Canard-Wing Shape Optimization with Aerodynamic Requirements

Abstract

THIS paper demonstrates a numerical technique for canard-wing shape optimization at two operating conditions. For purposes of simplicity, a mean surface wing paneling code1 is employed for the aerodynamic calculations. The optimization procedures2 are based on the method of feasible directions. The shape functions for describing thickness, camber, and twist are based on polynomial representations. The primary design requirements imposed restrictions on the canard and wing volumes and on the lift coefficients at the operating conditions. Results indicate that significant improvements in minimum drag and lift-to-drag ratio are possible with reasonable aircraft geometries. Calculations were done for supersonic speeds with Mach numbers ranging from 1 to 6. Planforms were mainly of a delta shape with aspect ratio of 1, with the canard and wing in the same plane. Contents The shape functions for the thickness,3 and camber, and twist4 were each expressed as a ten-term polynomial function of the Cartesian coordinates defined in the canard-wing plane. The coefficients of these polynomials had the status of optimization variables. Volumes of the wing and canard are constrained to specified values and correspond to the volumes of the base configuration in which both the canard and wing have 5% parabolic sections. The study initially explored minimizing wave drag through wing-canard shaping by calculating the optimum thickness distribution with zero camber and twist. The results are shown in Fig. 1 for two canard sizes as well as for a wing-along case. Wave drag reductions of up to 50%, relative to the base configuration with constant thickness ratio airfoils, are feasible while still meeting canard-wing internal volume limits. The improvements in drag become more pronounced at high Mach numbers. The optimum shapes were found to be similar to those reported by Strand 3 for the wing-alone case, indicating that the presence of the canard does not introduce significant perturbations in the shape functions. The second study explored the reduction in drag due to lift through optimization of the camber and twist of the lifting surface with zero thickness (Fig. 2). Again, results are shown for two canard sizes as well as for a wing-alone case. The configurations with subsonic leading edges show drag reductions of up to 36% by use of optimum camber and twist of the lifting surface. The potential for improvement tends to diminish with increasing Mach number in contrast with the results for the optimization of thickness. Figure 3 shows, in terms of LID, the data of Fig. 2 and includes a simple flat