SPS
Society of Physics Students
The Physics of Human Athletic Motion: An Analysis of Vaulting Events
Kimberly Murley
2005 Anderson Summer Research, Physics Department, Denison University (Granville, Ohio)
Advisors: Dr. Kim Coplin and Pan Fanaritis
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Abstract
The application of physics to athletic events has the potential to be extremely useful in identifying flaws in technique, revealing sources of injuries, and discovering possible beneficial modifications in equipment used in the events. The intersection of physics, biomechanics, and athletics adds a new level in understanding the ways human motion occurs and how it might be altered. The aim of this study is to understand the physics and biomechanics involved in vaulting events, specifically the pole vault in track and field and the vault in gymnastics. A comparison of the two vaulting events will allow for a deeper understanding of each event individually. In both vaulting events, the takeoff is a critical aspect of the full vault; therefore, it is extremely difficult during the later phases of the vault to compensate for errors made during takeoff. For this study, VideoPointTM software package was used to track the center of mass positions as a function of time. I then investigated the effects of initial speed, takeoff angle, takeoff speed, and percentage of speed (at takeoff) converted from horizontal to vertical on the "push height index" of each vaulter. I also investigated the energies of the vaulters; these quantities follow expected patterns, considering the apparatus used.
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Introduction
Pole Vault
Gymnastics Vault
- Gymnasts often make good pole vaulters because of their strength, coordination, timing, proprioception, and attention to technique.
- In both the pole vault and gymnastics vault, linear momentum is converted to angular momentum with the aid of an external apparatus.
- The pole vault is judged objectively by clearance of a bar, while the gymnastics vaults is judged subjectively by a panel of judges.
- Push Height Index:
PHI = (Ymax-H)/Ys
where Ymax is the maximum height of the center of mass, H is the grip height (for pole vaulters) or the height of the horse (for gymnasts), and Ys is the height of the center of mass of the athlete while standing. - If the maximum height achieved by a vaulter was purely determined by her initial kinetic energy, then
Ymax = v2/2g + Ys - Throughout this study, it was crucial to recognize the limitations in applying physics to the human body. What physics predicts to be optimal may not be biomechanically possible.
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Methods
Athletes:
- campers attending Slippery Rock University (Slippery Rock, PA) pole vault camp
- gymnasts at Buckeye Gymnastics (Westerville, OH) and Olympic Academy Gymnastics (Newark, OH)
Videotaping:
- Canon ZR-65 digital video cameras (or other cameras in that series)
- One camera focused on the takeoff, while a second camera focused on the full vault.
Gymnastics Vault Takeoff
Full Gymnastics Vault
Pole Vault Takeoff
Full Pole Vault
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Data Analysis
The computer program VideoPoint was used to analyze each of the video clips. After clicking on the centers of mass of each of the 14 body segments, VideoPoint calculated the total center of mass of the vaulter and provided position-time data for the jump. That data could then be used to find velocities, accelerations, forces, energies, momenta, angles, distances, and other quantities for any portions of the vaults.
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Takeoff Data
- Goal of the pole vault: to convert kinetic energy generated during run-up into gravitational potential energy. The maximum height reached by pole vaulters is greater than that of the gymnast vaulters.
- The data shows that the takeoff angle and percentage of speed converted from horizontal to vertical is significantly less for the pole vaulters (22 degrees and 28%) than for the gymnasts (38 degrees and 48%), while the takeoffs speeds are similar (pole vaulters averaged 4.8 m/s and gymnasts averaged 5.1 m/s).
- This suggests that in the pole vault, the kinetic energy lost at takeoff due to "jumping up" is significant. Also, the pole vaulter remains on the pole longer than the gymnast remains on the springboard and a double pendulum system is created, allowing the pole vaulter to swing up and gain the angular momentum needed to jump higher.
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Energy Data
- PE follows the path of the center of mass of the vaulters.
- KE of the pole vaulter decreases until the athlete leaves the pole.
- KE of the gymnast decreases during takeoff, preflight, horse contact phase, and part of the flight.
- KE + PE decreases as springboard compresses or pole bends.
- KE + PE increases as springboard decompresses or pole straightens.
- KE + PE remains fairly constant in the latter stages of both vaults.
- Pole vaulter ends with more energy than she started, while the gymnast ends with less.
- Linthorne suggests that it is reasonable to treat the pole vaulter as a heavily damped linear spring which dissipates all energy transferred to it:
dE = [Fo^2 cos2(ø+ß)]/2k [3] - Computer simulations with passive and active vaulters also show that muscle work is a significant source of energy in the pole vault [4].
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Pole Vault Data
- Slower initial speeds seem to result more frequently in negative push height indexes.
- There appears to be a similar trend among the gymnasts, but more data is needed.
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Conclusions
- VideoPoint is an effective tool in understanding complex human movements such as those associated with vaulting events.
- Similar initial horizontal speeds lead to large variances in push height between the pole vault and gymnastics vault.
- The takeoff angle and percentage of speed converted from horizontal to vertical for the pole vaulters is significantly less than those of the gymnasts.
- Plots of energy vs. time follow expected patterns.
- For the pole vaulters, greater initial speeds seem to result in more positive push height indexes.
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Future Work
As part of my senior Honors thesis, I plan to
- continue the comparative analysis of the pole vault and gymnastics vaults.
- investigate the effects of the angular displacement from vertical of the center of mass in both types of vaults.
- compare the angular momentum of the giant swing on the high bar in gymnastics to that of the swing phase of the pole vault.
- compare the angular momentum of the free hip circle on the high bar in gymnastics to that during the inversion phase of the pole vault.
- complete an uncertainty analysis of the quantities I obtain.
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Acknowledgements
This work was supported by the Anderson Summer Research Assistantship Program and the Denison University Research Foundation Venture Grant. I also thank Dr. Coplin (Denison), Pan Fanaritis (Denison), Dr. Laws (Dickinson College), and Melanie Cluss (Denison alumni) for their contributions and ideas and all athletes for their participation in this research project.
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References
[1] Launder, Alan G. & Gormley, John T. From Beginning to Bubka: An Australian Approach to Developing Pole Vaulters. Hyde Park Press, 37. [2] Hay, James G. (1993). The Biomechanics of Sports Techniques, Fourth Edition. Prentice Hall, Upper Saddle River, NJ, 322. [3] Linthorne, Nicholas P. (2000). Energy Loss in the Pole Vault Takeoff and the Advantage of the Flexible Pole, Sports Engineering 3, 211. [4] Ekevad, Mats & Lundberg, Bengt. (1995). Simulation of 'Smart' Pole Vaulting, Journal of Biomechanics 28(9), 1079-1090.