Christmas Warning
http://fare.livejournal.com/174589.html :
Let's assume Santa visits all NYC households with children at midnight, delivering a measly average of .2 kg of toys at each place. With 30% of 3 million households having children, that's 9e4 stops. Assuming the households more or less equidistributed over the 4e8 m^2 area of city, a circuit to cover them with 9e4 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) = 6e6 m. Let's assume one order of magnitude savings because of non equidistribution, so only 6e5 m, to cover in 60s. Therefore the average speed of Santa, assuming instant stops, is 1e4 m/s. The average weight of toys he has to carry is 9e4*.2/2 kg = 9e3 kg. So his kinetic energy while traveling is .5 * 9e3 * (1e4)^2 J = 4.5e11 J. But since he has to stop and resume 9e4 times, the total energy released in the air while decelerating alone is 9e4 * 4.5e11 J = 4e16 J, which is a hundreds of times worse than the Hiroshima Bombing, except directly delivered to households with children. I recommend you not be in town or anywhere near children at midnight on this (or any) Christmas.
Let's assume Santa visits all NYC households with children at midnight, delivering a measly average of .2 kg of toys at each place. With 30% of 3 million households having children, that's 9e4 stops. Assuming the households more or less equidistributed over the 4e8 m^2 area of city, a circuit to cover them with 9e4 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) = 6e6 m. Let's assume one order of magnitude savings because of non equidistribution, so only 6e5 m, to cover in 60s. Therefore the average speed of Santa, assuming instant stops, is 1e4 m/s. The average weight of toys he has to carry is 9e4*.2/2 kg = 9e3 kg. So his kinetic energy while traveling is .5 * 9e3 * (1e4)^2 J = 4.5e11 J. But since he has to stop and resume 9e4 times, the total energy released in the air while decelerating alone is 9e4 * 4.5e11 J = 4e16 J, which is a hundreds of times worse than the Hiroshima Bombing, except directly delivered to households with children. I recommend you not be in town or anywhere near children at midnight on this (or any) Christmas.