
13-Year-Old Makes Solar Power Breakthrough by Harnessing the Fibonacci Sequence - jedwhite
http://inhabitat.com/13-year-old-makes-solar-power-breakthrough-by-harnessing-the-fibonacci-sequence/
======
pigbucket
Inhabitat credits treehugger.com as its source. Treehugger's article is not
breathless about biomimicry, not spread over two pages, and not interrupted by
adsense and images. [http://www.treehugger.com/files/2011/08/13-year-old-
makes-so...](http://www.treehugger.com/files/2011/08/13-year-old-makes-solar-
breakthrough-with-fibonacci-sequence.php)

Edit: The source of treehugger's article is Aidan's own article, which is
better still, and addresses briefly some of the issues raised in comments here
(e.g., about fixed vs. tracking pv arrays).
[http://www.amnh.org/nationalcenter/youngnaturalistawards/201...](http://www.amnh.org/nationalcenter/youngnaturalistawards/2011/aidan.html)

~~~
waterlesscloud
Last paragraph sums up the possible advantages-

Aidan wrote: "The tree design takes up less room than flat-panel arrays and
works in spots that don't have a full southern view. It collects more sunlight
in winter. Shade and bad weather like snow don't hurt it because the panels
are not flat. It even looks nicer because it looks like a tree. A design like
this may work better in urban areas where space and direct sunlight can be
hard to find."

~~~
anamax
> The tree design takes up less room than flat-panel arrays

The tree takes up less "floor area", but it takes up considerably more volume
because it is significantly taller. That's why, in most places, you probably
don't want to replace large panels with a single tree, but with a forest of
mini-trees.

Trees also have a "concentration of weight" problem, which can be an issue for
roof-top installations. The entire weight of the tree is on its trunk, which
has a lot smaller cross-section than a comparable panel. Roofs that can handle
weight that is spread out often have problems with concentrated weight. Again,
the solution is a forest of mini-trees.

Note that the optimal spacing for solar-panel mini-trees is different from
tree spacing in nature because nature's trees aren't just trying to optimize
energy collection, they're also trying to crowd out their neighbors.

~~~
djb_hackernews
Just because it's shaped like a tree doesn't mean it has to have a central
trunk.

However, mini trees are probably better for aesthetics, weather, maintenance,
etc.

------
colanderman
I don't get what his results have to do with the Fibonacci sequence. Between
his "control" and the design he was testing, he changed:

1\. panel heights 2\. panel angles 3\. whether panels were stacked or not

I would guess that any of those three things matter way more than the position
of the "leaves" following the Fibonacci sequence. He needed to compare his
design to a similar tree-shape whose "leaves" were, say, uniformly or randomly
spaced; not to what amounted to a patch of moss.

(Which brings to mind: solar panels which were shaped more like moss (i.e.
rough) would probably perform even better. I'm pretty sure I remember MIT or
some place building a prototype like that.)

Finally, he measured voltage but made claims about power, which is a huge no-
no for solar PV. Solar PV panels have highly nonlinear voltage/current
characteristics, which means that increased voltage does _not_ correspond to
increased power, especially in setups such as the tree where the solar panels
are not uniformly illuminated.

~~~
jobu
Pretty sure you're missing the point. This kid is 13, and he went and did his
own research and experimentation, and followed through with a patent and a
very well-written letter to the American Museum of Natural History.

My kids are younger, but I would be happy if I could give them the sort of
environment/encouragement to follow their curiosity even half as well as this
kid.

~~~
colanderman
Oh I get the point. I hope he reads my message because that's the kind of
feedback he needs, not the deluge of "oh you're so smart for a kid!" comments
he's probably getting.

(Disclaimer: I get paid to teach engineering to precocious youngsters part of
the year. I'm quite familiar with the demographic.)

~~~
run4yourlives
I hope you realize then that there is much more to teaching than telling a
child - no matter how precocious - "pfft, that ain't so great."

Being an asshole is never excusable. While I understand your point about not
over-praising, this actually is something that few of his peers are able to
do. Proper praise for the boy would be to appreciate the effort, applaud his
commitment to the problem and recognize that he may be able to make the
solution "better".

Once you do that you can point out areas for improvement.

~~~
colanderman
I hope you realize my initial comment wasn't addressed to the child in
question, or I would have e-mailed it directly to him and worded it less
strongly. Rather, I intended to discuss with the HN community the technical
merits of the article. (If treating his article as the work of an adult isn't
praise I don't know what is!)

On a side note, I feel mildly insulted that you feel the need to tell me how
to do my job. If you're interested in the intricacies of the art of teaching
self-directed youth (which mostly involves understanding the child in
question, and saying the right thing at the right time) I'd be glad to discuss
them with you.

