Objectives and Constraints for Transonic Wing Optimization

Consideration of the aerodynamic shape optimization problem definition is presented. An issue with drag minimization is that shocked-free solutions often result which have isolated performance improvements. As such, in this paper, optimizing the range parameter is considered enriched with the operating point as a design variable. A constraint on dimensional lift is therefore required. Analytical treatment of this problem is used to demonstrate that supercritical solutions result providing the lift is above a critical threshold. Also, three-dimensional effects penalise lift coefficient and promote higher optimum Mach numbers. Single- and multi-point optimizations of the NASA CRM wing are considered, inspired by the AIAA ADODG Case 4, as well as a range optimization. A shocked solution is found for the range optimization.