Introduction: The Magnus effect (often called the Magnus force and named after its 1852 discoverer Gustav Magnus) is a lift force of tremendous importance to all athletes who want to bend the flight of a ball. You see the Magnus effect at work in the curved flight path of balls that are thrown, hit, or kicked and at the same time are given a spin. Golfers, baseball pitchers, and soccer, tennis, and table tennis players all employ this effect to curve the flight path of the ball. The game of baseball in particular is made more fascinating by the Magnus effect. The ability of a pitcher to throw curveballs, sliders, screwballs, and knuckleballs that have very little spin—and then have a batter hit these pitches—is the essence of baseball.
The Magnus effect operates in the following manner. As a spinning ball moves through the air, it spins a boundary layer of air that clings to its surface as it travels along. On one side of the ball the boundary layer of air collides with air passing by. The collision causes the air to decelerate, creating a high-pressure area. On the opposing side, the boundary layer is moving in the same direction as the air passing by, so there is no collision and the air collectively moves faster. This sets up a low-pressure area. The pressure differential, high on one side and low on the other, creates a lift force (the Magnus force) that causes the ball to move in the direction of the pressure differential (i.e., from high to low).
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. If the body is moving through the fluid with a velocity V, the velocity of the thin layer of fluid close to the body is a little less than V on the forward-moving side and a little greater than V on the backward-moving side. This is because the induced velocity due to the boundary layer surrounding the spinning body is subtracted from V on the forward-moving side, and added to V on the backward-moving side. If the spinning body is regarded as an inefficient air pump, air will build up on the forward-moving side causing higher pressure there than on the opposite side. Another explanation of the Magnus effect is since there is less (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. This layer of spinning air, however, is very thin, and it is more likely that most of the Magnus effect is due to the earlier detachment of the air flow on the forward-moving side, which results in a diversion of the flow (acceleration of air) with a perpendicular component towards the forward-moving side, coexisting with an opposing aerodynamic force with a perpendicular component towards the backward-moving side.
Calculation of Magnus force: Given the angular velocity vector and velocity of the object, the resulting force can be calculated using the following formula:
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
= density of the fluid
v = velocity of the ball
A = cross-sectional area of ball
CL = lift coefficient
The lift coefficient CLmay be determined from graphs of experimental data using Reynolds numbers and spin ratios. For a smooth ball with spin ratio of 0.5 to 4.5, typical lift coefficients range from 0.2 to 0.6.
In sport: The Magnus effect explains commonly observed deviations from the typical trajectories or paths of spinning balls in sport, notably association football (soccer), table tennis, tennis,volleyball, golf, baseball, cricket and in paintball marker balls. The curved path of a golf ball known as slice or hook is due largely to the ball's spinning motion (about its vertical axis) and the Magnus effect, causing a horizontal force that moves the ball from a straight-line in its trajectory. Back-spin (upper surface rotating backwards from the direction of movement) on a golf ball causes a vertical force that counteracts the force of gravity slightly, and enables the ball to remain airborne a little longer than it would were the ball not spinning: this allows the ball to travel farther than a non-spinning (about its horizontal axis) ball.