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Buckminster Fuller has popularized Geodesic Domes (invented by Dr. Walther Bauersfeld who based it on the use of convex polyhedrons), and thus, making buildings with a very large roofs that don't need pillars. In popular science magazines it's said that if you just make the Geodesic Dome large enough, it would float by it self because the air pressure underneath the dome would be bigger than the weight pressing it down, and so, it would float.

Question: Has there ever been an serious attempt to prove that this was theoretically or even practically possible?

In the sense that has there ever been a serious paper published about this, at a university or institute?

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  • $\begingroup$ Interesting question. I remember reading about this in literature too. It SHOULD be possible, but AFAIK, there has been no attempt to prove this theory. And I have no scientiific paperwork to back that up, so I'm just commenting not answering. $\endgroup$ Dec 1, 2019 at 4:31
  • $\begingroup$ If the dome was large enough that there is a significant vertical pressure gradient outside the dome then surely there would be the same pressure gradient inside the dome and any lift would be cancelled out. Wouldn't it? $\endgroup$
    – Transistor
    Dec 2, 2019 at 9:26
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    $\begingroup$ @Transistor if you take a paper/plastic cup and invert and place in a sink/tub full of water the cup does not sink to the bottom immediately. It tries to float. Because the centre of gravity is so high it then tends to flip at which point it fills with water and sinks. This same principle should apply for the dome. I would image its similar to taking a clear glass and doing the same thing you will note that the water level inside the glass is lower than the water outside the glass. you would need to design it so that the weight of the displace water is equal to the weight of your struct. $\endgroup$
    – Forward Ed
    Dec 3, 2019 at 15:58
  • $\begingroup$ @ForwardEd: There was no mention of water or any other liquid in the question. $\endgroup$
    – Transistor
    Dec 3, 2019 at 18:52
  • $\begingroup$ @Transistor apologies, when I read float I took it as floating on a fluid much like a boat $\endgroup$
    – Forward Ed
    Dec 3, 2019 at 19:57

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You question makes mention of "float" but you later make the point that you made "no mention of water or any other liquid". That certainly creates confusion.

If you are talking about a self-supporting (aka rigid) dome, that is "the nature of the beast" when it comes to Buckminster Fuller domes. However, I need to point out that those are usually "thick-skinned" domes (or dual-domed truss frameworks). Many designs of this type exist and have been conceived, analyzed and built by architectural/engineering firms world-wide. No mystery to those in the know.

If you are referring to a non-rigid dome, namely sheets of polygons (or other patterns) bound together (bonded, glued or stitched) in the appropriate pattern, then inflated, you are simply referring to an inflatable dome, and there is no requirement for that to be a bucky-styled dome; only that it be properly anchored to the foundation and sufficient compressed air volume pumped into the dome to ensure "positive-pressure", which would create a net force greater than the weight of the membrane, thereby supporting the membrane and keeping it from collapsing. Again, many designs of this type exist and have been conceived, analyzed and built by architectural/engineering firms world-wide. No mystery here, either, to those in the know.

If, on the other hand, you did intent to have a dome floating on a lake (or the ocean), you need to ensure that either of the two above design concepts are implemented on a sufficiently inflated base such that the majority of the dome is above the surface of the water. Otherwise, if it is fully submerged, then the flotation must be enough to provide "neutral boyancy" such that the dome is neither surface-piercing, nor so heavy as to sink to the bottom. (On second-thought, surface-piercing might be he most stable configuration.) In this configuration, the "ballast" weight must be below the domed structure and be such that there would be no tendency for the dome to "right" itself (a.k.a. flip upside-down). Without detailed analysis, I could not say whether such a design would be possible. If you did pursue this type of structure, my personal recommendation is to approach (or engage) a naval architect who would be most knowledgeable in the design of maritime vessel buoyancy/stability applicable to this kind of design.

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One way to interpret this scenario is to envision a rigid geodesic dome completed into a sphere, and ask if it could float in the atmosphere because the weight of the contained air is less than the air displaced.

In order for this to happen, the density of the contained air would have to be less than that of the air immediately outside the dome/sphere. With a balloon, you achieve that by heating the air inside, or using a different gas. But, if we want this to work just based on the physical properties of a geodesic dome, you could imagine pumping some of the air out to reduce the density.

Under this interpretation of the question, I strongly suspect that the answer is No. I realize there is a theoretical analysis saying that geodesic domes are stronger the larger they get, but they are effectively an approximation to a thin spherical shell, and, the larger they get, the easier it is for there to be a small irregularity that leads to an uneven force distribution and failure under pressure.

This is not a solid theoretical analysis, and I am open to correction from experts (which I am not). But, since their heyday in the 1970s, geodesic domes have been used less and less to cover large open spaces. My sense is that, if the structural benefits were as significant as popular magazines made them sound, they would have been used more in practice over the past five decades.

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Geodesic dome is one lightest structures per capita in terms of volume. Inflated with air in a sealed structure is doable. And possible based on concepts presented by seasteaders and oceanic building advocates.

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