Calculation of Magnus Forces on Axisymmetric Bodies at Small Angles of Attack with Incompressible Turbulent Boundary Layers

The Magnus force is found by adding the boundary layer displacement surface to the body and then calculating the force on the resulting non- axisymmetric body. The displacement surface is calculated by the simultaneous integration of a differential equation for a streamline, two partial-differential boundary layer integral-momentum equations with the boundary layer thickness and the tangent of the angle between the local direction of the surface friction and potential flow streamline as dependent variables, and a partial differential equation for the displacement surface thickness. The method is applied to a half-ellipsoid of fineness ratio 5 at 4 degrees angle of attack. Slender-body theory is used to calculate the force.