Is a dome really the most efficient way to contain gas in a vacuum?

Question

It's pretty common to see some artist or even engineer come up with an idea of a lunar or Martian colony with a big ol' glass dome up top. And we seem to have been doing this since the 60's.

But barring other engineering issues like meteor vulnerability, radiation, etc. is it really sensible to use a dome? Balloons are stable because the pressure outside is interacting with the pressure inside to keep them rigid. Inflatable habitats can be rigid with only fractions of Earth's atmosphere.

But we would be containing an entire atmosphere of air in a structure with an apparent single weak point (the dome's zenith). Structurally, arches (e.g. masonry arches and dams) point the peak of their curve towards the source of the pressure, in order to redirect it towards the ends of the arch.

To that end, what about something like an inverted dome? Would this contain the pressure better?

EDIT Since I forgot how specific questions need to be on here, let me elaborate with some, uh, "diagrams":

Answer 1

Structures under internal vacuum or compressive loads can be fairly complex to analyse, as they can buckle. Structures under tension or internal pressure are much simpler. These structures use materials that are much stronger in tension than they are in bending, so the best designs assume no bending strength at all.

For a suspension bridge, that means cables pulled straight and tight. For a pressure vessel, watch what balloons and bubbles do - they form round shapes that maximise internal volume for the given surface area.

The most common shapes are cylinders, sometimes spheres (and very occasionally, domes). Most tanks are cylinders because forming spherical ends is much more complicated than forming a cylinder body, but the sphere is the most structurally efficient shape. Aircraft use cylinders. Rockets use cylindrical tanks and a very small number (Starship, Atlas) use balloon tanks where internal pressure is required to avoid collapse in certain load cases. Spheres are only used in very special cases, due to the difficulty of manufacture, despite needing only half the thickness for a given diameter as an infinite cylinder would.

The most likely shape for a space habitat is a cylinder, as with your typical airliner. Most of these are perfectly cylindrical. This avoids any weak point - the air pressure (which is a considerable load, 7 pounds on every single square inch at 0.5 atmosphere differential pressure) is spread equally around the circumference. There is no concentration of load at the zenith. There may be a concentration of weight load at the zenith when the airliner is depressurised, but that is insignificant compared to the pressure loads it must withstand.

Note that aircraft are made as complete cylinders - they don't have a flat on the bottom. That's because if they had a flat on the bottom there would be a huge concentration of load there, with the internal pressure trying to push the shape into round. The awkwardly shaped space below deck is therefore used for cargo. This could be avoided in a space habitat by using a vertical cylinder, with pressure containing domes at top and bottom. There could then be several internal flat floors, with only one awkward dome at the bottom.

If a foundation is used, a flat bottom can become attractive. You could have a flat concrete base internally lined with some airtight floor seal material - either metal or polymer. But the internal pressure is going to try to pull it into a curve, which means you will get a significant tension load at the edge, balanced by a significant compression load at the centre, requiring a very strong foundation.

Taking Starship at an internal pressure of 100kPa as an example, the air pressure on a circle of 9 metre radius is PI x (4.5)^2 x 100 = 6362kN or 649 tonnes force, spread around the 28.3m circumference. That's the equivalent of 23 tonnes per metre of circumference. You need nicely rounded top and bottom domes to efficiently contain that pressure. Even a drinks can employs a carefully engineered reverse dome in the bottom to spread the load, rather than a flat bottom.

For the walls of Starship, we have (per metre of length) 9 x 1 x 100 = 900kN or 92 tonnes circumferential force. This is spread over the two opposite walls, meaning each must bear 46 tonnes per metre (exactly double that for the dome, as mentioned above.) This considerable force keeps the walls well rounded and is actually necessary to prevent buckling under vertical loads at launch (from the tanks and payload above, not so much the structure itself.)

Conclusion: The challenge in designing a habitat is withstanding the pressure needed to make it habitable, not withstanding the structure's own weight. Round tops and round bottoms are best - unless you have an exceptionally sturdy foundation that allows a flat bottom, or a well engineered solution like the inverse dome bottom of a drinks can.

EDIT

This edit is added to address the question edit 25 May 2024.

Balloons work in the exact same way in space/vacuum as they do under normal atmospheric pressure. The relevant thing is the difference between the internal and external pressure. Here's an example of an early American "communications satellite" which was nothing more than a balloon, inflated to a low pressure in space.

The pressure inside an enclosed space does not concentrate at the top, it acts equally in all directions. The most efficient shape is the shape adopted by a bubble - a sphere in the case of a free floating bubble and a hemisphere in the case of a bubble on the surface of a liquid. The flat bottom would be difficult to achieve in a space habitat, however, due to the need to transfer the load to foundations.

OP has provided two diagrams, one with a conventional outward dome and the other with an inverse, inward dome. As per the 9m diameter Starship example I considered previously, this dome will need to accomodate 649 tonnes of force around its circumference (23 tonnes per metre.) It is hopefully clear that the weight of the dome will be negligible in a well engineered solution, maybe around 10-20 tonnes total.

The most efficient shape is the spherical, conventional outward dome per the diagram on the left. The dome material is not subject to bending load and the material can be considered flexible in design calculations. Any dent from a meteorite which does not puncture the dome will tend to be pushed back out by the internal pressure. No bracing is required, because of the natural bubble shape of the dome.

