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Could the physics of spin bowling turn the Ashes around?

After the first day of the third Ashes test cricket match between England and Australia it may be a good time to consider how spin bowling might affect the outcome of the series - and how science can be…

The science of spin bowling yields some interesting – and practical – results. Wallula Junction

After the first day of the third Ashes test cricket match between England and Australia it may be a good time to consider how spin bowling might affect the outcome of the series - and how science can be used to describe the effects of spin bowling.

In our recently-published paper in the journal Physica Scripta we mathematically modelled the effects of spin and wind on a rotating spherical projectile, such as a spinning cricket ball.

The basics of spin bowling

Spin bowlers attempt to deceive batsmen through movement of the ball through the air, and by deviation of the ball as it bounces off the wicket. Ball movement through the air occurs as a result of the angular velocity imparted to the ball by the bowler.

Terminology of cricket ball spin directions. Robinson & Robinson, 2013

This movement can manifest itself as a “drift” away from the batsman or a drift towards the batsman. The ball can also “hold up” (or “lift”) so that it bounces, or pitches, further down the wicket towards the batsman than if the ball had no spin. Alternatively, it can “dip,” so that it pitches shorter than it would had it had no spin – as English test cricketer Graeme Swann does to great effect in the video below:

There can also be combinations of drift and lift, or drift and dip.

The techniques used to impart spin on the ball by the bowler fall loosely into two categories: finger spinners and wrist spinners.

A right-handed finger spinner will predominantly bowl off-spinners, in which the ball rotates approximately clockwise (from the bowler’s perspective) as it travels down the pitch, and typically turns off the pitch from the off-side (the right side of the wicket for a right handed batsman) towards the leg-side (the left side of the wicket for a right-handed batsman).

A right-handed wrist spinner will predominantly bowl leg-spinners with the ball rotating approximately counter-clockwise (from the bowler’s perspective) and typically turning off the pitch from the leg-side towards the off-side.

Of course, this is an over-simplification because class bowlers of both varieties will have quite a few variations of deliveries that they can bowl to produce different movements through the air and off the pitch. Swann talks through some variations in the video below:

They will also attempt to disguise their bowling action in order to convince the batsman the ball they’re receiving is something other than what it really is.

Use the force

A spinning ball has three forces acting on it:

  • a gravitational force acting vertically downwards
  • a drag force
  • a lift or “Magnus” force, which occurs only if the projectile is spinning, as shown in the diagram below:

Rotating sphere exhibiting underspin and showing the gravitational, drag and lift forces as well as the velocity and angular velocity vectors. The lift force is vertically upwards and the wake is deflected downwards. © The Royal Swedish Academy of Sciences. Reproduced by permission of IOP Publishing. All rights reserved

Cases in which the spin vector is perpendicular to the projectile velocity (“top-spin”, “under-spin” or “side-spin”) have been studied before but cases in which the spin vector is in an arbitrary direction and in the presence of a wind are significantly more difficult to treat.

Such arbitrary spin directions are of interest for a spin bowler’s delivery in cricket, where the spin axis may be approximately in the direction of the velocity vector, at least in the initial stages of the flight.

In our calculations, we made some assumptions about the motion of a cricket ball, including:

  • The ball is spherical
  • The effects of the seam are ignored
  • The drag force is proportional to the square of the velocity and acts in the opposite direction to it
  • The lift force is proportional to the square of the ball’s velocity and acts perpendicular to this velocity and to the angular velocity vector

The diagram below shows the trajectory of an off-spin delivery, or “wrong ‘un” as delivered by a leg-spin bowler. Such a delivery may exhibit sideways drift in flight and, in the presence of a crosswind, may dip or lift vertically before pitching.

A cricket pitch with important features labelled, assuming a right-hand batsman and bowler. Also shown schematically is the trajectory of a typical off-spin delivery (or leg-spinner’s “wrong ‘un”). © The Royal Swedish Academy of Sciences. Reproduced by permission of IOP Publishing. All rights reserved

In our study, we quantified the effects of a cricket ball’s spin, in the presence of crosswinds and headwinds, and showed that the ball can exhibit sideways drift and vertical dip and lift.

Sideways drift

To demonstrate the effect of spin and wind on the sideways motion of a cricket ball as it travels through the air before pitching, consider the trajectories in the diagram below of five deliveries bowled from a height of 2m, at 79km/h and an angle of elevation of 5°, with:

  • No spin (solid blue line)
  • Pure off-spin of 1,432rpm, no wind (purple dashed line)
  • Pure side-spin of 1,432rpm, no wind (black dashed line)
  • Off-spin of 1,432rpm into a headwind of 27km/h (light blue dotted line)
  • No spin, but with a 5.4km/h crosswind from the leg side (solid red line)

The effect of sideways movement of off-spin, side-spin and various winds on the sideways motion before pitching of a cricket ball. © The Royal Swedish Academy of Sciences. Reproduced by permission of IOP Publishing. All rights reserved

The two off-spin deliveries first drift slightly to the leg-side as the ball rises and then to the off side as the ball falls, the effect at 18m down the pitch being more noticeable if the headwind is present (2cm) than if there is no headwind (1cm).

For pure side-spin the effect is far more dramatic, even with no wind, the ball drifting to the off side by 10cm after having travelled only 11m down the pitch. It would therefore appear that the bowler can control the amount of drift by altering the mix of side-spin and off-spin components – something which is, no doubt, well known to spin bowlers.

