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Dr Ian Plummer

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Technical
Physics of Croquet

Abstract

Croquet is a sport that is similar to billiards in that it involves the collision of one ball with another. Measurements and calculations are presented for three typical shots, one known as a straight croquet, one known as a split croquet and the other known as a push or roll shot. Each exhibit collision phenomena that could serve to illustrate aspects of an introductory course in mechanics, and that could also provide challenges even for more advanced students.

http://iopscience.iop.org/article/10.1088/0143-0807/38/1/014001/meta

This paper can be found at the link above but requires an academic logon to download the full paper.

Rod Cross, diagram 8

Review

Given many people may not be able to access the paper I offer the following review.

The article considers the croquet stroke initially as a sequence of separate collisions: mallet-striker's ball; striker's ball-croquetted ball; this is the approach adopted by Calladine & Heywood. Numerical solutions are generated when considering the croquet stroke as a single collision where there are forces (springs) between the mallet-striker's ball and the striker's ball-croquetted ball. It was not clear how the force constants of the springs were chosen. Neither angular momentum nor friction was considered.

Experimental single ball and straight croquet strokes were carried out on an uncharacterised carpet and filmed with a high speed camera. From the data, the effect on the apparent mass of the mallet head, coefficient of restitution and relative velocities of the balls were derived as the striker's hand moved from the mallet head to 50 cm up the shaft.

Finally the ball and spring model was applied to a split croquet stroke and followed up with experimental measurements.  The latter showed the angle of split of the striker's ball increased as the hands were moved higher up the shaft; also the relative velocities of both balls were measured dependent on the hand height.

The details of the experimental procedures are vague, e.g. what attempts were there to make sure the mallet face was perpendicular to the ground at the moment of impact, what was the equivalent 'plummers' (lawn speed) of the carpet and how was consistency achieved? Also the use of speed instead of velocity in the early part of the paper is puzzling.

Ian Plummer

Author: Rod Cross
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Updated 28.xii.16
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