Getting wind of spin bowling’s secrets

Just in time for the Ashes test cricket series this week, two Australian physicists have presented equations highlighting the trajectory of a spinning ball as it moves through the air in the presence of wind. Brothers Garry and Ian Robinson, Honorary Visiting Fellows at the University of New South Wales and the University of Melbourne respectively, published their paper in the journal Physica Scripta.

The equations took into account the speed of the ball, gravity, the drag force caused by air resistance and the Magnus or ‘lift’ force (where the spin of a ball causes it to curve away from its set path), while at the same time incorporating the effect of wind. They were numerically solved using the computer software program MATLAB and the solutions were used to produce illustrative model trajectories.

“Perhaps the most interesting result is that in cricket the lift force, generated by a slow bowler’s off or leg spin (spin about a horizontal axis, directed along the line of the pitch), can cause the ball to move in a subtle manner in the air before it pitches,” noted the researchers.

They said spin can cause the ball to drift sideways in both directions while in flight - first to the leg and then the off side for an off spin bowler, and vice versa for a leg spin bowler - and the “amount of sideways drift is increased by the presence of a head wind”.

Furthermore, they added, “The presence of a crosswind, depending on its sense of direction, may cause the off or leg spinning ball to ‘lift’ or ‘dip’ with respect to the trajectory of a ball bowled without spin”, thus changing the point at which the ball pitches on the wicket. They stressed that the crosswind does not merely hold the ball up in flight, as proven by the reverse wind direction having the reverse effect. Rather, they said, “the effect is caused by the Magnus force resulting from the interaction between the crosswind operating in the y direction and the spin about the x axis”; the combination of wind and spin.

The potential effect of these changes is demonstrated by the researchers through the example of a high 14.4 km/h crosswind. Their equations show that this could change the point of the ball’s pitch by 14 cm - “large enough to potentially cause the batsman to misjudge the flight and ‘spoon up’ a catch. Thus a lift or dip of even 1 cm, resulting from a modest wind of ~1 m/s or 3.6 km/h, may well be of significance in practice.”

Although the researchers believe spin bowlers will probably be aware of the outcomes, Garry Robinson said they “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”.

The research paper comes around one year after another cricketing discovery, which debunked the myth that swing bowling is assisted by high levels of humidity.