Yes, Santa can deliver all those presents on Christmas Eve: Do the math

Yes, Virginia, physics does show that Santa could fly around the world delivering presents on Christmas Eve. Photo: Santa Claus (youtube)

WASHINGTON, December 16, 2013 — While other scientists have classified Santa Claus’ behavior as categorically impossible, perhaps it is worth another look.

We begin with our most basic understanding of Santa Clause and his actions. Physics is a scientific field that is centered on applying mathematic principles to naturally occurring phenomena. That means we need to see what we can see, and then figure out the numbers. Then use those numbers in math to discover new information.

Those scientists who dismiss the possibility of Santa Claus flying around the world delivering presents make assumptions about his behavior first, without relying on what we actually know about the man.

So, to avoid the same mistakes, what can we say that we do absolutely know about Santa? We know that he flies to your house, lands on your roof, and drops down your chimney to bring you toys.

According to DisasterSafety.org the upper limit of weight most roofs can support is 60 pounds per square foot. That means that when Santa and his 9 Reindeer land on top of your roof, with the sleigh and sack and all the gifts, they can only have 60 pounds per each square foot of roof they occupy. Otherwise you would end up with Santa in your living room instead of your gifts. So 9 deer, all hitched up, along with the sleigh, probably take up about 201.28 square feet. That means they would clock in around 12,076.8 pounds.

A deer is about 300 kilograms (661.4 lbs), Santa is probably around 250 (which would be significantly pudgy given the average height of men around when he was born) and the sleigh is most likely right around 100 pounds. That leaves us with 5,774.2 pounds for gifts.

Now, Christmas nay-sayers will surely interject here: “Bah Humbug!” they will say, “that means that the gifts for each kid is only going to weigh 0.000015 pounds.” Not true. We have only calculated what Santa’s sleigh has to weigh. There is no reason why some of Santa’s trademark “Christmas Magic” couldn’t come into play to lighten the load. All we have done is solve for the weight of the sleigh itself: A number that will be crucial to find the energy taken to drive around the world.

Before we can calculate the energy though, we need to figure out the speed of the sleigh. This is probably the most hotly contested issue surrounding the physics of Santa Claus. From the time the sun sets in Fiji to the time the sun rises in American Samoa, Santa Claus has 34.2 hours (or 123,120 seconds) to leave something (either toys or coal) at the house of every Christmas celebrating child on earth.

If we use the standard numbers of 378 million children on earth, with about 3.5 kids per house, Santa has 91.8 million stops to make in 34.2 hours. That equals 745.6 stops per second. Not an easy task surly, but let’s not assume it’s an impossible one. The surface area of the Earth is 510.1 million square kilometers. But people don’t inhabit all of it (or really, very much of it at all). Only 29% of that is land, and only 1% of that is home to human beings. That is 1,479,290 square kilometers. That means that Santa and his Reindeer need to knock out 12.01 square kilometers every second.

The other thing we can find is how many stops there are per square kilometer: 62.06. If we assume an average distance of 3 meters between stops (more for the country, less for the city, so this is a realistic averate) then we end up with a travel distance of 186.2 meters per square kilometer. Coupling this number with our 12.01 square kilometers per second gives us a traveling velocity for Jolly Old Saint Nicholas: 2236 meters/second or 5002 miles per hour.

Now there’s no arguing about it: that is fast. But it isn’t approaching-the-speed-of-light-fast. It isn’t even fast-enough-to-leave-Earth’s-orbit-fast. It’s just fast. But it isn’t out of the question to assume that every-house-in-one-night-fast would have to be pretty quick.

The kinetic energy required to fly around the world can be found using just these two numbers: the mass of the entire load (reindeer and all) and the speed with which the whole kit-and-caboodle moves. When we plug those numbers in we get a final answer of 13,693,917,360 Joules. That’s a huge number. But it is only about 1/5 the amount of energy consumed by an average automobile in the United States in 2000. So it is a big energy output for one night. But even that isn’t a completely ludicrous number. It is a number that normal, everyday people deal with for their transportation needs about every 10 weeks.

In summation, Yes, Virginia, (and Maryland, and the general DC Metro Area), there is a plausible scientific underpinning for a Santa Claus. It exists as certainly as the Higgs Boson and subatomic particles that travel the wrong direction in time exist. And those abound and give science its highest beauty and joy.

Alas! How dreary would be the world if there were no scientific possibility of Santa Claus.

 


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Ryley Trahan

Ryley J. Trahan is a writer and physics teacher in Virginia. He is a graduate of the University of Mary Washington, in Fredericksburg Virginia, with undergraduate degrees in English and Physics. He loves comic books and super heroes. He also writes a blog about Physics in New Media.

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