Addendum, Cars, physics, Space, thought experiment

Addendum: A City On Wheels

While I was proofreading my City on Wheels post, I realized that I’d missed a golden opportunity to estimate just how heavy a whole city would be. When I was writing that post, I wanted to use the Empire State Building’s weight as an upper limit, because I was pretty sure that would be enough space for a whole self-sufficient community. Trouble is, the weight of buildings isn’t usually known. The Empire State Building’s weight is cited here and there, but never with a very convincing source. I couldn’t figure out a way to estimate its weight that didn’t feel like nonsense guesswork. That’s why I used the Titanic’s displacement as my baseline.

The reason estimating the mass of a building was so tricky is that, generally, buildings are far form standardized. Yeah, a lot of houses are built in similar or identical styles, but even if you know their exact dimensions, converting that into a reasonably accurate weight turns into pure guesswork, because you don’t know what kind of wood was used in the frame, how much moisture the wood contained, how many total nails were used, et cetera. But, just now, I realized something. There is a standardized object that represents the shape, size, and weight of a dwelling pretty well: the humble shipping container.

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You may notice that that’s not a shipping container. It’s a bunch of shipping containers put together to make a rather stylish (if slightly industrial-looking) house. Building homes out of shipping containers is a big movement in the United States right now. They’re cheaper than a lot of alternatives, and they’re tough: shipping containers are built to be stacked high, even while carrying full loads. For example:

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The things are sturdy enough that they far exceed most building codes, when properly anchored. Their low price, their strength, and the fact that they’re easily combined and modified, has made them popular as alternative houses.

Because different shipping containers from different manufacturers and different countries often end up stacked together, they all have to be built to the same standard. Their dimensions, therefore, are standardized, which is good news for us. I re-imagined the rolling city as a stack of shipping containers approximately the size of the Titanic, with their long axes perpendicular to the ship’s long axis. You could fit two across the Titanic‘s deck this way, and 110 along the deck, and if you stacked them 20 high, you’d approximate the Titanic’s shape and volume. To account for the fact that the people living in these containers are going to have furniture, pets, physical bodies, and other inconvenient stuff, I’ll assume that each container would have twelve pieces of the heaviest furniture I could think of: the refrigerator.

Amazon is a great thing for this kind of estimation, because from it, I learned that an ordinary Frigidaire is about 300 pounds. Multiply that by twelve, add the mass of the container itself (3.8 metric tons each), round up (to keep estimates pessimistic), and you get 6 metric tons per container. Considering that a standard 40-foot intermodal container (which is the standard I worked with) can handle a gross weight (container + cargo) of over 28 metric tons, we’re nowhere near the load limit for the containers. There are 4,400 containers in all, for a total mass of 26,400 metric tons. Increase the mass by 25% to account for the weight of the nuclear reactor, chassis, and suspension, and we get 33,000 metric tons. That’s still a hell of a lot, but it’s only just over half of the 50,000 tonnes we were working with before.

As you might remember, I wrote off the Titanic-based city on wheels as probably feasible, but requiring a heroic effort and investment. But using the shipping container mass, which is 1.5-fold smaller, I think it moves into the “impressive but almost sensible mega-project” category, along with the Golden Gate Bridge, the Burj Khalifa, the Great Pyramid of Giza, and Infinite Jest.

Another note: There’s one heavy, mobile object whose weight I didn’t mention in the City on Wheels post: the Saturn V rocket. I did mention the Crawler-Transporter that moved the Saturn V from the Vehicle Assembly Building to the launchpad, however. And the weight of the fully-loaded Saturn V gives us an idea of how massive an object a self-propelled machine can move: 3,000 tonnes. Because, to nobody’s surprise, NASA knows the weight of every Apollo rocket at liftoff. Because it’s mildly (massively) important to know the mass of the rocket you’re launching, because that can make the difference between “rocket in a low orbit” and “really dangerous and expensive airplane flying really high until it explodes with three astronauts inside.”

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Addendum, Space, thought experiment

Addendum: The Moon Cable

Reader Dan of 360 Exposure, pointed out something that I completely neglected to mention, regarding cable strength. Not only would the Moon Cable be unable to connect the Earth and Moon without breaking (either by being stretched, or by winding around the Earth and then being stretched), but it couldn’t even support its own weight.

There’s a really cool measurement used in engineering circles: specific strength. Specific strength compares the strength of a material to its weight. It’s often measured in (kilonewtons x meters) / kilograms. But there’s another measurement that I like better: breaking length. Breaking length tells you the same thing, but in a more intuitive way. Breaking length is the maximum length of a cable made of the material in question that could dangle free under 1 gee (9.80665 m/s^2) without the cable’s own weight breaking it.

Concrete’s breaking length is only 440 meters. Oak does better, at 13 kilometers (a really bizarre inverted tree. That’d make a good science-fiction story). Spider silk, which has one of the highest tensile strengths of any biological material, has a breaking length of 109 km (meaning a space-spider could drop a web from very low orbit and snag something on the ground. There’s a thought.) Kevlar, whose tensile strength and low density make it ideal for bullet-proof vests, has a breaking length of 256 kilometers. If you could ignore atmospheric effects (you can’t) and the mass of the rope (you can’t), you could tie a Kevlar rope to a satellite and have it drag along the ground. Zylon is even better. It’s a high-tensile synthetic polymer with a higher tensile strength than Kevlar, and a larger breaking length: 384 kilometers. You could attach a harpoon to a Zylon rope and use it to catch the International Space Station (no you couldn’t).

And, funnily enough, specific strength is one of those things that has a well-established upper limit. According to current physics, nothing (made of matter, magnetic fields, or anything else) can have a breaking length longer than 9.2 trillion kilometers. This is demonstrated in this paper, which I could get the gist of but which I can’t vouch for, because I understand the Einstein Field Equations about as well as I understand cricket, or dating, or the politics of Mongolian soccer. But the long and the short of it is that it’s not possible, according to current physics, to make anything stronger than this without violating one of those important conservation laws, or the speed of light, or something similar.

Not that we were ever going to get there anyway. The strongest material that has actually been produced (as of this writing, July 2016) is the colossal carbon tube. Think of a tube made of corrugated cardboard with holes in it, except that the cardboard and the corrugation is made of graphene. Colossal carbon tubes have a breaking length of something like 6,000 km (remember, this is under constant gravity, not real gravity). And that’s theoretical. So we’re not building a giant ISS-catching harpoon any time soon.

You might have noticed that I skipped over the one material that I was actually talking about in the Moon Cable post: steel. There’s a reason for that. I want to leave the big punch in the gut for the very end. For dramatic purposes. Ordinary 304 stainless steel has a pitiful breaking length of 6.4 km. Inconel (which is both surprisingly tough and amazingly heat-resistant, and is often used in things like rocket combustion chambers) only does a little better, at 15.4 km. There’s no handwaving it: you can’t attach the Moon to the Earth with a metal cable.

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