Calculated cavort

Ever wondered why the dancer jumps at many instances during the dance recital? Leaps and jumps are the essential steps of Bharta Natyam dance items. The jumps or leaps remain choreographed, not just for visual beauty. Its existence is mainly for space management. Traditionally, most jumping steps, are always followed by Theermanam adavu with/without pauses. The physics in the jump is an exciting area to explore and the forces acting on the human body under the jumping action.

Few jumps are longer in time, and few hops are short sometimes. The leaps of the shorter duration are quick. Hence the effort of the dancer and the physics involved in it might go unnoticed. A forward jump emerges at the end of Alarippu, the first dance in Bharata Natyam Margam. The timing of the jump is choreographed approximately to one second. Hence the dancer will raise their body above the ground level and land back on the floor within the specified time. A new world of physics can be seen here with precise observation and analysis. 

My guru always insisted that the specific jump in Alarippu should be with greater force and the body must cover a certain distance, instead of jumping off and landing at the same place. Before mastering the leap to a particular duration, I could observe and feel that I was landing either early or late. It took me a few classes to understand that the amount of time in the air depends on the vertical component of the velocity. It doesn't rely on the mass or the horizontal component of the velocity. To understand the physics and mathematics of jump, one needs to understand the concept of the centre of gravity.

                                           

The centre of gravity (CG) is a theoretical point at which the forces of gravity appears to act. A moment where the entire mass of the body concentrates. Try balancing a pencil at the tip of your finger to understand what the centre of gravity is. Observe the anatomical position of the human body; the centre of gravity lies at the second sacral vertebra approximately.

Since the dancer is not standing still throughout the dance, the centre of gravity changes as the dancer moves; often, the posture of the dancer is the most discussed topic. The centre of gravity remains displaced as the posture changes.

By observing the figure and its CG, one can conclude, the first posture has its CG over the pivots in the hips. This action puts an end to the usage of mussels to balance the body. And in the case of poor posture, the requirement mussels are necessary to balance the body to maintain the CG.

The CG changes according to the activities performed by the body. Observe the figure below to understand how the CG changes as one carries his kid on his shoulders, lifts a bag to walk and hold books against the chest while walking.

When the dancer is mid-air during the jump, gravity is the only force acting on the dancer. Before the sixteenth century, the world of physicists and mathematicians believed that the acceleration of the falling body was proportional to its mass. Galileo experimented by dropping the two objects of different mass from the leaning tower of Pisa, which disapproved of the belief that the purpose of 5kg, expected to accelerate five times faster than the object of 1 kg. The acceleration due to gravity remains the same irrespective of the mass. It remains approximated to 9.8m/s.

The value g = 9.8 m/s can also be written as g = 32 ft/sec when converting the units from meter to feet. This indicates that the dancer's speed in the air changes by 32ft/sec.

If the initial velocity of the dancer is 32 ft/sec. Then the height jumped by the dancer can be calculated using 

h = v₀²/64

h = (32)²/64

h = 16 feet

Then, the total time taken by the dancer to complete the jump can be calculated by

This analysis indicates that by jumping with an initial velocity of 32ft/sec, the dancer's centre of gravity will travel up for a second and spend the next second falling. Hence the total time taken by the dancer to complete the jump is 2 seconds.

If the dancer starts with an initial velocity of 16ft/sec, the dancer's centre of gravity will travel up only for half a second and spend the next half a second falling. During the last jump in an Alarippu, a dancer will be moving at a speed of 16 ft/sec approximately. In order to successfully complete the jump in 1 sec, a Bharata Natya dancer should possess, a minimum velocity of 16ft/sec.