The Twisty Physics of Simone Biles’ Historic Triple-Double

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What. The. Heck. Did you see that? Simone Biles appears to defy the laws of physics with this epic tumbling pass from the 2019 US Gymnastics Championships. It’s called a triple-double. That means she rotates around an axis going through her hips twice while at the same time rotating about an axis going from head to toe THREE times. Yes, it’s difficult—but it doesn’t defy physics, it uses physics.

Let’s go over the three key parts of this move. You can follow the physics, but I don’t recommend trying this triple-double in your backyard.

Jumping

If you want to do any kind of flip, you pretty much need to be off the ground for some amount of time. Otherwise, you are just a human rolling around on the floor. That might be fun, but it’s not really tumbling.

Once a human leaves the floor, there is essentially only one force acting on him or her—the gravitational force. This is a downward-pulling force that depends on the local gravitational field (g = 9.8 Newtons per kilogram) and the mass of the human (or whatever object). This constant downward force causes a person to accelerate downward. But because both the force and the acceleration depend on mass, the mass cancels out. All free-falling objects on the surface of the Earth have the same acceleration of -9.8 m/s2.

Rhett Allain, an Associate Professor of Physics at Southeastern Louisiana University, writes about physics for WIRED.

The other great thing about the gravitational force is that it only acts in the vertical direction. This means that there are no net forces in the horizontal direction. With no net force, there is no CHANGE in velocity. Once she’s in the air, Simone’s center of mass will move along with a constant speed—with the same horizontal velocity at which she was running before the jump.

But in the vertical direction, she launches upward with some vertical velocity. This velocity decreases as she travels up until it reaches zero at the highest point of the jump. At that point, she starts moving down and increasing in speed until she returns to the floor.

Since this motion has a constant acceleration, we can model it with what’s called a “kinematic equation.” It is a relationship between position, velocity, and time and it looks like this.

Rhett Allain

For this tumbling pass, we know Simone’s starting and ending position—they are the same, so let’s just say they are both zero. Now, if I know the total time, I can find her initial upward velocity. Looking at the video (and using Tracker Video Analysis), I get a total in-air time of 1.18 seconds. Yes, it seems longer than that—but that’s an impressive hang-time. This gives a launch speed of 5.78 meters per second (that’s about 13 mph).

What if she increased this launch speed to 7 m/s? That would give her a hang time of 1.43 seconds. Yes, that’s still super short. The key here is that it’s really hard to be in the air for a long time. If you want to do some twists in the air, you need to focus on rotating faster more than on staying in the air longer. Jumping is hard.

Flipping

Just to be clear on terminology—a flip is a rotation of a human around an axis that runs through your hips. Here is an animation I made for an older post (yes, this is created in python with GlowScript).

Rhett Allain

The rotation is represented by the red arrow, which points along the axis of rotation. That’s a flip.

The key here is to rotate your body all the way around that axis while in the air. If you don’t do a full rotation, bad things happen. Fortunately for Simone Biles, she has a head start in the flipping aspect of this tumbling move. She’s already rotating before the jump even starts. During the moves before the triple-double she starts off with a fairly significant rotation rate of about 11.8 radians per second (1.9 rotations per second).

Once she’s in the air, she speeds up slightly to about 12.2 rad/s by tucking in her arms and legs. In the absence of external torque, she will have a constant angular momentum. Angular momentum is a measure of the rotation of an object that takes into account both the rotation rate and the distribution of mass. Since some of her body mass moves closer to the axis of rotation, the mass influence on the angular momentum decreases. To conserve angular momentum, the rotation rate must increase. This is why a “tuck” flip is easier than a layout (where the body remains straight).

Twisting

The last element of this triple-double is the triple twist. A twist is a rotation of the human body about an axis that runs from head to feet. Here is an animation.

Rhett Allain

But notice there is a big difference between the twist and the flip in Simone’s gymnastics move. She was already rotating about her hips before she left the floor—but she was not already twisting. She had to add this twist on the last part of this tumbling pass. There are two ways you can twist in the air.

The first way is called a torque twist. Torque is the rotational equivalent of a force. Where a force changes the momentum of an object, torque changes the angular momentum. However, you can’t apply a torque to yourself while you are in the air—you have to do it while you are still in contact with the ground. If you push forward with one foot and back with the other foot, you will exert a torque. This torque will result in your twisting motion once you leave the ground. It’s simple. You can try it yourself.

Rhett Allain

Alas, a torque twist will only get you so far. The second option is an angular momentum twist. Once a person is in the air, he or she can change body positions. This position change will result in a non-symmetric mass distribution and produce an amazing result. Even though the angular momentum stays constant, the angular velocity (the direction of rotation) will change. If both the angular velocity (red arrow) and the angular momentum (yellow arrow) are represented with arrows, this twist would look like this.

Rhett Allain

Notice that the angular momentum is constant—as it should be because there are no torques in the air. But exactly how do you do this? Notice that in the air Simone moves one arm up and one arm down? That changes her mass distribution and starts the twisting. Remember—she does THREE twists. Is that crazy? Yes, it’s a tough move. Simone does it anyway.

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