Comment by D_Alex | Hacker News Reader

Comment by D_Alex | Hacker News Reader

>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.

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.

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.

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!

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.

> 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?

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

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