(Ken Cable compiled the following article for The Friday Flyer 10 years ago, at Christmas 2004.)
Ever since Virginia was assured in 1897 by New York Sun Editor Francis P. Church that there was, indeed, a Santa Claus, there have been those who question how, given the numbers of good children and the enormous weight of the gifts, Santa visits every house and child in one, magical night. An Engineer's Perspective (engineer unknown), circulating on the Internet, outlines in scientific and mathematical discourse, the physical and time constraints that give rise to doubt. A copy made its way into a large corporation and wound up on a project manager’s desk – a project manager who just happened to be my son. The perspective follows:
Santa's Challenge: An Engineer's Perspective
There are approximately two billion children (persons under 18) in the world, however since Santa does not visit children of Muslim, Hindu, Jewish or Buddhist religions, this reduces the workload for Christmas night to 15 percent of the total, or 378 million (according to the population reference bureau).
At an average (census) rate of 3.5 children per household, which comes to 108 million homes – presuming that there is at least one good child in each – Santa has 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 (which seems logical).
This works out to 967.7 visits per second. This is to say that for every Christian household with a good child, Santa has around 1/1000 of a second to park the sleigh, hop out, jump down the chimney, fill the stockings, 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 on to the next house.
Assuming that each of these 108 million stops (not counting bathroom breaks), are evenly distributed around the earth (which, of course, we know they won’t be), we will accept that number for the purpose of our calculations. We are talking about 1.25 kilometers per household (or a total of 120.8 million kilometers) to be traveled Christmas night.
This means Santa's sleigh is moving at 1040 km per second, or 3,000 times the speed of sound. For purposes of comparison, the fastest man-made vehicle, the Ulysses space probe, moves at a poky 43.8 km per second.
A conventional reindeer can run (at best) 25 km per hour. The pay load of the sleigh adds another interesting element. Assuming that each child gets nothing more than a medium Lego set (two pounds), the sleigh is carrying over 500 thousand tons, not counting Santa himself. On land, a conventional reindeer can pull no more than 300 pounds, even granting that the “flying” reindeer could pull ten times the normal amount, the job can’t be done with eight or even nine of them . . . Santa would need 360,000 reindeer.
This increases the payload, not counting the weight of the sleigh, another 54,000 tons, or roughly seven times the weight of the Queen Elizabeth (the ship, not the monarch.) Six hundred thousand tons traveling at 1040 km per second creates enormous air resistance. This would heat up the lead reindeer in the same fashion as space shuttle re-entering the earth’s atmosphere.
The lead pair of reindeer would absorb 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. 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 1040 kps in .001 seconds, would be subjected to centrifugal forces of 17,500 G’s. A 250-pound Santa (which seems ludicrously slim) would be pinned to the back of the sleigh by 4,315,015 pounds of force with the predictable result.
After considering this perspective my son, the project manager, responded with following:
"Wayfarer of the Extra-Dimensional Winds"
You are quite correct in assuming that I find this treatise interesting. However, this is perhaps for a different reason than you may expect. It is interesting in that it reveals how engineers often think in such a narrow fashion that they over look obvious solutions (understand that I know this about engineers firsthand.)
It is obvious to anyone who endeavors to look into the subject just how Santa accomplishes all of his annual philanthropic duties – and at leisurely pace to boot! Let me explain.
Santa very clearly has the ability to move two dimensionally through time. Think of a Cartesian coordinate system with both X and Y axes, where Midnight, December 24, Greenwich Mean Time (GMT) (Santa’s presumed hour of embarkation), is represented at X=0 and Y=0.
Moving to the right in the second Cartesian Quadrant, GMT will advance such that at 1 a.m. X will equal the value of 1, at 2 a.m. the value of 2, and so on.
Here is where it becomes interesting. Santa will not only move along the X axis in time. He will indeed move along the Y axis as well! He moves upward, still in Quadrant 2, along the Y axis so that to all of us observing Santa in the standard space-time perspective, he may appear to be everywhere at once. This is because there are an infinite number of points along the Y axis that he could choose to occupy while not necessarily moving forward on the X axis at all!
Think of your house as the first point on the Y axis, and then think of your neighbor’s house as the second point, your cousin's as the third, and so on. You can now easily see how our beloved beneficent barnstormer could visit every house on earth at the same time! Moreover, he could visit each house as many times as he chose. All of this makes clear several things:
• Santa is not constrained by the 31-hour rule, so the time restrictions in the engineer’s model become irrelevant.
• As Mr. Kringle may make any number of visits to each house, he could in fact return to the North Pole as often as necessary, making the reindeers’ task relatively light (if often repeated.) This obviates the issues of payload expressed in the engineer’s treatise.
• The points raised by the engineer concerning air resistance, energy dispersion and absorption, as well as the sad effect of G forces, are also nullified by the capacity for X/Y time advection (the ability to be everywhere at once).
The engineer’s sad, pre-mortem, conjecture is the product of a kind of one-dimensional thinking that should be abjured by its author and ignored by the reader. Everyone may indeed take heart that the jolly old elf continues as “Wayfarer of the Extra-Dimensional Winds” spreading joy to all that believe.
MerryChristmas! Jeff Cable, PhD, Project Manager, Strategic Alliances/IT