The Physics of Ballet

I love to dance! It might not seem like the most normal activity for an aspiring scientist, but I’m passionate about both ballet and Irish dance and actively dance 5 to 10 hours a week and used to train as a gymnast. So what can a science writer do with that? Well, explain the Physics (and perhaps some Biology as well) behind so many of these elegant moves of course! Ballet dancers often carry up to 3 times their body weight on the tips of the toes in many steps, but Irish dancers completely out-do that by carrying up to 14 times their body weight on their ankles and feet! That’s some incredible force and most of it comes down to Physics!

This first post is on ballet and we’ll look at two main points: jumps and turns.

 

Jumps

Typically people think of a grande jeté when thinking of ballet jumps, where the dancer jumps in a perfect split and appears to just hang in the air for a split second before landing. But she never actually hangs. The whole jump is an example of projectile motion and the dancer reaches her full split right at the peak height of the motion.

center20of20mass20jump
Projectile motion of a dancer’s grande jeté, from GrandeJete

This is very intuitive to us, but when looking at the physics, we have to consider the different forces. Firstly, the obvious force is gravity which is what causes the dancer to actually come down again rather than sailing off into space! Second is the horizontal force that the dancer generated by jumping off the ground and travelling forward rather than just up. The two forces combined mean that the dancer is initially travelling up and forward, but the gravitational force decreases the upward acceleration until the dancer is at the peak of her jump and begins to land again. Meanwhile, she continues to travel forward, creating the parabolic projectile motion curve above.

 

 

Turns

These are the more complicated aspect, as the dancer experiences angular momentum, torque, friction and then he or she has to balance all of these to face-planting!

When a dancer begins a turn (called a pirouette), she will push off the ground from a plié. Just as before a jump, the plié is the dancer’s potential energy, as her legs are bent and propel her either up or forward when she snatches her leg straight. The friction of the floor allows her to push off her feet onto one foot, either on the balls of her feet or en pointe (generally only girls go en pointe). This friction also allows her to twist her foot slightly to generate a little torque to help her start turning around.

She will also begin with her arm out to the side and whip it in to generate angular momentum (turning momentum). This, along with the torque generated previously, allows her to turn around.

However, she’s only going to stay turning perfectly instead of falling off to the side if her centre of mass is exactly over her foot. This means that there could be a straight vertical line drawn going right down through her head down through the centre of her foot. Obviously, a pointe shoe has a far smaller tip than a flat foot, so the dancer must maintain her centre of mass almost perfectly to turn en pointe compared to demi-pointe (balls of her feet). However, dancers often don’t find it so much harder turn en pointe because the smaller tip means there is less friction between the dancer and the floor and she can do multiple turns more easily.

The other part of balance is where Biology comes in. Dancers generally have spent so long working on their balance in turns and other balances that their brains adapt to this. Firstly, just balancing en pointe without turning requires highly developed visual (eyes), vestibular (ears) and proprioceptor centres that allow the brain to involuntarily correct muscles to balance. Those senses are developed simply through practice as neural pathways are used and almost widened like a highway because they’re used so often. The other part of balancing is in turning … avoiding getting dizzy. Remarkably, MRI scans have shown that dancer’s brains actually learn to shut off a significant proportion of the signals from the vestibular (ears) system as they turn. So despite the fact that fluid is still sloshing around inside their ears just as much as anyone else, their brains have simply learnt to ignore it! Isn’t that incredible!

This TED-Ed video explains the physics of a fouetté turn far better than I can, so I’d encourage you to check it out.

 

 


5 thoughts on “The Physics of Ballet

    1. Thanks so much! I guess that’s really the whole point of science communication- that we can share how science is behind so much that we take for granted. Thinking about it, everything you eat, or touch is made up of atoms and chemicals which will trigger more reactions within your body, and every action you perform is a result of chemical reactions in your body that are impacted by the laws of Physics around! Sorry if this is a bit long, but I just find it so cool and the whole ‘wanting to explain everything’ is what got me into science myself 🙂

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