Stacking toy wooden blocks: a *theoretical* limit as to how high?

I’ve occasionally tried to stack Jenga blocks sideways or end over end, one on top of another, and it always seems there’s a point where no matter how carefully I’ve balanced and how still the air is, the next block on top will topple the whole edifice. Assuming perfect conditions, maybe stacking blocks by a robot in a vacuum, is it theoretically possible to keep stacking blocks up to infinity or is there some property of physics that’d prevent it?

Well, it’s going to depend to the perfection of the blocks (they’re wood, after all), and ultimately the weight of the blocks is also going to be a factor. I highly doubt that it’s possible to name an exact figure, though.

The bottom blocks will be compressed by the weight upper blocks, but I’m not sure how that impacts stability.

Brian

But if the stack gets really high, the upper blocks will press on the bottom blocks less and less. Due to centripetal force of the spinning Earth.

I think it depends on the stacker. I’ve seen a guy balance rocks on top of each other that defies understanding, yet there they are. Your limit might not be his limit.

With perfect blocks and perfect stacking, and excluding weather and seismic considerations, it’s hard to know what would be the limiting factor. I’m thinking probably the gravitational forces of the moon and sun.

It depends on what you mean by perfect blocks. Assuming they’re not made of unobtainium, they will give out before long, and I assume before the moon’s gravity becomes a factor.

Look at the pyramids. Early ones were built at too step an angle. While some argue that other reasons might have been a factor, the Bent Pyramid was apparently changed to a shallower angle during construction to avoid a collapse.

Even some of the interior stones of later, larger pyramids are broken due to the weight issues and trying to keep everything aligned.

And these were made of stone and brick. I don’t see wood being all that great at withstanding compressive forces on such a grand scale. You have to go with a pyramid type sloping shape otherwise the other walls will bulge out, leading to weakness and then a feedback loop of more bulging, etc. until it collapses. Even then, I don’t see it getting as big as the Great Pyramid.

Another potential problem is spontaneous ignition. You can’t dry the wood out entirely without sacrificing strength. With just a bit of moisture, some breakdown/decay is going to happen. The interior will heat up, speeding the breakdown, until it will try to catch fire. Even assuming a lack of Oxygen, anaerobic breakdown would eventually generate enough heat to weaken the fibers and under pressure you’d get core that’s too soft to resist pressure and it will start to flow. (Wood glacier anyone?)

Well then, the exact nature of the blocks’ imperfection will determine the stacking height. This will either be uneven shape (this is the limiting factor in the real world) or material properties.

Considering material properties, wood is very strong in compression, and while I don’t know what kind of wood is used, I have little doubt (intuitively) that a Jenga block could support a weight of 1 tonne without being significantly unevenly deformed. A Jenga block has a volume of 28 cm[sup]3[/sup] so let’s call it 22.5 grams. 1 tonne of blocks would be 44,444 blocks and would be 666 metres high.

If the blocks are made of a soft wood, they would not be able to support as much weight, but on the other hand each block would be lighter.