1) No known species of reindeer can fly. But there are 300,000
species of living organisms yet to be classified, and while most of
these are insects and germs, this does not COMPLETELY rule out flying
reindeer which only Santa has ever seen.

2) There are 2 billion children (persons under 18) in the world. BUT
since Santa doesn't (appear) to handle the Muslim, Hindu, Jewish and
Buddhist children, that reduces the workload to 15% of the total -
378 million according to Population Reference Bureau. At an average
(census) rate of 3.5 children per household, that's 91.8 million
homes.
One presumes there's at least one good child in each.

3) Santa has 31 hours of Christmas to work with, thanks to the
different time zones and the rotation of the earth, assuming he
travels east to west (which seems logical).

This works out to 822.6 visits per second. This is to say that for
each Christian household with good children, Santa has 1/1000th of a
second to park, hop out of the sleigh, jump down the chimney, fill
the stockings, 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 91.8 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 .78 miles per household, a total trip of 75-1/2 million miles,
not counting stops to do what most of us must do at least once every
31 hours, plus feeding and etc.

This means that 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 on earth, the Ulysses space probe, moves at
a poky 27.4 miles per second - a conventional reindeer can run, tops,
15 miles per hour.

4) The payload on the sleigh adds another interesting element.
Assuming that each child gets nothing more than a medium-sized lego
set (2 pounds), the sleigh is carrying 321,300 tons, not counting
Santa, who is invariably described as overweight.

On land, conventional reindeer can pull no more than 300 pounds.
Even granting that 'flying reindeer' (see point #1) could pull TEN
TIMES the normal amount, we cannot do the job with eight, or even
nine.

We need 214,200 reindeer. This increases the payload - not even
counting the weight of the sleigh - to 353,430 tons. Again, for
comparison - this is four times the weight of the Queen Elizabeth.

5) 353,000 tons traveling at 650 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 of
reindeer will absorb 14.3 QUINTILLION joules of energy. Per second.
Each.

In short, they will burst into flame almost instantaneously, exposing
the reindeer behind them, and create deafening sonic booms in their
wake. The entire reindeer team will be vaporized within 4.26
thousandths of a second.

Santa, meanwhile, will be subjected to centrifugal forces 17,500.06
times greater than gravity. A 250-pound Santa (which seems
ludicrously slim) would be pinned to the back of his sleigh by
4,315,015 pounds of force.>
In conclusion - If Santa ever DID deliver presents on Christmas Eve,
he's dead now.

(NOTE: This appeared in the SPY Magazine (January, 1990))

'If one wishes to obtain a definite answer from Nature one must attack the question from a more general and less selfish point of view.'