Transform kinetic energy into vertical potential energy

A pole vaulter performs the extraordinary feat of converting his forward kinetic energy to vertical potential energy. Using this information we are able to estimate the maximum height possible for a pole vault. We assume not quite correctly that the pole itself can't store and release energy during the vault. As well assume that the conversion is lossless.

Assume the vaulter can run at 20.5 mph. This is about 30 fps Then his kinetic energy at the start of the vault is KE = mv² /2 = 450m. His potential energy at the top of the vault is PE = mgh = 32mh. So

h = 450/32 ft = 14 ft.

However this height refers to the height of the center of gravity of the vaulter. At the begining of the vault his center of gravity is about 3.5 ft above the ground. When he clears the bar it is about 5 in = 0.41 ft above the bar. Therefore the maximum height of the bar must be 3.5 + 14 - 0.41 ft = 17.1 ft above the ground.

This height was in fact reached during the 1960s and established a world record at the time. By 1991 the record had ascended to over 20 ft a height which was achieved by Ukranian athlete, Sergei Bubka. The enhanced heights are largely due to improvements in the pole which allow the vaulter to store energy in the pole by flexing it just before the jump. This energy is returned during the jump to contribute to the largely height. It is clear a taller pole vaulter has an advantage over his shorter competitors by the increased height of his center of gravity. Conceivably in the future a handicap system would be appropriate.