 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 seen.
 There are 2 billion children (under 18) in the world. But
since Santa doesn`t appear to handle Muslim, Hindu, Buddhist and
Jewish children, that reduces the workload to 15% of the total
378 million or so. At an average rate of 3.5 children per
household, that's 91.8 million homes. One presumes there's at
least one good child in each.
 Santa has 31 hours of Christmas to work with, thanks to time
zones and the rotation of the earth, assuming he travels east
to west. 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 gifts under the
tree, eat the snacks, get back up the chimney, get back
in the sleigh, and move on to the next house.
 Assuming that each of these 91.8 million homes are
distributed evenly (which we know to be false but for
the sake of these calculations we will accept) we are
now talking about .78 miles per household, a total trip
of 75.5 million miles, not counting bathroom stops.
 This means that Santa`s sleigh is traveling at 650
miles per second, 3000 times the speed of sound. For
comparison, the fastest man made vehicle, the Ulysses
space probe moves at a poky 27.4 MPS; the average
reindeer runs at 15 MPH.
 The sleigh's payload 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 one) could pull TEN TIMES the usual amount, we
can not do the job with 8 or even 9. We need 214,000
reindeer. This increases the weight, not even counting
the sleigh, to 353,430 tons. Again, for comparison this
is 4 times the weight of the Queen Elizabeth 2.

A mass of 353,000 tons traveling at 650 miles per second creates
enormous air resistance. This will heat the reindeer in the same
manner as a spacecraft reentering 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 next pair of reindeer,
and creating deafening sonic booms in their wake. The
entire team will be vaporized within 4.26 thousands of
a second.
 Santa, meanwhile, will be subjected to centrifugal
forces 17,500.06 times the force of gravity. A 300
pound Santa would be pinned to the back of his sleigh
by 4,315,015 pounds of force.

Conclusion: There was a Santa, but he's dead now. Merry
Christmas!
