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.

5 Responses to “Explaining the Fibonacci solar breakthrough (that isn’t one) – UPDATED”

  1. 13-Year-Old finds Fibonacci Solar Power Breakthrough, or: Media are so in love with the good story they shut down their brains « write.less writes:

    […]  UPDATE: Trying to explain how the misunderstanding/hoax comes about: Explaining the Fibonacci solar breakthrough (that isn’t one)   […]

  2. Fabio Riesemberg writes:

    Dear Mr. Editor,

    I was interested in repeat in my page Fibonacci post from a page called http://www.ciclovivo.com.br when I decided to investigate. Well, I found your post in counterpoint. However I’m a mere jounalist and don’t know physics deeply. So I ask:
    – Are there other setups with solar boards out of normal setup which can have superior or equal results than Fibonacci has?
    – The second graphic is dated by 2008. Is that when you made this comparision? Is that meas Fibonacci was attempted at that time already, so the “breakthrough” is completely false.
    – As I see Fibonacci supposed higher performance is due to a simple solar board positioning, nothing to do with the amount of power achieved in certain period of time. Am I right?
    – I’d like to know your name.
    – Your domain has “dk”. Are you danish?
    – What is your occupation? Are you a physician? Where do you work?

    I ask these questions in order to write a good non-tendentious article.


  3. INTERVIEW – Nothing is new in Dwyer’s solar device | Esquentadinho writes:

    […] This week we had news which committed mistakes on an american teenager experiment. It’s the Aidan Dwyer’s school project involving Fibonacci sequences to obtain more  solar power. According Dwyer, who won the Young Naturalist Award of The American Museum of Natural History, the scheme gets from 20% to 50% more power than conventional flat solar panels. This issue provoked some controversy in the science world due to a media over reacting on Dwyer’s invention. You can see details at this link. […]

  4. Mitch writes:

    Nice try, but no. Yes it’s better to monitor voltage under load, i.e. power, rather than open circuit voltage, but there’s no reason to assume power under load doesn’t simply follow voltage. In other words, consider the increase in light to be like stacking additional aa batteries in series. The more you stack the higher the open circuit voltage, just like Aidan’s results.
    With batteries, though, it’s easy to see that it would work also under load.

    Aidan’s curves are wider, i.e. more voltage at the beginning and end of the day. If under load there would most probably also be more power output proportionally due to this voltage.

    I think the better experiment is to mount the cells in a curve, such that some are directly facing the sun at the beginning and end of the day. Mid-day they lose in comparison to traditional array. The item of interest is the difference in the integrated total power output (and by above reasoning, also the less direct integrated total voltage output).

    My guess is that it is non-linear and that it pays to sacrifice some dawn and dusk power in order to maximize the midday power.

    (fyi, I’m EE MIT ’73, now a software engineer & electronics hobbyist)

  5. sebastian writes:

    Mitch, thanks for the comment –


    1) ” but there’s no reason to assume power under load doesn’t simply follow voltage” – yes, there is – that is one key point here. power under load does NOT follow voltage.

    2) the comparison with stacking in series is wrong – that s not whats being done here.

    3) “If under load there would most probably also be more power output proportionally due to this voltage.” – no – see 1)

    4) you are absolutely right on the meaningful experiment being: measuring integrated power output over whole days.

    thank you!

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