John Malkovich’s voice and spectacular cadence in your head:
- “It is estimated that Santa’s sleigh weighs 353 thousand tons. So, traveling at 650 miles per second would create such enormous friction that Santa and his reindeer would burst into flames. You understand? Like a meteor entering the atmosphere. This is a scientific fact.”
The friction (and resulting heat) I am assuming would come from wind resistance. Think along similar lines to this classic XKCD article.
650 miles per second, as Malkovich said in the skit, translates to about 2.3 million miles per hour, or about 3.8 million kilometers per hour for the more mathematically reasonable among us out there.
A much lighter meteor traveling much slower than that through the atmosphere is enough to generate the heat needed for combustion, so it would probably apply to Santa in this hypothetical scenario, too.
The wind resistance shouldn’t be dependant on the mass. Shape of the sleigh would be the real factor.
But another thing to consider is that the gigantic mass and heat capacity. Given that the sleigh has a good heat distribution, it would take a lot of air resistance to actually make the sleigh combust. I don’t have a decent guess for the average heat capacity, so I don’t actually know if it’s significant enough, but the calculation is more complex than just looking at the speed.