Biomedical Engineering Issue II Volume XIX

The Science behind the Perfect Pirouette – and How It Has Changed the World of Prosthetics


Many people admire ballet for its artistic qualities, but few look beyond these qualities to appreciate the science that allows the beauty of ballet to exist. This paper takes a look at the science behind dance, and breaks down the fundamental physics concepts that allow dancers to execute the perfect pirouette. It discusses the implications of this research, and connects it to a seemingly unrelated field – prosthetic and bionic limbs. It then examines how the same principles that are used when performing a pirouette or a rumba could be applied to creating prosthetic limbs that function with the same capabilities as human limbs.

“Hold in your core, maintain a high relevé, straighten your leg, shoulders down, have a long neck, keep your passé high and connected to your knee, keep your hips level, and don’t forget to smile.” These commands, which may sound like instructions given to a member of the royal family in etiquette training, are actually a few of the many components that go into executing the perfect pirouette turn. Another often overlooked component? Physics.

With over 800 years under its belt, ballet has had a long, illustrious history, and has come a long way from the aristocratic social gathering it began as during the Italian Renaissance. When watching a ballet dancer perform a pirouette today, the grace and beauty of their movements suggests this dance has the art of rotating the entire dancer’s body weight on a two-inch block of wood down to a science [1]. What most don’t realize, however, is that all of the techniques garnered over the years are actually just ways to manipulate existing phenomenon, such as physics and biomechanics, to the dancer’s advantage, producing an effortless, stunning result. Recently, engineers have tapped into this field as well. The simple swing of the hips in a salsa dance or the pas de bourree of a ballerina can give valuable insight into the mechanics of the body, and engineers are beginning to use this new approach to create some of the most advanced and responsive prosthetic limbs the world has ever seen. Before engineers can create this, however, they must have an intimate understanding of exactly how ballerinas are able to do what they do.

When a dancer prepares to perform a pirouette, they begin in a stance with one foot forward, one foot back, legs slightly bent, and their body balanced in the middle. Then, the dancer pushes off their back foot, creating momentum and giving them enough speed to turn around themselves [2]. This type of prep is extremely effective due to the fundamental physics concept of torque. By definition, torque is any type of force that causes an object to rotate around an axis [3]. In the case of the dancer, the force is the foot pushing off the ground, and the axis is the body. The more torque the dancer can produce, the more force they have going into their pirouette, allowing them to turn multiple times before friction slows them down [2].

Fig. 1 A ballerina prepares for a pirouette by bending her legs and making sure her weight is centered. Her arms are also extended to maximize her torque when she pushes off [4].

Friction, however, is not the only thing that can end a pirouette prematurely. A successful pirouette combines both the momentum created by torque and balance to sustain the dancer’s turns. Due to the fact the dancer is their own axis, it is imperative they keep this axis as close to vertical as possible [2,5]. Ballerinas accomplish this by ensuring that their center of mass stays centered on top of their supporting leg. This is why a strong core is extremely important for dancers, and often requires countless sit-ups and other abdominal exercises (much to the dismay of the dancers) as a warmup technique. If a ballerina can “hold their core” as they turn, they are able to keep their center of mass in line with their turning axis, allowing the torque and balance to work together [5]. This is also why dance teachers instruct their students to keep their passé – a dance position where one leg is bent and the foot is pressed against the side of the knee – high and attached to the knee, to keep their hips level, and their supporting leg straight. Any deviation throws the center of mass off, ruining the dancers balance and not allowing them to sustain their turns.

Fig. 2 It is extremely important for a ballerina to keep their turning axis as straight as possible while they perform a pirouette to keep them balanced [14].


Fig. 3 A diagram shows many of the physics principles that are applied when a ballerina performs a pirouette. These include torque, center of mass, moment of inertia, and angular momentum [7].

Another physical concept that plays a prominent role in the perfect pirouette is moment of inertia. Moment of inertia, defined by the equation I=mr2, is equal to the mass of an object (m) times the square of the distance from the edge of the object to its axis of rotation (r2); it is essentially the rotational version of the relationship between mass and velocity [6]. If something is very massive, it is more difficult to move it with a high velocity, such as pushing a heavy box. Similarly, if something has a high moment of inertia, it is more difficult to rotate it. When a dancer performs a pirouette, they begin with their arms extended out, and as they push off the ground, they swiftly bring them closer to their body in a rounded position. This action not only produces more torque, but also lowers the moment of inertia by reducing the distance from the axis, and thereby creating more momentum [2]. This is also common for ice skaters, who can spin seemingly endlessly on the ice by slowly bringing their arms extremely close to their body, greatly decreasing their moment of inertia.

With origins dating back to the 15th century, ballet has evolved through dancer experimentation to find the most effective techniques by trial and error [1]. These techniques, when broken down in terms of science, are finding simple ways to harness the power of physics and using it in the most effective way. If dancers had known the physics behind a pirouette 800 years ago, they could have discovered the tricks and tips that are used by so many dancers today. Even more so, modern-day dancers can utilize this knowledge in physics to improve their own dancing by knowing the basic fundamentals of what makes a pirouette work, expanding their own repertoire.

Dancers are not, however, the only people who could benefit by knowing the science behind dancing. By understanding how ballerinas dance, we can learn more about the biomechanics of the legs in general. This knowledge can be applied to improve upon the prosthetics being created by biomedical engineers for those who are born with disabilities or have suffered debilitating injuries.

At approximately 2:49 pm on April 15, 2013, two bombs detonated near the finish line of the 117th Boston marathon, killing three people and injuring another 246 [8]. Among the 246 was Adrianne Haslet-Davis, a professional ballroom dancer who decided to attend the marathon as a spectator on a whim. With the detonation of the bomb, Haslet-Davis lost a leg and, along with it, her beloved dance career [9].

