Ever wondered how Shane Warne bowled that "Ball of the Century"?



Two researchers have revealed the inner workings of spin bowling, or as they call it "the motion of an arbitrarily rotating spherical projectile".

The Robinson brothers, Garry and Ian, are Australian physicists and cricket fans. Their research paper, out on Friday in Physica Scripta, provides a mathematical model for the action of gravity, drag, and lift with regards to cricket and golf balls.

The article models the action of spin on a cricket ball to show how the movement in spin-bowling is achieved.

Ian Robertson told Guardian Australia that their work demonstrated the importance of wind in contributing to the movement of a delivery.

"Probably the most interesting aspect of the work was the fact that, for example, an off-spinning delivery exhibits a "lift" in the presence of a cross-wind coming from the off-side and exhibits a "dip" in the presence of a cross-wind coming from the leg-side".

The study shows a swing from right to left of a few centimetres for a right-hand bowler bowling an off-spin ball. This swing then increases when wind is added to the equation. Spinning the ball creates lift, or Magnus force, by disturbing the air flow around the ball in a certain direction. This allows the ball to curve in flight.

Robinson said they performed the study mainly to engage physics students with a real-world equation, but added their model might also be used by cricket teams to develop bowling skills or predict conditions.

Professor Derek Leinweber, who has done similar research on the physics of footballs, told Guardian Australia: "They've done a really good job of addressing the details of this issue of spin and trajectories."

He said the most interesting part was how the researchers modelled the movement of the ball in two directions.

"What happens when you're bowling a ball is you throw it up a bit, so in the early stages of the trajectory there's a small component of the airflow past the ball, where the ball is rising and that vertical motion against the spin will give it a small side force, which will move it to the right a little bit.

"But then once the ball hits the top of the trajectory then that side force goes away and then as the ball starts to come back down due to gravity you now have a vertical flow past the ball coming from below and that changes the direction of the side force.

"So initially the batsman would be watching the ball coming towards them, and all of a sudden at the top of the trajectory it starts to come down and it's suddenly moving away from them."

And this is what makes spin bowlers so dangerous, as Leinweber said, people find it hard to track objects that don't move in a linear trajectory.

The authors say this is the first time such a model has been published for cricket, though they cautioned it was only an approximation of the real thing.

"For example, the effects of the seam have been ignored," Robinson said.

Previously, a NASA scientist has examined cricket balls in a wind tunnel to investigate swing (PDF). More recently a PhD student at the University of Sydney has used motion-capture technology to look at the biomechanics of spin bowling.