Definitions

# Magnus effect

[mag-nuhs]

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 and away from the direction of spin. The overall behaviour is similar to that around an aerofoil (see lift force) with a circulation which is generated by the mechanical rotation, rather than by aerofoil action. In many ball sports, the Magnus effect is responsible for the curved motion of a spinning ball. The effect also affects spinning missiles, and is used in some flying machines.

German physicist Heinrich Magnus first described the effect in 1853, but according to James Gleick Isaac Newton described it and correctly theorised the cause 180 years earlier, after observing tennis players in his Cambridge college.

## Principle

When a body such as a sphere or circular cylinder is spinning in a 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 fluid close to the body is a little greater than V on one side, and a little less than V on the other. This is because the induced velocity due to the boundary layer surrounding the spinning body is added to V on one side, and subtracted from V on the other. In accordance with Bernoulli's principle, where the velocity is greater the fluid pressure is less; and where the velocity is less, the fluid pressure is greater. As the result of the difference in fluid velocity on either side of the body, the fluid pressure is different causing a force on the body. The force acts in a direction to move the body perpendicular to the vector representing the velocity of the body relative to the fluid.

## Calculation of lift force

The following equations demonstrate the manipulation of characteristics needed to determine the lift force generated by inducing a mechanical rotation on a ball.

$\left\{F\right\}=\left\{1over 2\right\} \left\{ rho\right\} \left\{V^2Al\right\}$

F = lift force
$rho$ = density of the fluid
V = velocity of the ball
A = cross-sectional area of ball
l = lift coefficient

The lift coefficient l may be determined from graphs of experimental data using Reynolds numbers and spin ratios. The spin ratio of the ball is defined as ((angular velocity * diameter) / ( 2 * linear velocity)).

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 is commonly used to explain the often mysterious and commonly observed movements of spinning balls in sport, especially tennis, volleyball, golf, baseball, football (soccer) and cricket.

The undesirable curved motion of a golf ball known as slice is due largely to the ball's spinning motion (about its vertical axis) and the Magnus effect, causing a horizontal force. Back-spin on a golf ball causes a vertical force that counteracts the weight of the ball a little, and allows the ball to remain airborne a little longer than would be the case if the ball were not spinning. This allows the ball to travel farther than it would if it were not spinning (about its horizontal axis).

In table tennis the Magnus effect is observable because of the small size and low density of the ball. An experienced player can place a wide variety of spins on the ball. Table tennis rackets usually have outer layers made of rubber to give the racket maximum grip on the ball to facilitate spinning.

However, the Magnus effect is not responsible for the movement of the cricket ball seen in swing bowling, although it does contribute to the motion known as drift in spin bowling.

In airsoft a system known as Hop-Up is used to create a back-spin on a fired BB which will greatly increase its range, utilizing the Magnus effect in a similar manner as in golf.

## In external ballistics

The Magnus effect can be found in advanced external ballistics. First a spinning bullet or missile in flight is often subject to a crosswind. If the crosswind is exactly perpendicular, the Magnus effect causes an upward or downward force on the bullet. This force can cause an observable deflection in the bullet's flight.

Even in calm air, a bullet experiences a small sideways wind component due to yaw motion. This causes the nose of the bullet to point in a slightly different direction from the direction in which the bullet is traveling (i.e., the bullet is "skidding" sideways at any given moment, and thus experiences a small sideways wind component). (yaw of repose)

The effect of the Magnus force on a bullet is usually insignificant compared to forces such as aerodynamic drag. However, it greatly affects the bullet's stability because it acts on the bullet's center of pressure but not its center of gravity. Thus it affects the yaw angle of the bullet: it tends to twist the bullet along its flight path, either towards the axis of flight (stabilizing) or away from the axis of flight (destabilizing). It is destabilizing if the bullet's center of pressure is ahead of the center of gravity, and stabilizing if the center of pressure is behind the center of gravity. The location of the center of pressure depends on the flowfield structure, which depends on the bullet's speed (super-sonic or sub-sonic), shape, density and surface features.

## In flying machines

Many flying machines use the Magnus effect to create lift with a rotating cylinder at the front of a wing that allows flight at lower horizontal speeds. (Flettner rotor plane)

A remote controlled prototype that used the Magnus effect as the primary lift and thrust mechanism was featured on the DIY network show Radio-Control Hobbies. It consisted of a fan-like rotator generating the Magnus effect, which allowed it to lift off after traveling only a few feet forward.

A series of prototypes was built of a design called FanWing. Wind-tunnel tests were conducted in 1998 by Pat Peebles at the University of Rome.

A patent was filed by Fred Ferguson in the 1980s for an airship which used the Magnus effect as its primary lift and propulsion.

The Rotor and UFO kites use the Magnus effect for lift.