Recharge Dome

Purpose

This dome is intended to be a large shade structure for lots of people to lounge in. With a 32-foot diameter circle floor (with full headroom everywhere), even with furniture strewn about it is pretty comfortable for more than 25 people.

This page avoids repeating information on this page. You should really read that page first.

Frame - Struts

As with the smaller dome we use 3/4" EMT cut to lengths averaging about 5 feet. The goals with the struts are: To solve this puzzle first go to the frequency-four table on this page to get the strut quantities and hole-to-hole-length ratios. It's a really good idea to make spares, maybe 4 spares each of the C's and D's (there are more of them), and 2 spares of each of the others. However, because the entrance modification i'm planning to do replaces 2 C's, 2 D's, and 2 E's, i'm going to only make 2 spares of the C's and D's. (I don't want to eliminate all the spares of E's in case the entrance modification is not used some point in the future.) So now i am going to just have 2 spares of each length.

Whew, still with me? Here's the fun part. Next we notice that if the B's and C's are around 5 feet long, their strut ratios are so close to each other that the length difference is nearly a measly 1/8 inch. If you take advantage of this lucky fact, you can just plan to let that extra 3/4" outside the hole on each end of the strut be 3/4" plus 1/16" on each end - this will work fine, in fact the variations in that end bit will be more than 1/16" anyway. This means you will cut the B's and C's the same length, and only differentiate between them later. Now from playing with different permutatations of sums of pairs of strut ratios, you can get the following cutting plan which i believe is optimal:
Struts to cut from each 10-foot conduit Quantity of 10-foot conduits Comment
C + D62cut C's as if they were B's
B + D10actually the same as previous cut
B + B + waste11
A + E + waste32
F + F + waste16
Things to notice:

And one final important detail: what are the lengths? And hey, what the heck is the size of this dome, anyway? Since B + D = a whole 10-foot piece, you use the strut ratios for those two pieces to solve: X * (0.29524 + 0.31287) + 0.125 + 0.125 = 10. (The 0.125 values are the total excess --- 2 times 3/4" --- for each strut.) This gives you X = 16.0333 feet as the dome radius, which you can then multiply by each strut ratio (or enter into the Dome Calculator) to get the hole-to-hole lengths. Then remember to add the excess back in to get the pipe-cut lengths.
Strut
letter		 Color code on
assembly diagram		 Quantity
(including 2 spares)		 Strut ratio
(ratio of hole-to-hole-length
to dome radius)		 Hole-to-Hole
length		 Pipe cut length
(hole-to-hole-length plus
2 times 3/4" excess)
A yellow 32 0.25318 4.059' = 4' 0" 11/16 4.184' = 4' 2" 3/16
B red 32 0.29524 4.734' = 4' 8" 13/16 4.859' = 4' 10" 5/16
C blue 62 0.29453 4.722' = 4' 8" 11/16 4.847' = 4' 10" 3/16
D green 72 0.31287 5.016' = 5' 0" 3/16 5.141' = 5' 1" 11/16
E purple 32 0.32492 5.210' = 5' 2" 8/16 5.335' = 5' 4" 0/16
F orange 32 0.29859 4.787' = 4' 9" 7/16 4.912' = 4' 10" 15/16
Two useful doublechecks are that the pipe-cut lengths of B and D add to 10 feet, and that as promised B and C differ by only 1/8 inch.

One practical tip i figured out after many difficult cuts: open up the pipe cutter and put a drop of oil on each of the three pins that the three rotating thingies (2 rollers and a blade) rotate on. It really makes cutting about 5 times easier.

Frame - Entrance Modification

See this page for the full details of how to do this. Here are the calculations for the strut lengths for this radius dome.

