The Physics of Trapeze

Investigation 8: Forces on the Catcher

Catching seems a particularly gruelling part of the trapeze. The catcher must spend a good proportion of his time on the trapeze hanging upside down, and when he is not, he can only sit on the trapeze bar, which is very hard and not kind on the buttocks.

Catchers seem to have to have great deal of strength in their arms, since they must be able to climb up a rope to get to the catch trap (this looks best if done in a piked position: without using the legs). They must also be able to support the weight of the performers they catch. I did some brief experimentation with catching, and I found that if you try to support the weight of even small children, when you are hanging from your knees, this causes stress on your knee-joints which makes them very painful afterwards. The catcher's lock (the position used on the flying trapeze) is adapted so the bar rests on the front of your thighs, preventing this stress on the knees.

How much weight must you be able to support in this position:

Let us assume that a heavy person weighs 100kg.

We know that the point where most centripetal force acts is at the point of highest speed (see Investigation 7).

The catcher and the flyer will be modelled as a pendulum, length 3.8m, and with mass 170kg (two people). Since they swing up to approximately the same angle as the fly bar, we can calculate their maximum speed.

Maximum speed v = (2gh)^1/2

v = (2 x 9.8 x 3.8 (1 - cos(0.83)))^1/2

v = 4.9ms-1

We know that centripetal force F = mv^2/r

If we use 100kg as m, the mass of the man, we can find the force due to the motion that the catcher feels in his arms.

F = 100 x 4.92/3.8

F = 631N but we also need to add the force due to gravity (1000N).

In total, the catcher must support a maximum of 1631N on his arms during the swing. This is the equivalent of hanging from a stationary bar and supporting two average sized men!

But as you will find if you try to do pull-ups in the gym, it is much easier to hang from the bar without moving, than it is to try and support yourself with bent arms. This is because, when your arms are straight, the strength comes from the properties of the materials that make up your arm. Your bones (weight for weight) are stronger than steel, and the only weak points are the joints. With your arms bent, you are relying solely on the strength of your muscles, if they relax then they no longer support you.

Providing the catcher can keep his arms straight throughout the catch, then he can rely on the strength of his arms to spread the force along his body, and not his muscles, which concentrate the force on the joints in his arm (naturally weak points). This is why it is not a necessity to have immense upper body strength as a catcher, just a good technique. In fact, you often find many women catching for this reason. As an aside, the danger for women catchers is that the catcher's lock position can damage your hips and cause complications in childbirth.

Timing is crucial

The need to catch with straight arms highlights another reason why timing is crucial. If you have a ball attached to a string, which you want to make perform circular motion about a fixed point, you ideally pull the string taut, and throw the ball perpendicular to the string (on a tangent to the proposed circle). If you were instead to throw the ball into the circle, it would move until the string became taut, and would jolt the string (the component of the momentum along the length of the string being lost) and would continue round the circle at a greatly reduced rate.

The same principal can be applied to catching. If the catch is made at the point at which the flyer has no forward motion, he is moving only downwards (i.e. approximately tangentially to catch trap) this will mean he performs the smoothest arc, and there is no jolt on the catcher's arms. If he lets go too early, and flies into the circle, providing he does not hit the catcher and is able to be caught, there will be a jolt on the catcher's arms as the arms exert an impulse to destroy any momentum that is not tangential. Not only will this be painful on the arms of the catcher, but it will also reduce the speed of the swing performed by the catcher and the flyer together, reducing the chances of a return to the fly bar.

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