The Physics Behind Tonya Harding’s Triple Axle

 

Tonya Harding made history at the 1991 at the US Figure Skating Championships in Minneapolis, Minnesota when she successful completed a notoriously difficult, some say physics-defying, triple axle. The triple axle consists of a skater releasing off the outside edge of one skate, rotating 3.5 times in the air to land backwards on the outside edge of the opposite skate. The physics behind the jump makes it easier said than done. 

First, the skater must generate enough vertical velocity and height to give enough time to complete 3.5 rotations before landing. This requires a great amount of strength and body control to obtain a velocity to start rotating as quickly as possible while getting enough height to finish all the rotations in the air. This relies on the skater exerting a large force on the ice to accelerate upwards against the force of gravity to obtain a large vertical displacement and velocity. The skater will only successfully land if their landing leg is positioned to absorb the force exerted by the ice which takes a bent leg to reduce the force on the landing leg. This is a consequence of the impulse momentum principle. Since the time of impact increases by bending the knees, the average force exerted is reduced (Impulse=F𝚫t). 

The skater must also generate enough rotational velocity. This ultimately decides the difference between a single, double, or triple axle. The triple axle requires the greatest amount of rotational velocity to complete the rotations in the shortest amount of time. Skaters use the principles of  angular momentum to increase their rotational velocity. 

Angular Momentum = L = mvr 

As you will notice when watching this maneuver, the skater will start the rotations with their arms and legs farther from their body and start to bring them closer as they increase speed. Since momentum is conserved because no external forces are acting on the skater, decreases the radius will increase the angular velocity to conserve momentum. Therefore, skaters will bring their arms and legs tightly around them to decrease their radius and increase their angular velocity. With all these different factors contributing to the difficulty of the move, the move has become a notoriously difficult move and a sign of a technically great figure skater. 

References:

https://www.vox.com/videos/2018/2/12/16978946/triple-axel-tonya-harding-mirai-nagasu

https://www.scientificamerican.com/article/the-physics-of-figure-skating1/

https://www.vanderbilt.edu/AnS/physics/astrocourses/ast201/angular_momentum.html