Christmas is a magical time all around the world. Tomorrow night, millions of children will be putting out their stockings, ready to wake the next morning to delights delivered by the fat red man (and his reindeer) we all hold close to our hearts, St Nick himself, Father Christmas, Santa Claus. However, his one-night-only trip may just cost nearly the same as a luxury yacht, and that doesn’t include the presents!

In this post, we are going to be talking about how Santa will travel. I’m sure I’m not the only one that wondered about the logistics of one man, with a vehicle powered by flying reindeer, visiting every celebrating child in world so this year, I decided to actually look into it! We will be looking at the distance he travels, how much energy he needs and how much that could cost.

The first thing I considered was the distance he has to travel. Whilst researching the post this week, I came across this website. It is trying to calculate the speed that santa has to go, something I will do later. They take the approach of calculating the number of households he has to visit and assuming, though acknowledging it is not as simple as this, that they are equally distributed across the world. I think we are going to take a different route than this, the result just didn’t seem far enough. Instead, I think that most efficient method is similar to what you would find on the back of your fridge:

This pattern of rows means that he can cover as much of the earth as possible in the shortest distance. It also means he can take advantage of time zones. Starting in the east, he could travel for a full 31 hours under the cover of one night. I decided that 160 rows would be a fair number of rows. This is the equivalent of going around the earth itself 160 times from north to south to north again. The maths is a bit harsh, so if you want to hear about that go down to the end of the post where I will be going through specifics. The distance he travels then, is about 5 million kilometers. This is about a thirtieth of the distance from the earth to the sun and thirteen times the distance from here to the moon. Suffice to say that he would have to moving pretty fast!

As I said, if he is tactical (and seeing as he has done it for at least 200 years, you can assume he is), he would take advantage of the fact that night moves across the world, giving him 31 hours to cover the 5 million kilometers. That means he has to travel at about 160,000 kmh or 45,000 ms. That is 132 times the speed of sound and 46 times the speed of the fastest vehicle we, as a species, have ever created, the Lockheed SR-71 Blackbird plane.

This speed, though immense, is not actually the biggest problem for santa at his point. That comes when you start to think about air resistance. Again, the physics here involves some nasty equations, but there are a few things to take into account. The amount of drag increases exponentially as the velocity of the object increases, but the higher you go in the earth’s atmosphere, the density of air decreases. Overall though, at a speed as high as this, the drag force will be huge! Again, look at the bottom for the actual calculations, but it comes to about 207 million newtons, the equivalent of the weight of the amount of water in 8 olympic swimming pools pushing on every square meter of the vehicle.

The amount of power required to over power this is the force times by the velocity and seeing as this velocity is so high, this means a huge amount of power is required. Namely 9.3 million MegaWatts.You would need to open up 414 of the largest power stations in the world (the Three Gorges Dam) to create this amount of power. From this, by dividing by the time he is doing this for, we get the amount of energy he needs, 300,000 MWh (MegaWattHours) or  1,081,356,687 MJ (MegaJoules).

When you burn 1000 litres of petrol (gasoline), this releases 10 MWh of energy. This means that if santa was using petrol and the heat from it to power his flight, he would need 30 million litres of it! The price of this varies where he buys it but if he was to buy it in the UK, it would cost  almost £36,000,000 (\$58,000,000) though buying in the USA would be a bit cheaper at only £14,000,000 (\$23,000,000).

But Santa doesn’t use petrol. His vehicle is animal powered. So, how much would that cost? Well lets assume the diet that santa feeds his reindeer is pretty bland, they just eat oats. Oats are 66% carbohydrates and 2% fat. We also know that within every kilo of carbohydrates, there is 17MJ of contained energy, and within every kilo of fat there is 37MJ. We also know that respiration, the way that animals get energy , is not totally efficient, 60% of the energy is released as heat.  Using all this and the energy we know we need, we can calculate the mass of oats we need…and it is a lot! Santa would have to stockpile over the course of the year, as he couldn’t buy it all at once, 226,000 metric tons of oats! That is 540,000,000 litres of raw oats! This could cost him around £40 million (\$63 million).

So I ask you all, lets spread the word! Not only does santa deliver presents, not only is he a symbol of christmas, but he is a millionaire that spends huge amounts of money on oats, he has a supersonic sleigh that is 46 times faster than any man-made vehicle ever and his reindeer can eat 540 million litres of oats over the course of one night! Anyway, we wish you a merry christmas and a happy holiday from us here and hope that you get a visit from the fat, red, supersonic man from the north pole.

We hope you’ve enjoyed this post!

If you did like the post then please check out our last two posts:

Nuclear Power: What is it and why is it important. (Fusion + Fission) – We take a look at the mechanics behind the power source of 18% of the world’s energy.

Matter and Antimatter: Why hasn’t the whole universe exploded? - When they come together, matter and antimatter explode, so why hasn’t that happened to the whole universe?

### Appendix

When calculating the distance santa travelled, I thought of 160 separate rings equal distance apart around earth. I assumed the earth to a perfect sphere, though I know it isn’t, as this makes the calculation easier and does not corrupt the results very much.

The equation of each radius is simple. We use Pythagoras:

Where ro is radius of the earth and n is the number ring it is, where the equator is 0, the north pole is 80 and the south pole is -80.

The circumference of all of these rings is therefore the sum of all of them from ring -80 to ring 80 times by 2 pi:

Inputting the radius of the earth, 6371 Km, we get our distance.

Here is how we worked out the drag:

Key

Those are the main calculations that I did, however, if you want to look at others such as details on the oats and look at our sources, download the excel spreadsheet I used for this:

Calculations