-T are very close, and the centers of pressure locations of these configurations coincide at M=1.0. Comparisons of the data presented in Fig. 4 with that of

Fig. 3 yields good agreement. In particular, the polar tests corroborate the proximity of the transient curves of configurations E080-T and C100-T at near sonic Mach numbers. The aerodynamic efficiency is defined by e=max(CL/CD) (1) Samples of CL/CD vs. angle of attack data, for M=0.7 and M=1.8, are shown in Fig. 6. As expected, configuration E125-T features highest efficiency and configuration E080-T the lowest. The aerodynamic efficiencies obtained for the extreme test Mach numbers, in both wind tunnels, are given in Table 1. The values found for M=1.13 are about 25% lower than those found for M=0.7. This reflects the higher axial-force coefficient at the transonic range. The average ratios of the efficiency of configuration E125-T to that of the baseline configuration are 1.09 for the subsonic and transonic ranges and 1.05 for the supersonic range.

Table 1 Typical aerodynamic efficiencies.

e M E125-T C100-T E080-T 0.7 4.92 4.54 4.21 1.13 3.56 3.34 3.20 1.8 3.41 3.23 3.06 3.0 3.33 3.15 2.90

The axial-force coefficients at zero angle of attack were obtained from the polar tests. The dependence of forebody (base contribution excluded) axial-force coefficient on Mach number is shown in Fig. 7. The differences between the three configurations are very small. Additional test data are given in Ref. 4.

Comparisons

The longitudinal characteristics of the test configurations were estimated using three methods: a) A specialized component buildup (CBU) method that uses tail-elliptic-body mutual influence coefficients which are based on slender body theory. The characteristics of the components were obtained from the CL-Cm-CD code (Ref. 5); b) The Missile Datcom code, Ref. 6; and c) A hybrid method that uses the Vorlax code (Ref. 7) for the analysis of the contributions of the tail units and databases for those of the bodies. For details see Refs. 1 and 8.

The Baseline Missile A comparison between predicted and experimentally obtained stability derivatives of the baseline configuration is shown in Fig. 8. In the subsonic range, (M=0.7 and 0.9) the CL-Cm-CD code overestimates the test data for the normal-force curve slope by about 9.0%. In the transonic and supersonic ranges, the estimates by this code are in very good agreement with the data. The M-Datcom code over predicts the subsonic normal-force curve slopes by 19%. The gap decreases in the transonic range, leading to good agreement for high supersonic Mach numbers. (Since the characteristics of the components used in the present CBU method were obtained from the CL-Cm-CD code, its predictions for the baseline configuration are identical to those of the code itself.) Both codes predict accurately the center of pressure location, except for the subsonic region, where the predictions are about 0.25d more aft than test data. Elliptic Body Configurations Fig. 9 compares predictions with test data for the two elliptic body configurations. (The CL-Cm-CD does not feature capability for noncircular fuselages.) The predictions by the hybrid method are very close to those obtained by the present CBU method. Both, the present CBU method and the M-Datcom code, overestimate the experimentally obtained normal-force curve slope at subsonic Mach numbers. The average gaps between predictions by the former method and test data, in this range, are 15% and 16% for configurations E080-T and E125-T, respectively. The M-Datcom code yields higher estimates of the subsonic normal-force curve slope, than the other methods. This is notable for configuration E125-T, where the subsonic gap, relative to the data, reaches 26%. In the supersonic range the CBU method provides very good estimates for configuration E080-T, and slightly overestimates the test results of configuration E125-T. In the same range, the M-Datcom code predictions of the normal-force curve slope match those of the CBU method for the “prolate” missile, and are a little larger than them for the “oblate” one. The two methods predict well the center of pressure location, except for the subsonic range where the estimates are about 0.25d more aft than the test data. . The trends observed in the case of the elliptic body and tail configurations are similar to those found for the baseline model.

Acknowledgements

This study was partially supported by the US Air Force, European Office for Aeronautical Research and Development, (EOAR&D) under contract No. F 61775-99-WE102. Dr. Charbel Raffoul was contract monitor for the USAF.

Mr. Z. Rafael designed the models, and Dr. M. Victor was test engineer.

