CATENARY SOLAR REFLECTOR
In my mind, there are two main ways of using a catenary reflector. The
most obvious is that you can make a symmetrical mirror and then rotate
it so that it traces the path of the sun. This is the same
implementation as the conventional "parabolic trough' used in power
producing plants. Another way is to make use of the inexpensive cost of
building a catenary reflector and build a very large, imobile
asymmetric one then mount it facing south and accept some degrees of
efficiency as the sun moves through the sky.
Catenary Trough Reflector
Because of its shape, the trough (catenary or parabolic) is
usually
used for heating a pipe along its focal points. Conventional parabolic
designs claim a 30x to 60x intensity increase in light intensity along
the pipe.

The main disadavantage of a trough compared to a (parabolic) dish is
that it focuses the solar energy into a line and not single point, so
the the maximum energy focus is less than that of a dish with
everything else equal. I think that there are several ways to improve
on the efficiency of a trough by making the "target" more concentrated
by using a trapezoid instead of a rectangle, or perhaps a series of
reflecting secondary mirror.
However, as many commercial systems can attest, the parabolic
trough
is still quite good at doing its job. Many system employs the "line"
target to good advantage, pumping hot oil from a black pipe into a heat
exchanger to boil water for driving steam turbines for residential
power needs.
Being flexible, the catenary reflector cannot be tilted to
just any
position. Above about 45 degrees, you run the risk of errant wind
blowing the reflector to the wrong side. The designer should try to
accomodate for this until the wind slows down. This can be done by
restricting the movement of the sheet with ropes, or by using a heavy
weight sheeting and backing materials.
The basic design for a catenary trough would be a rectangular
frame,
built sufficiently oversized so that stray solar rays won't
accidentally burn it. It should be tilted so that it faces the sun. It
can be rotate to track the sun through the day.
As mentioned, the hot zone target for this design would
generally be
a pipe. Of course, it can be made out of a metal plate or elongated box
also. Using dark metal will make it more efficient in converting
sunlight into heat. For high efficiency, many designers use an internal
black pipe, surrounded by a transparent glass tube. I won't go too much
into how the target should be made, because it is really no different
than the designs used by conventional parabolic solar trough. We can
just imagine the normal uses for such a design: heating oil for a heat
exchanger to drive turbines, heating water flowing through a pipe for
purification, etc.
For household use in developing regions, a long black oven can
be
placed in the focal region for baking bread, cooking meat and poultry,
etc.
Asymmetrical Stationary Reflector

1:2 ratio (equivalent to 1:4 symmetric design) catenary, simulated with
45, 35, 25, and 15 degrees sun angle (from the horizon)

Despite its lower efficiency in focusing the incident light, I feel
that the asymmetrical design holds more promise for large scale use of
the catenary refletor.
This is because it is not only self-forming, but it is also
self-tracking. By placing a large reflector facing directly
south, it can capture and focus sunlight late into the day.
The
fact that is is less focused than other concentrator makes it more
suitable for photovotaic application, where a highly concentrated beam
can degrade the efficiency or destroy the photovoltaic cell.
I have made some preliminary experiment to investigate the asymmetric
catenary reflector (ACRe) and showed that the the self forming and self
tracking characteristics can reduce the cost of photovoltaic
power generation by a factor of 2 or 4 (50 to 75 % cost reduction per
watt of electricity generated).