Gymnastics and the Olympic Games, that's where it all started for me. As a 9-year-old gymnast watching the Barcelona Games on TV, my fate was sealed as a sports fanatic. Years of involvement in the sport as a competitive gymnast and coach guided me along the path to working in sport science, and biomechanics, in particular. With the Tokyo Olympic Games finally kicking off this week, here is a brief biomechanics primer on one of its keystone events.
While the “GOAT” (Greatest of All Time) debates rage on across many disciplines, in the gymnastics world there is no room for discussion. Simone Biles, with 30 Olympic and World Championship medals, 23 of them gold, is it. She has dominated the sport by performing the most difficult routines in history and consistently does so with near-perfect execution. Pushing the limits of performance, Biles has four skills named after her and, in May, became the first woman to compete the Yurchenko double pike vault – something only a handful of male gymnasts have done in competition. Her feats are regularly described as “gravity-defying” but, believe it or not, the laws of physics do still apply to this phenomenal gymnast.
The Yurchenko family of vaults, where an athlete performs a roundoff onto the board and then flips backwards to make contact with the vault table with their hands, is the most popular type performed by elite women gymnasts. What the gymnast does during the flight period after leaving the vault table (the “post-flight”) can vary widely in terms of the number of somersaults and twists, and this determines the difficulty level of the vault. This post-flight period illustrates some of the most fundamental principles in biomechanics – in particular, the laws relating to projectile motion and conservation of angular momentum.
The Human Projectile
The only forces that act on an object (including a human body) in flight are gravity and air resistance. Air resistance on the body of a gymnast in a competition hall is almost zero, so gravity is really the only force that can change the motion of the gymnast once they take-off from the vault table and it pulls them downwards towards the Earth. Even though the movement of the limbs can alter the direction and speed of rotation of the body (more on that in the next section), the trajectory (flight path) of the athlete’s centre of mass is fixed once they are in flight. This trajectory is determined by three factors: (i) how high the centre of mass is at take-off compared to landing, (ii) the angle of projection of the centre of mass, and (iii) speed of the centre of mass at take-off. In a vault, the take-off height will always be higher than the landing height, and there is not a lot that the gymnast can do to manipulate this variable – they will always want to be fully extended at the point of take-off and at initial contact with the ground. So, the direction and speed at which the gymnast leaves the vault table will determine how high and how far they travel, and ultimately how much time they will have in the air to complete the twists and somersaults.
How does the gymnast achieve the optimal take-off angle and speed off the vault table? It starts with the run-up, where elite female gymnasts reach up to 8 m/s - more difficult vaults are associated with faster run-up speeds. Part of the horizontal velocity generated during the run-up is diverted in the vertical direction as the gymnast completes the roundoff entry and “blocks” with the hands on contact with the vault table. Putting this all together will result in a maximum height during the post-flight of ~2.5 m and a landing at a distance of ~2 m from the vault table in elite female gymnasts.
Flipping and Twisting
Angular momentum (the amount of rotational motion that a body has) also remains constant during the post-flight because there are no forces acting on the gymnast to change this angular momentum until they make contact with the ground. Now, the gymnast manipulates the position of their limbs to execute the desired number of twists (spinning about the long axis of the body) and flips (somersaulting about the mediolateral axis).
In Simone Biles’ latest ground-breaking vault, she performs 2.5 somersaults (starting from her hands on the vault table and landing on her feet) in a piked position. “Piking” means that she bends at the hips and keeps her knees straight, as opposed to a “layout” (extended hips and knees), or “tucked” (flexed hips and knees) position. These three positions illustrate the concept of moment of inertia, which represents the resistance of an object to rotation. In the layout position, moment of inertia is highest and the speed of rotation will be at its lowest. Conversely, the tucked position would produce the smallest moment of inertia and highest rotational speed. Biles chooses the middle option (pike) – in the video below you can see how she even “over rotates” this vault in competition and needs to take a big step back after landing. To avoid this, she could open up into a layout position fractionally before landing to slow down her rotation before she makes contact with the ground. With the risk involved in this vault, though, who can blame her for pulling as hard as she can to make the landing!
Biles might not even compete this Yurchenko double pike vault at the Tokyo Olympics. The risk-reward balance might not be worth it, as Biles is capable of outscoring other gymnasts with slightly less difficult vaults. However, a vault that you will definitely see her and a number of other competitors perform is called the Amanar (named after the 1996 Olympic vault champion, Simona Amanar from Romania). This vault involves 1.5 somersaults and 2.5 twists in the layout position.
The speed and angular momentum at take-off from the vault table is likely similar between these two vaults, so how does Biles produce these two distinctly different post-flight movements? Firstly, maintaining the layout position slows the somersault rotation. Secondly, she executes what is known as “trading” angular momentum between axes of rotation. A slight side bend of her body and lowering one arm towards her chest creates asymmetry that initiates the twist, trading momentum from the somersault axis to the twist axis. This picture captures it perfectly:
The skill, power, flexibility and mental strength that these athletes demonstrate is astounding. I, for one, cannot wait to watch them compete in Tokyo. I will also be watching out for Caitlin Rooskrantz and Naveen Daries – two young women that I had the pleasure of working with in their junior days. Caitlin became the first South African gymnast ever to qualify outright for the Olympics (i.e., not via a continental wild card berth) in 2019, and Naveen secured her spot when she placed 3rd all-around at the African Championships in May this year. It will also be the first Olympic experience for their coach, Ilse Roets-Pelser, herself a former national champion. Together, they are making history in South African gymnastics.
References
Schärer, C., Lehmann, T., Naundorf, F., Taube, W., Hübner, K. The faster, the better? Relationships between run-up speed, the degree of difficulty (D-score), height and length of flight on vault in artistic gymnastics. PLoS ONE. 2019; 14(3): e0213310. doi:10.1371/journal.pone.0213310