References

1. Sigal, A., “Analysis of a Missile Having Elliptic Cross Sectioned Body,” AIAA-2002-4513, accepted of presentation at the AIAA Atmospheric Flight Mechanics Conference, Monterey, CA, Aug. 2002.

2. Salomon, M., Bracha, J., and Rom, J., “Characteristics of the 60 x 80 cm Induction Driven Closed Return Transonic Wind Tunnel at the Aeronautical Research Center,” Israel Journal of Technology, Vol. 8, Nos.1-2, March 1970, pp. 111-118.

3. Kadushin, I., and Rom J., “Design of an Intermittent, Single Jack, Flexible Nozzle Supersonic Wind Tunnel for Mach Numbers 1.5 to 3.5,” TAE Report No. 86, Technion, Haifa, Israel, 1968.

4. Levin, D., and Sigal, A., “Analysis and Tests of a Missile Having Elliptic Cross Section Body,” Report TAE 760, Technion, Faculty of Aerospace Engineering, Haifa, Israel, Apr. 2001.

5. Anon., “CL-Cm-CD” – A Component Buildup Code for the Analysis of Wing-Body-Tail Configurations,” Rafael, Haifa 31021, Israel, 1985.

6. Blake, W. B. “Missile Datcom User’s Manual-1997 Fortran 90 Version,” USAF Research Laboratory, Air Vehicle Directorate, Wright Patterson AFB, Ohio, AFRL-VA-WP-1998-3009, Feb. 1998.

7. Miranda, L. R., Elliot, R. D., and Baker, W. M., “A Generalized Vortex Lattice Method for Subsonic and Supersonic Flow,” NASA CR-2865, 1977.

8. Sigal, A., “A Hybrid Method for the Analysis of Multiple-Fin Configurations,” AIAA 93-3655, Aug. 1993.

a) Baseline model.

b) Elliptic cross-sectioned body model.

Fig. 1. Schematics of the research configurations.

Fig. 2. Photograph of the test models.

a) CN/α vs. M.

b) Cm/CN vs. M.

Fig. 3 Results of transient tests.

a) Normal-force coefficient vs. angle of attack.

b) Pitching-moment coefficient vs. normal-force coefficient.

Fig. 4 Test data at M=0.7.

a) Normal-force curve slope.

b) Center of pressure location. Fig. 5 Experimentally obtained stability derivatives.

-3.2

-2.8

-2.4

-2

-1.6

-1.2

-0.8

-0.4

00.6 1 1.4 1.8 2.2 2.6 3

M

dCm

/ dCN

E125-TC100-TE080-T

0

2

4

6

8

10

12

14

16

0.6 1 1.4 1.8 2.2 2.6 3M

C Nαα αα

E125-TC100-TE080-T

a) M=0.7.

b) M=1.8.

Fig. 6 The dependence .of CL/CD ratio on angle of attack.

Fig. 7 Forebody axial-force coefficient.

0.04

0.08

0.12

0.16

0.2

0.24

0.28

0.32

0.36

0.6 1 1.4 1.8 2.2 2.6 3M

C XO

E125-TC100-TE080-T

2

4

6

8

10

12

14

16

0.6 1 1.4 1.8 2.2 2.6 3M

C Nαα αα

CL-Cm-CDM-DatcomTest data

a) Normal-force curve slope.

-10

-8

-6

-4

-2

00.6 1 1.4 1.8 2.2 2.6 3

M

X cp/ d

CL-Cm-CD

M-Datcom

Test data

b) Center of pressure location.

Fig. 8 Comparisons of the stability derivatives of the

baseline configuration.

0

4

8

12

16

20

0.6 1 1.4 1.8 2.2 2.6 3M

C Nαα αα

E125-T, M-DatcomE125-T, CBUE125-T, HybridE080-T, M-DatcomE080-T, CBUE080-T, HybridE125-T, Test dataE080-T, Test data

a) Normal-force curve slope.

-10

-8

-6

-4

-2

00.6 1 1.4 1.8 2.2 2.6 3

M

X cp/ d

E125-T, M-DatcomE125-T, CBUE125-T, HybridE080-T, M-DatcomE080-T, CBUE080-T, HybridE125-T, Test dataE080-T, Test data

b) Center of pressure location.

Fig. 9 Comparisons of the stability derivatives of the

elliptic body configurations.