While it might sound flippant, building the best structures out of sand is a tricky civil engineering problem. That's why a team of scientists, led by Daniel Bonn from the Laboratory of Physical Statistics in Paris, set to a complex series of experiments involving theoretical and practical modelling of sand castles.
By testing different levels of sand wetness, they studied how columns of sand buckled as they were built higher and higher. Eventually, they found that there's an optimum sand wetness: you should be aiming to have a liquid volume fraction of 1 per cent. That means that, by volume, you need to combine 99 parts of perfectly dry sand with 1 part water to build the ultimate castle. The result is published by Nature.
From there, the team were able to work out how the maximum height of a sandcastle varies with its width. If you can imagine building perfectly cylindrical columns of sand, they found that the height varies with the 2/3 power of the base radius of the column. In other words, the height-to-radius ratio decreases the wider you make your column.
But while that's saddening, don't be too disheartened: using 1 percent-wet sand, the team were able to create a tower with a base radius of 20cm that stands an impressive 2.5m tall. Beat that! [Nature]