Sunday, February 19, 2006

The Physics of Santa

Can the Jolly Fat Man really exist?

This essay appears in many places on the internet, with no obvious author. I have modified it slightly to SI units and fixed a few terms that bugged the physics pedant within me.

1) There are 2 billion children in the world (persons under 18), but since Santa doesn't (appear) to handle Muslim, Hindu, Jewish, or Buddhist children, or even many christian groups, that reduces the workload by 85% of the total - leaving 378 million according to the Population Reference Bureau. Furthermore, since the introduction of the Gregorian Calendar, the orthodox religions and the catholic religions disagree on when December 25th happens, meaning Santa has two Christmas eves to distribute gifts over. Lets assume that the split is roughly even, meaning Santa has 189 million children to deal with each night.

2)At an average (census) rate of 3.5 children per household, that's 45.9 million homes. One presumes there is at least one good child per house.

3) Santa has 31 hours of Christmas to work with, thanks to the different times zones and the rotation of the earth, assuming he travels east to west (which seems logical). This works out to 411.3 visits per second. This is to say that for each Christian household with good children, Santa has 1/500 th of a second to park, hop out of the sleigh, jump down the chimney, fill the stocking, distribute the remaining presents under the tree, eat whatever snacks have been left, get back up the chimney, get back into the sleigh and move on to the next house. Assuming that each of these 45.9 million stops are evenly distributed around the earth (which, of course, we know to be false, but for the purposes of our calculations we will accept), we are now talking about 3km per household, a total trip of 120 million kilometers, not counting stops to do what most of us do at least once every 31 hours, plus feeding, etc. That means that Santa's sleigh is moving at 1040 miles per second, 3,000 times the speed of sound. For purposes of comparison, the fastest man-made objects - depp space probes like Voyager one travel at around 20 kilometers per second - a conventional reindeer can run, at top speed, 24 kilometers per hour.

4) The payload on the sleigh adds another interesting element. Assuming each child get nothing more than a medium-sized Lego set (1 kg), the sleigh is carrying 189 million kilograms, not counting Santa, who is invariably described as overweight. On land, conventional reindeer can pull no more than 150 kg. Even granting the "flying reindeer" can pull TEN TIMES that normal amount, we cannot do the job with eight, or even nine. We need 107,100 reindeer. As the typical January weight of a reindeer is about 60kg, this increases the payload - not even counting the weight of the sleigh to 195 million kilograms (not accounting for the fact that Santa's reindeer are probably better fed during winter than their wild counterparts. Again, for comparison, this is twice the weight of the Queen Elizabeth II.

5) Any object traveling at 1040 miles per second creates enormous air resistance. This will heat the reindeer up in the same fashion as spacecraft re-entering the earth's atmosphere. The lead pair will absorb 14.3 QUINTILLION joules of energy per second, each. In short, they will burst into flames almost instantaneously, exposing the reindeer behind them, and creating a deafening sonic boom in their wake. The entire reindeer team will be vaporized in 4.26 thousandths of a second. Santa meanwhile, will be subject to an average acceleration 8700 times greater than gravity as the sleigh speeds up and slows down between stops. A 120kg pound Santa (which seems ludicrously slim) would be pinned to the back of the sleigh by an average force of 10 million newtons.

In conclusion, if Santa ever DID deliver presents of Christmas Eve, he's now dead. (This will be something you can tell your kids someday!)

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