Catch on the flying trapeze

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 trapeze ('catch trap'). Obviously, in order for the catcher to meet the flyer 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 flyer and catcher. When ready, the flyer will shout 'LISTO!', this is Spanish for 'ready'. The catcher will then take over, saying 'READY' when they are half a swing away from the starting position, then 'HEP', which is the signal for the flyer to leave the board.

Our model for this experiment will be as in previous experiments, with both the catcher and flyer modelled as simple pendulums. Although the catcher changes their body position radically in preparation for a catch, once the trick has started, they move little, so this model is valid. We will look at the simplest type of catch, taught to most beginners, the knee hang:

Knee Hang Catch Model

It should be noted from this diagram that the flyer changes their position versus simply hanging under the bar, 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 flyer are known. They must start from the board (at the back of the swing), swing out, back, and out again, and catch the catcher at the far front of the swing. This is therefore one and a half complete swings, therefore it takes them one and a half periods to complete.

We know that:
\[T=2\pi\sqrt{\frac{l}{g}}\]

...and therefore that the period of the flyer's swing is 4.3s.

Therefore the total time for 1.5 of these swings is 1.5 x 4.3s = 6.45s.

The catcher's trapeze has a different length and the catcher is in a different body position to the flyerh (originally).

His swing will be modelled like this:

Catcher Model

His time period is therefore:

\[T=2\pi\sqrt{\frac{l}{g}}\\ (l=3m,\ g=9.8)\\ T=2\pi\sqrt{\frac{3}{9.8}}\\ T=3.47s \]
In 6.45s they will make:

6.45/3.47 = 1.85 swings

This can be approximated in this case, given our model, to 2 complete swings – this agrees with the timings we observe in reality for a knee hang position.

The catcher must therefore start from the end closest the flyer, and in the time it takes the flyer to swing out, back and out again, they will have swung twice, to end up where they 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.

Catcher Model