Magnus Force Calculator

Your details

Sphere uses the aerodynamic lift model; cylinder uses the Kutta-Joukowski vortex model.
Radius of the sphere or cylinder cross-section.
m
Speed of the object through the fluid (or, equivalently, the wind speed past a stationary rotor).
m/s
Rotational speed in revolutions per minute.
rpm
Select a preset fluid or enter a custom density below.
Dimensionless lift coefficient for the sphere. Typically 0.2 to 0.5 for sports balls at moderate spin.
Mass used to compute lateral deflection. A soccer ball is about 0.43 kg.
kg
Time of flight over which the lateral deflection is estimated.
s
Magnus forceModerate spin
6.286N

Lift force perpendicular to the velocity vector due to spin

Spin parameter (S)0.576
Angular velocity157.08rad/s
Surface speed17.279m/s
Lateral deflection1.8275m
Fluid density used1.225kg/m³
Magnus force (N)6.286
Surface speed (m/s)17.279
Angular velocity (rad/s)157.08

Magnus force: 6.29 N (spin parameter: 0.576)

  • The spin parameter S = 0.576. Values above 0.5 indicate a strongly spinning regime where Magnus lift becomes comparable to aerodynamic drag.
  • Over 0.50 s of flight, the object deflects laterally by approximately 1.827 m - about 182.7 cm.
  • For sports balls (soccer, baseball, tennis), increasing topspin adds a downward Magnus force that brings the ball onto the court or field faster, while backspin lifts the trajectory.

Next stepSpin intensity is moderate - the Magnus effect meaningfully curves the path. The quasi-steady Magnus model is a reliable first estimate at this spin level.

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