Is the art of spin bowling all in the cross-wind? Ahead of the Ashes, England and Australia could learn from these two physicists

Equations that govern the trajectory of a
spinning ball as it moves through the air have been published

How can a spin bowler improve his googly or doosra, his leg break or slider? Cricketers may well spend years honing their techniques to improve the flight, pitch and bounce of the ball but a pair of Australian physicists has discovered that by just waiting a few moments for a cross-wind to pick up could prove crucial to taking wickets.

Brothers Garry and Ian Robinson publish equations today that govern the trajectory of a spinning ball as it moves through the air in a swirling wind. England and Australia’s Ashes squads may want to pay attention to the paper as they seek to gain an advantage in the series, which begins at Trent Bridge, Nottingham, next Wednesday.

The brothers reveal that the presence of a cross-wind from either side of the cricket pitch can cause the spinning ball to either slightly ‘hold up’ or ‘dip’, depending on which direction the wind comes from and which way the ball is spinning. This will significantly change the point at which the ball pitches on the wicket leaving a batsman bamboozled.

The Robinsons showed that when a 14 km/h cross-wind interacts with the spinning ball, the point at which it hits the ground can change by around 14 cm, which they believe may be enough to further deceive an opponent.

Other factors they took into account were the speed of the ball, gravity, the drag force caused by air resistance and the Magnus or ‘lift’ force, while at the same time incorporating the important effect of wind.

The Magnus force is a common effect, particularly in ball sports, when the spin of a ball causes it to curve away from its set path. Wrist spinners like Shane Warne especially utilise the effect to get the ball spinning as fast as possible. The effect on a topspin delivery makes the ball dip faster in the air and bounce further away from the batsman than he originally thought it would. The extra dip also means that the ball will hit the ground at a steeper angle and therefore bounce higher.

Isaac Newton first correctly observed and inferred the Magnus effect when watching tennis players at Trinity College, Cambridge. The effect itself is named after German physicist Heinrich Gustav Magnus who described it in an 1852 paper while investigating how to make German artillery more accurate.

Footballers such as David Beckham also utilise the effect when curling the ball around defenders or a wall of players from a set piece.

Garry Robinson said: “Our results show that the effects on a spinning ball are not purely due to the wind holding the ball up, since a reversal of wind direction can cause the ball to dip instead. These trajectory changes are due to the combination of the wind and the spin of the ball.

“The effects of spin in the presence of a cross-wind, and how to fully exploit it, may or may not be completely appreciated by spin bowlers. Either way, we have provided a mathematical model for the situation, although the model of course awaits detailed comparison with observations.”

Once the equations were constructed, they were solved using a computer software program: the solutions were then used to create illustrative examples for cricket.
The Robinsons, from the University of New South Wales and the University of Melbourne, also showed that a spinning cricket ball tends to ‘drift’ in the latter stages of its flight as it descends, moving further to the off-side for an off-spinning delivery, which Graeme Swann specialises, and moving further towards the leg-side for a leg-spinning delivery. Their research is published in the Institute of Physics’s Physica Scripta journal.
Garry added: “We hope that this work can be used to cast new light on the motion of a spinning spherical object, particularly as applied to cricket, whilst also stirring the interests of students studying differential equations.”

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