## Investigation 8 - Forces on the catcher

We look how much weight the catcher is holding during a catch, and why timing is crucial for a smooth catch.

Catching is a particularly gruelling part of flying trapeze. The catcher spends a good proportion of their time swinging upside down, and when they are not, they can only sit on the trapeze bar, which is very hard and not kind on the butt!

Catchers seem to have to have great deal of strength in their arms: they must also be able to support the weight of the performers they catch. The catcher does not hang from their knees, but adopts a position called a lock, with their legs wrapped around the cables and the bar against their thighs. This position reduces the amount of strength needed in the knees to keep the catcher (and flyer) on the bar.

### How much weight does a catcher hold?

Let's look at an extreme and assume we are catching a heavy person, weighing 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.

$$Maximum\ speed\ v = 2gh\\ v = 2 \times 9.8 \times 3.8 (1 - cos(0.83))\\ v = 4.9ms^{-1}$$ We know that for the centripetal force: $$F=m\frac{v^{2}}{r}$$ If we use 100kg as m, the mass of the flyer, we can find the force due to the motion that the catcher feels in their arms. $$F=100kg\times\frac{4.9^{2}}{3.8}\\ F=631N$$ ...but we also need to add the force due to gravity (1000N) which is also pulling downwards on the flyer.

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

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 their arms straight throughout the catch, then they can rely on the strength of their arms to spread the force along their body, and not their muscles, which concentrate the force on the joints in their arms (naturally weak points). This is why it shouldn't be necessary to have immense upper body strength as a catcher, just a good technique.

However this clearly isn't telling us the whole story, given our observation that most catchers are in fact often powerful men who clearly do have great upper-body strength. So why is this? Holding the weight of the flyer is only half the challenge. The catcher needs to be able to get a good grip on the flyer's wrists. A wrist-to-wrist grip uses friction to keep the catcher and the flyer together. To create this friction, the catcher needs to be able to squeeze hard (which requires strong forearms). In addition, you'll often notice that good catchers do bend their arms during catches, to help to smooth the flyer's swing. They are able to do this because they have the muscles to be able to support the flyer with bent arms. So while strength shouldn't be necessary, in practice it is a huge asset.

### Timing is crucial

All of this assumes that the catch is very smooth. 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, they are only moving downwards (i.e. approximately tangentially to the catch trapeze) this will mean they swing in a smooth arc, and there is no jolt on the catcher's arms. If the flyer lets go too early, and flies into the circle (providing they do not hit the catcher and are 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 (and could cause them to let go), 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.

This highlights yet another reason why catchers benefit from being strong. It's a good idea to have some extra strength 'in reserve' in case the catch is poor and they experience a jolt. If they have the strength to resist the impulse exerted on them by the flyer (a high force in a short time), then they will manage to continue holding on. If they can't, the flyer will be dropped.