How this calculator works
Kutta-Joukowski lift per unit cylinder length equals density times free-stream speed times circulation. The rotating-cylinder approximation sets circulation to circumference times surface speed. It neglects viscous separation, end effects, turbulence and limits on the circulation a real spinning surface can establish. A supplied circulation is more general than the rotation approximation. This cylinder model should not be used as a spinning-ball formula.
Formula
L = rho V Gamma ell. Surface speed Vr = omega r = 2 pi r f. Ideal rotating-cylinder circulation Gamma = 2 pi r Vr = 4 pi^2 r^2 f.
Worked example
With r = 0.1 m, length = 1 m, f = 10 Hz, rho = 1.2 kg/m3 and V = 10 m/s, ideal lift is 47.37410113 N. At 20 Hz it doubles to 94.74820225 N.
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Frequently asked questions
What direction does Magnus force act?
Perpendicular to the free stream and cylinder axis. Reversing rotation reverses the lift direction; this calculator reports magnitude.
Can I enter rpm?
Divide revolutions per minute by 60 to obtain Hz, or use angular speed after converting rpm to rad/s.
Will a real cylinder produce exactly this force?
No. Actual circulation and separation depend on the surface and flow regime. The result is an ideal estimate.