Extension of Multhopp's quadrature method to cyclic periodic lifting systems

In this contribution Multhopp's quadrature method for the calculation of the circulation distribution in the framework of lifting line theory is extended to cyclic periodic lifting systems. Further a viscous correction term allows to account for finite airfoil performance. It is shown that the method is capable of predicting an optimal radial circulation distribution for wings operating in swirling flow situations if coupled with an optimization procedure. An example is given where the thrust maximizing airfoil circulation is calculated for a given vortex structure and airfoil characteristic. With the help of some simple performance considerations the method is able to translate the obtained circulation distribution into the actual geometry of the wing assembly.