Explaining the Fibonacci solar breakthrough (that isn’t one) – UPDATED



 (updated 28 August, 2011)


It is no fun being negative, especially not when it is about something one cares for.

A number of people have seen the need to debunk what looked like good – even fantastic! – news in the first place: a solar power breakthrough.
Original post here, and my first comment here.
Unfortunately, there s no breakthrough – just a chain reaction of one website after the other, one tweet after the other copying the good news – without checking.
I would like to offer a more positive view on these measurements
i.e. not just state that they are not saying anything,
in particular no breakthrough and no solar revolution

but instead,

i would like to explain why one is getting these results
that seem to indicate an improvement,

why Aidan was seeing what he was seeing.


This is only an attempt, and there is some guessing involved,

as Aidans article does not provide the necessary information – e.g. we do not even know what solar cells were being used.
So, here is my best guess :) .. hope it is useful to some – maybe we can even discuss it?

We have to start with looking at the

IV curve of a solar cell:

IV curve of a typical solar panel, at different light intensities

IV curve of a typical solar panel, at different light intensities















This curve shows

current I

voltage V

power p

at different light intensities.

Note that voltage is the fat line, power is the thin line.
Power is what we really need from a solar cell.

The experiment measured the so called open circuit voltage, that means,

no load is connected,
the current is ZERO: I = 0.

This open circuit voltage is almost independent of how much light precisely you have – as long as you are above a certain threshhold.

I have tried to indicate this area in which we are moving with some orange dots.

More orange, more light.

But the important point is: as long as there is just some light, there will be some voltage –
and it does not matter very much, how much light that is.

(As a reminder, the power produced is zero – as there is no current, and no load.)

Now, we can see from the pictures that the panels were placed in an environment with lot of diffuse reflection –
in front of a wall painted white, it seems.

The test setup, picture from original post

The test setup, picture from original post



This means, that as the sun wanders around the cells, the fibonacci cells will always catch some light – from the side, from behind, and so forth.
The optimized normal panel arrangement will only get light as long as the sun is within its angle, i.e. in front of it.

So, it is clear that the fibonacci arrangement will collect some light for longer hours each day.

At peak time, around noon, there will be enough reflections to bring all individual cells above the limit –

it means, all of them will be able to produce the open circuit voltage.


So, both arrangements can produce roughly the same voltage while the sun is up high,
and then, while the normal panel arrangement will go dark at some point, the fibonacci setup will still catch some light.

This is exactly what you see when you put the two curves on top of each other.

Aidans 2 measurements combined

Aidans 2 measurements combined












But – the longer days of the fibonacci setup will not produce any more power than the normal setup.
The total power in this measurement is always just zero.

Take a look back at our first picture – the IV curve – and see how high power output only occurs when there is a lot of light!

So IF we connected a load, we would see how the normal setup outperforms the fibonacci setup.



To conclude: the experiment’s two main flaws are

  • The experiment measured open circuit voltage, believing it to be equivalent to power/energy. However, open circuit voltage says nothing about power/energy.
  • The experiment assumes that the sum of N suboptimal values can be larger than the sum of N optimal values. This is plain wrong.