~~~
tokenadult
_If you're interested in the intricacies of the art of teaching self-directed
youth (which mostly involves understanding the child in question, and saying
the right thing at the right time) I'd be glad to discuss them with you._

I'd love to hear about that. That is my occupation as a teacher of
supplementary math lessons, and that is my daily life as a homeschooling
parent. I can always afford to learn more about doing what I do better.

~~~
colanderman
I'll do my best to sum up what I do. I've never put this in words before.

My modus operandi involves building a mental model of what the student knows,
doesn't know, and how they think about the problem in question. Usually I do
this through targeted questioning, and watching faces for signs of confusion
in a group session. e.g. let's say we're working on Newtonian physics. I might
take a model car with occupants, roll it along a table, and ask what happens
when the car hits something. From this I can judge whether the students
understand momentum.

If their mental model is wrong, next you have to break it down. How to do this
varies based on how committed they are to their model -- if you challenge
their views in too dramatic a manner you can lose their trust and frustrate
future lessons. For students whom are less committed to their incorrect model,
it suffices to demonstrate a counterexample. Those who are more commited can
require several weeks to shake their beliefs.

Actually teaching involves three parts: definitions, questioning, and
experience. Definitions are KEY. You can build an entire lesson around a solid
definition. For example: "speed is how far something travels every second" (or
"in a certain amount of time" for the ones able to handle abstraction). Keep
definitions few and far betweens and simple. Refer back to them often.

Next follow up with questioning: how can we measure speed? do we know how to
measure the things in the definition? if something moved ten meters in five
seconds, how many meters did it move every second? This has been covered
elsewhere in depth. Don't overdo it though, some kids hate questioning. Just
tell them facts.

Oh, be consistent. Use vocabulary consistently, don't throw around new terms,
stick to one system of units, etc. Minimize distraction and confusion.

Experience is key to solidifying rules deduced from questioning. Roll that
cart down the hill. Practice those factoring problems. Not everyone needs
experience but most do. Experience can help break down incorrect mental
models. As with definitions, minimize distraction. Experience one thing at a
time until it is understood.

Finally, don't be afraid to go off on tangents. If a kid expresses interest in
something, that means they will be focused and eager to learn it. You can
teach almost anything to a student who wants to learn it. Motivation is
everything.

I hope this helps. It's early in the morning and I'm writing this on my Kindle
so it's probably rambly and missing things. I'll try to remedy that throughout
the day.

------
felipemnoa
The comparison is against a flat row of cells that do not track the sun. I
suspect that it will not do better compared to an array of cells that do track
the sun.

Basically the tree of cells are arranged in different angles so that as the
sun moves some of them will always be receiving optimal sunlight when their
normal is parallel with that of the incident light.

Very nice insight, especially for a kid his age. I certainly would not have
thought of it.

~~~
uvdiv
_"Basically the tree of cells are arranged in different angles so that as the
sun moves some of them will always be receiving optimal sunlight when their
normal is parallel with that of the incident light."_

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 < E_opt (for i <\- 1..N)

Σ E_i < N * E_opt

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...](http://www.amnh.org/nationalcenter/youngnaturalistawards/2011/aidan.html)

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...](http://www.bpsolar.us/products/3-series-solar-panels-
polycrystalline)

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.

~~~
pixcavator
>If there is an unqiue optimal orientation for a single static panel (which
under realistic assumptions there is)...

If you have some kind of “continuous function attains its max” argument here,
I think you should elaborate. Because it’s interesting but not really
“trivial”.

~~~
Edog
He used the extreme value theorem. The theorem asserts that a continuous
function on a compact set (for our purposes closed and bounded set) has a
maximum (and a minimum). In this case the the closed and bounded set is the
sphere of all possible orientations for solar panels. The theorem is mentioned
in most introductory calculus courses, but the proof is definitely not
'trivial'.

<http://en.wikipedia.org/wiki/Extreme_value_theorem>

~~~
uvdiv
That's not actually sufficient to show _unique_ extrema; there an be a set of
points on which a function achieves the same, maximal, value.

i.e. cos(x) over x <\- [0,4π] -- multiple maxima at {0,2π,4π}.

But we don't really need unique extrema here. Oversight on my part -- there
can be (although I believe there aren't) multiple optimal panel orientations.
Then the optimal array is an array with each panel having _any one of_ the
optimal orientations.

------
tiddchristopher
The description, "The study earned Aidan a provisional U.S patent," is
misleading. A provisional patent is merely a completely automated recognition
of your claim to an invention. You submit your provisional filing, and then
have one year to file an actual patent, which is reviewed by patent examiners.
You don't "earn" a provisional patent--you just pay a couple hundred dollars
and submit a few forms.

