Focusing on the wide-Mach-number-range airfoils, taking the high-speed lift-drag ratio as the optimization objective, the single-objective optimization for geometric layout is carried out. The principal vector analysis method is used for geometric parameterization. Then, the pareto frontier data is extracted from the samples generated in the optimization process, taking the minimum drag coefficient and maximum lift coefficient in transonic state and the minimum drag coefficient and maximum lift coefficient in hypersonic state as the design objectives. Based on principal vector analysis, isometric mapping, and some other methods, the implicit aerodynamic shape design knowledge of wide-Mach-number-range airfoils is mined, as well as the sensitivity relationship between design variables and target performance and the trade-off relationship between multi-objectives. As an expectation, these knowledge and rules could be used for further multi-objective design optimization of wide-Mach-number-range airfoils. The analysis results show that there is a certain change trend law between the design variables and the principal vector coefficients. In a specific aerodynamic characteristic range, the design variables value tend to be stable. It can be seen from the analysis that the intermediate process data generated by optimization implies abundant design knowledge and rules, which are helpful to reduce optimization design space and improve optimization efficiency.