Can physics calculate the spin of a cricket ball?

The game of cricket is complex, and the team captain must consider his bowlers as well as the order in which to send them.

In a captain’s arsenal, there are pace bowlers (fast) and spin bowlers both of whose primary goal is to dismiss the batsman or get him out.

Pace bowlers rely on speed to do this. Instead of using speed, spin bowlers or “spinners” impart rotation on a ball to confuse a batsman.

Spinning the ball makes its movement difficult to predict as the ball’s trajectory curves through the air.

To better understand the dynamics of spin bowling,Drs. Garry and Ian Robinson of the University of New South Wales and the University of Melbourne respectively, created a MATLAB simulation to look at the effects of spin on a ball’s trajectory.

Their findings were published recently in the journal *Physica Scripta*. Though the article focuses on the games of golf and cricket, the equations can equally apply to other ball games such as tennis, soccer or baseball.

## The Aerodynamics of Spin Bowling

In the sport of cricket, the bowler throws the ball towards the batter. Unlike the sport of baseball, the cricket ball strikes the pitch or ground. Depending on the ball’s speed, spin and overall condition (whether it is worn or not) a bowler can change its trajectory, making it difficult for a batter to anticipate its motion. This also makes it difficult to anticipate where the ball “pitches” or strikes the ground and what direction it bounces.

To simplify the problem, the study’s authors only look at the dynamics of spin bowling and what happens before the ball hits the pitch.

The authors assume three forces are acting on a ball: (1) gravity, (2) drag and (3) lift (see above Figure). If we consider only gravity, analyzing projectile motion is simple. Once we include forces other than gravity, however, obtaining an analytical solution becomes difficult and we must turn to numerical methods.

Both the drag and lift forces are the result of the Earth’s atmosphere acting on the ball. In the case of drag, as the ball moves through the air, it must push air molecules out of the way to move forward. The magnitude of this drag force depends on several factors, such as the speed of the ball, the viscosity of the air as well as the smoothness of the ball.

For the purposes of this study, the researchers assumed the ball was smooth.

Wind also plays a crucial part in ball dynamics. As both the drag and lift force vectors are dependent on a projectile’s velocity relative to air, wind speed and direction affect the magnitude and direction of these forces.

While a skilled batsman may sometimes pick up on the type of delivery bowled by watching a bowler’s hand position, wind speed and direction can affect a ball’s trajectory – making anticipating its path more difficult.

## Numerical Analysis of Spin Bowling on a Computer

As the equations of motion governing the trajectories of a spinning ball generally have no analytical solutions, (solutions which we can express as a simple equation), we must solve them numerically.

While scientists have been writing programs to simulate and solve the differential equations typically found in spinning balls, writing such a program requires some thought and computational skill on the part of the user – as in the case of FORTRAN.

Programming packages, such as MATLAB, have made the numerical solution of differential equations simple and routine, especially for students with limited mathematical and programming skill. As the fundamental equations derived in the paper have not appeared anywhere in literature, the authors believe there is inherent scientific value in the study.

The researchers also believe that this will help cultivate student interest in the numerical solution of differential equations and better help those who actively participate in ball-games compare their experience to a computer simulation.

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