black-swan

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We all know the story. Virginal girl, pure and sweet, trapped in the body of a swan. She desires freedom but only true love can break the spell. Her wish is nearly granted in the form of a prince, but before he can declare his love, her lustful twin, the black swan, tricks and seduces him. Devastated, the white swan leaps off a cliff, killing herself and, in death, finds freedom.

Black Swan (2010) dir. Darren Aronofsky

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Black Swan (2010) dir. Darren Aronofsky

“We all know the story. Virginal girl, pure and sweet, trapped in the body of a swan. She desires freedom but only true love can break the spell. Her wish is nearly granted in the form of a prince, but before he can declare his love her lustful twin, the black swan, tricks and seduces him. Devastated the white swan leaps of a cliff killing herself and, in death, finds freedom.”

The physics of the "hardest move" in ballet

In the third act of “Swan Lake”, the Black Swan pulls off a seemingly endless series of turns, bobbing up and down on one pointed foot and spinning around and around and around … thirty-two times. It’s one of the toughest sequences in ballet, and for those thirty seconds or so, she’s like a human top in perpetual motion. 

Those spectacular turns are called fouettés, which means “whipped” in French, describing the dancer’s incredible ability to whip around without stopping. But while we’re marveling at the fouetté, can we unravel its physics? 

The dancer starts the fouetté by pushing off with her foot to generate torque. But the hard part is maintaining the rotation. As she turns, friction between her pointe shoe and the floor, and somewhat between her body and the air, reduces her momentum. So how does she keep turning? Between each turn, the dancer pauses for a split second and faces the audience. Her supporting foot flattens, and then twists as it rises back onto pointe, pushing against the floor to generate a tiny amount of new torque.

At the same time, her arms sweep open to help her keep her balance. The turns are most effective if her center of gravity stays constant, and a skilled dancer will be able to keep her turning axis vertical.

The extended arms and torque-generating foot both help drive the fouetté. But the real secret and the reason you hardly notice the pause is that her other leg never stops moving. During her momentary pause, the dancer’s elevated leg straightens and moves from the front to the side, before it folds back into her knee.

By staying in motion, that leg is storing some of the momentum of the turn. When the leg comes back in towards the body, that stored momentum gets transferred back to the dancer’s body, propelling her around as she rises back onto pointe.

As the ballerina extends and retracts her leg with each turn, momentum travels back and forth between leg and body, keeping her in motion. 

In Tchaikovsky’s ballet, the Black Swan is a sorceress, and her 32 captivating fouettés do seem almost supernatural. But it’s not magic that makes them possible. It’s physics.

From the TED-Ed Lesson The physics of the “hardest move” in ballet - Arleen Sugano 

Animation by Dancing Line Productions