Dome radius is 16.033 feet. Declination (from top) of apex is 66 degrees, i.e. 16.033 times cos(66) = 6.521' = 6' 6" 4/16.
Strut Strut ratio
(ratio of hole-to-hole-length
to dome radius)		 Hole-to-Hole
length		 Pipe cut length
(hole-to-hole-length plus
2 times 3/4" excess)
Top C0.19143.069' = 3' 0" 13/163.194' = 3' 2" 5/16
Top D0.20123.226' = 3' 2" 11/163.351' = 3' 4" 3/16
Middle C0.33015.292' = 5' 3" 8/165.417' = 5' 5" 0/16
Middle E0.34585.544' = 5' 6" 8/165.669' = 5' 8" 0/16
Bottom D0.43817.024' = 7' 0" 5/167.149' = 7' 1" 13/16
Bottom E0.44637.156' = 7' 1" 14/167.281' = 7' 3" 6/16
Note the middle and bottom pieces are made from stronger conduit as described on the other page.

Frame - Assembly

See this assembly diagram. The entrance modification will be for one of the large bottow hexagons. (Notice that there are only two types of bottom hexagons: larger ones and smaller ones that are even more asymmetric. Half of the bottom hexagons are twins of others mirrored in the opposite direction.)

Frame - Assembly Bottom-Up (Attempt)

On August 11, 2001 some of us gathered in Precita Park in SF to see how far we could get assembling the dome. At some points there were as many as 7 people working on it, but the average work was probably more like 4 people for 3 hours. The bottom 76% of the pieces were put together, though it's worth noting that when building from the bottom up it gets much harder to put the higher pieces on. Anyway, this gave some idea how much work would be involved to do the whole thing, plus we learned to avoid one major mistake: make sure you're looking at the right color on the assembly diagram (orange/yellow and blue/purple are confusable).

Here are some photos of the extent of the assembly. Click to enlarge.

This attempt convinced me that bottom-up was not the way to go. Read on...

Frame - Assembly Top-Down

Just after the bottom-up attempt, my brother gave a book about Bucky Fuller, in which i found the following bit of wisdom (referring to construction of another dome-type structure): "Units were built from the top down by pulling the assembly up a temporary mast as parts were added at the bottom. The mast-hoist method kept most workers on the ground, speeding the work and reducing the risk of injuries. Bucky would use this top-down building tactic repeatedly in the future." Specifically, with this dome, this technique would allow never having to take a nut off of a bolt to add more struts, which had consumed much time and energy with the bottom-up attempt. Each vertex could be assembled once, and only revisited to do a final tightening on the nut.

This made perfect sense to me, but how would i make a temporary mast for this dome? After hours of online research, i found a solution. There is a materials lift, the Genie SLC-18, which is perfect for the task, and readily available for rental at many equipment rental shops. (An older model, the SL-18, is essentially the same.) It lifts up to 650 pounds to a height of 18 feet. (I weighed the dome struts and calculated that with hardware the weight should be under 600 pounds.)

To get started, you set up the lift in the center of where the dome should be. You construct the top pentagon, with all the extra struts hanging down from it (in other words, a total of 25 struts) around the mast of the lift, so that the mast is going up through one of the triangles of that top pentagon. Then, with one continuous piece of rope (rated to well over one-tenth of the total dome weight; i used 400-pound "truck" rope) you rig the five outer vertices of the top pentagon to the lift, hanging under the fork. The top vertex should be centered very well on the lift in the left-right direction, and as close as possible to the mast in the in-out direction while leaving a little room for the dome to sway (say, 3 inches clearance). The top vertex should be as high as possible, since it will eventually be 16 feet high but the fork only goes up to 18 feet high (well, not even quite that high) --- and keep in mind that your rope will stretch more after more load is placed on it. Using one continuous piece of rope allows you to easily adjust the assembled struts to be as close to level as possible, and also allows the load to be perfectly distributed between the five vertices, which is highly desirable. Do take the time to make sure the height, centering, and leveling are as good as you can get them before going on since its difficult or impossible to fix this later. The photos below (taken after more than just the initial 25 struts were assembled) show how the rigging should look. It's worth mentioning that Genie makes a boom attachment which would be better than the standard fork attachment, but it seems most rental places don't have it. If you use the fork just make sure your rigging is tied to the back part of the fork --- not the sides, from which it could slip off.


