Physics

# The Science of a ball in flight

The curved flight path of a spinning ball was first noticed by Sir Isaac Newton over 340 years ago and not more recently by David Beckham or Roberto Carlos. Newton observed that a tennis ball struck with an oblique racket would curve in flight.

Newton explained this phenomenon:“For, a circular as well as a progressive motion…,its parts on that side, where the motions conspire, must press and beat the contiguous air more violently than on the other, and there excite a reluctancy and reaction of the air proportionably greater.”

In 1686, Philosophiae Naturalis Principia Mathematica was published. Newton set up the first mathematical system to describe the dynamics of the universe. However, he still could not explain the curved flight path from his three basic laws of motion.

If Newton found it so hard it would be unreasonable to expect David and Roberto to offer an explanation for their ability to move a football in flight.

The effect takes its name from Gustav Magnus the German physicist who investigated it.

Later on Bernoulli also determined that as speed of a fluid is increased, its pressure decreases as stated in his famous Bernoulli’s Principle. Later on people who were playing golf found out that rough balls actually traveled farther than smooth balls.

# The Magnus effect: Sports science

Newton’s laws of Motion can be applied to a football in flight. They describe the relationship between the forces acting on a body and its motion due to those forces.His three laws do not have an exact wording but loosely they can be stated:

**First law**: If an object experiences no net force, then its velocity is constant: the object is either at rest (if its velocity is zero), or it moves in a straight line with constant speed (if its velocity is nonzero).**Second law**: The acceleration**a**of a body is directly proportional to the net force**F**acting on the body, is in the direction of the net force, and is inversely proportional to the mass*m*of the body, i.e.,**F**=*m***a**.**Third law**: When a first body exerts a force**F**_{1}on a second body, the second body simultaneously exerts a force**F**_{2}= −**F**_{1}on the first body. This means that**F**_{1}and**F**_{2}are equal in magnitude and opposite in direction.

# The Assignment: The science behind bending a ball in flight

Watch both videos carefully then:

- Complete your own research on the Magnus effect
- prepare a presentation to help train the first XI in the art of bending a soccer ball in flight predictably.
- comment on the difference in technique between Roberto Carlos and David Beckham.

Aspects could include discussion of the following:

- The relevance of the equations used in your level 1 science course to the bending of a soccer ball in flight
- How to bend the ball to the left or the right
- How to bring a ball down more quickly with a greater force than it would experience under gravity alone. (do you bend the ball around a defensive wall or lift it over and bring it down quickly so that it doesn’t clear the wall and the crossbar?)
- You may want to make your own video of a ball in flight and look at the slowmo to determine direction of spin
- Players often have a best foot. How would you chose who will take corner kicks