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This is more a theoretical than practical question...

If one wanted to build a 40-metre tower out of only Lego using the fewest pieces or cost, what design would be a good one, e.g. types of pieces and overall shape?

I've just read that some builders in Budapest broke the world record for the tallest Lego tower at 34.76 metres. It looks like a simple elongated pyramid.

The previous record holder used a cross-shaped cross-section.

BBC has also featured some research to calculate the maximum theoretical height.

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How broad is your definition of, 'pieces?' Would a Technic frame still count as a Lego tower, or are we talking about only basic bricks stacked flat? –  Windfire Jul 16 at 20:38
    
Are you limited to generic pieces or can you use custom parts; for example pieces used to create walls and wall corners in Castle? –  JoshDM Jul 16 at 22:13
    
@JoshDM you mean BURPs? I was thinking either 32 long axles or the unfortunately rare 2635 crane leg parts because they're tall and pyramidal already. –  Mσᶎ Jul 17 at 2:18

3 Answers 3

If you could design using Technic Axle 32 as your primary member that would probably be cheapest. You can get 500 of them for under $1 each on BrickLink, and making an Eiffel Tower shape out of those could be fairly strong. You'd be using axles in compression which isn't ideal so you'd need to be careful about bending forces, but in terms of cost per metre of height that's about as good as you can get. 32 studs is about 25cm, so your 40 metre tower is about 160 axles high. Assuming four legs (because Lego makes rectangles easier than triangles) you'd need 480 axles for the legs, plus another hundred or so for bracing. If you could work out a way to use only 3 legs the structure would be lighter.

Lego tower

You'd use axle connectors to join them end to end and either Technic liftarms or string for bracing (compression and tension respectively). There are Technic link parts in a few lengths that are lighter than liftarms, like this 15-long one and the tension member at the bottom would be a baseplate (or several baseplates)

If you made it modular using a "platform" that was, say, 16 studs square you'd end up with extra internal legs but a very easy to build structure. Say you make a tower that's two metres tall (8 axles) and tapers from 32x32 to a point. Four of those next to each other would support another similar tower on top of all of them. And so on, but the inside towers will end up with 2,3 or 4 towers sitting on top of them. A better design would make set of four symmetrically located parts "unique" and thus use fewer total parts but at the cost of the whole model being significantly more complex. On the other hand, I think you'd be able to get more than 2m out of each stage of such a tower.

I might have a go at a short version of this tonight if I can find my collection of long axles and see how stable it is. Somewhere in the garage is about 20 of them, so I should be able to get a metre tall fairly quickly and easily... if I can find those axles.

An alternative part that would involve a lot of SNOT techniques would be single train rails. Or even the modern click-together rails. I can't think of a good design for those off the top of my head, though.

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Couldn't find the axles easily, this one will have to wait until I unpack the collection (after we move, hopefully in not too many months time) –  Mσᶎ Jul 18 at 0:30

Just using bricks the cost argument becomes more important. Unfortunately large quantities of bricks really require that you deal with The Lego Group directly (and they're usually quite happy to deal). For rough price guides we can look at bricklink again. Sorting by quantity available from a single seller for some common parts (we don't care about price per metre if we can only get 20 of the part), cost per 2x4 brick volume in bold:

The bold figures give you a direct comparison, suggesting that 1x1 bricks are the same price as 2x2 bricks but more fiddly to work with and probably both heavier and weaker. Note that volume available increases with brick size for the most part.

So it looks as though your cheapest bet via BrickLink would be a containment wall of whatever larger bricks you could find with a core of 1x1 and 2x2 bricks. I suspect if you built a want list with the more common 1x1 bricks you could find one or two sellers who have lots of that size and do a deal "I'll buy all of them", because 1x1 bricks are a slow seller but you get a lot of them in the "bulk bricks" sets when sellers part them out.

Or just ask TLG for a couple of hundred kilogrammes of 1x1 or 2x2 bricks and see what you can get cheap. If you have media and charity tie-ins organised and some plans for the tower I suspect you'd get a better reception. I'd be tempted to add 2x3 or 1x3 bricks to tie things together, since compressive strength is not the limiting factor (see Ben's answer). If you're doing that it's probably better to model a few different bricks (or find the data online) so you can have an informed discussion about which bricks you want.

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The research from the OU indicated that the 1x1 bricks would be stronger than a 2x2, which in turn were stronger than a 2x4, presumably due to the greater amount of "wall" to surface area. –  Zhaph - Ben Duguid Jul 18 at 10:51

The key point that the team at The Open University calculated made was that while you could in theory build a tower about 3.5km high of bricks before the ones at the bottom would be crushed by the weight of the ones above - this was based on the load-bearing ability of a single 2x2 brick - they also stated that a 2x4 would fail sooner (less support on the sides I assume).

However, in practice this wouldn't be possible as:

"There isn't a chance you could do it in reality," Johnston says. "Long before the brick fails, the tower would fail as a structure itself, by buckling. The other thing you have to remember is that we were very careful to load this equally down the middle, so that all four walls were loaded."

A 3.5km tower would have to be built so straight that it was no more than 2mm off centre at the midway point

The 12m high (40ft) Christmas tree that was built in St Pancras was built around a metal frame for additional support and rigidity.

Note that the GWR is for "Interlocking Plastic Bricks" which would certainly rule out the use of string, and might also rule out the use of axles as they are not "bricks".

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yeah, GWR are quite specific and rule out basically anything using Lego Technic parts. Technic cranes often top 4m using truss frames of liftarms, but GWR doesn't allow that either (even if you use "technic brick with holes"). It's stacked bricks or nothing. –  Mσᶎ Jul 18 at 0:05
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I have done some research into this as well. eprints.usq.edu.au/20528/1/Lostroh_LegoTesting_2012.pdf Might be helpful –  tl8 Jul 18 at 0:29
    
Actually, the 3.5km limit is easily reachable just by making the pyramid wider. If the base was 3.5km on a side and tapered straight to a point at 3.5km high it'd be pretty stable. And heavy. And use a lot of Lego. –  Mσᶎ Jul 18 at 0:31
    
But building a pyramid would also result in more than the supported 4000N of force on the bottom - so you wouldn't really manage to reach the upper limit as the bricks would crush at a lower height... –  Zhaph - Ben Duguid Jul 18 at 10:42
    
@Zhaph-BenDuguid: Not necessarily. Building a pyramid would cause less load on each of the bottom bricks compared to a straight tower with the same height. If the pyramid is built solid, the inner bricks would also have additional support from the side, most likely increasing the weight they can carry before breaking. –  jarnbjo Jul 18 at 10:54

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