Figuring out Santa Claus: Aaron Santos has the answers

Note: Aaron Santos and his fun Santa Claus calculations was the subject of a Des Moines Register story.

How long would it take for Santa to deliver all his presents?

How heavy would his sack of presents be?

How many cookies would he eat?

You can stop guessing now. Aaron Santos, an assistant professor of physics at Simpson College, has figured out the answers.

Call them “The Claus Calculations” or “Santa By the Numbers.” Whatever the case, it’s an effort to make math less imposing and more accessible and fun.

“As a country we’re very scientifically illiterate, and even more so, we’re math illiterate,” Santos says. “And that becomes a huge problem when people can’t balance their checkbook, or they don’t know what policies to vote for because they hear all these big numbers,” such as the national debt.

If you can describe the national debt in terms of, say, doughnuts, that’s something that people can visualize, he says.

Santos also hopes his fun way of solving problems will appeal to young people. Iowa Gov. Terry Branstad has created an advisory council to improve opportunities and awareness in the fields of Science, Technology, Engineering and Mathematics (STEM), especially among young women.

Back to Santa Claus.

Santos has written two books of amusing calculations, “How Many Licks: Or, How to Estimate Damn Near Anything,” and “Ballparking: Practical Math for Impractical Sports Questions.”

In those books, he answered the questions, “How many licks does it take to get to the Tootsie Roll center of a Tootsie Pop? (Answer: about 800 licks), and, “How fat would you need to be to completely block a hockey goal?” (Answer: more than five tons.)

As a result. Desiree Schell of the Canadian radio program, “Science for the People,” posed a series of Santa-related questions to Santos. You can find the questions and answers below.

You can find the podcast of the program here (the Santos segment begins at the 36:20 mark):

Finally, if you would like to pose your own question for Santos to try and figure out an answer, you can write to him at his blog: 

Holiday Fun 

How long would it take Santa to deliver presents to every child in the world?

The answer to this clearly depends on how fast Santa is moving.  If we assume half of the seven billion people in the world are children and spread them uniformly over the surface of the globe, then on average there’d be roughly one quarter of a mile between children.  Presumably, Santa’s reindeer have access to the world’s fastest jet engine technology, which would mean they could travel at about Mach 10 (roughly 10 times the speed of sound.)  At this speed, Santa would be able to visit every child in about 14 years. Most of us would agree that Christmas night lasts, at most, 24 hours, and that 14 years is indeed a great deal longer than 14 hours.  If we instead assume that Santa has developed hyperdrive technology and can move close to the speed of light, he’d be able to make the trip in about 1.3 hours.

How heavy would the sack of presents be?

Some kids want a nice shiny red balloon for Christmas, others want a new set of Olympic barbells.  Present weights vary wildly, but we’ll be simple and assume an average of ten pounds of presents per child.  That would give a total weight of approximately 18 million tons, or roughly the equivalent of 100 Empire State Buildings.  However, since Santa is obviously traveling at extremely large speeds, Einstein’s theory of relativity would predict the length of the presents would contract and fit comfortably inside a reasonably sized bag.

How many cookies would he eat? How many calories would that be? What would he have to do to work it off?

At one cookie per stop, Santa would need to eat and successfully digest about 3.5 billion cookies and, in the process, would consume about 350 billion calories.  It would take roughly 1.5 billion years on a stair climber to burn off this extra fat.

How many elves would it take to make gifts for every child within 1 year? (how big is Santa’s staff?)

If each elf makes 10 toys per day for 365 days per year, Santa would require about one million elves working in sweatshop conditions.  This number is, perhaps, not as impressive as traveling at relativistic speeds, however, it is not surprising. Toy companies around the world routinely employ less than one million short humans working 365 days a year in sweatshop conditions. 

How much energy would each reindeer have to expend to travel that distance?

There are many energy requirements for this trip: lifting the reindeer off the ground, accelerating them up to speed, etc.  Perhaps the biggest energy cost is overcoming the extreme drag force that results from moving at relativistic speeds. If we consider spherical reindeer, then the drag force is easy to calculate.[1] The energetic cost is about 6×1028 Joules.  It helps to put this number in context.  Given its current rate of consumption, the United States will use this much energy in about 4.5 billion years.  Needless to say, that’s a lot of energy, and it needs to come from somewhere…

How much food would they have to eat to create that amount of energy?

While we typically think of calories as a measure of how much food there is, scientists use calories as a unit of energy.  To provide the 6×1028 Joules of energy, Santa’s reindeer would need to consume roughly 5×1023 pounds of candy canes. If you’re having a difficult time conceptualizing 5×1023 pounds of candy canes, imagine a candy cane roughly the same shape and size of the (ex)planet Pluto.

How much space would the reindeer waste (read: poop) occupy?

When it comes to reindeer, a general rule of thumb is that what goes in must come out.  If the reindeer consume a planet worth of candy canes, there’s going to be some major clean up afterwards.  In this case, there would be a 50 km high pile of reindeer poop covering the entire Earth.  Yes, the entire Earth, even the oceans.

[1] Some might bristle at the assumption of “spherical reindeer” with the logic that reindeer couldn’t possibly obtain this shape.  I would counter that (1) these are the types of assumptions that scientists an engineers make on a daily basis, and they do not significantly effect the magnitude of the approximation, and (2) seriously, people, we’re talking about a morbidly obese 1700 year old who flies around the globe at relativistic speeds using magic reindeer.  Is reindeer shape really the thing you want to quibble about?!