This paper discusses response surface methods for approximation model building and multidisciplinary design optimization. The response surface methods discussed are central composite designs, Bayesian methods and Doptimal designs. An over-determined D-optimal design is applied to a configuration design and optimization study of a wing-body, launch vehicle. Results suggest that over determined Doptimal designs may provide an efficient approach for approximation model building and for multidisciplinary design optimization.

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As part of phase 2 of the X-33 Program, NASA selected an integrated lifting body/aerospike engine con guration as the study vehicle for the conceptual analysis of a single-stage-to-orbit reusable launch vehicle. A team at NASA Langley Research Center participated in the screening and evaluation of a number of proposed vehicle con gurations in the early phases of the conceptual design process. The performance analyses that supported these studies were conducted to assess the effect of the vehicle's lifting capability, linear aerospike engine, and metallic thermal protection system on the weight and performance of the vehicle. These performance studies were conducted in a multidisciplinary fashion that indirectly linked the trajectory optimization with weight estimation and aerothermal analysis tools. This approach was necessary to develop optimized ascent and entry trajectories that met all vehicle design constraints. Signi cant improvements in ascent performance were achieved when the vehicle ew a lifting trajectory and varied the engine mixture ratio during ight. Also, a considerable reduction in empty weight was possible by adjusting the total oxidizer-to-fuel and liftoff thrust-to-weight ratios. However, the optimal ascent ight pro le had to be altered to ensure that the vehicle could be trimmed in pitch using only the ow diverting capability of the aerospike engine. Likewise, the optimal entry trajectory had to be tailored to meet thermal protection system heating rate and transition constraints while satisfying a crossrange requirement. NomenclatureC L = lift coef cient I sp = speci c impulse, s M e = edge Mach number M 1 = freestream Mach number O=F = total oxidizer-to-fuel ratio q = dynamic pressure, psf q ¢ ® = dynamic pressure times angle-of-attack,psf ¢ deg Re µ = momentum thickness Reynolds number S = aerodynamic reference area, ft 2 T =W = thrust-to-weightratio .T =W / eng = engine thrust-to-weightratio W = entry weight, lb W empty = empty weight, lb W ins = inserted weight, lb X=L = body position over vehicle length ® = angle of attack, deg 1 payload = change in payload from

.jectories that met all vehicle design constraints. Significant improvements in ascent performancewere achieved when the vehicle flew a lifting trajectory and varied the engine mixture ratio during flight. Also, a considerable reduction in empty weight was possible by adjusting the total oxidizer-to-fuel and lifloff thrust-toweight ratios. However, the optimal ascent flight profile had to be altered to ensure that the vehicle could be trimmed in pitch using only the flow diverting capability of the aerospike engine. Likewise, the optimal entry trajectory had to be tailored to meet TPS heating rate and transition constraints while satisfying a crossrange requirement.