PARIS (AFP) – Twenty years ago, Australia's Shane Warne flighted the "Ball of the Century" that famously bamboozled England's Mike Gatting and reminded everyone of the marvels of leg-spin bowling.
Behind such deliveries lie some powerful principles of physics, a pair of Australian scientists said on Thursday, in a study published just ahead of a new Ashes series.
Not only their team, but also England will be able to benefit from the formulae uncovered -- if they can get past the layers of mathematical equations and graphs, that is.
The study by brothers Ian and Garry Robinson, published in the journal Physica Scripta, provides tools with which to measure the impact of forces like gravity, atmospheric drag, wind and "lift" on the trajectory of a randomly spinning ball.
"The average cricketer could not be expected to fully understand the details of the physics of the paper," co-author Ian Robinson of the University of Melbourne told AFP.
But luckily, a special poster has been prepared with pictures to illustrate the on-pitch meaning of the equations.
And a "user-friendly, interactive version" of the simulation programme is under development for computer, said a statement.
"It should be emphasised that the examples presented in the paper are just that -- examples," said Robinson.
"They do not pretend to provide a definitive answer to questions such as: 'How do I bowl the perfect off-spin delivery?'"
Spin bowlers use their fingers or wrist to put movement into the ball as they release it, causing it to deviate from a straight trajectory when it bounces off the pitch, hopefully fooling the batsman.
Spin balls travel much slower than those despatched by fast bowlers, who seek to deceive the batsman through speed rather than surprise.
The Robinson brothers said their paper was motivated by an interest in physics "and a long love of sport" -- and insisted its timing just ahead of the Ashes series, starting on July 10, was purely coincidental.
"The effects... are probably very well known to class spin bowlers, so we are not attempting to tell them what they already know," they wrote.
"However, the paper has served to quantify the effects and provide a means of treating other combinations of spin and winds."
Among other things, the paper was able to measure the impact of wind on "lift" or "Magnus" force, a course-changing effect that only occurs with a spinning ball.
A cross-wind of only 14 kilometres per hour (nine miles per hour) could divert the point of pitching of a spinning ball by as much as 14 centimetres (5.5 inches), wrote the brothers.
"These effects may well be enough to deceive the batsman."
They added the effects of the ball seam were not included in their calculations, and the results "are really an approximation to the real situation".
So what was the secret of the Ball of the Century?
Well -- since you asked -- it was a combination of drag force (Fd), Magnus force (Fl), velocity vector (V) and angular velocity vector (w).