Christmas would not be Christmas without the jolly fat man. While I cherish Santa's contribution to the holiday, I have always been stymied to imagine how he does it, how he delivers all those packages.
I try to understand the magic that brings presents to people all over the world, dropped down chimneys and laid beneath the tree and I ponder the many questions that arise from that tradition:
Since Santa remains silent in his passing we know he does not exceed the speed of sound, he leaves no sonic boom in his wake. Thus Santa's maximum speed can never exceed the speed of sound: 343.2 m/s.
To achieve the monumental feat of reaching every home, Santa must then accelerate at an absolutely amazing rate, both upon reaching each home and again upon leaving.
Military experiments in the 1940s and 1950s determined that between 4 and 8 Gs will knock you out and that a human could slow down at a rate of 45 Gs and live to tell about it. So, remain breathing, an imperative to completing his appointed rounds, Santa must accelerate and decelerate no faster than, let's say, 40 Gs. That is still giving the big guy a lot of credit. But to finish his rounds he must take off and land each time at these kinds of accelerations.
Our approximation for acceleration time (T) we determined above might be as much as 0.87489766637945 seconds.
Acceleration due to gravity is 9.8 m/s², and at 40 Gs that translates into wrenching 392 `m/(s^2)`. So Santa can achieve maximum speed -- and here again, we assume the speed of sound -- in less than a second. To compute this time for your own assumption of acceleration and max velocity, CLICK HERE.
So, if Santa takes off and lands at max velocity just the number of times to travel between all the houses in the United States he would have to visit approximately 160 million households in just the united states (according to the census bureau). So, if he just accelerated and decelerated for each household in the United States (ignoring the rest of the world, the combined time of his take-offs and landings would be:
`T = 160,000,000 * 2 * 0.87489766637945 seconds = 279,967,253 "seconds"` or about 77,768 hour.
The explanation for how he can squeeze that time into a night eludes me. That is over 925 weeks!