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I know that for airships, the maximum practical size could be limited by factors like air resistance, the danger of a collision with the earth when landing, the need to build huge hangars, etc. But for a tethered balloon that is designed to remain in one location rather than fly from place to place, and which could be held stable by tethers when landing, and which would need at most only one humungous hangar, what might the maximum size of such a balloon be?

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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Dec 29, 2021 at 20:35
  • $\begingroup$ You can make the balloon itself as large as you want. The devices for controlling the balloon are a different story, and they will create structural problems. How far you can push it depends on what you intend to use the balloon for, on how long you intend to use the balloon, in what kind of weather, and how large a budget you can justify. $\endgroup$
    – AlexP
    Dec 29, 2021 at 20:46
  • $\begingroup$ I guess that the moon's orbit is a limiting factor, unless you point the thing orthogonally to it's plane of orbit. What's the balloon supposed to be for? $\endgroup$ Dec 29, 2021 at 21:22

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The weight of your balloon won't be an issue.. size could be 80km or so

Supposed the balloon is filled with a gas that would normally leave the planet atmosphere, e.g. hydrogen, its own weight would not limit upforce inside the atmosphere. It can always be designed in such a way, it can carry its own hull. Surface of the balloon goes 3th power, volume (which will decide the lift) will go 4th power. When it would not be attached to the surface, max size at first glance will be the height of the atmosphere that can provide a lift (say 80km).

Pressure of the gas inside the balloon

A limiting factor at stratospheric heights and above is inflation of the balloon. The higher you go up, the lower the external pressure will be and the more pressure your balloon hull will get from the gas inside. The balloon gas will want to escape. This could inhibit your balloon to penetrate too deep into space. Of course, you could add (much) more balloon material, like it is done with weather balloons. This will increase the weight of your balloon without it gaining extra volume. Stratospheric weather balloons don't enter space.

A challenge will be the tether cable

When the balloon is huge, but smaller than the height of the atmosphere, you'd need a long tether cable. That must be very strong and very firmly anchored. I think the max size of your balloon will be such, that it sticks out into space, balancing forces, to lower the pulling force on the tether cable.

On the other end, a tethered balloon should maintain enough pulling force, to keep its tether cable in a vertical position, else the tether could bend and break. To achieve that, your balloon should be able to carry multiple times the weight of its tether, and the tether cable should be able to carry its own weight, while resisting the pull. Your balloon can always provide sufficient upforce. Being attached to earth, the centrifugal force of earth's rotation could even provide a lift of your tethered balloon further into space, enabling it to become even larger than 80km in size.

Actually.. When your technology is able to produce a a balloon, a tether cable light enough, long enough and strong enough, I don't expect any real limits on the balloon size itself, except for available resources: you'll have to fill a giant balloon with hydrogen or helium, which will not be a cheap enterprise !

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  • $\begingroup$ Wonderful answer, thanks very much! That is cool to know that theoretically the limits could be pushed so far. As a follow up, what might a more conservative, practical, but still gigantic size be for a tethered balloon? For example, what issues might a 5km-diameter balloon face, rather than the full 80km you mentioned? How practical would a tether be for a balloon that big? How much lifting capacity would the balloon have? What uses might the balloon be able to serve? $\endgroup$ Dec 29, 2021 at 22:19
  • $\begingroup$ @Jshupac I can't do these calculations, but I believe gathering the hydrogen needed will be the largest issue. In the year 2020, roughly 87 million tons hydrogen were produced. For your balloon 5km diameter, you would need about half this production to fill its 523,598,775,598 cubic meters, 42 million ton. Find calculators at omnicalculator.com/math/sphere-volume and aqua-calc.com/calculate/volume-to-weight $\endgroup$
    – Goodies
    Dec 29, 2021 at 22:25
  • $\begingroup$ Wow, that is a hell of a lot of hydrogen. Does that mean it could lift 42 million tons of stuff, in theory? Because that would be about the weight of 200 container ships.. $\endgroup$ Dec 29, 2021 at 22:37
  • $\begingroup$ Absolutely ! No problem... if you can make the hull and tether.. just use Archimedes.. the difference in density of air and hydrogen will provide you with the upward force. A balloon of 1m diameter works, a balloon of 5000m diameter will work as well. And provide very much more upforce. That tether cable of yours better be good, it needs an ANCHOR and you don't have to fill all the balloon's volume. Say, 5-10% will do for this huge size of balloon. Look at weather balloons, you get an idea of the volume of hydrogen used in daily practice. Up high, it expands to its full size. $\endgroup$
    – Goodies
    Dec 29, 2021 at 22:44

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