From Slashdot, something so obvious you wonder why nobody tried it before: arrange solar panels like tree leaves for better efficiency. See the story and graphs I’ve provided below.
13-Year-Old Uses Fibonacci Sequence For Solar Power Breakthrough
An anonymous reader tips news of 7th grader Aidan Dwyer, who used phyllotaxis — the way leaves are arranged on plant stems in nature — as inspiration to arrange an array of solar panels in a way that generates 20-50% more energy than a uniform, flat panel array. Aidan wrote:
“I designed and built my own test model, copying the Fibonacci pattern of an oak tree. I studied my results with the compass tool and figured out the branch angles. The pattern was about 137 degrees and the Fibonacci sequence was 2/5. Then I built a model using this pattern from PVC tubing. In place of leaves, I used PV solar panels hooked up in series that produced up to 1/2 volt, so the peak output of the model was 5 volts. The entire design copied the pattern of an oak tree as closely as possible. … The Fibonacci tree design performed better than the flat-panel model. The tree design made 20% more electricity and collected 2 1/2 more hours of sunlight during the day. But the most interesting results were in December, when the Sun was at its lowest point in the sky. The tree design made 50% more electricity, and the collection time of sunlight was up to 50% longer!”
His work earned him a Young Naturalist Award from the American Museum of Natural History and a provisional patent on the design.
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Good for him! Here’s the output graphs:
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And as others and you have gotten it wrong. Clearly in the text (if you bothered to click the link)
“The second model was a flat-panel array that was mounted at 45 degrees. It had the same type and number of PV solar panels as the tree design, and the same peak voltage.”
There are 10 cells on the back of the flat panel assembly, since about half the cells on the tree face the rear as well.
C’mon Y’all! The kid is 13! He did well. Most of you ‘critics’ didn’t even have a Playboy hid under your bed yet, let alone started thinking about mathematic series and solar cell arrays.
HankH says:
August 19, 2011 at 3:45 pm (Edit)
steven mosher says:
August 19, 2011 at 11:31 am
ideally what you would do is minaturize the cells and put them on a flexible substrate in the shape of leaves, no more ugly solar. hehe.
Something like they’re doing for cellular towers? I realize the antennae on these trees aren’t the leaves but there’s folks already building steel trees economically so at least a structural start.
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yes. I saw one in santa rosa. Ugly looking fake tree.
But you can well imagine an artifical tree with solar leaves that capture light and C02 fixing leaves,
and a camera/zapper combo to discourage fido, all mesh networked, with little nests for surviellence micro planes that look like birds.
and apples
Great idea for a study by a youngster – but I really hope it wasn’t conducted as sited in the photo. I haven’t read a lot of the comments, but aside from issues noted of elevation and albedo from the house, it’s pretty clear that there are shade issues from nearby trees and with such tiny solar panels, the shade from a branch can wipe out collection from several of the panels.
Also, others noted that it looks like there are more panels on the ‘tree’ but I suspect that the flat panel array only clearly shows one side, and that the opposite side is on a triangle in effect between the side easily seen, the horizontal base, and a back side for the third side of the triangle… with a set of matching panels on that opposite side of the triangle. If so, that makes the siting next to the house all the more problematic.
We’d need better photos or a diagram or something to be able to tell, along with info about where the rig was actually sited for the experiment – and assurrances that there were no shading or other confounding factors.
The classical phyllotaxis pattern on a planar sunflower model is maximised when the angle between successive seed formation is 137.5 degrees or so. One formula suggests that the classic angle is the golden angle, γ = 2π(1 – 1/Φ), where Φ is the golden ratio. However, plots of patterns show that small variations in the angle, as little as 0.2 degrees, soon lead to loss of parastichy, see http://algorithmicbotany.org/papers/abop/abop-ch4.pdf Parastichy and chirality are terms related to the presence of spiral-like patterns between the dots, some which curve to the left and some to the right, classically related by one of the Fibonacci series. The series starting 0,1,1,2,3,5,8,13,21,34….each number being the sum of the pair before, is but one Fibonacci series, albiet the most commonly quoted. Thus, when the correct divergence angle is used on a planar example, the count of spirals is often like 5 to the left and 8 to the right. For larger variations in the divergence angle, rather different patterns are generated, see http://www.flickr.com/photos/twak/3115930730/
It is unclear in my reading how there can be a transition from an 8:5 pattern to a 13:8 pattern. Yet sunflowers can be observed with each, on the same plant. It seems that there is a disruption to the nicety when a transform happens and one can have trouble tracing the spirals, some of which have discontinuities.
