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Details for constructing a
Small Geodesic Dome
Plans for making a dome.
16 foot diameter steel conduit frame. 24-foot nylon parachute. 200 square feet of floor space.
by MiJa Gourlay
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Details for constructing aSmall Geodesic DomePlans for making a dome.16 foot diameter steel conduit frame. 24-foot nylon parachute. 200 square feet of floor space. by MiJa Gourlay |
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The materials for this dome include
Although smaller conduit has some popularity among dome builders, I do not recommend using 1/2 inch diameter conduit because it will not survive being climbed or hung on and this invariably happens. In fact, 3/4 inch diameter poles will not usually survive climbing or hanging either. If you intend to have a lot of gymnastics on your dome, use 1 inch or 1-1/4 inch diameter EMT, or use rigid pipe. Also, 1/2 inch diameter conduit is not strong enough for the "entrance" modification described below. 1/2 inch diameter conduit is also 25% cheaper.
The above number of nuts and bolts exceeds the number required; this dome has only 26 vertices. Extra nuts and bolts are desirable because some of these small parts will be lost (often at the worst possible moment).
Note that bolts with a 3/8 inch diameter shaft have 9/16 inch hex heads. This is important when choosing a wrench. (Of course, you would figure out this detail on your own, but it is worth mentioning that when I write 3/8 inch diameter bolt, I am referring to the shaft diameter, not the size of the hex head.) When you obtain the bolts, the hardware store will list the bolts by the size of their shaft, not the size of their heads. (This whole paragraph is far too phallic.)
Bolts with a diameter of 5/16 inch could be used instead at the loss of some strength. Smaller bolts would be slightly cheaper, and would also work better for a dome made of 1/2 inch diameter conduit poles.
When buying bolts, note the extent of the threads. Some hex-head cap bolts have thread only along about 1 inch of the end of the bolt. Using extra long all-thread bolts allows you to have a long bolt so that you can fit all of the edges at the vertices easily even if they are bent out of shape (as will happen if the ends are not parallel) but still allow you to tighten down the vertex as far as it can go.
The bolts listed above significantly exceed the length required for simply fastening the poles. The extra length is a hazard if the bolts are not capped. The extra length can also be used to attach a covering, such as tarps strategically cut and grommetted to rest on the dome vertices.
I purchased the parachute from the Boulder Army Store. The parachute was marked with a label, ``May 1945 Eagle Parachute Corp.''. It has 24 radial ribs with cotton twine running along the ribs, terminating at the bottom with about 2 feet of twine to attach to something (and the ends of the ribs are numbered for your convenience!). At the top of the parachute is a hole, about 1 foot in diameter, where all of the twine ribs cross. (This hole is always present in circular parachutes to let air pass through to keep the parachute from collapsing when it is deployed.) The cost was $96 including sales tax. My understanding is that similarly sized parachutes are available for far less money (as little as $30) although it is not clear whether there is a difference in quality (e.g. in the thickness of the material.)
The tools I used to construct the dome included
One drill press I used was not excellent, and I could have done without it, but it helped. If you do not have a drill press, just use a hand drill, and be very careful about where you drill the hole. Make sure to use an excellent drill bit for drilling through metal. Keep the bit sharp and well-oiled.
The ladder was used as a support (like a tall saw horse) for the dome during assembly, in lieu of an assistant. If you have at least 2 people working on assembling the dome, the ladder is not necessary.
There are at least two approaches to deciding the pole lengths for a small dome. One is to make the largest dome possible using each 10-foot EMT pole to make two dome poles, thereby maximizing the use of each 10-foot pole. Another approach is to fit the dome to the parachute covering as closely as possible. The subsections below describe each of these approaches.
| (lengths in inches) | Longer edges | Shorter edges |
|---|---|---|
| Nominal | 62 | 55 |
| total | 63.5 | 56.5 |
Imagine that we want to make the largest 2-frequency dome we can out of 10-foot poles while minimizing waste. That is, we want to use each 10-foot conduit pole to make 2 dome poles. We want to find the dome pole lengths such that they add up to exactly 10 feet, and still have the correct length ratio. Assume 3/4 inch of padding at each end and 1 inch between the vertex and the bend. After doing the math, you will find that the corresponding dome has a height of about 100.5 inches (about 8' 4.5"). This yields dome poles with nominal lengths of 62 inches and 55 inches. Accounting for bending and padding would yield total lengths of 63.5 inches 56.5 inches, which adds up to 10 feet.
There is a subtle issue with the above calculations: There are 35 longer poles and 30 shorter poles, so 5 of the longer poles will have no corresponding shorter poles. That means you will have to waste 5 of 56.5 inch long poles if you use the lengths given in the previous paragraph. If you make an entrance, then 5 more of the shorter poles will also not be used, for a total of 10 unused shorter poles.
