An approach to the aerodynamic inverse shape design problem is considered where the shape update at each iteration is found using an analytical Fourier series solution to a set of two linear differential equations with interrelated boundary conditions. The design technique requires knowledge only of the surface pressure distribution on the body to perform a shape update. Thus, it can be implemented without modifying an existing aerodynamic flow-field analysis code. Formulations are given for both the two-dimensional airfoils and three-dimensional wings. The Fourier design technique was successfully tested in conjunction with a panel code, an Euler code, and a turbulent Navier-Stokes flow-field analysis code, at subsonic and transonic speeds. The Fourier series method was found to converge within 6-25 flow-field analysis while simultaneously determining spanwise variation of wing thickness, camber, twist, and dihedral.
