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Measuring a Pirouette: Tackling the challenge of quantifying dance

Posted By Catherine Haber on behalf of the IADMS Dance Educators’ Committee, Tuesday, February 26, 2019

Pirouettes are incredibly challenging for dancers to perform, but also for scientists to study! As we heard from January’s post, physical principles – such as torque, force couples, angular acceleration, and conservation of angular momentum – can help us gain better insights into performance. However, beyond these principles, there are a multitude of crucial elements that go into the performance of a pirouette. The dancer must balance in a proper passé position, reach a high relevé on the supporting foot, hold the arms in first, engage the core, spot his head, and many more! With all these components to coordinate, what should the dancer focus on, and what should the scientist measure?


With a double Bachelors in Dance and Physics, I was thrilled to begin working as a research assistant during my Graduate studies to Dr. Andrea Schaerli, in her research of the influence of spotting on postural stability in the ballet rotations of pirouettes and fouettés. We recorded dancers in motion capture labs performing rotations, and I was eager to direct my knowledge in physics to my passion of dance. I calculated everything from the displacement of the supporting foot, the trajectory of the center of mass (COM), the velocity of the head spotting, the separation of the head, trunk, and pelvis coordination, and many more variables that triggered my interest. However, it quickly became overwhelming when I realized the magnitude of possibilities for analysis. The question became not only what should we measure, but also – at the end of the day – what measure is the most relevant and applicable to the dance population? How can we as researchers find meaningful outcome measures that most closely capture the dancer’s experience of performance?


In a day and age of great technological advances, movement can be measured in many ways - from 2D video analysis to 3D motion capture, force platforms and electromyography (EMG) measures of muscle activation, and even the direction of eye movements. Yet dance inherently relies on experiential and aesthetic variable that can be challenging to quantify. Studying dance thus calls for the creation and validation of dance-specific measures. Therefore, we performed two small studies to integrate dancers’ impressions of performance into our analysis.


The first of these two studies was a pilot study that aimed to validate a balance measure that best predicts the performance of pirouettes. To this end, eight intermediate dancers performed many pirouettes in our movement lab and rated their performance after each turn, while the researcher independently did the same. Followingly, we correlated the most predominantly used measures of pirouette performance in dance science research with the dancers’ and researcher’s impression of the turn.


Here, it was found that the dancers’ performance was highly correlated with the angular deviation of the pelvis center from vertical – that is, how far off the center of the pelvis is from the vertical line drawn up from the supporting toe. This follows previous findings of smaller angular deviations between the center of mass (COM) and a vertical line from the base of support (here, approximated at the supporting toe) during successful pirouettes. In our study, the dancers gave their turns higher performance ratings when their pelvis – rather than the COM – was closer to this vertical line. This was an interesting finding for two reasons. From a research perspective, the deviation of the pelvis was highly correlated to the deviation of the COM (with this ‘true center’ actually residing within the pelvis of these female dancers during the pirouette). This means that researchers could use the pelvis center as an economical approximation for the tediously calculated COM during pirouettes. From the perspective of the dancer, while it may be challenging to have a clear understanding of your ‘true center’ throughout dynamic movements, being in tune to where your pelvis is can be a good starting point for pirouettes.


A second interesting finding was that from the observers’ perspective, performance was best associated with the instantaneous axis of rotation – that is, the deviation of the best-fit line through the head, torso, and supporting leg, from vertical. The observer perceived better turns based on this holistic impression of verticality. Therefore, this pilot validated additional measures of pirouette performance that best represented the impression of the dancer and the observer.


In a second effort to incorporate dancers’ opinions into research, we performed a Delphi Method survey to gather expert opinions on the characteristics and uses of spotting. While many measures have been used to describe balance in pirouettes, little research has been done on spotting itself. Therefore, we asked professional ballet dancers, professional ballet teachers, and dance scientists to participate in a Delphi Method survey, bringing together expert opinions over iterative rounds to generate ideas and to evaluate levels of consensus. After three rounds of first brainstorming ideas, then rating agreement on the group’s ideas, and finally ranking the most important ideas, the consensus of the group was actually quite low in defining the most important characteristics and uses of spotting. However, a novel variety of topics were proposed. Building on the traditional suggestions of spotting for balance and reduction of dizziness, spotting was suggested to have further functionality for orientation, rhythm, and particularly in multiple turns.


The value of integrated expert opinions was quite apparent when it came to aspects of rhythm. When splitting the group into dance practitioners (teachers and dancers) and dance scientists, it appeared that the practitioners had a great affinity for topics relating to rhythm. In contrast, dance scientists tended to rank these topics relating to rhythm very low. This survey was thus able to bring new perspectives to the understanding of spotting that can serve as meaningful hypotheses for future movement-based research. As such, we performed a study last fall capturing professional dancers performing the multiple rotations of fouetté and a la secondé turns to examine exactly these proposed functionalities of spotting.



Analyzing dance from a scientific perspective can be a challenging feat. However, we must not forget why we are motivated to do such research: to help improve dancers’ performance! Particularly from the perspective of movement analysis where one can become fixated on degrees of difference or centimeters in jump height, the perception of the dancer must not be lost. Dance is an interdisciplinary, physical system yet to be fully analyzed. With collaborative efforts of the community of practitioners and researchers, we can determine comprehensive, dance-specific measures and methodologies to benefit the well-being and training of dancers.


