Sunday, August 25, 2013

Formula One - winning by a mile?

This afternoon (Sunday 25 August 2013) the Formula One Belgian Grand Prix was held at Circuit de Spa-Francorchamps.  I listened to the start of the race on Radio Five Live (while driving) and heard one of the commentators point out that Sebastian Vettel was gaining 0.7 seconds per lap over Lewis Hamilton (then in second place) “which doesn’t sound like much but is an absolute mile”. 

I think he was using the phrase “absolute mile” to mean “a long way”, but would an advantage of 0.7 seconds in every lap work out as being a mile? 

First off, what information do we need to work this out?  They had already told me that the race was over 44 laps.  44 x 0.7 = 30.8 seconds, so if they drive at an average speed of 120mph then this would be about a mile.  Is an average speed of 120mph reasonable?  It feels like it to me, because I know they can drive faster than that but also drive more slowly through some of the corners.

I am happy with that as an approximate solution, but let’s work out a more accurate answer anyway.
According to Wikipedia, the length of the track is 4.352 miles.  Over 44 laps that gives a total race length of 4.352 x 44 = 191.488 miles.
Sebastian Vettel (the eventual winner) took 1 hour 23mins and 42 seconds.  
This gives an average speed over the race of 137.3 mph.  30.8 seconds at that speed equates to 1.17 miles.

As it happens, at the end of the race Vettel beat Fernando Alonso by 16.9 seconds, with Hamilton in third place, 27.7 seconds adrift of Vettel.  This means that Hamilton finished 1.05 miles behind Vettel.  Not bad!

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