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, this
reduces the workload for Christmas night to 15% of the total, or 378
million (according to the population reference bureau). Assuming an
average (census) rate of 3.5 children per household, that computes 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. This amounts to 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 pokey 27.4miles
per second, and a conventional reindeer can run (at best) 15 miles
per hour. The payload of the sleigh adds another interesting element.

Assuming that each child gets nothing more than a medium sized LEGO
set (two pounds), the sleigh is carrying over 500 thousands 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 travelling at 650
miles per second creates enormous air resistance - this would heat up
the reindeer in the same fashion as a spacecraft re-entering 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 4.26 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 .001 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 dribbling mess of twitching innards.

Therefore, if Santa ever did exist, he's dead now.

Merry Christmas everybody.