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The Science of Santa: In the Nick of Time

It’s Christmas Eve. And you’re preparing for the biggest day of the entire year; the only day, in fact, that you’ll get any real work done. The other 364 days have been spent overseeing subordinate clauses, planning your route for this evening’s journey, and most importantly, making a list and checking it twice.

Your mission: deliver Christmas gifts to all those good children, who are eagerly anticipating seeing if you’ve paid them a visit. This will take some doing. Where to begin?

Well, there are 2.2 billion children on the earth, spread out over 58 million square miles. And you have only one night in which to finish this mammoth operation. So how can you, just one man and some reindeer, be expected to pull this off?

You want to maximise your time, therefore it seems logical to begin at the International Date Line and head west. You’ll essentially gain back an hour with each 15 degrees of longitude traversed. So you don’t just have a single evening to finish this ludicrous undertaking, you have 32 hours!

Of the 2.2 billion children worldwide, only 15% come from a household that would be expecting you to visit. With an average of 2.67 children per household, assuming there’s at least one “good” child in each, you’re now only stopping off at 124 million unique locations.

So in your 32 available hours, you’ll need to make 1076 visits per second. That gives you less than 1/1000th of a second to park, get down the chimney – awkward, given that you are rotund – fill the stockings, distribute presents, eat your mince pies, drink your milk, get back up the chimney and back in the sleigh, before moving on to the next house. And we haven’t even taken into account any breaks to answer the call of nature and the like.

Let’s say that the 124 million homes you’ll be stopping at are uniformly distributed across the globe, and have an average distance of 1.63 miles between them; ahead of you is a round trip of 202 million miles. So, your reindeer-drawn sleigh will need to travel at a whopping 6.3 million mph, 8,227 times the speed of sound. Fingers crossed the massive sonic boom doesn’t wake every child on earth.

What about the payload? Assuming that each child will receive a gift weighing no more than 1kg, your cargo alone will weigh 330,000 metric tonnes. On land, conventional caribou can pull around 135kg. Let’s say your flying reindeer can pull five times the normal load, you still haven’t a hope in hell in accomplishing this with eight, or even nine reindeer.

You need some new recruits, well 488,000 new recruits. This then increases the total weight even further – still not counting the weight of the sleigh or your cumbersome self – to 403,000 tonnes. Just for comparison, that’s 462 times as heavy as Cutty Sark.

It’s Christmas Day. Owing to the heat created by the enormous air resistance that comes with dragging 403k tonnes at just less than 1% the speed of light, somehow, you, your numerous reindeer, sleigh, and the hundreds of millions of gifts you had in tow, didn’t instantaneously combust.

You also managed to avoid being crushed by the gigantic centrifugal forces pinning you to the seat of your sleigh. You can be mighty proud that you’ve not only survived but also that you completed your mission, just in the nick of time.

That was no mean feat. So give yourself a pat on the back, put your feet up and enjoy a well-deserved glass of sherry.