## Building an EMT geodesic sphere

EMT = Electrical Metallic Tubing = thin wall electrical conduit = galvanized seam welded steel tubing

There are numerous places on the web to find the lengths of the members. There's also a fair amount of web literature on how to flatten the ends (vise, hammer and anvil, and arbor press seem to be the most popular) and drill for the bolts. The "burningman" thing has really inspired people to come up with a cheap, fast, easy to build structures. Building a model is highly recommended! I built my model from skewers and ring lugs, but other methods would work (soda straws, K'nex, etc.). Nothing beats being able to hold something in your hand when planning how to put it together.

In my case, I'm building a "2 frequency octahedral geodesic sphere". It's designed with a radius of 1.3 meters (48 inches). The dimension was chosen to maximize the size of the sphere, but still be able to slide it in and out of my garage (as if there was actually room for an 8 foot polyhedron in my garage). I also want it small enough that I can put it on top of the car to carry it around. Bearing in mind that there are all manner of rules about vehicles taller than 14 feet and wider than 8 feet, it seemed like 8 feet was a practical diameter.

The real thing is to minimize the amount of work involved. One could just do a brute force approach, calculate the lengths of the struts you need, get out the saw or tubing cutter, and hack away. There are 48 struts (in my sphere), so there's 48 cuts, 96 ends to flatten, 96 holes to drill, 96 ends to bend, and so forth.

There's also these joints where 4 or 6 struts meet, which makes quite a stack of pieces. I started thinking that one could make two struts out of one piece, flattening and drilling in the middle of the strut. A bit of contemplation will result in the observation that all geodesic spheres are made of circles (geodesics), and that furthermore, there are an even number of struts in each circle (in mine, the circles are composed of either 6 or 8 struts). Now, if one chooses the arrangement properly, you can make that stack of 6 struts as few as 3, and the stack of 4 as few as 2, although I'm not sure you can do that for ALL vertices.

Aha.. one only needs make 24 cuts! And, one only needs to flatten and drill 3 holes in each of the 24 pieces, for 72 holes total. The struts are exactly twice the length (plus the excess on each end). The drawing below shows one of the double "short" struts. The included angle between ends is 90 degrees, so it's from one of the octagonal geodesics.

For my sphere, it took about an hour to figure out how long to cut the tubing, find the cutter, do the cuts, get coffee, etc. As a practical matter, it's easier to measure the "cutoff" section, than the whole thing. A hack saw will work, as will a power reciprocating saw ("Sawz-all"), but for this thin wall steel, a tubing cutter works quieter, easier, doesn't leave ragged edges and filings all over, etc. Spend the few bucks for a cheap tubing cutter. If you were using 4130 steel or titanium or black iron water pipe, other cutting technology might be more appropriate.

 Strut length Length of two struts Actual length adding 3/4" on each end Cutoff piece 48" 96" 97.5" 22.5" 36.73" 73.47" 74.96" 45"

The next thing to do is to figure out how to arrange the double struts appropriately around the sphere, when building it. The trick is to minimize (or eliminate, if possible) the "stack of six lug" bolted joints.

Notes from 28 March 2004:

I wound up just using longer bolts and not worrying about where the stacks are. You're going to get some stacks of six, some of less, regardless. Perhaps this optimization would be a nice challenge for a mathematician to work out an elegant and generalized proof.

If I did it again, I wouldn't fool with trying to make double length struts. Just make the extra cuts, because assembly is easier.

### Fabrication

I chose the smash the end with a hammer approach, because I have hammers, I didn't want to clear the bench off to use the vise, and I don't have an arbor press. I figured I'd use the sledge hammer, but, in the interest of experimentation, I tried three different kinds of hammers, illustrated below. The sledge hammer on the left is to be preferred over the ball peen or carpenter's hammers on the right.

Here's what you get when you use the carpenter's hammer. Note the small dings in the end of the tube. It also takes a bunch of whacks to get it to this point. While time probably isn't money if you're building one of these spheres or domes, many whacks means more work, more time, and more work hardening of the tube.

Here's the sequence of bashing with the sledge. The left photo is after one hit, the right after three. This is clearly the way to go. Three whacks and you're done. If it takes more than 15-20 seconds, you're a really slow worker.

Watch out for splitting the tube. Choosing where the weld is (if you can find it) before bashing is the way to solve this. The following two pictures show a split in the middle (really bad, when it comes to drilling the hole), and along the side (probably not as big a deal). No matter how you're going to "form" the metal, you probably should allow for a few wasted pieces.

### Strength of materials

You won't find much on the web about the strength of conduit, for good reason. A manufacturer of conduit is making it to hold wires, not to be used as structural material. Even if they do know the structural properties, the manufacturer is probably not going to publish the data. However, we can make some educated guesses. It's a galvanized welded steel tube and the alloy and temper are chosen to be quite soft (because you need it to be easily and smoothly bendable without cracking or wrinkling). The following table has some dimensional properties of EMT

 Trade size lb/100ft ID (inch) OD (inch) Wall (Calculated) Cross Sectional Area (inch^2) Moment (inch^4) Section Modulus (inch^3) Radius of Gyration (inch) 1/2" 30 0.622 0.706 0.042 0.0876 0.004848 0.01373 0.2352 3/4" 46 0.824 0.922 0.049 0.1344 0.012843 0.02786 0.3091 1" 67 1.049 1.163 0.057 0.1981 0.030364 0.05222 0.3915

robot/emtsphere.htm - 29 November 2002 - Jim Lux