It has been said by some (e.g. the late John Rouse, a friend from Physics Dept of Melbourne University) that the pattern, applied to a column of leaves on a stem rather than to a planar pattern akin to the sunflower, maximises the probability of light hitting leaves and so allows better photosynthesis. (Think of a palm tree and the scars left after leaf fall). This is OK if you look along the line of the stem – fewer leaves seem to be blocked to view by ones above. However, the prettiness falls apart when the sun is not axial with the stem. The theory is nice, but not adequate to explain the reality of Nature.
Further complications arise when the geometry changes to quasi-conical, as on a strawberry, or quasi-cylindrical, as on a pineapple. The Fibonacci ratios will often hold, but it is harder to determine a natural advantage in the pattern. By extension, it is hard to determine any natural advantage in the apparatus for solar collectors in the article. If I had my druthers, I’d model on this vegetable, a Brassica romanesque. http://www.fourmilab.ch/images/Romanesco/
Aidan Dwyer deserves high praise for lateral thinking with the solar collector, but maybe the lesson is that sexy discoveries in science can be romanticised beyond the level nature intended.
Dirk H says:
Nice idea, but i think it will go the way of Solyndra – complicated structures are more expensive than simple ones
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Heh: why make a structure? Just grow one, ie: use the natural structures—-trees—with PVPs replacing leaves. Now there’s something for gengineering researchers to get their teeth into—to save the world.
A new acronym: “RTFL” == Read The Flippin’ Link!
So many s-righteous strawman putdowns.
Reasons for mounting a strawman argument:
1) Deliberate distraction
2) Misunderstanding through superficial reading
3) Misunderstanding through lack of background
4) Misunderstanding through lack of intelligence
and, featured prominently here:
5) Laziness — can’t be bothered to read the actual material.
Ugh.
Wow, someone looked into nature instead of just sitting down and reading about it.
This guy doesn’t need University – he’d be teaching his teachers.
Good for him. I hope he makes some money from it.
George E Smith;
‘And the added cost of these “micro-inverters” is ???
What is the inversion efficiency of these micro-inverters, over the full zero to maximum insolation range.
The purveyors of existing solar cell arrays also have access to the use of micro-inverters, I presume; so where does the tree approach gain an advantage ?
There’s almost always a way to design around the shortcomings of any approach. Nuclear powered aeroplanes were never too popular, because of the limited weight capability left over for carrying passengers or freight; Otherwise it seemed like a good idea.
So what fraction of the existing installed solar cell array base, is presently using micro-inverters to overcome the limitation of unequal illumination or conversion efficiency ?’
In turn;
Cost is now approx similar to string inverters and dropping, at least for residential PV.
Inversion efficiency probably a percent or two less, but compensated for by optimizing the harvesting for each panel individually.
Tree? I just made the comment that the simpler wiring with micro-inverters makes the tree approach a little more practical that it would have been otherwise.
Fraction of base? Tiny. Mainly because the micro-inverters have only recently come good (price, performance). We will see an explosion of them over the next year or so.
Check out Enphase or Enecsys.
See http://www.efficientenergy.net/p/102149.htm
Ryan says:
August 19, 2011 at 4:16 pm
The optimal direction for a solar cell is indeed trivial – “normal” to the Sun. (Normal is a confusing physics/geometry term. In this case, it means the Sun’s rays are at 90° to any line drawn on the solar panel.) It can be off by 10 or 20 degrees and not have a big impact on power output.
The catch is, as I noted in a comment yesterday, it’s really expensive to maintain that angle as the Sun moves across the sky. In fact, if you try a compromise like aiming the solar panel at the Sun’s highest point at the beginning of spring or fall, then the panel only sees sunlight for 12 hours in the summer. Repositioning it every season make sense for a homeowner, matching orientation to power needs and storage make more sense, but that’s a whole different topic.
Suppose you had two panels and aimed one somewhat to the east and the other somewhat to the west. That way you’d get better power generation in the morning and in the evening, especially in the summer. Good deal, perhaps. Suppose you covered a dome with solar cells. That could work out pretty well on the equator, though the cells pointing due north or south would be shaded six months of each year. A dome at the north pole would have all the cells dark six months of the year, and the cells on top wouldn’t get much light any time.
Basically, the goal here was to fix in place cells in orientations to provide more hours of power generation. In particular, how do patterns from natural solar collectors compare with typical patterns? The goal was not to maximize power generation, especially with expensive things like solar trackers. It was a goal to provide more power (unfortunately, measured as voltage) than a fixed flat array.
