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December, 2003 Archive Story

LIGHTNING v SANTA - THE ULTIMATE CONFRONTATION

At this time of year, the perennial question crops up in households across the land. Does Santa exist? Is it possible for a portly old man to travel around the world, pulled by flying reindeer, and give presents to all the good boys and girls everywhere on the planet? This Christmas, we have decided to put Santa under the microscope to answer this question once and for all.

Firstly, could it be done using known technology? If we use the Lightning as our mode of transport, rather than these less well documented flying reindeer, we can calculate the odds against it. Brian Carroll gave me the following figures, although I had to ask him to make some assumptions about continuous flight for the sake of comparison with Rudolph & Co. The first problem that springs to mind is engine limitations. As you can see from the detailed table below, rules would have to be severely bent to repeatedly accelerate to high supersonic speeds.

POWER RATING % RPM MAXIMUM JPT
1C
TIME LIMIT
(PER FLIGHT)
MAXIMUM (with and without reheat) 104 800 15 minutes combined duration
INTERMEDIATE 98 755 30 minutes
MAX CONTINUOUS 97
720
Unrestricted

After a couple of goes, the engine's limitations would have been exceeded and the remainder of the sortie flown at a slower speed. Also, the Lightning was limited to a maximum flight time of 8 hours, after which engine oil had to be replenished. With these points in mind, and ignoring the 8 hours limitation, Brian produced some figures, using the Max Continuous RPM. At FL 360, this will/should produce a supersonic cruise, slower than we would like, and he had to make an educated guess at the fuel consumption.

Unfortunately Brian no longer has all the flight planning charts, especially the ones giving specific fuel consumption at various speeds, but has estimated that 97% on both would give an average speed of around Mach 1.2, or 12 miles a minute. So, from the initial take-off and climb he came up with the following figures for a 24-hour period. Distances are in Nautical Miles.

  TIME
(minutes)
DISTANCE
(n. miles)
1. Brakes off to level at 30,000 feet - join the tanker and fill up, taking on 1,720 lbs of fuel.
12
55
2. Power to 97% speed, now at Mach 1.2 at 36,000 feet - fuel flow 300 lbs/min
22.9
275
3. Reduce to 300 kts - join tanker and take on 8,600 lbs
8
42
4. Accelerate to Mach 1.2 again.
1
5
5. Cruise at Mach 1.2 at 36,000 feet - fuel flow to 300
lbs/ min
26.7
320
6. Repeat 3, 4, & 5 above, 38.358543 times in 24 hours (1,440 minutes)
1369.4
14,092
TOTAL TIME AND DISTANCE
1440
14,789.8

Of course, Santa's little elves will have spent the previous two weeks, 10 hours a day, polishing the aircraft so that it gleams shiny and bright to reduce the drag factor by several % to achieve the projected speed, by which time they would be completely knackered and probably unable to load up with presents. As for the pilot (Santa), crossing his legs in the cockpit is near impossible.

Before going on, it is interesting to see that if Santa were simply trying to circumnavigate the Earth, this would still leave around 9,210.2 miles to complete circumnavigation (assuming a nice round figure of 24,000 miles). The time for this last part would be approximately 894.95605 minutes or 14.915934 hours, so the total time to fly right round the world would be 39.915934 hours (39 hours 54 minutes 57 seconds).

However, the Lightning would have to do a bit more than that. There are 2 billion children (persons under 18) in the world. However, since Santa does not appear to deal with the Muslim, Jewish and Buddhist children, that reduces the work-load down to 15% of the total - 378 million (Population Reference Bureau figures). At an average (census) occupancy of 3.5 children per household, that is a 91.8 million homes. One presumes that there is at least one good child in each household.

Assuming that each of these 91.8 million stops are evenly distributed around the surface area of the Earth (which of course we know is false, but it makes the maths easier), that makes 0.78 miles per household - a total trip of 75.5 million miles. So, travelling at 14,789.8 NM per 24 hours, the Lightning would take 5105 days, or nearly 14 years! And that would just be to travel the distance, never mind deliver the presents, eat, drink or do the other essential things which most of us do every day. So the Lightning, excellent though its performance undoubtedly is, could not do the job.

Someone will probably work out how much fuel the Lightning would use and how many round trips to Alpha Centauri it would propel a Mini travelling at 30 mph, while others will undoubtedly write to say that some of the children waiting for their presents would be married with three kids, a negative equity mortgage and a severe case of clinical depression by the time their train set dropped down the chimney. All I can say to them is that the Lightning Association will donate a voucher for one anorak at a dry-cleaning emporium of your choice to the writer of the saddest letter based on our figures.

However, what about Rudolph and the legendary reindeer? No known species of reindeer can fly, but there are 300,000 species of living organisms yet to be classified (if you believe the scientists) so this does not completely rule out flying reindeer. Payload makes interesting reading. Assuming that each child gets nothing more than a medium-sized Lego (2 lbs), the sleigh is carrying 321,430 tons - not counting Santa, who is invariably described as overweight. On land, conventional reindeer can pull no more than 300 lbs. Even granted that 'flying reindeer' could, since they do not have to overcome the same static and kinetic frictional forces, pull ten times that amount, we could not do the job with a team of eight. We would need 214,200 flying reindeer. This increases the payload - not even including the weight of the sleigh - to 353,430 tons, or four times the weight of the QEII liner.

To accomplish his task, Santa has 31 hours of Christmas to work with, thanks to different time zones and the rotation of the earth and assuming he travels east to west. If he visits the 91.8 million homes, this works out at 822.6 visits per second. At each Christian household with good children, Santa therefore has 1/1000th of a second to park, hop out of the sleigh, jump down the chimney, fill up the stockings, distribute the remaining presents under the tree, eat whatever snacks have been left out, get back up the chimney, get back on the sleigh and move on to the next house.

To cover the 75.5 million miles, Santa's sleigh must travel at 650 miles per second, or 3000 times the speed of sound. The fastest man-made vehicle, a space probe at its maximum velocity, moves at 27.4 miles per second. A conventional reindeer can run at 15 miles per hour tops. If we allow 1/3000th of a second to decelerate, 1/3000th to deliver and 1/3000th to accelerate again, Santa would be subjected to a centrifugal force of 2,000,000 times the force of gravity. A 250lb Santa (which seems ludicrously slim) would be pinned to the back of his sleigh by 500 million lbs of force.

But that would just be the start of his problems. A 353,000 ton body travelling at 650 miles per second creates enormous air resistance - this would heat up the reindeer like a spacecraft re-entering the earth's atmosphere. The lead pair of reindeer would absorb 14.3 quintillion joules of energy. Per second. Each animal. In short, they would burst into flames instantly, adding a whole new dimension to 'Rudolph The Red-Nosed Reindeer', exposing Prancer and Dancer etc. behind them and creating a series of sonic booms in their wake. The entire reindeer team would be vaporised into an ionised gas at a temperature of several million degrees Centigrade within 4.26 thousandths of a second.

In conclusion, if Santa ever did try to deliver presents on Christmas Eve, he's comprehensively carbonised by now. But hold on. Every Christmas Eve, the NATO chain of radars from North Cape, Norway, southwards pick up an 'Unknown' track heading towards the United Kingdom, which eventually, having been passed from radar to radar, is re-categorised as 'Allied' until it descends and fades approaching the north of Scotland. If the above is true, who is it that our professional radar operators are watching.........?

Charles M Ross

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