Cambyses’ Lost Army and the Physics of Sandstorms

[Mark]

http://blogs.scientificamerican.com/cocktail-party-physics/2013/08/05/cambyses-lost-army-and-the-physics-of-sandstorms/

Over the weekend Jen-Luc Piquant found herself pondering the works of Herodotus, specifically the tale of the Lost Army of Cambyses. Sometime around 524 BC, priests at the oracle of the Temple of Amun decided they didn't much care for their new ruler, Cambyses II, son of Cyrus the Great. Cambyses decided that he didn't much care for their insubordination. And he had soldiers — 50,000 of them, sent marching through the Sahara from Thebes to put those rebellious priests in their place.

But they never reached their destination (the Oasis of Siwa, where the mutinous temple was located).  Seven days into their march, a massive sandstorm broke out and buried Cambyses' entire army, never to be seen again. Per Herodotus: "A wind arose from the south, strong and deadly, bringing with it vast columns of whirling sand, which entirely covered up the troops and caused them wholly to disappear."

It's most likely myth, according to leading Egyptologists. But it inspired a cautionary mention of Cambyses in the prologue to Chaucer's Canterbury Tales, when the Pardoner is advocating moderation in drinking alcohol (he seemed to think Cambyses dispatched his army in a drunken rage). And it also inspired various archaeological expeditions over the past 100 or so years to try and locate whatever evidence might remain of the lost army of the Egyptian ruler.

At least one such claim, in 1977, turned out to be a hoax. Most recently, in 2009, two Italian archaeologists claimed to have found remnants of the lost army, in the form of bronze weapons, a silver bracelet, an earring and hundreds of human bones. But this claim, too, seems suspect: let's just say they didn't have the blessing of the Egyptian Supreme Council of Antiquities for their 13-year quest, and they presented their evidence not in an academic journal, but in a documentary film screened at the archaeological film festival of Rovereto.

Jen-Luc does not make Herodotus a regular part of her weekend reading, but a new paper in Physical Review Letters described the results from computer simulations of midair collisions between grains of sand during a sandstorm, and reminded her of the doomed desert army. And it turns out those collisions may play a pivotal role in determining the strength of a sandstorm — known as the flux — increasing that strength the more they collide.

Physicists love to study granular media like sand, and sandstorms offer a rich trove of fascinating physics, notably in how these meteorological phenomena can transport huge amounts of sand from one place to another in a fairly short period of time. The grains are especially loose in dry, arid conditions, so when strong winds blow over the dunes of the Sahara, for example, they first start to vibrate, and then to pop up in the air, striking the ground after they fall and often breaking into a splash of even smaller particles of dust (called "leapers") — all part of a process called "saltation."

If the winds get strong enough, those fine grains of sand end up suspended in dusty clouds into the air. There are two types of these kinds of grains, reptons and saltons, and it's the saltons that make up most of the particles one sees during a sandstorm.

It's been quite the challenge to study these mid-air collisions, even via computer simulations, because it requires so much computing power. But Hans Hermann of the Institute for Building Materials in Zurich and his colleagues devised a nifty 3D simulation code that simplified matters just enough to make the task more manageable.

Hermann and friends ran simulations both with and without these midair collisions and compared the results. And they found that the flux was three times as strong in the runs that figured in those midair collisions. Furthermore, the flux peaked under conditions where the grains lost about 30% of their kinetic energy.

Hermann acknowledged to Physics Focus that the conclusion is "counterintuitive — one would naively expect that collisions between grains would shorten [their] trajectories," instead of lengthening them. He and his colleagues think it's the "leapers" (reptons) that might be to blame — those grains that usually don't become airborne like the saltons, or so physicists used to think. An alternative approach is that when two leapers collide, one shoots just a bit higher into the air, colliding with another particle, thereby getting an additional boost. If it achieves sufficient height, it becomes a salton, and that means it will make more saltons when it slams back into the dune.

This isn't the usual state of affairs when it comes to sand dune dynamics, but the density of the grains is so high in a sandstorm, such collisions are much more common. And that means other models for sandstorm dynamics, which have ignored such collisions, will need to be revised accordingly. Granted, we're talking about computer simulations, and such models are difficult to verify experimentally.

Hermann et al's research probably won't explain what happened to the Lost Army of Cambyses. But for those asking, "So what?", a quick scan of Wikipedia reveals that in the Sahara desert, the frequency of sandstorms has increased tenfold since the 1950s, possibly due to poor agricultural practices (such as ignoring the fallow system), with a concomitant impact on climate. Remember that collectively, those individual particles add up and can significantly impact the distribution of soil, drastically reshaping beaches, for example.

