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

649 points by jedwhite 15y ago

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felipemnoa 15y ago
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.
- rycs 15y ago
  it makes a lot of sense, nature has been doing it for a lot of time :), I hope that other scientists elsewhere can also confirm that the improvements are so dramatic, I mean, having still/motionless cheap arrays that can perform 20%-50% better than the flat ones are great news!
  - deleted 15y ago
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- ebzlo 15y ago
  Now I don't disagree that an array of cells that track the sun would produce better results, but it would be fair to assume that this would cost energy. Keeping that in mind, do you think it would still provide better results?
  - deleted 15y ago
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  - rycs 15y ago
    I'm not an expert here, but it's pointless to make tracking sun panels that costs a lot more if the outcome wasn't that great, I bet tracking sunlight is still more efficient even after spending energy to move the panels, it makes no sense otherwise. The real benefit of this is that you get a cheap motionless panel that performs a lot better than the flat version, this is specially important in places like Africa where you need to be as efficient and cost effective as possible.
    - palish 15y ago
      Indeed. The boy's design is extremely rugged and simple (no moving parts). It should be highly reliable someday.
    - TeMPOraL 15y ago
      SolarFlower.org - the open source solar collector - has a non-electronic sun tracking system that I think might be more efficient than PV-powered tracking. See http://www.solarflower.org/faq.htm http://www.solarflower.org/faq.htm.
  - sankalpk 15y ago
    According to Wikipedia (http://en.wikipedia.org/wiki/Photovoltaic_system#Tracking_the_sun http://en.wikipedia.org/wiki/Photovoltaic_system#Tracking_th...): "tracking systems can increase viable output by up to 100%...For large systems, the energy gained by using tracking systems outweighs the added complexity (trackers can increase efficiency by 30% or more)" The new tree design can make 20%-50% more electricity. Wouldn't know till they do some legitimate tests but it seems like the sun trackers fare better.
    - tomp 15y ago
      Why compare the designs, when you can combine them? I'm sure that the tree design can be improved a lot more, by just slightly turning the "leaves" so that they face the sunlight more directly.
      - ebzlo 15y ago
        I am willing to wager the suggested "combined" design would produce a very similar results anyway. The tree design is likely not necessary if the panels are moving.
  - eric-hu 15y ago
    Tracking panels may prove to be a better design for maximum power output. However, there are other constraints to engineer for. Cost and durability (through simplicity of parts) come out ahead in a design with no moving parts. At the end of the day, it's better to have knowledge of both designs to know what's most appropriate for your needs.
  - lutorm 15y ago
    The real benefit of a tracking system is that it makes it possible to use a concentrator to focus more sunlight on a smaller PV area. The panel cost is mostly in the PVs, so increasing collecting area by using mirrors is more cost effective than just using more PVs. However, this setup only works if it's pointing right at the Sun, so it requires a tracker.
- yxhuvud 15y ago
  Moving parts cost a lot though. There is a reason for trees not to have them.
  - MichaelApproved 15y ago
    But sunflowers have moving parts and they track the sun beautifully.
    - sjs 15y ago
      Sunflowers don't stick around for dozens of years or more.
    - randomdata 15y ago
      But the equipment starts to fail quite rapidly, especially when compared to a tree.
  - baq 15y ago
    most plants try to aim leaves at the sun. don't know about trees, but certainly whatever i've got growing in pots does that.
  - sliverstorm 15y ago
    http://www.youtube.com/watch?v=Ze8NV7cvW8k http://www.youtube.com/watch?v=Ze8NV7cvW8k
- uvdiv 15y ago
  "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/2011/aidan.html 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 http://i.imgur.com/SWGjV.png This from the solar module datasheet here: http://www.bpsolar.us/products/3-series-solar-panels-polycrystalline 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.