~~~
icode
I guess someone paid the fee for him.

~~~
tiddchristopher
That would be the cynical way to look at it. For a sole inventor, working
independently of any company, I think the filing fee is about $150. It's
possible he had enough saved to pay for it himself. :) Heck, judging from his
report, the kid might have even figured out the whole application by himself.
That alone would be just as impressive as any invention.

~~~
monochromatic
$110

:)

------
robinhouston
Towards the end of his life, Alan Turing spent some time trying to explain
Fibonacci phyllotaxis. [http://user29459.vs.easily.co.uk/wp-
content/uploads/2011/05/...](http://user29459.vs.easily.co.uk/wp-
content/uploads/2011/05/swinton.pdf)

I wonder if Aidan Dwyer is pleased by the thought that his scientific career
is beginning where Turing’s left off. I would be, in his shoes.

------
zacharyvoase
Everyone always talks about the Fibonacci sequence w/r/t the golden ratio, but
in nature it's usually a variant on a Lindenmayer system:
<http://en.wikipedia.org/wiki/L-system>

------
marknutter
Is it just me, or do most articles about young kids doing intellectually
notable stuff start out with something along the lines of "while most 13-year-
olds spend their free time playing video games or cruising Facebook...."

~~~
postfuturist
Yes, it's a journalistic cliche. I would hazard to say that the average adult
is also more likely to be playing video games or cruising Facebook than
pursuing scientific research.

------
Protagoras
A couple of points:

1\. Like others said this is in comparison to a flat non tracking solar panel,
the tree configuration would lose out significantly against a tracking panel.

2\. Fairly disingenuous graph on the second page, but then again professionals
in business and science do this all the time as well.

3\. With the current state of solar technology this patent is useless. But if
someone invents solar cells who are so cheap that they cost less than the
solar tracking equipment, this could become quite a lucrative patent.

4\. I wasn't aware you could patent things which are this directly copied from
nature. I was under the impression that you could say patent a mechanism which
emulates the motion of a specific fish but not the motion itself, or can you ?

~~~
earbitscom
It's provisional.

------
scorchin
On Aidan's own article[1], you can see that he's referenced work that's guided
him in making this breakthrough. Hidden in the bibliography is a Dr Suess
children's book!

 _Geisel, Theodor Seuss (Dr. Seuss). The Lorax. New York: Random House
Publishers, 1971._

[1]
[http://www.amnh.org/nationalcenter/youngnaturalistawards/201...](http://www.amnh.org/nationalcenter/youngnaturalistawards/2011/aidan.html)

------
tripzilch
Explanation why this actually doesn't have a lot to do with Fibonacci from the
other thread:

<http://news.ycombinator.com/item?id=2903073>

Additionally explains/shows that the Fibonacci sequence, or the golden ratio,
both do _NOT_ generally occur in nautilus shells, spiral galaxies, ancient
design principles, body ratios nor are they perceived as significantly more
aesthetically pleasing than other ratios of small numbers.

------
martinkallstrom
Wait... so there is a _reason_ trees look like that? This was awesome, all the
more for being a discovery by a 13-year old kid.

~~~
pigbucket
Exactly. In fact, the guy didn't discover that trees branch according to the
Fibonacci sequence (which was long known) but rather began his investigation
by asking, Why the Fibonacci sequence? Then he hypothesized that it optimized
the gathering of sunlight for photosynthesis. Then he tested the hypothesis
with a new pv array.

~~~
taliesinb
<http://www.wolframscience.com/nksonline/page-410#previous> has something to
say about how the golden ratio can pop out without being encoded directly in
plant phylotaxis.

------
waterlesscloud
I wonder if some genetic algorithm style testing of angles and placements
could yield even more efficiency?

Seems possible that nature hasn't yet hit optimal design in this area.

~~~
guelo
After 500 million years nature has tried a lot of designs.

~~~
Peaker
There may be hidden variables or different fitness considerations that apply
to nature/trees but not to solar panels.

~~~
drivebyacct2
Not only that, but is there a theoretical peak for that which is necessary for
survival, another peak for wide spread population and dispersion, and yet
another peak for max efficiency?

------
cperciva
He "discovered" the Fibonacci sequence in how trees branch? Seriously?

Maybe I'm just being a grumpy old guy here, but when I was in school this was
_in our math textbooks_ as an example of how the Fibonacci sequence appears in
nature.

