There are approximately two billion children (persons under 18) in the world. However since Santa does not visit children of the Muslim, Hindu or Jewish religions, this reduces the workload for Christmas night to 15% of the total, or 378 million.
Santa has about 108 million homes to visit and 31 hours of Christmas to work with, thanks to the different time zones and the rotation of the earth, assuming he travels from east to west. This works out at 967.7 visits per second.This is to say that for each Christian household with a good child, Santa has 1/1000th of a second to park the sleigh, hop out, jump down the chimney, fill the stockings, distribute the remaining presents under the tree, eat whatever snacks have been left for him and get on to the next house.
Assuming that each of these 108 million stops are evenly distributed around the earth, we are now talking about 0.78 miles per household and a total trip of about 75.5 million miles. This means that Santa’s sleigh is moving at a speed of 650 miles per second. The payload of the sleigh is another interesting element. Assuming that each child gets nothing more than a medium sized Lego set (weighing two pounds), the sleigh is carrying over 5,000 tonnes, not counting Santa himself. On land a conventional reindeer can pull no more than 300 pounds. Even granting that a “flying” reindeer could pull ten times the normal amount, the job can’t be done with eight, nine or ten of them. Santa would need 360,000 reindeer. This increases the payload, not counting the weight of the sleigh, another 54,000 tonnes, or roughly 7 times the weight of the QE2 (the ship, not the monarch).
600,000 tonnes 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 last 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 vaporised within 4.26 thousandths of a second, or right about the time Santa reached the fifth house on his trip. Not that it matters since Santa, as a result of accelerating from a dead stop to 650 miles per second, would be subject to centrifugal forces of 17,500g’s. A 250 pound Santa (which seams 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 quivering blob of pink goo and messy cartilage.
Therefore if Santa did exist, he’s dead now.