# COMPUTER MODELLING OF A PARABOLIC SOLAR COLLECTOR

Posted by zeb on March 12, 2006, 3:54 am

Hi,

I am planning to build a Scheffler type solar cooker (around 2-3 meter
dia). I have looked at the Scheffler website (www.solare-bruecke.org)
for the design parameters. I have found that the parabolic reflector
has to change its depth, with the seasons, to be able to focus solar
energy at a fixed point. This means that a simple mechanical means have
to be contrived to
do so. However my idea is even simpler, which I need to test. It is
that instead of changing the shape of the parabola, why not move it
backwards or forwards. This should (I think) have the same effect as
changing the depth. However for a 2-3 meter dish this would be easier
given that it could be mounted on a chassis with four wheels, running
backwards and forwards on a rail. Since the distance is likely to be of
the order of a meter or so, the
issue of cost would also not be significant. I think that such a system
would be definitely simpler than one that changes the depth of the
parabolic dish.

Can somebody comment on the soundness (or otherwise) of such an
approach. Secondly can someone guide me as to how I can model this on a
computer. I have looked at some of the shareware ray tracing programs
but I found them to be very complicated. Does someone know of an Excel
(or Mathcad) based tool to model this kind of optical system. I would
greatly appreciate any pointers in this regard.

TIA

Aurangzeb Haque

Posted by Morris Dovey on March 12, 2006, 4:26 am

| Hi,
|
| I am planning to build a Scheffler type solar cooker (around 2-3
| meter dia). I have looked at the Scheffler website
| (www.solare-bruecke.org) for the design parameters. I have found
| that the parabolic reflector has to change its depth, with the
| seasons, to be able to focus solar energy at a fixed point. This
| means that a simple mechanical means have to be contrived to
| do so. However my idea is even simpler, which I need to test. It is
| that instead of changing the shape of the parabola, why not move it
| backwards or forwards. This should (I think) have the same effect as
| changing the depth. However for a 2-3 meter dish this would be
| easier given that it could be mounted on a chassis with four
| wheels, running backwards and forwards on a rail. Since the
| distance is likely to be of the order of a meter or so, the
| issue of cost would also not be significant. I think that such a
| system would be definitely simpler than one that changes the depth
| of the parabolic dish.
|
| Can somebody comment on the soundness (or otherwise) of such an
| approach. Secondly can someone guide me as to how I can model this
| on a computer. I have looked at some of the shareware ray tracing
| programs but I found them to be very complicated. Does someone know
| of an Excel (or Mathcad) based tool to model this kind of optical
| system. I would greatly appreciate any pointers in this regard.
|
| TIA
|
| Aurangzeb Haque

You'll probably discover that you care about where the focal point is.
All you'll accomplish by moving the reflector foreward or backward is
changing the position of the FP by the amount you move the reflector.

Modeling tips: All you need to remember is that the angle of
reflection is equal to the angle of incidence and that the slope of an
(unrotated, untranslated) parabolic curve is the first derivative of
the defining function. If you're a little wobbly on parabolas, I'll
recommend Burington's "Handbook of Mathematical Tables and Formulas"
or a web search for tutorials.

--
Morris Dovey
DeSoto Solar
DeSoto, Iowa USA
http://www.iedu.com/DeSoto

Posted by Anthony Matonak on March 12, 2006, 7:03 am
zeb wrote:
...

Are you entirely positive on this point? To my knowledge the difference
in distance from the Earth to the Sun from one season to the next is
a very small percentage. Most solar cookers are not made to very tight
tolerances. The seasonal difference in focus would be easily orders of
magnitude smaller than the manufacturing tolerances of the reflector.

You might try looking at the solar cooking website. They have all kinds
of plans.
http://www.solarcooking.org/

Anthony

Posted by zeb on March 15, 2006, 3:02 pm
Morris and Anthony,

Thanks for the responses. I am taking the liberty of replying to both
in this one.

Which means that the idea is basically useless since I would like to
keep the FP static.

I would like to quote here from the Scheffler website.

-----Start Quote----

The reflector is a small lateral section of a much larger paraboloid.
The sunlight that falls onto this section of the paraboloid is
reflected sideways to the focus located at some distance of the
reflector.

......The distance between focus and centre of the reflector depends
on the selected parabola. During the day the concentrated light will
only rotate around its own centre but not move sideways in any
direction. That way the focus stays fixed, which is very useful, as
it means the cooking-pot doesn't have to be moved either.

This is only possible by shaping the reflector after another parabola
for each seasonal inclination-angle of the sun, i.e. for each day of
the year. THIS MEANS THE REFLECTOR HAS TO CHANGE ITS SHAPE.

----End Quote----

The last sentence in the above quote seems significant to me. This
means an additional mechanical contraption for changing shape. I thus
need to understand as to how much of a change would be warranted
between say, December and June. Thus the need for modeling software.

The above does not solve my problem at least to my understanding. This
is because the Scheffler cooker uses a lateral portion quite distant
from the parabola's vertex (on the origin) which is the normal
practice. While this is easier to model (and construct) it seems to
place the focus at an inconvenient location. In the Scheffler scheme
the reflector focuses energy on a position which is about 1 to 1.5
meters above the ground- an ideal cooking position.

Anthony, said,

Yes I am. Please refer to the quote above particularly the last
paragraph. A visit to the Scheffler site and referring to the page
titled "The Idea" further clarifies the matter. The page also has a
drawing that drives home the point quite vividly.

It is the Angle and not the distance that is relavent. The seasonal
variation in the Sun's position is over 50 degrees, at any location.
This means that to keep the energy focused at a fixed point, the
reflector will not only have to change its angle but also its depth. In
effect the reflector becomes a section of different parabolas (by
changing its shape) in summer and in winter. This is illustrated in the
drawing referred to above.

I hope I have been able to explain myself. In the meanwhile I have been
surfing the net to see if there is some evaluation version of an optics
design program that can help me. I have found OSLO and ZEMAX and a
select one. It should be easy to use and help me model the above
problem.

Thank you again and regards.

Aurangzeb

Posted by Anthony Matonak on March 15, 2006, 4:59 pm
zeb wrote:

What they are saying is that instead of a full paraboloid where
the focus is in the center and the reflector is completely symmetric,
they are taking just one side piece of that reflector. You can
just take the parabolic shape and cut out the section you desire.
This doesn't take sophisticated optics modeling software but might
require a large piece of drawing paper. :)

Perhaps the Scheffler design is not the best for your application.
It seems to me that there are some dangers associated with the
design if the tracking goes off or someone wanders too close to
the focal area.

Perhaps you would be better off building a large flat mirrored
heliostat or coleostat that reflects on to your focusing mirrors.
This makes the parabolic reflector fixed and unchanging and the
path between the heliostat to the focusing arrangement relatively
safe. You could perhaps use one of those spiral wound reflector
things for the focusing. Yes, I admit that it would use two
reflections and therefore would be less efficient but also much
easier to build and you can compensate for inefficiency by just
making it bigger.

Anthony