Can a Floating Tensegrity Sphere Support a Mini-City in the Sky?

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Discussion Overview

The discussion revolves around the feasibility of constructing a floating tensegrity sphere capable of supporting a mini-city in the sky. It explores theoretical concepts related to buoyancy, pressure differences, and structural integrity, as well as practical implications and potential challenges associated with such a structure.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant references Buckminster Fuller's idea that a sufficiently large geodesic sphere could lift a significant mass due to the volume of air it encloses and proposes a formula for calculating the mass supported by such a sphere based on temperature, height, and radius.
  • Another participant suggests that while a large sphere could theoretically support a floating city, the need for structural integrity against pressure differences could complicate the design, potentially negating the benefits of buoyancy.
  • Some participants propose using helium or hydrogen instead of air to achieve buoyancy, noting the cost and safety considerations associated with these gases.
  • Concerns are raised about the security risks of living in a floating city, with one participant humorously suggesting it could be weaponized.
  • A later reply discusses the structural challenges, indicating that as the radius of the sphere increases, the required thickness of the shell must also increase to handle stress, which could lead to impractical mass increases.
  • Another participant mentions additional factors such as low oxygen levels and cold temperatures that could impact the viability of living in such a structure.

Areas of Agreement / Disagreement

Participants express a range of views, with some supporting the idea of a floating city while others highlight significant structural and safety challenges. The discussion remains unresolved, with no consensus on the feasibility of the concept.

Contextual Notes

Participants note various assumptions regarding pressure differences, material properties, and safety measures, which remain unexamined in detail. The discussion also highlights the dependence on specific gas properties and environmental conditions.

Cannon
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I came across this online the other day:

As a sphere gets bigger, the volume it encloses grows much faster than the mass of the enclosing structure itself. Fuller suggested that the mass of a mile-wide geodesic sphere would be negligible compared to the mass of the air trapped within it. He suggested that if the air inside such a sphere were heated even by one degree higher than the ambient temperature of its surroundings, the sphere could become airborne. He calculated that such a balloon could lift a considerable mass, and hence that 'mini-cities' or airborne towns of thousands of people could be built in this way. These 'cloud nines' could be tethered, or free-floating, or perhaps maneuverable so that they could 'migrate' in response to climatic and environmental conditions.

I came up with a formula for calculating the mass supported by such a sphere of air (as a function of temperature, height and radius), and just wanted to see if my math checks out.

http://designbyninjas.com/calculation.jpg

Also, since the air pressure is the same inside as out, would there be any feasible way to pressurize such a system?
 
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Do you by chance recall the link to that?
 
Indeed, a large enough sphere could be used to build a floating city. Also, as a sphere gets bigger the mathematics of heating it up works out to be more and more economical. However, there is the issue of pressure difference. A sphere built to contain even a small pressure difference might need walls so thick it could end up defeating the purpose.

But you don't really need pressure difference or even temperature difference. Just replace the nitrogen in the air inside the sphere with helium. Helium too expensive? Then replace it with hydrogen; but include safety measures so as to avoid super-Hindenburg scenarios.
 
Not to burst anyone's bubble(pun intended) would anyone really want to live in a floating city that would be an ultimate, and easy, target for terrorists?
 
pallidin said:
Not to burst anyone's bubble(pun intended) would anyone really want to live in a floating city that would be an ultimate, and easy, target for terrorists?

Yes!
Alternatively, it could be turned into a miniature Death Star. If fitted with electronic countermeasures and lots of missiles, it could be used to invade enemy territories...
 
The stress on the shell, due to buoyancy, is quadratic in radius. The cross-section area of the shell, however, given constant thickness, increases linearly. That means, at some point, you'll have to start increasing thickness of the shell linearly with the size. If you start scaling thickness linearly with the size, the mass of the shell goes up as a cube of the size, same as the mass of enclosed air.

In other words, no, it won't work.
 
Love this discussion, I summarized it on my blog, http://lawoftheair.com. While you mention the density and defense issues, you leave out low oxygen and the COLD.
 

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