Twelve or thirteen years ago, young Dean was browsing some bookstore and happened upon The Physics of Christmas: From the Aerodynamics of Reindeer to the Thermodynamics of Turkey by Dr. Roger Highfield. Had to have it of course. I like to bring it out around Christmas, usually after a couple drinks, and find my favorite couple pages. The nerd in me comes out and I giggle a bit.
In my first Holiday Blog Post That’s Mostly Me Plagiarizing Someone Else, I share with you selections from pages 241-244 of said book. (Wait, it’s not plagiarism if I credit the author… Need another drink. Happy Holidays. Be Merry.) Enjoy!
Santa’s Challenge
Santa has a huge market. There are 2,106 million children under age eighteen in the world, according to the United Nations Children’s Fund (UNICEF). Given the pagan origins of the festival and the holiday’s emphasis on charity, I will assume that Santa delivers presents to each and every child, and not just to Christian children or to the 191 million who live in industrialized countries. It is Christmas, after all.
If we assume that there are 2.5 children per household, Santa has to make 842 million stops on Christmas Eve. Now let’s say these homes are spread equally across the landmasses of the planet. Earth’s surface area is, given a radius of 3,986 miles (6,378 kilometers), 196.6 million square miles. Only 29 percent of the surface of the planet is land, so this reduces the populated area to 57.9 million square miles. Each household covers an area of 0.069 square miles. Let’s assume that each home occupies a square plot, so the distance between households is the square root of the area, which is 0.26 miles.
Every Christmas Eve Santa has to travel a distance equivalent to the number of chimneys – 842 million – multiplied by this average spacing between households, which works out to be 221 million miles. This sounds daunting, particularly given that he must cover the entire distance in one night.
Fortunately, Santa has more than twenty-four hours to deliver the presents. Consider the first point on the planet to go through the international date line at midnight on December 24. From that moment on, Santa can pop down chimneys. If he stayed right there, he would have 24 hours to deliver presents to everyone along the date line. But he can do better by traveling backward against the direction of Earth’s rotation. That way he can deliver presents for almost another 24 hours to everywhere else on Earth – making 48 hours in all, which is 2,880 minutes or 172,800 seconds.
From this one can calculate that Santa has a little over 2/10,000 second to get between the 842 million households. To cover the total distance of 221 million miles in this time means that his sleigh is moving at an average of 1,279 miles per second. Ignoring quibbles about air temperature and humidity, the speed of sound is something like 750 miles per hour, or 0.2 miles per second, so Santa is achieving speeds of around 6,395 times the speed of sound, or Mach 6,395.
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The preceding discussion assumes that Santa throws the presents down each chimney while whizzing overhead. In fact, he stops at each house, so he has to achieve double the speed calculated above. From a standing start, he has to travel the distance between houses in 2/10,000 second. That means going from 0 to 2,558 miles per second in 2/10,000 second, an acceleration of 12.79 million miles per second per second, or 20.5 billion meters per second per second.
The acceleration due to gravity is a mere 9.8 meters per second per second, so the acceleration on Santa’s sleigh is equivalent to about 2 billion times that caused by the gravitational tug of Earth. Given that Santa is somewhat overweight, say around 200 kilograms, the force he feels is his mass times his acceleration: around 4,000 billion newtons. Even fighter pilots can’t cope with accelerations more than a few times that of gravity, and they have to use special breathing techniques and G (gravity) suits to keep the blood in their heads. As the physics professor Lawrence Krauss puts it, the acceleration Santa has to cope with would normally reduce a person to “chunky salsa.”
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There is one other problem Santa has to contend with: his cargo. Assuming that each of the 2,106 million children gets nothing more than a medium-size construction set (2 pounds, or 0.9 kilograms), he has a payload of 4,212 million pounds (about 2 million tons), or 1,895 million kilograms, of toys. Then there is the supply of fuel required to achieve the high speeds he must maintain. Any way you look at it, Santa has some serious hurdles to overcome.
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