15
This related question asks about considerations for Santa's sleigh (particularly weight), but my question is more basic: how do you design a vehicle that satisfies Santa's design requirements, including the very tight schedule, in a way that doesn't turn Santa into a puddle of goo from high-Gs and vaporize the reindeer from wind-speed?
Key design requirements, as I understand them:
The vehicle must be able to support take-off and landing at the homes of all good children on Earth in a span of roughly 24 hours. (Good children on space colonies are excluded.) We can't afford a long pre-flight check; really, we probably don't even have time to open and close a hatch. (Art never shows a hatch anyway.)
Without knowing the number and distribution of stops we can only guess at the one-night mileage, but even at conservative estimates... mach-what? Gotta support super-high speed.
It's ok if maintenance and repairs take the next 363 days, but there's not going to be time on delivery night for pit stops and spot-repairs -- the vehicle needs to operate continuously during the delivery run. (Santa would probably prefer to be able to do a test-drive tuning check between deployments, however, so less-extensive maintenance is preferred.)
Santa, a well-padded humanoid, needs to survive the trip without long-term damage. As far as we know it's the same Santa every year.
The reindeer need to survive the trip. Santa is pretty cagey about the reindeer, though -- who'd know if Blitzen is the same Blitzen as last year? It's ok to assume that Santa runs a breeding program, though protections for the lead reindeer with the light-emitting mutation would be advisable.
There are no explicit requirements about materials or fuel sources.

I think we have to assume that Santa, his reindeer, and the sled are all made of massless.......stuff. That would let him travel at the speed of light, or more specifically, always travel at the speed of light, which would (hopefully) have the side effect of protecting him from being jellified as well as not obliterating his destination. – Draco18s no longer trusts SE – 2015-12-22T17:19:15.110
The sled and its payload can't be massless, though. Are you saying that a massless Santa et al would still work? – Monica Cellio – 2015-12-22T17:23:12.880
Darned if I know if you can construct Santa from massless particles. Probably not. But the question you are asking is "how do we protect Santa from being jellified?" to which: basically you can't, unless Santa has no mass ($F = ma, m = 0, F = 0$). – Draco18s no longer trusts SE – 2015-12-22T17:29:40.307
Santa must go in and out of faster-than-light travel; this will be a key factor to your answer: what happens to you when you break the laws of physics? – Mikey – 2015-12-22T19:57:47.860
Actually, I think you could afford a long pre-flight check; the fact is that Santa could probably devote some workers to the pre-flight check, maintenance and preparations for the better part of a year between each delivery run. What we can't afford is a long turnaround time during the delivery run, but that's rather different. – a CVn – 2015-12-22T20:03:17.457
@MichaelKjörling sorry, I meant pre-each-flight -- running any check at all before each of a couple billion take-offs would really chew up the time, I'd think. – Monica Cellio – 2015-12-22T20:08:42.680
Santa owns a Bag of Holding (Except... his is magical)
– WernerCD – 2015-12-22T23:38:35.3632Redbull gives you Wings! – Cort Ammon – 2015-12-23T03:38:43.513
+1; my first favourite marked question here. Right question at the right season:) – None – 2015-12-23T05:15:02.447
I think most of you are missing a few key points. A) Santa (mostly) only visits Christian homes. B) Santa only visits good boys and girls. C) I think we are all being lazy with our math because (if we ignore any down time between stops and we ignore acceleration\deceleration) this can be achieved at sub-light speeds. If we don't ignore those things then it can't be done at any speed (unless time travel is a factor) without setting the bar for 'good' very high. In short, the best way to do it is to only visit the most saintly of children. – krowe – 2015-12-23T12:12:48.820
@krowe sounds like you have the beginnings of an answer. Though my impression is that Santa visits plenty of secular (non-Christian) homes, at least in the US. But if you can make a sub-light-speed argument that's consistent with observed behavior, please do! – Monica Cellio – 2015-12-23T16:07:43.123