Ice Station Thuban Prime

Another temporary enclosure made entirely of water

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This is a double water hack. When the temperatures are cold enough, it is possible to construct a geodesic dome made from water ice. In addition to building the dome out of water, the ice bricks are made using recycled plastic water bottles for forms. Small water containers are used to make a giant container out of water.

 This is the second iteration of a geodesic ice dome, the first version was Ice Station Thuban.

The spherical photograph is actually the eye of a krill.

Krill eye

It's analogous to what is going on with the Thuban Prime dome, and as you can see, makes a pretty good sphere, with small units of mostly hexagonal shape.

If you use an icosahedron as your basis, twenty equal triangles can be projected onto a sphere. An icosahedron is a pretty poor approximation of a sphere, which is why Ice Station Thuban used a rhombic triacontahedron as its basis, which is a bit better. However, an icosahedron has the benefit of having very few vertices (twelve) per sphere, and this is actually a benefit for a very practical reason.

Consider the triangle of the icosahedron. If you were to subdivide it as per the following diagram, you would get a hexagon in the middle, and the triangles in red would join with the triangles from the adjacent icosahedral faces, to form pentagons. The result would be a polyhedron with twelve pentagons and twenty hexagons. This composite polyhedron approximates a sphere more closely than an icosahedron - in fact, this pattern is quite similar to the very familiar Telstar soccer ball (proportions slightly different).

If you decided to double the linear precision, and instead of dividing the icosahedral edge into three, you mensurated by six, you could tessellate the triangle as per the following diagram:

As you can see, you will now have five and a half hexagons per icosahedral face, instead of only one. But you still only have three red triangles, which form the twelve pentagons. A projected sphere will now have 110 hexagons, and this will be much more spherical than an icosahedron. All hexagons are not quite the same, they are distorted once you project the vertices on to a sphere, as per the following diagram, which is a bit exaggerated for illustration (and somewhat poorly - the red triangles really should all be equivalently proportioned).

For a dome, to do this precisely, you would now have to create a lot of different, uniquely shaped forms, We don’t want to do that. (Or at least I don’t want to - that is not an optimized procedure, it is labor intensive and highly susceptible to derailment due to practical concerns. With Ice Station Thuban, I had only four unique shapes, and it was more than enough. Too much, really.)

But let’s go further. In the following diagram the icosahedral edge has been mensurated by twelve (double again!), leading to a tessellation that has 23.5 hexagons per face. 

This will give you an approximate sphere with 470 hexagons… and still only 12 pentagons. Projected onto a sphere, the hexagons will still be very different, a lot of unique shapes.

The thing is, if you continue this process, you will get more and more tiny hexagons, and exactly twelve pentagons every time. At a certain point, the size of the hexagon is within your manufacturing tolerance. This effectively makes all the hexagons statistically “the same” - plus or minus.

This is what you see in the krill eye. Nature has a certain amount of time to grow these units, so they are all going to be just about the same size. But in order to make a sphere, they will jam together and naturally from hexagons (primarily) - except for some number of dislocations to correct for sphericity. If nature did things exactly repeatably, there would need to be twelve pentagons to account for the dislocations. (Note I did not say perfectly, because nature is the gold standard of perfection - perfection does not necessarily mean repeatable. It means robust, optimized for production quality per energy usage.) In the krill eye, you can see a handful of dislocations. They are not perfect pentagons, but I am guessing, if you average all krill eyes ever to have existed, there will be pretty close to twelve per idealized full-sphere eye. (Obviously an eye is not an entire sphere, it...

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  • Calculating probability of opportunity

    Kenji Larsen12/04/2014 at 04:04 0 comments

    The large snowstorm that hit my area in November reminded me to check my stock of hexagonal ice forms, get them prepped for an opportunity. The snow accumulated about 30 cm in my area but it was wet snow, dense, very difficult to shovel due to weight. It has since turned completely into groundwater.

    What I need is a stretch of cold temperatures, below freezing for approximately ten days to two weeks (forecasted) to begin deployment. I've played this game before - the weather forecasts are sensitive to initial conditions, and long term forecasts are more or less meaningless. So it is a probability game. Short term forecasts are very good, however. In the 10 day range, the idea is to estimate, or more properly bet, that temperatures will stay below freezing, with a few excursions above freezing tolerable, as long as they are short in duration, perhaps one or two hours (usually around 2 pm - lagging the sun).

    This is a tough game. How fast can one freeze two to three tons of water? The answer depends on a few things, like how much below freezing the weather is (delta T determines the efficiency of heat transfer); the surface are to volume ratio of the item to be frozen; the characteristic minimum distance (from surface to centroid) of the item; ... and more practical things, like - how fast does the water flow out of the hose, and how many hours do I have to fill the buckets! Also, ground temperature, which dominates the temperature of the water source, and affects freezing rate through contact patch. But generally, it's a long time. 15 hours or more for a 1 gallon brick in typical just-below-freezing conditions.

    This determines the number of bricks required to be in progress at once, since about 3000 bricks are needed. It's a race against the weather. Ice Station Thuban had relatively few panels, but they were large. But they were flat, so minimum distance was small. But the large area meant they were spread over the ground, so that meant that ground temperature dominated their freezing schedule. The new bricks have a larger height to ground cover ratio, so they should stick out like heat sink fins in the cold air (in comparison to the flat panels).

    Will we get enough days in a row to deploy this year? I hope so. The snow made me hopeful. The lack of snow now, however, reminds me of the statistics.

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James Duvall wrote 12/18/2015 at 13:45 point

Thanks for the explanation.  Very interesting

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James Duvall wrote 10/13/2015 at 12:59 point

Would you mind showing the process for re-forming your ice buckets?  It seems interesting that you are able to form them easily, yet still get them to rigidly hold shape during the freezing process

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Kenji Larsen wrote 12/18/2015 at 05:20 point

i certainly do not mind. I'll post pictures at a later time but let me describe it now. The rigidity comes from the six vertical folds of the hexagon.  It's not totally rigid, however, which is good, because you sometimes need to flex the plastic to get the ice out.  But certainly rigid enough to hold liquid and frozen water when upright. I inflate a nearly cylindrical water bottle to around 10 psi, more is not necessary.  I hit it with a heat gun lightly to remove easy grip handle indents and soften adhesive so I can remove the label.  I then cut the top off and insert the wooden inserts cut for the angle I need to create the diameter dome I want.  I then hit it with a heat gun again, and the residual stress in the plastic causes it to shrink around the wooden form, it all gets very compact and the form itself is compressed together.  I remove the shims from the form and the pieces come out, leaving a pretty good, slightly conical, hexagonal prism.  The final wall thickness on the plastic is much thicker than the original water bottle, because it has contracted quite a lot.  And the best part - they stack easily for storage!

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zakqwy wrote 12/09/2014 at 13:51 point
As a resident of Minnesota, this project is up my alley. I'd like to build one in my yard. Looking forward to what you come up with!

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Kenji Larsen wrote 12/10/2014 at 05:29 point
Prepare for back pain! Even a little at a time, it is still tons of matter to move manually.
I'm hoping that distributing the load in smaller bricks will prevent exceeding certain bodily stress and fatigue limits, but I can tell you from my test section last year, it's not easy.

The real project is to build a robot (or several) to do the assembly for me. We'll get to that... someday.

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