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Where Art Meets Science: The Physics Behind Ballet

Elina WisungBallet, science Leave a Comment

By Anagha Madhan

Ballet is often described as poetry in motion. As dancers, we aim to captivate audiences and make difficult movements that require a complex mixture of concentration and coordination look absolutely effortless. What is presented is not only a culmination of hard work and practice, but it is also the seamless application of scientific principles. So, let’s dive into the science behind the curtains, where the dance meets the laws of physics, to discover the forces and laws that make these performances possible.

The Fundamentals of Movements

physics centre of massBalance & Our Centre of Mass

The centre of mass is defined as the point in any body, where all the mass can be considered to be concentrated. We use the centre of mass to aid us in analysing motion, since any body can be considered as a point mass at the centre of mass. It is the balance point at which we can say the entire mass is distributed in all directions. If you support an object at its centre of mass, it would remain perfectly balanced.

As budding ballet dancers, we aim to maintain control over our centre of mass to firstly, achieve balance, and more importantly, maintain it. Balance is the foundation of all movements, and it is applied whether a dancer is standing en pointe, turning, or jeteing through the air.

physics centre Some examples of movements that rely heavily on balance:

  1. Going En Pointe: The only way to rise onto the tips of your toes and go en pointe, is by aligning your centre of mass directly above the supporting foot. Learning to execute such control, and essentially mould ourselves into one line where our mass meets the tip of our toes, is why it takes years of training.
  2. Arabesque: The arabesque is a classic example of balancing our weight on two sides. In an arabesque, we stand on one leg with the other leg extended behind. The upper body leans forward in order to counterbalance this extended leg, and thus keeps our centre of mass over the supporting leg. This is why, sometimes, if our weight isn’t balanced, we feel like we’re tipping over this way or that while in an arabesque!
  3. Pirouettes: Standing on one leg is one thing, but spinning on it leads into a whole other realm of physics. The first step to this, however, is to find and maintain the centre of mass over the supporting leg throughout the spin. This ensures that we remain upright and controlled. This is also why, sometimes, while spinning, we feel like we are falling forward or backward – our centre of mass isn’t over the supporting leg.

Newton’s Laws of Motion

While Newton was changing the world of science with the three laws of motion in the 16th century, ballet was putting it all into action in the renaissance courts of the time!

First Law – Inertia:

Newton’s First Law states that an object at rest, will stay at rest, and an object in motion will stay in motion unless acted on by an external force.

Once we achieve a pose, we remain without additional movement unless another force (like muscle adjustments, or shifting our balance) acts on us. This is evident when we have to snap into a pose and stay still for an extended duration, our inertia will inherently keep us in place until we decide to move.

Second Law – F=ma

In his second law, Newton states that force is the product of mass and acceleration. This is crucial when we consider allegro steps – jumps and leaps. When we prepare to jump, we apply a force on the ground. The greater this force, the higher and further we can jump – the more power there is behind our jumps. Our muscles exert this force by pushing down against the floor, and then we accelerate upwards, converting the work our muscles do into motion.

Third Law – Action Reaction Pairs

Newton’s third law, his most famous, states that for every action there is an equal and opposite reaction. This is evident in the way in which we interact with the floor. When we push down into the floor to jump, the floor pushes back with an equal force and propels us into the air.

We also see the action reaction pair during turns. As we push off the ground to initiate the spin, the ground gives us enough reaction force (we gain the momentum required) to enable the turn.

Grand Allegro: The Physics of Elevation

Energy Conversion: From A Crouch to A Leap

The concept of energy conversion- energy can neither be created nor destroyed; rather, it transforms from one form to another – is what governs our world. Understandably, it also governs a lot of ballet steps.

In a grande jete, dancers convert potential energy – energy stored by the body due to the work done by crouching – into kinetic energy – energy of motion as they leap. The muscles generate the power needed to spring off the ground, turning stored energy into the graceful arc of a grand jete.

The same concept can be applied to any leap or jump, glissades, sautes, ballones, they all follow the law of energy conversion.

