Somersaults and Twisting

How can you achieve somersaults on the Trapeze?

In order to create angular momentum for rotation, an impulse must be exerted on your body. This is achieved by effectively pulling down on the bar before you leave, and kicking your legs. This impulse gives you angular momentum, so once you leave the bar, you start to rotate.

The relative angular velocities of the double layout and the tucked double back somersault demonstrate the principal applied to the ice skater in the information document. The layout is performed with a straight body, so I about the axis (through the hips) is very large. Angular momentum is constant throughout, so a relatively slow angular velocity is achieved. This slow rate of rotation is very visible to spectators. In comparison, the tucked double back somersault is performed in a tucked position. I is therefore much less (body is more compact), and since the starting angular velocity is approximately the same as in the layout, the angular velocity is much higher. The faster rate of spin is why triples are performed tucked (you have to spin fast to get round three times in time to be caught).

More Advanced Tricks

More advanced tricks on the trapeze involve combinations of somersaults and twists before the catch. Although it is possible to twist before a catch, the movement before you leave the bar is different to that preceding a somersault, making it very difficult to combine the two. What the performer needs to do is start to somersault, and twist while he is in the air.

This may appear to be a violation of the conservation of angular momentum rule, since the man starts with no angular momentum about his twisting axis, and during the flight, he seems to create some. This is not the case.

In order to understand how this is achieved, we must appreciate that a person is not a rigid object, and therefore there is only a certain distance that we can go, using a person modelled as a rod.

Let us assume that the performer leaves the bar with a large, non-zero angular momentum, this is a vector parallel to the axis of rotation through his hips, so he starts to somersault (no twist to start with). Since this angular momentum is conserved, the vector it corresponds to remains in the same direction, regardless of how much the flyer wiggles or squirms. However, the axis about which the man rotates can change (the axis of rotation is always in the same direction as the angular velocity vector). In order to initiate twisting, the flyer 'throws' his arms round. This causes his axis of rotation to wander off the direction of the angular momentum vector. This then represents a threat to the conservation of angular momentum principal, since the magnitude of angular momentum in any given direction has changed. This initiates a twist, creating exactly enough angular momentum so that the vector sum of the two separate angular momentums is still the same as the original value. Angular momentum has been conserved, and the flyer has initiated a twist in mid-air.

In laymans terms: he has created the twist by stealing a bit of the rotation from the somersault so that the total amount of rotation stays the same.

It is interesting to note that this is only possible if the flyer starts with angular momentum in the first place.

Some figures can help to demonstrate the relationship between the angle between the axis of rotation and the angular momentum vector and the rate of twisting. In a layout (back somersault with body straight), throwing his arms to create an angle of just 11^o, causes his body to twist at a rate of 3 twists per somersault. In a double back somersault, when the flyer's body is tucked or piked, throwing the arms will create an angle larger than 11^o (since I is smaller). For an angle of 20^o, the body will twist at a rate of five and a half twists per somersault.