13-Year-Old Makes Solar Power Breakthrough by Harnessing the Fibonacci Sequence

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Your last link has now been submitted by someone as a separate item and is just so much better.

http://news.ycombinator.com/item?id=2902496

If leaves are space a rational number divisor a/b of 360 degrees around a trunk, then after b turns, leaves will directly shadow each other. To avoid this you need the amount of turn between leaves to be as difficult as possible to approximate by a rational number.

Using continued fractions we can see that the most difficult rational to approximate is

1 + 1/(1 + 1/(1 + 1/(...)))

which is (1+sqrt(5))/2 which is the Golden Ratio.

You can also get better packings by using the Fibonacci Spiral, which again gives the Golden Ratio:

http://en.wikipedia.org/wiki/Fibonacci_sequence#In_nature

You can look these things up if you're interested.

Except it's trivially impossible to generate more energy like this (as he claims)! If a set of solar panels is independent and non-interacting (e.g., they don't shade or heat each other), then their total power output is simply the sum of their individual power outputs. And so their total energy outputs (integrated power) is the sum of their individual energy outputs. (Necessary distinction because their power peaks may occur at different times).

P_tot = Σ P_i

∫ P_tot dt = ∫ (Σ P_i) dt = Σ (∫ P_i dt)

E_tot = Σ E_i

If there is an unqiue optimal orientation for a single static panel (which under realistic assumptions there is) -- optimal in terms of maximizing energy output, E -- then the optimal orientation of a array of independent solar panels is just the same orientation, iterated. Combine inferior panel orientations, and their total remains inferior.

E_i Σ E_i And all those panel angles in his "tree", facing non-South, up, down, towards a wall... they are individually inferior to the single 45° south-facing panel in his static array. So combined together they are still inferior.

Where did his experiment go wrong? I'd start with the shade issue. The whole setup is in intermittent shade (note the tree shadows); and one experiment is sitting near the ground, the other is mounted on a pole. Looks like different shade environments. His output graphs show that the entire flat array is sometimes in total shade, at a time when the pole-mounted "tree" is not:

http://www.amnh.org/nationalcenter/youngnaturalistawards/201...

Another fatal flaw (I had to look this up to check) is that he is measuring voltage, not power, and they are not linearly related in photovoltaics. Actually, the open-circuit voltage (what you get if you stick a voltmeter over a solar cell, when it's not hooked up to a load) is practically independent of irradiance:

http://i.imgur.com/SWGjV.png

This from the solar module datasheet here:

http://www.bpsolar.us/products/3-series-solar-panels-polycry...

Open-circuit voltage going from 200 W/m^2 to 1,000 W/m^2 only increases from 34 V to 38 V. Power output, with a real load, would go up by about 5 times.

So, he never really measured energy production, or anything that remotely approximates it.