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So it's a trope in SF that Lunar colonies would use underground domes either naturally formed or formed by applying various excavation means. You get domes of various sizes used for living space, air storage, etc.

For example, in Menace from Earth, Heinlein has a dome used for air storage that is large enough for people to fly with human-powered wings. The air pressure is slightly above 1 atmosphere and it is 1/6 gravity on the moon, so flying is possible. And in Steel Beach, Varley has domes up to 50 miles in diameter set up to provide a simulacrum of living outdoors on Earth. An artificial sun travels across the dome each day, stars are projected at night, and various weather is artificially generated.

Using current tech, or at most slightly advanced past current tech, how big could such an underground dome be constructed on the Moon in 1/6 gravity?

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Rough estimate: the load capacity of a dome is proportional to its section, while its weight is proportional to its volume.

Considering that the weight for the same dome on Moon is 1/6 of its weight on Earth, the biggest dome you can have on Moon in $6^{2/3}$ times the biggest dome you can have on Earth, which is about 3.3 times.

Considering that, as of today, the largest dome on Earth is Singapore National Stadium with 310 meters of diameter, on Moon you should be able to get to 1 km diameter.

For comparison, the largest cave on Earth is reported to be 150 meters wide, which would make your dome to be no more than 500 meters wide.

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    $\begingroup$ I'm not sure this is quite right, because the domes and caves on Earth are purely self supported, because inside air pressure is more or less the same as outside. A sort of "rock balloon" with vacuum on one side and positive air pressure on the other should be capable of being larger, though I can't tell by how much. $\endgroup$ Dec 14, 2022 at 14:29
  • $\begingroup$ Sarawak Chamber, largest cave chamber, ~600x435m, 115m high at highest point. With your (probably) pessimistic scaling you might get a chamber 1.5-2km in diameter and 3-400m high, which is pretty spacious. $\endgroup$ Dec 14, 2022 at 14:40
  • $\begingroup$ Except assuming constant thickness, the volume of the materials of the dome itself, (not the volume enclosed) is proportional to the domes area. This gives us 6 times larger in diameter. $\endgroup$ Dec 17, 2022 at 8:10
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Suppose you make a brick arch on the Earth, one brick thick. You reach a limit when the weight of the number of bricks is enough to crush a brick. If you build it on the moon, then you can use six times as many bricks before you meet this limit.

That is over-simple. The actual failure modes of an arch will be from buckling, rather than crushing. However, there are engineering solutions for that. A dome is stronger than a single arch. Two domes, one inside another, such as the dome of the Pantheon, is stiffer. I think the size of the dome of a particular design would scale as 1/g.

A one-mile geodesic dome Cloud Nine is feasible on Earth, so six miles is probably possible on the Moon. More, if you use the difference in pressure to keep the roof up. The actual limit is probably financial - the amount of material will go as the cube of the radius. The cost will probably go as a higher power, as you have to get some of your material to the highest point. The time the site remains as a building site while you pay interest makes things worse. And if the dome is pierced by a meteorite, you lose the lot, and the odds of that go as the dome area.

I cannot see a design for one big dome being preferred to an array of less big domes. Unless you have auto have a dome of a certain size for some other reason.

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Here is data about the largest domes by diameter of various types from this list:

https://en.wikipedia.org/wiki/List_of_largest_domes

The Global Vipassan Pagoda in Mumbai, India (2006) has the widest stone dome in the world, at 86.15 meters or 279.4 feet.

The list gives the previous record holder as the Western Thermae in Gerasa, Jordan, (2nd Century AD) with a diameter of 15.0 meters or 49.2 feet.

However, another part of the list mentions the dome of the Gol Gumbaz, Bijapur, India (1659) at 44.0 meters or 144.36, which I think is also made of stone.

And I believe the dome of HItler's planned Volkshalle in Berlin would have made of stone and have a diameter of 250 meters or 820 feet. A plan for the railroad station in Munich called for a dome 265 meters or 869 feet in diameter.

https://en.wikipedia.org/wiki/Volkshalle#:~:text=Its%20dimensions%20were%20so%20large,Peter's%20Basilica.

https://en.wikipedia.org/wiki/M%C3%BCnchen_Hauptbahnhof#The_Reichsbahn_and_Hitler%E2%80%99s_reconstruction_plans

The widest reinforced concrete dome was the Kingdome (1976-2000) in Seattle, Washington at 201.17 meters or 660 feet. The previous record holder was the Norfolk Scope (1971) at Norfolf, Virginia, 134.1 meters or 440 feet.

The largest steel dome is the Singapore National Arena (2013) at 310 meters or 1,017.1 feet. The previous record holder was the Louisiana Superdome (1975) at 207.0 meters or 675.1 feet.

