Hooptedoodle #84a - The Big Drop

Our resident artist's impression of the alternative Lottery Rainfall system 

Further Mathematical Rambles with a 10-year-old

The only connection with the previous post is that this one also is prompted by conversations with my son. For a while we have chatted idly about the idea of the rain falling as a single drop – which is potentially amusing and environmentally catastrophic at the same time, but doesn’t actually convey very much unless you try to put some numbers on it.

Numbers would also involve defining some boundaries. It seems unlikely that Nature would distribute rainwater to match municipal or parliamentary dividing lines, but we can well imagine what, say, an inch of rain looks like, in the measuring glass, in the puddle on the lawn, in our garden, in our county...

We spend a significant amount of time watching, or being aware of, rain falling outside the windows. Our own county seems a reasonable area to consider – we know it pretty well, can envisage it. An inch of rain is a reasonable concept, too – it is not uncommon to get an inch on a particularly wet afternoon. I am confident that I have taken part in many picnics, hill walks, barbecues, football matches and so on which involved an inch of rain. I have also, I am reminded, visited the odd battlefield in such weather.

OK – to specifics. We had a go yesterday. The results are the sort of thing that prompts reactions such as:

1) Wow

2) Imagine that

3) What shall we play now?

4) I wonder what’s for tea?

This is an honest effort here, but we make no guarantees about the decimal point always being exactly in the right place – decimal places are not a strong part of my act. East Lothian is a small county on the East coast of Scotland. It seems it has a land area of 679 sq Km, which is certainly not large. If we take 1 inch as 2.5-something centimetres, an inch of rain all over the county (imagine, if you will, a rain cloud the same shape) gives a volume of almost exactly 17 million cubic metres – that’s 17 million metric tonnes of water. Two tangential thoughts – firstly, that represents 867 metric tonnes for each resident in the county, and – secondly – intuitively it seems astonishing that such a delivery doesn’t batter us to our knees and flatten everything in sight. And remember, an inch is not an exceptional amount of rain for a single day.

Obviously this all works because the stuff is sprinkled gently over the area, trickles into ditches and streams and drains, then into rivers and eventually into the North Sea, apart from any bits we choose to keep for later use. Our original idea, though, was to examine the effect of applying a National Lottery principle to rainfall, and dumping a single, giant drop on some poor fellow at some random point in the county [tee-hee]. One inch for East Lothian, we calculate, would require a spherical drop of water 318 metres in diameter – i.e. a bit larger than the average football stadium.

That’s big, isn’t it?

For later use - Hopes Reservoir, Lammermuir Hills, East Lothian

I wonder what is for tea?

If you realise that we’ve messed up the arithmetic, and the required droplet is disappointingly smaller than this, there’s probably no point in letting us know, since our attention span has now been exceeded. We are bored with this now, and are moving on to consider other sources of wonder, like how much does the moon weigh, and why wood-pigeons always say exactly the same thing.