The idea is to make a Parabolic Trough with a pipe through the length of
its focus, to have sunlight heat liquid in the pipe.
http://stonetaberacle3.yolasite.com
In this particular development I wanted to be able to fully utilize the entire 48 inch width of a roll of reflective mylar to surface the trough.
I calculated the arc length of a 2-D slice of the parabola using Calculus.
I used my nested parabolas solution http://www.stonetabernacle.com/NESTED_PARABOLAS3.html to account for 1/4 inch plywood to create the parabolic trough surface. I chose the focus of the parabola at (0., 5 inches).
The resulting equation was complex, so I drew a graph of it and
qualitatively deduced where the curve intersected the abscissa, which was
the solution to the width at the top of the parabola, which resulted in 34 3/4 inches, well within the use of a 4' x 8' sheet of 3/4 inch thick
plywood to make the frame to the trough.
While there are infinite combinations that will work to construct a Solar Parabolic Trough, I chose this one for depth, range and the availability
of materials. A flatter parabola doesn't have to be adjusted as much to
face the sun but suffers from lesser heat. A deeper parabola has to
follow the sun more closely but produces more concentrated heat.
There may be infinite combinations, but the equation remains the same for
all of them.
Jon G.
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