Santa Claus

The logistics and physics of his delivery service

The logistics of Santa's delivery service:

Joel Potischman and Bruce Handy (and others) computed certain speed and payload performance criteria for Santa's sleigh. ₁ Unfortunately, they based their calculations on an incorrect estimate of the numbers of Christians in the world. The following are believed to be a more accurate calculation. It is based on a number of assumptions:

	Santa delivers no gifts to naughty children. There is a tradition in some areas of the world that a naughty child receives a lump of coal. That would change the calculations slightly.
	Only one Santa distributes all of the gifts. Multiple Santas could reduce some of the extreme values calculated below. However, NORAD regularly reports only one sleigh tracked on their radar screens each Christmas eve from the North Pole.
	There is only one family per household.
	Santa bypasses Buddhist, Hindu, Muslim, and other non-Christian homes.
	The percentage of households in which there is at least one child who has been not naughty, but was nice is 90%.
	Santa loads all of the presents before starting his journey. i.e. he does not return to the North Pole periodically to reload. This is probably correct, because NORAD has never reported any return and repeat trips.

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Calculations follow:

	Amount of time Santa spends per household: Number of humans in the world: 6.0 billion. Number of children (humans under 18 years of age) about 2.0 billion. Percentage of children whose parents are Christian: 33%. Maximum number of children who might receive gifts: 667 million. Average number of children per household: 3.5 Number of destinations where Santa might deliver presents: 189 million. Number of destinations for Roman Catholic and Protestant families: 173 million. (The remainder are Eastern Orthodox locations which Santa would handle in his second trip on JAN-5. The Eastern Orthodox church has not yet adopted the Gregorian calendar; the current gap between the calendars is 12 days and expanding). Total number of destinations where Santa delivers gifts: 156 million. Santa cannot arrive until the children are asleep. Some people suggest that he start to distribute presents in each time zone at perhaps 9 PM local time, finish within an hour, and then move one time zone to the west. But that is a higher level of performance than is really needed. He could take longer in each time zone, as long as the entire job was finished comfortably before children woke up in the last zone. Assuming that the children sleep for 7 hours, this gives him 31 hours (or a total of 1860 minutes, or 111,600 seconds) to finish all deliveries. Average number of homes to visit per second = 1,398. This only gives him about 715 microseconds in which to decelerate the sleigh, land on the roof, walk to the chimney, slide down the chimney, distribute the presents and retrace his steps. Adjustment for special circumstances: If one considers that: Santa's competitor Befana distrubtes gifts in Italy. Santa distributes some gifts on Boxing Day (DEC-26) to poor children in some British Commonwealth countries. Santa distributes some gifts in bulk quantities to orphanages, children's hospitals etc. before Christmas. Sinter Klass distributes some gifts on DEC-5 to children in Belgium, Germany and Holland. then the average number of homes to visit per second on Christmas Eve is only perhaps 1,000. He would deliver gifts to about 500 million children.
	Ddistance traveled: Assuming that Antarctica is essentially uninhabited, and ignoring the various inland lakes, the total inhabited land on earth is about 79.3 million square miles. 2 Assuming that the destinations are evenly distributed over the available land, the average distance between destinations is on the order of 0.71 miles. Total distance traveled =  111 million miles -- a little longer than the distance from the earth to the sun!
	Average speed of sleigh: 111 million miles over a 31 hour interval = 3.6 million miles an hour, or a little under 1000 miles a second. This is the average speed of the sleigh. Some time is taken to decelerate the sleigh to a stop, for Santa to deliver the presents, for him to return to the sleigh and for the sleigh to accelerate to cruising speed. The latter would be on the order of 2000 miles a second. Potischman and Handy estimated that at a lower speed of 650 miles a second, air resistance would cause the lead reindeer to absorb 14.3 quintillion joules of energy per second. We are not familiar with the effects of such a high energy loading. However, we intuitively feel that the reindeer would be converted almost instantly into charcoal without magical protection.
	Payload: Potischman and Handy estimated the weight of the average toy to be 2 pounds. The sleigh would thus have to carry about 1 billion pounds or 500,000 tons of cargo for the 500 million children. At perhaps 0.2 cubic feet per toy, the payload would occupy a space of 100 million cubic feet.
	Summary: Santa would visit perhaps 1,000 homes per second. The average speed of the sleigh would be on the order of 3.6 million miles an hour. This would be a sufficient speed to allow travel to the moon in about 4 minutes, except that the reindeer need a steady supply of oxygen.) The acceleration and deceleration loads on the reindeer, Santa and the sleigh would be astronomical. The sleigh would carry about 500,000 tons of cargo, many times the weight of the Queen Mary. The sleigh would carry about 100 million cubic feet of cargo, about equal to 4,500 homes.

	Santa Claus does not exist, except as a symbol or a myth. Some adults believe this, but most young children do not.
	Santa Claus has magical, near god-like powers. This is part of the Santa tradition: From his location at the North Pole, he sees the children  when they are sleeping. He knows when they are awake. He knows they are bad and good. There is even a tradition that he can travel up the chimney with near-infinite speed by simply rubbing the side of his nose.

Links to other scientific calculations are at references 3 &4 below.

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References used:

The following information sources were used to prepare and update the above essay. The hyperlinks are not necessarily still active today.

1. Joel Potischman & Bruce Handy, "Is there a Santa Claus," at: http://www.ucl.ac.uk/ 
2. "The MacMillan Visual Desk Reference," Macmillan, (1993)
3. "Santa Claus: An engineer's perspective," at: http://www.baltimoremd.com/
4. Alice Deal Junior High School Mathcounts Team, Washington DC, "Mathematics of Santa Claus," at: http://www.nifl.gov/ {Web site is no longer online]

Copyright � 1999 to 2015, by Ontario Consultants on Religious Tolerance
Originally written: 1999-DEC-24
Latest update: 2015-OCT-24
Author: B.A. Robinson

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