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There are approximately two billion children (persons under 18) in the
world. However, since Santa does not visit children of Muslim, Hindu,
Jewish or Buddhist (except maybe in Japan) religions and doesn't see
Orthodox children until 3 Kings Day, this reduces the workload for Christmas
night to 15% of the
total, or 378 million (according to the population reference bureau).
At an average (census) rate of 3.5 children per household, that comes to 108
million homes, presuming there is at least one good child in each. Santa
has about 31 hours of Christmas to work with, thanks to the different time
zones and the rotation of the earth, assuming east to west (which seems
logical).
This works out to 967.7 visits per second. This is to say that for each
Christian household with a good child, Santa has around 1/1000th of a second
to park the sleigh, hop out, jump down the chimney, fill the stocking,
distribute the remaining presents under the tree, eat whatever snacks have
been left for him, get back up the chimney, jump into the sleigh and get
onto the next
house.
Assuming that each of these 108 million stops is evenly distributed around
the earth (which, of course, we know to be false, but will accept for the
purposes of our calculations), we are now talking about 0.78 miles per
household; a total trip of 75.5 million miles, not counting bathroom stops
or breaks. This
means Santa's sleigh is moving at 650 miles per second--3,000 times the
speed of sound.
For purposes of comparison, the fastest man-made vehicle, the Ulysses space
probe, moves at a poky 27.4 miles per second, and a conventional reindeer
can run (at best) 15 miles per hour.
The payload of the sleigh adds another interesting elements. Assuming that
each child gets nothing more than a medium sized LEGO set (two pounds), the
sleigh is carrying over 500 thousand tons, not counting Santa himself.
On land, a conventional reindeer can pull no more than 300 pounds. Even
granting that the "flying" reindeer can pull 10 times the normal amount, the
job can't be done with eight or even nine of them---Santa would need 360,000
of them.
This increases the payload, not counting the weight of the sleigh, another
54,000 tons, or roughly seven times the weight of the Queen Elizabeth (the
ship not the monarch). 600,000 tons traveling at 650 miles per second
creates enormous air resistance - this would heat up reindeer in the same
fashion as a spacecraft reentering the earth's atmosphere. The lead pair of
reindeer
would absorb 14.3 quintillion joules of energy per second each. In short,
they would burst into flames almost instantaneously, exposing the reindeer
behind them and creating deafening sonic booms in their wake. The entire
reindeer team would be vaporized within 4.2 thousandths of a second, or
right about the time Santa reached the fifth house on his trip.
Not that it matters, however, since Santa, as a result of accelerating from
a dead stop to 650 m.p.s. in seconds, would be subjected to acceleration
forces of 17,000 g's. A 250 pound Santa (which seems ludicrously slim)
would be pinned to the back of the sleigh by 4,315,015 pounds of force,
instantly crushing his bones and organs and reducing him to a quivering blob
of pink goo.
Therefore, if Santa did exist, he's dead now.
Merry Christmas