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# The secret to staying dry

To walk or to run? What to do when you are caught in a shower without an umbrella.

A London commuter gets caught in a summer shower. [Getty Images]

It may seem to be the sort of intellectual conundrum which would be well suited to a storyline in the award-winning comedy show Big Bang Theory. Three geeky physics geniuses, plus Howard the engineer, trying to work out the best way of keeping as dry as possible when caught in a downpour without an umbrella.

Common sense would tell most of us to dash for cover as quickly as possible. But, as we all know, common sense and theoretical physics – and mathematics for that matter – do not always go hand-in-hand.

You would like to hope that leviathans of the theoretical world would think to check the weather forecast before leaving the house. But there are obviously enough of them who fail to do so to make the problem worthy of detailed analysis.

So the question is, “Do you walk or run when heading for cover when it rains?”

The debate began in mathematical journals in the 1970s.

In 1987 an Italian researcher asserted that running or walking made little difference as to how wet the person became.

Last year, it was suggested that there was an optimal speed at which to proceed, based on the wind direction.

Most recently, Professor Franco Bocci, writing in the European Journal of Physics, claims that the ‘wetness’ depends upon both the wind direction and the person’s stature.

But before we reveal the best strategy for remaining dry, let us look at the problem. (Many of us would subscribe to the view that life is too short to consider this this a ‘problem’.  But, for the sake of argument, we will describe it as such.)

If a person is standing still, assuming no wind, they will receive all the drops falling directly above their head. If the rain does not stop they will probably end up getting soaked and contracting pneumonia. Let’s agree this is not a good strategy.

So if standing still is not an option, how best to make our way towards shelter?

As a person moves forward they will be hit by all the drops that fall through the volume of air through which they pass.

The argument goes that the faster they run, the more drops will hit them, suggesting that walking slowly may be a good strategy.

The ‘slower is better’ theory  carries even more weight when you think about what happens when we increase our walking speed or begin to run.

Moving faster requires greater arm and leg extension and running causes our upper body to angle forward. All these changes in body position increase the surface area exposed to falling raindrops.

This is the key to Professor Brocci’s research. Previously, calculations were carried out using thin sheets or upright rectangular blocks.

Applying the mathematics to the human shape, Brocci found that the solution depends on an individual’s height-to-circumference ratio plus wind direction and raindrop size.

‘Let’s say that, in general, the best thing is to run as fast as you can – not always, but in general. If you’re really thin, it’s more probable that there will be an optimal speed. Otherwise, it’s better to run fast.”

So there you have it, unless you are really skinny, run like the wind, safe in the knowledge that science has relieved you one of life’s ‘problems’.

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