Several of the comments in the thread talk about how to combine the output of solar cells. That turns out to be a challenging task in its own right. Most of what I have to say about that has been said, I might cover the rest later.
jaymam says:
August 19, 2011 at 4:41 pm
We don’t have jet planes flapping their wings just because birds do that. And jet planes don’t have to come out of tiny eggs and reproduce and eat whatever they can find.
Fair enough, but birds have been around for 100 million years and still will be around after jet engines are long forgotten.
Well done Aidan. Teenagers are a resource of immense intellectual creativity, which in our politically correct cosseted education system goes largely to waste. Teenage brilliance in the classroom often illicits jealousy from an intellectually inferior teacher and resultant bullying and abuse, such talent seen as a threat to the sociobiological primate heirarchy of the classroom.
WE DONT NEED NO EJOOKAYSHUN!!! WE DONT NEED NO FORT KONTROL!
Somehow in past ages young teenagers seemed much more free to excercise creativity at a professional level. Some examples of inventions by teenagers can be found at:
http://www.ideafinder.com/features/classact/young.htm
My apologies to Aidan, his text does indeed state;
“The second model was a flat-panel array that was mounted at 45 degrees. It had the same type and number of PV solar panels as the tree design, and the same peak voltage.”
However his graphs do not support his “same peak voltage” statement. Hence my statement about the number of cells.
I stand by my assertion that the open circuit voltage from an array of PV cells is not an accurate measurement of the “electricity” produced. I suspect that if the power delivered by both arrays was properly measured there would be no more total power produced by the tree.
His mentors and the award judges did him a disservice by letting him think that he has invented something that “generates 20-50% more energy than a uniform, flat panel array. “
Cheers, Kevin
Doug Proctor says:
August 19, 2011 at 9:00 am
“If we want cheapness and efficiency, how about growing trees and then burning them in wood stoves: free fuel, good exercise and a zero-sum CO2 game. Forget solar panels entirely. Go Green. Nature is way ahead of us.
Should be a business plan here, perfect for Africa, if not New York City.”
No good for Africa. We burned all of the trees for firewood long since. Not easy to establish new woodlands as with the trees gone the water doesn’t flow any more where it used to. Send some more aid money and with what little bit finds it way down to us we’ll be able to buy coal.
“”””” Geoff Sherrington says:
August 20, 2011 at 1:33 am
The classical phyllotaxis pattern on a planar sunflower model is maximised when the angle between successive seed formation is 137.5 degrees or so. One formula suggests that the classic angle is the golden angle, γ = 2π(1 – 1/Φ), where Φ is the golden ratio. However, plots of patterns show that small variations in the angle, as little as 0.2 degrees, soon lead to loss of parastichy, see http://algorithmicbotany.org/papers/abop/abop-ch4.pdf Parastichy and chirality are terms related to the presence of spiral-like patterns between the dots, some which curve to the left and some to the right, classically related by one of the Fibonacci series. “””””
Interesting Geoff that you should be talkng about the sunflower patterns, as a natural adaptation that presumably gives some advantage.
Is it not also true, that those very same sunflowers do in fact track the sun’s journey across the sky.
I’m looking at a couple of plants that are right outside my window. One of them is some non descript decorative yard tree, and the leaves I can see, which are low on the tree, ar very well shaded by the leaves above. I’m sure the upper ones are getting plenty of sunlight being at the top, and not shadowed. The other plant happens to be a white grape vine, and it has leaves densely all over it. So dense in fact that you almost can’t see any of the hanging bunches of grapes that are developing on the plant.
No it couldn’t possibly be, that plants may have other interets than just gathering the most sunlight. Grapes certainly do seem to want to protect the fruit from a lot of sun..
So some plants may arrange their leaves in ways, that ensure some sun gathering, but let’s not kid ourselves that that is the best possible energy gathering strategy. The sunflower clearly sees the avantage of scanning.
This Fibonacci tree is about on a par with “organic” farming. Without engineered crops, we likely would not all be starving; but you can be sure that the earth would have far fewer of us living on it.
