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In this question here there is an answer telling that it would be possible to make a vacuum balloon using superconductors, however, we are nowhere close to a room-temperature superconductor.

Assuming we use accessible electromagnetic structure similar to a space fountain or anything that can be used as a tissue to make a sphere, how much energy I would require to make a vacuum balloon?

If it is possible and viable, you could use a vacuum balloon to reach space, what could be excellent for space exploration.

Fulano
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    to reach space you need to go fast, not high. I don't see how a vacuum balloon would help – L.Dutch Apr 02 '21 at 15:18
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    @L.Dutch-ReinstateMonica starting from high up means you don't need to worry nearly as much about aerodynamics and drag, or rocket nozzles that work at sea level as well as higher altitudes, and you've potentially cut right down on your gravity drag, too. "Ballockets" aren't useless, but they're not nearly as useful as they might appear on paper, see spaceexploration.SE questions ad nauseam. – Starfish Prime Apr 02 '21 at 15:29
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    @L.Dutch - Reinstate Monica: Sort of. You could reach space by going high, slowly. It's just that when you stop thrusting, or your vacuum balloon pops, you come right back down again. (See e.g. sounding rockets, the X-15, SpaceShip 1, &c.) You need to go fast (orbital velocity, at least) to STAY in space. – jamesqf Apr 03 '21 at 18:55

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You can think of your superconducting balloon a little like a conventional party balloon... energy is required to inflate it, but once inflated no additional work needs to be done. In the party balloon, energy is stored in stretched polymer chains and in the compressed gas trapped inside, and in your superconducting balloon it is stored in the magnetic field that is holding its shape.

Working out the energy required to "inflate" your magnetic balloon is fiddly, but you could imagine using the old "work done = force x distance" to model the force required to evacuate a 1x1x1m box by pulling a 1x1m plunger out leaving a near-perfect vacuum behind. This would be ~100000N * 1m or 100kJ per cubic metre (or 100 J/l).

You'll need to maintain appropriate conditions for your superconductor to continue functioning, eg. keeping it at a suitable working temperature, and that might consume power but that's not directly related to the magnetic field as such.

If it is possible and viable, you could use a vacuum balloon to reach space

You could not.

The force of bouyancy is $F_b = \rho_f V g$ where $\rho_f$ is the density of the fluid the object is in (eg, the atmosphere), $V$ is the volume of the object and $g$ is the acceleration due to gravity at the location of the object. This is of course opposed by the weight of the object.

Assuming the object has a constant mass, as it rises gravity will slowly fall and hence its weight will reduce. Unfortunately, the density of the air will also fall, and it falls much faster... it falls by a factor of $e$ (~2.718) each time you rise by the atmosphere's scale height. The scale height on Earth is about 8.5km, so the force of bouyancy is reduced by a factor of 2 every time you rise by about 5.9km. The force of gravity is reduced by a factor of two when you rise up by ~2640km (a distance of $R_e \sqrt{2}$ from the centre of the Earth, where $R_e$ is the radius of the Earth)... that's a 300 times lower rate of decrease.

You can see that even with a vacuum balloon you just can't get that high up because the bouyancy force becomes negligible compared to your weight, and in the end you can't get that much higher than with a plain old hydrogen balloon (and you may find the hydrogen balloon can use a lighter canopy, and is a lot simpler and cheaper to boot!). People have used rockoons (or "ballockets", which is clearly a better term) for years, and they're useful for small rockets and specialist tasks but really they just aren't that great compared to a regular rocket launch, especially as you'd still need >7km/s delta-V even if you could float up to low orbit. Which you can't.

Starfish Prime
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    A hypothetical situation where vacuum balloons become useful is if you have a low thrust engine with very high deltaV and a thick atmosphere/high g planet. You can also use them to make solarpunk spacecraft if you imagine you have access to a low thrust reactionless drive. Other than that: not super useful. +1 – Joe Bloggs Apr 03 '21 at 06:28
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    @JoeBloggs it depends how high up you can get with it, which depends very much on material constraints. A hydrogen balloon can have a very simple, very light canopy by comparison. Here's a relevant spaceexploration.SE answer... getting up to an altitude where an ion drive might be useful seems like it may be impractical, and even if it were practical it isn't clear that doing it with a balloon is better than eg. a rocket. – Starfish Prime Apr 04 '21 at 07:55
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    Yeah, the thing that thick atmosphere and high g’s does is make rocketry increasingly difficult and makes a heavier envelope less of a disadvantage, not that it makes balloons much better. – Joe Bloggs Apr 04 '21 at 21:08
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The amount of energy to bring a volume V from pressure $P_1$ to a pressure $P_0$ would be $E=\int_{P_0}^{P_1} Vdp$. That amount of energy depends only on the $V(P)$ and doesn't care if you are using a donkey, a human or any other mean of evacuation.

Assuming with a very gross simplification that the volume stays constant during the entire process, that there are no losses and that the gas can be treated like an ideal gas, the energy needed would be $E=V(P_1-P_0)$, measuring the pressure in $Pa$ and the volume in $m^3$.

L.Dutch
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