Santa: Math and Science

NORAD has for many years maintained a Christmas Eve tradition of tracking Santa by satellite as he allegedly travels around the world. What began as a clever spoof has evolved in to a major operation, with volunteers manning the phones to… yes, wait for it… LIE to children. Sigh!

We can’t even trust the scientists to be truthfully scientific any more. Is this harmful? I think it is always wrong to lie, especially to lie to children; but as a culture we have moved so far beyond any logical or ethical consistency in separating fantasy and “truth”  that I suppose this playing along with the myth can’t do any more harm.

Maybe they’ll even learn a bit of geography!

Let’s hear what the mathematicians think…

Santa Claus: Fact or Fiction?

Does Santa Claus really exist? And if he does, how does he manage the seemingly impossible task of delivering presents to the world’s Christmas-celebrating good little girls and boys in a single chilly December night?

The question has stirred the imagination and emotions of much of the Earth’s population and calls for an objective analysis.

Santa’s first obstacle is that no known species of reindeer can fly. However, scientists estimate that out of the earth’s roughly 2 million species of living organisms. About 300,000 or so have yet to be classified. So, even though most of these undiscovered species are insects and germs, we can’t rule out the slight possibility that a species of flying reindeer does, in fact, exist. And that no one besides Santa has ever seen one.

A bigger obstacle for Santa is that there are 2 billion children under the age of 18 in the world. Fortunately, Santa needs to deliver presents only to those who have been good. But at an average rate of 3.5 children per household, Santa has back-breaking 91.8 million homes to visit on any Christmas Eve.

Thanks to the rotation of the earth, Santa has 31 hours of Christmas Eve darkness to visit all these homes if he travels from east to west. But, this still works out to 822.6 visits per second! So, for each household, Santa has just over a thousandth of a second to land, hop out of his sleigh, jump down the chimney, fill the stockings, distribute the rest of the presents under the tree, eat whatever snacks have been left out, get back up the chimney, climb back on the sleigh, and take off and fly to the next house.

How fast is Santa moving? Assuming all 91.8 million stops are spread evenly over the earth’s landmass, Santa must travel 0.79 miles per household—a total trip of 72,522,000 miles. Given the 31-hour time period, Santa’s sleigh must maintain an average speed of 650 miles per second, or more than 3,000 times the speed of sound.

Let’s take a closer look at Santa’s vehicle. First of all, assuming a not overly generous 2 pounds of presents per child, the sleigh must still be able to carry a load of 321,000 tons—and an overweight Santa. On land, a reindeer can’t pull more than 300 pounds of freight, and even assuming that flying reindeer could pull 10 times that amount, Santa’s massive sleigh has to be drawn by 214,200 beasts. Assuming a mean length between harnesses (at 2 abreast) of 6 feet, they would create a chain approximately 121.7 miles long and increase the weight of the overall Santa payload to 353,430 tons.

As for Santa, he will be subjected to centrifugal forces 17,500.06 times greater than gravity. A 250-pound Santa will be pinned to the back of his sleigh by 4,375.015 pounds of force (after we deduct his weight).

Now, 350,000 tons of reindeer (and presents) is going to create an enormous amount of air resistance – especially at 650 miles per second. This air resistance will heat the reindeer such that the lead pair of reindeer will absorb 14.3 quintillion joules of energy per second each, causing them to ignite almost instantly, thereby exposing the reindeer behind them to the thermal blast. All 214,200 reindeer will be vaporized within 4.26 thousandths of a second!

So even though the existence of Santa Claus may seem highly improbable, especially to clever folks like WordPress bloggers, we continue to hold out the hope that Santa is as much as part of reality as we are.

And if Santa does exist, and if he dares to step onto his sleigh and take to the night skies this Christmas Eve, we suspect he’ll have enough of an adventure to last another 364 days.

From a blog with lots of interesting material about Christmas… 

I especially enjoyed Barbie’s letter to Santa!

And LogosConCarne also posted an interesting rebuttal on the proposition that Santa is a Woman