Catherine Haber is a Graduate student, currently finishing a MAS in Dance Science and a MSc in Sport Science Research, and a research assistant to Dr. Andrea Schaerli at the Institute of Sport Science at the University of Bern, Switzerland.

Tags:  dancers  pirouette  research  turn 

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Can Physics improve your pirouettes?

Posted By Margaret Wilson and Jennifer Deckert on behalf of the IADMS Dance Educators' Committee, Wednesday, January 23, 2019

Successful completion of a pirouette (turn on one leg) can sometimes feel like an impossible task, but understanding more about the mechanics behind the turn may help you find more stability, produce more rotations and have better balance.  There are several principles from physics that are useful in understanding the preparation and turning action in a pirouette.

1.     Torque – a turning force that helps start the turn

2.     Force couple – torque that is created in the placement of the legs and feet in the preparation for the turn

3.     Angular acceleration – how to build up turning speed

4.     Conservation of angular momentum – how to maintain the desired turning speed. 


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But first, let’s examine Newton’s laws of motion to help put these principles into context and help describe our understanding of dance movement.  The first law has to do with inertia (the tendency to maintain the current state of motion or a resistance to change).  Newton's second law deals with acceleration and momentum and the third law describes action/reaction. Each of these laws comes into play in the preparation and continued turning motion in pirouette.  To start turning we must overcome inertia through the creation of torque – and we do this in the preparation for the turn.  While turns can start from a variety of positions of the legs, if we look at 4th position in external rotation, we can see easily see how the dancer creates torque to overcome inertia and begin the turn. The distance between the two feet, rotating away from each other creates an equal and opposite force which is transferred to the supporting leg in the turn. This generation of torque can be described as a force couple. In 4th position plié a moderate amount of torque is created, in 5th position, where the distance between the feet is very small, less torque is created. If a dancer takes an open fourth allongé (a lunge position where one leg is bent and the other extended), the torque generated is greater (Sugano and Laws 2002). 


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The force couple and torque help start the turn, but angular acceleration also determined by the contribution of all related body parts in a turn.  For example, when the arms and legs are extended away from the center of the body, as when the arms and gesture leg are à la seconde, rotation is slower since more mass further away from the body’s center of rotation. As that mass gets pulled closer to the center of rotation, conservation of angular momentum dictates that the dancer must turn faster. Dancers can feel this when they pull their arms in tight, and it is clearly visible on a low-friction surface like when watching figure skaters.


Angular momentum is lost to friction – the amount of surface contact for the turning foot.  A dancer will experience less friction en pointe than on a low relevé in plié as is sometimes seen in a jazz turn. The interaction of the surface of the shoe and the floor also contribute to the coefficient of friction: a satin pointe shoe on a vinyl surface has relatively low friction when compared to a bare foot on the same surface. The more friction the slower the turn, and therefore fewer rotations are possible.


Take Away Ideas:


1)     Develop a strong supporting leg: In a pirouette the dancer is rotating around a vertical axis so balance in the turning position is important. Imura and Iino (2018) found that dancers need good strength in the supporting leg to help find balance and endurance for multiple revolutions. 


2)     Focus on the arms in the preparation –Kim, et al, (2015) found that skilled dancers generated larger vertical angular momentum by skillfully using rotation of the upper trunk and arms. The closing arm after the moment of inertia makes the largest contribution to whole-body angular momentum – not the arm that opens as the trunk begins to rotate.


3)     While the supporting leg should be strong, the body should be slightly relaxed.  The same is true in pirouette.  If a dancer holds the body rigid, the slightest displacement from equilibrium will cause gravity to exert a torque on the body, and the dancer will topple. Keeping the body somewhat relaxed enables the dancer to make the slight adjustments necessary to correct for small perturbations from balance.


Additional Reading:

1)     Laws, K. Physics and the Art of Dance (2002)

2)     Sugano A and Laws K.  Physical analysis as a foundation for pirouette training.  Med Probl Perfom Art, 17 (1) 29-32.

3)     Imura A. and Iino Y. Regulation of hip joint kinetics for increasing angular momentum. The results suggest that dancers need to regulate hip joint torques along with the thigh angles in the pirouettes depending on the number of revolutions. Human Movement Science 60(2018)18-31.

4)     Kim J, Wilson M, Singhal K, Gamblin S, Suh CY and Kwon YK Generation of vertical angular momentum in single, double and triple-turn pirouette en dehors in ballet.  Sports Biomechanics, Volume 13, 2014 - Issue 3

5)     Lott, MB and Laws KL The physics of toppling and regaining balance during pirouette.  Journal of Dance Medicine & Science 2012, 16(4) 167-174.




Margaret Wilson, PhD

Professor, University of Wyoming


Jennifer Deckert, MFA

Associate Professor, University of Wyoming

Margaret and Jennifer are the co-directors of the Dance Science Program at the University of Wyoming in Laramie, WY USA


Tags:  physics  pirouette  teachers  turn 

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