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QUESTION: Pirouettes are a challenging skill to master in ballet due to the small base of support and the difficulty in controlling the rotary forces which are acting on diverse segments of the body. At the present moment you can only complete a single pirouette; however you need to perform a quadruple pirouette for an upcoming performance. What can you do to accurately increase the number of rotations whilst applying the correct technique and remaining on balance during and at the conclusion of the turn?

An introduction to a pirouette: A rotation around a vertical axis with the ball of the supporting foot remaining on the ground is the description of one of the most common movements in classical ballet- a pirouette. If the pirouette is not performed with the body on balance it is not considered as successful and although it is a common movement in ballet it is also an extremely difficult movement to master. Even professional dancers have significant difficulty performing more than two or three rotations in a pirouette before losing balance, despite continued trial and error efforts to improve. Numerous studies have been conducted which reveal particular characteristics that contribute to the success of a pirouette such as most favourable weight distribution during pirouette preparation, how the preparation width or the coordination of shoulder-hip movement affects the success of the pirouette, and how spotting the head (a technique learnt by dancers to assist with dizziness and accuracy) affects the angular momentum of the turn. It is important to understand that angular momentum refers to a vector quantity that represents the product of a body's rotational inertia and rotational velocity about a particular axis. According to the parallel axes theorem a pirouette is referred to as a “remote” term where the moment of inertia of a body is rotating about its external pivot and is equal to the product of mass and distance squared (Blazevich, A. J. 2012).

How does the body balance?

In a pirouette the body is balanced, or in equilibrium when a vertical line is drawn from the centre of mass (CM) and lies within the boundaries of the area of the support at the floor (in this case the base of support is the ball of the foot on the supporting leg) (Lott and Laws, 2012). An object’s CM is the point at the center of its weight distribution, where the force of gravity can be considered to act on the body as a whole (Laws, 2008). Dancers are often taught to perform successful pirouettes by beginning the movement on balance and then keeping the body stiff in that configuration, as opposed to correcting for an imbalance with small adjustments during the turn (Lott and Laws, 2012). However, this is not completely correct or most beneficial for the dancer. Dancers in practice should keep their bodies strong but slightly relaxed while holding a static pose, such as balancing in relevé retiré position (see Figure 1). If a dancer makes his/her body too rigid, the slightest displacement from equilibrium will cause gravity to exert a torque on the body, consequentially leading the dancer to topple. However, if the dancer allows for some movement his/her body is able to make the slight adjustments necessary to correct itself during the turn and regain balance.

FIG 1. Sourced from:

Google Images

The Biomechanics of a pirouette – Force & Acceleration.

Lott & Laws (2012) state that there are two distinct mechanisms to correct for imbalance: 1. accelerating the CM back to a position over the supporting foot, or 2. moving the supporting foot back under the CM. The way in which a dancer manages to move the supporting foot back under the CM is by hopping and although this will essentially assist in regaining balance, it is considered as an unaesthetic adjustment, therefore declaring the pirouette as unsuccessful. So, how does a dancer move the CM over the supporting foot or subtly slide the foot back under the CM without hopping? If we imagine a dancer beginning to topple to the right from a balanced retiré position she/he would need to accelerate the CM back to the left. To accomplish this, an external force must be applied to the dancer in that direction. For this particular movement the friction at the floor can provide the force needed. If the dancer exerts a force on the floor to the right, the floor will exert a force back on the dancer in the opposite direction (Newtons 3rd Law), which will accelerate the body back to a balanced position. How can a dancer achieve this? As dancers attain many skills, one skill that they are exceptionally accustomed too, regards the manipulation of the body. By rotating the body at the hip, the torso will automatically move to the right (toward the direction of the topple), the supporting leg will then react by rotating through an arc around a horizontal axis at the hip allowing the dancer‘s supporting foot to exert the required horizontal force onto the floor. If there is enough friction at the floor, the frictional force will be directed to the left (back toward balance), and the CM will be accelerated back over the supporting foot. If there is not enough friction at the floor, the same manipulation of the body can still lead to a regaining of balance. However, instead of the foot relying on friction to exert a force to move the CM, through the momentum and motion of the turn the supporting foot can slide to the right, to a position beneath the CM. The dancer will regain balance via mechanism “2”. It is also extremely important that a dancer does not think too hard about trying to maintain balance while attempting a pirouette as the sensory feedback from one’s eyes; ears and proprioceptors can induce “automatic responses”. Automatic responses influence the equilibrium in the form of muscle contractions that in turn cause the body to attempt to fix itself, generally in an incorrect manner.

Image A. Sourced from:Journal of Dance
Medicine & Science. (2012).

Image B. Sourced from:Journal of Dance
Medicine & Science. (2012).

FIG 2. Sourced from: Journal of Dance
Medicine & Science. (2012).

