, there are about 526 million children under the age of 14 who are due a visit from Santa on Christmas Eve. At an average of 3.5 children per home, that's about 150 million households, assuming at least one good child in each.
Santa has 31 hours of Christmas Eve to work with, thanks to the different time zones and the rotation of the Earth (assuming he travels east to west, which seems logical). This works out to 1,344 visits per second. Per household, then, Santa has less than 11,400th of a second to park, hop out of his sleigh, jump down the chimney, fill the stockings, distribute the remaining presents under the tree, eat whatever snacks have been left, get back up the chimney, into the sleigh and travel to the next house. This would be impossible for Usain Bolt, let alone a man of considerable girth.
It's quite a long way
Let's assume that each of these 150 million stops is evenly distributed around the surface area of the Earth. If we do so, we can calculate the distance Santa has to travel as follows:
Area of a sphere = 4R
Where R = radius of Earth: 6,371km
So Area = 510 million km
But since about 70 per cent of the surface is covered with water, we actually have less land mass to work with. So we only have 153 million km. Divide this by our 150 million households and we have a house roughly every 1.02 km. This gives us a total trip distance of about 150 million km.
Santa would have to be pretty quick
This means that Santa's sleigh would need to move at a very high velocity:
Velocity = 150,000,000km31 hours = 4,839,000kmhr
That's 1,344kmsec. This is more than 3,900 times the speed of sound, so Santa would leave deafening sonic booms in his wake (so much for Silent Night).
For comparison, the fastest human-made vehicle (moving relative to Earth) is the New Horizons space probe bound for Pluto, which travels at 58,536kmhr.
But let's be charitable again. Although conventional reindeer can only run, tops, at about 24kmhr, maybe one of those undiscovered organisms we spoke about includes flying reindeer that can comfortably outrun a space probe. And maybe we are all so excited about Santa's arrival that we fail to hear the constant booms of his progress. But there are still problems.
The sleigh would need to be massive
The payload on the sleigh adds an interesting element to the whole idea. Assuming that each child gets nothing more than a medium-sized Lego set (0.908kg), the sleigh is carrying 477,608,000kg (or 477,608 metric tons), not counting Santa, who is invariably described as overweight.
On land, a conventional reindeer can pull no more than about 136kg. Even granting that flying reindeer exist and can pull 10 times the normal load, we cannot do the job with eight, or even nine. We need 350,670 reindeer.
Also, assuming an average reindeer mass of 170kg, this increases the payload to 537,220 metric tons - and that's not counting the mass of the sleigh itself.
That is more than six times the mass of the Queen Elizabeth (the largest cruise liner of its time, not the monarch it was named after).
This mass would be problematic
To have 537,220 metric tons travelling at 1,344kmsec would create enormous air drag, and the friction would heat up the sleigh like a spacecraft re-entering the Earth's atmosphere. The amount of energy dissipated as heat (assuming a nice, laminar flow) would be immense. We can do the calculation like this:
Pd = Fd v = 12 ?v3ACd
Where Pd = power (energy per second) dissipated Fd = force of air drag ? = the density of air: 1.2754kgm3 v = speed: 1,344kmsec or 1,344,000msec A = frontal area of reindeer and sleigh 4m Cd = drag coefficient (assuming a long cylinder) = 0.82
Putting all this together gives us:
Pd 5.08 x 1018 joulessec
For comparison, the largest nuclear weapon ever detonated - the Tsar Bomba - yielded about 2.10 x 1017 joules worth of energy. So Santa's sleigh would have to absorb more than 20 times the total energy output of the largest nuclear bomb ever detonated every second. In short, Santa and his entire reindeer team would be vaporised within the blink of an eye.
Acceleration would be problematic, too
Even if Santa had the mother of all heat shields to absorb and dissipate this astronomical amount of energy, he would still have to deal with some pretty testing forces that result from the rapid acceleration caused by starting and stopping so quickly between houses. Specifically:
Acceleration = ?v?t
Where ?v = change in velocity between starts and stops 1,344,000 msec
?t = time between starts and stops 11,400 sec
So the acceleration Santa would feel is 1.881x109msec
For reference, jet pilots are often said to experience "g-forces", where g is equal to about 9.8msec2 worth of acceleration. So it seems that Santa would experience roughly 192 million g of acceleration. The largest g-force ever experienced by a human being who survived the experience was 214 g.
So, if Santa wasn't immediately vaporised by the heat, he and his entire reindeer team would still be squashed into jelly by the force of acceleration.
Thus, in conclusion.
If Santa ever did exist and tried to deliver presents on Christmas Eve, he's definitely dead now. Happy holidays!
Matthew Lowry is a physics teacher at Lake Forest High School in Illinois, US. He blogs at www.skepticalteacher.org
For a scientific spin on festive spirit, give this quiz a try.
Keeping the magic of Christmas alive
Matthew Lowry makes a convincing case against Santa, but you may decide that the non-existence of Father Christmas is not something you want to share with your primary-aged students.
Fortunately, children's charity the NSPCC is on hand to help you to prove the opposite - that old St Nick really does fly around doing good on the 24 December.
For a suggested donation of pound;5, a child (or adult) can receive a personalised missive from Santa. Last year more than 300,000 letters were sent to children across the world from Santa's workshop at the NSPCC.
For most children, Christmas is the most carefree time of year. But this is not the case for thousands of young people across the UK.
In December 2013, the NSPCC's ChildLine service received more than 87,000 calls from children who needed help.
Santa's workshop is open until 15 December. For more information, visit www.nspcc.org.uksanta