13-Year-Old Makes Solar Power Breakthrough by Harnessing the Fibonacci Sequence
inhabitat.com
inhabitat.com
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.
In Submissions
...
Please submit the original source. If a blog post
reports on something they found on another site,
submit the latter.
Your last link has now been submitted by someone as a separate item and is just so much better.
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
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)
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.
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
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.
Anyway, go ahead, do the experiment yourself! Its not rocket science. No need to guess, when the answer is only a little effort away.
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.
(Disclaimer: I get paid to teach engineering to precocious youngsters part of the year. I'm quite familiar with the demographic.)
Being an asshole is never excusable. While I understand your point about not over-praising, this actually is something that few of his peers are able to do. Proper praise for the boy would be to appreciate the effort, applaud his commitment to the problem and recognize that he may be able to make the solution "better".
Once you do that you can point out areas for improvement.
On a side note, I feel mildly insulted that you feel the need to tell me how to do my job. If you're interested in the intricacies of the art of teaching self-directed youth (which mostly involves understanding the child in question, and saying the right thing at the right time) I'd be glad to discuss them with you.
I'd love to hear about that. That is my occupation as a teacher of supplementary math lessons, and that is my daily life as a homeschooling parent. I can always afford to learn more about doing what I do better.
My modus operandi involves building a mental model of what the student knows, doesn't know, and how they think about the problem in question. Usually I do this through targeted questioning, and watching faces for signs of confusion in a group session. e.g. let's say we're working on Newtonian physics. I might take a model car with occupants, roll it along a table, and ask what happens when the car hits something. From this I can judge whether the students understand momentum.
If their mental model is wrong, next you have to break it down. How to do this varies based on how committed they are to their model -- if you challenge their views in too dramatic a manner you can lose their trust and frustrate future lessons. For students whom are less committed to their incorrect model, it suffices to demonstrate a counterexample. Those who are more commited can require several weeks to shake their beliefs.
Actually teaching involves three parts: definitions, questioning, and experience. Definitions are KEY. You can build an entire lesson around a solid definition. For example: "speed is how far something travels every second" (or "in a certain amount of time" for the ones able to handle abstraction). Keep definitions few and far betweens and simple. Refer back to them often.
Next follow up with questioning: how can we measure speed? do we know how to measure the things in the definition? if something moved ten meters in five seconds, how many meters did it move every second? This has been covered elsewhere in depth. Don't overdo it though, some kids hate questioning. Just tell them facts.
Oh, be consistent. Use vocabulary consistently, don't throw around new terms, stick to one system of units, etc. Minimize distraction and confusion.
Experience is key to solidifying rules deduced from questioning. Roll that cart down the hill. Practice those factoring problems. Not everyone needs experience but most do. Experience can help break down incorrect mental models. As with definitions, minimize distraction. Experience one thing at a time until it is understood.
Finally, don't be afraid to go off on tangents. If a kid expresses interest in something, that means they will be focused and eager to learn it. You can teach almost anything to a student who wants to learn it. Motivation is everything.
I hope this helps. It's early in the morning and I'm writing this on my Kindle so it's probably rambly and missing things. I'll try to remedy that throughout the day.
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.
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:
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.
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”.
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!)
:)
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.
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 ?
Geisel, Theodor Seuss (Dr. Seuss). The Lorax. New York: Random House Publishers, 1971.
[1] http://www.amnh.org/nationalcenter/youngnaturalistawards/201...
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.
Seems possible that nature hasn't yet hit optimal design in this area.
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.
Not sure these exist everywhere. Here is a Google Image search: http://www.google.com/search?q=cell+towers+look+like+tree...
http://www.amnh.org/nationalcenter/youngnaturalistawards/201...
disclaimer: sarcasm
Search for "Solar Powered Bonsai Tree".
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.
They've even made solar cells that look like leaves before http://techon.nikkeibp.co.jp/english/NEWS_EN/20080527/152443..., but nobody bothered to test if a tree-like structure gathered more energy.
Remember, a tree only has leaves in the summertime, not the winter. :)
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.
Way to go kid! The force is strong with you! Best of luck! :)
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.
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.