Maximizing efficiency of the The geodesic sphere (literally being on cloud nine)

Question

I’ve read about the geodesic sphere from other questions here and the underlying thing that confuses me isn’t the materials or the physics since both work, it’s making people live inside one. But what about just using the spheres to lift an island or a city by attaching it to the outside/top of the sphere instead of the inside of it. I know that you’d logically need to attach it to the ground via cables to stop it from flipping but I think this could be feasible. But I need to know if this would work, for context the structure would involve the spheres underneath the mass of land placed on top and the rocks and plants and people and animals would be on top of that. Would this model work? Or would a floating building with this method be a better idea/more feasible.

The planet this city is on has identical atmosphere and gravity to earth, and the normal laws of physics apply here. The alternative assembly of these cities would be for the geodesic spheres full of hot air to be above the city and suspending it like a balloon tied to a stick. This city would be positioned below the clouds in any scenario since that’s the best living condition for anyone on the surface of this sky city and water access is just some raindrops away (after being filtered of course) the low distance to the ground and likely being teathered in place to the surface also means that it has an easy way to get supplies to and from the surface. Those are the main specifications altitude and mobility wise for the city, it doesn’t move from its spot and no matter how high the spheres float in the sky the city musts be beneath the clouds where the air is still adaptable. So the flying height is most comparable to mountains that aren’t above the tree line.

Answer 1

Well, for starters, placing the load on top of the sphere is a bad idea because the arrangement is unstable. Any sideways force will encourage it to rotate until it hangs from the bottom. Hence why weights hang from the bottoms of balloons.

Placing the living areas outside the volume of hot air means placing people in the high altitude elements, which they would rather be sheltered from if placed inside the structure instead.

I'm not engineer but I'd wager that the tension cable mass is going to be similar between both approaches, inside or outside the envelope. The outside approach would require more mass for wind screens/shelter. The inside approach has the benefit of distributing the tension forces across the larger inner surface of the tensegrity sphere (which itself distributes stress nicely throughout itself). The outside approach, assuming the settlement isn't dangling miles below the balloon, sees a smaller bottom area to rig the cables (unless some cables reach through the outer envelope and gaps between tensegrity structural elements).

In the end, placing the settlement outside wastes the "waste" heat produced by the occupants and machinery, and forces the occupants out into the wind and cold, and forces the megastructure to deal with additional loads, from weight and turbulence.

Answer 2

This is mostly about scale.

Theses are basically hot air balloons, which generate lift by the hot air in the sphere weighing less than the normal atmospheric air displaced by the sphere. Air is pretty light and the lift force will not be able to support anything similarly sized of heavier materials. Think about the size comparison between the small basket and the rest of a hot air balloon. These ratios will be always be comparable. So any city or land area supported by the sphere will be very much smaller than the sphere.

Other issues:

Putting structures on top is inherently unstable. This could be fixed with multiple spheres or other stabilizing methods, but it would be a problem.

Many proposals use solar heating to help with heat generation, having stuff on top will make this less effective.

The geodesic structures can be light in comparison to other structures by always staying in tension. Putting loads on the inside of the structure mostly only adds more tensile forces. Putting loads outside of the sphere will add compression forces to the structure, requiring heavier structures to support the stresses.