No known species of reindeer can fly, but there are 300,000 species of living organisms yet to be classified. While most of these are insects and germs this does not completely rule out flying reindeer that only Santa has ever seen.

There are 2,000,000,000 children, persons under 18 years, in the world. Since Santa doesn’t appear to handle Muslim, Hindu, Jewish and Buddhist children that reduces the prospective workload to 15% of the total 378,000,000, according to the USA Population Reference bureau, at an average of 3.5 children per household, that is 91,800,000 homes. One presumes there is at least one good child in each.

Santa has 31 hours of Christmas to Work with, thanks 49 the different time zones and the rotation of the earth, assuming he travels east to west, which is the most logical. This works out at 822.6 visits per second, one for each Christian household with good children. Santa has 1/000^{th} of a second to park, hop out of the sleigh, jump down the chimney, fill the stockings, distribute remaining presents under the tree, eat and drink whatever snacks and refreshments have been left carefully remembering the appropriate drink-driving and flying rules that apply, get back up the chimney, get back into the sleigh and move on to the next house.

Assuming that each of these 91,800,000 stops are evenly distributed around the earth, which of course we know to be false but for the purpose of our calculations we will accept the approximation. We are now talking about 0.78 miles per household, a total trip of 75,000,000* *miles, not counting stops to do what most of us must do at least once every 31 hours, plus feeding etc. This means that Santa’s sleigh is moving at 659 miles per second, Mach 3,000. For the purposes of comparison the fastest man made vehicle on earth, the Ulysses space probe, moves at a poky 27.4 miles per second, Mach l26 and a conventional reindeer can run at 15 miles per hour, tops, Mach 0.02.

The payload on the sleigh adds another interesting element. Assuming each child gets nothing more than a medium sized Lego set, 2 pounds, the sleigh is carrying some 321,300 tons, not counting Santa, who is invariably described as rotund and jolly, i.e. overweight. On land, conventional reindeer can pull no more than 300 pounds. Even granting that “flying reindeer” could pull 10 times the normal weight, we cannot do the job with eight or even nine – we will need 214,200 “flying reindeer”. This increases the payload, not counting the weight of the sleigh, to 353,430 tons. About 4 times the weight of the Oprah, Nashville, Tennessee.

353,000 tons travelling at 650 miles per second creates enormous resistance, this will heat up the reindeer in the same way as a spacecraft re-entering the earth’s atmosphere. The leading pair of reindeer. Or according to some Sources Rudolph on his own will absorb 28’000,000,000,000,000,000,000,000 Joules of energy. In short, he or they will burst into flame almost instantaneously exposing the reindeer behind and creating a deafening sonic boom in their wake. The entire team would be vaporised within 0.00426 seconds. Santa, meanwhile, will be subjected to centrifugal forces and centripetal acceleration 17,500.06* *times greater than the force of gravity. A 250 pound Santa, which seems ludicrously slim for a real Santa, would be pinned back by 4,315,015 pounds of force.

Conclusion: If Santa ever did deliver presents on Christmas Eve, he is dead now!

Merry Christmas!