Finally a delivery with no spin in the presence of a sidewind is displayed where a sideways movement of about 8cm results by the time of pitching.

To see the effect of crosswinds, we calculated the trajectories of three off-spin deliveries, rotating at 1,432rpm, and with the same height, speed and angle of elevation as the examples above, in the presence of three wind conditions:

  • No wind (solid blue line)
  • A crosswind of around 14km/h blowing across the pitch from the off side (black dashed line)
  • A crosswind of around 14km/h blowing across the pitch from the leg side (red dashed line)

The effect of crosswinds on an off-spin delivery. © The Royal Swedish Academy of Sciences. Reproduced by permission of IOP Publishing. All rights reserved

There will be a small sideways drift of about 1cm to the off side in the no-wind case. This drift is purely due to the Magnus force as a result of the rotation of the ball.

The presence of a cross-wind completely dominates this effect, as is expected, and moves the ball in the direction of the wind by more than 20cm, the effect being larger when the wind aids the drift due to spin, again as expected.

Vertical dip and lift

If we look at those same three deliveries from the side, we can see how crosswinds, combined with spin, can affect the length at which a delivery pitches.

The right hand graph below also shows a delivery with no spin in the presence of a 14km/h crosswind from the leg side (dotted purple line) for comparison.

The effects of crosswinds on the dip and lift of off-spin deliveries, and differences in range as a result. The graph on the right is an expanded view of the vicinity of impact in the graph on the left. © The Royal Swedish Academy of Sciences. Reproduced by permission of IOP Publishing. All rights reserved

A wind blowing from the off side causes the spinning ball to lift above the no-spin trajectory, and a wind blowing from the leg side causes the ball to dip below the no-spin trajectory.

The variation in height from the no-spin trajectory is about ±4cm and, more importantly, the variation in the point of pitching is about ±14cm.

Even a more modest wind of about 1m/s (3.6km/h) would cause a variation in the point of pitching of about ±3.5cm.

The trajectories for the no-wind case (solid blue line) and the no-spin case in the presence of a crosswind from the leg side (dotted purple line) in the graph on the right lie very close together and approximately central between the other two lines.

Importantly, this indicates that it is the combination of the crosswind and the spin - not the spin or wind alone - which causes these effects.

These sideways and vertical movements can be large enough to cause the batsman to either misjudge the position of the ball and “edge” it to a fieldsman, or to misjudge the point of pitching and lift it in the air.

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6 Comments sorted by

  1. Jonathan Kelly

    IT Consultant

    For what it is worth, some simple experimental insights.

    My son (as a research project for Yr 9 science this year) said he wanted to look at how cricket balls swung.

    I suggested he use water as a medium rather than air to make it manageable and slow enough to measure.

    He set up a tall vase with water and used a small "superball" that had one side roughed up using a file and sandpaper (the other side remained smooth).

    He rigged up a piece of PVC pipe that allowed the ball to roll along it (building up spin) until it dropped out into the column of water.

    We then filmed it using a go-pro camera at 100 frames per second.

    I was expecting a small 'swing' movement that we might just be able to measure when looking at the film frames.

    Instead the ball moved significantly (towards the smooth side) - 5cm or more over about 50 cm drop and was easily observed by eye.

    It did this consistently and repeatedly.

    I was impressed by how strong the effect was.

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  2. John Crest

    logged in via email @live.com.au

    "...some assumptions about the motion of a cricket ball, including:
    •The ball is spherical
    •The effects of the seam are ignored"

    I'm, not sure I would have made those two assumptions.

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  3. David Stephens

    Writer and activist

    Fascinating. Worth looking also at the effects of bowling off a bent middle finger, as did Iverson (mostly off spin) and Gleeson (mostly top spin and leg spin) and I think one of the newer Sri Lankan bowlers. Right hand leg spin action with bent finger gives drift off to leg, often sharp and late, then spin off to leg (ie in the same direction). Right hand off spin action with bent finger gives drift leg to off and spin in the same direction. The latter much harder to bowl. Bowling off a bent third finger rather than middle finger produces a sort of flipper with low bounce. The hardest thing perhaps is choosing the right angle and direction from the bowling crease. A clever proponent of bent finger off spin in Canberra used to bowl from close to the stumps and aim at second slip to allow for drift back in, producing almost boomerang effect with sharp spin and bounce at the end. I speak from experience of bowling this stuff but I was not the clever proponent, unfortunately.

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  4. Peter Hindrup

    consultant

    'In our recently-published paper in the journal Physica Scripta we mathematically modelled the effects of spin and wind . . .'

    For a moment there I thought that you were talking politics!

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  5. Will Hardy

    logged in via Twitter

    What a nice way to get school kids interested in physics, let's put this in the curriculum.

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  6. Tony Thomas

    Project Manager

    The batsman seems most vulnerable to these effects when the the line of the ball is angled into leg stump or the batsman's feet.

    This could be because the ball is pretty much in a vertical plane from their eyes and they therefore have no sideways view of the vertical component of the flight and so cannot see how much a ball is "dipping". Add to this a little sideways swing, even if the ball is slightly off this vertical plane and trying to add these inputs together, the batsman can be deceived into miscalculating where the ball will bounce. This is case for yorkers, as much as the spinning ball.

    We often interpret replays of what a ball is doing by looking at queues of the reacting batsman. So, the most sensational replays of this seem to be for a ball angled into the batsmen's feet.

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