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An engineer’s view of Santa Claus

By Murray Bourne, 18 Dec 2012

Here's some Christmas fun. It's an analysis of Santa's amazing Christmas Eve journey each year.


Santa = ho^3

1) 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 which only Santa has ever seen.

2) There are 2 billion children (persons under 18) in the world. BUT since Santa doesn't (appear) to handle the Muslim, Hindu, Jewish and Buddhist children, that reduces the workload to 15% of the total - 378 million according to Population Reference Bureau. At an average (census) rate of 3.5 children per household, that's 91.8 million homes.

One presumes there's at least one good child in each.

3) 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 822.6 visits per second. This is to say that for each Christian household with good children, Santa has 1/1000th of a second to park, hop out of the sleigh, jump down the chimney, fill the stockings, distribute the remaining presents under the tree, eat whatever snacks have been left, get back up the chimney, get back into the sleigh and move on to the next house.

Assuming that each of these 91.8 million stops are evenly distributed around the earth (which, of course, we know to be false but for the purposes of our calculations we will accept), we are now talking about 1.26 km per household, a total trip of 121.5 million km, not counting stops to do what most of us must do at least once every 31 hours, plus feeding and etc.

This means that Santa's sleigh is moving at 1,000 km per second, 3,000 times the speed of sound. For purposes of comparison, the fastest man- made vehicle on earth, the Ulysses space probe, moves at a poky 44 km per second - a conventional reindeer can run, tops, 24 km per hour.

4) The payload on the sleigh adds another interesting element. Assuming that each child gets nothing more than a medium-sized lego set (1 kg), the sleigh is carrying 321,300 tonnes, not counting Santa, who is invariably described as overweight. On land, conventional reindeer can pull no more than 135 kg. Even granting that "flying reindeer" (see point #1) could pull TEN TIMES the normal anoint, we cannot do the job with eight, or even nine.

We need 214,200 reindeer. This increases the payload - not even counting the weight of the sleigh - to 353,430 tonnes. Again, for comparison - this is four times the weight of the Queen Elizabeth.

5) 353,000 tons traveling at 1000 km per second creates enormous air resistance - this will heat the reindeer up in the same fashion as spacecraft re-entering the earth's atmosphere. The lead pair of reindeer will absorb 14.3 QUINTILLION joules of energy. Per second. Each.

In short, they will burst into flame almost instantaneously, exposing the reindeer behind them, and create deafening sonic booms in their wake. The entire reindeer team will be vaporized within 4.26 thousandths of a second.

Santa, meanwhile, will be subjected to centrifugal forces 17,500.06 times greater than gravity. A 110 kg Santa (which seems ludicrously slim) would be pinned to the back of his sleigh by 1.9 million kg of force. In conclusion - If Santa ever DID deliver presents on Christmas Eve, he's dead now.

(Story originally attributed to Richard Waller)

Happy Christmas, everyone.

See the 8 Comments below.

8 Comments on “An engineer’s view of Santa Claus”

  1. Joseph says:

    1.9 million kg of force? That does not make sense at all. Force as we all know is measured in Newtons or Pounds. The mass of said Santa would be 110 kg independent of his velocity.

  2. Murray says:

    @Joseph - Actually, the unit is OK. It refers to the kilogram-force, that is the force exerted by 1 kg acted on by Earth's gravity. So the force referred to here is actually equivalent to 1.9 × 9.8 = 18.6 million N.

    "Pounds" of thrust is a similar concept. It's the amount of force needed to keep a one-pound object stationary against the force of gravity.

  3. Daniel says:

    Number one item:

    No one has seen the Big Foot but everybody says it exists, maybe the reindeer exist too

  4. wamriew says:

    that's very interesting. the conclusion of the calculations implies therefore that santa do not exist and if he does he is infinite.
    Merry Christmas to you all

  5. Philip Petrov says:

    Who told you that Santa Claus is working in our time dimension? What if our time is running much, much, much more slower than his?

  6. Smart Chick says:

    But aren't there multiple Santas? There's at least one on every corner in NY. 🙂 They share the load and it all works out.

  7. Duke says:

    Then, If you consider Santa utilizing some quantum physics vectors then the above exercises in mass, speed, weight and time itself are meaningless. He will be perfectly capable of being in all the homes at the same moment. (As long as nobody looks at him.) The Vacuum of Space is not as empty as one might think. In fact, empty space is a bubbling soup of various virtual particles popping in and out of existence -- a phenomenon called "vacuum fluctuations." A one pound box of Legos would be challenging since they'd currently only exist for a fraction of a femtosecond.

  8. Murray says:

    @Duke: Thanks for the bubbling Santa soup image!

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