the lightest (floating) geodesic structure

[giulio zanni]

Hello everyone, my goal is to find the lightest spherical geodesic structure (possibly tensegrity) able to support a membrane in order to withstand an external pressure. Inside the sphere there is a void (no gas). the spherical shape is not mandatory, the idea is to maximize the volume and the pressure resistance minimizing weight. The structure, if sufficiently large, should be able to float in the air ... What do you think about this project?

[TaffGoch]

If you are referring to atmospheric pressure, on the outside of a vacuum vessel, I can tell you that the vessel must be tremendously strong. The larger the vessel, the more-drastic the results.

Memorize two rules, for any sphere:

 • the surface-area goes up as the square² of the radius

 • the volume goes up as the cube³ of the radius

For example, as the radius of a spherical vacuum-vessel doubles, the surface area quadruples. That's why you only (commonly) see small vacuum vessels. The large vacuum vessels, used for vacuum-drying biological materials, have VERY thick walls of welded steel.

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Note that Buckminster Fuller postulated a lightweight geodesic dome/sphere, containing heated air (solar or urban sourced,) which would be self-supporting, or would float like a hot-air balloon. So, you don't, necessarily, need a vacuum. Less-dense gas may, perhaps, be sufficient for your goal.

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The "vacuum bouyant" concept is not new. Various scientists, for decades, have postulated such, but found no solution, due to the non-existence of structural material that is lightweight, yet, strong enough. Some scientists think that, perhaps, a future form of carbon nanotube-weave material may someday be developed, which would meet the strength requirements.

-Taff

[giulio zanni]

Hi Taff, thanks for the reply.

I know, at least in part, the history and the arguments against this idea as well as the elementary aspects of the relationship between radius, surface area and volume of solids.
However I am still interested to explore the issue in terms of quantities  involved and feasible optimizations.

For example: the vacuum can be more or less high or forced, a membrane in pure tension supported by struts could be stronger and lighter than a convex compressed shell ... and so on.

In other words, this is the question:
lead the well-known difficulties to an impossibility numerically and mathematically proven?

In any case, from a geometric and structural point of view, regardless of the question of the "vacuum bouyant" concept, the problem is quite attractive to me, so I renew my question:

What is the lightest (spherical) geodesic (or not) structure for the same volume and resistance?

I imagine that the best one should have many rods and less struts, because struts have to be heavier to contrast instability ...
For example I considered, for its simplicity, a tensegrity (?) icosahedron made of internal struts passing through its center and all the edges in tension (tension rods)... 

thanks for your help.

Giulio

[giulio zanni]

The icosahedron I thought of, is likely a hyperbolic icosahedron  for the effect of the elastic deformation of the membrane and of the rods under the action of the external pressure:

[TaffGoch]

The image you provided clarifies the inquiry -- either an internal or external rigid framework, to support a membrane stressed by external pressure.

Any contributions or comments, for the question?