A very common sight in a football game has a highly interesting reason.
A footballer steps up for a free kick 40 metres away from the goal and strikes the ball. It curves from one side to the other, falls and lands in the goal in spectacular fashion, leaving the goalkeeper dumbstruck. It is as if the ball has a mind of its own, deciding to traverse a path which leads it to the goal. How does this happen? Is it the wind or perhaps a particular trick which only footballers know how to execute?
In the above image, Roberto Carlos, a Brazilian footballer, scores one of the best free kicks in history against France in the 1997 Tournoi de France. Here, the ball swerves from right to left, dips suddenly and seems to defy the laws of physics.
This amazing phenomenon is not some specialized trick, but just physics. It can be explained by understanding the properties of fluids. A fluid is a substance (such as a liquid, gas or combination of the two) tending to flow or conform to the outline of its container. The word “fluid” is derived from the Latin word fluere, which means “to flow”, which describes its characteristic property. Fluids can be made to flow or move in any direction. In any fluid, the molecules themselves are in random, chaotic motion, constantly colliding with each other and with the walls of the container. The study of fluids and their properties is governed by an entirely separate branch of physics, known as fluid mechanics. The motion of fluids and their reaction to external forces are very interesting and described by the Navier-Stokes equations, something we do not fully understand. In fact, determining their exact solution is one of the popular “Millennium Prize Problems,” and is worth a million dollars. So where do curving footballs fit into all this?
Whenever a spinning body (like a football) moves through a fluid, like air, it experiences what is known as the Magnus effect. When additional spin is added to the ball, it behaves very differently from a projectile, which is akin to a ball dropped from a certain height or a cannon launched at a certain angle. The path of the spinning object can be explained by the difference in pressure of the fluid on opposite sides of the spinning object. The body “pushes” the air in one direction, and the air pushes the body in the other direction. This force is termed the “Magnus force.” The effect of the spin was first described by Gustav Magnus, a German physicist, in 1852 hence the name “Magnus Effect.”
As a spinning object moves forward through the air, the air flies around the object from front to back. The object spins in the same direction as the airflow at the top but in the opposite direction at the bottom. Because of the friction between the air and object surface, the air is dragged around the top of the object down towards the back. At the bottom, however, the air stops quickly instead of being deflected upwards because of the opposite directions of the air flow and spin. The net result is that air is deflected downwards and due to Newton’s Third Law, an equal and opposite force is exerted back on the moving and spinning object, altering its trajectory. This is the Magnus Force.
Any spinning object experiences a force perpendicular to its spin axis; this is what Magnus observed. If it is spinning clockwise, defined as topspin in ball games, the force makes the ball swerve downwards and a counterclockwise spin, defined as backspin, the force acts upwards and prolongs the flight of the spinning ball. Footballers, cricketers and golfers use this to their advantage and add spin accordingly. In figure 1, Roberto Carlos struck the football with the inside of his boot and “sliced” the ball in such a manner that it spun counterclockwise, which made that goal possible. Technical mastery from Carlos combined with the laws of physics produced that stunning free kick. Aside from football, baseball pitchers and table tennis players use it too. A “curveball” is notoriously difficult to play because it is very tough to predict the ball’s path in the air. While it seems challenging to play, it is nothing more than a significant amount of topspin added to the baseball to confuse the batter. Table tennis players frequently add topspin to their serves and actions when playing the game. When executed perfectly, there is no way for the opponent to win the point. This means that an understanding of the science behind the skill can enhance the technique with which a sport is played. Aside from sport, the Magnus Effect has some engineering uses, for instance in the design of rotor ships. These ships have specially designed sails to make use of the Magnus effect for propulsion. Certain types of aircraft, known as Flettner aeroplanes, are designed in a similar way which helps in maintaining stable flight at lower speeds and higher efficiencies. Another extremely fun experiment which demonstrates the Magnus Effect is dropping a ball from a high altitude while adding a small amount of spin. Instead of falling straight to the ground, the ball takes its own path and glides through the air for quite a while before finally descending. When videos of this exact experiment are viewed, many people find it impossible and are convinced that it is just a camera trick. Well, it’s no trick but just physics!
The Magnus Effect is a highly fascinating phenomenon which challenges our perception of the world around us and demonstrates the beauty of physics and its applicability in all fields.
References 1. Veritasium. What Is The Magnus Force? (2011), youtube.com
Wikipedia. Magnus Effect, wikipedia.org
(Image source) BVB1992PAO. Roberto Carlos Best Goal - Free Kick Goal vs France (Tournoi de France 1997), youtube.com