Game of Thrones: Engineering The Wall
Today sees the end of Game of Thrones for another year. If you don’t watch it- start now; aside from being a fantastic slide-show of the Irish countryside, and tour de force of British actors, it’s also an epic fantasy that makes Lord of the Rings look like a cure for insomniac children.
To commiserate I thought I’d take a look at one of the most impressive structures in the whole of the Seven Kingdoms (spoiler free, of course). Forget the gilded fortifications of Kings Landing, or the castle of Winterfell- I’m talking about The Wall.
For those of you who don’t know, The Wall is, well, a wall (-obviously), 300 miles (482 km) long, 700-800 feet (213-244 m) tall and made entirely of ice. Although not specified explicitly, it is known that the wall is wide enough at its peak to fit “a dozen mounted knights to ride abreast” (isn’t the Internet amazing…). As a dozen horses are the width of six British railway gauges, we’re looking at a top width in the region of 8-10m.
For once, we’ve got at a structure within the realms of probability: the Bur Al Arab is 322m tall, the Wall of China was 13,171 miles long, and there are man-made structures of ice. The concern, however, is the combination of all these aspects…
Ice is actually a little less dense than water (which is weird), but for the sake of the maths let’s leave the bulk unit weight at the famous 10kN/m3, which makes the total stress (from self-weight) at the bottom of the structure somewhere in the region of 2.2 MN/m2. From a surprisingly interesting paper (discussing the use of ice to create a giant ‘berg-ship‘) it turns out that the ice at the foundation should be perfectly fine with this (~25% utilization).
The bigger concern, however, is wind. Unfortunately Westeros has been omitted from the Eurocodes, which is just as well given how much of a pain the backside EC Wind loads are to calculate. Making the massive assumption that blizzard and snow-storm winds are comparable, this slightly dubious source (comment if you’ve got a better one,) puts the wind pressure in the region of 0.622 kN/m2.
Taken over a unit meter the wall is safe from over-turning by a factor of ten, which is reassuring- and it’s probably alright to assume that it won’t go sliding away anytime soon. The stresses created by the wall bending cause the maximum compression (our wall doesn’t go into tension, it seems) to reach 3.4 MN/m2. While this is still within the working range of ice (~40% usage), it does move the material well within the brittle/ductile behaviour zone.
So what does that mean? It means that our wall is going through the ‘giant-ice-structure’ equivalent of fatigue. Tiny cracks are forming each time the wind blows, which could, over numerous cycles, form a failure plane. There is a saving grace, however; exposed ice is self-healing if it is given a chance to anneal. Luckily the cycle of day and night provides a chance for water to fill and heal these cracks and the ice to release the stresses caused by the wind.
Before I declare The Wall structurally sound (a first, since I started looking at fantastical structures) it is worth noting that the ultimate destruction of the wall will come from slump. Given the Wall’s erosion through sun and wind, the plastic flow of the fatigue and annealment cycle, and how thin it is; it seems safe to assume a fairly fast glacial flow. Given that Greenland’s Jakobshavn Isbræ is moving at 20-30m per day, even assuming a slow ‘1 m/day’ flow doesn’t give our Wall a life-time longer than a year.
Let’s hope whatever’s on the other side isn’t very patient…