  - toppy 15y ago
    This guy is 13 ;)
- ForrestN 15y ago
  Wouldn't it be possible to track the sun with the tree model as well?
auston 15y ago
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/2011/images/aidan_large_08.jpg http://www.amnh.org/nationalcenter/youngnaturalistawards/201...
- jdelsman 15y ago
  Probably not, but I would have to say, THIS is the kind of stuff we should be awarding US patents to...
  - robryan 15y ago
    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.
  - Shenglong 15y ago
    Really? Instead of 1-click buttons? Are you serious? disclaimer: sarcasm
Protagoras 15y ago
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 15y ago
  It's provisional.
waterlesscloud 15y ago
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 15y ago
  After 500 million years nature has tried a lot of designs.
  - Peaker 15y ago
    There may be hidden variables or different fitness considerations that apply to nature/trees but not to solar panels.
    - drivebyacct2 15y ago
      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?
- mleonhard 15y ago
  I would guess that trees are optimal for their environments, which include lots of things that are not relevant to solar panel arrays. For example, trees grow and compete with other trees and plants for sunlight. Trees also have different structural constraints and structure cost/benefit ratios than solar panel arrays. Deciduous trees drop their leaves and hibernate through the winter, replacing them in spring. So I think you're right that nature's design isn't quite optimal for solar panel arrays, but it's a great source of inspiration. :)
- rorrr 15y ago
  http://www.ted.com/talks/view/lang/eng//id/450 http://www.ted.com/talks/view/lang/eng//id/450
  - wazoox 15y ago
pigbucket 15y ago
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-solar-breakthrough-with-fibonacci-sequence.php http://www.treehugger.com/files/2011/08/13-year-old-makes-so... 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/2011/aidan.html http://www.amnh.org/nationalcenter/youngnaturalistawards/201...
- waterlesscloud 15y ago
  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."
  - felipemnoa 15y ago
    >>The tree design takes up less room than flat-panel arrays Very true. That is a huge advantage if space is a concern.
    - sushumna 15y ago
      TO be specific - If "horizontal space" is a concern. Solar Tree consumes vertical space.
  - anamax 15y ago
    > 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.
cperciva 15y ago
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 15y ago
  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 15y ago
    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 http://fractalfoundation.org/OFC/OFC-11-1.html
    - romansanchez 15y ago
      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 15y ago
        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.
RobertHubert 15y ago
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 15y ago
  Ponder that when you have impacted wisdom teeth. Teeth are a good argument against intelligent design as well!
  - RobertHubert 15y ago
    Well I didnt say she's perfect lol. Trees are just a great example of how evolution has done a pretty good gob on a specific trait. Now compared to how long humans have been around and our constant changing environments and diet, medicine and other advancements keeping us alive, trees have had quite a head start for getting stuff "right"! But yes intelligent design is garbage. But what happens if we design an intelligent race and set it loose on another planet and they start doing stuff they weren't designed to do? lol. Bad designer or stupid creatures? I'm just having fun here...
  - toyg 15y ago
    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 15y ago
      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.
martinkallstrom 15y ago
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 15y ago
  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 15y ago
    http://www.wolframscience.com/nksonline/page-410#previous 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.
tiddchristopher 15y ago
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 15y ago
  I guess someone paid the fee for him.
  - tiddchristopher 15y ago
    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 15y ago
