Multiple Taps in Croquet Strokes - Electrical Conduction Tests
Abstract: Electrical conduction was used to investigate whether multiple contacts occurred during single-ball and croquet strokes. Single ball strokes and most croquet strokes showed no sign of multiple contacts but roll-shots indicated multiple contacts were taking place under the experimental conditions. The strokes neither appeared nor sounded to be 'double taps'.
Carbon paper tests have indicated that multiple contacts may be taking place between the mallet and the ball during certain croquet strokes. Stan Hall's work demonstrated that the ball-mallet contact time is in the order of a millisecond. Domestic video cameras take an image only every 40 milliseconds (25 frames a second) and hence cannot see the detail of strokes. Thus special techniques are required. High-speed video has been used by Bob Kroger using expensive video equipment. Photography using spark strobes operating in the sub-millisecond range would be another method, but were unavailable. Consequently the electrical contact between the mallet and ball was used to indicate contact time and multiplicity. The apparatus is described in the method section. Given the climate in England in December (currently snow), the strokes were played indoor on a carpet.
The lower trace is the calibration signal completing a cycle each millisecond. The vertical dotted line is the point at which the traces were triggered (time = 0) when first contact was made. The vertical axis shows the voltage between the mallet and the ball. When the mallet touches the ball, the voltage drops; when they separate it rises again. Hence a low signal is a contact. Each trace is vertically offset from the others to make the display clearer. The top and middle traces have triangles/squares marking where each data point lies (5 microseconds apart in this case). These have been suppressed on subsequent graphs.
The middle trace is a single-ball shot hit softly and the upper one a swift
hard stroke. The full traces extend for 20 milliseconds and show no further
detail. The softly hit stroke shows intermittent contact at the after ~3.4
milliseconds. A millisecond is 1/1000th of a second.
The chart above is the collection of traces obtained by playing different
strokes. The time scale is 20 milliseconds full scale. (Click on image for
full size image).
SINGL1/2/3. These routinely produced just a single indication of contact, three examples are depicted. The first two were taken at the start of the experiments and the latter at their conclusion to demonstrate that the properties of the system had not changed, e.g. loose pieces of foil causing double taps. The difference in the contact times depends on the speed of the mallet head on impact.
STOP1/2. A number of straight stop shots were attempted (hands near top of mallet shaft, standing back, lower part of mallet face presented to the striker's ball and a stab action with little follow-through).
The contact times are greater than for the single ball shots. It is speculated that this is due to the larger inertia of the pair of balls in the croquet stroke and, as the mallet face is angled up on contact, a possible lifting of the back ball leaving it in contact with the mallet face for longer. For harder shots the contact time is reduced, possibly because the grip is firmer.
DRIVE1/2. These were played similarly to the single ball strokes but a touch harder. Again the contact time is greater than for the single stroke, but less than for the stop shot. This could be due to the mallet face not being angled.
ROLL1/2. The technique used for roll strokes was to hold the shaft about 1 cm above the mallet head, stand over the balls and play a smooth stroke with a little follow through. The mallet head was kept flat (parallel) to the ground where indicated. The majority of strokes played in this fashion produced multiple contacts. Initial contact times 1.5 - 2.1 milliseconds followed by subsequent contacts (see below) starting 10 -15 milliseconds afterwards.
It is impossible to tell if the second contact is due to the mallet catching up with the striker's ball or if the striker's ball is oscillating between the croqueted ball and the mallet.
ROLL3. The striker's and forward ball were spaced apart by the thickness of two sheets of card (0.5 mm total) prior to the stroke. This produced a single contact, but insufficient tests were done to determine whether this was indicative of the typical behaviour.
ROLL4. Here the balls departed at 90º and there is a prolonged second contact. This is interpreted as the mallet catching up with the departing balls as they have a reduced forward momentum caused by their trajectories.
ROLL5/6. The major difference here is that the mallet face is angled down by ~40º and the stroke is a scoop with the initial impact angled at 40º into the ball. Clearly there are multiple contacts and the foil mallet face shows 'skid marks' after the stroke.
This is considered to be an initial contact, the mallet rebounds and then the momentum of the arms and mallet causes a subsequent hit.
The technique of playing the shots is the author's choice, and there are other methods, however the techniques are by no means strange and unusual. These represent strokes that are played everyday on the court and are infrequently faulted. The typical duration of the contact (~1-2 milliseconds) is around the same as the single click when you depress a mouse button. Further tests are planned to determine what is easily distinguishable by ear as a double click.
Firmer croquet strokes produce shorter contact times than soft ones. Croquet strokes have longer contact times than single ball strokes. Only rolls shots showed multiple contacts. Angling the mallet face upwards could increase the contact time. With the mallet face is angled down multiple hits were totally reproducible.
Referees tend towards what is sensible and practicable; if a normally equipped person* cannot detect a multiple tap then the shot is not faulted. It is unscientific (and unfair) to assume that a multiple hit must have occurred because someone has played a stroke in a certain way. They may just have the knack of executing it without a fault. Unless the referee has evidence that a multiple hit has occurred in that particular stroke they have no remit to declare it a fault.
It has taken specialist equipment to obtain these results which is not available or in any way sensible for use in a real match. If people wish to get pedantic then I am confident that arguments based on quantum mechanics could make a meal of all of the adjectives in the current Laws.
Oxford, December 2000
An old Jaques Eclipse ball was thickly sprayed with aerosol graphite coating (Radio Spares, RS 568-483) and allowed to dry. A 0.5 mm insulated wire was stripped for 20 mm and that length cemented to the graphited surface with silver conductive paint (Electrolube, 0.03 ohm/sq). The adjacent 30 mm length of the insulated wire was glued (Araldite) to the ball's surface for strengthening. The resulting electrical resistance to any part of the ball's surface from the conductor did not exceed 17 ohms. After the experiments the maximum resistance measured was slightly lower probably due to the coating drying out. The forward ball used in the croquet strokes was another Jaques Eclipse ball coated with graphite.
Aluminium foil from a 'mince pie' container, 0.02mm thick, was glued using PrittStick to the face of a wooden composite ('Permali') croquet mallet head. The purpose of the glue was to increase the strength of the foil and stop it tearing or flapping about. The mallet had a wooden Jaques shaft. The electrical resistance between a connecting wire and any part of the face was =< 0.5 ohm.
2.65 volts was applied to the face of the mallet through an 82K ohm resistor from a low impedance source (NiCad batteries). The ball was connected to the electrical return. The voltage between the mallet face and the ball was recorded on a Thurlby DSA524 Digital Storage Oscilloscope (DSO). The DSO was set to trigger when the voltage fell as the ball made contact with the mallet face. The DSO also allows the pre-trigger signal to be observed. The majority of the data traces display 500 microseconds of the pre-trigger trace. Data is digitised to 8-bits (256 levels) and 4096 data points are recorded for each run. Consequently the trace details the events for approximately the first 1/50th of a second.
A Fluke 79 multimeter was used to measure the test signal (1.004KHz) provided by a conventional oscilloscope test point and this was recorded under the same conditions as the rest of the data in this paper to confirm the time scales. The full cycle spans 200 data points, hence 1KHz yields a 1 millisecond cycle which is digitised into 200 points; thus each point is 5 microseconds apart. To demonstrate that there were no large time constants in the circuit, the mallet face was lightly brushed against the ball and a 'hairy' trace resulted which demonstrated that the time constant is less than 30 microseconds. E.g. the middle trace in the first figure above.
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