# Superconducting hoop balloon calculation

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