Building the tallest sandcastle

The Canadian National Exhibition (CNE) opens in Toronto next Friday (can’t wait!) and they hold an international sand sculpting competition every year. I’m always impressed by the size and detail of these sculptures and wonder if the competitors ever consider the science that’s behind their work?

Recently, I came across an interesting piece of research on Nature.com‘s Scientific Report on How to construct the perfect sandcastle. Maryam Pakpour of the Institute for Advanced Studies in Basic Sciences in Iran, and colleagues from the University of Amsterdam in the Netherlands and the Laboratorire de Physique Statistique de l’ENS in France investigated the answer to this question by determining the relationship between height and stability of a sandcastle.

Just by scooping up a handful of dry beach sand, you know that you can’t build a sandcastle with it. Dry sand simply won’t hold any kind of shape as it can hardly support its own weight. You can transform these loose grains of sand into an “adhesive”, formable material by adding water. Wet sand holds because water forms liquid bridges between sand grains. But add too much water and you’re left with an unstable pile of sand that ultimately collapses (think landslides).

Aside from water content, the stability of sandcastles is equally dependent on having a sturdy base. Just look at the world’s tallest sandcastle which stands at 11.53 m high. Built by Ed Jarrett of the United States, his sandcastle has a fairly large base and progressively narrows towards the top.

World’s tallest sandcastle (Source: http://jarrettscastle.com/)

In this research, the team started by investigating the stability of columns of wet sand, which would allow them to determine the maximum height of sandcastles that could be built. The idea is that a column of sand reaches its maximum high when it starts to buckle under its own weight.

The team reported a mathematical model that considered the maximum strength of sand packing, density, and gravity, and also verified their model experimentally. They found that the maximum height (h) varies with the radius of the column (R) as h_max ~ R^2/3. Beside the size of the sandcastle base, the model shows the height of the sandcastle could be increased by increasing the compaction of sand (a known technique to sandcastle builders). Furthermore, decreasing the density of the sandcastle would also allow a taller sandcastle to be built. The team tested this idea by building their sandcastle underwater, decreasing the effective density of the sandcastle.

A sandcastle built underwater

The team notes that normal beach sand can’t be used to build underwater sandcastles because the liquid bridges holding the sand grains together get destroyed. But they show it’s possible to build an underwater sandcastle using commercially available hydrophobic (water-hating) sand because air rather than water forms the bridges between sand grains.

The tallest “sandcastle” the team built was a uniform cylinder that stands at 1 m tall, so it is unlikely that competitive sandcastle builders will follow the team’s “recipe” on building the perfect sandcastle–especially when it comes to building sandcastles with complex shapes and designs. However the study offers an improved understanding of the behaviour of partially saturated granular materials, and may be useful to those working with geophysical applications such as soil stability.

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Pakpour M, Habibi M, Møller P, & Bonn D (2012). How to construct the perfect sandcastle. Scientific reports, 2 PMID: 22870378

Featured image by Flickr’s marc e marc

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