~~~
bragh
Depends from the school and the textbook. My math textbooks didn't even
mention the Fibonacci sequence and it wasn't until Project Euler that I found
out about it.

~~~
Jach
I learned more about Fibonacci and the golden ratio in nature and art through
my high school Art History course than I ever did in a math course. Though I
had played with fractals a little bit before that course so the fractal
geometry of nature and Fibonacci-fractal relationships weren't a complete
mystery to me. <http://fractalfoundation.org/OFC/OFC-11-1.html>

~~~
romansanchez
Same here, I learned about the golden ration in my high school Art class.
Weird, because it was never mentioned through my college years despite how
important and ubiquitous it is.

~~~
sesqu
This probably has a bunch to do with how the Fibonacci sequence is attributed
with a lot of mysticism and attributes it doesn't actually have.

The golden ratio does not depend on the Fibonacci sequence, it depends on the
recursion equation, and it's only ubiquitous if you add error margins of 10%
or so so that it covers ratios like 3/2 and 7/4. Nautilus shells _aren't_
described by the Fibonacci sequence, and the golden box isn't all that pretty.

It's a great and motivational story, but it's not the magic bullet some
authors make it out to be.

------
scdc
They should combine this with the cell-tower that looks like a tree _. Could
reduce the cell tower's electricity draw.

_ Not sure these exist everywhere. Here is a Google Image search:
[http://www.google.com/search?q=cell+towers+look+like+tree...](http://www.google.com/search?q=cell+towers+look+like+tree&hl=en&client=safari&rls=en&biw=1425&bih=869&site=webhp&prmd=ivns&source=lnms&tbm=isch&ei=SVdOTremK8Tr0gGj4rykBw&sa=X&oi=mode_link&ct=mode&cd=2&ved=0CCAQ_AUoAQ)

------
auston
Question: Does his tree have nearly double the number of panels? If so, does
that have anything to do with him getting more power?

[http://www.amnh.org/nationalcenter/youngnaturalistawards/201...](http://www.amnh.org/nationalcenter/youngnaturalistawards/2011/images/aidan_large_08.jpg)

~~~
jdelsman
Probably not, but I would have to say, THIS is the kind of stuff we should be
awarding US patents to...

~~~
robryan
Possibly, or is this to a solar company like the patent that was brought up on
here last week that basically described link/skip lists is to a computer
scientist.

------
tintin
[http://farm4.static.flickr.com/3206/2807030740_25f3f2fa53.jp...](http://farm4.static.flickr.com/3206/2807030740_25f3f2fa53.jpg)
This 'tree' to charge your phone was designed in 2008. I wonder if it charges
better than a flat design.

Search for "Solar Powered Bonsai Tree".

------
pge
While this is interesting, the most important metric for solar power is not
Watts per square meter but Watts per dollar of production cost. Complex
configurations like this may be more efficient from a W/m2 but unlikely to be
more efficient from a W/$ perspective.

------
ForrestN
It seems like trees are trying to maximize the density of leaves they can
accommodate, balancing that against the decreasing usefulness of each leaf. I
suspect using the tree placement you could produce much more energy per square
meter of land, because you could fit so many more panels.

Imagine if a tree's leaves were arranged in a grid. The footer would be
enormous. If you are making a solar farm. In the desert with sun-tracking
panels, I don't know how much this improves things, because there isn't much
limit on land. But in a city, on rooftops, in backyards, etc, you might be
able to get a lot more total energy out of a given plot this way.

------
colanderman
Apparently in the "flat" design, half of the solar panels are on the back roof
of the model house, facing his _actual_ house, and thus likely not getting any
significant light at all.

~~~
thestranger
Well he did say in the source article that he moved the test location around a
few times, but another flaw is that the height of the solar "tree" means that
it would put the "flat" design in its shade at times. I wonder if he
controlled for that, although the images would suggest he did not.

------
jshort
Trees have been attempting to capture the suns energy for a long time and I'd
like to see a comparison to other plants efficiency at capturing energy.
Nature is powerful.

------
pedalpete
I find it amazing that with all the interest in bio-mimicry, this hasn't been
tried before. Did nobody ever ask why all plants share a very similar
architecture?

