The Solar
Catenary
Reflector
Build 21st-century renewable technology using 17th-century mathematics. By Tho X. Bui
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.
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.
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.
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.
Photography by Tho X. Bui
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.
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.
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.
You are welcome to join me in this grassroots
research. Email me at blahx3@thoxbui.com.
HOW TO FAKE A PARABOLA: (Clockwise) Backyard
solar catenary reflector (SCR) cooker built in 20
minutes using sheet steel and wood; experiments
with miniature catenary reflectors doubled the
output of a solar PV cell; overlaid symmetrical
catenary (red) and parabola (black) show their
closest match at 1: 4 height-to-width ratio.
Tho X. Bui ( thoxbui.com) lives in Phoenix, Ariz., with his lovely
wife and three turtles. He used to do research for a living, now
he’s doing it for fun.
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