      $110 :)
robinhouston 15y ago
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/swinton.pdf http://user29459.vs.easily.co.uk/wp-content/uploads/2011/05/... 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.
benmlang 15y ago
Need more 13 year olds like that.
- toyg 15y ago
  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.
redthrowaway 15y ago
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.
- extension 15y ago
  Yeah, that's a bit fishy. Without an explanation, I'm skeptical that the Fibonacci sequence is actually important. Perhaps any branching arrangement of solar panels performs better than a flat one.
- ColinWright 15y ago
  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 http://en.wikipedia.org/wiki/Fibonacci_sequence#In_nature You can look these things up if you're interested.
scorchin 15y ago
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/2011/aidan.html http://www.amnh.org/nationalcenter/youngnaturalistawards/201...
zacharyvoase 15y ago
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 http://en.wikipedia.org/wiki/L-system
tintin 15y ago
http://farm4.static.flickr.com/3206/2807030740_25f3f2fa53.jpg http://farm4.static.flickr.com/3206/2807030740_25f3f2fa53.jp... 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".
tomp 15y ago
Now that is something that really deserves a patent!
- TeMPOraL 15y ago
  No, it doesn't, I have prior art growing in my pot. ;).
sarabob 15y ago
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.
doyoulikeworms 15y ago
This is much harder to keep clean than a simple, flat array of panels.
- CrLf 15y ago
  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.
deleted 15y ago
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prtk 15y ago
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! :)
pge 15y ago
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.
bobds 15y ago
I wonder if this concept could somehow be applied at a microscopic level.
scdc 15y ago
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&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 http://www.google.com/search?q=cell+towers+look+like+tree&#3...
ck2 15y ago
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 15y ago
  Dan Brown's The Da Vinci Code had some Fibonacci hocus pocus in them according to Wikipedia.
colanderman 15y ago
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.
- JoeAltmaier 15y ago
  Its not a science experiment unless you quote some famous math principle :) Anyway, go ahead, do the experiment yourself! Its not rocket science. No need to guess, when the answer is only a little effort away.
- jobu 15y ago
  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 15y ago
    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.)
jshort 15y ago
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.
ForrestN 15y ago
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.
marknutter 15y ago
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 15y ago
  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.
TeMPOraL 15y ago
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 http://www.solarflower.org/faq.htm.
tripzilch 15y ago
Explanation why this actually doesn't have a lot to do with Fibonacci from the other thread: http://news.ycombinator.com/item?id=2903073 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.
colanderman 15y ago
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 15y ago
  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.
winsbe01 15y ago
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.
pedalpete 15y ago
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 15y ago
  I'd bet that it's because tree-like structures are actually less efficient for general practice despite what this article claims.
jagtesh 15y ago
First genuinely interesting article I've read ever since M.G.Siegler hit Techcrunch
joshaidan 15y ago
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 15y ago
  The second page said something about "The most interesting results were in December..."
  - joshaidan 15y ago
    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.
jsg 15y ago
I wonder what Eden Full (http://www.odec.ca/projects/2006/full6e2/index.htm http://www.odec.ca/projects/2006/full6e2/index.htm) thinks about Aiden's project...
tete 15y ago
It is a miracle that curiosity survives formal education. -- not Albert Einstein (according to Wikiqoutes)

