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.

The report reviews both theoretical and experimental investigations of the Magnus effect on arbitrary bodies of revolution. The main emphasis is on spinning projectiles at angle of attack, both with and without fins. Flow visualization measurements are used to assess the accuracy of the existing theories. Laminar, turbulent, and mixed boundary layers are considered. (Author).