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.

A team of researchers from the Open University in the UK decided to settle speculation — including burning debates on Reddit — by tackling the question scientifically. Here’s how they did it.

## Under pressure

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 2×2 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 2×2 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 2×2 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* 2×2 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 1×2 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

gravity would also play a role in taking down the structure before it gets very high. It would just start whipping around before falling over to one side.

That would be wind, not gravity. Gravity is fairly constant. pulling towards the centre of the planet.

Gravity plays a role in 'taking down' anything.

I'm wondering why in the article they say that 375,000 blocks is 20km but the illustration shows it as only 3.6km especially when 375,000 9.6mm blocks end on end is 3.6km...

Maybe we can all pitch in and buy Gizmodo a calculator and dictionary to share around the office.

Last edited May 15, 2013 10:43 am

"you could, theoretically, create a tower 20km high" but then you say 3km later on. Either way very impressive!

I was a little confused myself, especially when the picture says 3.5km.

Maybe they meant 20 furlongs

375000 * 9.6 mm = 3600 m.

EDIT: found it: http://lego.wikia.com/wiki/Brick

Last edited December 5, 2012 11:28 am

The chart is all over the shop. Baumgartner's jump was from around 25,000m, not 2,500. Olympus Mons (I assume they mean Olympus Mons) is around 29,000m, not 2,900. Who proof's these things?

Mount Olympus in Greece is 2,917m tall. Baumgartner

pulled his chuteat approximated 2,500m (from my quick Google) and he actually jumped from 39,045m.Chart seems accurate to me.

*proofs

" Olympus Mons (I assume they mean Olympus Mons) is around 29,000m '"

No, it's as stated on the chart.

It's 2,900 meters.

Your suggesting it's 29km high?

Who proofs your writing?

:P

Olympus Mons, which they were referring to, is a mountain on Mars. While not 29km tall, it is 22km tall which makes it the tallest in the Solar System.

http://en.wikipedia.org/wiki/Olympus_Mons

:)

Last edited December 6, 2012 12:13 pm

Good call.

(Who proofs MY reading?)

:)

The jump was, yes. But the illustrations shows where he opened the parachute, not where he jumped from.

375000 * 9.6mm = 3600 meters

Where did the author pull 20km from even though the illustration says 3591m??

He fucked up. The takeaway point here is that a lego Eiffel Tower at 1:1 scale (or greater) is totally doable. Get to work people.

Or a scale model of Mount Olympus.

"To save you jumping for a calculator, I'll make up some numbers."

Anyway, I came up with 3.58333333 Kilometers.

Last edited December 5, 2012 9:48 am

You're right - I missed reading the chute opening part. I'm an idiot. Apologies all round.

" To save you jumping for a calculator, turns out that figure is 375,000 bricks "

You need a better calculator.

430Kg = 430,000 grams

430000g divided by 1.152g = 373263.8888 bricks. 373,263 bricks. Not 375,000 bricks.

373263 bricks x 9.6mm = 3583324.8 mm = 3583.3248 meters = 3.5 kilometers (rounded into human numbers)

20 k high??

20 kilometers = 20million mm.

20million divided by 9.6mm = 2,083,333.333 bricks.

Lets call it 2 million bricks then.

To build a tower 20Km high would require 2 million bricks. (plus a few leftovers picked up off the floor)

That would weigh 17,361,111 grams = 17'361 kilos.

If that bottom brick (or indeed all of them) was made of indestructible unobtanium (that coincidentally weighs the exact same as the ABS used normally), it would be shoved down into the Earths crust with the pressure of 17 Tonnes over a 1.5cm2 area. (the size of a 2x2 brick.)

It wouldn't be 20k high for long.

(I'm pretty sure my math is right, but am happy to be corrected as I'm not betting any ranches on it)