## Liquid walls: some thoughts on the ice wall from Game of Thrones

Last week I noticed that HBO is celebrating the ten year anniversary of the airing of Game of Thrones. As a big fan of the books, I paused a bit to think and realized that I never wrote anything on the science that we can see in either the books or the tv show, so I think now is a good moment to solve that.

I remember getting a copy of the first book in the early 2000’s from my cousin, and that he told me “you are going to enjoy this, it is not the typical fantasy book”. And boy he was right. I still remember how I lost my mind when Ned lost his head, or the night I could not stop reading after the red wedding, or how bumped I felt when… well you get my point: I really enjoyed the world and its characters. Time to pay my debts.

## The wall

Early in the series we find out that there is a gigantic wall made of ice in the north that has been protecting the realm of men for more than 8000 years. This wall is described as being ~480 km long, ~213 m tall and ~91 m in width. After I recovered from the first shock about the size of that (just to compare, the border between USA and Mexico is about 6 times longer than this, and there are some sort of physical barriers along ~1000 km) I started thinking whether such a structure would be viable.

While I am not very good at building structures, I am assuming that the construction would be tricky, but possible, given that big blocks of ice would behave in a similar way to big blocks of rock (maybe a bit more slippery), which we have been using to build big stuff since forever.

However, we have super big icy structures in our world, and they have very intricate behaviours: glaciers. Glaciers evolve over time, they get bigger or shrink in size, and they move around. I think this characteristic would be the main limiting point in building such a wall. Let’s do some fast numbers:

Ice has a density of ~0.9167 g/cm3 at 0 °C, which means that a cube with 1 cm lateral size weights 0.9167 g. Given that we have the size of the wall, we can calculate how much pressure the wall itself will generate on its base. A wall column with a 1 m2 base would have a volume of 213 m3, and by using the density of ice (and the correct units) we can calculate its weight as $213 \times 0.9167 \times 10^{3}\approx 195257$ kg.

With the weight, we can just calculate the pressure as $P= \frac{Force}{Surface} = \frac{mass \times g}{Surface}$, calculation that gives us a total pressure on the base of the wall of ~1.9 Mega Pascals (MPa). Here, the problem with ice is that at high pressure, it melts. This is why glaciers move around, because the ice on their base becames water, and then the ice on top starts to flow in any direction. The question now becomes, would the pressure on the wall make if flow around? The answer seems to be a big YES: usually glaciers start to flow with pressures on their base of 0.1 MPa, so the wall would exert a pressure about one order of magnitude higher than that. You can read a little more on the forces and movements that generate glacier dynamics here.

So, even if we do not care about temperature changes, erosion, etc. It seems that the wall would just move around in a few years, making the defense of the realm a really hard task… Thank to the old gods that Bran the Builder used magic!