Cycling at the speed of light

Suppose you are in a Zwift race that comes down to a sprint finish. How long does it take for your avatar to respond to your heroic effort in the final dash for the line? Could a time lag cost you the race?

Consider the steps involved. First the ANT+ signal travels from your power meter to your device (i.e. computer or phone) then it goes to your router and on to Zwift’s server somewhere on the cloud. At some point your watts per kilo are converted into a velocity, taking account of your previous speed, the gradient, rolling resistance, drafting and any PowerUps in play. This calculation can be performed pretty much instantaneously compared with signal transmission time.

The ANT+ signal travels at the speed of light to your device, which is likely to be very close by, so there is little to be gained as long as there is a clear line of sight. The next step, to the router, can be slower, especially if you are relying on a wireless signal from your garage, while running a raft of other applications on your device (best to shut these down). Serious e-gamers often use a direct wired link to the router. It also helps if you have a super-fast high bandwidth internet connection. However, the time taken for the signal to travel from your router to Zwift’s gaming server, called latency, typically introduces the longest delay, especially if it has to go halfway around the world.

We don’t know the precise location of Zwift’s server, but let’s suppose it is in San Francisco. You can check the latency from your location to other parts of the world on web sites like this one. When I looked, the latency from London to San Francisco was 136ms (milliseconds) and from Cape Town it was 281ms.

In the past, banks have moved their trading desks as close as possible to exchanges, in order to obtain prices nanoseconds earlier than their rivals. As a general rule for interactive online gaming, you need a latency of less than 100ms for acceptable gameplay and over 150ms can become frustrating. But we are not talking about playing DOTA, so how do these figures apply to Zwift?

Zwift not DOTA

Let’s go back to our sprint finish, where the bunch is riding at 60kph. This equates to 16.7 metres per second, which is just a bit less than one bike length every 100ms. However, your ability to overtake your rival depends on your relative speed, not the absolute figure. Imagine a situation where you make a Herculean effort to increase your speed to 18 metres per second (64.8kph), drawing level with the leader’s rear wheel with 30 metres to go. To win the race, you have to make up a bike length, say 1.8m, travelling at a measly 1.3m/s faster than the leader. Who will cross the line first?

If you have 30m to go and the leader is a bike length ahead, he only has 28.2m left, taking 1.69 seconds. But at your higher speed you will cover 30m in 1.67 seconds, so you win by about half a wheel. However, if your avatar had responded to your acceleration with a 100ms lag, you would certainly have lost the race. If you experience this level of latency, a slower rider could beat you, just because he is located closer to the gaming server. The speed of your avatar really is limited by the speed of light.

However, sometimes it can feel like a zPower rider is overtaking you at an appreciable proportion of the speed of light. If this really were the case and Zwift wanted to represent the avatar correctly, what would it look like?

E. A. Cryer-Jenkins and P. D. Stevenson Gamow’s cyclist: a new look at relativistic measurements for a binocular observer Published:03 June 2020 https://doi.org/10.1098/rspa.2019.0703

The physicist George Gamov posed this question back in 1938. He highlighted the effect of relativistic length contraction, predicted by Einstein’s theory of special relativity. In fact, the avatar would change colour, due to the Doppler shift, and light intensity would fluctuate. These effects would be further be complicated by our binocular vision, causing an unnerving blurring effect. This is helpfully explained in detail by physicists in a recent scientific paper. Surprisingly, there are practical applications for this work that may help interpret data gathered by spacecraft passing objects at very high speeds.

Author: science4performance

I am passionate about applying the scientific method to improve performance

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