
How tall can a Lego tower get? - jofo25
http://www.bbc.co.uk/news/magazine-20578627
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bediger4000
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?

~~~
wiredfool
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.

~~~
ars
> 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?

~~~
wiredfool
As a tower? Mainly because the base gets exponentially larger as you get
taller. You'd start talking about a mountain that's significantly taller than
the diameter of the earth.

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.

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meaty
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!)

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ComputerGuru
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...

~~~
jerf
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
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:)

~~~
brk
Assuming the rest of the pyramid base doesn't end up flexing around that one
brick (which would not be very tall) and distributing more of its weight on
the ground...

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sp332
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
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?

~~~
sp332
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.

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dhx
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>

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UnoriginalGuy
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.

~~~
archangel_one
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.

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coroxout
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!)

~~~
sp332
You could just hold the second-to-last brick while you clip the last brick on
it :)

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cadab
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
So more like embers then.

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ggchappell
> 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.)

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

~~~
derefr
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.

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

~~~
billysilly
Oh yes, you do. You do indeed :)

<http://vimeo.com/22439234>

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

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skylan_q
It looks like a space elevator to me.

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

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Zedronar
Those resources could have been spent in something more useful.

~~~
robotnixon
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.

