Many nights, to relax a little before bed, I play a few minutes of Minecraft. I’ve been playing the same instance for a long time so I’ve amassed a lot of supplies, and a while ago I realized that rather than sticking some of the key stuff in chests, it would be more fun to just build huge towers out of it.
Most impressive so far is my tower of solid copper. Presumably made of literally pure copper, it measures (here I am assuming a block in Minecraft is a cube of exactly one meter in width, length and height, which is the canonical size) five meters by five meters at its base and now towers 240 metres high.
If my calculations are correct, my tower of copper now weighs a rather staggering 52 million kilograms, making it about as heavy as a battleship. That is a hell of a lot of copper. But it occurred to me the other day - is this even physically possible?
Assume for a moment that it would be possible to get 52 million kilograms of pure copper together and price is no object. Could you actually form that much copper into a tower five by five metres and 240 metres high? Or would the copper at the bottom compress and warp and collapse?
Incidentally, I also have a tower of pure iron, also 5x5 at the base, but a mere 90 metres high. Never mind that one for now. I think that could support itself.
My tower of pure gold is four by four and stands 38 metres high - much smaller than the copper tower, but still a very impressive 11,723,456 kilograms of gold, worth roughly seven hundred billion dollars if you could have it in real life. It’s a way smaller tower than the copper tower, but gold is heavier and softer than copper - could that tower stay standing?
I think the biggest problem is stability. Even solid metal may not be rigid enough when you’re talking about a tower 48 times as high as it is wide. Then in real-world terms you have to allow for resistance to wind. Also, I think there are practical limits to how large and thick a solid piece of metal can be cast.
Copper is soft (ductile). Like you, I wonder if the lowest levels can sustain that weight without squashing. I guess the question is - if you put a block of copper in one of those engineering presses, what amount of force would it take to make it “give”? (i.e. compression strength) I can find references to the mechanical properties, but have no easy experience in translating those into the real world. If my math is right, that’s about 208kg of weight on each 1cm^2. I suspect from real-world experience that it is sustainable but pushing the close to the limits.
52 million kg (I trust your numbers) on a 500 cm x 500 cm base = 52 x 106 kg/ 250.000 cm2 = 208 kg/cm2. Easy peasy, copper can handle that under reasonable temperature limits. It gets softer close to the melting point ( 1357.77 K (1084.62 °C, 1984.32 °F)).
But your gold weighs 117.34 million kg (yes, you are richer than you think! You have one seventh of all the gold ever dug up.), and has only 400 x 400 = 160.000 cm2 to rest, that is 733 kg/cm2. That could be close to the plastic deformation limit before warping.
Your thinking is right on track. This is the reason that tall brick chimneys have such wide bases - so the compressive strength of brick and mortar is not exceeded. Not only that, they can only be built a few feet tall at one time. Then you have to wait for the mortar to cure before proceeding. Takes a long time to build a 200 foot chimney.
Logistically, I’m not sure how it would be possible to manufacture it. If you had the means to cast something like that in one piece, it would experience tremendous deformation as it cooled - and I don’t think you’d end up with a solid piece as the outside would cool first, becoming rigid, then voids would open up in the centre as that cooled and contracted. On normal scales, this is overcome by adding filler channels that contribute additional liquid metal to the core of the casting as it cools, but I don’t feel like that would scale all the way up to this.
Come to think of it, is there any material that could be used to build the mould? It has to withstand the pressure of a column of 240 metres of copper
You could cast it horizontally and right it up afterwards, but I would go by sections, stacked afterwards. I would mill the contacting surfaces to make them flat after cooling and melt the swarf to recycle it in the next batch.
That’s easy: Build a 240-meter-tall pyramid out of, well, pretty much anything, with a 5-meter square shaft in the middle. Pour in molten copper, as slowly as is needed to let it set properly. Then deconstruct the pyramid around it.
There must be some differences between building it out of blocks vs solid, even if you machined them to perfect cubes, when they deform, the discontinuities will make a difference.
If you machined them to perfect cubes and then stacked them that high, I would expect that the uniform surfaces and high pressure would result in them contact-welding, so they would be solid.
Even after getting past the construction and assuming it can be made stable, will this be out in the sun or experience exposure to temperature gradients?
A solid metal structure that large is going to have some serious thermal expansion issues. Steel and concrete structures take this into account in the design. Heck, even my concrete driveway has expansion joints.
For the copper that’s only 3000 psi at the base and obviously linearly decreasing up to the tip. I’d be very surprised if any of it contact welded and it certainly would not throughout the entire structure or even on the vertical faces of the cubes.
Uniform expansion (what expansion joints are intended to address) wouldn’t be an issue, because the top is free: The tower would just get slightly taller when it was hot, and slightly shorter when it was cold.
Uneven heating, though, would be an issue. If the Sun is shining on one side of the tower, for instance, that side would get hotter than the shaded side, and so the sunward side would expand more, and so you’d get a slight curvature. But it wouldn’t take much curvature for a 240-meter-tall tower to put its center of mass outside of its footprint.
Would it be enough? I’m not sure, off the top of my head. Copper does have two things going for it, in this regard: It’s fairly highly reflective, so it won’t couple strongly radiatively, and it’s an excellent conductor of heat, so even to the extent that the sunward side does absorb more heat, that heat would travel to the other side internally.