Mike's Spacetime

When we returned from Whistler in early March 2009 i began drawing various technical drawings of possible cube designs including the original design ideas with 8ft facets as well as several down sized versions with 6ft and 5ft basic lengths (cubie widths).

The first set of cube models we considered

I also started toying with the idea of putting the cube on its corner. We had all agreed that that would be super cool but dismissed it as too difficult (remember we wanted to keep it all simple and off-the-shelf). I had looked at scaffolding types, one of which (Tube & Clamp Scaffolding) allows you to build practically arbitrary shapes. So I started thinking about the possibility of building a hexagonal base (The projection of a cube on its axis is a hexagon) to hold up the cube with its diagonal axis vertical. One design had the corner on the ground while the other had the lower corner about 8 ft off the ground.

Cube on it's corner

Cube on it's corner with an extra level

This design had many desirable qualities, most importantly it would allow all sides to be visible from the ground. Further, it creates an obvious 3 fold on the ground, such that all the three axes of the cube have equivalent projections onto the ground meaning that the controllers could all be identical and just needed to be placed in positions 120 degrees apart.
Aesthetically this was the right choice, and since we had, by this point, decided that we had to downsize the cube to 15ft from 24ft (halving costs of scaffolding and fabric if i recall correctly), we felt that we needed to add more spice instead. Putting the cube on it’s corner seemed like an appropriately mad challenge for this purpose.

While the electronics were being worked out I was iterating through various designs all of which had their advantages and disadvantages. The scaffold support structure under neigh the cube was annoying because of the additional scaffolding work, the optical occlusions and general messyness and because it was not clear how to ensure that the cube would be perfectly cubical and not warped. Another possibility that was suggested by a friend of ours who’s name i forget (Matt?) which was to build the cube out of EMT tubing with custom welded connectors. He then suggested putting the cube on an 8 ft post. Aesthetically this was very appealing, since nothing would occlude the cube.

Cube on a post ?

I started running calculations on cost and feasibility. EMT is expensive, the tubing alone came to around 1000$, the connectors added another $600. Plus the daunting task of welding 64 custom connectors  as well as a custom christmas tree like structure to run through the diagonal. All that with none of us having much experience with welding. I actually went to Home Depot to get some 1.5″  (or was it 2″ ?) EMT and tried finding metal tubing with the right outer diameter to slide in snuggly into the EMT. Fail. This turned out to be rather difficult. Plus the structure was getting rather expensive. Not getting a good lead on how to do this i returned to the scaffolding support and started making more detailed plans.Many features seemed unappealing as detailed above, but it seemed the only viable option at the time: Scaffolding was cheap to rent.

Planning in more detail where the scaffold tube would go and where people constructing it would stand.

Until one afternoon I get a memo from Barry saying, come to Kevin’s House, he’s got a crazy idea for how to get the cube in the air. Kevin’s ingenious brain added an idea none of us had considered before, which was to *hang* the cube. His idea was to just lift the cube using a crane or fork lift. And leave the crane in place. Basically just have it hanging there. The big unknown was the cost of rental for such an opperation. While clever, the thought of having a crane there permanently was repulsive to me from an aesthetic standpoint since it would look like a failed or unfinished, rescued-at-last-minute art project (To my delight the crane turned out to be prohibitively expensive, unless we could get it from BM Org , which remained unclear till the end).

But the idea of *hanging* the cube was absolutely brilliant! I was sold. No visual obstructions, the cube could be built on the ground with easy access and then lifted into place ! So clean. So neat. We could build the cube out of lighter materials too! But what to lift it from ? Over the BBQ we talked about a number of possibilities. Theater truss ? That stuff can be rented, maybe we could build an inverted U to hang the cube from ? A bit of research quickly showed that a center hang of several thousand pounds required top end heavy-duty truss, esp when we’re talking about a 40ft span. Basically hanging the cube straight down was no an option, although aesthetically is was very pleasing. Hanging it from cables running from the tops of the vertical parts of the U would be an option but then the towers would need to be quite a bit taller so avoid very shallow hanging angles. All of this was not clicking into place and the costs for renting truss were out of bounds already.

This design was appealing but quickly turned out to be not to be practical

Another idea was to reuse truss the we already had access to as a community. Eric Schurman had built a 70 ft tower out of radio towertruss in 2000, so he owned 7 10ft tower segments. I looked up the specs for the truss and did a number of buckling calculations and it seemed the towers were sufficiently strong in compression to hold up the cube.I spent several evenings working on a design, initially involving 3 50fttowers. Each tower would be guyed down to the playa by 3 steel cables. A4th cable would run to the center of the triangle, where the cube would be suspended from it’s top vertex. As before the problem was that to geta hanging angle of >60 degrees (thus avoiding ridiculous tensions in the cables as the force increases with the tangent of the angle and quickly runs of towards infinity as you approach 90 degrees) the towers had tobe quite a bit taller then the top of cube, which we wanted to be at37ft, leaving the bottom vertex 10ft off the ground. This however meant erecting 3 50ft towers (a daunting task in it self) and then raising a2500 lbs object in between them. Also it meant buying 8 more tower segments, at 140$ each. A minimum of 9 guylines were needed. All in all the costs were soaring up into the 2000-3000$ range, like, it seemed,every attempt i tried to lift this cube up in the air. Nothing was truly jumping out at me, and by this point we had considered at least 6 or 7 designs.

Three Tower Design - Note the three-fold symmetry and the UI stations, one for each axis. We liked this design a lot because it created an illusion of a 3D volume in which the cube was hovering as if by magic.

