How to Bend the Ball: Magnus Force


One of the most interesting things about the game of soccer to someone that is watching it played for the first time is the phenomenon that a person can make the ball "Bend" in mid air. When watching this for the first time, it is actually quite mind boggling how a ball can not only move vertically through the air, but also move with horizontal motion as well. Let's take a look at the Physics behind this concept:


Image
                        of a bending soccer ball
source: http://www.sciencedaily.com/releases/2014/06/140619210631.htm




The Magnus Force

The main force responsible for "bending" a ball's trajectory (displacing the ball out of it's vertical plane) is called the Magnus Force. This is named after the German physicist Heinrich Gustav Magnus in 1853. Magnus discovered that the difference in speeds on either side of a spinning ball relative to the air caused the ball to deflect out of it's vertical plane of motion and "bend."

Image of Magnus Force on Ball
source: http://www.unc.edu/~lwander/Group%20Project.html

As you can see from the image above, the ball is spinning about an axis that is perpendicular to the direction of the airflow that is streaming across it. As stated in the June 1, 1998 edition of the Physics World magazine, "The air travels faster relative to the center of the ball where the periphery of the ball is moving in the same direction as the airflow. This reduces the pressure, according to Bernoulli's principle. The opposite effect happens on the other side of the ball where the air travels slower relative to the center of the ball. There is therefore an imbalance in the forces and the ball deflects" (Asal, Akatsuka, Haake).


This Magnus Force can be calculated just like any other force in Physics.  The general formula for this force is:

Fm=S(w x v)


where w is the angular velocity of the object, and v is the velocity of the object in the direction of motion. S is dependent upon the drag coefficients across the object.

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