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In this world, there is a land isolated by a lava line, and the only way to get in there, is across a bridge levitated by hot air balloons.

I had the idea of making a wooden bridge being supported by those hot air balloons, which would levitate through the warm air of this volcanic region. However, I know that balloons can only levitate if the air around them is colder than its interior. So I had the idea of using pipes of some light metal (such as aluminum) that would connect the hot air of the lava to the balloons, which would be at a higher, but steady, height.

Would it be possible? Or just impractical? Since it would be easier to make small trips to the place?

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    $\begingroup$ balloons can only levitate if the air around them is denser than its interior... $\endgroup$ – nzaman Apr 19 at 15:51
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    $\begingroup$ Wood, silk & aluminium don't sound like very great materials to use in a region of extreme vulcanism. Especially in an area with continuous extreme vulcanism. $\endgroup$ – elemtilas Apr 19 at 16:12
  • $\begingroup$ Most steampunk doesn't seem to care much about real science -- why not just handwave the bridge? $\endgroup$ – Zeiss Ikon Apr 19 at 16:37
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    $\begingroup$ Alternatively, you could use parachute wings to lift the bridge through the continuous ascending hot air currents from the lava line. Not necessarily more plausible, but an option for varying the aesthetics $\endgroup$ – Eth Apr 19 at 17:03
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    $\begingroup$ @JBH: Nope, I was correcting precisely that statement made in the original question. Temperature isn't important, density is. It's just that hot air tends be less dense than cold air at the same pressure. Paul TIKI's answer makes the point clearly $\endgroup$ – nzaman Apr 21 at 14:23
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Not going to work, at least not quite like envisioned.

The key to Hot air Ballooning, or other kinds of ballooning for that matter, is gas density. The gas in the balloon has to be significantly less dense than the surrounding gas. For something like a balloon suspended bridge, the density of the whole balloon bridge system has to be less than the surrounding atmosphere. That means total volume and mass has to be accounted for. Then it has to be less than the surrounding atmosphere. Here is where your first problem comes up. The air around lava is going to be hot, and not very dense. That means regardless of how you get hot air in the balloon envelope, You will still need a very large envelope.

Next, you don't want the envelopes, or even the bridge, too close to the surface of the lava field. Not only is the air being heated, it's also probably giving off all sorts of nasty fumes and such. These are certain to be un breathable and also likely to be caustic. Wood and natural fibers are going to rot quickly, requiring near constant maintenance. Using steel would slow the process, but it would be way too heavy to be practical.

Finally, you need to consider that the closer to the lava field, the hotter the air will be. It will cool quickly as it mixes with outside air, but if you are too close to the surface, anyone standing on the bridge runs a chance of being baked alive. How long could you stick your head in a 400 degree oven and breath that air? It would dry lungs out in a flash. Your bridge has to be high enough so that you don't cook your travelers.

So here is what might do. A bridge in need of enormous amounts of maintenance. You could protect the envelopes somewhat by affixing them to very long lines above the bridge. That would add to bouyancy as well. Downside to that is you would then add complications of different winds the higher up you go. The travelers would have to ascend to the bridge surface well back from the lava field. They would then have to descend a good ways from the field on the other side.

So it could work, but it becomes something so strange that simply going up and over in an airship would be simpler, safer, and much more certain. Kind of like the apocryphal story of the US spending a lot of time and development going into a zero gee pen and the Russians just using a pencil.

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This sounds really impractical but it can be possible (probably).

Firstly: The air around the exterior of the balloon needs to be cooled down significantly so as to ensure that the air inside the balloon is sparser (less dense) than the exterior air. In order to do so, it would be advisable to have a cooling system placed inside the basket that instead of providing lift through heating (as opposed to the working of a normal hot air balloon). This cooling system will cool the air around the hot air balloon and allow the naturally vented air rising from the volcano to provide a lift to the balloon.

Secondly: Since now the air vented is highly distributed and not concentrated directly into the balloon, it would require a change in the structure of your balloon to allow the air to either generate enough lift or require an "air-concentrator" system that can concentrate your air into the balloon. Basically, ensuring that the venturi effect plays a significant role. Note that this system can not be composed of metals, fabrics or any material that gets negatively affected by the heat emerging from the ground.

Thirdly: Even after doing so you cannot quite guarantee that the structure will be able to provide enough stability. Since the land is surrounded by a lava-line, the structure will be prone to movement due to a constant fluctuation in the wind patterns that happen in the vicinity of such places of high air turbulence.

All in all, it's quite impractical, if not impossible.

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