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A PHYSICIST WRITES . . .
(September 2005)
In each of my last two columns I mentioned stopping distances, in passing. This month let’s stop and give them a closer look. It’s an important topic, so stay with me if you can. I’ll assume you have a copy of the Highway Code within reach, with its diagram of Typical Stopping Distances — if not, then click here to see the table.
As you can see, Stopping D = Thinking D + Braking D. The physics surrounding this is not difficult (for me, anyway!). The TD assumes you have a reaction time of 2/3 of a second, before you actually apply the brakes. The BD then assumes that while you are braking you will cut about 15 mph from your speed each second. So stopping from 60 mph (in an emergency) should take you four seconds, plus the two-thirds.
The diagram shows that the Thinking Distance goes up in proportion to your speed. But the Braking Distance does not — if your speed doubles, the BD multiplies by four. This makes sense, when you think about it: you’re moving (before you brake) now at twice the speed, and it takes twice the time to slow down from it. But when you’re driving it’s easy to forget how large the Stopping Distance can get, at high speeds. Still, the good old two-second rule will keep you safe, surely?
Oh no it won’t — the ‘two-second distance’ is merely proportional to speed! When you’re up at 70 mph, in two seconds you travel 63 metres, but the total Stopping Distance is listed as 96 metres. If something fell off a car or a lorry that was two seconds in front of you, and it landed stationary on the road, I calculate that when you collided with it (having first Thought and then Braked) you would still be moving at 46 mph.
At higher speeds the same situation would be even more destructive. At 100 mph, for instance: your two-second distance = 89 metres ... your SD = 182 metres ... your colliding speed = 78 mph (I don’t really mean you at 100 of course, but other motorway drivers).
In fact, the rule ought to be three seconds at 70 and four seconds at 100. Believe it or not, the two-second rule only keeps you safely at the Stopping Distance from the vehicle in front when you’re driving at 40 mph (or less).
If that hasn’t set you worrying, consider this: the ‘Typical’ Stopping Distances in the Highway Code are probably highly untypical — I doubt if they ever apply in real life, even approximately. Take the Thinking Distance first: if you’re on the alert and your foot is already covering the brake pedal, the TD could be halved. But if visibility is poor it might easily be doubled, as your brain struggles to identify a hazard and then react correctly to it.
As for Braking Distance, this is greatly affected by the road surface, as well as by the condition (and pressure) of your tyres. High-grip surfaces, like you may find in advance of a crossing, probably give you a significantly shorter BD than in the Highway Code — as might ABS if your car has it. But a wet or icy road, or even one that is newly surfaced (see July’s column), can extend the BD by a factor of two or more. And don’t forget too that when you’re on a bend you are already using tyre grip just to get round (as I said back in Sept. 2002), so there may not be much left to brake with!
I’ve no idea how old the present table of Stopping Distances is, though I do know that it is being ‘reviewed’ for the next edition of the Highway Code. But will the result be any more meaningful? Instead of attempting to memorize metres, feet or car lengths, I think you would be better off trying to learn the look and the ‘feel’ of the distance you can safely stop in, under as many different circumstances as possible.
That leaves the question I raised in July: what happens to safe stopping distances (I mean the ones you have learnt to judge correctly) when the road is on a hill? It’s a tricky calculation! The thinking distance won’t be affected, of course, so what I need to tell you is roughly how much your braking distances will vary, according to the percentage gradient of the road (as displayed on the steep-hill warning sign).
Take a hill marked 15%: the minimum braking distance when you are climbing will be about 15% shorter than it would be for the same road on the level, at your same speed. When you’re going downhill the BD will instead be longer, as you would expect, but now it’s a 30% increase. Likewise on other slopes — the uphill braking distance shrinks (helpfully) by the same % figure as the gradient, but the downhill one extends (worryingly) by twice this, approximately anyway.
Still with me? I hope so. Safe driving — and safe stopping!
Peter Soul
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