Bharatanatyam Biomechanics April 5 th 2012 Aarti Mistry

Definition • ‘Bharata’ is derived from the three syllables meaning BHAva (expression), Raga (music), TAla (rhythm), ‘Natyam’ means dramatic art. • Characteristics – Demi-plié stance “aramandi” • Balance – Structured and geometric movements • Symmetry – Intricate foot movements • Force / Impulse – Delicate facial expression

Research Questions Balance 1. Does my center of mass change when performing different steps? Symmetry 2. Are my arm movements symmetrical? a) Position? b) Velocity? c) Momentum? Force/Impulse 3. Do my jumps require the same impulse to take off from the ground?

Videos 1. Walking Jump 2. Stationary Step 3. Clock Step

Balance & Center of Mass • Definition: point in space where the entire mass of a body assumed to be concentrated. – Slightly below belly button (geometric center ) – Female center of mass slightly lower vs. male • COM to height ratio: 0. 543 vs. 0. 560 • To maintain balance COM must remain directly above area of contact with floor – Fgravity and Fground align directly through COM and there is no total force – Smaller the area (balls of the feet), harder it is to balance

Balance & Center of Mass • In dance, must maintain demi-plié stance for – Form – Weight distribution – Balance • Standing COM – COM = COM: height ratio * height – COM = 0. 543 * 153. 7 cm = 88. 46 cm • Estimated COM in neutral demi-plié stance – COM = 66. 47 cm (average) – Height in demi-plié = 138 cm (average) – COM: height ratio = 0. 482

Position (y. COM) vs. Time • Walking Jump – – Initial: 63. 49 cm Cross over peak: 78. 92 cm Jump peak: 81. 56 cm * Final: 66. 50 cm * • Stationary Step – – Initial: 68. 52 cm Jump peak (1): 79. 89 cm Jump peak (2): 80. 20 cm Final: 62. 83 cm • Clock Step – Initial: 67. 81 cm – Jump peak : 82. 43 cm – Final: 69. 69 cm

Symmetry & Clock Step • • Position (y. RH & y. LH) vs. time Arm movements trace the pattern: I. III. IV. V. VIII. 12 o’clock 1 o’ clock/ 11 o’clock 2 o’clock/ 10 o’clock 3 o’clock / 9 o’clock 4 o’clock / 8 o’clock 5 o’clock / 7 o’clock 6 o’clock Center LH lower than RH except during jump phase and 6 o’clock • – ∆yaverage = 4. 18 cm Greatest difference is a 3 o’clock/9 o’clock position • – ∆ymax= 13. 49 cm, i. e. LH 13. 49 cm lower than RH

Fluidity & Clock Step • Velocity (vy, RH & vy, LH) vs. time • Position differs but velocities similar • Momentum – ρ = m * v – m = mass * body segment proportion – Arm: 0. 05 body mass • Sample calculation (LH peak height) – – vx = 0. 062 m/s, vy = 4. 022 m/s, v = 4. 029 m/s ρ = 39 kg * 0. 05 * 4. 029 m/s ρ = 7. 845 kg m/s • Momentum appears to be inconsistent – Initial lag in LH vs. RH then recovery – Lack of fluidity? • Is the clock on time? – Yes – taverage= 0. 52 s ± 0. 1 s Time (s) LH Momentum (kg m/s) RH Momentum (kg m/s) peak jump 0. 52 7. 845 6. 728 12 o’clock 0. 76 0. 527 0. 703 1 o’ clock/ 11 o’clock 1. 4 0. 352 1. 241 2 o’clock/ 10 o’clock 1. 84 0. 635 1. 228 3 o’clock / 9 o’clock 2. 24 1. 050 1. 636 4 o’clock / 8 o’clock 2. 88 1. 293 0. 802 5 o’clock / 7 o’clock 3. 28 1. 289 1. 210 6 o’clock 3. 88 1. 354 0. 375 Center 4. 36 0. 576 0. 749

Footwork & Impulse • Clock Step and Stationary Step contain same vertical jump • From personal perspective, jump in the clock step requires more momentum to jump from standstill – Similar to an athlete’s vertical jump (vs. running jump) • Measured impulse on take off and landing in RF, LF and COM – Impulse = ∆ρ = m * (vafter- vbefore) – m = mass * body segment proportion • Foot: 0. 0145 body mass • Calculating Ilanding is less meaningful since landing is an inelastic collision IMPULSE TAKE OFF (Ns) LANDING (Ns) RF LF COM CLOCK JUMP 0. 137 0. 145 -2. 641 -0. 0787 -0. 135 -4. 141 STATIONARY JUMP 1 0. 238 0. 597 -12. 942 -0. 156 -0. 233 2. 234 STATIONARY JUMP 2 0. 230 0. 225 -12. 538 -0. 843 -0. 365 -1. 336

Footwork & Impulse • Difference in momentum between COM and feet measurements attributed to the fact that the COM moves faster than feet – Body slows down as it reaches peak height before the feet lose contact with the ground

Footwork & Force • FORCE TAKE OFF (N) LANDING (N) RF LF COM CLOCK JUMP 236. 537 249. 947 -66. 019 -135. 769 -232. 323 -103. 516 STATIONARY JUMP 1 821. 939 1030. 134 -323. 548 -537. 617 -802. 020 111. 713 STATIONARY JUMP 2 792. 619 774. 670 -313. 449 -2907. 332 -1258. 499 -66. 817

Considerations • Imperfect technique Out of practice Feet did not take off/ land simultaneously on some occasions – – • Measurement error Center of mass difficult to compute Only one trial used – – • • Scoliosis – – • Statistical significance of results? Curvature of spine Asymmetry Complicated movements – – Dynamic vs. static Twisting/rotation Out of plane Speed

Conclusions 1. Does my center of mass change when performing different steps? In general, upon completion of each sequence COM is raised. When jumping, my center of mass drops initially then raises. – – 2. Are my arm movements symmetrical? a) Position • b) Qualitatively the movements appear symmetrical but video analysis shows LH generally lower than RH Velocity • c) Hands /arms may differ spatially but travel at the same speeds Momentum • LH initially slower but then recovers. 3. Do my jumps require the same impulse to take off from the ground? – Same jump performed in clock step requires less impulse than jumps performed in the stationary sequence. 4. For a beautiful dance, the physics are certainly ugly.

Future Directions • Compare biomechanics of symmetry and balance to – A more seasoned dancer – Someone with a normal spine – Dancing with bells (added weight) • Use force plates to measure 1. Force • • • 2. Address differences observed in the jumps Compare dance jump to vertical standing athletic jump Determine maximal force required for take off and generated upon landing Center of Mass • Numerous possibilities as dance biomechanics is not well studied

References • Gambino, Stephanie et al. Center of Mass of a Human. The Physics Factbook. 2006. http: //hypertextbook. com/facts/2006/centerofmass. shtml • Kuznetsov, Natalia. Physics of Dance. Fermilab. 2003. http: //ed. fnal. gov/trc_new/demos/present/physofballet. pdf • Sampradaya Dance Academy. 2011. http: //www. sampradaya. ca/_bin/dance. Creations/bharatanatya m. cfm • Sanskriti Dance Academy http: //sanskritidance. com/index. php/About/ • Winter, D. A. Table of Body Segment Parameters. Biomechanics and Motor Control of Human Movement, 2 nd edition, Toronto: John Wiley & Sons, 1990.

Questions