Sensitivity Analysis of a Supersonic Airfoil’s Optimal Design Using Taylor Series

In this study, we conducted a sensitivity analysis to determine the optimal design of a supersonic airfoil. The design includes four independent variables: angle of attack, thickness of the upper surface, and the locations of the upper and lower surfaces' maximum thicknesses. The output is the maximum lift-to-wave drag ratio. First, we used a first-order Taylor approximation to analyze the impact of each design variable on the output. The first three variables have similar effects, while the fourth has less influence. Next, we applied a second-order Taylor approximation to further explore how each variable affects the output and the response function near the optimal design point. The results show that small variations in the design variables lead to minor changes in airfoil performance. We also identified the variable ranges around this point that satisfy the constraints through numerical calculations. Finally, we compared our approach with factorial design, a common sensitivity analysis method, and found that Taylor approximations offer a more detailed theoretical explanation of the results.