What is the shortest way to drive down a motorway? Sounds like a simple question but it has been taxing my brain for some time. The obvious answer is to drive in as straight a line as is possible, cutting all of the corners, switching from lane to lane and even using the hard shoulder if necessary. Using slip roads may even shave off a few metres. But this is not practical and not what was meant by the question.
What I would really like to know is, is it shorter to drive down the nearside lane, the middle land or the outside lane of a three lane motorway, assuming that the lanes where always side by side and that you were able to keep in the same lane for the whole of the journey (I know, this is not practical either but bear with me)?
Sometimes I think that there would be no difference as the left hand corners would eventually cancel out the right hand corners and anything you managed to gain by being on the inside of the curve would be wiped out by the next opposite swing. The middle lane would be the least curvy and so would not suffer the excesses of the other two. All lanes must be of the same length when they are averaged out.
But then I’ve come to the conclusion that the shortest lane must be the outside lane, the fast lane, the one closest to the central reservation. How so? My logic is that if the further you are away from the centre of the motorway the greater the curves are pronounced, either longer outside curves or tighter inside curves, then the closer you are to the centre the smaller the deviation is from the most direct route.
I think I’m right in that the shortest way to drive down a motorway is to stick in the lane closest to the central reservation but I am not clever enough to prove it. There must be a mathematical formula with Xs and Ys and square brackets which would give me an absolute and unequivocal proof and there must be people out there who are clever enough to work it out. It’s certainly no Fermat’s last.
I wonder if the outward journey on a motorway is always the same length as the return.
Thoughts from a Guerrilla Worker 