a pre-Olympic minipost

About a year ago I taught a course on the physics of sport. Recently a high frame rate video of Simone Biles was posted. Making a few frame by frame measurements (helped by another view and knowing her size and some simple home-brew software) it’s possible to do a quick back of the envelope analysis.

First the this slow motion video from a meet on the 4^{th} of June -watch it even if you’re not interested in the analysis. Her motions are beautiful.

Some background information .. she’s 142 cm tall - a shade under 4’8” and her weight is currently listed at 52 kg (about 114 pounds) Her top sprint speed is 8.0 m/s (18 mph), although she doesn’t reach it here (not enough room)

It’s important to note that a couple of innovations around 1980 revolutionized gymnastics. The floor is one of them .. notice how springy it is. It’s a thin carpet bonded to a layer of hard foam that’s glued to plywood sheets. All of this is mounted on a large array of heavy springs which are attached to the main floor. Think of it was a stiff trampoline that allows the gymnast to trade some of her kinetic energy into a higher jump. A pole vaulter uses the pole to do the same thing.

She launches at about 7 meters per second (about 15.7 mph) at an angle of about 70°. Her center of mass reaches a height of about 2.9 meters (9.5 feet) and she lands about 2 meters (6.5 feet) from her launch point. She lands on a piece of foam to slow the landing a bit. Even with that and the springy floor she’s experiencing a deceleration of over five times the force of gravity.

What goes on in flight is the remarkable part. Once launched, Simone is a projectile that is only acted on by the force of gravity (ok - there’s a small correction for wind resistance, but it can be ignored). She has three axes of rotation to play with. All three go through her center of mass, which is near her waist. Call the one that runs from head to toe her “twisting” axis. Call the second her tumbling axis ‘’ this one's at a right angle to her twist axis and is described by the motion about her waist when she falls forward. The third is at right angles to the other two and is the rotation to the left or right. She doesn’t use that one here, so we’ll ignore it.

Back to her sprint. She wants to go as fast as possible so she has the largest possible time in the air to accomplish her motions. Launch angle and speed together determine how high she’ll go and how much “hang time” she has. She also adds a bit of a twisting motion when she launches. She can speed it up by pulling her arms in like a skater. Likewise the tumbling motion can be speeded up by pulling her arms and legs in to lower the moment of inertia about that axis. The high speed of her flips - each is about two thirds of a second long and the smoothness of control is testament to her athleticism and precise control of her moments of inertia.

I did the calculation of a launch speed required to get another flip - another two thirds of a second - in… it would have to be about 10 meters per second (22.4 mph). Even with a very long runway we’re not going to see four full flips. A faster sprinter (world record for the 100m women’s sprint peaks around 12 meters per second) wouldn’t have the space and would be too tall and would lack the core body strength to do flips that fast anyway. We’re probably at the limit given the floor design and size along with human capabilities. Of course there are other innovations that can appear in future performances.

This is a great example of a sport that dictates body size and type - at least for the elite level. That's an interesting subject on its own...