Santa speed calculations and parcel tracking

I've been watching a parcel addressed to me being tracked across the globe from China over the last few days. It made good progress from Shanghai to Cologne but then seems to have slowed down a bit.

It reminded me of the Santa Calculations, which I first published back in 2006 and then updated in 2010. The world population has increased since my earlier calculations and I decided to use the 2012 world population estimate of 7.06 Billion instead of my prior calculation of 6 Billion.

To set the scene, here's the 2012 link to the Santa tracking system created by NORAD.

And my usual reminder that an ideal last minute gift is, of course, the rashbre novel - The Triangle, now also available as a Kindle download for around a dollar.

For those of you who are more interested in the technology of Santa, NORAD's FAQs provide the following:

I've again used the Joel Potischman and Bruce Handy calculations as the basis for the speed calculations, with my own adaptations:

The most notable corrections to be applied are:

- Santa delivers no gifts to naughty children (not even coal)
- Naughty to nice ratio is 1:9
- As confirmed by NORAD, one Santa distributes all of the gifts.
- There is only one family per household.
- Santa bypasses non Santa belief system houses.
- Reindeer have recently eaten fresh magic acorns.


Calculation Assumptions (2012):

- World population = 7.06 billion
- Children under 18 = 2.353 billion (Hmm may be higher)
- Global Santa based belief systems: 33%
- Max children requiring delivery therefore 784 million
- Children per household: 3.5 (may seem high?)
- Number of households requiring distribution 224 million
- Naughty to nice factor applied but not many all naughty households
- Remove all naughty households (25% 0f 10%) = 5.6 million
- Eastern orthodox using Jan 5 instead of Dec 25 = 16 Million
- Target Households = 202 million on Dec 25
- Estimated child bed time 21:00 (9pm) with 7 hours sleep.

(child sleep duration on Dec 24 may also require revision)

Gives circa 31 hours (24+7) for all deliveries
Time is 1860 mins or 111,600 seconds

Average number of homes to visit per second = circa 1810.
So average delivery per household is 552 milliseconds, which is why Santa normally appears a bit blurry (I previously thought it was the sherry)

Land surface minus Antarctica is around 79 million square miles. Distribute destinations evenly = 0.7 miles between households creating a total distance of circa 110 million miles.

So 110 million miles in 31 hours = 3.6 million miles an hour or circa 1000 miles per second or Mach 4770 at a linear speed.

This explains Rudolph's red nose because of air resistance creating around 20 quintillion Joules of energy per second, which would convert a non reindeer nose to charcoal at such energy levels. I think the acceleration and deceleration per household may also need some examination.

Luckily Santa has lots of special powers so these mere physics facts are no problem to such a superhero.