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.
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!
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?
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.
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.
"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.
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.
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.
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.
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.
"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:
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:
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.
Agreed with the experiment flaws, plus the article is way too shady to make anything even remotely reliable out of it. It reads awfully like "Child pwns scientists, saves world and his dog"
Still, what if you consider a fixed volume as the constraint in establishing the comparison? For a flat panel assembly, a given volume would constrain the surface quite obviously. If you consider a tree structure one might be able to pack some more panels in the same volume, and Fibonacci might give us some solution about how to maximize panel density in the volume while minimizing shading interference from other panels and supporting infrastructure.
And how should that work? The sun is point light source, so the light comes from one direction only and you need to face your solar cells in exactly that direction.
If you want to maximize the given volume a tree doesn't seem like the optimum ... covering the whole surface of the volume should be the optimum (to receive every reflected light).
Also the tree has a lot more solar cells than this kids flat panel and he is still only measuring voltage.
Doesn't it make sense that an empirical test would not reach a theoretical max? For instance you've discounted shade effects as where he went wrong. Maybe its exactly the shade issue that makes his findings significant. Every urbanite will have to deal with it, and his array may do a better job in intermittent shade.
If mass-distributed, most folks would not be optimizing anything - install-and-forget - so its a real solution to create something that works in most environments.
The shade issue implied by the parent post is that the tree configuration was mounted in a generally less shady position, as the Fibonacci-configured panels were located significantly further from the ground than the classic configuration. It is possible that the test was set up in a manner that puts the classic configuration at a disadvantage.
To control for that effect, the two panel configurations should be mounted at an equal average distance from the ground, and their positions swapped in different test runs.
This was where I was going too. (However, I'm not sure the power output of a panel is simply the sum of the individual cells. I thought that in a series array, the least illuminated panel essentially limits the panel current. Not that this matters in this case, since he wasn't actually measuring power. The voltage certainly adds.)
The experimental issue I thought about is that the experiment is situated next to a large wall. While the flat panel is facing away from the wall, it looks like some of the panels on the "tree" would also receive diffuse light from the wall. So effectively, the tree seems to have a larger collecting area than the flat panel. This would also make the tree less sensitive to shading.
>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”.
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'.
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.
Well, the Calc 1 version isn't good enough because there are several variables here. You have to consider a continuous function defined on the sphere -- to capture all possible orientations of the panel. In fact, it could be a closed subset of the sphere -- to take care of all possible shadows, obstructions, etc. This is nice, you don't see a lot of direct applications of pure existence theorems...
No, results specific to solar panel orientation. Math is not trivial at all, but the results are intuitive: roughly, point the panel in the direction which, in mean, is in the direction of the sun. So tilted towards the equator, at the same angle as your latitude.
"The default value is a tilt angle equal to the station's latitude. This normally maximizes annual energy production. Increasing the tilt angle favors energy production in the winter, and decreasing the tilt angle favors energy production in the summer."
(Couldn't find a clear proof of this (under any modelling assumptions), sorry.)
A unique optimum isn't really necessary here (I shouldn't have required it!)
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.
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 ?
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?
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. :)
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...
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."
> 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.
It seems a great deal of your comments have begun to fall into either the "this has already been posted" or "you're not following the rules" category.
Do you see the problem with "contributing" material on top of material you see as less than satisfactory? You're only adding more cruft to the cruft.
We get it. You don't like reposts. We get it. You don't like it when people don't follow the rules to a "T". Guess what? This is what happens. It's the real world where people don't always make the best choice all the time.
If you would get over that fact and focus on making insightful comments I think you'd be doing everyone a favor.
Lastly, to cite the oft quoted Guidelines:
"Please don't submit comments complaining that a submission is inappropriate for the site. If you think something is spam or offtopic, flag it by going to its page and clicking on the "flag" link. (Not all users will see this; there is a karma threshold.) If you flag something, please don't also comment that you did."
Edit: here is a list of links to Colin's comments from the first and second page of his comment history where he is either complaining about resubmissions or the rules not being followed:
2) However, he's not "complaining" about duplicates in those links. He's cross-referencing previous discussions in order to let people learn from them.
3) For what it's worth, he's been here almost two years -- you've been here barely half a year.
It pretty much demonstrates just how difficult it is to apply mathematics to analyze real-world problems, which is really interesting and thought-provoking IMO.
Anyway, my point is, Colin has good taste, and you're doing him a serious disservice. He does good, helpful work, and I hope he doesn't stop, and doesn't straight-up leave, because the community would be worse off. I'd certainly be tempted to leave after reading something like what you wrote.
