Magnus Effect

The Magnus effect is the effect in which one can observe a ball or cylinder curving from its initial path of motion through the air. Contents

   1 The Magnus Effect
       1.1 A Mathematical Model
       1.2 A Computational Model
   2 Examples
       2.1 Simple
       2.2 Middling
       2.3 Difficult
   3 Connectedness
   4 History
   5 See also
       5.1 Further reading
       5.2 External links
   6 References

The Magnus Effect

The Magnus Effect is the lift force created on a rotating spherical or cylindrical object about an axis as it moves through a fluid. The force is perpendicular to the forward motion and causes the object to deviate from its standard flight path. Areas of high and low pressure are formed around the object, and the object tends to curve in the direction of low pressure.

A Mathematical Model

The Magnus effect is an application of Bernoulli's theorem. This theorem states that if a fluid has velocity v, the pressure p of that fluid is equal to 1rv^2, with r being the constant fluid density. Since the pressure is normal to the surface of an object, the upward component is -sin(q)p(q). If we integrate the pressure times the surface area of a cylinder with radius r, we get the lift:

F_p = -(rho*Gamma)/4 (1+1/r^2)

If we say r = 1, the net lift can be shown as:

L = -rho*v_0*Gamma

This is the Magnus effect.

A Computational Model

A computational model of the Magnus effect can be observed by this graphic created in VPython: Magnus effect [1]

Connectedness

The Magnus effect can be seen perhaps most commonly in the world of sports. In baseball, pitchers vary their grip, release, and pressure placed on each finger in an effort to maximize the Magnus effect and achieve large levels of break on their pitches.

A breakdown of the Magnus effect in baseball can be seen in this video showing the pitches of legendary Yankees closer Mariano Rivera.[2]

History

Sir Isaac Newton recorded the effects in 1672 after observing the flight of tennis balls at his college in Cambridge. Benjamin Robins also described what would come to be known as the Magnus effect in 1742 after observing the curving of musket balls. However, the effect would be named after German physicist and chemist Gustav Magnus (1802-1870). He experimented