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Christmas Warning!

Let's assume Santa visits all NYC households with children at midnight, delivering a measly average of .5 kg of toys at each place. With 30% of 3 million households having children, that's 9e5 stops. Assuming the households more or less equidistributed over the 7.8e8 m^2 area of city, a circuit to cover them with 9e5 stops, using either a linear scan or a fractal scan a la Hilbert Curve or Polya sweep has a length of the order of sqrt(surface*households) = 2.6e7 m. Let's assume one order of magnitude savings because of non equidistribution, so only 2.6e6 m, to cover in 60s. Therefore the average speed of Santa, assuming instant stops, is 4.3e5 m/s. If he carries all his undelivered toys all the time, the average weight of toys he has to carry is 9e5*.5/2 kg = 2.2e5 kg. So his kinetic energy while traveling is .5 * 2.2e5 * (4.3e5)^2 J = 2e16 J, which is that of an atomic bomb hundreds of time more powerful than the Hiroshima bomb. But since he has to stop and resume 9e5 times, this energy is released in the environment at every stop while decelerating and then again while accelerating, so the net result of the visit is a dissipation of energy of 2 * 9e5 * 2e16 J = 3.6e22 J, which is hundreds of thousands of times worse than the greatest nuclear weapon of all times, the Tsar Bomba, except directly delivered to households with children. Of course, all these numbers are lower bounds and constitute a very optimistic scenario. To be even more optimistic, let's suppose that Santa is even more clever, and actually makes intermediate stashes of toys that he manages to instantly load and offload, and arrange his circuit so that on each segment of his fractal path he only carries the toys for that destination; this way, he might reduce the average weight of toys to something of the order 1kg or so. Assuming he is himself a weightless elf and that so are his sleigh and reindeers, so that only the toys are physical objects subject to the law of physics, that's a hundred-thousand fold saving in energy, which brings us back to only a few Tsar Bombas. Again, delivered directly to households with children. I recommend you not be in town or anywhere near children at midnight on this (or any) Christmas.

Comments

That's brilliant! It looks like the evil Santa from Futurama is not that far from reality.

Christmas Warning

User dmytrish referenced to your post from Christmas Warning saying: [...] http://fare.livejournal.com/174589.html [...]
By stashing half his toys half way, then half of what's left, etc., in log(N,2) stashes, Santa can greatly reduce the average weight he carries, and thus his kinetic energy. Instead of N*W, he only carries an average of log(N,2)*W around, and though the distance he has to go is slightly longer, this is more than compensated by the reduced weight while travelling, and the much shorter trip while carrying heavy gear. The energy saving is a factor about a hundred or more, which brings down the energy dissipation to a single Hiroshima bombing — delivered directly to where children live.
Brilliant and a good laugh, thank you!

However, with some math challenged readers (like myself) this calculation raises questions.

900,000 households (30% of 3,000,000) is 9e5, not 9e4; assuming, of course, e stands for "times ten raised to the power of" (does it?)

Further, Wikipedia (mostly accurate) tells us that the area of NYC's *land* is 784 km2, which gives us the area of 7.84e8 m^2, or almost twice as much as Santa's chief scientist would have us think.

Now, calculating sqrt(surface * households) we get the length of circuit that is about 4 times of the original estimate, i.e. 26.5e6 m.

Santa now has 26.5e5 m to cover in 60 s. Therefore the average speed of Santa, assuming instant stops, instant chimney travel, instant gifts-to-socks delivery and instant take-off (oh, the poor deers), is 26.5e5/60 = 4.4e4 (again, much higher than the original estimate).

The average weight of toys, then, is 9e5*.2/2 kg = 9e4 kg, and the kinetic energy is .5 * 9e4 * (4.4e4)^2 J = 1.98e13 J. Deceleration in the air energy release becomes 9e5 * 1.98e13 = 1.78e19 J.

The mostly accurate one also tells us that Little Boy released 15 kilotons of TNT equivalent, which, one ton of TNT being equal to 4.184e9 J, gives us 0.63e14 J.

So Santa's deceleration is *hundreds of thousands* (just shy of 3e5) of times worse than the Hiroshima Bombing, wouldn't you agree?

I'd rather not be on the planet, not to mention anywhere near the U.S., were Santa to deliver gifts this way.

Also, all of this is stuff for xkcd's what-if blog; we should have also taken in account Santa's instant accelerations which not only require massive amounts of energy, but also generate massive amounts of heat as the sleigh compresses the air up ahead. Other effects might include changes to Earth rotation and orbit, as well as time anomalies.

If you do exist, you *are* a dangerous guy, Santa.

Thanks for the correction!

Indeed, you caught glaring underestimations in my data. On the other hand, Santa could have improved his strategy to carry fewer toys at once. I have revised the numbers. We're still at a few Tsar Bombas worth of released energy.
By comparison, a baseball accelerated to .9c is only 148g * c^2 * (1-.9^2)^(-1/2) ~ 3.1e16 J. https://what-if.xkcd.com/1/
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