The Effects of Shooting a Basketball

This article is guest blogged by University lecturer Dr. Vassilios McInnes Spathopoulos, author of An Introduction to the Physics of Sports.   You can read my review in Introduction to the Physics of Sports. 

He also wrote Windy Records in Track & Field and The Effect of Wind on Curve Running.  To read all his articles on this Blog, click here.

The Areodynamics of Basketball

Although at first it may sound strange, the motion of a basketball when it leaves the hands of a player is governed by the same physical laws that define the flight of an airplane. The path of any object, whether a ball or a complex flying machine, is determined by Newton’s laws, which most of will remember from school. The formulation of these laws was the most important scientific achievement of the great physicist, who realized that the same laws that apply to the fall of an apple also apply to the movement of planets millions of miles away from Earth.

According to Newton, the forces acting on a body are ultimately responsible for the accurate description of its motion. So what are the forces acting on a basketball in flight, determining if the result will be a successful three pointer or an air ball? Apart from the weight of the ball, which is constant and with a direction towards the center of the Earth, in this short article¹we will concentrate on two other forces, forces that are known as “aerodynamic”. They are known as such since they are created from the interaction of the ball with the air molecules through which it flies. In other words, in outer space, where there is no atmosphere, these forces do not exist.

The first one is more commonly referred to as “air resistance”, whereas aeronautical engineers call it “drag”. It is the force that we feel decelerating us when riding a bicycle or pushing our hand back when we stick it out from a car window. Any object that moves in the air is decelerated by this force; airplanes use the thrust from their engines to overcome it.

The second aerodynamic force coming into play is the so called “Magnus force”, only present when the body rotates. It is the force that is responsible for the famous “banana shot” in soccer, causing the ball to swerve. Most shots in basketball are taken by putting some spin on the ball. The rotation of the ball is such that it creates an upward Magnus force in exactly the opposite direction of the weight. It thus helps the ball to fly for longer! The spin also stabilizes the motion and provides the ball with a better chance of entering the hoop if it hits its back end or the board.

So what role does the player have in all this? Well the player is the one that determines what in physics are referred to as “initial conditions”. In other words, the initial parameters of the flight of the ball, e.g. the initial speed and inclination, on which Newton and his forces will then act on in order to determine the exact path. In a sense, the player is passing the ball to Newton , a pass that should be perfect in order for the shot to be successful. So next time you are watching or playing basketball just think that a good result requires the perfect cooperation between shooter and Newton!

[1] One can find a more detailed analysis of aerodynamic forces in sport in chapter 6 of my book “An Introduction to the Physics of Sports”.

About the Author

Dr. Vassilios McInnes Spathopoulos graduated from the University of Glasgow (UK), with a joint honours degree in Aerospace and Electronic Engineering, in 1995. The following year he completed a MSc course in Flight Dynamics at Cranfield University (UK). In 2001 he obtained his PhD from the University of Glasgow, conducting research on the validation of a rotorcraft mathematical model by means of flight testing a gyroplane. He teaches undergraduate subjects at the Department of Aircraft Technology, at the Technological Education Institute (TEI) of Chalkis, Greece. His research interests include the aerodynamics of sports balls and improving engineering education.