On the Inversion of the Camber Line Problem

Often airfoil shapes are given by specification of camber line and thickness functions. The camber line of an airfoil extends from the leading edge of the airfoil to the trailing edge and its position is given as a function of distance measured along the chord of the airfoil. The thickness function measures the perpendicular distance from the upper and lower surfaces of the airfoil to the camber line. The inverse problem where the upper and lower surfaces are specified and camber line and thickness functions are to be determined give rise to a first order semi-explicit nonlinear differential algebraic equation with boundary conditions. Examples are given where there are no solutions and multiple solutions.