The OP proposes an alternate design with an inverse, inward dome. This dome will be subject to buckling load due to the internal pressure. It will, effectively, want to pop out on the other side (upwards.) Typically pressure vessels are on the order of 10 times less strength-efficient when used in this mode. Stiffness must be considered in the design, and for a material to be stiff, thickness is of benefit. Bracing may help improve stiffness. Additionally the design encloses less overall volume. If a flatter roof is desired, ballast or internal tie points may be considered, as in the design of an inflatable mattress.

OP is advised to observe the design of existing pressure-containing equipment: pressure vessels, aircraft, sports equipment, water toys. All typically have outwards curves. Inwards curves are used for special reasons (such as the inverse dome in the bottom of a drinks can, a design adopted to prevent it falling over.)

Here is an example website selling inflatable sports domes. A space habitat will need to handle a much larger differential pressure internally so will likely be more optimal in shape (not a rectangle base as is convenient for sports domes) and perhaps use stronger material such as aluminium (though inflatable polymer space habitats are already being tested.) But the design concept will be the same - in order to avoid issues with stiffness of material, an outward curve that works with the internal pressure will be preferred over an inward curve that works against it.

Finally, regarding the image of the classic stone arch in compression: I would note that a modern suspension bridge with a cable in tension is far more weight efficient.

The ancients had to use compression structures as they had no suitable material that was strong in tension (the mortar joints were particularly a problem). Steel-chain suspension bridges have been around since the early 1800s, and any structure in space is going to make a lot of use of the weight advantages of tension structures.

Answer 2

It all depends on the material.

A dome/balloon is mechanically same thing as an arch, just loaded in the opposite way. The material of a balloon is all under tension, the material of a masonry arch is all under compression. Which of the two works better depends on whether your material of choice is stronger in tension (plastics, metals) or under compression (stone, bricks). The materials good in compression are typically quite dense and thus perhaps not as convenient for a huge aerial structure.

(Note that there's no single weak point anywhere, all points of a dome or an arch are typically under the same stress. This always holds for a balloon thanks to Pascal's law, but for arches and the like it's also the optimal way to design them to make the most of what the material can take.)

Answer 3

Engineering Trade Offs

Everything in Engineering is about trading something for something else (cost for time, strength for weight, etc.)

In the 1960s, solar panels and grow lights were both immature technology, so the trade off of "getting natural light for growing crops by using an expensive, single point of failure glass dome" made good sense.

Today, probably not so much. Structurally, the dome is a fine answer. The real problem is all the stuff OP waves away - catastrophic risk of even a tiny asteroid strike or accident involving heavy machinery, expense of hauling a giant glass dome to the colony site, radiation, etc.

Today, solar power and grow lights are mature and the need for natural light is completely gone. Any realistic modern colony plan should be heavy on in-situ resource utilization - making concrete out of regolith, digging tunnels to create living space, etc.

Our first colonies probably won't have any windows at all - but the deep influence of science fiction on our conception of Moon and Mars bases will ensure that steel and glass domes keep cropping up in the renderings.

Answer 4

Technically, assuming the dome was made of a material strong enough to hold in the air, and the internal atmospheric pressure doesn't get too high, the dome should keep from exploding. The main Achilles heel with transparent domes on Luna and Mars is likely to be the solar and cosmic radiation, which is the main reason why proposals for bases and settlements on these worlds have largely switched to an underground "bomb shelter" style format. That and on Luna, the day-night cycle is such that unless you had a system of shades and mirrors to simulate the day-night cycle we have on Earth, a structure that lets light in wouldn't make much sense at all. It's possible that one day, we could have the technology to build such an orbital shade and mirrors system. It's also possible that one day, we may be able to create large scale artificial magnetic fields strong enough to block most of the radiation.

Answer 5

Frame challenge: Your question makes no sense because you don't understand the physics

The question hinges on a basic misunderstanding:

But we would be containing an entire atmosphere of air in a structure with an apparent single weak point (the dome's zenith)

A dome absolutely does not have a "single weak point". Forces are distributed through the structure, and this doesn't make the structure more prone to collapse from damage to the top than damage elsewhere.

You're also missing the fact that the dome is enclosing atmosphere, and the outward pressure of 1ATM is definitely non-negligible. For domes made from lighter materials, as in most proposals for space habs, the "dome" would effectively be a balloon and its strength would need to go into holding the air in, not holding the structure out. Most hab designs are intended to be prefabricated on Earth and shipped to the destination to be assembled, so the Rocket Equation means their weight is a significant factor in what's practical to ship.

You absolutely could make your hab instead by digging out bricks of local rock, cementing them together, and sealing the inside with some kind of plastic coating. In that case your hab could look exactly like a regular house, just with airlock doors. Ray Bradbury would be overjoyed at the concept of 1950s suburbia recreated on the Moon! It's not highly practical though.

There's another design though which is worth mentioning. The big risk for inhabitants is radiation, and a good way to solve that is with a couple of metres of rock between you and it. Tunnelling would seem the obvious solution, but tunnelling is slow and dangerous. A much quicker and safer solution is to use bulldozers to dig a really big hole, roof over the top, and cover it back up. And with this design, some kind of prestressed arch for the roof is the only game in town if you want to minimise the number of supporting pillars. This still would not have a single weak point though - you'd design it so that at least one pillar could be removed/damaged and the structure would still hold together.