Thanks for taking the time Ric, I’m not trying to pick apart a schoolboy’s science project, I still don’t understand why this is labeled a ‘breakthrough’ though even after thoroughly reading your post. You said that the “the goal here was to fix in place cells in orientations to provide more hours of power generation”. That problem is very simply solved with any number of arrangements superior to all cells facing the same way. (Duh, facing many directions gives you a better chance to be at least partially exposed to sunlight). Perhaps you could be more specific about what the fibonacci numbers and tree brings to the problem that any of the obvious arc/dome arrangements do not. I’m still struggling to understand any scientific mechanism as to how the cells operate any differently in fibonacci tree formation than if they were placed at the same angle/inclination on the ground. In short, I still don’t get it.
Always the skeptic I suppose. Oh well….
Sunflower technology already exists, http://www.greenandgoldenergy.com.au/ where the ‘cubes’ track the sun on both lat and long. Good old Aussie invention
Ryan says:
August 20, 2011 at 1:19 pm
Well, “breakthrough” was used by the person posting on Shashdot. My guess is he didn’t understand the limitations. The article he linked to did not use the word breakthrough, but did quote Dr. Seuss (The Lorax). I wouldn’t call it a breakthrough, just interesting, entertaining, and pretty well done for a teen whose age is a Fibonacci number.
I think Aiden is more interested in math and nature than generating solar power. This is a standard “pit” that many of us fall into and don’t always get out. I was about 13 when Martin Gardner wrote about Fibonacci numbers and the Golden Ratio in Scientific American (reprinted in a book, republished as http://www.amazon.com/Origami-Eleusis-Soma-Cube-Mathematical/dp/0521756103/ in 2008. Nope, the first book was published in 1961 when I was 10 or so.)
Natural occurences of Fibonacci numbers are intriguing, but can be explained by fairly simple processes. Still, plants do put them to pretty good use for things like intercepting sun or packing seeds. You’ll enjoy http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm and http://goldenratiomyth.weebly.com/phyllotaxis-the-fibonacci-sequence-in-nature.html . The latter says:
Unfortunately, the link to “Earlier” makes no mention of “the most irrational number” – even people writing about myths seem to get lost in the myths.
As for your last point, about how the “cells operate any differently in fibonacci tree formation than if they were placed at the same angle/inclination on the ground,” that brings up some significant issues that are discussed in other comments but no has really described the problems well. Nor will I, but I’ll get closer.
In a photovoltaic (PV) cell, sunlight knocks electrons on to the other side of an electrical barrier (barrier is a misleading word). Those electrons can be collected, run through something to extract their energy, and go back into the other side of the PV cell. (Well, the real electrons don’t go very far, as there’s a huge number of electrons that are moved. Think water hose – turn it on, water comes out instantly at the other end, but the water you added to the hose is still in the first few feet of the hose.)
The voltage produced is pretty small. You can put several cells together “in series” to get a higher voltage, but there’s a problem. If one of the cells is shaded, there are very few loose electrons in that cell, and that stops current through all of them. You can also put cells together “in parallel” where each cell provides its own current but the overall voltage is low. If the cells are a little different, then high voltage cells may block current from the low voltage cells. Also, illumination is important in both configurations.
That’s why people are talking about micro inverters and other add ons to keep energy flowing. I a lot of these issues are minimized in flat arrays – cells in series get even illumination, or at least it’s easy to ensure. Both parallel and series can be used productively.
Except for decorative tree-shaped solar collectors, I suspect we’ll be using flat panels for years to come.
George E. Smith says: August 20, 2011 at 12:57 pm Sunflowers follow the sun.
Yes, they do, but the “solar tree” in this articles does not. That is its weakness in comparison with Nature, in terms of flux capture.
More generally, there are many plants with roughly vertical inflexible stems that have opposing leaf pair patterns that do not spiral, but are pair-below-pair. If the sun is directly overhead, the top pair of leaves cast a shade on all of the pairs below. OTOH, the spiral arrangement is thought by some to to minimise the shade on lower leaves. It’s quite interesting to set up a model leaf shape (thin, long ones are best for the math), then examine leaf arrangements that allow light down to the lowest leaves. e.g. count how many leaves you make before one of them gets no light. Nature seems to avoid plants that have a single, circular leaf atop a vertical stalk. (Some water plants are this way, like the lotus). It’s almost as if, given the need for a stem to gain height and compete with neighbours, Nature found that the stem was more efficient if leaves all along it were photosynthesising, not just the top one taking all the light.
BTW, many of these comments apply to leaves and flowers similarly, because a flower is just a leaf that has had some extra gene activity.
As I said, full marks to Aidan for lateral thinking. Phyllotaxis is a fascinating topic, but the fascination should not be a diversion from sound design principles. The solar harvesting engineers worked out long ago the available, practical designs and their benefit:cost ratios for various applications.
