1) No known species of reindeer can fly,
but there are 300,000 species of 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 (defined as persons under 18) in the world;
However, since Santa doesn't appear to handle Muslim, Hindu, Jewish, or Buddhist children,
that reduces the workload down to 15% of the original total,
378 million according to the Population Reference Bureau.
At an average census rate of 3.5 children per household, that's only 91.8 million homes.
One presumes that there is 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.
This works out to 822.6 visits per second.
That 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 chiminey, fill the stockings, distribute the remaining presents under the tree,
eat whatever snacks have been left, get back up the chiminey, 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 we know to be false but will accept for the purpose of these calculations),
we are talking about .78 miles per household, a total trip of 75.5 million miles,
not counting stops to do what most of us must do at least once every 31 hours, plus eating, etc.
This means that Santa's sleigh is moving at 650 miles per second, 3000 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. A conventional reindeer can run 15 miles per hour at the most.
4) The payload on the sleigh add another interesting element.
Assuming that each child gets nothing more than a medium-size set of Lego building blocks
(about two 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 exist (see point 1), can fly very quickly (see point 2),
and can pull ten times the normal amount, we cannot do the job with eight, or even nine, reindeer.
We would need 214,200 reindeer. This increases the payload - not counting the weight of the sleigh,
to 353,430 tons. Again, for comparision, this is four times the weight of the Queen Elizabeth 2.
5) 353,000 tons travelling at 650 miles per second creates enormous air resistance.
This would heat the reindeer up 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 flame almost instantaneously, exposing the reindeer behind them,
and creating deafening sonic booms in their wake.
The entire reindeer team would be vaporized within .00426 seconds. Santa, meanwhile,
would be subjected to forces 17,500 times greater than normal gravity.
A 250-pound Santa (which seems 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.