I want to create a hyperboloid out of pipes. The pipes should be approximately touching. It doesn’t need to be exact, but the distance between them should be consistent.
A simple way to create a hyperboloid is to put points on a circle at the bottom and at the top, then twist these points clockwise and counterclockwise. Finally one connects the bottom and the top points with lines.
Now I used circles with an offset for twisting in one direction, and without offset for twisting in the other direction. At first sight, this works:
However, when I look at the distances between the pipes, I see that they fluctuate quite a bit (the two large values at the bottom can be ignored, of course):
Thanks for the suggestion, but this is not what it’s about. Maybe my original subject was confusing. And likely I’m bad at explaining.
Actually, there are two hyperboloids. One has a slightly smaller radius. They are twisted in opposite direction. The idea is that their poles are touching at crossing points. People have built similar structures out of bamboo, which has some flex. But here we want to use scaffolding poles, which have very little flex.
To reduce complexity, I now made the top and the bottom radius identical, and I twisted by exactly opposite angles top and bottom. This gives a perfectly symmetric hyperboloid, well as symmetric as it can get. Still the lengths of connections at the crossing points fluctuates.
The only parameter that I see that can be tweaked is the twist angle of the inside poles. I tried that, and indeed that can minimize the distances, but I cannot achieve 0:
Yes. The more members, the less skew, the taller the structure. But the argumentation that was being considered above, was whether it was geometrically possible to have all intersections at equal distances from each other, or all zero, to which the answer is “no”.
Very interesting! But I cannot read the image. Is that some kind of projection?
Thanks for sharing! I was thinking about running an optimizer on it. Have never tried Galapagos, although I did work with genetic algorithms ages ago. For the fitness function, I’d probably lean to standard deviation now, because a few large deviations are more of a problem than many small ones. Also, I need to make sure that there is never any overlap between poles. IRL they’re galvanized iron scaffolding poles, and they have negligible flex.
All intersections points of this line with other lines in the figure will lie on this point, and on the right you can see how you cannot approach this point with a tube profile without intersecting the figure. Although, the situation is a bit exaggerated because this is a perspective and not a parallel projection.
Those are the standard swivel couplers used here. They allow some flexibility regarding gaps. I am currently evaluating wether I can trust them. The structure should last a few years.
I have a local engineer who has some advice. He is worried that people may steal them, and so he proposes welding the pipes. But I don’t see how we could assemble it that way.