That's why granular media are so fascinating. You only have to look to the high priest Imhotep, in the 1999 film The Mummy,  to see the power that tiny grains of sands can have when they work collectively:

References:

Almeida, M.P.; Andrade Jr., J.S; and Hermann, H. (2006) "Aeolian Transport Layer," Physical Review Letters 96: 018001.

Bagnold, R.A. The Physics of Blown Sand and Desert Dunes. New York: Methuen, 1941.

Carneiro, M.V. et al. (2013) "Midair Collisions Enhance Saltation," Physical Review Letters 6: 86.

Hermann, H.R. (2006) "Aeolian Transport and Dune Formation," Modelling Critical and Catastrophic Phenomena in Geoscience 705: 363-386

Herodotus. The History of Herodotus, Volume I, Book II.

[Dave Beatty]

Wow Mark!  Interesting stuff here.

As it happens, I have traveled extensively in the Western Desert between Cairo and Siwa and thence south to Khartoum, both on land and in the air (I was stationed at Cairo West as an adviser to the Egyptian Air Force for a year and did a few Bright Stars with the 82d and 101st out there as well as some work with the US Navy etc etc). 

I've been in several sandstorms in the Sahara, which usually occur as khamseen (so called because they tend to come in a 40 day period in March and April - Arabic for 40 is khamseen).  The first year I was there in the early 1980s we had, as I recall, just one sandstorm - but it lasted four days!  It was pretty nasty.  We did not mind flying in it but the EAF refused to do so.  The storm itself went up to about 12,000' and actually stretched for hundreds if not thousands of miles.  The last time I was out there (1997) there were two storms, each lasting about the same amount of time - 4 days.  By the way, all the sandstorms I experienced came from west by southwest - about 245 degrees - not out of the south as Herodotus reports.

Based upon my personal experience over just 15 years or so I question the statement that sandstorms have increased 50 fold.  I have not seen that.  I wonder what metric is being used.

During my wanderings, we were aware of Herodotus' legend of the Lost Persian Army and actually spent the odd moment or two looking around for it and never found anything odd (we did find a few WWII aircraft crash sites).

As far as the physics of sandstorms go, there is a rather specific wind velocity required to cause "rising sand" (as the Egyptian Air Force calls it) and, as I recall, that is about 12 knots.  Anytime the wind shifted around to 245 degrees and hit 12 knots, flying was cancelled (except for the crazy Americans).  Also, the height of the storm is directly related to the wind velocity - the stronger the wind, the higher the storm top.  Lastly, in my personal experience, larger grains of sand are picked up by the wind and bounced along the ground with enough force to take the skin off anyone foolish enough to have exposed ankles.  The really stinging sand rarely rises above knee height.  Particles that get much higher than that are much finer, more like dust actually, and the stuff up at the top is very fine. 

It is pretty miserable on the ground in one of those things, the dust gets into everything (even screw-top canteens) and engine air filters become clogged VERY quickly.  It is also very  difficult to maintain any sort of unit cohesion in a khamseen - even with the lights on, it was impossible to follow another vehicle.  We usually chained all the vehicles together if we had to travel and took it very slowly.  Would it be possible for a storm to bury an army?  I kind of doubt it.  More likely they just got lost in one and wandered around until they all died of thirst and heat stroke.  Given the problems we had maintaining contact with other elements of our units, it would be very possible for the entire Persian army to have just become fragmented and sort of dissipated into the sand like a bucket of water.  So chances of finding more than a few dead Persians together in one bunch are few and far between.  More likely they are scattered over dozens of miles in little clumps.  Assuming of course that the legend is correct.

Our engine maintenance guys liked to see us fly around in a khamseen - the old J79s in our Phantoms loved it - blasted all the stray carbon out of the compressors and saved the engine guys from having to do it.  The paint guys hated it because it had a tendency to sandblast the paint off the leading edges of the wings and stabilator and the useful life of our plexiglass canopies were significantly reduced due to scratches and pitting.

[Patrick Waterson]

A lot of interesting detail there, David - the disorientation and getting lost was, as you say, probably what got Cambyses' force killed (I bet any guides took the chance to make themselves scarce).  Once they were down and out, windblown sand could cover them up quickly enough.

[aligern]

Very nteresting Dave, I recall from Engels on the logistics of Alexander the Great  that  an army can only carry water for about four days and that Alexander himself with a much smaller force than Cambyses army very nearly came a cropper on the journey to Siwa. If the sandstorm created any sizeable delay for the Persians it would likely be fatal. You are almost certainly correct about the scattering effect of running out of water. groups of men would head back or strike out for the Oasis with the strongest getting furthest.
Roy