Every building material has a theoretical limit which it can't be used beyond: at some point, the weight of material above is enough to crush what's below. Now, a team of engineers has worked out that limit for Lego — and it's surprisingly high.
To work out how high a tower can be before it crushes itself, you need to know two things: the mass of material, and its yield strength. The yield strength describes how much loading a material can take before it begins to deform.
To work that out, you need a fancy device called a hydraulic testing machine. So, the engineers took their test specimen — a 2x2 Lego brick — and placed it into device. Then they ratcheted it up until things started getting interesting. They sailed past 350kg and wondered if they were doing something wrong. Eventually, the load reached 430kg and the brick began to slowly deform — which is known as plastic failure.
It's not loud, it's not dramatic, but it was definitely the end of the lego brick, as you can see in the picture: it's squashed completely flat. Repeat experiments confirmed that the average 2x2 brick, each of which is made of ABS plastic in Lego's factories, can take 430kg.
Do the maths
Once you know how much load a brick can take, then working out how tall you can build a tower is fairly easy. A normal 2x2 Lego brick weighs just 1.152g. From that, you can work out how many you need to create the whopping 430kg that the brick at the bottom of a tower could take.
To save you jumping for a calculator, turns out that figure is 375,000 bricks. You could pile 375,000 2x2 bricks on top of each other before the one at the bottom was crushed like in the experiments. Multiply that number by the height of the brick — which is 9.6mm — and you realise that you could, theoretically, create a tower 20km high before anything went wrong.
It's also worth bearing in mind that clever Lego builders have a bunch of techniques at their disposal to create taller towers by minimising mass, and the researchers even believe that 1x2 bricks would likely withstand more. So in theory, an even taller tower could be made.
That is, however, all theory. In reality, crafting a 3km tower would be virtually impossible: in real life, the loading wouldn't be perfectly equal or symmetric, so a tiny flaw in the structure would be massively amplified. Sorry. [BBC]
Image: BBC, Open University and Sami Niemelä