2) Though "cross-referencing previous discussions in order to let people learn from them" sounds good, if you read Colins profile, he seems quite angry at all this reposting. There is a little to a lot snark in most of those comments (though some really are just links to similar discussions).
3) That should by all means be completely and utterly irrelevant.
I think the OP recognizes Colins contributions, but is pointing out that there seems to be a lot of complaining / slight passive aggression in those comments. Isn't that a fair observation to make?
I'm not bothered by Colins postings. I sure would be bothered though, if HN turns in to your typical internet forum, where older members starts policing newer members about following the arbitrary forum rules ("use the search function, you dimwit!" style).
Yup, OK. I'll stop. Despite lots of people saying they appreciate it, you've convinced me.
I won't cross-reference, I won't point out when people break the guidelines, I'll just silently downvote and flag, leaving people - often newbies - with no idea why their contributions disappear or get negative karma.
That might or might not lead to still more bewildered posts saying they don't understand, but that's OK. There's no point trying to educate them. Let them learn the hard way.
As a mathematician by training, an engineer at heart, and a teacher by vocation, I hate seeing the waste of constantly repeated submissions and the redundancy of split discussions. I had hoped to add value by helping people become enculturated, but I've decided I've failed.
Just ignore him. Really, he's not worth it, and his behavior shouldn't be rewarded (publicly calling someone out and framing them in a bad light without context).
As civil adults and in all seriousness, would you stop? Do you see why I've complained? Cruft is cruft is cruft. Clearly your strategy to mend the dupe problem isn't having a positive effect. Maybe this is because new users aren't aware of the rules (but there will always be new users) maybe it's because people are willfully ignoring the rule (but in this case why should they pay you any attention?) or perhaps there are a multitude of reasons that all contribute to the gradual decline of the richness of information as a community grows. Whatever the case may be, as a long time reader of HN and a recent user, I find that the kinds of comments you make where you show a post is a duplicate does nothing to increase the richness of the content. Instead, your comment is yet another I have to try to ignore in search of meaningful content. Please don't take this personally. I'm sorry to have called you out like this publicly, but I don't know how else to reach you: please stop.
As a long time HN reader and contributor, please do not ask other community members to stop helping the community. If I go to the discussion page for a submission, but find it mostly empty except Colin's link to a dupe, I can then read the discussion that happened.
I agree. I've found the links to dupes extremely useful, because usually people will only comment in one such thread and without the links, I'd have no easy way of 1) knowing that there already was a discussion and 2) finding the discussion.
I wasn't going to contribute further to this, but after considerable thought, I've decided that you have me confused.
When do you get afflicted by this "cruft"?
If it's in the item that is a duplicate of an earlier item, isn't it better to have the cross-reference?
If it's in my comment history, why are you looking there - it's full of "cruft."
It seems to me that the only times you'll come across it are when you actively seek it - and that's no basis for a complaint - or when it helps you avoid splitting a discussion, and that's surely a good thing.
But no mind, never matter, I'm not doing it any more.
=======
ADDED IN EDIT: For what it's worth, in the current top 30 items on the "newest" page there are 5 duplicates of previously submitted items. If people start a discussion on those then they will be missing out on the discussions that have already happened. I think that's a shame, and it offends my sense of "taste" as an engineer.
Perhaps a "merge with other post" option in HN would suffice. Both posts get merged (with the links of the submissions there), the conversation threads are merged and people with an urge to curate can enjoy doing so and we can all enjoy not having duplicate (or near duplicate) posts clogging up HN?
And I really appreciated that. It was the first time I had read a comment by him that wasn't putting down someone's submission or complaining about there being a similar article. I wish he'd spend more time contributing comments like that. By the way, thank you for your comment there Colin. I truly was glad to see you don't only make comments on dupes.
> * that wasn't putting down someone's submission or complaining about there being a similar article*
You're getting downvotes galore by the folks here, but on the off chance you're not a native English speaker or something, I don't read his comments that way at all. I actually checked through every one of your links posted above and I don't take his comments to be mean spirited at all. More like he's designated himself the friendly community cross referencer.
This one[1] in particular, is about as good of a comment as you can get. Cross referenced to other submissions, interesting links raised in the HN discussion, and a comment of his own.
All I'm asking is that if he wants more quality he contribute more quality. Yes; I'm doing what I'm complaining about him doing, however I've done it exactly once, how many pages and pages of his comment history are filled with these aforementioned comments?
I already contribute items I believe to be of quality, both submissions and comments. Ceasing to comment on duplicates and breaches of the guidelines won't change that.
