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A vacuum airship is an airship which uses vacuum as a "lifting gas" instead of helium or hydrogen. The main problem one faces when attempting to design such a vacuum airship is that no practical materials are both strong and light enough to make a vacuum "balloon" as they would all buckle under standard atmospheric pressure or themselves mass more than the displaced air.

One potential solution, mentioned on worldbuilding.se, is to actively prevent the (probably spherical) vacuum balloon from collapsing by holding it open with a magnetic field. To do so, the balloon could be wrapped in superconducting wire and then current would be sent through the wires. The answer mentions that the magnetic field built up would force the wire into a ring shape and be strong enough to hold the balloon open despite atmospheric pressure.

Questions:

  • Would running enough current through a loop of superconducting wire really force it into a hoop or ring shape?
  • How would I go about calculating the current required and the thickness of the wire?

Assume that the superconductor doesn't require cooling

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Hoops in the form of a solenoid do have weak points.

Although the magnetic field pushes out radially to expand the cross-sectional area of the hoops, it also pulls in axially to minimise the length of the solenoid, crushing the hoops together. See Does a current originates a magnetic force against itself?

I do not think it is possible to construct hoops around a sphere in such a way that you do not run into the above problem. This is related to the Hairy Ball Theorem. In topology a cylinder or cigar shape is equivalent to a sphere.

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  • $\begingroup$ In a solenoid, the magnetic field perpendicular to the hoop's area is important but in this case couldn't this effect simply be avoided by wrapping each loop with an identical loop with the current running in the opposite direction? $\endgroup$
    – Dragongeek
    Jan 12 '20 at 14:37
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    $\begingroup$ If you put two hoops together with the current running in opposite directions then the magnetic fields are also in opposite directions so they cancel out. There will be no resultant magnetic field to protect the airship. $\endgroup$ Jan 13 '20 at 7:27

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