Putting the physics into spin
4 Jul 2013 by Evoluted New Media
As the Ashes series gets underway next week, physicists from Australia have been exploring the physics behind the spin of a cricket ball. Siblings Garry and Ian Robinson, Honorary Visiting Fellows at the University of New South Wales and the University of Melbourne respectively, have presented equations that govern the trajectory of a spinning ball as it moves through the air in the presence of a wind. According to the research, 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 therefore changes the point at which the ball pitches on the wicket.
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.” Once the brothers created the equations, they were numerically solved using a computer software program called MATLAB; the solutions were then used to create illustrative examples for cricket. The equations take into account 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 commonly observed effect, particularly in ball sports, when the spin of a ball causes it to curve away from its set path. This is observed in football when players purposely put spin on the ball to make it bend around a defensive wall.
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 said.
paper can be downloaded from:
http://iopscience.iop.org/1402-4896/88/1/018101
