The Physics of the Pole Vault

At the RAS Club Dinner last Friday I chatted for a while with my former DPhil supervisor, John Barrow. I’m not sure how, but the topic came up about how helpful it is to use sports to teach physics. By coincidence he chose the same example as I have used in the past during first-year tutorials,  the pole vault.

Years ago I went to watch an athletics meeting at Gateshead Stadium and sat right next to the pole vault area. I can tell you that the height the vaulters reach is truly spectacular, especially when you’re close to the action. The current world record for the pole vault is 6.14m, in fact, set by the legendary Sergey Bubka in 1994, so the record hasn’t been broken for 17 years. Here’s a clip of him a few years earlier clearing a mere 6.10 metres (pretty comfortably, by the look of it)…

One might infer, from the fact that the record has not been broken for such a long time, that pole vaulters are working pretty much at the limit of what the human body can achieve. And a bit of physics will convince you of the same.

Basically, the pole is a device that converts the horizontal kinetic energy of the vaulter \frac{1}{2} m v^2,  as he/she runs in, to the gravitational potential energy m g h 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 10 ms^{-1}, and work out the height h = v^2/2g that the vaulter can gain if the kinetic energy is converted with 100% efficiency. Since g = 9.8 ms^{-2} the answer turns out to be about 5 metres.

This suggests that  6.15 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.  Nor does the centre of mass of the vaulter-pole combination reach 6.15 metres. The pole does not go over the bar, but it’s pretty light so that probably doesn’t make much difference. However, it’s not  obvious that the centre of mass of the vaulter actually passes over the bar.  That certainly doesn’t happen in the high jump – owing to the flexibility of the jumper’s back the arc is such that the centre of mass remains under the bar while the different parts of the jumper’s body go over it.

Moreover, it’s not just the kinetic energy of the vaulter that’s involved. A human can in fact jump vertically from a standing position, using elastic energy stored in muscles. One can’t jump very high like that, but it seems likely to me that this accounts for a few tens of centimetres.

Anyway, 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 terrifed being shot up to 6.15 metres on the end of  a bendy stick, even with something soft to land on!

12 Responses to “The Physics of the Pole Vault”

  1. I guess the centre-of-mass of the vaulter starts at a finite height too (say 1m).

    I once saw a man carrying a long stick. Are you a pole vaulter I asked?

    No, he said, I’m German. And how did you know my name was Walter?

  2. Blimey. Apparently Bubka’s average was about 9.9m/s. Usain Bolt’s average 100m speed (after reaction time) is about 10.6 m/s. Assuming there’s a peak speed let’s say at 11 m/s that converts to 6.16m (at 100% efficiency). I assume energy released from the arms and body, as well as at the apex makes up for the energy losses, as well as the initial centre-of-mass argument (notice how top-heavy bubka looks).

    • Anton Garrett Says:

      As I recall, the world record triple jumper Jonathan Edwards was also shifting as fast as any sprinter at his moment of take-off. These guys aren’t built like sprinters so it seems that the muscly look of 100m men is to do with the ability to sustain it for 10s, rather than the peak speed.

  3. Anton Garrett Says:

    It’s a nice trick question to ask (high) school physics students whether a pole vaulter could improve the record by using ever longer poles.

    I gather that what pole vaulters are frightened of is pole breakage during a jump. It happens occasionally. Pole material and shape play a key part in converting kinetic energy to gravitational ‘potential’ energy, and I’d be interested in the history of the pole design and its relation to improvements in the record.

    • telescoper Says:

      Also, this can happen…

    • Due to improvements in technology, it is difficult to compare performance from today to that earlier. In some sports, of course, where technology plays less of a role (though one might be surprised how much of a role it play where one might not expect it), it is fair to compare performance. The fact that the records continue to increase doesn’t necessarily reflect any real improvement, but is simply due to the laws of chance: if we wait long enough, that 5-sigma event will occur, even if the underlying distribution is the same.

  4. Anton Garrett Says:

    What in the small print of this event prevents a man from turning up with a fiberglass telegraph pole, digging a hole in the sandpit to plant it in, then shinning up it as high as he likes before going over the bar?

    • I wondered the same thing. But apparently

      “Once the vaulter leaves the ground, he/she may not move the lower hand above the upper hand on the pole, nor may he/she move the upper hand higher on the pole.”

    • telescoper Says:

      There’s a much subtler trick pole vaulters employ, which is to deliberately press the bar down with one hand on the way over, curving it to make a bit of extra clearance, but making sure that it doesn’t fall off. It takes a lot of skill, but probably helps win a few centimetres. I believe this technique is now illegal.

  5. We’ve used this pole vault example as an interview question at undergraduate admissions in the past. We found some people had no clue how to approach it; good candidates managed to figure out energy must be conserved and therefore there was a limit to how high you could jump; but nobody could say why the world record was apparently higher than this limit. Almost everyone who got to that stage waffled something about how the technology of the pole must be creating the extra energy to push the vaulter over or something.

  6. Actually, from looking at that video it seems that pole vaulters are more likely to have their centre of mass passing under the bar than high jumpers, because they go over feet first, facing the floor, and so can bend much more.

  7. Caroline Says:

    I’m terrified of open heights, and I’m a pole vaulter… people always say it looks really hard. But I guess after 3 years you get pretty used to it.

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