Pole vault: what is the physical limit?

By Jacques Treiner - Theoretical Physicist, Université Paris Cité

On July 5, during the Paris 2024 Olympic Games, Armand Duplantis not only secured the gold medal in pole vault, but he did so with a spectacular performance.

Facing competitors like Sam Hendricks and Emmanuel Karalis, who jumped 5.95 m (19 ft 6 in) and 5.90 m (19 ft 4 in) respectively, Duplantis started with a 6 m (19 ft 8 in) jump, securing his gold medal. But he still had three attempts left.


After a "warm-up" jump of 6.10 meters (20 ft) to break the Olympic record, he requested the bar be set at 6.25 m (20 ft 6 in), just 1 cm above his previous world record set in April in China! It was his way of saying: winning gold at the Olympics is great, but being the absolute best—isn't that even better? And as we saw, he succeeded.

The history of world records

If we exclude the 20 years following the outbreak of World War II—when humanity had more pressing concerns than pole vaulting—the world record progressed steadily from 1910 to the mid-1990s, at an average rate of about 2.5 cm per year (approx. 1 inch).

Since then, progress has slowed significantly: Sergei Bubka was the first to clear 6 m (19 ft 8 in) in 1985, and he held his world record of 6.15 m (20 ft 2 in), set in 1993, until Renaud Lavillenie surpassed it, jumping 6.16 m (20 ft 3 in) in 2014. It took pole vaulters 21 years to gain just 1 cm! Armand Duplantis, on the other hand, has been improving his own world records by 2 cm per year, moving from 6.17 m (20 ft 2 in) in 2020 to 6.25 m (20 ft 6 in) by 2024. Could this hint at a new rate of progress?

The physics for a clearer understanding

A pole vault can be broken down into three phases:
- The vaulter runs and reaches their top speed (v) at the end of the track.
- They plant the pole in the box at the bar's vertical, transferring their kinetic energy into elastic energy as the pole bends.
- The pole springs back, returning the stored elastic energy, propelling the vaulter into the air.

Let's call H the elevation of the vaulter's center of gravity. Though the combined motions of the vaulter and pole might seem highly complex at first, a purely energetic approach makes things surprisingly simple. The pole's role is essentially to convert the kinetic energy from the vaulter's run, denoted 1/2Mv², into gravitational potential energy MgH, where 'g' is the acceleration due to gravity and 'M' the vaulter's mass. An optimal pole should ensure this energy transfer with minimal internal energy storage (vibration, permanent deformation).

Since the introduction of carbon fiber poles in 1964, following metal and early bamboo poles, performance greatly improved up to the 1990s, thanks to a much better energy return ratio.


In this context, the ideal pole transfers all the kinetic energy into gravitational energy. So, we can write directly ½ Mv² = MgH, which gives H = v²/(2g). This shows that top speed is crucial in determining jump height. Assuming a speed of 10 m/s (22.4 mph), we find H = 5.10 m (16.7 ft)... What? Only 5.1 m (16.7 ft)? That's far from 6 m (19 ft 8 in) and higher! But wait—remember that the vaulter's center of gravity doesn't start at ground level. They're standing, with their center of gravity approximately 1 m (3 ft) above the ground. So, the bar can be set at 5.1 + 1 = 6.1 m (20 ft). QED.

How, then, can we explain jumps beyond this favorable estimate, especially considering we've assumed an ideal pole that absorbs no energy? Careful observation of a jump reveals that when the pole reaches vertical, the vaulter can push off with their arms to gain height just before curling their body over the bar—this is where precious centimeters are gained!

What's the future height?

Increasing end-speed would be decisive. Take, for example, the world record in the 100 meters set by Usain Bolt. He ran the race in 9.58 seconds, averaging a speed of 10.44 m/s (23.4 mph), but his top speed was recorded at 12.42 m/s (27.8 mph). If a pole vaulter could reach such speed by the run-up's end, the previous calculation indicates they could clear a bar at... 8.86 m (29 ft)!

Of course, it would require someone to run while carrying a 7-meter-long (23 ft) pole weighing around 15 kg (33 lbs). For now, with Armand Duplantis' top speed recorded at 10.3 m/s (23 mph), the (ideal pole) calculation suggests a height of 6.41 m (21 ft).

The difference compared to the vaulter's performance could likely be attributed to the pole's imperfections. With a speed of 10.5 m/s (23.5 mph), the cleared height would rise to 6.62 m (21 ft 9 in). So, we see there is still room for improvement compared to the current record of 6.25 m (20 ft 6 in)!

And that's not even accounting for potential gains from improving the technique of pushing off the pole when passing over the bar. In short, exciting times lie ahead—bring on the 2028 Los Angeles Olympics!