Formula One and relativity

It would be not inaccurate to say that relativity theory has something of a low profile in Formula One. The recent announcement that gravitational waves have been detected for the first time aroused little more than a grudging blip of interest within the region of the autistic spectrum occupied by F1 vehicle dynamicists, strategists, and aerodynamicists.

It's worth noting, however, that modern F1 operations are heavily dependent upon relativity theory. F1 utilises GPS for its timing systems, and almost all teams use GPS for their trajectory analysis; and GPS, of course, is crucially dependent upon relativity theory.

To accurately establish the position of a car on the surface of the Earth, a GPS receiver must compare the time-stamps on signals it receives from multiple satellites, each one of which is orbiting the Earth at 14,000km/hr. To maintain the desired positional accuracy, the time on each such satellite must be known to within an accuracy of 20-30 nanoseconds.

However, there are two famous relativistic effects which have to be compensated for to maintain such accuracy: (i) special relativistic time dilation; (ii) general relativistic time dilation inside a gravitational well.

Because the satellites are in motion at high speed relative to the reference frame of a car on the surface of the Earth, their clock-ticks are slower by a rate of about 7 microseconds per day. Conversely, because a car lies deeper inside a gravitational well than the satellites, its clock-ticks will slow down by about 45 microseconds per day. The net effect is that the clocks on-board the satellites tick faster than those on-board an Earth-bound GPS receiver by about 35 microseconds per day.

As Richard W. Pogge points outs, "This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy, and 38 microseconds is 38,000 nanoseconds. If these effects were not properly taken into account, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers each day! The whole system would be utterly worthless for navigation in a very short time. This kind of accumulated error is akin to measuring my location while standing on my front porch in Columbus, Ohio one day, and then making the same measurement a week later and having my GPS receiver tell me that my porch and I are currently somewhere in the air kilometers away."

Which is worth recalling the next time GPS reveals that Dudley Duoflush is repeatedly missing the apex in Turn 4, or overtook under yellow-flag conditions between Turns 7 and 8.