They've even made solar cells that look like leaves before
[http://techon.nikkeibp.co.jp/english/NEWS_EN/20080527/152443...](http://techon.nikkeibp.co.jp/english/NEWS_EN/20080527/152443/),
but nobody bothered to test if a tree-like structure gathered more energy.

~~~
suivix
I'd bet that it's because tree-like structures are actually less efficient for
general practice despite what this article claims.

------
joshaidan
He needs to do the same experiment during the wintertime when the angle of the
sun changes. You won't get accurate results until the experiment is performed
year round. Different angles of inclination perform better at various times of
year, and there are some thoughts that multi-inclined arrays average the same
output as uniform arrays.

Remember, a tree only has leaves in the summertime, not the winter. :)

~~~
marshray
The second page said something about "The most interesting results were in
December..."

~~~
joshaidan
I may have my logic backwards, it should be tested in the summer time when the
sun is higher in the sky. Either way, the test needs to be done year round to
see how the results vary.

------
RobertHubert
Cant get much better than millions of years of try and die I guess. Mother
nature is pretty crazy! We should copy her work more often :)

~~~
Anti-Ratfish
Ponder that when you have impacted wisdom teeth. Teeth are a good argument
against intelligent design as well!

~~~
toyg
Actually the "technology" behind wisdom teeth is quite smart. How many
organisms feature resources timed to "spring" 20 or 30 years from birth, to
replace lost "components"?

You experience them as painful because your teeth don't rot as they used to;
until the XX century, it was common for people to lose many of their teeth by
the age of 30, so they were grateful for an extra set. They'd probably be dead
before 45 anyway, so just a few would suffice to chew your way through the
last years of your life.

~~~
Anti-Ratfish
Not sure if it's a good resource or not and I can't see to even find which
book it was. But I recall reading a Dickens description of toothache. I'm not
sure that the tooth-rotting-out-to-make-space-for-more-teeth experience or
yore was anything other than deeply unpleasant.

------
TeMPOraL
A lot of comments mention tracking the sun. I'd like to remind everyone about
SolarFlower.org - the open source solar collector with a clever, non-
electronic sun tracking system. See <http://www.solarflower.org/faq.htm>.

------
bobds
I wonder if this concept could somehow be applied at a microscopic level.

------
jsg
I wonder what Eden Full (<http://www.odec.ca/projects/2006/full6e2/index.htm>)
thinks about Aiden's project...

------
winsbe01
i think this is great. not that he was 13 (though it is impressive), but that
he thought enough to challange the typical panel array that we've gotten solar
power from in the past. it seems that he got some interesting results, too.
sure, maybe he didn't take some things into account, or maybe it's not super
practical, but breaking out of the mold of large, 2d rectangular panels may be
something the solar energy world needs to innovate on ways to harness more
energy from the sun efficiently.

------
prtk
NASA designed antenna using genetic algorithms. This guy can use GA to
optimize his solar-fibonacci-tree further.

Way to go kid! The force is strong with you! Best of luck! :)

------
sarabob
The panels on the tree are higher than those on the flat plane - you'd expect
to get more light for longer from that alone.

------
tete
It is a miracle that curiosity survives formal education. -- not Albert
Einstein (according to Wikiqoutes)

------
redthrowaway
So perhaps this is a question that others have answered, but what springs to
mind for me is: _why?_ I get that trees that follow the Fibonacci sequence are
more productive, but without an answer to why that is, it remains a bit of a
kludge. I would love to see some explanation of why this configuration is
optimal.

~~~
ColinWright
Broadly speaking ...

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.

------
jagtesh
First genuinely interesting article I've read ever since M.G.Siegler hit
Techcrunch

------
doyoulikeworms
This is much harder to keep clean than a simple, flat array of panels.

~~~
CrLf
Maybe not. Trees have to keep their leaves clean, and perhaps the Fibonacci
placement doesn't only improve sunlight collection, but also rain collection
for cleaning.

------
tomp
Now that is something that really deserves a patent!

~~~
TeMPOraL
No, it doesn't, I have prior art growing in my pot. ;).

------
ck2
If he wanted better mainstream press he should have thrown the word "fractals"
in there. I bet most reporters know the word fractals than Fibonacci sequence.

~~~
eru
Dan Brown's The Da Vinci Code had some Fibonacci hocus pocus in them according
to Wikipedia.

------
benmlang
Need more 13 year olds like that.

~~~
toyg
I wouldn't be so sure. A lot of child-genius types end up regretting their
youth and feeling like failures for the rest of their (long) lives; the risks
of peaking too soon are well documented.

I hope he stays humble and does what he really wants to do, which might be in
a completely unrelated field, with the same intensity he's shown in this
endeavour.

