| Timing for a catch |
 The catch is perhaps one of the most exhilarating parts of the trapeze. One person performs a trick on the fly bar, and is subsequently caught by the catcher, who is hanging from the catch trap. Obviously, in order for the catcher to meet the performer at the right time, the timing of the trick must be carefully calculated. In this experiment, it will be taken for granted that the 'right time' for a catch is when both the catcher and flyer are at the extremes of their swings (closest to each other), however, for a more detailed investigation of the correct time to catch, see Investigation 5. Perhaps the most important factor involved in timing is the communication between performer and catcher. When ready, the performer will shout the 'LISTO!', this is Spanish for 'ready'. The catcher will then take over, saying 'READY' when he is half a swing away from the starting position, then 'HEP', which is the signal for the performer to leave the board. The catcher will also say 'HEP' to signal the performer to leave the fly bar at the moment of the catch. Our model for this experiment will be as in previous experiments, with both the catcher and performers modelled as simple pendulums. Although the catcher changes his body position radically in preparation for a catch, once the trick has started, he moves little, so this model is valid. We will look at the simplest type of catch, taught to most beginners, the knee hang:  It should be noted from this diagram that the performer changes his position, but that the centre of gravity remains at approximately the same point. As I have shown in Investigation 2, such small changes are negligible therefore they will be ignored. Whatever the movements of the catcher, the movements of the performer are known. He must start from the board (at the back of his swing), swing out, back, and out again, and catch the catcher at the far front of his swing. This is therefore one and a half complete swings, therefore it takes him one and a half periods to complete. We know that:
The catcher's trapeze has a different length and he is in a different body position to the performer (originally).
...and therefore that the period of the performer's swing is 4.3s. Therefore the total time for 1.5 of these swings is 1.5 x 4.3s = 6.45s. His swing will be modelled like this:  His time period is therefore: 
In 6.45s he will make: 6.45/3.47 = 1.85 swings He must therefore start from the end closest the performer, and in the time it takes the performer to swing out, back and out again, he will have swung twice, to end up where he started. In wave terms, they start in phase, and, due to the frequency difference, end up completely out of phase after the catcher has made two complete swings.  |
