In the last article in this series, the question was asked as to how fast a billiards ball is moving as it leaves the cue tip. It was noted that experiments with pool balls in the U.S.A. had led to the conclusion that speeds of more than 20mph were very hard to achieve and it was observed that no corresponding experiments with the English billiard ball (The U.S. pool ball is bigger and heavier) seemed to have been made. Here, clearly, was an omission to be rectified by the Laboratory of Quantitative Billiards, and one of us (I.S.) teamed up with an external professor, Roy Bacon (English Amateur Championship semi-finalist,) to investigate the matter on the latter's table, the cash-strapped laboratory not having yet acquired this desirable piece of apparatus. The resulting report (Ref. LQB/92) is reproduced below.
The table was fitted with steel block cushions and was thermostatted at a temperature of about 20°C; fitted with a good quality woollen cloth, it ran about 4.5 lengths. It was not thus an especially fast table. The ball used was a standard size billiard ball which weighed 140 grams. Two cues were used: one of 17.5oz (11mm tip) and one of 21oz (12mm tip.) They were ash cues with ebony butts. A video recorder with playback facilities was employed, positioned as shown in the diagram.
In this experiment, the cueball was placed 10ft from the top cushion and was struck towards this cushion. The video camera was so positioned that it recorded both the striking of the ball and its arrival at the top cushion. This arrival was," Event marked, "y the placing of a second ball on top of the cushion above the point of impact: this ball executed a lively jump upwards under the impact (affording excellent slip-fielding practice for the non-striker.) The striker hit the cue ball as hard as he felt he was compatible with accurate striking - he had to hit the top cushion in the right place. The time of travel up the table was in the order of 0.5 seconds and its measurement was thus problematical. Direct measurement by stopwatch was subject to an unacceptably large error (of the order +/- 100%) To reduce this error, use was made of the slow-motion facility of the video equipment. The time of travel in slow-motion playback was measured. The camera was calibrate by recording the passage of 5 seconds on a digital watch. On the slow-motion play-back this took 54.5 +/- 0.5 seconds.
Times of travel in slow motion over 10ft on the table were found to lie in the range 5.2 - 7.2 seconds making the real time range 0.48 - 0.66 seconds. The velocity range corresponding to these times is 15.2 - 20.8 ft/sees. The estimated overall error in this velocity is unlikely to exceed +/- 1ft/sec. (Signed Ivan IV and R. Bacon).
The above result will be more meaningful to the general reader when we point out that a speed of 22ft/sec corresponds to 15mph. This surprising result will be discussed in our next article.
"The trouble with billiards," said our visitor, Professor Hall (Whose knowledge of the game is purely theoretical,) "Is that it is too easy to score. For instance, to make a cannon, one has only to make contact with the first object ball with a full-strength shot to be reasonably certain that the random path thereafter followed by the cueball will sooner or later lead it to the second ball."
At lunch-time we invited the professor to our club and suggested that he verify his proposition on the club table, with predictable results. But what, if we suppose the cueball travels five lengths of the table after making its contact with the first ball, is the chance of it making the random second contact and thus scoring a cannon. In other words, if one has an almighty bash at the first ball what are the chances of fluking a cannon?