The

**Magnus effect**is the phenomenon whereby a spinning object flying in a fluid creates a whirlpool of fluid around itself, and experiences a force perpendicular to the line of motion.

In fluid dynamics,

**Bernoulli's principle**states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. But it doesn't mention the effect when an object is spinning through a fluid (that's what happened in Magnus effect), that has an incremental energy due to the spinning object.

## Principle

When a body (such as a sphere or circular cylinder) is spinning in a viscous fluid, it creates a boundary layer around itself, and the boundary layer induces a more widespread circular motion of the fluid. One explanation of the Magnus effect is since there is more (forward) acceleration of air on the forward-moving side than the backward-moving side, there is more pressure on the forward-moving side, resulting in a perpendicular component of force from the air towards the backward-moving side (watch the video bellow).

## Calculation of Magnus force

Given the angular velocity vector and velocity of the object, the resulting force can be calculated using the following formula:

where

*S*is dependent on the average of the air resistance coefficient across the surface of the object.^{[8]}The denotes the vector cross product.###

An example of spin ball in the air

The following equation demonstrates the lift force induced on a ball that is spinning along an axis of rotation perpendicular to the direction of its translational motion:

*F*= lift force*ρ*= density of the fluid*r*= radius of the ball*v*= velocity of the ball*A*= cross-sectional area of ball*C*= lift coefficient_{L}

The lift coefficient

*C*may be determined from graphs of experimental data using Reynolds numbers and spin ratios._{L}^{[9]}For a smooth ball with spin ratio of 0.5 to 4.5, typical lift coefficients range from 0.2 to 0.6.