
How tall can a Lego tower get? - darrhiggs
http://www.bbc.co.uk/news/magazine-20578627
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wbracken
I already knew legos were strong without this research.

For instance, I know for a fact from legos left on the floor by kids that one
lego can hold my entire weight (240 pounds) when I step on it in the middle of
the night walking to the bathroom with no signs of damage to said lego.

Further, I know that one lego can by itself topple a fully grown man.

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D_Alex
>The average maximum force the bricks can stand is 4,240N. That's equivalent
to a mass of 432kg (950lbs). If you divide that by the mass of a single brick,
which is 1.152g, then you get the grand total of bricks a single piece of Lego
could support: 375,000.

>So, 375,000 bricks towering 3.5km (2.17 miles) high is what it would take to
break a Lego brick.

>"That's taller than the highest mountain in Spain. It's significantly higher
than Mount Olympus [tallest mountain in Greece], and it's the typical height
at which people ski in the Alps," Ian Johnston says (though many skiers also
ski at lower altitudes).

>"So if the Greek gods wanted to build a new temple on Mount Olympus, and
Mount Olympus wasn't available, they could just - but no more - do it with
Lego bricks. As long as they don't jump up and down too much."

Well, in theory you can go as high as you want, by tapering the tower towards
the top. The 3.5 km limit is only valid for straight, constant cross-section
structures.

Which mountains certainly are not.

~~~
jessriedel
Actually, I don't think this is true. Your tower has to taper exponentially,
which means there's characteristic length scale L (probably in the dozens of
kilometers) such that cross-section has to double every time you move that far
down the town. The width of the tower that is 1 cm at its peak exceeds the
Earth's diameter (12,700km) at its base after only 60 doublings, which happens
at a height of 6,000km if L=100km. (Obviously, things get more complicated as
the height becomes comparable to the distance from the Earth, but the order of
magnitude should be right.)

Also, this only works if, for any given slice, the weight of the legos above
is evenly distributed over the legos below. Without stronger materials to
transfer this weight, the legos in the center of the bottom of the tower will
fail before those on the side of the bottom.

~~~
gweinberg
I think it only has to get wider quadratically, not exponentially. And the
weight doesn;t have to be exactly evenly distributed at the bottom, all that's
necessary is that some of tghe weight of the upper cneter bricks is suppoorted
by the lower outer bricks.

~~~
jessriedel
> I think it only has to get wider quadratically, not exponentially.

No. The total mass above a distance H from the top of the tower is

M(H) = \rho \int_0^H a(h) dh

where a(H) is the cross-sectional area of the tower a distance H from the top,
and \rho is the density of the tower material. This total mass must obey

M(H) = a(H) * r / g

where r is the force per unit area that the material can support and g is the
acceleration of gravity. Setting the right-hand sides of the two equations
together and differentiating by H gives

r/(g \rho) (d/dH)a(h) = a(h)

which means

a(h) = exp(h (g \rho/r))

> And the weight doesn;t have to be exactly evenly distributed at the bottom,
> all that's necessary is that some of tghe weight of the upper cneter bricks
> is suppoorted by the lower outer bricks.

The distribution problem gets worse and worse as the taper continues, because
more and more of the new area is further away form the center.

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sdfx
> The average maximum force the bricks can stand is 4,240N. That's equivalent
> to a mass of 432kg (950lbs). If you divide that by the mass of a single
> brick, which is 1.152g, then you get the grand total of bricks a single
> piece of Lego could support: 375,000.

But the weight it can support will be determined by the weakest link not by
the average. If the lowest brick is of below average quality the tower will
fall sooner. So if you plan on building a 3.5 km tower I'd advise you to
consider the variation of the brick quality. Bonus points for taking into
account that each additional brick has to support less weight.

~~~
ZoFreX
It did slightly annoy me that they say "they were impressed at the consistency
of Lego manufacture" and then go on to tell us the average. What's the
variance?!

~~~
ctdonath
About a year (?) ago, someone did do a study of Lego manufacturing variance.
They throw away a _lot_ of bricks to keep the variance very small. Granted it
focused more on fit than compressive strength, but should help you get nearer
the answer.

~~~
2muchcoffeeman
I hope the plastic can get recycled to make more bricks.

~~~
mattmillr
It's ABS, the same plastic that some 3-D printers use, so they should be able
to just chip it up and feed it right back into the hopper for the molds.

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nathell
>That's taller than the highest mountain in Spain.

Not quite, unless by "Spain" one means "continental Spain." Spain's tallest is
Pico del Teide on the Tenerife, measuring 3718 m from the sea level.

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chrisBob
I see two issues not addressed by the other comments:

1) I would start with a 2x2 plate not a 2x2 brick. They are heavier per
height, but I think they will also be much stronger because the weight is not
supported by the sidewalls alone.

2) They didn't account for compression of the bottom bricks in their height
calculation. If anyone is going to take them seriously they need to publish
the strain at the yield point. Then we get to use some calculus to figure out
the actual height!

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gglon
As noted building high tower is not feasible in practice. Pyramid though would
be much more feasible. It is only 1/3 weight of equivalent tower (polyhedron
that is cube) so can be theoretically 3 times higher while simultaneously way
more stable. Though if high, curvature of earth has to be considered as well
since the lengh of base edge is equal to height.