To make an entrance for this dome, use two poles which have a length of
80 3/4" with holes drilled 3/4" in from each end. Attach these in the
usual way for an entrance. This is discussed in more detail below.
An alternative to optimizing the dome size is fitting to some prescribed size, such as the size of a parachute to be used to cover the dome. Usually, this is not desirable because you will want ventilation through the bottom, but in case you find yourself wanting to match the dome size exactly to a cover size, I present here a method to calculate the dome size.
In order to have the parachute barely tucked under the frame, I used
the lax length of the parachute when deciding the dome size. My
parachute has a lax diameter of 23 feet, 3 inches (279 inches).
This corresponds to a dome with a diameter of
(279*2/
)=177 19/32 inches, or a radius
of 88 25/32 inches. The nominal edge lengths would then be 54 7/8
inches and 48 17/32 inches.
| (lengths in inches) | Longer edges | Shorter edges |
|---|---|---|
| Nominal | 54.8868 | 48.5346 |
| bending | +0.1872 | +0.1872 |
| vertex holes | 55.0740 | 48.7236 |
| padding | +3.00 | +3.00 |
| total | 58.0740 | 51.7236 |
Assuming a pre-vertex-hole bend of 2 inches at each end, the pole was lengthened by 3/16 inch to account for bending effects.
The distance between vertex holes is the nominal edge length plus the extra added to account for bending effects. For the longer edges, the distance between vertex holes was 55 1/16 inches. For the shorter edges, the distance between vertex holes was 48 23/32 inches.
For drill-hole padding, I added 1.5 inches to each end (3 inches, total) outside the vertex holes. Using 1.5 inches of padding seems perhaps a bit excessive, but the resulting flange is useful at the assembly stage for attaching C-clamps. If you can be more precise with your flattening and bending than I was, then you might be able to get away with having as little as 3/4 inch of padding. For the most part, though, having an extra flange does little or no harm and is potentially useful. Remember that if you shorten your padding, then you may also shorten the bending length and will have to recalculate the bending length modifier.
Tally the length modifiers (drill hole padding and bending effects): In total, I had to add 3 3/16 inches to the nominal lengths of the poles. This made the desired lengths of poles 58 1/16 inches and 51 23/32 inches. These are the cut lengths.
I cut the lengths from the conduit using a high-tension hack saw. Some people recommend using a chop saw.
I flattened the pole ends as discussed in ``Design and Implementation'' in the Flattening section. The length of the flat part should be marginally longer than twice the distance from the vertex hole to the pole end, in order to allow for the poles to overlap without their butts hitting other poles. For the 100.5-inch diameter dome, using the lengths described above, flatten each end at least 2 inches. The flat parts at each end should be parallel to each other. If the flattened pole ends are not sufficiently parallel, assembling the dome will be much more difficult.
Drill each vertex hole 3/4 inch from the end of the pole. Measured the distance carefully using the distance between vertex holes calculated above. I marked the positions of the vertex holes, and carefully drilled them.
For 3/4 inch diameter conduit poles, the circumference is 2.356 inches, so, when flattened, the width is 1.178 inches (1 3/16 inches). A third of that is about 3/8 inch, which is the size I used for the vertex bolt diameter.
I thought it would be easier to assemble the dome if the vertex holes were slightly larger than the bolt shafts, so I drilled 7/16 inch diameter holes instead of 3/8 inch diameter holes. I thought the larger holes would give me some play which would account for errors in hole placement. Ends up, I probably did not need to drill over-sized holes. If I had to do it again, I would not drill over-sized holes. Oversized holes end up making washers even more crucial than otherwise because the nuts and bolt heads grind their way through the poles, causing a disaster.
I marked a line across each flattened pole end 2 inches inside of the center of the vertex holes. This is the place where the bend would be.
Using the vise, I bent the end of each pole by 18 degrees, as discussed in ``Design and Implementation'' in the Bending section.
You might find it useful later to have the poles marked to indicate their length. For example, you might want to paint the shorter poles white and leave the longer poles unpainted. This is not crucial, and I did not do such marking, but there are times when the dome is part-way completed, and the symmetries are obscured. For a dome of frequency higher than 2, color coding or some other marking scheme would be crucial.
It might be useful to assemble a collection of triangulated pentagons as the poles are fabricated, to make sure that the vertices are in the right place. Start at the center of each pentagon, connect the 5 short poles, then connect the longer perimeter poles. If an error has been made in the positioning of the vertex holes, then it will be more difficult to complete the pentagons.
The intermediate pentagons will have shared vertices so if you have enough nuts and bolts to make all of the intermediate pentagons, some of those nuts and bolts will be redundant. Nuts and bolts are cheap, so having extra is worth their cost and will come in handy when they are lost.
