How Fast Does Santa Fly?
 By Ari Daniel
 Posted 12.21.17
 NOVA
To make their delivery schedule, how quickly must Santa and his reindeer travel the world?
Transcript
Onscreen: How fast does Santa need to travel? There are ~2 billion children in the world. If Santa visits just under 1/3 (roughly 600 million) and there are two kids per household on average…
Talithia Williams: That’s about 300 million homes that Santa’s got to visit all around the world in one night.
Hannah Fry: Presumably, to minimize his chances of being spotted, he’s going to try and make his whole trip under the cover of darkness.
Onscreen: Suppose each child sleeps for 8 hours. (Shorter than usual due to Xmas excitement.) That gives Santa an 8hour window.
Fry: But Santa has got one trick up his sleeve. Because he can use the fact that the world is turning to his advantage.
Williams: Let’s assume he’s gonna start in the east, so probably all the way in Eastern Russia.
Fry: Almost by the Date Line.
Williams: And he’s gonna travel westward. He’s moving with the night.
Fry: Which can add on an additional 24 hours to his total time.
Williams: So that gives him a total of 32 hours to make it all the way around the world and deliver presents.
Onscreen: That’s Santa’s time limit. How much distance does he need to cover?
Williams: Houses aren’t just equally distributed around the world. We live in cities and towns, and we’re sort of clustered. But then other places, folks live out in the country. Santa’s gotta travel some distance to go from house to house.
Onscreen: Plus, Santa skips over much of the desert and wilderness and ocean.
Williams: Fishes and whales, they don’t get any gifts from Santa.
Fry: We can use a mathematical problem called the Traveling Salesman Problem. It’s exactly the same setup. It’s a salesman that’s traveling around different houses and wants to do so as efficiently as possible.
Onscreen: There’s just one hiccup. At a global scale with 300 million waypoints, it’s impossible to calculate. We just don’t have the computing power. (Though Santa must.) So we have to simplify. An approach that relies on fewer waypoints yields a distance of almost 3 million miles. Assuming Santa spends half his time delivering presents and half his time traveling, so 32/2 = 16 hours, his speed is: 3 million miles/16 hours = 187,500 mph.
Fry: Now that is quite a lot slower than the speed of light but substantially more than the speed of sound.
Williams: If he’s traveling at supersonic speed, where’s the sonic boom? Like, that would wake up all the kids and they’d stop Santa in his tracks.
Fry: NASA themselves have said that it may well be possible to build a jet that can get up to supersonic speeds without making a boom. I mean, if NASA can do it, well, Santa can, surely.
Onscreen: At supersonic speeds, with extreme air resistance, wouldn’t all the reindeer simply vaporize?
Fry: Santa could have a NASAstyle heat shield that protects all of the reindeer from those aerodynamic forces. You just don’t know what sort of amazing objects he’s using to pull off these kinds of speeds.
Onscreen: So if Santa doesn’t bring exactly what you asked for, maybe cut the guy some slack? He’s under some pressure. (Literally.)
Credits
PRODUCTION CREDITS
 Digital Producer
 Ari Daniel
 Editorial Review
 Julia Cort
 Production Assistance
 Theresa Machemer
 Math Assist from:
 The Indisputable Existence of Santa Claus by Hannah Fry & Thomas Oléron Evans
 Special Thanks
 Judy Augsburger
 © WGBH Educational Foundation 2017
MEDIA CREDITS
 Visuals & Videography
 flickr.com  Cindy Shebley/CC BY 2.0
Google Earth
Lockheed Martin
NASA
Noun Project  Blair Adams, Adrien Coquet, Fantastic, Oksana Latysheva, Landan Lloyd, Kalen Yul Zheng
pixabay.com
shutterstock.com  Traveling Salesman/Santa Calculations & Visualization Provided By
 David Applegate, Google, Inc.
William Cook, University of Waterloo
Keld Helsgaun, Roskilde University  Population Density Visualization
 Center for International Earth Science Information Network & Joe Schumacher
 Music
 APM
 Sound Effects
 freesound.org & SoundBible.com
POSTER IMAGE
 (main image: Santa in flight)
 shutterstock.com
Related Links

Making Stuff Faster
Host David Pogue tries to find out if there are physical limits to how fast we can go.

Zombies and Calculus
The zombie apocalypse is here, and calculus explains why we can't quite finish them off.

Zombies and Calculus, Part 2
You're being chased by zombies, and understanding tangent vectors may save your life.

Amazing Calendar Trick
With a dash of math, know the day of the week for any date on the calendar.