High jump vs. gymnastics floor routine center of mass Olympics are going on now so:


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*The gymnists doing floor routines do some very high jumps after somersaulting a few times. 

*High jumpers also jump very high using the Fosbury flop technique.
Question: Of all athletic motions, is it one of these techniques that moves the body's center of mass highest (excluding sports that use other objects like pole vaulting)?

Some caveats:


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*I believe the floor has increased flexibility/springiness added intentionally, although arguably the track material also has added springiness.

*Also, gymnists tend to be of shorter stature, so they may appear to move higher in absolute terms even though they are just moving high in relative terms.

*It's almost certain that no single technique is universally best, i.e. for some body types one motion would allow the highest attainable increase in COM, while for other body types a different motion would be most effective.
 A: 
The gymnists doing floor routines do some very high jumps after somersaulting a few times. I believe the floor has increased flexibility/springiness added intentionally, although arguably the track material also has added springiness. You can see the springs in the illustration below.

From Floor Exercises

The floor involves a 40 foot by 40 foot spring floor. It is typically constructed of wood or composite mounted on springs. Covered with closed cell foam, which is in turn covered by carpet.

I watched the gymnastics tonight. The floor is aiding in the heights achieved. When you watch the competitor walking across the floor, there is only a slight amount of spring under their feet. 
Then, when they run across the floor, it deforms a little further. When you see them going for the greatest height, as soon as they land, I mean immediately, they can then jump high enough, without using their leg strength, no leg bending involved, to jump straight back up for another 360 degree rotation  before they land. 
They can  only do this because they have enough momentum from the first, highest  jump , to compress the floor and let it do the work of pushing them up.
When you look at the floor, it's actually on a raised platform, about 20cm high, so there is room for a trampoline effect.


Also, gymnists tend to be of shorter stature, so they may appear to move higher in absolute terms even though they are just moving high in relative terms

Yep, the women are smaller than average height,,and a lot of the men are shorter than average.
From Fosbury Flop Scientific American

Keep this equation in mind: U2 = 2gH. It explains why most of jumpers do the backward flip known as the Fosbury Flop.  The Fosbury Flop keeps one’s center of gravity low to the ground, and the lower one’s center of gravity, the less energy is required to successfully jump over the bar. In the above equation, U is the speed of the jumper (and thus the energy required), g is the acceleration caused by gravity, and H is the height of the center of gravity. Surprisingly, it is possible for the high jumper’s body to fly over the bar while his or her center of gravity passes below it.

