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

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":

• Why do you think the zenith is a weak point? Commented May 17 at 10:15
• One factor: a spherical dome has the smallest surface-area-to-volume ratio, so encloses the most air for the least glass (or whatever material). Commented May 17 at 10:50
• Even the deep space ships in Silent Running and The Starlost had those big ole domes!
– uhoh
Commented May 17 at 15:30
• @gidds surface-area-to-total-volume is not necessarily the best metric. Empty volume for empty volume's sake is not necessarily efficient. If all the usable space is within several meters of the ground, you're not necessarily saving on glass with a grand sweeping dome with much of its volume dozens of meters above anyone's head.
– R.M.
Commented May 17 at 17:42
• Question for moderators: Is "the OP doesn't understand the relevant physics" a valid reason to close? Commented May 18 at 11:45

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.

• @OrganicMarble Thanks. I know how to design a pressure vessel (and get paid to do so), but I apparently still have difficulty reading today's date from a calendar. Commented May 25 at 13:17
• A possible relevant home experiment is to take an inflated balloon, then try to 'invert' a section of it, making a model of the inverted dome in the Q. Can certainly be done, but requires substantial additional supporting structure to do so over just letting the balloon be a balloon shape. Commented May 26 at 0:26
• @GremlinWranger Here's another one, though I don't recommend you try it youtube.com/watch?v=rTLN0xQtp9I . See how he puts the can in the fire upside down, with the inverse dome in the bottom uppermost. At 1:26 the inverse dome has been completely pushed out into a conventional outwards dome. At 1.31 the can finally fails. Commented May 26 at 0:57
• Hey, thanks for taking your time on this. Even if it's just a simple curiosity of mine, I appreciate the effort. So outward curves are 10 times more efficient than inward curves, is what you're saying? Is there a reason, then, why dams curve inward toward the reservoir instead of outward to the outflow? For the other examples: other than streamlining, I had figured they helped keep the structures rigid from outside forces (wind, water pressure). Some types of tension always came across as being more fragile than compression, but that's only my very non-physicist perspective. Again, thank you Commented May 26 at 2:51
• Permanent dams require so much material that concrete/earth are the only viable materials. These are poor in tension (especially at joints) so the only option is a compression arch. The ancients used compression arches for the same reason. Steel was the first viable structural material that's strong in tension, around year 1800. A steel compression arch will weigh less than a concrete one, but a steel suspension bridge (used in tension) will weigh even less. Tension dams are used as temporary defences yellowshield.co.uk/products/boxwall-flood-barriers Anchoring the ends may be an issue Commented May 26 at 23:53

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.)

• Failure modes of internal & external loaded curves in thin sheet material are quite different. Internally loaded curve will be deformed to a round shape (if it isn't round already) then fail due to tensile strength. Externally loaded curve will buckle. Cylinder designed exclusively for internal pressure will be a simple skin. If it has to withstand vacuum it may need welded on hoops to arrest buckling. A vessel designed for +10 atm internal & separate vacuum case (-1 atm internal) will probably need hoops. If designed for +50 bar internal, walls may be thick enough not to need hoops for vacuum Commented May 18 at 11:00
• It's not loaded in an opposite way. An arch is loaded by the weight, such that a catenary curve (if self-weight is dominant and constant) blended with a parabolic curve (if external weight is dominant and constant) creates a pure compressive force (which stone is good at). A pressure dome is loaded such that a sphere will produce a pure tensile load. Commented May 18 at 17:15
• @KevinKostlan Of course, "opposite way" is just a very crude approximation. Feel free to suggest an edit making it less oversimplified while still keeping it simple enough for a general audience. Commented May 18 at 18:01

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.

• Although I like your answer, I'm not sure that a lack of solar power is really the reason that the domes were originally imagined. After all, they had nuclear power in the 1960s and fluorescent grow lights. I think it's more that people like windows (hence the unpopularity of windowless offices) and the feeling of being outside (hence the popularity of glass and steel sky scrapers). The idea of living underground like a troll isn't very inspiring. Commented May 17 at 16:06
• @WaterMolecule - I buy that the glass dome is at least part "utopian space propaganda" on behalf of people wanting to "sell" space - but I also think the straight engineering case for a dome was significantly stronger in 1960 than today Commented May 17 at 16:52
• No windows in the colony, but the OLED-screen simulated windows built in to the walls will show awesome footage of the giant glass dome everybody wants to imagine is there :) Commented May 19 at 2:24
• There will be windows. Maybe not many, and probably quite small.
– JCRM
Commented May 19 at 15:44

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.

• Welcome to Space SE. It might be worth adding some words specific to misunderstanding about dome shape, and the issues with an inverted dome if unbalanced forces cause it to buckle and invert. Your points about damage to dome material making them invalid in most cases other than 'artist wanting something cool to draw' are certainly valid. Commented May 17 at 6:31
• Your last sentence is a bit confusing. A magnetic field can block some solar wind, in the form of charged particles traveling away from the sun. Those can strip away an atmosphere on a lower-gravity planet over time. Solar electromagnetic radiation, light from infrared to ultra violet, is not affected by a magnetic field, only an atmosphere or shielding. Cosmic rays are somewhat deflected by a magnetic field but are mainly blocked by mass. A glass dome would not block the intense light energy that a low atmosphere planet / moon receives, nor the cosmic rays. Commented May 17 at 15:33

### 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.

• If the trench is placed so there's a consistent sunward side, and the excavated material is used to build a berm on that side, I would think a lightweight roof whose main stress is tension from air pressure inside (which would only be present when the pressurized) would suffice. I don't see a need for prestressed arches. Commented May 18 at 19:02
• @supercat Depends if that's enough to block radiation, I guess. Commented May 18 at 19:44
• That approach wouln't work if the sun can pass directly overhead, but if one chooses a latitude where that doesn't happen a berm should be cheaper to construct than a roof. Commented May 18 at 20:12
• >"You're also missing the fact that the dome is enclosing atmosphere, and the outward pressure of 1ATM is definitely non-negligible." | The habitat exerting outward pressure was literally the entire premise of the question. Commented May 25 at 9:45
• @ThesaurusRex Literally every part of the body of the question concerned external forces on the arch/dome. Even the diagrams you added showed that. If you ask a different question, I'm afraid you get a different answer. Feel free to ask the question you intended to ask, and then maybe you'll get answers to that question. Commented May 25 at 16:52