Magnus Force Calculator

Magnus Force

The Magnus effect produces a lift force on a spinning object moving through a fluid. Spin creates asymmetric flow, generating a pressure difference and a force perpendicular to both spin and flow direction. This explains curveballs in baseball and spin in table tennis.

Formulas

Spinning sphere (common approximation):

$$F = \frac{8}{3}\pi^2 \rho r^3 \omega v$$

Spinning cylinder (Kutta-Joukowski):

$$F = 2\pi r^2 \rho \ell \omega v$$

Here $\rho$ is fluid density, $r$ is radius, $\omega$ is angular velocity, $v$ is flow speed, and $\ell$ is cylinder length.

Practical Notes

Higher spin rate, larger radius, and faster flow all increase Magnus force. Air density at sea level is about 1.225 kg/m³. Soccer balls, tennis balls, and baseballs all exhibit this effect when struck with spin.

Related tools: Buoyancy Calculator and Force Calculator.

Frequently Asked Questions

What causes the Magnus effect?

Spin alters airflow speed on opposite sides of the object, creating a pressure difference via Bernoulli's principle. The resulting force deflects the object's path.

Which formula should I use for a ball?

Use the spinning sphere formula with the ball's radius. It is a widely used approximation for sports balls in air.

What is angular velocity?

Angular velocity $\omega$ is spin rate in radians per second. One revolution per second equals $2\pi$ rad/s.

Does fluid density matter?

Yes. Denser fluids produce stronger Magnus forces. Air at sea level is about 1.225 kg/m³; water is roughly 1000 kg/m³.

What are Flettner rotors?

Large spinning cylinders mounted on ships use the Magnus effect as a sail substitute. The cylinder formula applies to these rotors.

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Magnus Force Calculator

Magnus Force

Formulas

Practical Notes

Frequently Asked Questions

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