On the Magnus Effect
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Abstract
A formula for the Magnus force on a rotating and translating solid cylinder in a fluid is constructed for two different fluid models. In both cases the flow is steady and frictionless with no formation or shedding of eddies behind the cylinder. However, model one is founded on the assumption of irrotationality whereas model two is not but rather makes explicit use of the centrifugal force acting on the curving streamlines above the cylinder. Model two’s Magnus force comes out to be 15% larger in magnitude which is probably more than that can be accounted for by approximations made within the models. Observations will be needed to help decide which model comes closer to the truth. In the force formula the following factors are multiplied together: constant, fluid density, translation speed, and rotation frequency. For model one constant = 2; for model two constant = 2.3.
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