The Science of Santa
By John Michael Keller
Based on an original letter in the US Skeptic 2(3), 6-7, 1994, here updated and converted into metric equivalents.
Thanks to time zones, and assuming travel is east to west (which seems logical), Santa has a maximum of 31 hours in which to visit every good child. So he needs to average 130 million / 31 hours = 4.2 million home visits per hour or 1160 per second. This means that for every home with a good child, Santa has less than 1/1000th of a second in which to park, jump down the chimney, distribute presents, eat the snacks left for him, get back up the chimney, and move on to the next home. Your camera will need a fast shutter speed.
Again, to keep it simple, assume that these 130 million homes have the same average density as homes in the USA (10 per sq km), which means that on average the homes are (1/10)0.5 = 0.32 km apart. However, only one-third of the Earth is land, which will increase the average distance apart to 3 x 0.32 = 1.0 km. So Santa has to travel a total of 130 million x 1.0 = 130 million km in 31 hours, not counting stops for reindeer games etc.
In other words Santa's sleigh has to average 130 million / 31 = 4.2 million km per hour or 1160 km per second, which is roughly 1160 / 0.344 = 3370 times the speed of sound and 1160 / 300,000 = 1/250th the speed of light. For comparison, the fastest space probe moved at a poky 44 km per second. A conventional non-Santa reindeer can reach 24 km per hour, at which speed it would take 130 million / 24 = 5.4 million hours or 615 years to reach every good child. Yes, flying at Mach 3370 is quicker. However, the acceleration needed to reach 1160 km per second in less than 1/1000th of a second is more than 1160 x 1000 / 0.0098 = 118 million g, so Santa has to hold on tight.
What payload is the sleigh carrying? Assuming that each child gets no more than a medium-sized set of Lego weighing 2 kg, the sleigh at lift-off is carrying 2 x 130 million kg or 260,000 tonnes, not counting Santa, who is traditionally described as overweight (perhaps inevitably after 130 million snacks). On land a conventional reindeer can pull about 150 kg or 0.15 tonne. Assuming that a flying reindeer can lift ten times this or 1.5 tonnes, to lift 260,000 tonnes Santa will need 260,000 / 1.5 = 170,000 flying reindeer.
Assuming each flying reindeer weighs 0.5 tonne, 170,000 will increase the total takeoff weight to nearly half a million tonnes, which is roughly five times the weight of the world's largest passenger cruise ship. Now half a million tonnes travelling at 1160 km per second will encounter the same enormous air resistance as a spacecraft re-entering the earth's atmosphere. The lead pair of reindeer will burst into flame almost instantaneously, exposing the next reindeer pair, and so on, creating a deafening sonic boom at the same time.
In no time at all the entire reindeer team, Santa, and 130 million presents will be vaporised in a huge fire ball. If for some reason the good children in your household received no presents this Christmas, that's why.