It wasn’t until Haslet-Davis was introduced to MIT professor Hugh Herr that she began to believe her dream to dance again was not a lost cause. Herr was the head of the biomechatronics group at the Massachusetts Institute of Technology (MIT), using his personal experience of losing both his legs from a hiking accident to fuel his research for creating the world’s first bionic legs. After meeting Haslet-Davis and hearing her story, Herr made it his personal mission to create a prosthetic so advanced and responsive that Haslet-Davis’ dance career could continue on, and within the span of 200 days, that is exactly what he did [10]. (There is an extremely inspiring Ted Talk speech given by Hugh Herr which both goes into great detail about the technology behind his prosthetics, and debuts Adrianne Haslet-Davis’ first dance performance since receiving her new leg. You can see it here [11].)

At the time, the only prosthetics available to amputees were made of wood, rubber, or plastic, with the “new technology” being carbon fiber composites. For a long time, material updates were the only advancements being made to the field of prosthetics. Herr thought it was time for a change. The leg he created for Adrianne Haslet-Davis did not simply include premium materials, it completely revolutionized what is expected from a prosthetic leg.   


Fig. 4 Adrianne Haslet-Davis, victim of the 2013 Boston Marathon terrorist attack, appears in her first dance performance since losing her left leg. This was made possible through the advanced technology prosthetic made for her by engineer Hugh Herr [12].

He added something that had been lacking in all previous models – power – thereby making the “first lower-leg system to use robotics to replace muscle and tendon function” [15]. Furthermore, he utilized onboard microprocessors, a lithium battery, electrodes and sensors to seamlessly intertwine the neurological responses of the brain with the mechanical actions of the bionic leg [15].

The work of Hugh Herr and others like him have opened up countless new doors in the world of prosthetic limbs. The ankle is historically one of the most intricate anatomical systems in the body, making it difficult to replicate successfully. Therefore, while developing his advanced leg for Haslet-Davis, Herr and his team studied dancers and their ankles at length. He took a special interest in the way their bodies move, and how they put pressure on different parts of the leg/foot at different times. He coupled this with his knowledge of physics to fuse the dancing and prosthetics in perfect harmony. Herr explained that his team is able to make such responsive prosthetics by modeling “the body part that is missing,” then modeling “the muscles and how the muscles are controlled by the spinal cord,” and using that information they “extract principles that dictate how the mechanics are designed,” essentially using the natural interactions within the human body as their guide [10]. Because dance is such an intricate art form, dancers act as the perfect people to model these ideas on.

The gold standard of prosthetics is reaching a point where the artificial limb is unrecognizable from a human limb, possibly even with greater capabilities. Where historically these prosthetics have been clunky and difficult to maneuver, prosthetic technology today is lighter, more comfortable, and more agile than ever – but there’s a catch. These prosthetics are designed to make walking, climbing stairs, and driving as normal as possible for people who have suffered limb loss [13]. They are not, however, designed for more involved or intricate movement such as doing yoga, kicking a soccer ball, or performing a pirouette. The work Herr and other engineers are doing is revolutionary; it is no longer enough for patients to just walk again, they should be able to hope for a future that mimics or surpasses the life they lived before their loss. Whether this is dancing, as in Haslet-Davis’ case, or rock climbing as in Herr’s case, engineers are raising standards for prosthetic limbs along with their range of capabilities, and as Herr discovered, this might just be done through dance [11]. By continuing to study dancers, those paving the way for the evolution of prosthetics could gain valuable insight into their biomechanics, how they manipulate their bodies, and their movement patterns in an effort to engineer a world in which uninhibited movement is not an exclusive right.


[1] M. Kant and I. Guest, “Ballet,” Encyclopædia Britannica, 15-Jan-2017. [Online].

[2]“The physics of the “hardest move” in ballet – Arleen Sugano,” TED-Ed. [Online].

[3] “Torque (article),” Khan Academy. [Online].

[4] Jdiana, “3 Different Approaches to Mastering the Pirouette,” Dance Teacher, 30-Aug-2017. [Online]

[5]“Module 1 — Choosing an Axis of Rotation and Describing the Direction of Rotation,” Module 1 — Choosing an Axis of Rotation and Describing the Direction of  Rotation – PER wiki. [Online].

[6]“Rotational inertia (article),” Khan Academy. [Online].

[7] “grace.on.pointe truly got everything, even the science!,” Pinterest, 03-Jan-2018. [Online].

[8] “Boston Marathon Terror Attack Fast Facts,” CNN, 29-Mar-2017. [Online].

[9] TEDxTalks, “What people say when they don’t know what to say | Adrianne Haslet-Davis | TEDxBeaconStreet,” YouTube, 19-Dec-2014. [Online].

[10] K. Whiteside, “Advanced bionic limbs could redefine disabilities,” USA Today, 19-Apr- 2014. [Online].

[11] H. Herr, “The new bionics that let us run, climb and dance,” TED: Ideas worth spreading. [Online].

[12] J. Lee, “TED2014: Boston bombing victim trips the light fantastic with new leg,” [Online].

[13] Hangar Clinic, “Hangar Complete System,” Hangar Clinic – Empowering Human Potential. [Online].

[14] YouTube. [Online]. Available: 1smmkUxqbGkokm098Od8MTUyNTMzOTQ1NEAxNTI1MjUzMDU0.

[15] M. Shaer, “Is This the Future of Robotic Legs?,”, 01-Nov-2014. [Online].

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