649 points by jedwhite 15y ago

deleted 15y ago

[deleted]

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.

rycs 15y ago
it makes a lot of sense, nature has been doing it for a lot of time :), I hope that other scientists elsewhere can also confirm that the improvements are so dramatic, I mean, having still/motionless cheap arrays that can perform 20%-50% better than the flat ones are great news!
- deleted 15y ago
  [deleted]
ebzlo 15y ago
Now I don't disagree that an array of cells that track the sun would produce better results, but it would be fair to assume that this would cost energy. Keeping that in mind, do you think it would still provide better results?
- deleted 15y ago
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- rycs 15y ago
  I'm not an expert here, but it's pointless to make tracking sun panels that costs a lot more if the outcome wasn't that great, I bet tracking sunlight is still more efficient even after spending energy to move the panels, it makes no sense otherwise. The real benefit of this is that you get a cheap motionless panel that performs a lot better than the flat version, this is specially important in places like Africa where you need to be as efficient and cost effective as possible.
  - palish 15y ago
    Indeed. The boy's design is extremely rugged and simple (no moving parts). It should be highly reliable someday.
  - TeMPOraL 15y ago
    SolarFlower.org - the open source solar collector - has a non-electronic sun tracking system that I think might be more efficient than PV-powered tracking. See http://www.solarflower.org/faq.htm http://www.solarflower.org/faq.htm.
- sankalpk 15y ago
  According to Wikipedia (http://en.wikipedia.org/wiki/Photovoltaic_system#Tracking_the_sun http://en.wikipedia.org/wiki/Photovoltaic_system#Tracking_th...): "tracking systems can increase viable output by up to 100%...For large systems, the energy gained by using tracking systems outweighs the added complexity (trackers can increase efficiency by 30% or more)" The new tree design can make 20%-50% more electricity. Wouldn't know till they do some legitimate tests but it seems like the sun trackers fare better.
  - tomp 15y ago
    Why compare the designs, when you can combine them? I'm sure that the tree design can be improved a lot more, by just slightly turning the "leaves" so that they face the sunlight more directly.
    - ebzlo 15y ago
      I am willing to wager the suggested "combined" design would produce a very similar results anyway. The tree design is likely not necessary if the panels are moving.
- eric-hu 15y ago
  Tracking panels may prove to be a better design for maximum power output. However, there are other constraints to engineer for. Cost and durability (through simplicity of parts) come out ahead in a design with no moving parts. At the end of the day, it's better to have knowledge of both designs to know what's most appropriate for your needs.
- lutorm 15y ago
  The real benefit of a tracking system is that it makes it possible to use a concentrator to focus more sunlight on a smaller PV area. The panel cost is mostly in the PVs, so increasing collecting area by using mirrors is more cost effective than just using more PVs. However, this setup only works if it's pointing right at the Sun, so it requires a tracker.
yxhuvud 15y ago
Moving parts cost a lot though. There is a reason for trees not to have them.
- MichaelApproved 15y ago
  But sunflowers have moving parts and they track the sun beautifully.
  - sjs 15y ago
    Sunflowers don't stick around for dozens of years or more.
  - randomdata 15y ago
    But the equipment starts to fail quite rapidly, especially when compared to a tree.
- baq 15y ago
  most plants try to aim leaves at the sun. don't know about trees, but certainly whatever i've got growing in pots does that.
- sliverstorm 15y ago
  http://www.youtube.com/watch?v=Ze8NV7cvW8k http://www.youtube.com/watch?v=Ze8NV7cvW8k
uvdiv 15y ago
"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/2011/aidan.html 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 http://i.imgur.com/SWGjV.png This from the solar module datasheet here: http://www.bpsolar.us/products/3-series-solar-panels-polycrystalline 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.
- toppy 15y ago
  This guy is 13 ;)
ForrestN 15y ago
Wouldn't it be possible to track the sun with the tree model as well?

auston 15y ago

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/2011/images/aidan_large_08.jpg http://www.amnh.org/nationalcenter/youngnaturalistawards/201...

jdelsman 15y ago
Probably not, but I would have to say, THIS is the kind of stuff we should be awarding US patents to...
- robryan 15y ago
  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.
- Shenglong 15y ago
  Really? Instead of 1-click buttons? Are you serious? disclaimer: sarcasm

Protagoras 15y ago

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 15y ago
It's provisional.

waterlesscloud 15y ago

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 15y ago
After 500 million years nature has tried a lot of designs.
- Peaker 15y ago
  There may be hidden variables or different fitness considerations that apply to nature/trees but not to solar panels.
  - drivebyacct2 15y ago
    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?
mleonhard 15y ago
I would guess that trees are optimal for their environments, which include lots of things that are not relevant to solar panel arrays. For example, trees grow and compete with other trees and plants for sunlight. Trees also have different structural constraints and structure cost/benefit ratios than solar panel arrays. Deciduous trees drop their leaves and hibernate through the winter, replacing them in spring. So I think you're right that nature's design isn't quite optimal for solar panel arrays, but it's a great source of inspiration. :)
rorrr 15y ago
http://www.ted.com/talks/view/lang/eng//id/450 http://www.ted.com/talks/view/lang/eng//id/450
- wazoox 15y ago

pigbucket 15y ago

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-solar-breakthrough-with-fibonacci-sequence.php http://www.treehugger.com/files/2011/08/13-year-old-makes-so... 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/2011/aidan.html http://www.amnh.org/nationalcenter/youngnaturalistawards/201...

waterlesscloud 15y ago
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."
- felipemnoa 15y ago
  >>The tree design takes up less room than flat-panel arrays Very true. That is a huge advantage if space is a concern.
  - sushumna 15y ago
    TO be specific - If "horizontal space" is a concern. Solar Tree consumes vertical space.
- anamax 15y ago
  > 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.

cperciva 15y ago

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 15y ago
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 15y ago
  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 http://fractalfoundation.org/OFC/OFC-11-1.html
  - romansanchez 15y ago
    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 15y ago
      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.

