## Thursday, January 5, 2012

### Let's Cut This Kid Some Slack!

With my science fair project from March, 1964 (Miami Herald image). Note the "dual geometry" structure at right which was to have represented a dual matter-antimatter universe.

Aidan Dwyer (below) with his solar tree model which he has tried to show is superior to a flat solar panel to collect solar energy.

Well, it seems another Internet outburst has erupted, in the wake of a 13-year old's recent science project which purported to show that solar energy is much better collected using a model from nature, namely the arrangement of tree branches. Indeed, Aidan Dwyer won a national science competition this past summer by proposing the novel idea that solar panels arrayed like leaves on a tree colelct sunlight more efficiently than traditional setups.

Apparently the creative germ of the idea was launched when his parents acquainted him with the famous Fibonacci series. This is the series generated whereby the successive entries are just the sum of the preceding ones. For example: 1, 1, 2, 3, 5, 8, 13, 21, etc.

The ratios of the successive numbers can then be used to derive intriguing geometric arrangements, e.g. see:

Aidan apparently had this in mind when he began his project, believing the outcome might allow for a 'tree-like' panel that could deliver solar energy to his parents' home which was otherwise too small, apart from the fact the roof wasn't suitable. He thereby ended up comparing two models: one with his spiralled, tree structure with panels like outstretched 'branches', the other the standard flat panel design.

To compare their solar energy use Aidan measured the voltage for each, but he ought to have been measuring power (P = IV) the product of voltage and current. Thus, if we imagine a water pipe, voltage is analogous to the water pressure, while the current determines the width of the pipe. Power is the flow out of the pipe as determined by both.

The uncovering of Aidan's error led to an uproar on the net which almost rivalled that marshalled against my brother, Pastor Mike, in August and September last year (after he posted the idea for an "atheist national registry"). As in the Pastor Mike case, Aidan had to watch as he was made a spectacle of from net commentators around the globe, who debated his intelligence and abilities and even went to so far as to designate him an "alien" (of the ET type) while others decried him as part of a vast global conspiracy (WSJ, today, p. A1) Blogs erupted with bombast labeling his project "bad science" and "impossible nonsense"- the sort of vitriol usually reserved for political blogs, or those like Pastor Mike's.

At the end of it all, we need to give the kid a break already! He elicited enough curiosity to arrive at a novel idea, which - maybe in another parallel universe- would have garnered him kudos and more appreciation for the effort. But alas, in this one, to use Aidan's parlance, he had to face "haters" who get off more on tearing down than building up. Well, so it is.

While most people berate his measurement of voltage instead of power, the more fundamental error is one any of us could commit, hell I've done it myself in a science fair project on the 'Structure of the universe' from 1964 (admittedly, before the microwave background radiation was discovered). That is, being so entranced by the beauty and elegance of an idea or concept that we overlook its possible flaws.

In the case of my own project, I postulated (and used math, physics to prove it) that the universe was equally divided between matter and anti-matter, and the then discovered quasars represented "breaches" through which anti-matter was entering our universe. I also posited the differing universes assumed different non-Euclidean shapes, with the matter universe Riemannian or spherical, and the anti-matter universe Lobachevskian or like a horse saddle shape. (If you look closely at the photo shown, from a March 31, 1964 Miami Herald piece, you can see on the right the latter shaped universe inserted into the spherical one for matter).

In truth then, I had been so mesmerized by the sheer beauty and symmetry of what I had proposed, I couldn't see coming anything that would knock it off my mental pedestal! But barely five months later, Val Fitch and James Cronin in landmark work, showed in what is called their CPT invariance experiments, that a slight asymmetry was built into the cosmos in terms of matter production being slightly favored over anti-matter yielding a universe preponderant in the former over time. Thus, no symmetrical bi-universe of both (in dynamical equilibrium) could possibly exist.

In a similar vein, I suggest Aidan became mesmerized by the beauty of the Fibonacci sequence and the relation to his solar stucture. He had mentally integrated the two to such an extent he couldn't see any other way viable. Moreover, even after he began measuring power, he has maintained that his tree "outperforms" his flat panel. But has he factored in everything? And what are his measurement errors? (Hint here: What are the sensitivities of his ammeters, voltmeters?)

A more authentic take is shown in the diagram, which he might do well to consider. That is, the key factor affecting available solar power and efficiency is the insolation. When solar energy is directly incident on a surface, such as via intensity I1 in the diagram with surface diameter d1 = 1 meter, then that represents the most power collected per unit surface area. When the angle is oblique, on the other hand, as shown with intensity beam I2, then a broader area is covered, i.e. in this case d2 = 2m, but per unit area the power is diminished as the sine of the angle (it may also be as the cosine, if there's a different orientation (e.g. angle taken from the meridian, vertical plumb line or zenith).

Thus, for I2 the per unit insolation is 1360 W/m^2 (sin 30) = 1360 W/m^2 (0.5)= 680 W/m^2.

This suggests that if Aidan is obtaining superior power ratings from his solar "tree", he will need to check the angles at which the sunlight is incident on it, and also compare those with the angles of incidence on his flat panels. Only when he does this, and also takes into account the respective areas on which the sunlight is incident (since we are looking at power collected per unit area) will he be able to say for sure his "tree" represents a novel step forward in the solar energy sphere.