Application of two procedures for dual-point design of transonic airfoils

Two dual-point design procedures were developed to reduce the objective function of a baseline airfoil at two design points. The first procedure to develop a redesigned airfoil used a weighted average of the shapes of two intermediate airfoils redesigned at each of the two design points. The second procedure used a weighted average of two pressure distributions obtained from an intermediate airfoil redesigned at each of the two design points. Each procedure was used to design a new airfoil with reduced wave drag at the cruise condition without increasing the wave drag or pitching moment at the climb condition. Two cycles of the airfoil shape-averaging procedure successfully designed a new airfoil that reduced the objective function and satisfied the constraints. One cycle of the target (desired) pressure-averaging procedure was used to design two new airfoils that reduced the objective function and came close to satisfying the constraints.