At the risk of rabbiting on, this topic is one of the few that links observations of Nature’s grand designs to mathematics of reasonable complexity. A lesser DNA helix example, if you like. If you are into art derived from science, try ‘The Algorithmic Beauty of Plants’, a 1970s book by Przemyslaw Prusinkiewicz and Aristid Lindenmayer. It’s the first comprehensive volume on the computer simulation of plant development (L-systems). The book is no longer in print but a pdf version is available free online. Then follow the later references.
One reason none of them overeducated adult scientist “has thought of this” is because after thinking about it for a minute (as many have, even though they may not always have thought of flowery “like in nature” language at the same time), you realize that having some of your cells pointed to different time-of-day optimal directions simply even your chances re cloud cover etc., instead of peaking all at once — but you still have each cell at a suboptimal direction much of the day.
Since th cells are the most expensive part of the setup, your sensible choices are still: Either you turn all your aligned cells together towards the sun, which optimizes space use, or you arrange mirrors to direct max. sun at your cells all the time, to minimize mechanism and its power use.
When and where I was a kid, kids would build electronic sun-following mechanisms for science/engineering competitions for this purpose.
What this kid has done is dress up the bleeding obvious (non-equal direction distributes the optimal generation periods of different cells) with irrelevant language (Fibonacci, “nature”) and covered it with spotty data. I read the relevant sections of the article, and the voltage measurements which mean NOTHING are all there is.
He also quite possibly got a less-than-optimal baseline by the way he aimed the flat array.
I don’t know why some commenters here who have (going by what they’re writing in support of the poor kid) made no effort at all to understand how this should/would/doesn’t work (beyond reading and believing the “new and improved” conclusion, call the criticisms that try to understand what’s going on and fail to see any reason for the magical results “strawmen”.
It’s sad to see this kid understood so little of what he was doing, and got no help. No physics teacher to point out that a load and A/V measurements where a minimum requirement to make useful measurements? No clue fairy to point out that each cell by itself still acts as if in a flat array statically arranged in some (maybe good, maybe not) manner?
These writeups about motivation and development are usually BS, but in this case, the text apparently more than sums up the thinking process.
It is noteworthy that he made no experiments comparing different tree shapes.
At best, the kid is a budding con artist.
The awarders sadly seem to also have no clue about anything related to the subject.
Saying “like in nature” seems to be the only thing being rewarded.
Why is everybody here so credulous? I just happen to be an electrical engineer, but a math/physics-inclined 10-year-old armed with one solar cell, a photocell, a resistor and a multimeter could disprove these claims in half an hour.
Between his lack of desire to test his own ideas rigorously, and his clueles environment, the project kid looks like a future green-money-to-develop-nothing-grant recipient. Well done.
“”””” Geoff Sherrington says:
August 20, 2011 at 8:22 pm
George E. Smith says: August 20, 2011 at 12:57 pm Sunflowers follow the sun.
Yes, they do, but the “solar tree” in this articles does not. That is its weakness in comparison with Nature, in terms of flux capture. “””””
My entire point Geoff is that the Sunflower example is ample proof that Fibonacci trees are not even the best scheme that Mother Gaia can come up with for an efficient solar collector.
Yes it is remarkable that some of the schemes that Nature evolves over some time, can be shown to be rather efficient schemes, such as the CPC eyes, and plant shoots.
But don’t count the homo sapiens sapiens engineer out when it comes to who is better at solar collection. And I am not even a great supporter of it; but we are a whole lot better than Fibonacci trees, that we know have solar cells where the sun never shines.
This might be a good opportunity for skeptics to learn how to be erm, more skeptical.
Solar-panel “trees” really are inferior (or: “In which hopelessly inept journalists reduce me to having to debunk a school science project”)
http://news.ycombinator.com/item?id=2906538
http://webcache.googleusercontent.com/search?q=cache:JmlMNqVPKlsJ:uvdiv.blogspot.com/2011/08/solar-panel-trees-really-are-inferior.html+http://uvdiv.blogspot.com/2011/08/solar-panel-trees-really-are-inferior.html&cd=1&hl=en&ct=clnk&gl=us&source=www.google.com
Oh that is really great idealistic post. agreed with you yes we should use solar panels as nature has developed. keep on sharing such a great informative post.am impressed.
Suggestion: Use transparent tubes for the supports so that they do not block light to the solar cells when the light is at certain angles.