Santa Claus. The mystic god of present giving. How can this one man supply presents to the entire world? There has been much debate from scholars and academics alike about the plausibility of his existence. Some even say he may not exist. It is time for us to investigate the engineering and science around Santa, and try to separate facts from fiction this Christmas.

## Distance Travelled on Christmas

It is hard to quantify the number of households Santa has to visit on Christmas, or indeed the distance he has to travel. To get a good estimate, we need to make some assumptions. First, let’s calculate the number of kids Santa has to visit. Let’s assume a standard family consists of two parents, two grandparents and 3 children, coming to 7 in total. Then let’s assume Santa only gives gifts to children (because us adults are too old to believe in Santa apparently…). From the Earth’s population of 7.4 billion, divided by the average family size of 7, gives us 1.06 billion households. Now let’s assume Santa only visits Christian households and 50% of non-religious households (Christmas has always been a mid-winter pagan festival after all). According to Wikipedia, 31.5% of the Earth’s population is Christian, whilst 15.35% is non-religious. Therefore 1.06 billion x 31.5% x 15.35%/2 = 256 million households.

Now we need to quantify the distance this equates to. Let’s assume the planet surface area equals to 510 million km². 510/256 gives us 1 house per every 2km², giving us an average 1.41km between houses. 1.41 x number of houses (256 million) gives us 360 million km for Santa to travel. If Santa is smart he will have 32 hours to work with over one night. Assuming he does not stop all night, he will need to travel 11,280,000 km/hr or 3,100,000 m/s. It is less than the speed of light (300 million m/s) so it is physically possible, but still a tall order.

## Sleigh Weight and Energy Required To quantify the energy required to travel this speed, we also need to enumerate the weight of the sleigh. 256 million households with an average of 3 kids mean Santa will need to carry 768 million gifts. In times gone these gifts may have been toy cars, doll houses or games. But times have changed; let’s assume that he is getting every child a PS4. An average PS4 weighs 2.18 kg, that means the total gift weight of the sleigh will be 1.674 billion kg. We also have to consider the weight of fuel and the weight of the sleigh structure to handle the goods weight, so let’s multiply this number by 4 as a conservative estimate of the total weight of the sleigh. That comes to 6.7 billion kg. This is, of course, neglecting the relativistic increase in mass caused by the incredibly high speeds.

To calculate the energy required, we must calculate ‘work done’. This is equal to force x distance travelled. Force is mass x acceleration. Let’s assume the acceleration is 1% of the total speed, giving an acceleration of 31,000 m/s². Force therefore equals to 6.7 billion kg x 31000 m/s² = 21×10¹³N. This multiplied by distance travelled in meters gives 750 x10²³ J of energy. To put that in perspective, the sun emits 3800×10²³ J of energy in one hour. 