The widest wooden dome is the Superior Dome, Marquette, Michigan (1991) at 163.4 meters or 536 feet. It is a geodesic dome.

Richard Kirk mentioned that a one mile wide geodesic dome is feasble on Earth, about 10.095 times a wide as thelargest existing one. And possibly in some cases domes of other typescould be built ten times as wide as the widest existing examples of their types.

So there is no evidence that the present largest dome of a type is the largest possible dome of that type. Probably significantly larger domes of each type could be built on Earth. And of course on the moon with lower gravity and thus lower stresses on structures, a dome could probably be built much wider than the widest possible dome of that type on Earth.

The fourth largest buildng by volume on Earth is not supported by any columns. It is the Aerium in Hallbe, Brandenburg, Germany (2000). It was built as an airship hanger and now houses a tropical beach resort. It is 210 meters (688 feet) wide, 360 meters (1,181 feet) long, and 107 meters (351 feet) tall.

At 5.5 million m³ (194 million ft³), it is one of the largest buildings on Earth by volume, and is the world's largest single hall without supporting pillars inside.

https://en.wikipedia.org/wiki/Tropical_Islands_Resort

The covered dry docks for ship building at the Meyer Werft shipyards at Pappenburg, Germany are also huge.

"Dockhalle 2" is the world's largest shipbuilding hall. This is the world's first covered dry-dock - opened in 1987. The hall has length 370 m (1214 ft), width 101,5 m (333 ft) and height 60 m (197 ft). In 1991, the drydock was extended with 100 m (328 ft). In 2004, here was constructed a second roofed drydock, that was later extended to 504 m (length), 125 m (width) and 75 m (height). The project resulted into building capacity of 3 cruise ships a year.

https://www.cruisemapper.com/ports/papenburg-port-4004

An enclosed space without columns 504 meters (1,653.54 feet) by 125 meters (410.105 feet) by 75 meters (246.043 feet) has even more square feet than the Aerium.

I note that the widest clear span roof in ancient times was in the throne room of the Flavian Palace in Rome (1st century AD) with a span of 31.67 meters (103.9 feet) though its existance is uncertain. The widest clear span of a surviving Roman roof is that the Aula Regia or Basilica at Trier Germany (early 4th century aD0 with a span of 26.05 meters (85.46 feet).

https://en.wikipedia.org/wiki/List_of_ancient_Greek_and_Roman_roofs#cite_note-Ulrich_2007,_149-6

So there has been considerable progress in in roof spans the last 2,000 years.

Part two: Shellworlds.

A shellworld13 is any of several types of hypothetical megastructures:

A planet or a planetoid turned into series of concentric matryoshka doll-like layers supported by massive pillars. A shellworld of this type features prominently in Iain M. Banks' novel Matter.

A megastructure consisting of multiple layers of shells suspended above each other by orbital rings supported by hypothetical mass stream technology. This type of shellworld can be theoretically suspended above any type of stellar body, including planets, gas giants, stars and black holes. The most massive type of shellworld could be built around supermassive black holes at the center of galaxies.

An inflated canopy holding high pressure air around an otherwise airless world to create a breathable atmosphere.7 The pressure of the contained air supports the weight of the shell.

Completely hollow shell worlds can also be created on a planetary or larger scale by contained gas alone, also called bubbleworlds or gravitational balloons, as long as the outward pressure from the contained gas balances the gravitational contraction of the entire structure, resulting in no net force on the shell. The scale is limited only by the mass of gas enclosed; the shell can be made of any mundane material. The shell can have an additional atmosphere on the outside.5

https://en.wikipedia.org/wiki/Shellworld

Any of the first three types could be built on the Moon, with the tird type the least advanced technology.

I note that inflatable structures don't have to have a spherical shape. inflatable rubber rafts are an example. Holiday parades often involve giant ballons shaped like living beings who retain their complex shapes. I have seen photos of ballons shaped like buildings.

https://www.pinterest.com/pin/20125529555581997/

So builders on the Moon could build a flat airtight floor on the moon, with a triangular, square, rectangular, or hexagonal shape, and with some airlocks at the edges. And then they could attach an airtight fabric that has a roof shape dlike the floor with walls hanging doen to the floor (or to the airlocks, and attach the fabric to the floor and airlocks, make certain it is sealed airtight, and then inflate with a breatheable atmosphere. And a number of them could be built side by side connected by the airlocks. And possibly the vertical walls between connected balloon structures could eventually be cut away to make larger spaces.

And if the lunar regolith that was removed when they leveled the ground and built an airtight floot is then placed on top of the inflated areas, held up by air pressure, the enclosed areas will then be technically under lunar regolith and thus "underground". A thick enough layer of lunar regolith might provide protection against micrometeorites and solar and cosmic radiation.

On Earth air supposrted roofs have been built of considerable size but Ihav ebeen unable to find the larges tone.

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