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 rule out flying reindeer which Santa has only seen.
2. There are 2 billion children (persons under 18) in the world. BUT since Santa doen'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 Refernce Bureau. At an average (census) rate of 3.5 children per household, that's 91.8 million homes. One presumes thaere's at least one good child in each.
3. Sant has 31 hours of Christmas to work with thanks to the different time zones and the rotation of earth, assuming he travels east to west (which seems logical). This works out to 822.6 visits per second. This is to say for each Chiristian household with good children, Santa has 0.01 of a second to park, hop out of the sleigh, go down the chimney, fill the stockings, distribute the remainging presents under the tree, eat whatever snacks have been left, get back up the chimney, get back on 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 is false but for the purpose of our calculations we will accept), we are now talking about 0.78 miles per household, a total trip of 75-0.5 million miles, not counting what most of us must do every 3.1 hours, plus feeding and etc. This means Santa's sleight 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 sleight 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 granted "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 Ocean Liner.
5. 353,000 tons traveling at 650 miles per second creates inormous air resistence (not counting the huge sonic boom)-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 flames almost instantaneously, exposing the reindeer behind them, and creating deafing 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 centrifical forces 14,500.06 Gs. A 250 pound Santa (which seems ludicrously slim) would be pinned to the back of his sleight by 4,315,015 pounds of force.
6. If each reindeer team needs 214,200 "flying reindeer" (see point #4) and if each reindeer team is vaporized within 4.26 thousandths of a second (see point #5) then he needs 5,572,196,015,400 of these "flying reindeer".

In conclusion-If Santa ever DID deliver presesnts on Christmas Eve, he's dead now.
Hope I didn't shatter any illusions.

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