You can divide most solar power research into two camps: increasing efficiency or reducing cost. A few years ago, when I decided to do some amateur solar research of my own, I chose the “cheap” route.
I had the idea to use mirrors with a catenary curve to concentrate sunlight. The catenary, described by y = cosh x, is the curve that ropes or other flexible materials naturally fall into between two supports. This curve was mistaken for the parabola (y = x2) until the difference was cleared up by 17th-century mathematicians.
Parabolas are often used for concentrators since they focus parallel rays into one point. I reasoned that if I could find parameters under which catenaries and parabolas are similar, I could make a solar catenary reflector (SCR) that would effectively concentrate sunlight.
The advantage of the SCR is that it’s self-forming. Solid parabolic shapes don’t occur naturally, and you need to make them stiff and strong to maintain their shape against wind, snow, and other destructive outdoor forces.
And the SCR is quick and inexpensive to build, requiring no special tools or knowledge. Just hang some flexible, reflective material and you have it. SCRs could ultimately be more durable than rigid parabolic reflectors because of their Zen-like ability to deflect with the wind, instead of fighting against it.
To determine when a catenary will reflect like a parabola, I modeled the problem mathematically on a computer. As expected, I found an aspect ratio where a catenary reflector almost matches a parabolic mirror at concentrating light: 1 high to 4 wide, for a symmetrical reflector.
In other words, let the material hang down ¼ the distance between the posts. Following this formula, a couple of teenagers built an effective SCR cooker using hand tools in 20 minutes, under my guidance.
Surprisingly, it turns out that a properly proportioned asymmetric catenary reflector (ACR), where one support is higher than the other, will do a good job at concentrating light that’s not exactly perpendicular to the axis of the curve. This means that within certain limits, an ACR can concentrate the light as the sun travels across the sky.
Large, inexpensive ACRs hold promise as a way of getting more out of smaller, more precious photovoltaic panels. I’m currently researching this pairing, and want to explore whether such designs are better than parabolas at focusing diffused light — the Achilles’ heel of the parabolic concentrators. To keep the program within my kitchen-science budget, I’m working with miniatures. In my early experiments, I doubled the output of my photovoltaic cell.
You are welcome to join me in this grassroots research. Email me at email@example.com.