How the cricket ball goes around

Scientists explain how a spinning cricket ball moves with mathematical model

Cricket ball in a spinner's arm

Garry and Ian Robinson, Honorary Visiting Fellows at the University of New South Wales and the University of Melbourne respectively, have presented mathematical equations that govern the trajectory of a ball bowled by a spinner as it moves through the air.

The researchers have calculated that wind blowing across the pitch can have a profound effect on the aerialpath of a spin-bowler's delivery.

As per the research, the cross-wind from either side of the cricket pitch can cause the spinning ball to either slightly "hold up" or "dip", depending on the direction of the wind and the direction of the spin on the ball. As a result, point at which the ball lands on the wicket is affected.

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."

As an example, the researchers show that a 14 km/h cross-wind can change the point of landing by around 14 cm, which they believe may be enough to deceive a batsman.

The researchers also show 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 and moving further towards the leg-side for a leg-spinning delivery, effects which are well-known and regularly utilised by spin-bowlers.

"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," Garry continued.

The research was published in Physica Scripta, a journal published by IOP Publishing on behalf of the Royal Swedish Academy of Sciences for the Science Academies and the Physical Societies of the Nordic Countries.

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