Interactive Demonstration of a Pole Vault
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The pole vault is an Olympic event that demands a very high level of athletic ability. Nevertheless, it illustrates very simply the law of conservation of energy. The vaulter tries to achieve maximum kinetic energy by sprinting down the runway. At the end of the approach, the flexible fiberglass pole is planted in the box at the base of the pit. The kinetic energy gained in the sprint is converted into potential energy stored by elastic deformation of the pole. This, in turn, is converted into gravitational potential energy as the vaulter attempts to clear the crossbar.For a person with a height of meters, the body’s center of gravity is estimated to be at 0.55. Suppose the athlete can achieve a maximum speed of meters/second (world-class sprinters can do 10 m/sec). For the center of gravity to successfully reach the height of the crossbar, the energy relation must be satisfied, where is the acceleration of gravity, 9.81 m/sec. This result assumes perfect technique as well as 100% efficient conversion of energy at each stage. The effects of wind resistance, crowd noise, and other distractions are neglected. Likewise neglected is the possibility of additional lift achieved by pushing down on the pole just before release.The above energy relation has been found to be remarkably accurate. The world’s record pole vault was set by Sergei Bubka (USSR/Ukraine) with a 6.15-meter pole vault. Only 15 men have achieved the 6-meter mark. The women’s record is just over 5 meters.-http://demonstrations.wolfram.com/OlympicPoleVaulting/
Another “max” vault height calculator can be found here.
I entered my height (6 ft or 1.83 m) and maximum speed (9.5 m/s, estimated max speed while running an 11.1 s 100-meter sprint – my personal record), and it was calculated that I would be able to clear 5.6 meters, or about 18′ 4″ — my personal best was a mere 14 ft (in practice, with a bungie cord).
However, the explanation for the demonstration failed to mention two other factors that can increase clearance height (besides the ignored extra lift from jumping vertically at the point of take-off). I believe that this model does not account for the extra force a vaulter can exert on the pole after the pole straightens back out. At the top of the vault, when the pole is completely unbent and has no angular velocity, the vaulter is able to exert a downward force down the length of the pole by essentially doing an inverted push-up. The normal force exerted back by the ground propagates up the pole to the vaulter so their center of gravity can rise even higher.
Another variable that is not represented by these models is the body manipulation that takes place at the top of the jump. Through proper technique, a vaulters body should look like a tucked diver as they go over the bar. This allows for the body’s center of mass to be below the bar while still being able to clear the bar.
Here is an example of these extra factors contributing to a greater realized height than theoretically calculated. Sergey Bubka‘s world-record 6.15 m jump: