How tall can a Lego tower get? | Hacker News Reader

How tall can a Lego tower get?

bbc.co.uk

115 pointsdarrhiggs38 comments

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.

>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.

But isn't a tower characterised by its straight construct as compared to a mountain (or say, castle)? Although, I guess you could describe a mountain as 'towering'.

Of course, you are right, if they built a LEGO mountain, they might pull it off; but that wasn't what they was asking for.

According to Wikipedia a tower is just a tall, free standing structure, meant for regular access by humans, but not for living in or office work. Whereas a mast can have guy-wires (like in the article picture).

The constraint of having a constant cross section is not part of the definition of a tower, I really don't understand why they make that assumption in the article. It was really an awkward read, thinking "just build from a larger base" at each paragraph.

If we look at Burj Khalifa or the Eiffel Tower, they certainly have large bases.

edit: actually the debate on the definition of tower vs mast vs tall building, habitable, free-standing, and the discussion pages on various articles (Tower, List of tallest towers, etc.) were a more interesting read than the article :-)

True. But maybe it is the definition of a LEGO tower? It seems like this is a form of competition. The same is true for this tower in Budapest: http://www.theguardian.com/lifeandstyle/video/2014/may/26/le...

If hust the outer dimentions need to be constant you could presumably make it more hollow as you go up.

Or just use lighter 2x16 blocks at the top moving down to a mix of 2x4 and 2x2 at the bottom. Still wind is probably the largest issue.

Because this is an argument in semantics. Sometimes it's ok to let it go and just read about a subject in the way the author intends. This is hard for me too sometims!

> as high as you want

I'm assuming you're spreading the weight, but lego bricks have quantised sizes, wouldn't that put a limit on the rate you can spread it?

Some really wet-finger math: a cone is one third the volume of a cylinder with the same base and height. That means you could build the mountain 3 times as high as the tower for same weight. So you can get a 10.5km high mountain. Assuming, ofcourse, the weight is perfectly distributed over the entire base area.

So, we can just about build Mauna Kea with bricks.

not only that, but so what if the bottom does get crushed? How is that no longer a lego tower/mountain/whatever?

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.

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.

> 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.

If you estimate how high mountains on earth can get before their weight makes them fluid at ground level (like what happened with the lego brick), you get to about 8 km. It just so happens the highest mountains on earth are about 8 km high. That is not coincidence.

> 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.

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?!

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.

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

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.

> If the lowest brick is of below average quality

LEGO bricks have remarkable yield consistency due to stringent precision tolerance.

>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.

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!

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.

I like the pyramid idea for one other reason, none of the tower ideas are feasible outside of a vacuum. How much stress is applied to the brick from even a slight wind? Torque to the structure at varying heights because of the wind?

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

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.

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

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?

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.

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.

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.

Master Builders http://aboutus.lego.com/en-us/lego-group/programs-and-visits...

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... )

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.

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)

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.)

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.

Science: fucking up childhood dreams since forever.

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