# Cricket Physics: Spin Bowling Simulations and Dynamics on MATLAB

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Spin bowling pitch showing the trajectory as a right-handed batsman delivers a typical off-spin delivery. The ball veers first to the bowler’s on side and then to the batter’s off side while in midair. Note that upon hitting the ground, the ball breaks from the off side to the leg side to hit the stumps. ©The Royal Swedish Academy of Sciences. Reproduced by permission of IOP Publishing. All rights reserved.

The study’s authors report that the trajectories obtained by their simulation conform to what is observed in practice, but the most interesting result found was the case of off or leg-spin.

This spin causes the ball to drift sideways in both directions while in flight and in presence of a cross-wind, the wind direction can either cause the ball to “lift” above or “dip” below its no spin trajectory.

While this is a small effect, causing the ball to rise or fall by no more than 4cm, the variation in the point of pitching can be as much as 14cm.

Many cricketers believe that humidity also plays a part in affecting a ball’s trajectory. Changes in humidity could change the air density which, in turn, may change both the lift and drag forces on a ball.

The study’s authors admitted that factoring this variable would be enormously difficult to do and was beyond the scope of the paper.

We can safely ignore this, as there is some doubt as to whether humidity is responsible for swing in any way according to James, MacDonald, & Hart’s 2012 article, The effect of atmospheric conditions on the swing of a cricket ball.

## Fast Bowling

Though “simplified”, the authors admit it is possible to apply their computer model to fast bowling, provided the ball does not spin.

Fast bowlers create asymmetries in a new ball by polishing one side while roughening the other to make it curve in flight. As the paper only looks at the effects of spin on smooth balls, this was also beyond the scope of the paper.

In addition to investigating the effects of spin on other types of balls and the possible effects of spin changing during flight on a ball’s trajectory, the study authors say they are working on a more user-friendly version of their model. This model will allow users to easily vary the model’s parameters and observe its effects.

By varying parameters in a controlled way, the researchers hope to identify whether a specific set of circumstances may produce something unusual.

Does this research impact the authors’ ability as cricketers? Dr. Ian Robinson tells Decoded Science, “It is some considerable time since either of us have played cricket. We have both played tennis at quite a respectable level so we are familiar with the curved paths that can be achieved in serving as well as the dip and lift that can be achieved in various ground strokes in that sport.”