In the Dark

One of the many highlights of the 2024 Olympics was the amazing achievement of Armand Duplantis in winning the Gold Medal in Pole Vault and in the process breaking his own world record at a height of 6.25m. Here he is

He seemed to clear that height quite comfortably, actually, so I dare say he’ll break quite a few more records in his time. On the other hand, when I first wrote about this back in 2011 the world record for the pole vault was held by the legendary Ukrainian athlete Sergey Bubka at a height of 6.14m which he achieved in 1994. That record stood for almost 20 years but has since been broken several times since. The fact that the world record has only increased by 11 cm in 30 years tells you that the elite pole vaulters are working at the limits of what the human body can achieve. A little bit of first-year mechanics will convince you why, as I have pointed out in previous posts (e.g. here).

What a pole-vaulter does is rather complicated and requires a lot of strength, flexibility and skill, but as in many physics problems one can bypass the complications and just look at the beginning and the end and use an energy conservation argument. Basically, the pole is a device that converts the horizontal kinetic energy of the vaulter ,  as he/she runs in, to the gravitational potential energy acquired at the apex of his/her  vertical motion, i.e. at the top of the vault.

Now assume that the approach is at the speed of a sprinter, i.e. about , and work out the height that the vaulter can gain if the kinetic energy is converted with 100% efficiency. Since the answer to that little sum turns out to be about 5 metres.

This suggests that  6.25 metres should not just be at, but beyond, the limit of a human vaulter,  unless the pole were super-elastic. However, there are two things that help. The first is that the centre of mass of the combined vaulter-plus-pole does not start at ground level; it is at a height of a bit less than 1m for an an average-sized person.  Note also that the centre of mass of pole (which weighs about 15 kg and is about 5 m long) only ends up about 2.5 m off the ground when it is vertical, so there’s a significant effect there.  Note also that the centre of mass of the vaulter does not actually pass over the bar after letting go of the pole.  That  doesn’t happen in the high jump, either. Owing to the flexibility of the athlete’s back, the arc is such that the centre of mass remains under the bar while the different parts of the athlete’s body go over it.

Moreover, it’s not just the kinetic energy related to the horizontal motion of the vaulter that’s involved. A human can jump vertically from a standing position using elastic energy stored in muscles. In fact the world record for the standing high jump is an astonishing 1.9m. In the context of the pole vault it seems likely to me that this accounts for at least a few tens of centimetres.

Despite these complications, it is clear that pole vaulters are remarkably efficient athletes. And not a little brave either – as someone who is scared of heights I can tell you that I’d be absolutely terrified being shot up to 6.25 metres on the end of  a bendy stick, even with something soft to land on!