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An efficient numerical approach for the design of optimal aerodynamic shapes is presented in this paper. The objective of any optimization problem is to find the optimum of a cost function subject to a certain state equation (governing equation of the flow field) and certain side constraints. As in classical optimal control methods, the present approach introduces a costate variable (Lagrange multiplier) to evaluate the gradient of the cost function. High efficiency in reaching the optimum solution is achieved by using a multigrid technique and updating the shape in a hierarchical manner such that smooth (low-frequency) changes are done separately from high-frequency changes. Thus, the design variables are changed on a grid where their changes produce nonsmooth (high-frequency) perturbations that can be damped efficiently by the multigrid. The cost of solving the optimization problem is approximately two to three times the cost of the equivalent analysis problem. Nomenclature

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To achieve closure on the physical and economic performance metrics of air-breathing hypersonic vehicles, their components and functions must be highly integrated. Such extensive integration challenges conventional design paradigms, approaches and tools. Unconventional approaches must therefore be developed and employed to achieve design success, among them parametric configuration definition, automated engineering and highfidelity discipline analysis, and multidisciplinary optimization, to name a few. These and other advanced design technologies are being developed and applied at Boeing to the design of hypersonic vehicles, as well as to other Boeing aerospace platforms. This paper describes recent Boeing progress in developing and applying the elements of a multidisciplinary analysis and optimization system to hypersonic vehicle design, and outlines future work aimed at further developing this critical capability.

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