Q&A: Parabolic Solar Concentrators

Question: I want to build a solar cooker using mirrors for our high school science fair. My teacher tells me the best shape for concentrating sunlight is a parabola. But parabolas are curved and mirrors are flat, so now I’m thinking of just bending a sheet of shiny aluminum. Would that work? — WB, Portland, Oregon

Answer: If you’re determined to use a parabolic shape you’ll run into a few complications, but it can be done as demonstrated in the slideshow. As you can see, my design is fairly complex compared to those “black box” solar cookers you just set on a table out in the sunlight. In addition, a parabolic cooker has to stay pointed directly at the Sun so you need to occasionally adjust it. Mine is mounted on a rotating base for azimuth adjustments, and has a variable-length support arm for elevation. We’ve used that cooker for everything from hot dogs to muffins to corn on the cob.

If you use flexible sheet metal bent into a parabola you’ll get a tighter focus. But offsetting that gain, even polished sheet metal is 10–20% less reflective than a mirror. Take a look at the reflectivity values in this chart. So my design uses multiple flat mirrors along a parabolic surface to get the best of both worlds. The flat mirrors compose a segmented parabola.

The design process must start with choosing an aperture and focal length, both of which constrain the design. Once you have the aperture and focal length the equation for the parabola can be derived. I graphed that equation in pencil on two sheets of ¾” plywood, then cut them along the curve with a scroll saw. The ¼” plywood supporting the mirrors was bent into that parabolic curve by clamping, gluing, and screwing it to the side panels. Mirror mastic was used to attach the mirrors, but a good caulk would also work.

Figuring out the equation for the parabola (from the aperture and focal length) involves some math. I chose f = 0.20 m for my focal length to easily fit the cauldron. The equation for a parabola is: Y = X2/4f. That’s the equation I had to plot on the plywood.

How much of that equation you plot will determine the aperture. I wanted around 500 W of solar power for cooking, so with an average solar constant (on a clear day) of 1000 W/m2, an aperture of A = 0.50 m2 was indicated. I went with A = 0.60 m2 just to provide some leeway. The width of my design is W = 0.51 m, so the required aperture is A = 1.17 m. That requires the parabola to be plotted from X = −0.585 m to X = +0.585 m.

Here’s the geometric specs for my design:

parabola equation: Y = 1.25X2
focal length = 1/(4×1.25) = 0.20 m
aperture = 0.51 m x 1.17 m = 0.60 m2 solar input 600 watts
equivalent focal ratio = f/0.33
solar insolation equivalent = 18 suns

That last spec is noteworthy. It says that at the location of the cauldron, it’s like there’s 18 suns shining down on it. Putting it another way, if your eye was in the cauldron (which you don’t ever want it to be) you could see the Sun reflected in every one of the 13 main mirrors, and another 5 (estimated collective contribution) in the less-accurately-aligned side rows of mirrors.

The graphic below shows why parabolas work so well as solar collectors/concentrators. Rays of light from the Sun are parallel and, if on-axis with the parabola, will be focused to a point. In my segmented parabola design, as you can see in the last slideshow image, the focus is to a volume instead of a point. Since that volume is about the size of the cauldron, little light is wasted. The cauldron was removed for that photo to better show the light rays converging to a volume.

Interestingly, over 10 years ago, my design was imitated by one Mangalam Jambunathan, presumably an amateur scientist, located somewhere in India (his channel’s About page provides few details). He found the design on my website and adapted it to his own purposes. Thanks Mangalam! Let me know how that water project worked out.

Heimhenge Solar Collector: https://www.youtube.com/watch?v=PA56O77pPP0

I hope this helps with your project WB. Just remember, if you decide to go with the structurally simpler sheet metal design, you’ll need about 20% more collector area than my 0.60 m2 to get the same cooking temperatures. If you go with mirrors for a segmented parabola you might want to look into something that wasn’t available when I built mine — flexible self-adhesive sheets of small square mirror tiles. Small mirrors are less fragile, and using sheets would simplify construction. Either way, good luck with your project!

Next Week in Sky Lights ⇒ Arizona Starset

Photographing the Leonid Meteor Shower
Arizona Starset