Question: Could I beat Usain Bolt over 100 metres, if he ran and I biked?
First thoughts: it might be possible, but I need to do some calculations to get an idea of whether it’s feasible or not.
To win the Olympic Gold on Sunday, Bolt ran 100 metres in 9.63 seconds. That’s an average speed of 10.37m/s. The first thing one needs to figure out is: can I bike that fast? Because if I can’t even match his average speed, then I clearly can’t beat him. The speed 10.37m/s is equivalent to 37.34km/h (23.2mph): I can certainly ride faster than that over short distances; I might be able to manage 50km/h (31mph) at a stretch. So, as the MythBusters say, we are at the ‘Plausible’ stage thus far.
The key to this will be to attain top speed as quickly as possible. I can certainly bike faster than Usain Bolt can run but only once I’ve reached top speed.
Let’s assume a simple mathematical model for this task. For calculation purposes, consider the 100m race split into two sections:
- Accelerate smoothly from stationary to top speed, and then
- Continue at that top speed until the end of the race.
It’s probably a reasonable model for cycling over a short distance. With this model, we must make two assumptions to plug into our model:
- What is my top speed? (let’s call this V_max for “Velocity-max”)
- How quickly can I reach that top speed? (let’s call this T_accel for “Time to accelerate to max velocity”)
Calculating one’s finishing time for 100 metres based on the above model works as follows. Ignore this bit and skip to the table below if aren’t interested in the method and just want to see the results:
- Given T_accel, one must calculate the distance over which the acceleration takes place. This is calculated as (V_max*T_accel)/2 – let’s call that distance D_accel
- Assuming that we finish accelerating before we reach 100m, we then work out how long we take to finish the remaining 100-D_accel metres, riding at our top speed of V_max. Let’s call that time T_steady, beecause it’s the time we spend at our steady top speed: T_steady = (100-D_accel)/V_max
- Our finishing 100m time T_finish is therefore: T_accel+T_steady
To make everything work properly, units of measurement must be consistent. Times must be measured in seconds, distances in metres and speeds in metres per second. Conversion between “metres per second” and “kilometres per hour” is very simple: one metre per second is 3600 metres per hour, i.e. 3.6km per hour. Let’s try running the numbers with V_max speeds of 12m/s, 13m/s and 14m/s (equivalent to 43.2km/h, 46.8km/h and 50.4km/h). What about acceleration times? I’m less sure of suitable values here, but let’s try 5 seconds, 7 seconds and 10 seconds.
|Top speed:||12 m/s||13 m/s||14 m/s|
Aha! If I can get my speed up to 14m/s (50.4km/h or 31.3mph) in five seconds and hold that speed, I can finish in 9.64 seconds, just 0.01s behind Usain Bolt, based on Sunday’s performance!
Is that possible, could I do that? It sounds like an awfully tall order. I can beat Bolt if I can go faster or accelerate quicker than above, of course, but realistically I think that’s beyond my capabilities.
If I can’t do it, what about real cycling professionals? Let’s apply the same sort of mathematical model to the recent Velodrome cycling at the Olympics, I see some sprint cyclists recorded “first lap” times of just over 17 seconds. This is a distance of 250 metres from a standing start. If one assumes a smooth acceleration over the entire lap I calculate that these cyclists pass 100 metres at around 10.7 seconds (detailed calculations available on request) – Bolt still wins. However, if the cyclist achieves top speed much earlier in the lap, they will reach 100m sooner. Jason Kenny completed his gold-medal-winning sprint final 200m (not quite a full lap), presumably at his absolute top speed, in around 10 seconds: this is an incredibly quick 20m/s (72km/h or 45mph!). So how quickly would he be able to complete 100m, from a standing start? Assuming a top speed of 20m/s, to reproduce the 17 second first lap time, this would be a 9-second acceleration (covering 90m in that time) and a further 8.0 seconds to cover the remaining 160m at 20m/s; as a side-effect that shows us that such a cyclist would cover 100m in approximately 9.50 seconds. This beats Bolt!
To answer my own question: could I beat Usain Bolt over 100m on my bike? No. Not a chance.
Further question: could any cyclist beat Usain Bolt over 100m? Possibly, just, although it might be very close.
I wonder how fast I could actually bike 100 metres, though, from a standing start? I think I should try timing it…
And of course it goes without saying that I’d be able to beat the sprinters over 200m, because I’d be up to top speed for longer 🙂