Oh, wow, I didn't realize it has been you doing all this serious cross referencing to previous discussions. THANK YOU. It has been a huge help to me in the past, especially when I land on Hacker News results from a Google search.
I think it's good to have someone who remembers. I, for example, forget this. I want to provide the maximum value, but I just forgot about it, and when I submit articles I'm not quite careful. His comment made me remember and the next time, I'll be more careful.
Pointing out where other discussion on the same topic happened, or is currently going on, is a Good Thing. You are confusing helpfully pointing out where more discussion exists as a complaint.
The implication of spamming a list of links over and over and over again (paired with the blatant admission in his profile that he mostly doesn't read HN anymore due the amount of dupes) is that Colin is dissatisfied and is trying to make a point which in doing so is only contributing more of what is evidently causing him distress (lack of richness in content); it can't be argued that bludgeoning posters and readers over the head with a wall of links is comparable to real discussion imo.
See why I'm having a problem with this?
I don't see it as a good thing. I see it as more shit to wade through in order to get to the content I'm after. Unfortunately, it's something I'm seeing more and more often, over the course of the past several weeks... Colin isn't the first person to do this and I believe the consensus before was that ultimately it's a disservice to the community, well intentioned or not. (RiderOfGiraffes had a script that did something similar I think?)
Edit: As I can't reply to you directly yet Scott, I'll add this here:
"It is not itself discussion, but it points readers to discussions."
You understand exactly how I feel! :) You're absolutely correct: it adds nothing to the discussion and is therefore misplaced in the comments.
Now if there were a way to add some kind of list of similar or duplicate articles to an article that was independent of the comment threads, I would definitely be in support of this! But as comments, they feel like more spam. :(
RiderOfGiraffes did it by hand, and he was similarly driven away by what I understand to be a minority of people who did not like the practice. He was our semantic dupe-checker, and losing him was bad for the community.
I've explained why I see it as beneficial: it connects related discussions. It is not itself discussion, but it points readers to discussions. So, no, I do not see why you have a problem with it.
If you perceive that Colin is repeatedly linking to dupes or calling out policies, isn't that a flaw in the UI and UX of HN rather than him just being a complainer? If someone picks up an Android phone and is confused by what the menu button does, and someone kept telling them that they're doing it wrong, wouldn't we be missing the point? If the user doesn't get what the menu button is, it's not the other person's problem for pointing out what it is; It's the manufacturer's problem for not making it clearer. I, too, see Colin's contributions as helpful, and I wish there was a "mark as duplicate" or "redirect" option so he didn't have to type the same stuff every time.
The kid's own article is great. He explains all the steps he went through and the things he learned along the way. He learned about history, biology, the scientific method while doing something that interested him. Props to his parents and/or teachers who stimulated him to go through with this.
I don't think his 'invention' is that revolutionary. If you don't want your solar panels to overlap, it makes sense to choose step sizes that are coprime (which consecutive fibonacci numbers are). I don't think the invention matters that much here though. Aidan is obviously a bright kid and I'm sure he'll go on to do interesting things.
Most (nearly all?) inventions aren't revolutionary in their novelty but are just an increment above what already existed. So I'm agreeing with you but want to make sure the inventiveness of this kid is not understated--especially since I think the intelligence demonstrated in his article is above that of a typical US college graduate.
"Most (nearly all?) inventions aren't revolutionary in their novelty but are just an increment above what already existed."
This is true. If you're interested in the history of invention, try Steven Berlin Johnson's "Where Good Ideas Come From." Fascinating book, lots of depth, much recommended.
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.
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.
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
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.
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.
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...
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.
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.
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.
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.
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.
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.
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.
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.
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:
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.
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
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.
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.
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.
150 comments
[ 6.0 ms ] story [ 167 ms ] threadBasically 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.
Keeping that in mind, do you think it would still provide better results?
"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.
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.
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...
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...
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.
Still, what if you consider a fixed volume as the constraint in establishing the comparison? For a flat panel assembly, a given volume would constrain the surface quite obviously. If you consider a tree structure one might be able to pack some more panels in the same volume, and Fibonacci might give us some solution about how to maximize panel density in the volume while minimizing shading interference from other panels and supporting infrastructure.
If you want to maximize the given volume a tree doesn't seem like the optimum ... covering the whole surface of the volume should be the optimum (to receive every reflected light).
Also the tree has a lot more solar cells than this kids flat panel and he is still only measuring voltage.
