In Space, no one wants your Domes

RMF Radio Station, Poland
Photo from Docent X. Thanks!

i-eclectica brings news of the RMF radio station in Poland, which, though terrestrial, perfectly represents the space colony archtype: modular construction, domes, shiny steel, glass, and concrete, airlock-like entrances, exposed mechanical systems, etc. It makes the Trekkie in me squeal. However, I’m thankful they built it on Earth because it’s a horrible design for other planets. To explain at length in an intro to structural mechanics sort of way:

There are many different ways to load (put weight/force on) an element. In the diagram below, you can see an element under (from left to right) compression, tension, bending, torsion, and shear.

Stresses2
Sketch from the Bridge Encyclopedia. Thanks!

The strength of an element depends on what material it is and the way it is being loaded. Concrete is strong in compression, but weak in tension. Steel is strong in tension, which is why we reinforce concrete with it. An element can resist more load along its axis (in tension or compression) than orthogonal to its axis (in bending), which means that the most efficient use of materials is to load all members axially.

In practice, this is difficult. We want to have space to walk around inside our buildings, so we push our walls far apart and put a roof over them. The roof has a large weight which has to be carried by beams that span from one wall to the next, and those beams are in bending. This means large members, which is why house walls are often 2x4s, but roof beams are 2x10s. A tried and true alternative: arches.

For any kind of loading, there is a funicular shape, or shape that ensures that the element experiences only axially loads. For constant, distributed loads (by far the most common) that shape is a parabolic arch. Turn an arch into a 3D shape, and you have a dome (almost — most domes are spherical, not parabolic, but the principal is similar). This means that you don’t need big roof beams; a smaller, correctly shaped member will do the job just fine.

However, structures on other planets would not be loaded the same as earthly ones; they would have to deal with air pressure, since breathing is pretty important and most potential colony sites are near-vacuums (Mars, the Moon). At sea level, air pressure is 2120 pounds per square foot, which is an absurdly high load for a structure — most are designed for less than 200 psf. This means that air pressure dwarfs any other loading consideration of a structure. Look at how this affects the funicular shape, with Earth loading at right and Mars loading at left:

Funicular Shapes
Sketch from Little Green Engineers. Thanks!

It reverses! While a parabolic arch is an ideal shape here, under heavy internal air pressure loading, it would be better to use an inverted circular arch. A dome, used off-world, would be loaded opposite to the ideal, and I’d challenge anyone to show how a compression dome can take 2000 psf in the same direction as its curvature without being ridiculously gargantuan.

Unfortunately, you can’t really turn a dome inside out and use that shape instead. The best one can do is take an inverted arch and rotate it around an axis to form a hyperbolic parabola like this:

Parallel Arches
Sketch from Little Green Engineers. Thanks!

This shape allows each element to resist high pressure loads in compression only. Tie each end of each arch to the ground with cables, and you have yourself a floating roof. Just don’t lose air pressure, as it’ll all come crashing down.

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