A theoretical flotation device using a vacuum (for a novel)

[JeffCyr]

I'm writing a serialized Steampunk-fantasy story in which the cities float high in the planet's atmosphere using a combination of Magic and technology (sci-fi-ish steampunk technology) Though I want to bring it as close to real science as I can.

From some google searches it seems that a vacuum would be more buoyant than hydrogen due to how low it's density is (functionally 0 if I recall right) So assuming an unobtainium structure to house it, how much mass would a vacuum be capable of support a 1 atmosphere's worth of pressure (assuming average air pressure at sea level on earth) per volume, say 1 cubic meter or such.

(the following is purely context of the story)
The basic idea is to have the artificial landscape (including buildings, greenhouses, people, animals etc) be supported by massive structures of rings towering above it that would function similar to say a blimp's balloon. It would never need to be brought back down to the ground (in fact the whole idea is for the surface to be a long lost thing waterworld style) It will contain some magic and sci-fi to make due for what has yet to be made possible (I.e unobtainium) and if this wouldn't be possible short of having a structure equivalent to a space elevator I'd probably go full fantasy to make it happen anyway, I'd just prefer it be based on science for those few people who read fantasy/scifi and like to ask themselves "would this work?" and do the math.

Thanks!

 

[PeterDonis]

Moderator's note: moved to the Sci-Fi/Fantasy forum.

 

[JeffCyr]

Oops my bad didn't realize there was a dedicated section for this.

 

[Bystander]

https://www.google.com/search?q=den...ome..69i57.20876j0j9&sourceid=chrome&ie=UTF-8

 

[JeffCyr]

Yes thank you... The reason I haven't used this is that I'm a high school dropout. This gets me confused more than anything which is why I was hoping someone would be kind and give me the raw info of "X cubic meters of Vacuum could support Y mg at sea level"

 

[Drakkith]

So assuming an unobtainium structure to house it, how much mass would a vacuum be capable of support a 1 atmosphere's worth of pressure (assuming average air pressure at sea level on earth) per volume, say 1 cubic meter or such.

Archimedes principle can be stated as: (apparent weight of object) = (weight) - (weight of displaced fluid)

So a brick that weighs 10 lbs and displaces 2 lbs of water would feel as if it weighed 8 lbs when immersed.
However, when an object weighs less than the fluid it displaces, the result above is negative, and thus the object floats, acting as if it had negative weight.
Aa balloon full of helium that weighs (including the helium) 1 lb and displaces 5 lbs of air would act as if it weighed: 1 - 5 = - 4 lbs.

So the amount of weight that your vacuum container could hold up depends on how much air or water it displaces. To find that, simply take the density of the fluid and multiply it by the volume displaced. If your container's volume is 10 m³ and the air's density is 1.29 kg/m³, then the container displaces 12.9 kg of air. Plugging the density of a vacuum and the density of air into the above formula gives a result of -12.9 kg, indicating that it could support up to 12.9 kg of weight, including the weight of the container vessel itself.

Note that the density of air changes with height, temperature, and ambient air pressure, so there's no one single value that you should use. However this level of detail is rarely necessary to worry about in fiction.

Yes thank you... The reason I haven't used this is that I'm a high school dropout. This gets me confused more than anything which is why I was hoping someone would be kind and give me the raw info of "X cubic meters of Vacuum could support Y mg at sea level"

For every cubic meter of vacuum, you can support 1.29 kg of weight at sea level and 15°C, which includes the weight of the container vessel itself.

 

[JeffCyr]

Thank you very very very much! Both for giving me the simple answer I asked and for explaining it in detail. My intension was to have air density be overall much denser on the surface than at altitude, having the altitude where they "settled" their cities be at the same air pressure as sea level on Earth (didn't take into account temperature, though it could have seasonal tides rising and lowering as the temperature and thus density of the air shifted.)

Thank you very much!

 

[BillTre]

You might also have actual tides in the atmosphere (similar to the oceans) affecting the the levels at which your structures are in equilibrium at if you have something like the earth-moon system.

 

[JeffCyr]

You might also have actual tides in the atmosphere (similar to the oceans) affecting the the levels at which your structures are in equilibrium at if you have something like the earth-moon system.

Oooh that's an interesting idea thanks!

 

[Vanadium 50]

You're all working way too hard. (Or maybe that's "weigh" too hard)

Air has a molecular weight of about 29. Hydrogen has a molecular weight of about 2. So going from 29 to 0 gets only 7% more lift than going from 29 to 2. Even before adding whatever you need to hold the vacuum, there's just not a significant additional lift to be had.

Why not use Cavorite? What could be more steampunkish than that? (I'll send you an address to send my share of the royalties)

 

[JeffCyr]

I don't know what "Cavorite" is, while I love the steampunk aesthetic I'm rather shallow in my familiarity to it. Also 7% can be quite significant when you're talking tonnes, Plus hydrogen is flammable, I don't want the obvious "Hindenburg" foreshadowing. Yes instead it's catastrophic collapse that becomes obvious but I find that more appealing than "Giant fire ball explosion". I'll leave that for Michael Bay

 

[Vanadium 50]

I don't know what "Cavorite" is

It's a fictional material in H.G. Wells "The First Men In The Moon."

. Also 7% can be quite significant when you're talking tonnes

Not really. The reason we don't have floating cities today is not that we need to squeeze a few percent more lift out of balloons.

 

[JeffCyr]

Yeah I looked into Cavorite a bit, I don't really like the idea of borrowing terms from other fiction I'd prefer come up with my own or leave the unobtainium un-named

 

[rumborak]

Wow, that's crazy, I was just yesterday googling exactly this, i.e. how feasible suspending an object purely by vacuum would be. One interesting thing I found was that most calculations I saw online presumed a spherical shape, and then calculating the necessary compression strength of the material. I was actually thinking more along the lines of a cube whose corners are fixed but the sides would be stretchy material. This way you could rely on material tensile strength again like in a normal balloon, not compression strength.

 

[JeffCyr]

I think the reason why spheres are the assumed shape is due to the inherent benefit of having all the pressure be evenly distributed. The reason though why I wanted to use a vacuum rather than gas is mostly because I don't want a simple blimp or balloon shape I wanted something distinctly unique which is why I was imagining a series of massive rings made of some ultra-light yet resilient material (I.e: Unobtainium, a material that doesn't exist but fits the bill perfectly)