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# Trampoline Limits

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A trampoline is a great example of spring potential energy and a restoring force, but it also brings up another question: why is there a 'maximum' height and why can you "double bounce" someone to make them fly higher than that maximum height. As a person begins jumping on a trampoline, their kinetic energy is converted to spring potential energy when they contact the trampoline, and then converted back to kinetic and gravitational potential energy as the person leaves the trampoline towards the sky. Since the first bounce is small, the kinetic energy and therefore spring potential energy is low, but the subsequent jumping motion increases this energy, allowing the person to continue to reach higher heights. If a person does not bend their knees and contribute to the jump themselves, they will not get any higher, in fact they will decrease their maximum altitude as some of the energy is dissipated to surroundings. However, a person cannot continuously jump higher and higher as the force of gravity opposing the springs restoring force on the human decreases the potential height as well as limits to the stretching of the springs. Trampolines have a whole bunch of springs around the outside, working at an angle, but also arranged in series. Due to the large number of springs with relatively high spring constants, it takes much, much larger forces to displace them more than a few inches. In addition to the springs, the trampoline material itself is elastic, allowing the springs to maximize their effect.

The last question is how one person can "double bounce" another person by landing slightly before them. The first person to hit the trampoline stretches the spring, storing potential energy, and then when the second person impacts the trampoline, the already stretched material stretches a bit more, and most of the total potential energy is transferred to the second person. The first person does not receive much of the potential energy because they are essentially waiting for the potential energy to spring them upwards, but then the second person concentrates the energy under their impact, propelling them upward while the first person barely moves.

Warning: If you don't have a net around your trampoline (like my old one), be careful about double bouncing because it is easier for somebody to land outside of the trampoline on the ground. Don't ask me how I know.

## 1 Comment

The largest damping force is the air resistance on the mat.  "Fly mats" are mats made from 4 mm wide webbing on 10 mm spacing.  Or made  from pairs of string  about 1.5 mm wide per pair on 4 mm spacing.  The net effect is that it's a net.  With over 50% holes.

One thing you notice on first jumping on a fly mat:  You don't lose energy as fast.   If you are used to losing a third of your energy doing a doggie drop, and then do this same trick on a fly mat and get 90% of your energy back it will scare the pants off of you.

Good mats are not stretchy.  You want all the energy storage to be in the springs, which are better at returning it.  Most elastics fabrics are very poor at returning energy -- 40-60% especially in directions not along the weave.

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