Geodesic Dome

A few weeks before Lisbon Maker Faire we were discussing about the projects we would present this year. We wanted to take there something big, something different, and then it came to us, what about a geodesic dome? As we were working on the SatNOGS project, which we will post soon, we came across the domes for protecting the antennas, basically a radome. It started out as a crazy idea, but eventually we thought it was simple enough for us to do it in a short amount of time, using 3D printed connectors and PVC pipes and clamps. Sponsored by Grupo Rolear!

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We started by looking up for some online dome calculators, which there are a few ones. We mostly used the one from the website Desert Domes, and the first thing it asks for, is the type of dome. So let’s back up a little bit.

Geodesic domes are spherical architectonic structures formed by triangular elements that have local triangular rigidity and also distribute the stress evenly across the structure, therefore presenting great sturdiness while keeping the structure very light. For this reason they are quite popular.

The first dome that could be called “geodesic” was designed by Walther Bauersfeld for the Carl Zeiss Planetarium in Jena, Germany, after World War I. A few years later R. Buckminster Fuller named the dome Geodesic when he worked on the dome’s physics and engineering principles of tension and compression. Although Fuller didn’t invent it, he’s responsible for the popularization of the idea, because he developed the intrinsic mathematics of the dome, for which he received its patent in 1954.

Although its main shape is a sphere, most construction materials are flat, therefore it needed to evolve into something that used flat triangular formed shapes that resemble a sphere. Preferably using equilateral triangles all with the same size, but there are only 3 mathematical forms for this, the tetrahedron, the octahedron and the icosahedron:

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The more surfaces it has, the more similar it is to a sphere, so the icosahedron is the best solution. But still, 20 faces it’s still not enough, this would meant that the struts would be really long and would have to support a greater force. So the solution is to divide each face into more equilateral triangles, for example into 4, 9, 16 or any other perfect square number:

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The problem is, if we just divide the triangles, we’ll still get a flat surface which won’t be as resistant as it could be, so we need to push this triangle subdivisions inside-out. This adds a three-dimensional perspective to it and it means that the triangles are no longer flat nor equilateral, and the math becomes more complex, that’s why it’s a good idea to use the online calculators.

This level of subdivisions is what defines the types of geodesic domes. For example when we go to the Desert Dome calculator it asks what type and offers the options from 1V to 6V, but what is this? Well that’s the subdivisions of the original equilateral triangles of the icosahedron:

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So 1V is 1 subdivision, 2V is 4 subdivisions, 3V is 9 subdivisions, 4V is 16 subdivisions, 5V is 25 subdivisions and 6V corresponds to 36 subdivisions. The more subdivisions, the more similar it looks to a sphere, but also the more complex it is to build, since the struts will have a wider variety of measures.

We wanted to build this with PVC pipes which are generally sold 3m a piece. So it would be convenient if our amount and dimensions of struts would match the pipe. We also wanted the dome to be relatively big, at least with 2m radius. So after a few calculations and trial and error, we figured the best option for us would be to use the 3V dome with a radius of 2.4m, because this 3V domes only have 3 different measures of struts and all just under 1m, which means the 3 strut sizes could be fitted into a single 3m PVC pipe with almost no waste:

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Now it comes the choice about how much of the dome we’ll want to build. As we can observe on the table above, it offers the amount of materials to 3/8 or 5/8 of a sphere. Domes which have odd numbers of subdivisions for example the 3V (9 subdivisions) or 5V (25 subdivisions),  don’t have a center line or “equator” line to divide them in half so we have to choose between a slightly smaller or larger than half sphere. Unfortunately this also means that these odd domes won’t fit the floor so well, because the final layer of struts is not parallel to the ground. We opted for the 5/8, so even though the radius is 2.4m, at the center it will actually be higher than that, it will be approximately 2.8m high.

So according to the calculations, for 5/8 of a sphere, we’re gonna need, 30 A struts with 836mm, 55 B struts with 968mm and 80 C struts with 989mm.

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For the connectors we’re gonna need, 15 four-way connectors, 6 five-way connectors and 40 six-way connectors.

There are many different types of connectors for domes but we wanted to do something different and practical with the tools we have. So for these, we thought about designing a model to 3D print, after all it’s just 3 different designs and a total of 61 pieces. We tried several different designs, some of them based on PVC pipe fittings:

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But they all used too much material or were not strong enough or didn’t prove practical during the dome assembly and disassembly process.

Eventually we reached a design using PVC pipe clamps and M5 screws and nuts. This way we only needed the 3D part to support the clamps, giving them the angle needed for the dome’s curvature. Generally for a 3V dome, the angles are between 10º and 12º, so to simplify things, we just made them all with an average of 11º:

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We made all the designs are available on Thingiverse.

Then it was just a matter of dividing all the printing work by all our hackerspace members with 3D printers.

And in a matter of days, all the 61 connectors were ready:

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After this it was time to get the PVC pipes and the respective clamps. Fortunately we were able to get sponsored by Grupo Rolear, which very kindly provided us with some of the materials we needed. Rolear is a Portuguese company which represents several brands providing solutions for automation, hydraulics, electricity, among other areas.

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According to the calculations, we needed approximately 170m of PVC pipes and a little over 300 clamps. We used PVC pipes with a diameter of 20mm.

After we had the material we started by fitting the clamps in the connectors and fixing them all with the M5 screws and nuts:

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For the pipes, we used a cutting optimization software to make sure we wouldn’t waste more than we had to. After the optimization was complete and we had the optimized results, we moved on and started cutting the pipes:

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In less than 20 min, all the struts were cut and we were ready to start assembling the dome:

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The assembly was actually quite fast, took us a bit less than an hour to complete and it was pretty entertaining 😛

This 3D printed connector with clamps system proved out to be quite useful during the assembly and disassembly process, making it faster than other more common alternatives, however it makes the structure a bit less sturdy since the pipes can jump off a connector if the force applied to them is too much. We had this problem in the 3/8 of a sphere section but only after we assembled the full 5/8. Because that point is the most exterior part of dome, the force of the curvature tends to try and open that section. But we fixed it by passing a nylon fishing line inside the pipes, around the dome on that section, tightening it all together.

We then took the dome to Lisbon Maker Faire 2015 where it was a great addition to the faire, causing quite a great impact:

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So thank you Grupo Rolear for the support!

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