Finding a Needle in a Haystack

The newspapers are full of the search and location of a radioactive pellet somewhere along Great Northern Highway in Western Australia,

How a tiny radioactive capsule was found in Australia's vast outback

Of course Western Australia’s one million square miles was not the focus of the search.

The search focused on 1347 kilometres of highway where, it was supposed, the pellet fell off the truck. The pellet has been described as pea-sized.

Well of course, pea-sized it was, but deadly in terms of radiation

Authorities believe it fell through a hole in the truck where a bolt had been dislodged after a container collapsed in transit due to vibrations

I have read that the radiation is strong enough for today’s detecting device to recognize it at a distance of twenty meters , so that suggests that a Geiger counter traveling along each side of the highway would detect the radiation. The pellet was supposed to have dropped off a truck between January 11 and January 16, and was recognized as missing on January 25th. Given that a couple of weeks of road traffic was in force, statistically the pellet like any pea-sized piece of laterite gravel would have been flung of the bitumen surface and onto the verge.

As long as the pellet didn’t hitch a ride in the tread of a tyre, chances were very good that it was within an area of 1347 kilometres by 40 metres. I make that an area of 53,880,000 square metres.

I estimate the diameter of a pea to be five millimetres, or half a centimetre. The cross-sectional area (which is all we can see anyway) is thus 1.57 square centimetres or 0.00015714 square metres.

The ratio of these two areas is 0.00015714 divided by 53,880,000 square metres, roughly 0.000000000002917.

Pretty small, eh? And yet two vehicles driving 50 Km/hr could cover the area in about twenty-seven hours; Call it 28 if we swap drivers along the way.

Back to that needle in a haystack: I have just measured one of the steel needles I use for sewing buttons back on to my shirts. It is difficult with my poor eyes, but a needle seems to be about two millimetres in diameter and about three centimetres long. Lying flat on the road it would present an volume of about .06 square centimetres, which yields 0.000000094285714 cubic metres

And what is the volume of a hay stack? The largest haystack measured 9.51 m tall (31 ft 2 in) and had a diameter of 17 m (55 ft 9 in). The event was organized by a committee of the Old Professions of the Flaeijelfestivities in Friesland, Netherlands, on 6 July 2006. which is a volume of about 2,160 cubic metres.

Now the ratio of the volumes of my needle to the Nederland haystack is about 0.000000000043662

The haystack search is about fifteen times easier than the highway search.

Unless, of course, you could use a giant electro-magnet. After all, THEY were allowed to use a Geiger counter.

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