This is a slideshow of one aspect of my alternate energy research.
I derived a set of equations to make spherical structures (to tesselate regular polyhedra, or Platonic Solids) and wrote a computer program that handled all the math from a choice of simple inputs (inner or outer radius, edge or face count, maximum edge length, etc.). In the end, the user (a layman) would only have to pick a size and cut the materials as listed.
My brother wanted to build a shed, and I told him spheres (domes) yield the most volume using the minimum amount of materials, maximum strength, etc. I estimated that for the same money < $2,000, we could build a superior structure to house 6 home-improvement-store-sized sheds, each almost costing that much. Spheres are the most efficient volumetric shape, which is why nature uses them from atoms, to cells, to planets, etc. If you compare surface area (which is your cost in materials) to enclosed volume (which is what you want the most of) then the spherical shape will always win mathematically, regardless of material choice (wood, aluminum, carbon fiber, rock, concrete, steel, whatever). The only reservations in building spherical structures is each of our opinions of aesthetics, and simplifying the mathematics which was the part I was focusing on here. Also note: domes are optically misleading - they look small from the outside yet massive from the inside. I am aware of that, but I'm always reminded of it in these pictures - it looks so big from the inside, yet much smaller from the outside. Also, the walls and the roof are all made the same and of the same material - it's all continuous, so no seam problems and of equal strength, R-value, etc., from any direction. And finally, when empty, sound (heat, light, and other waveforms) are easily reflected all around inside, but 'perfectly reflected' from the dead center. If you stand there and whisper, it sounds like it's amplified through a microphone, and it echoes back at you in surround stereo! If you hum (meditate) then your head vibrates and completely resonates! Oh, almost forgot a huge advantage - you don't have to decide on the interior until later - you can pick room layouts, or not, or change it all at will later on, since the structure doesn't need any interior room walls for support! Pay for a shell, move in, and decide and pay for interior features later! This makes them very affordable upfront and completely flexible to every interior design style. You could spread sand on the floor, paint clouds/skyscape on the walls, plant some palm trees, haul in your yacht and live in that - neighbors would never know, HA!
The frame was made from approximately 4 foot long elements of half-inch thick rebar (ridiculously inexpensive). Most adults could bend a 4 foot long piece of half-inch rebar in half with their hands - they are not very rigid. Yet, when attached in triangular form and linked into a spherical shape then they are shockingly stout, as each reinforces the others in both tension and compression. Therefore, we could easily use the structure itself as its own scaffolding as we progressed upward and the frame alone could easily support our combined weights and much more even while not completed. The frame was so light for it's volume and strength, that we could lift the structure, yet it could also support dozens of us (tons). The foot print was so light compared to other structures that no slab or concrete footing was needed - the circular base only needed to support a ground pressure less than that of a human foot print. I placed an inner and an outer ring at the peak which could be used as a lift point from the inside, and as a repel/rope anchor for the later work around the outside - it was very convenient and very fun.
Three-quarter-inch thick OSB wood triangles were inlaid into the frame and attached to brackets wherein the structure instantly became highly rigid. The seams were filled with insulating spray foam. Corrugated plastic (insulating with trapped air in the corrugation space and smooth surfaced for the later mylar overwrap) was attached to the OSB, and mirrored mylar (for heat reflection) was attached to the corrugated plastic.
The triangular doorways housed opposing doors (left and right doors that joined in the middle) and I added rails so the doors could pull open outwards and then slide around the dome on the rails similar to the mechanisms of a minivan's sliding door.
Partway through, we decided to throw a tarp over the frame to get a feel for the volume and for some shade. We hung a swing which was capable of 360 degree motion and had a lot of fun with the neighborhood kids!
Turns out there were no mistakes so I had enough rebar/steel left over to also build a windmill tower, a trussed table, a bending brake, shelves for the first floor, a push cart, and more :)
Music: Peter Gabriel - "Down To Earth" (WALL•E [Soundtrack from the Motion Picture])
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