3D Magnus Effect Freekick — 2D Plan and Side View

Plan view (from above) and side view of a spinning football with drag and Magnus force, aimed over a defensive wall.

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Numerical checks

The science

A ball moving through air at speed v feels a drag force 1/2 rho Cd A v^2 along -v (Cd = 0.25 for a football, rho = 1.2 kg/m3). If it also spins with angular velocity w, the asymmetric flow adds the Magnus force, perpendicular to both w and v: F = 1/2 rho A CL v^2 in the direction of w x v, with the lift coefficient approximated by CL = 1 / (2 + v / (r w)).

Sidespin curls the ball sideways, backspin keeps it up longer and topspin makes it dip. The plan view shows the curl; the side view shows whether the ball clears the 1.9 m wall (9.15 m away) and still gets under the 2.44 m bar at 22 m. The dashed line is the same kick with the Magnus force switched off.

Simplifications: constant CL law and Cd (real values change with speed, the drag crisis and the panel seams), spin held constant, no wind, no goalkeeper, a flat pitch. The checks use the vacuum range formula, the zero work done by the Magnus force and the direction of the curl.