Doesn't it make sense that an empirical test would not reach a theoretical max? For instance you've discounted shade effects as where he went wrong. Maybe its exactly the shade issue that makes his findings significant. Every urbanite will have to deal with it, and his array may do a better job in intermittent shade.
If mass-distributed, most folks would not be optimizing anything - install-and-forget - so its a real solution to create something that works in most environments.
To control for that effect, the two panel configurations should be mounted at an equal average distance from the ground, and their positions swapped in different test runs.
The experimental issue I thought about is that the experiment is situated next to a large wall. While the flat panel is facing away from the wall, it looks like some of the panels on the "tree" would also receive diffuse light from the wall. So effectively, the tree seems to have a larger collecting area than the flat panel. This would also make the tree less sensitive to shading.
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”.
http://en.wikipedia.org/wiki/Extreme_value_theorem
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.
http://www.nrel.gov/rredc/pvwatts/changing_parameters.html#t...
"The default value is a tilt angle equal to the station's latitude. This normally maximizes annual energy production. Increasing the tilt angle favors energy production in the winter, and decreasing the tilt angle favors energy production in the summer."
(Couldn't find a clear proof of this (under any modelling assumptions), sorry.)
A unique optimum isn't really necessary here (I shouldn't have required it!)
http://www.amnh.org/nationalcenter/youngnaturalistawards/201...
disclaimer: sarcasm
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 ?
Seems possible that nature hasn't yet hit optimal design in this area.
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...
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."
Very true. That is a huge advantage if space is a concern.
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.
However, mini trees are probably better for aesthetics, weather, maintenance, etc.
Your last link has now been submitted by someone as a separate item and is just so much better.
http://news.ycombinator.com/item?id=2902496
It seems a great deal of your comments have begun to fall into either the "this has already been posted" or "you're not following the rules" category.
Do you see the problem with "contributing" material on top of material you see as less than satisfactory? You're only adding more cruft to the cruft.
We get it. You don't like reposts. We get it. You don't like it when people don't follow the rules to a "T". Guess what? This is what happens. It's the real world where people don't always make the best choice all the time.
If you would get over that fact and focus on making insightful comments I think you'd be doing everyone a favor.
Lastly, to cite the oft quoted Guidelines:
"Please don't submit comments complaining that a submission is inappropriate for the site. If you think something is spam or offtopic, flag it by going to its page and clicking on the "flag" link. (Not all users will see this; there is a karma threshold.) If you flag something, please don't also comment that you did."
Edit: here is a list of links to Colin's comments from the first and second page of his comment history where he is either complaining about resubmissions or the rules not being followed:
http://news.ycombinator.com/item?id=2902905
http://news.ycombinator.com/item?id=2902882
http://news.ycombinator.com/item?id=2902745
http://news.ycombinator.com/item?id=2901255
http://news.ycombinator.com/item?id=2900909
http://news.ycombinator.com/item?id=2900877
http://news.ycombinator.com/item?id=2899857
http://news.ycombinator.com/item?id=2899687
http://news.ycombinator.com/item?id=2897109
http://news.ycombinator.com/item?id=2896827
http://news.ycombinator.com/item?id=2896677
http://news.ycombinator.com/item?id=2896311
2) However, he's not "complaining" about duplicates in those links. He's cross-referencing previous discussions in order to let people learn from them.
3) For what it's worth, he's been here almost two years -- you've been here barely half a year.
I read through his history and found this really cool submission: http://news.ycombinator.com/item?id=2878264 Computer Graphics? Or Real? "Ultimate Batting Practice"
Which led to the analysis of the video: http://m.wired.com/wiredscience/2011/08/exposing-a-fake-vide...
Which led to another analysis, "Water Slide Jump" http://m.wired.com/wiredscience/2010/05/preemptive-mythbuste...
http://scienceblogs.com/dotphysics/2009/08/more-on-the-giant...
It pretty much demonstrates just how difficult it is to apply mathematics to analyze real-world problems, which is really interesting and thought-provoking IMO.
Anyway, my point is, Colin has good taste, and you're doing him a serious disservice. He does good, helpful work, and I hope he doesn't stop, and doesn't straight-up leave, because the community would be worse off. I'd certainly be tempted to leave after reading something like what you wrote.
3) That should by all means be completely and utterly irrelevant.
I think the OP recognizes Colins contributions, but is pointing out that there seems to be a lot of complaining / slight passive aggression in those comments. Isn't that a fair observation to make?
I'm not bothered by Colins postings. I sure would be bothered though, if HN turns in to your typical internet forum, where older members starts policing newer members about following the arbitrary forum rules ("use the search function, you dimwit!" style).
