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 cihldren, that reduces the workload to 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 108 million homes. One presumes there's at least one good child in each.
3) If Santa delivers all of the gifts during normal night-time hours (between 11:00 PM and 6:00 AM), he 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 967.7 visits per second. This is to say that for each Christian household with good children, Santa has a thousandth of a second to park, get out of his sleigh, jump down the chimney, fill the stockings, distribute the remaining presents under the tree, eat whatever snacks have been left, get back up through the chimney, get back into his sleigh and move on to the next house. These houses are obviously not evenly distributed around the world, but we can estimate that each of these 108 million stops are evenly distributed around the earth's surface, and we will only count 30% of Earth's surface area, 197,360,000 mi², as land. This makes for about .548 miles per household, making a total trip of 59,200,000 miles, not counting eating, feeding the reindeer, and stops to do what most of us must do at least once every 31 hours.
This means that Santa's sleigh is moving at 650 miles per second, which is 6,800 times the speed of sound at room temperature(22°C / 72°F). For purposes of comparison, the fastest man-made vehicle on earth, the Ulysses space probe, moves at only 27.4 miles per second. A conventional reindeer can only run a maximum of 15 miles per hour, which is .0042 miles per second.
4) The payload on the sleigh adds another interesting element. Assuming that each child gets nothing more than a small 2 pound lego set, 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" could pull TEN TIMES the normal amount, eight, or even nine reindeer could not do the job. 214,200 reindeer would be needed. This increases the payload, excluding the weight of the sleigh, to 353,430 tons.
5) 353,000 tons travelling at 650 miles per second creates enourmous air
resistance. This would heat up the flying reindeer like
spacecrafts re-entering the earth's atmosphere. The lead pair of
reindeer would absorb 14.3 QUINTILLION joules of energy each second.
In other words, they would burst into flame almost instantly,
exposing the reindeer behind them, and create deafening sonic booms in
their wake. The entire reindeer team would be vaporized within 4.26
thousandths of a second. Santa, meanwhile, would be subjected to
centrifugal forces 17,500.06 times greater than gravity. A 250-pound
Santa (which even seems thin) would be pinned to the back of his
sleigh by 4,315,015 pounds of force.