Multipoint inverse airfoil design method based on conformal mapping

A method of multipoint inverse airfoil design for incompressible potential flow is presented. Multipoint design is handled by dividing the airfoil into a number of desired segments. For each segment, the velocity distribution is prescribed together with an angle of attack at which the prescribed velocity distribution is to be achieved. In this manner, multipoint design objectives can be taken into account in the initial specification of the velocity distribution. In order for the multipoint inverse airfoil design problem to be well posed, three integral constraints and several conditions arise that must be satisfied. Further restrictions are imposed if the airfoil is to have a specified pitching moment, thickness ratio, or other constraints. The system of equations is solved partly as a linear system and partly through multidimensional Newton iteration. Since the velocity distribution is prescribed about the circle in terms of the arc limit, specification of the velocity in terms of arc length is also handled through multidimensional Newton iteration.