The Effects of the Moments Of Inertia in a Pirouette: The images above are sourced from a Journal of Dance & Medicine Science (2012) and reflect a study that was undertaken to determine how many rotations a typical “rigid body dancer” can complete before reaching a point where he or she is forced to hop or fall out of the turn. The study combines theoretical analysis as well as experimental results in order to establish how close to a vertical plane a dancer must begin a pirouette in order to execute multiple turns. The method uses the physics of rotations in three dimensions and is adaptable to dancers based on their size, shape and mass. There are 14 distinct body segments that influence the dancers’ ability to turn: head, trunk, upper arms, forearms, hands, calves and feet. Knowing the masses, dimensions, and placement of these 14 segments, determine the principle moments of inertia of the dancer in pirouette position (see Figure 2.). The moments of inertia of a body can give a measure of how easy or difficult it is for the body to rotate around a certain axes—i.e., the spin (z) axis and the topple (x and y) axes.When analysing the moments of inertia of the diverse segments, it is important to note that the moments of inertia about the topple axes should be equal e.g., Ix = Iy. This indicates that the toppling will be independent of the angular position of the body during rotation (Sugano and Laws, 2002). Lott and Laws (2012) have defined the topple angle as the angle between the vertical and a line connecting the point of support at a dancers foot to the dancers CM. As shown in image A the dancer begins the pirouette with her CM nearly in line vertically over the PS (the vertical is represented by the white line). However, image B, pictured during a later stage of the pirouette, shows that force due to gravity is acting on the dancers CM and has caused the topple angle to increase significantly. The moment of inertia (I) of a rigid object takes into account the object’s mass and how it is distributed around an axis of rotation. More mass concentrated farther from the axis of rotation leads to an increase in I. A larger I means that it is harder to get the object to change its rate of rotation, for example, it requires more torque for the object to have a rotational acceleration. Results from the study show that if a dancer begins the pirouette between 0.1 and 1 degrees off the vertical plane their chances of executing multiple turns is higher.

In ballet there are diverse types of pirouettes and another popular pirouette is done with the leg held in a la seconde. This style of pirouette is even more difficult to execute as the mass is located further from the spin axis of rotation therefore creating a larger moment of inertia. Sourced from: http://balletclassroom.wordpress.com

THE ANSWER: It is incredibly difficult to provide a straight answer and solution for how to increase the number of rotations from 1 to 4 in a short amount of time, as each individual is different in weight, height and proportion. However, we have learnt that there are many contributing factors that affect a dancer’s ability to execute multiple turns successfully. Besides from practice, trial and error, there are some key notes that will improve technique and hopefully allow for an increase in number of rotations. Firstly, do not prepare for the pirouette or turn as a “rigid body”, there is a difference from being stiff and being strong. Present your body and posture with strength however, relax internally and allow for some movement during the turn. Lessening the moment of inertia by distributing weight equally around the body (keeping in mind the 14 segments) will also increase chance of maintaining balance therefore allowing for additional rotations. Often dance teachers will say to their students to “pull up out of the hips” due to the fact that if too much mass is distributed close to the topple axis of rotation of the floor it increases the chances of falling out of the turn. Holding limbs in the correct retire position close to the body also decreases moment of inertia and allows for a faster and easier rotation. However, the greatest tool is balance. A dancer should learn how to sense for imbalance and make corrections early enough in the rotation so that movements of the body and any sliding of the foot are subtle enough that the audience would not notice. Always remembering, that the dancer has two options in order to regain balance during the turn, 1. accelerating the CM back over the area of support or 2. sliding the supporting foot back under the CM.

How else can we use this information? 

The concepts discussed throughout this blog can transfer into various movements either in dance, gymnastics or acrobatics, where one is required to rotate around a vertical axis more than once. We know that in order to maximise the chances of turning multiple times successfully one should aim to begin with their centre of mass between 0.1-1 degrees within the point of support, decrease moments of inertia by distributing weight evenly throughout the body and prepare and turn in a strong (but not completely rigid) position, so movement during the turn to correct imbalance is allowed. Knowledge of these principles can help us teach young dancers and gymnasts the correct technique which will assist in an improved performance in their later years. By helping younger athletes understand the mechanics of a particular skill, we, as coaches or mentors, are essentially helping them to learn how to correct and better themselves. By attaining the ability to analyse their own technique and assess their own performance, young athletes are able to recognise when something goes wrong or if something did not feel quite right while performing the skill, they are then able to detect the problem and manipulate the movement using their knowledge of mechanics to fix it for next time. Dance teachers can use this information to generate teaching cues for their students to ensure optimal skill development during session times. 

References:

Ballet Classroom. (2012). Centre Floor- Centre Barre and Turns. Retrieved from http://balletclassroom.wordpress.com/2012/03/27/center-floor-center-barre-and-turns/

Blazevich, A. J. (2012). Sports Biomechanics the Basics Optimising Human Performance (2nd ed). London, UK: Bedford Square.

Crotts, D. F., Thompson, B., Nahom, M. (1996). Balance abilities of professional dancers on select balance tests. J Orthop Sports Phys Therap, 23 (1), 1-12.

Lott, M. B. & Laws, K.L. (2012). The Physics of Toppling and Regaining Balance
During a Pirouette. Journal of Dance Medicine & Science ,16 (4), 167-174.

Sugano, A. & Laws, K. (2002). Physical analysis as a foundation for pirouette training. Med Probl Perform Art, 17 (1), 29-32.

Wilson, M. (2009). Applying biomechanical research in the dance studio. International Association for Dance Medicine & Science: The IADMS Bulletin for teachers, 1 (2), 11-13.