An Engineering Perspective on Santa Claus

Yes Virginia, there is a Santa Claus (and he was obviously a quantum physics major at M.I.T.)

Children (and some adults) often ask very hard questions when it comes to Santa Claus and his physics-defying Christmas Eve journey. Catalyst would like to offer up some reality-based science to Santa’s trip so those little inquiries are not so difficult to answer. 

How does Santa visit all the children of the world in one night?

There are approximately 2 billion children (persons under 15) in the world. However, assuming that Santa does not visit children of all faiths, this reduces his workload for Christmas night to 15% of the total, or approximately 378 million kids.

At an average (census) rate of 3.5 children per household that comes to 108 million homes, assuming there is at least one good child in each. Santa has about 31 hours of Christmas to work with, thanks to the different time zones and the rotation of the earth, assuming he travels east to west. This works out to 967.7 visits per second. This means that Santa has around 1/1000th of a second to park the sleigh, hop out, jump down the chimney, fill the stocking, distribute the remaining presents under the tree, eat whatever snacks have been left for him, get back up the chimney, jump into the sleigh and get onto the next house.

If we assume that each of these 108 million stops is evenly distributed around the earth (though we know they are not), we are now talking about 0.78 miles per household or a total trip of 75.5 million miles. This means Santa's sleigh is moving at 2,340,000 miles per hour, which is 3,075 times the speed of sound. For purposes of comparison, one of the fastest man-made objects, the New Horizons space probe, achieved 36,373 miles per hour, and a conventional reindeer can run (at best) 15 miles per hour.

How heavy is Santa’s sleigh?

The payload of the sleigh adds another interesting element. For purposes of calculation, we will assume that there are no lumps of coal on board and that the snacks left for Santa are completely consumed by his metabolic rate due to his high activity level and, thus, no additional weight is gained. Assuming that each child gets nothing more than a medium sized LEGO set (two pounds), the sleigh will be carrying over 500,000 tons, not counting Santa himself. 

Can reindeer really fly?

No known species of reindeer can fly. But there are 300,000 species of living organisms yet to be classified, and while most of these are insects and germs, this does not completely rule out flying reindeer. On land, an average sized reindeer weighing 500 pounds can pull no more than 300 pounds.  Assuming that "flying" reindeer can pull 10 times the normal amount, the job can't be done with eight (or even nine if Rudolf is involved) -- Santa would need 360,000 of them which increases the payload by another 180 million pounds to just under 600,000 tons, or roughly six times the weight of a cruise ship.

600,000 tons traveling at 650 miles per second creates enormous air resistance - this would heat up the reindeer in the same fashion as a spacecraft reentering the earth's atmosphere. The lead pair of reindeer would adsorb 14.3 quintillion joules of energy per second each. In short, they would burst into flames almost instantaneously, exposing the reindeer behind them and creating deafening sonic booms in their wake (which might explain the “clatter” from the lawn…). The entire reindeer team would be vaporized within 4.26 thousandths of a second, or right about the time Santa reached the fifth house on his trip.

Not that it matters, however, since Santa, as a result of accelerating from a dead stop to 650 miles/second in .001 seconds, would be subjected to acceleration forces of 17,000 g's. A 250 pound Santa would be pinned to the back of the sleigh by 4,315,015 pounds of force, instantly crushing him.

On second thought, let’s just go with MAGIC!

Thankfully, Santa is a magical being and not bound to the laws of science. As Arthur C. Clark once quoted, "Magic is just science that we don't understand yet."

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