# Physics of a Trampolist

1. May 5, 2015

### MarkAU

I've recently started trampolining and trying to get a feel for the physics involved. I did a tiny bit of physics years ago, so I've got a vague idea whats going on. Could you please check my understanding.

1. Once you leave the trampoline mat, your trajectory is set, and you could model your your path using projectile motion. So if you travel forwards during a skill, its because your were leaning during takeoff, not because of the changes in body position during the performance of the skill.
2. In a forward tucked somersault/flip you pull yourself into a ball (Heels to butt, knees to face) and rotate, tighter the tuck more angular velocity. To stop rotating you open back out again. I believe its the same basic principle as spinning on an office chair with arm's out vs arms in, but don't really understand whats going on.
3. Related to 1 and 2, pulling into a tuck would change your center of gravity, which I believe can change your path mid flight. If so how great is this force and in which direction does it act.
4. Conservation of energy: When you pull into a tuck you are gaining velocity and the energy to do that is from your bodies own metabolic energy stores, ie if we ignore air resistance and assume the same force is produced by the legs each jump there's no reason why a series of straight jumps should be any higher than one involving different skills. Or to put another way, it's you getting tired and not jumping as high, nothing else.
Are there any other physics involved that I'm not aware of ?

2. May 5, 2015

### rcgldr

1. and 3. Your center of mass will follow the shape of a parabola (or straight up and down if there's no horizontal motion) regardless of any tucking or body motion while in mid-air. Horizontal motion and rotational motion is initiated by a combination of lean and the force applied by the feet. Body and arm rotation during contact with the trampoline can add further to the initiation of rotation.

2. and 4. While in mid-air, angular momentum is conserved, so angular velocity and angular kinetic energy increases while transitioning into a tuck. During the transition into a tuck, there's an internal radial force to move body parts towards the center of rotation, and this internal work equals the gain in kinetic energy.

By flexing at the middle of the body or by positioning of the arms, forwards or backwards rotation can be converted into spinning rotation. Again the total angular momentum is conserved, and if the spin is initiated in mid-air, there will be a slight "tilt" of the body since the axis of rotation, along with angular momentum doesn't change.

I used to bounce trampoline, and one of the more notable visual sensations occurs during a back flip in layout position, when bouncing at or above your body height. In the second half of the flip, you look "down" (upwards relative to your body) towards the trampoline below you, and since your head is rotating upwards while you're center of mass accelerates downwards, you get the visual sensation of "hovering" instead of falling.

Unusual movements include doing a back flip after bouncing off your stomach. It's not used much in competitions, but it's a common move for trampolinists, called a "Cody". Another one is a front flip off the back, but with a 1/2 twist just after you leave the trampoline so it ends up becoming a back flip, called a "Jonah".

Last edited: May 5, 2015