At some point I was explaining my design ideas and worries design to Kevin. I was trying to explain how the guylines would run and i evidently didn’t do a good job. Kevin made some sort of suggestion that indicated to me he though the guy lines attached at the bottom of the cube, which was not what i had intended in my design. However this total mis-communication made me think: what *if* we attached the guylines say to the center of the cube ? That would make the towers smaller, because the point of attachment would have moved down by 13.5ft, so the towers could be 37ft tall.. well 40ft at least since the truss elements are 10ft long. So what if we moved them down even further ? The lower 3 corners of the cube make excellent attachment points (better then the center of the cube in many ways since the cables wouldn’t have to run through the cube). That takes the attachment down another 7 ft, so 30 ft tower would be sufficient!

Tensegrity Cube Design

This design looked weird in many ways. The cube was suspended from below it center of mass, so I added three more guys from the upper 3 corners that run down directly to the playa. Essentially what this ended up as was a nice tensegrity style structure with the cube hanging in between three 30 ft towers held up by nothing but cables. Only two more 10ft tower segments would be required lowering the costs. Raising a 30ft tower is also much easier and can be done with simple manpower and without having a truck and a leverage arm. The guylines became considerably shorter. All in all i liked this design a lot. It appeared weird and impossible, and it had an inherent beauty. The three towers added a distinct three dimensionality to the whole object and increased its apparent size many times. The rigging was strange and unintuitive though. I looked through several books on tensegrity structures but in the end decided the most immediately useful thing would be to make a physical small scale model of the structure.

I built a small, cross-braced cube out of little pieces of dowel and erected three dowel towers on a thick plate of polystyrene that I found in Mark’s backyard. The towers were about about 8inches tall, and I guyed them down using string and rubber bands to adjust the tension, then the cube was suspended using more string. To my delight, once all the cables were tightened the cube appeared to be surprisingly stable. Because all the guys had rubber bands at one end (Another idea of Eric Schurman’s) it was easy to see where the structure took up most of the load when one pushed the cube around by hand.

Making physical models helped us get a feel for the mechanics and physics. This was the tensegrity model hung from 3 30ft towers and was our favourite model for quite some time, if it proved to be financially viable. Which sadly it did not.

OK, so in principle this would work. Kevin and I started doing load calculations and wind calculations as with the prvious designs. This one was tricky though due to the sheer number of guylines. I made a highly simplified model and made a spreadsheet on google docs including little 2×2 and 3×3 matrix solvers that would calculate force-vectors given parameters such as windload (see wind load section) The question remained how the cube would be lifted into place and  whether or not it would be taken down in a major windstorm, as we had  intended for the hang-from-crane design idea. We tried a variety of different designs for the movable rigging (i.e.  those guys that would be attached to winches), trying to avoid using too  many block and tackles and winches since these turn out to be very expensive. Winches were necessary not only to get the cube up there but also to make it acessible in case some of the electronics broke.

Any design we came up with ended up with basic material costs in the 3000$ range, accounting merely for the basic materials (i.e. not accounting for many smaller components, shipping and the inevitable 50-100% overruns that tend to happen with project like this). I made a number of fairly involved wind calculations to access the tension in the guy wires. The problem was that the guys running out from the towers would take all of the weight (since it’s pulling the twoerrs inwards) plus any windload (particularily on the upwind side, but also, surprisingly, on the downwind side, becaues the cube is also tethered to the ground). The windload for a object of this size is substantial and in the order of 3000-4000 lbs in a 70 mph windstorm.

My calculations indicated that without wind, the load in the outer guys was about 1600 ( + pre-tension), assuming a cube wiehgt of 2000 lbs. At 4000 lbs horizontal windload, the guy load upwind was about 6600 lbs. While one can easily buy steel calble strong enough to hold this sort of tension, it was not clear what the anchor points could hold. Kevin was researching any available information on this but without any luck, except for wild guesses. Even from DPW we could find reliable figures, although we found out that they tend to use anchor screws like these which can hold 4000lbs – but in what sort of soil ? Is the Playa weaker or stronger then average soil ? (We found out much later on the playa that DPW infact uses these, and pulls one out of the ground every year using a crane to see what it can take. Apparently conditions vary significantly every year, due to weather effects over the previous winter, position of the city on the playa, etc, etc. Apparently they vary from 3000-8000lbs, this year it was on the higher end). Either way our working loads were uncomfortable close to what the anchors could take. One thought was to winch the cube down in case of wind, but this would be quite dangerous once the wind picked up above 30 mph and it would require maning around the clock with several people. Further costs were spiraling out of control and frankly we felt quite uncomfortable with a rigging project of this magnitude, with essentially zero experience in this field. I was starting to feel very uncomfortable about all this – we couldn’t find any design that was satisfying and within our budget and safe and our go-no-go deadline was approaching fast.

Barry, Kevin and I met up again to make a call on the tensegrity design. We went through all the calculation, Kevin checked the math, we talked about costs, rigging options, safety, operability, accesibility etc. Finally we came to a conclusion: Yes it could be done and no we won’t be able to do it given our budget & expertise.

So what do do instead. What about just building the cube out of scaffolding and putting it on its corner with guylines ? This would have an excellent visual effect, it wouldn’t require too much rigging, no cranes, it could be built on the ground ( The original reason for considering hanging desings). Barry was unsatisfied – he insisted the cube should be at least a little off the ground. We figured a small pedistool, say a few feet high, shouldn’t be much of a problem.