# Holiday Speed-Round #1: Santa

**Posted on:**December 24, 2015 /

**Categories: Uncategorized**

**How long would Saint Nicholas’ beard be if he hasn’t shaved since 300 AD?**

Hair grows at a rate of 6 inches (15 cm) per year. If he hasn’t shaved in 1,715 years his beard will be 285 yards (261 m) long, which is about 3 football fields in length. If Santa’s sleigh was hauling ass across the sky in an area with significant light pollution his beard might look something like a shooting star, though the drag would probably break Santa’s neck.

**How many elves does Santa need in order to make a toy for every child in the world?**

The world population is 7.3 billion [1], with 26% being under 15 [2], which means Santa’s little helpers make 1.9 billion toys every year. If an elf can make one toy per hour while working 12 hours per day, a single elf can make 4380 toys in a year. With this level of production Santa needs to employ 430,000 elves, which is nearly the population of Ireland. Santa’s workshop must be the size of a city, which confuses me because I can’t find it on Google maps.

**What’s the GDP of the north pole?**

If the elves produce 1.9 billion toys per year, each valued at $10, then the GDP of the north pole is $19 billion, which is close to the GDP of Honduras [3] or Nepal [4].

**How big does Santa’s sleigh have to be to carry those toys?**

If each toy weighs 2 lbs (0.9 kg), the sleigh is hauling 1.9 million tons (1.7 million metric tonnes). A normal tractor trailer can’t haul much more than 80,000 lbs, so if the sleigh is comparable it would need to have 475,000 trailers hitched. Assuming these are normal cargo trailers this sleigh-train is 4,500 miles long (7,250 km). This is twice the distance from DC to LA as the reindeer flies, but it could fit comfortably on the Great Wall of China. Again, why can’t I find the hangar on Google maps?

**How fast does the sleigh go?**

Since there are nearly two billion kids let’s assume the sleigh makes one billion stops (2 kids per home). Thanks to the miracle of the earth’s rotation, Santa actually has at least 24 hours to complete his flight, assuming he can manage one timezone per hour.

The earth’s land area is 510 million km^{2}, so if there are a billion houses they are about 750 meters apart on average. Santa has to go

#### (750 m) / (24 hours / 1 billion) = 8680 km/s

This is about 3% of the speed of light, far faster than any other man-made craft. Fun fact: due to constant stopping and starting at each house, it means his typical max speed is actually twice this.

If I had to guess, I’d say Santa has solved the traveling salesman problem.

**How many g’s does the sleigh experience?**

This is an easy one to ballpark if we use our same numbers from above:

#### (750 m) / (24 hours / 1 billion)^{2} = 1.0 × 10^{10} g

I don’t have much to offer for perspective on *ten billion g’s of acceleration. *That’s near the maximum possible surface gravity of a neutron star – the only other place you can find accelerations like this is near black holes… and apparently the north pole too.

**How many reindeer does the sleigh need? How strong are they?**

*Eight*. Their names are Dasher, Dancer, Prancer, Vixen, Comet, Cupid, Donner, and Blitzen. Fear them, because each of them is putting out 10^{23} horsepower.

*“Oh but what about Rudolf! You’re forgetting the only reindeer I can even name!”*

And for good reason. Who needs Rudolf’s nose when the power output of every pair of reindeer is equal to the sun? The hilarious amounts of heat from friction with the atmosphere should be more than enough to light their way. Forget what I said about Santa’s beard looking like a shooting star- the entire sleigh is blazing like the surface of the sun.

image credit: Wikimedia Commons

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