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Speed and the chances of survival

One of my heroes is the Nobel-prize winning physicist PMS Blackett, who, during the war, applied statistics to combat situations. His transfer, at the low point in the Battle of the Atlantic, from the Air Ministry to Coastal Command, prompted Fighter Command to say they were 'losing their wizard'.

The tactic he used for U-boat hunting was to break the operation down into discrete events and then evaluate the statistical advantages of a series of incremental improvements. In a matter of weeks, the accumulated effect of these calculations led to the U-boats thinking we had invented a new weapon.

Blackett's approach gave rise to a new science: operational research. Anybody wanting to know more should read Kroner's The Pleasure of Counting (CUP).

This science will have underpinned the claim made by Peter Bottomley, that the Selby train crash had been predicted during his time in office as a one-in-a-million freak accident (Sunday Times 4 March). In such terms, we are lucky that it did not involve a later, busier, train, and that the train coming the other way was not a passenger train.

Back at the office we set about using Blackett's logic to recreate Bottomley's calculation. We first established that, in the last three years, there were 80 nonlevel crossing vehicle incidents, ten of which were hit by trains. Clearly what influences the odds of such an accident is the spacing and the speed of the trains.

What we calculated was how Bottomley's one-in-a-million odds would be shortened by the 50% increase in traffic promised by this Government.

Such increases can be achieved either by running trains at the same speed but closer together, or by keeping trains the original distance apart, but travelling faster.

What we discovered was that if you increase the number of trains by 50%, but keep the speed the same, you increase the risk of such an accident by two and a quarter times.

However, if you increase the speed but keep the original train separation (because of the signalling) you increase the risk five-fold.

While such calculations contribute only a little to the cost benefit analysis of the necessary safety measures that might be introduced as a result of the lessons learned from Selby, they illustrate the inherent costs associated with speed.

Our calculations for the Selby crash could equally be applied to pedestrians crossing two streams of traffic.

Reversing the calculations, it is possible to show that a reduction in speed, from 30mph to 20mph in built up areas, would more than halve the risk of an accident, and that's before you think of the increased chances of survival.

From the pedestrian's point of view the reduction in speed has the effect of making it twice as easy to cross the road.

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