I won't cross-reference, I won't point out when people break the guidelines, I'll just silently downvote and flag, leaving people - often newbies - with no idea why their contributions disappear or get negative karma.
That might or might not lead to still more bewildered posts saying they don't understand, but that's OK. There's no point trying to educate them. Let them learn the hard way.
As a mathematician by training, an engineer at heart, and a teacher by vocation, I hate seeing the waste of constantly repeated submissions and the redundancy of split discussions. I had hoped to add value by helping people become enculturated, but I've decided I've failed.
I'll stop.
PS: Besides, it plays hell with my average karma.
I appreciated your work, for what it's worth.
As civil adults and in all seriousness, would you stop? Do you see why I've complained? Cruft is cruft is cruft. Clearly your strategy to mend the dupe problem isn't having a positive effect. Maybe this is because new users aren't aware of the rules (but there will always be new users) maybe it's because people are willfully ignoring the rule (but in this case why should they pay you any attention?) or perhaps there are a multitude of reasons that all contribute to the gradual decline of the richness of information as a community grows. Whatever the case may be, as a long time reader of HN and a recent user, I find that the kinds of comments you make where you show a post is a duplicate does nothing to increase the richness of the content. Instead, your comment is yet another I have to try to ignore in search of meaningful content. Please don't take this personally. I'm sorry to have called you out like this publicly, but I don't know how else to reach you: please stop.
When do you get afflicted by this "cruft"?
If it's in the item that is a duplicate of an earlier item, isn't it better to have the cross-reference?
If it's in my comment history, why are you looking there - it's full of "cruft."
It seems to me that the only times you'll come across it are when you actively seek it - and that's no basis for a complaint - or when it helps you avoid splitting a discussion, and that's surely a good thing.
But no mind, never matter, I'm not doing it any more.
=======
ADDED IN EDIT: For what it's worth, in the current top 30 items on the "newest" page there are 5 duplicates of previously submitted items. If people start a discussion on those then they will be missing out on the discussions that have already happened. I think that's a shame, and it offends my sense of "taste" as an engineer.
(also edited for typos)
http://news.ycombinator.com/item?id=2831538
You're getting downvotes galore by the folks here, but on the off chance you're not a native English speaker or something, I don't read his comments that way at all. I actually checked through every one of your links posted above and I don't take his comments to be mean spirited at all. More like he's designated himself the friendly community cross referencer.
This one[1] in particular, is about as good of a comment as you can get. Cross referenced to other submissions, interesting links raised in the HN discussion, and a comment of his own.
[1] http://news.ycombinator.com/item?id=2896827
See why I'm having a problem with this?
I don't see it as a good thing. I see it as more shit to wade through in order to get to the content I'm after. Unfortunately, it's something I'm seeing more and more often, over the course of the past several weeks... Colin isn't the first person to do this and I believe the consensus before was that ultimately it's a disservice to the community, well intentioned or not. (RiderOfGiraffes had a script that did something similar I think?)
Edit: As I can't reply to you directly yet Scott, I'll add this here:
"It is not itself discussion, but it points readers to discussions."
You understand exactly how I feel! :) You're absolutely correct: it adds nothing to the discussion and is therefore misplaced in the comments.
Now if there were a way to add some kind of list of similar or duplicate articles to an article that was independent of the comment threads, I would definitely be in support of this! But as comments, they feel like more spam. :(
I've explained why I see it as beneficial: it connects related discussions. It is not itself discussion, but it points readers to discussions. So, no, I do not see why you have a problem with it.
I don't think his 'invention' is that revolutionary. If you don't want your solar panels to overlap, it makes sense to choose step sizes that are coprime (which consecutive fibonacci numbers are). I don't think the invention matters that much here though. Aidan is obviously a bright kid and I'm sure he'll go on to do interesting things.
This is true. If you're interested in the history of invention, try Steven Berlin Johnson's "Where Good Ideas Come From." Fascinating book, lots of depth, much recommended.
One of the best shows I've ever seen.
It's on Youtube. Here's the first link: http://www.youtube.com/watch?v=OcSxL8GUn-g
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.
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.
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.
:)
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.
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.
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.
Geisel, Theodor Seuss (Dr. Seuss). The Lorax. New York: Random House Publishers, 1971.
[1] http://www.amnh.org/nationalcenter/youngnaturalistawards/201...
Search for "Solar Powered Bonsai Tree".
Way to go kid! The force is strong with you! Best of luck! :)
Not sure these exist everywhere. Here is a Google Image search: http://www.google.com/search?q=cell+towers+look+like+tree...