My school is hosting a family night, and the math department has charged me with setting up a booth where visitors can grab a yard stick and a world map and, given Santa’s top speed, calculate how long it would take him to reach various cities on the map.

Seeing that none of my world maps have a scale that works in the way they had hoped, I want to refocus the booth, an instead show students just how complex supersonic flight is and let them try to make their own conclusions by considering all of the information.

Here are some things I know they’d need to consider:

  • If he accelerates above 4 G, Santa will experince blurred vision and possibly pass out.
  • If he accelerates about 64 G, Santa would will be crushed by the speed.
  • He can travel faster in the thin altitude at 35,000 feet, but reindeer can’t breathe beyond 20,000 ft as the air is too thin.
  • The outside of the SR-71 could reach temperatures of 600 °F in flight. Santa’s wooden sled would burn up at temperatures of 451 °F.
  • If Santa travels faster than the speed of sound in air (767 mph) in an urban area, he’ll break many windows.

Assume the only magic that breaks physics is the reindeer can fly, potentially as fast as an SR-71, but the laws of physics (e.g. they can't accelerate too fast that they'd melt) will limit their maximum possible speed.

What other considerations must be made when calculating how quickly Santa can get from one city to another?

  • $\begingroup$ Ok, you are going to destroy Santa's magic. One has to be able exploit the suspension of disbelief on which Santa's myth is based, otherwise one could ask how could happen that, say one tenth$^*$ of the about 80 million of families in the USA could be visited in one night, taking into account that even $1~s$ per family would imply continuous work for almost 93 days. ($^*$: conservative estimate of the families with at last one good child ). $\endgroup$ – GiorgioP Dec 11 '19 at 13:55
  • $\begingroup$ a yard stick on a flat map, with any 2 points...wwwwattt? (see: Plate carrée projection) $\endgroup$ – JEB Dec 11 '19 at 14:47
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    $\begingroup$ Santa's sled is quantum mechanical. Since it hasn't been observed it can be in many places at once and therefore doesn't need to travel. $\endgroup$ – rghome Dec 11 '19 at 15:11
  • $\begingroup$ How do you decide which laws of physics Santa must obey, and which laws is is allowed to ignore? If he doesn't ignore some physical laws, then he and his team and his sleigh can't fly at all. But if he doesn't obey some physical laws, then none of the constraints that you want to lay on him are valid. $\endgroup$ – Solomon Slow Dec 11 '19 at 15:15
  • $\begingroup$ Imagine the only magic involved is the reindeer can fly and quite fast. want to consider every other limitation provided by physics, e.g. if they fly against the wind, they can't go as fast. $\endgroup$ – Village Dec 11 '19 at 15:36

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