RobertHubert 15y ago

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 15y ago
Ponder that when you have impacted wisdom teeth. Teeth are a good argument against intelligent design as well!
- RobertHubert 15y ago
  Well I didnt say she's perfect lol. Trees are just a great example of how evolution has done a pretty good gob on a specific trait. Now compared to how long humans have been around and our constant changing environments and diet, medicine and other advancements keeping us alive, trees have had quite a head start for getting stuff "right"! But yes intelligent design is garbage. But what happens if we design an intelligent race and set it loose on another planet and they start doing stuff they weren't designed to do? lol. Bad designer or stupid creatures? I'm just having fun here...
- toyg 15y ago
  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 15y ago
    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.

martinkallstrom 15y ago

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 15y ago
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 15y ago
  http://www.wolframscience.com/nksonline/page-410#previous 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.

tiddchristopher 15y ago

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 15y ago
I guess someone paid the fee for him.
- tiddchristopher 15y ago
  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 15y ago
    $110 :)

robinhouston 15y ago

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/swinton.pdf http://user29459.vs.easily.co.uk/wp-content/uploads/2011/05/... 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.

benmlang 15y ago

Need more 13 year olds like that.

toyg 15y ago
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.

redthrowaway 15y ago

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.

extension 15y ago
Yeah, that's a bit fishy. Without an explanation, I'm skeptical that the Fibonacci sequence is actually important. Perhaps any branching arrangement of solar panels performs better than a flat one.
ColinWright 15y ago
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 http://en.wikipedia.org/wiki/Fibonacci_sequence#In_nature You can look these things up if you're interested.

scorchin 15y ago

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/2011/aidan.html http://www.amnh.org/nationalcenter/youngnaturalistawards/201...

zacharyvoase 15y ago

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 http://en.wikipedia.org/wiki/L-system

tintin 15y ago

http://farm4.static.flickr.com/3206/2807030740_25f3f2fa53.jpg http://farm4.static.flickr.com/3206/2807030740_25f3f2fa53.jp... 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".

tomp 15y ago

Now that is something that really deserves a patent!

TeMPOraL 15y ago
No, it doesn't, I have prior art growing in my pot. ;).

sarabob 15y ago

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.

doyoulikeworms 15y ago

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

CrLf 15y ago
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.

deleted 15y ago

[deleted]

prtk 15y ago

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! :)

pge 15y ago

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.

bobds 15y ago

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

scdc 15y ago

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&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 http://www.google.com/search?q=cell+towers+look+like+tree&#3...

ck2 15y ago

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 15y ago
Dan Brown's The Da Vinci Code had some Fibonacci hocus pocus in them according to Wikipedia.

colanderman 15y ago

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.

JoeAltmaier 15y ago
Its not a science experiment unless you quote some famous math principle :) Anyway, go ahead, do the experiment yourself! Its not rocket science. No need to guess, when the answer is only a little effort away.
jobu 15y ago
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 15y ago
  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.)

jshort 15y ago

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.

ForrestN 15y ago

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.

marknutter 15y ago

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 15y ago
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.

TeMPOraL 15y ago

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 http://www.solarflower.org/faq.htm.

tripzilch 15y ago

Explanation why this actually doesn't have a lot to do with Fibonacci from the other thread: http://news.ycombinator.com/item?id=2903073 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.

colanderman 15y ago

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 15y ago
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.

winsbe01 15y ago

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.

pedalpete 15y ago

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 15y ago
I'd bet that it's because tree-like structures are actually less efficient for general practice despite what this article claims.

jagtesh 15y ago

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

joshaidan 15y ago

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 15y ago
The second page said something about "The most interesting results were in December..."
- joshaidan 15y ago
  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.

jsg 15y ago

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

tete 15y ago

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