~~~
ctdonath
Brick count could be problematic though. How many 2x2 bricks would you need to
build your 3x3.5km high pyramid?

~~~
DanBC
Would hollow pyramids work?

Since LEGO™ pieces are pretty uniform and there are known pieces, it seems
that the engineering math would be easy enough. Once someone has done the work
of transcribing the 1x1, 2x1, 2x2, etc pieces and plates into a LEGO™
Calculator.

I am sure these already exist in a minimal form to help pack a cup with LEGO
pieces when you buy them from a LEGO™ store.

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gaelow
Good points here. Only many other limitations apply when building an actual
tower, so you would probably need a lot of engineering to design a tower even
remotely close to that height that can be built before it collapses. If that
kind of thing was so easy the carbon nano-tubes fiber cable for the space
elevator would be a reality and we would be sending packages to the ISS at
almost no cost. But if you take a look at the ideas for the project, you'll
find the amazing problems they are trying to solve just to be able to say: Ok,
we can do it. Let's build it!
[http://en.wikipedia.org/wiki/Space_elevator](http://en.wikipedia.org/wiki/Space_elevator)

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breischl
A few commenters here suggested building the base out of flat plates for
strength. But as I understood it, the maximum load was determined by the
properties of the plastic. The plastic became fluid, rather than the structure
of the pieces failing.

From TFA:

>>The material is just flowing out of the way now and it's not able to take
any more. We're getting a plastic failure. It means the brick keeps on
deforming, without the load increasing.

So, help out the not-a-real-engineer here. Doesn't that mean that changing the
shape of the pieces wouldn't help? ie, even if the base were a solid sheet of
Lego plastic it would just flow out of the way at that load?

~~~
wiredfool
The picture of the squished piece looks like there it was a combination of
buckling failure of the sides (a geometric instability) and a material failure
along the sides (ripping, to allow the buckling failure of the sides). It
doesn't look like a fluidlike or flow failure to me.

FWIW, Plastic deformation here is in contrast to elastic, it's not the
material. Elastic deformation is linear, Hooke's law deformation: f=kx.
Plastic deformation is when elastic breaks down, and you can have additional
deformation at the same (or lower) load. Generally, there's an elastic region,
then a plastic region, and then total failure.

The numbers suggest that legos are actually pretty similar to unreinforced
masonry, the strength looks like about 4000 PSI in compression and nearly no
tensile strength. That's about equivalent to bog standard concrete or concrete
blocks (CMU). The main difference is that Legos are much less dense. It would
be interesting to see something similar to Gothic architecture done in Legos
though there would have to be some tweaking to deal with flying buttresses due
to the density.

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kijin
Here's an alternative to the pyramid shape that everyone else is suggesting:

Just use different types of blocks.

The strongest Lego block is probably one of those thin (1/3-height) 1x1
plates. They are also the heaviest per unit volume. Build the base of the
tower using these plates. As you move up the tower, gradually replace them
with 1x2 plates, full-height 1x1 blocks, 1x2 blocks, 2x2 blocks, and finally,
2x4 blocks at the top.

Strong, heavy blocks go at the bottom. Weak, light blocks go at the top. This
strategy will probably let you increase the height of your tower by at least
twice, if not more.

~~~
rtkwe
Depends on the increase in crushing weight, if it isn't greater than the
increase in weight per lego unit height (~9mm) then you don't get a larger
tower in the end.

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gggggggg
Master Builders [http://aboutus.lego.com/en-us/lego-group/programs-and-
visits...](http://aboutus.lego.com/en-us/lego-group/programs-and-visits/lego-
certified-professionals)

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userbinator
I like how the experimental result of 375k bricks with a 2x2 brick is somewhat
close (within an order of magnitude) to the 220k bricks someone calculated
from FEA simulation in the linked Reddit thread (
[http://www.reddit.com/r/AskReddit/comments/iy0ew/how_many_le...](http://www.reddit.com/r/AskReddit/comments/iy0ew/how_many_legos_stacked_one_on_top_of_the_other/)
)

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tempestn
Did anyone else pedantically think that this phrase

> The average maximum force the bricks can stand is 4,240N. That's equivalent
> to a mass of 432kg (950lbs).

Should have instead read...

>The average maximum force the bricks can stand is 4,240N (950lbs). That's
equivalent to a mass of 432kg.

?

~~~
schrodinger
It seems it's become acceptable to use pounds for mass, equal to 0.45359237
kilograms. I've even seen it used as such in scientific contexts. Sometimes
it's clarified by saying pound-mass as opposed to pound-force.

[http://en.wikipedia.org/wiki/Pound_(mass)](http://en.wikipedia.org/wiki/Pound_\(mass\))

~~~
tempestn
Totally, hence pedantic. But it does still seem to flow better the other way,
if you discount the fact that most people tend to think of pounds in terms of
mass. (Which of course is relevant and shouldn't be discounted.)

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murbard2
If your tower gets exponentially thin towards the top, you can keep going
forever as the pressure resting on the each level is independent of the height
of the level. At least when the gravity field is approximately constant.

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NoMoreNicksLeft
Science: fucking up childhood dreams since forever.