We assembled the dome starting at the top vertex and added poles from the top, spiraling around, toward the bottom. As usual with assembling things, we kept the bolts only partially tight on the first pass so that the pieces had some freedom to settle into their natural positions.
The top triangulated pentagon (vertices 1 through 6) was relatively easy to assemble, since it only involved 10 pieces and they did not weigh each other down.
The next natural tier downward involved vertices 2 through 12 (7 through 12 being totally new, 2 through 6 already in place from the initial pentagon), which involved 20 new poles. It was possible to assemble this tier with only one person, but having another person hold up parts of the dome made assembly easier.
The final tier involved 25 new poles. The entire weight of the dome was working against us as we brought together each vertex. Having more than one person was helpful at this stage. (When working alone, I used a 7 1/2 foot tall ladder to hold up the dome at its vertex so that it was not touching the ground for the last tier of assembly.)
For vertices with 4 poles (the bottom ring), I used 1 1/2 inch long bolts. For vertices with 5 or 6 poles I used 2 inch long or 2 1/2 inch long bolts. I avoided the 2 1/2 inch bolts because they leave a very long piece of unused bolt sticking out, which could snag on things or poke people. However, sometimes the longer bolt is just easier to deal with. Sometimes (maybe once) I used a 2 1/2 inch bolt just to get all of the pole ends together, then C-clamped them, removed the bolt, and replaced it with a shorter one. For a temporary structure, that sort of attention to detail is only marginally valuable, but if the dome will be set up in your back yard for a patio or put to some other semi-permanent use, then such effort might be worth while.
Using longer bolts will speed up and simplify assembly at the cost of having long pieces of metal sticking out at people. It's all fun and games until someone puts an eye out. Hardware stores sell plastic bolt caps that mitigate this problem. The problem is worst for vertices close to where humans can easily reach, and for this small dome design, those bolts are at the level of vertices above the ground level (i.e. vertices 7-16 in the schematic diagram).
I always used a washer at each end of the bolt. If 1/2 inch holes are drilled and bolts with 3/8 inch diameter shafts are used, the hex heads on those bolts will be 9/16 inch, which is only 1/16 inch larger than the 1/2 inch holes. This implies that the hex heads could slip through the holes, especially if the holes are a little larger than the bit (which is always the case). Also, while tightening the bolts and nuts, they will grind away the soft metal of the conduit, and enlarge the holes, making it yet more likely that the bolts will slip through. It is therefore crucial that washers are used at each end of the bolt, to prevent the bolt head and the nut from slipping through the vertex holes. Using washers will also make tightening the bolts and nuts easier.
My worst problem came from when the pole ends were not perfectly parallel -- then I had to get out the C-clamps or use longer bolts. It was during the assembly of this dome that it occurred to me how it was possible to create the world in just 6 days by a single being: Use a lot of C-clamps. (I am told that duct tape was also employed, which accounts for the necessity of the weirdness of quantum mechanics, but fortunately, this dome obeys classical physics to a good approximation, since it is nearly spherical.)
If the flattened ends are not parallel or not perfectly flat (which is inevitable if a sledge hammer is used to flatten them, which is why I recommend using a vise), you will either have to use inelegantly long bolts, or find a way to force the pole ends into place. I found that adding one pole at a time solved the problem, at the cost of taking much longer than necessary. Here is the procedure I used:
If you want to use the exact same configuration for future assemblies of the same dome (as might be useful if any vertex holes had to be elongated), mark each pole near each vertex with a number. It might also be useful to indicate the stacking order of the poles, but this should not be critical. (I did not do any such marking.)
To strengthen the entrance, I added an edge from the middle of the top two edges of the pentagon to the bottom two vertices of the same pentagon. (e.g. if edges from vertex 12 are removed then add an edge from vertex 26 to mid-way along the edge between vertices 2 and 11, and add an edge from vertex 17 to mid-way along the edge between vertices 2 and 7.)
The bolt-to-bolt length of the new struts is 0.771681 times the radius of the dome. For a 100.3 inch tall dome, that yields a length of (0.771681*100.3 inches)=77.4 inches plus the usual length modifiers, for a cut length of 78.9 inches. The height of this entrance would be about (0.850651*100.3 inches)=85.5 inches off the ground.
If the entrance struts are to have a strength balance with the rest of the dome, then their diameter should be larger than those of the rest of the dome. E.g. the dome is made of 3/4" EMT so I made the entrance struts with 1" EMT.
When drilling a hole through the mid-way point, use a drill bit smaller than or equal to the bolt diameter. Use a 1/4" diameter bolt with washers. (A smaller bolt is preferable here because drilling a hole at the midway point will reduce the integrity of the pole precisely at its weakest point.)
After adding the struts, the strength of the dome was increased but some flexibility remains. If any vertices will be loaded heavily, the vertices adjacent to the missing pentagon are to be avoided.