The Missile Planform / Configuration Optimization Program OPTMIS couples a numerical optimization shell with subsonic and supersonic fast running panel method-based missile aerodynamic prediction programs which include nonlinear high angle of attack vortical effects, and a structural finite element code [1,2]. Program OPTMIS models missiles with arbitrary cross section bodies and up to two fin sections. Overall configuration, body and fin aerodynamic design objectives can be defined, as well as geometric, performance, and structural constraints. Program OPTMIS has been employed to optimize fin planform shapes for minimum axial center-of-pressure travel and for aeroelastically tailoring fins for minimum hinge moments.

The OPTMIS software, its development, and wind tunnel tests are described in AIAA Paper 98-4890 (Adobe PDF format). MISDL is employed as the aerodynamic prediction module within the design code. The VTXCHN methodology is used to model circular and noncircular body shapes within MISDL. The structural constraints are included through the CNEVAL-FEMODS module which employs automatic gridding and structural finite elements to compute displacements, stresses, fin weight, and natural mode frequencies.

Summary of Methodologies Employed
The optimization algorithm implemented in the OPTMIS design software is a direct search algorithm, Powell's Conjugate Directions Method. The Nielsen Engineering & Research (NEAR) panel method-based aerodynamic prediction software,

Fin Planform Optimization Study
Program OPTMIS was employed to develop fins which minimize the fin axial center-of-pressure travel from subsonic to supersonic flow. The fin normal force based on fin area was to be maintained. The design flow conditions were: (Mach , AOA) = (0.5, 2), (2.0, 15). For the trapezoidal reference fin, the low M number, low design condition gave a center of pressure forward on the fin, whereas the supersonic Mach number, high angle- of-attack condition gave an aft center-of-pressure location. The design objective was to minimize this center-of- pressure travel. The design variables were third-order Chebyshev polynomials describing the leading- and trailing-edge shapes. The geometries of reference (initial) and optimized fin are shown below.

A detailed comparison of experimental axial center-of-pressure data for reference FIN1 and optimized FIN3, along with predicted results, are shown in Figure 1 for the design Mach numbers 0.5 and 2.0. Measured and predicted results for FIN3 (optimized) and FIN1 (reference) are shown for deflection = 0. The axial center of pressure is plotted as a function of CNF (based on base diameter). Predicted results are shown from the OPTMIS code and the OVERFLOW Navier- Stokes CFD code. The experimental data, the results from the OPTMIS code, and the CFD results indicate that the optimized FIN3 has less center-of-pressure travel from subsonic to supersonic speeds and that the optimized fin has a flatter axial center-of-pressure variation with increasing CNF as compared to the reference fin. For CNF = 0.3 FIN3 has 50% less center-of-pressure travel than FIN1. There is, in general, good agreement between the predictions and the experiment. FIN3 produces less normal force than FIN1 for the same angle of attack, due to the smaller fin area. However, the normal force can be increased by a higher angle of attack or fin deflection without adversely affecting center-of-pressure travel.

Figure 2 compares the FIN1 and FIN3 axial center-of-pressure location for all four test Mach numbers and for deflection angles = 0 and 20. The vertical axis (xCP/cR) for both graphs in Figure 2 spans 0.32. For supersonic Mach numbers (1.5, 2.0, and 3.0), FIN3 shows only slight variations of xCP/cR with either or compared to the reference FIN1.

References

1. Lesieutre, D.J., Dillenius, M.F.E., and Lesieutre,T.O., Optimal Aerodynamic Design of Advanced Missile Configurations With Geometric and Structural Constraints , NEAR TR 520, September 1997.
2. Lesieutre, D.J., Dillenius, M.F.E., and Lesieutre,T.O., Planform/Configuration Optimization Program OPTMIS For Arbitrary Cross Section ConfigurationsWith Up To Two Fin Sets - Software User s Manual - Software Programmer s Manual , NEAR TR 519, October 1997.
3. Lesieutre, D.J., Dillenius, M.F.E., Love, J.F., andPerkins, S.C., Jr., Control of Hinge Moment by Tailoring Fin Structure And Planform , NEAR TR 530, December 1997.
4. Control of Hinge Moment by Tailoring Fin Structure and Planform - with M. F. E. Dillenius, J. F. Love and S. C. Perkins, Jr.. NEAR TR 530, December 1997.
5. Missile Fin Planform Optimization for Improved Performance - with M. F. E. Dillenius and T. O. Lesieutre. NEAR PAPER. To be presented at AGARD 82nd Fluid Dynamics Panel Symposium on Missile Aerodynamics, Sorrento, Italy, May 1998.
6. Engineering, Intermediate, and High Level Aerodynamic Prediction Methods and Applications - with M. F. E. Dillenius, M. C. Hegedus, S. C. Perkins, Jr., J. F. Love, and T. O. Lesieutre. NEAR PAPER 356, AIAA Paper 97 2278, June 1997. Presented at AIAA Conference, Atlanta, GA, June 1997.
7. Optimal Aerodynamic Design of Advanced Missile Configurations with Geometric and Structural Constraints - with T. O. Lesieutre and M. F. E Dillenius. NEAR TR 520, April 1997.
8. Planform/Configuration Optimization Program OPTMIS for Arbitrary Cross Section Configurations With Up To Two Fin Sets Software User's Manual and Software Programmer's Manual - with T. O. Lesieutre and M. F. E. Dillenius. NEAR TR 519, April 1997.
9. Leisieutre, D J., Dillenius, M. F. E., and Whittaker, C. H.: "Program SUBSAL and Modified Subsonic Store Separation Program for Calculating NASTRAN Forces Acting on Missiles Attached to Subsonic Aircraft." NAWCWPNS TM 7319, May 1992.
10. Control of Hinge Moment by Tailoring Fin Structure and Planform - with M. F. E. Dillenius, J. F. Love and S. C. Perkins, Jr.. NEAR TR 530, December 1997.
11. Missile Fin Planform Optimization for Improved Performance - with M. F. E. Dillenius and T. O. Lesieutre. NEAR PAPER. To be presented at AGARD 82nd Fluid Dynamics Panel Symposium on Missile Aerodynamics, Sorrento, Italy, May 1998.
12. Engineering, Intermediate, and High Level Aerodynamic Prediction Methods and Applications - with M. F. E. Dillenius, M. C. Hegedus, S. C. Perkins, Jr., J. F. Love, and T. O. Lesieutre. NEAR PAPER 356, AIAA Paper 97 2278, June 1997. Presented at AIAA Conference, Atlanta, GA, June 1997.
13. Optimal Aerodynamic Design of Advanced Missile Configurations with Geometric and Structural Constraints - with T. O. Lesieutre and M. F. E Dillenius. NEAR TR 520, April 1997.
14. Planform/Configuration Optimization Program OPTMIS for Arbitrary Cross Section Configurations With Up To Two Fin Sets Software User's Manual and Software Programmer's Manual - with T. O. Lesieutre and M. F. E. Dillenius. NEAR TR 519, April 1997.
15. New Application of Engineering Level Missile Aerodynamics and Store Separation Prediction Methods - with M. F. E. Dillenius, T. O. Lesieutre, and C. H. Whittaker. AIAA Paper 94-0028, January 1994.
16. Methodology for Aerostructural Analysis of a Missile Attached to a Maneuvering Aircraft - with M. F. E. Dillenius, S. C. Perkins, E. L. Jeter, J. C. Schulz. AIAA Paper No. 89-0480, AIAA 27th Aerospace Sciences Mtg., Reno, NV, January 9-12, 1989.