The Magnus Effect And Baseball

PITTSBURGH – In 1852, a German physicist by the name of Gustav Magnus was trying to figure out why spinning artillery shells sometimes curved in unpredictable ways. What he discovered was that a sphere or cylinder spinning in a moving airstream develops a force at a right angle to the direction of the moving air and curves away from its principal flight path.*

Hence, the Magnus Effect was born.

Today, some we see the Magnus Effect being applied everyday in baseball, golf, tennis and cricket, as well as many other sports.

Here, Dr. Rod Cross, who holds a PhD. in plasma physics from the University of Sydney, explains the Magnus Effect (click on the bottom left corner of the video for sound).

In terms of baseball, the Magnus Effect applies most to pitching. Or more specifically, the curveball.

A curveball, thrown with topspin, creates a higher pressure zone on top of the ball, which deflects the ball downward in flight. Instead of counteracting gravity, the curveball adds additional downward force, thereby gives the ball an exaggerated drop in flight.

A fastball, on the other hand, travels through the air with backspin, which creates a higher pressure zone in the air ahead of and under the baseball. The baseball’s raised seams augment the ball’s ability to develop a boundary layer and therefore a greater differential of pressure between the upper and lower zones.

The effect of gravity is partially counteracted as the ball rides on and into increased pressure. Thus the fastball falls less than a ball thrown without spin (neglecting knuckleball effects) during the 60 feet 6 inches it travels to home plate.

In previewing the 2007 World Series between the Boston Red Sox and Colorado Rockies, Dr. Alan Nathan looked at the affect of the mile-high altitude at Coors Field in Denver on the trajectory of a baseball in flight compared to a trajectory at Fenway Park in Boston. With this, he discussed the Magnus Effect:

“Regardless of whether the ball is pitched or batted, its motion is determined by the forces acting on it. These forces are the downward force of gravity that we are all familiar with as well as two principal aerodynamic forces: the drag force and the Magnus force. Both the drag and Magnus forces result from small imbalances of the air pressure on different parts of the ball. If the baseball is also spinning, it experiences the Magnus force, which is responsible for the curve or “break” of the baseball. The direction of the force is such that the ball breaks in the direction that the leading edge of the ball is turning. For example, a baseball thrown with backspin (e.g., an overhand fastball) has an upward Magnus force, opposing gravity, so that a typical fastball does not drop as much as it would if it were solely under the influence of gravity.

On the other hand, an overhand curveball (“12-6”) has topspin, so that the Magnus force is down, in the same direction as gravity. Such a pitch will drop more than it would from gravity alone. Other pitches (sliders, cutters, etc.) have a sideways component of spin, leading to a side-to-side break of the pitch.

The Magnus force also has an important effect on the flight of batted baseballs. For a fly ball on a typical home run trajectory, the ball usually backspin. The upward Magnus force opposes gravity, keeps the ball in the air longer, and leads to a longer fly ball.”

This video below gives an example of this through a detailed computational fluid dynamics calculation of a spinning baseball.

The unsteady top-to-bottom pressure difference on the ball aids gravity in forcing the ball toward the ground. The injected particles follow the instantaneous flow velocity and thus trace out the unsteady flow pattern behind the rotating baseball. In addition, the particles follow a slightly upward path which indicates that the reaction force on the ball (due to the change in air flow momentum) is also toward the ground.**

For further, more in-depth reading on Magus Force, please take a look at Dr. Nathan’s paper on the effect of spin on the flight of a baseball.



*Popular Science
**Tetra Research