The aim of the research described herein was to develop and verify an efficient optimization-based aerodynamic / structural design tool for missile fin and configuration shape optimization. The developed software was used to design several missile fin planforms which were tested in the wind tunnel. Specifically, this paper addresses fin planform optimization for minimizing fin hinge moments, as well as aeroelastic design (flexible fin structures) for hinge moment control. The method is also capable of shape optimization of fin-body combinations with geometric constraints. The inclusion of aerodynamic performance, geometric constraints, and structural constraints within the optimization software facilitates multidisciplinary analysis and design. The results of design studies and wind tunnel tests are described.

fin deflection angle, deg Predicted nonlinear aerodynamic characteristics of roll angle, deg several canard-body-tail missile models are presented fin set roll angle with respect to body-fixed and compared to wind tunnel data. Configurations with vertical axis, positive right wing down, deg both fin sets deflectable (tandem-control) are analyzed to investigate the effectiveness of canard-only, tail-only,

The MISSILE 3 engineering prediction method for missile acradynamic performance calculations has been improved to better predict missile longitudinal a n d lateral-directional forces a n d m o m e n t s a s well as individual fin forces a n d m o m e n t s . T h e m e t h o d considers nonlinear effects such as induced rolling moments due to the influence of asymmetric canard and body vorticity on missile tail fins. In addition, c o n r p a r i s o n s w i t h e x p e r i m e n t a t t r a n s o n i c (0.8 5 Mm 5 1.2) and high Mach numbers (Mm > 4 ) and high angles of attack ( a 5 45') indicate that this prediction method is applicable t o e x t r e m e flight conditions. Recent modifications to the MISSILE 3 code are described, and a number of measured and predicted aerodynamic characteristics are provided t o demonstrate the capabilitics and limitations of this last& version.

Studies of vortex-induced aerodynamic nonlinearities associated with body and fin vortices for missile configurations have been performed. As part of this effort, the vortex and fin modeling methodologies in the engineering-level and intermediate-level aerodynamic predictions codes MISL3 and MISDL have been reviewed and improved. The ability of the methods to predict detailed fin loads in the presence of external vortices is demonstrated. Both codes have been used extensively to predict missile performance including canard/wing vortex induced effects on tail fins. These effects often manifest themselves in pitching moments and most dramatically in induced rolling moments on tail fins which counter, and often times reverse, the direct roll control of canard fins. Both codes have shown the capability to capture these vortexinduced phenomena. For validation purposes, the methods were compared to detailed vortex-fin interaction studies, performed at Sandia National Laboratories, which measured fin loads influenced by a vortex generated by an upstream fin. Nomenclature AR= aspect ratio (two fins joined at root) C l = rolling moment/q ∞ S R l R C m = pitching moment/ q ∞ S R l R ; positive nose up C N = normal force/ q ∞ S R C NF = fin normal force/ q ∞ S R D = body diameter, maximum L = body length l R ,L REF = reference length q ∞ = freestream dynamic pressure S R ,S REF = reference area x CP = fin chordwise center of pressure, or overall configuration axial center of pressure y CP = fin spanwise center of pressure x HL = fin hinge line loaction x MC = moment center α = angle of attack, deg δ = fin deflection angle or angle of attack for fin alone, deg λ = fin taper ratio φ = roll angle, deg

The aerodynamic design of an asymmetric oversized payload fairing subject to stability constraints was used as an example of a derivative-free, expensive black box function to benchmark the relative performance of 16 different optimization methods, ranging from gradient-based to simulated annealing and genetic algorithms/evolution strategies, including four methods with surrogate-based accelerators. The focus of the present paper is on the practical attainability of getting an acceptable solution quickly. The various algorithms are compared using performance benchmarking in a statistical sense, yielding an "efficient frontier" with special emphasis on the case when designers are confronted with small computational budgets.