## Thinking and Breaking Distances

July 24, 2008 – 16:07I have been trying to find a way of remembering my thinking and breaking distances for my theory test, part of my problem is I think in metric not imperial except for road speeds which are always in miles per hour.

According to the book…

@20mph thinking distance is 6m and breaking distance is 6m

@30mph thinking distance is 9m and breaking distance is 14m

@40mph thinking distance is 12m and breaking distance is 24m

@50mph thinking distance is 15m and breaking distance is 38m

@60mph thinking distance is 18m and breaking distance is 55m

@70mph thinking distance is 21m and breaking distance is 75m

So from that I can deduce that thinking distance in meters is equal to the road speed in miles per hour multiplied by 0.3 (or mph divided by 10 and multiplied by 3 if your brain works that way).

Breaking distance is a little harder as it is a curve however the simplest equation I can muster is road speed in miles per hour divided by ten, multiplied by itself (i.e. to the power of 2) all multiplied by 1.5 [i.e. 1.5((x/10)²)].

It isn’t perfect by any means, and if anyone has a good formula they use then I would be greatful if you share in the comments. My formula is spot on for 20 and 40 mph, however it is off by 1.5 @ 70mph it does however give you a good idea of the magnitude of your answer. The creation of a formula also gives me the opportunity to work out some silly things, for example if there was a straight road from Land’s End to John o’ Groats you would have to be traveling at [[Wikipedia:Mach]] 10.5 to require the entire lenght of the road to stop… of course I have yet to see anyone traveling at Mach 1 along the M4.