Click to enlarge.
Next you start building one layer at a time. For each layer, you should first lay out all the struts needed to complete a new vertex at each new vertex location. Then, alternating working on each side in order to keep the dome as balanced as possible, hold together all the struts at a new vertex in about the right place, and add the nut and bolt to hold it all together. At this point the nut should be secure, but loose enough so that the down-hanging struts can rotate a little bit into place for the next layer. After all the new vertices are put together, the nuts of the vertices just above that (the previous layer you did) should now be tightened fully since all struts at that vertex are now held in exactly the right positions. Then, you use the lift to raise the dome up enough to do the next layer. This photo shows the dome partially assembled. The bottom vertices' nuts are loose, but all the nuts higher than that are fully tightened.

Click to enlarge.

One pitfall we ran into the first time we did this was that one of the verteces above the layer being worked on went concave (popped in) while the dome was partially assembled. To fix that, one person lashed a rope around the troublesome vertex, and pulled it out (while everyone else tugged the dome in the other direction) and held it out while the layer below was assembled. After that layer was assembled, the structure was stable at the previously-concave vertex.

Another slight problem was that the rigging was tied slightly too low --- maybe 4 inches too low for the maximum lift height. When we got to the bottom layer, one person had to lift up a little on one spot on the dome while others placed the very bottom struts in their vertices. This was not too bad, but it would have been better to have tied it up to the right height in the first place.

After the last nut is tightened (hooray), get out your 16-foot stepladder (uh, you have one, right?), untie the rigging rope, and carefully detach the fork so that you can shimmy it through a top triangle and bring it down the ladder. (See photo below.) Then lower the lift and take it out through the entrance. All done.


Click to enlarge.

It's worth it to use the lift at disassembly time too. You do the assembly procedure backwards --- crank up the lift mast all the way, shimmy the fork through a top triangle and attach it to the mast, tie up the rigging rope as before, and then start unbolting verteces one layer at a time, lowering the lift after each layer. You can take off each layer very quickly (we even had two wrenches going). Compare this to disassembling bottom down, for which you would have to keep moving the ladder (or scaffolding) around, and struts would be dropping from high up.

Covering

I must confess that when it came time to put the covering on all i did was watch, but here's the basic description. A 50-foot cargo parachute was used. First it was pulled over the frame using rope, the tall ladder, and long poles to occasionally poke the chute in spots where it got stuck on the outside of vertices. (The smooth carriage bolts kept snags to a minimum.) After it was centered on the frame (with a convenient vent hole top center), excess was folded over on itself on one side because the chute was slightly too large.

It was attached to the frame at one out of every (maybe) 8 vertices, where the attached vertices were evenly spaced over the surface. The attachment method required a large washer (or other round object) and two zip-ties (AKA cable ties) --- a handful of fabric was bunched up near the vertex, a washer was tossed into the bunch from the exterior, a zip-tie was used to trap the washer inside, then the washer (now trapped inside the fabric) was zip-tied to the frame's vertex. This is not a great picture but might give you some idea.


Click to enlarge.
At the bottom, the chute was rolled up inside to leave the bottom row of traingles uncovered. This is critical for ventilation in the desert heat. Before it was rolled up the temperature started rising fast inside.

Anchoring

As described here, straight rebar and rope was used.

Floor and Amenities

With carpeting on the floor and several couches inside, all i can say is that this was the best place to be in the middle of the day in the sizzling desert heat. At night, with a floor lamp lighting the interior, it was cozy. The only thing that would have made it better would be a water-mister (or air-conditioning!) to keep the heat down.

Costs

Here are some notes about costs for the materials. Fortunately i had already bought the shop press and the drill press. And we already had the chute from previous year's structures.

Item and quantity Cost (incl. tax and/or shipping)
3/4 inch EMT conduit 10-foot lengths, quantity 132 $322.18
1 inch EMT conduit 10-foot lengths, quantity 2 $8.10
1-1/4 inch EMT conduit 10-foot lengths, quantity 2 $10.74
Pipe cutter $9.69
Screw anchors, quantity 10 $42.12
Hardware (bolts, washers, nuts) ???
Titanium drill bit $15
Spray paint for color-coding pieces $22.83
Strapping tape for bundling pieces $9.05
Grand total $439.71 + ???

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