Magnus Force Calculator

Use our Magnus force calculator to find the total force generated by the Magnus effect on a spinning cylinder.

Lift force578.8125 mNupward

Drag force578.8125 mN551.25 Pa dynamic pressure × 0.25 × 0.0042 m²

Dynamic pressure ½ρv²551.25 Pa

Power to overcome drag17.3644 W0.02 hp — power goes as the CUBE of speed, because force goes as the square and power is force times speed

Drag area (C_d × A)0.00105 m²the product is what matters — this is the figure to compare between vehicles

Lift to drag ratio1the efficiency of a lifting surface — a glider reaches 40 or more, a light aircraft about 10

Mass this lift would support0.059 kg

At 0.5× the speed144.7031 mN0.25× the drag and 0.125× the power

At 1.5× the speed1.3023 N2.25× the drag and 3.375× the power

At 2× the speed2.3153 N4× the drag and 8× the power

Reference area conventionmust match the coefficienta car's C_d uses frontal area, a wing's uses plan area, and a sphere's uses its cross-section — mixing a coefficient with the wrong area is the commonest error here

The formula

F = ½ρv²C_dA for drag, ½ρv²C_lA for lift

Force squares, power cubes

Drag is dynamic pressure times a coefficient times a reference area. Because dynamic pressure goes as the square of speed, the force quadruples when the speed doubles — and since power is force times speed, the power required goes up eightfold.

That cube law is why top speed is so expensive and why efficient cruising is slow. A car needing 20 hp at 60 mph needs about 160 hp at 120 mph on drag alone, and it is why the last few miles per hour of a vehicle's top speed consume a disproportionate share of its engine.

The coefficient is meaningless without knowing which area it was defined against. Automotive drag coefficients use frontal area, aerofoil coefficients use plan area, and a sphere's uses its cross-section. This is why the drag area — the product of coefficient and area — is the honest figure for comparing vehicles: a low coefficient on a large frontal area is not aerodynamic.

Both coefficients vary with Reynolds number, sometimes sharply. A sphere's drag coefficient drops abruptly at around Re = 3 × 10⁵ when its boundary layer turns turbulent, which is exactly why golf balls have dimples.