How tall can a Lego tower get?

http://www.bbc.co.uk/news/magazine-20578627

by jofo25 • 14 years ago

122 46 14 years ago

bbc.co.uk

cadab• 14 years ago

They mention that there "There has been a burning debate on the social news website Reddit.". Yet that reddit debate was over a year ago!

nodata• 14 years ago

So more like embers then.

ComputerGuru• 14 years ago

I'm a little confused. That's the weight that a single Lego brick can withstand, correct? So assuming you made a "tower" that was essentially a vertical line of 2x2 Lego bricks, it'd collapse after 3,591m.

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...

nicholassmith• 14 years ago

Yeah that had me slightly puzzled, you'd never attempt a tower with so few bricks as the stability would see it topple over quite quickly.

mserdarsanli• 14 years ago

You are right but I'd prefer to have this answer as you can predict the maximum height of the tower that you designed using this. Also, a question that accounts for complex towers, would not be a question about legos much, I think.

tcgv• 14 years ago

You are correct, 3.5 Km is the maximum height only when building towers with constant horizontal cross section.

Tyrannosaurs• 14 years ago

It's not even that, it's the maximum height for a tower of 2x2 bricks.

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.

jerf2• 14 years ago

Probably the proper translation out of geek-speak and into reality is that there is almost certainly no real structure that can be made purely out of Lego bricks that will cause the lower level to mechanically fail. (I'm hedging for safety. I really want to say there isn't one at all, but I've learned not to underestimate people's ingenuity. But let me point out by "real structure" I mean one that can be reasonably built in the real world, not, for example, a structure a mile high with millimeter tolerances made out of mass-manufactured plastic bricks.)

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.

Almaviva• 14 years ago

A counterexample is if you build a huge non-inverted pyramid and then put an extra brick in the middle on the bottom. It wouldn't balance but you could easily imagine putting many tons of weight on that single brick sticking out on the bottom like this, thus technically causing the lowest level to mechanically fail. This is pedantic, but I think you asked for it:)

bcoates• 14 years ago

Couldn't you use flying buttresses to stabilize the inverted pyramid without lifting weight off the bottom brick?

RandallBrown• 14 years ago

The original Reddit question was simply "How many Legos, stacked one on top of the other, would it take to destroy the bottom brick?"

I would be interested to see how much stronger the 2x2 flat pieces would be.

dhx• 14 years ago

The current record is 32.5m and was set in Prague over the days of 5-9 September 2012.

Refer to the following site for a comprehensive list of historical LEGO records:

http://www.recordholders.org/en/list/lego.html

coroxout• 14 years ago

This seems to simulate the pressure due to the weight of the bricks, but I wonder how much the height comes down by if you factor in the extra pressure you have to put on the top brick to get it to clip on.

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!)

dfxm12• 14 years ago

If that's an issue, maybe you can add new bricks to the bottom.

sp3323• 14 years ago

You could just hold the second-to-last brick while you clip the last brick on it :)

sp3323• 14 years ago

If you're curious about the engineering that goes into a large Lego structure, James May ("Captain Slow" of Top Gear fame) built an entire house out of Legos. http://www.youtube.com/watch?v=qR2YqMrS_pM It's an hour long story, but if you want to skip to the final product: http://www.youtube.com/watch?v=qR2YqMrS_pM#t=2600s

njr123• 14 years ago

Its been a while since I watched that episode, but that was built with a steel superstructure surrounded by lego right? The lego was only partially load-bearing?

sp3323• 14 years ago

Around 23:30 you can see that they added a wooden safety structure, which did not (normally) hold any weight. It was just there in case the Lego failed. The Lego alone actually held itself, and the occupants, just fine. The first test is at 40:30.

gnyman• 14 years ago

Thank you that was a great episode, the only thing I would have wished they showed more of was how they finally got the Lego structure to hold.

