Our basic time-and-motion analysis starts off by telling us that there are roughly 2 billion children under the age of 18 in the world. This makes for a huge delivery task, but luckily for Santa, only about 15% of the children are Christian. So Santa does not visit Muslim, Hindu, Shinto or Buddhist children, but only some 380 million Christian children. On average there are 3.5 children living in each household, so Santa has to visit about 108 million separate homes.
If you work out the maths, Santa does not have a lot of time to deliver the presents. Luckily for Santa, the Earth rotates, and there are 24 different time zones. So if Santa travels from East to West, Christmas Day lasts for 31 hours. That works out roughly to 1,000 visits per second to the Christian households. So in a whole thousandth of a second, Santa has to park the reindeer and the sleigh, slip nimbly down the chimney, fill the stockings, neatly scatter whatever presents are left over under the tree, eat the lollies that have been left out for him, and get back up the chimney into the sleigh and then to the next house. That's a lot of stuff to do in just one thousandth of a second.
According to the numbers, Santa has to travel very quickly between the households. Now let's assume that these 108 million Christian households are evenly scattered around the Earth. That means that there are about 1.25 kilometres between each household, so Santa has a total trip length of about 120 million kilometres. Unfortunately, this means that his average speed is around 1,000 kilometres per second, or roughly 3,000 times the speed of sound.
So not only does Santa have a very short delivery time at each house (one thousandth of a second), he has to travel very rapidly between each delivery - about 1,000 kilometres per second. But if the speed of Santa's sleigh is one problem, so then is his payload. Suppose each kid gets about one kilo of presents. Then the sleigh is carrying around 400 thousand tonnes of presents. Now reindeer are not very good at pulling more than about 150 kilos. So Santa needs around 360,000 reindeer, which would weigh another 50,000 tonnes, giving us a total mass of (very roughly) half-a-million tonnes.
Now if you have half a million tonnes travelling at about 1,000 kilometres per second, you've got enormous wind resistance. The lead pair of reindeer would have to deal with some 15 quintillion joules of energy each second. No wonder they call him Rudolf, the red-nosed reindeer, as this enormous amount of energy would not only immediately make the lead reindeer burst into flames, as well as vaporising the entire reindeer team and the half-million tonne sleigh with Santa and the presents within a few thousandths of a second - but it would create sonic booms that would deafen everyone within about 50 kilometres, and enormous shock waves that would flatten every tree and building within 50 kilometres.
But on the other hand it wouldn't really matter, because Santa would be decelerated by the wind resistance from 1,000 kilometres per second to a dead stop in about a thousandth of a second, so our jolly 125-kilogram Santa would be thrown forward onto the vaporised reindeer with the equivalent weight of some 2 million kilograms, turning him into a thin red layer of protoplasm that would be destroyed by the expanding shock wave. Luckily, Santa Claus has lots of Little Franchisee Helpers (called parents) all around the world who turn his Vision Statement into World's Best Practice - otherwise Santa Claus would be a very Splattered - oops!, a very Sad Cause.
Great Moments In Science.