How tall can a Lego tower get?
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Backing out some numbers from the piece, the 2x2 held 950 lbs, which is roughly 1000 lbs in 1/2"x1/2", or 4000psi. That's roughly the strength of ordinary unreinforced concrete, at a far lighter density. Legos are also similar to unreinforced concrete in their tensile strength, which is low, variable, and brittle. The usual calculation is that tensile strength is ~ 10% of the compressive strength for concrete, but it depends greatly on the cracks and other discontinuities.
From the problem set though, there's an interesting effect. If you taper the tower with an exponential curve, 1/e^x, the pressure on the bottom of the tower can be constant as you increase the both the footprint and the height. Not coincidentally, that's the same curve you find in towers in the real world like the Eiffel Tower and the CN Tower.
The ultimate height that you could make with a tower would certainly depend on what constraints you're applying. Is there a limited number of bricks? A limited base area? Any supports at all? How do the people actually assemble the thing? What safety regs are there?
With no constraints, I don't see a reason that legos couldn't be built to the height of the great pyramids. Apart from the obvious one that it would be hellaciously expensive.
Once you start talking about constraints and something more tower shaped than mountain shaped, stability is the biggest concern. Elastic stability will affect the tower, at least as an upper limit to the height/cross section ratio.
And for extra credit, the tower should survive a run on the shake table.
So why can't we build a space elevator?
Earth's radius is 4k miles. Geostationary orbit is ~25k. Space elevators IIRC, are proposed for ca 60k miles out. Assuming a 10-20x height/width ratio, the base would be 3-6k miles on a side. Even just getting to geostationary orbit would require a mountain with a base the size of a continent.
It was stopped by one of the whingy old fart neighbours wondering what we were doing and threatening to complain to the management company. We had a good 5m left and probably enough bits left to cover it!
Smashing it was awesome and made one hell of a mess which took hours to clear up.
Most of the Lego came from a car boot sale in two large bins and was purchased for a mere 5 GBP. Went on ebay in 2001 for nearly 200 GBP (good investment!)
But that's not how we build towers. If you create a proper foundation with Lego bricks and distribute the weight evenly across them, and taper the tower as it goes up, am I wrong in assuming it could go a lot more than that? The entire weight of a structure never rests on a single brick...
The guy who did the assessment said that he felt other shaped/sized bricks would be more or less able to deal with the pressure.
All on the BBC More or Less Podcast.
For another example, one could try to create an inverted pyramid on one brick to crush it, but it will topple long before it crushes the brick.
The structural strength under that circumstance (pure Lego, nothing else) is so enormously high, as determined by this experiment, that there's no reason to ever worry about this eventuality.
I mean, were it just a matter of "a brick can support 100 meters of brick on top of it", I'd say, sure, obviously we can do that in real life. It'll be hard, but we can probably do it. But you have to put another ~1.5 orders of magnitude of pressure on... this is going to be "decidedly nontrivial", to borrow the mathematician's phrase. I'm not ready to say it's absolutely impossible, but it's in the "I'll believe it when I see it" class. That is a lot of bricks you are trying to stack on with no other failures getting in you way, and when you're dealing with that sort of accumulation of brick, micrometer variations you'd normally never even consider worrying about start stacking up....
I would be interested to see how much stronger the 2x2 flat pieces would be.
Refer to the following site for a comprehensive list of historical LEGO records:
There's an episode of James May's Toy Stories on Lego, where he builds a house from it; it turns out to be pretty tricky to build the floor of the upper storey to support him.
Does this add non-negligibly to the pressure on the bottom brick, or is it almost nothing once dispersed through the whole tower?
(You may be able to tell that I have very little knowledge of the physical sciences, so apologies if this is a stupid question!)
Ah, but that's not quite the issue, if the question is how high of a tower you can build.
If a tower is 3.5 km tall, then the lower 100m (to pull a number out of the air) are all supporting pretty much the same weight. And that 100m is about ... 10,000 bricks thick? If one of those bricks goes, then the tower goes. So what you want to know is not the average strength of a brick, but the expected strength of the weakest brick out of 10,000. I imagine that's significantly less.
Exercise for the reader: Given the probability distribution of brick strength, how do we compute the height at which we expect a one-brick-wide tower to fail? (Assume that vertical compression of bricks is the only issue; there are no lateral forces, the tower is perfectly balanced, etc.)
I really loved this quote:
'"... it's the typical height at which people ski in the Alps," Ian Johnston says (though many skiers also ski at lower altitudes).'
Really? I would never have guessed...
Both of these showing up just at the inflection point of the Christmas shopping season.
Good game, Lego.
More or Less is a great program that introduces statistics to current affairs topics and listener questions. This was in response to a listener question. It being on the news is the usual BBC thing of using BBC news as an advertising medium for BBC shows.
What were we talking about again? Oh, LEGO. Bleh.
Fun science stuff like this can get people who aren't normally into science interested in it, including children. There's definitely value in that.
People need relaxation.