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Comment by ghaff | Hacker News Reader

Yes. If you subdivide a solar panel into, say, 10 pieces and orient each of those 10 pieces in an orientation different from the orientation that produces the maximum power output over the course of the day for a single panel, the sum will still be less.

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But a distributed layout might have higher minimums than a single orientation. For an actual tree, at least, that might be important. The sun doesn't just move during the day, it changes its course over the year, so it might be very beneficial to the tree to ensure that it get's at least a certain amount of juice each day.

There might be other reasons than optimal solar exposure. Maybe structural reasons, or, I don't know, sap distribution ...

Finally, maybe the Fibonacci sequence gets selected in nature a lot because it's easy to select. What I mean is, the very best algorithms are not necessarily the ones that get selected - the ones that actually get tried and are good enough to survive are the ones that appear. My theory is that organisms stumble into stuff like the Fibonacci sequence or that fern fractal because they are likely to and because they work well enough for whatever purpose.

So there is some theoretical and experimental work arguing that the Fibonacci sequence minimizes the energy of soft particles interacting repulsively when constrained to the surface of a cylinder. In 2009, some physicists found the pattern when they made a "Magnetic Cactus": http://arxiv.org/abs/1002.0622

All about that bottom line. Trees do a pretty good business.

I was heavily involved in solar car racing in the past. All the best racing teams have rather flat, if only slight curved arrays on their cars. Our first fancy super computer modeled array was much more curved to attempt get more power over the race course over the various sun angles and longitudes of the race. Net result: a panel that was a pain to build, and had less than ideal power because of the difficulty of construction and fragility.

Out of interest, what was the theoretical gain of the optimized panel vs. the flat ones?

Certainly a constraint of that was for the panel to lay on a surface (however curved) as anything else would produce drag.

That's because you assume there is the same number/surface of panels in both cases. Change the constraint not to the surface but to the volume.

The problem might just not be "take 10 pieces of a solar panel and find optimal layout", but "take a 5x5x5m volume and find optimal layout". Maybe with a flat panel design you could be able to put 10 pieces at most in there, but it would turn out you could put 30, and at any time half of them are shaded. That leaves 15 generating power, which is more than the flat panel.

I really don't know if it's the case. I just say that everyone is comparing stuff on a wild assumption that you can't put more unshaded panels in a space than on a plane, and so discard a possibly valid solution without attempting to take it on.

Probably we would all see mushroom-shaped trees looking at the sun like Pinus Pinea[1] if it was so optimal. Most trees are not though so there has to have something to it.

[1] http://commons.wikimedia.org/wiki/Pinus_pinea

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