The effectiveness of this energy conversion relies heavily on our muscle strength and technique. Strong, well-conditioned muscles can generate more force, allowing for higher and more controlled jumps. Technique plays a critical role as well; proper alignment and timing ensure that the energy is efficiently transferred from the crouch to the leap.

physicsProjectile Motion

Once we’re airborne, we become human projectiles. Our paths through the air can be predicted by the same principles that govern that of a thrown ball. Two important factors are the initial speed and angle of take off:

  1. Initial Speed: The speed at which we leave the ground. A higher initial speed means more energy put into the height and length of the jump. We extend our legs to maximise this energy and put in a lot of power into the jump. This is why stretching our legs to the maximum is important to maximise the amount of energy we put into a jump.
  2. Angle of Take-Off: The angle at which we leave the ground fundamentally affects the shape of our path. The optimal angle is 45 degrees, which balances height and distance and creates a beautiful parabola. We constantly adjust this angle to change the ratio between height and distance travelled – compare the angle of take-off of a saute and a glissade, for example.

Landing is equally as important as the leap. We aim to descend gracefully and with control, for visual appeal and to avoid injury. Here, we convert kinetic energy back into potential energy stored in the body. To ease this transition, we extend from a powerful motion (the leap itself) into a plie, as we bend our knees and lower our body. This helps to absorb impact and hence reduce strain on the joints and muscles. This is why plie-ing after a jump is absolutely crucial. Take a look at this graph, which one do you think is more gentle on the body?

Spins & Turns: The Physics of Rotation

Spins and turns in ballet are as much of a marvel of physics as they are of artistic expression. We use the principles of angular momentum and friction to achieve these incredible rotations

Angular Momentum

Angular momentum is the measure of how much rotation a body has. It depends on the moment of inertia (how the mass is distributed), and the angular velocity (how fast is it spinning). It is conserved in a system where no other rotational forces are acting.

For a ballerina performing a pirouette, angular momentum is conserved the second they go into motion. That means, if they start spinning with a certain amount of angular momentum, it remains constant throughout the spin.

physicsControlling Spin Speed

The secret behind controlling the speed of spin is by changing our body positions:

  • Pulling Arms & Legs In: When we pull in our arms and legs closer to the body, we spin faster. This is because pulling our limbs in makes us more compact, and reduces our moment of inertia, which allows our speed to increase.
  • Extending Arms & Legs: When we extend our limbs, we spin slower. This is because it makes us more wide-spread, and increases our moment of inertia. This means our speed needs to reduce to conserve the value of angular momentum

We can see both of these movements in play during a fouette- by repeatedly extending and pulling in a leg, we can maintain or increase the speed over multiple turns.

Friction & Contact Points

Friction is the force that resists motion between two surfaces in contact. For ballet dancers, the friction between our shoes and the floor is absolutely crucial in controlling our spins.

Maintaining optimal friction is very important. It becomes difficult to spin if there is too much friction, it feels like our shoes are sticking to the floor and maintaining the spin is hard. If there is too little friction, we might slip and increase the risk of falling.

Role of Design

Dance floors are designed to be smooth but not slippery, which provides a balance between controlled spins and easy movements. They are also often made so that they will aid dancers in springing up during jumps!

Our shoes are made of materials like suede, canvas, or leather. This is not just an aesthetic choice, these materials provide enough grip to prevent slipping but are smooth enough to aid in spins.

Ballerinas also often use rosin to provide grip and traction. Crushed rosin is applied to the soles of ballet shoes to enhance friction. Rosin is actually made of tree sap and is solid. When crushed and applied, it creates a tacky surface which prevents slipping but allows smooth gliding movements.

The next time you dance, or watch a ballet performance, remember the forces and laws at play! As dancers we are constantly applying and maximising the principles of physics to create the illusion of effortless grace.

To read more interesting blogs on everything from food for dancers to adult beginner dancers and understanding the structure of a ballet company, click here
To see the physics of the ‘hardest move’ in ballet, click here

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