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The Coefficient of Restitution and Centre of Percussion - What are these?

Each month cricket bat maker James Laver writes a passage about cricket bats and the lore that surrounds them. Please feel free to print all or part of this message in your cricket clubs newsletter. You may print any Laver & Wood newsletter or web site content for any non profit purpose provided readers are referred to the Laver & Wood web site and James Laver is credited as the author.
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The Coefficient of Restitution and Centre of Percussion - What are these?

When selecting a new bat the average club cricketer is reliant on the integrity and experience of the manufacturer. Whilst the main criteria for the selection is the weight and feel of the bat (which is very much a personal preference), the quality of the willow can only be assumed.

It would seem that no batmaker has any form of scientific approach to grading bats. The bat maker can predict how a particular piece of willow will perform by looking at the grain, listening to the sound of a ball or mallet on the unpressed cleft of willow and relying upon experience. In an attempt to apply a more scientific approach a simple test is devised for analysing the potential performance of the willow.

On playing the shot the ensuing velocity of the ball is dependant upon several factors including the velocities of the bat and ball at impact, the masses of the bat and ball and their "coefficient of restitution".

The effect of the mass of the bat is discussed later, the mass of the ball is fixed and the relative velocities dependant upon circumstances. Therefore, by measuring the coefficient of restitution some indication of the performance of the bat can be gained. The coefficient of restitution is a simple relationship between the velocity just before impact of a ball dropped onto a solid surface and the velocity immediately after impact.

To obtain an indication of the coefficient of restitution of the willow, a steel ball is dropped 845mm vertically through a clear plastic tube onto the blade of a bat held firmly and horizontally by the handle in a vice. The height of the rebound is measured on a scale fixed to the tube and recorded at 135 different points on the blade. The results are plotted and although not significant in any other context, can certainly be used to provide a comparison with other bats, and will also identify any dead spots on the bat's surface.

An indication of the importance of the pressing process undertaken by the bat is obtained by performing the test on an unpressed piece of willow, no measurable height of rebound is attained at any point.

The cross sectional shape of the blade of the bat has changed little over the years, with the traditional shape giving a greater depth of wood along the centre line of the bat, tapering to a relatively thin bottom and edges. This profile developed to give an area on the bat where the greater thickness of wood was concentrated, the batsman always aiming to hit the ball in the so called sweet spot or middle of the bat. This concentration of wood is usually about 180mm above the bottom, which is lower than the actual centre of gravity of bats, which tends to be about 350mm above the bottom. The advantages of using the middle are numerous.

On impact both the bat and ball deform with the subsequent elastic recovery contributing to the velocity of the ball off the bat. Providing the ball strikes the middle of the bat, the face will be temporarily deformed into the shape of a circular dish before regaining its original profile. If the ball was to strike the bat close to the bottom or an edge, the full dished deformation is not achieved and the force from the elastic recovery is less. The same effect is seen when jumping at the edge of a trampoline instead of the centre.

The performance of the bat is dependant upon its weight, but whilst a bat may weigh 2lb7ozs, not all of that mass will contribute to the momentum of the shot. Any additional weight placed high on the handle will have no effect at all on the force of the shot, yet the same weight employed close to the striking zone certainly will. This would suggest that to consider the overall mass of the bat in calculations would be incorrect and that the effective mass of the bat is gained from a localised volume of wood around the point of impact.

Further away from the middle of the bat the effective striking area is restricted by the edge or bottom of the bat and the corresponding volume of wood is further reduced by the thinner sections.

A comparison can be made with golf, where all the mass is concentrated into the club head and the shaft is used only as a means of accelerating the club head to impact. Better players consistently using the middle of the bat could conceivably concentrate the mass of the bat into that area, and use a longer thinner handle, but, unfortunately not even the worlds best players have such ability and the current situation of compromise is likely to remain. Perhaps it should be suggested to world record holder Craig Macmillan (26 runs in an over) that he should use a bat with a thin handle with most of the weight at the bottom!

Most cricketers will have felt the wrist jarring of a miss-hit shot caused by striking the ball either too high or too low on the bat. Some of the jarring effect is caused by the transfer of shock waves from the impact but most is caused as a result of not hitting the ball at the bat's centre of percussion.

If the bat is considered as a vertical rod pivoted high up by the hands, with a centre of gravity about 350mm above the bottom, and is struck by a ball on the face at some distance from the pivot a force of reaction will be produced. The blow will tend to move the whole bat backwards. If the blow is nearer the splice the handle will be moved backwards and the toe forwards, if nearer the bottom of the face the handle will be moved forwards in reaction and the toe backwards. When the face is struck at its centre of percussion the hands should feel no reactive force at all.

For a cricket bat which has an unevenly distributed mass, the centre of percussion will depend on where the bat is gripped, but generally speaking it is situated at a point about 180mm from the bottom of the bat and coinciding with the sweet spot. Under these circumstances the loss of momentum on impact is reduced to a minimum and consequently the maximum power is obtained from the shot.

Any Questions? If so please email me.

Thanks to D.Collyer for information supplied.

Next Month: Pressing cricket bat willow - the process explained.

James Laver
Senior Bat Maker - Laver & Wood
james@laverwood.co.nz
www.laverwood.co.nz

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