UnoriginalGuy• 14 years ago

Is anyone else excited by the fact that your average Lego brick can easily hold a human's weight? So if you built things out of LEGO you could, at least in theory, stand on them.

seabee• 14 years ago

Anyone with kids is well aware of this fact - though they rarely intend to stand on them!

ceejayoz• 14 years ago

As a parent, I really, really, really wish they'd collapse under a human's weight. That shit hurts.

dalke• 14 years ago

Wear wooden shoes around the house? :) A Dutch woman told me that after you wear them for a year they start to get wear in and get comfortable.

archangel_one• 14 years ago

Unfortunately something else tends to go wrong first - so you can stand on a solid Lego structure fairly easily, but if you try to build a bridge it's very hard to keep it from failing when weighted in the middle because the weight tends to push the bricks apart from one another.

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.

Zedronar• 14 years ago

Those resources could have been spent in something more useful.

robotnixon• 14 years ago

So could the time spent typing that message.

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.

NegativeK• 14 years ago

Like an 80-hour workweek?

People need relaxation.

recursive• 14 years ago

I just wasted two hours. Doesn't that just drive you crazy?

bpratdesaba• 14 years ago

Actually in Spain we have Teide, a mountain taller than the Lego tower. http://en.wikipedia.org/wiki/Teide

billysilly• 14 years ago

Oh yes, you do. You do indeed :)

http://vimeo.com/22439234

What were we talking about again? Oh, LEGO. Bleh.

skylan_q• 14 years ago

It looks like a space elevator to me.

IheartApplesDix• 14 years ago

Does anyone here have enough 2x2 bricks to try getting it several meters high?

bediger40002• 14 years ago

Speaking as an ex-aerospace-stress analyst, I found the article lacking. 2x2 Lego bricks individually fail by plastic deformation. The weight of an unreasonably tall tower could cause it, but we know that such an unreasonably tall tower can't exist because of stability concerns. So: what actually limits the height of a Lego tower? Elastic buckling, or some other kind of buckling, or is it something weird because of the friction fit of Lego bumps in the bottom of the block above? That's where the really interesting stuff comes into play. The Prague tower in the picture appears to have a square cross section, but is it hollow, or solid? What special construction techniques did they use, or is it just a matter of craftsmanship and selecting exactly nominal bricks for construction?

wiredfool3• 14 years ago

As an ex-civil engineer, this would be an awesome, but expensive competition for freshman engineering students. I actually remember a problem set containing questions like "how tall a tower" ignoring things like stability for various materials.

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.

bediger40002• 14 years ago

SO the rules of Lego-tower-building have to have the slope of the sides of the tower steeper than the angle of repose of a mass of bricks, eh? Otherwise, it's just a pile, not a tower.

ars• 14 years ago

> 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.

So why can't we build a space elevator?

meaty• 14 years ago

A friend and myself managed a slightly less epic 9.45m in 1989. We did it in the gap in the stairwell of our old flats. The base was only 8x8 and tapered every couple of meters and it was essentially hollow (to reduce weight and because we didn't want to run out of bits). We provided horizontal stabilisation with some string between the banisters to stop it falling during construction.

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!)

SolarNet• 14 years ago

Wow, bbc is really hard up for news huh?

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...

hnriot• 14 years ago

so is hn it seems. these days hn is becoming a day-delayed digg list.

derefr• 14 years ago

There seem to be two Lego-related articles on the front page right now. One a piece nominally for "geeks", demonstrating how adults can continue to do novel and interesting creative things with Lego bricks; the other an emotionally-resonant piece (probably aimed at parents) showing that Lego-the-company/brand "cares about kids."

Both of these showing up just at the inflection point of the Christmas shopping season.

Good game, Lego.

pbhjpbhj• 14 years ago

>Wow, bbc is really hard up for news huh? //

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.

ggchappell• 14 years ago

> The average maximum force the bricks can stand is 4,240N.

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.)

How tall can a Lego tower get?

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