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Editor's Note: CR4 would like to thank Brian White (gaiatechnician) for contributing this story, which originally appeared in "Brian's sustainable development group".
The mechanical mathematician is a new device to help people make large parabolic reflectors for solar cookers. It evolved out of the solar cooker work that I did last summer. I was making funnel cookers in various forms but the problem is size. They concentrate light to a line that goes through the centre of the funnel, which means that the ideal food container is a long skinny one. The light line from a collector for 1 sq meter of sunlight might be nearly a half meter long! I had an idea that you could reflect sunlight all the way down a horn shape tube.
It didn't work!
When you do the math, you realize that it is impossible to do this!
I wanted something to shine on a bowl and heat it up. This drew me to parabolic reflectors (perfect for focusing sunlight to a spot)
But the math is SO intimidating! And I want to make a parabolic bowl, not a parabolic throff. More bloody calculations! GAWD
Not too happy was i.
Eventually, I found a website where a German guy working in Africa designed his parabolic curves just using a T square with string pinned to it and a pencil. AWESOME!
You can lengthen the string to get a different parabola or tie it at a different height to get a different parabola.
The rest of his procedure was pretty involved though (Wood model, metal rings and welding), and I wanted to keep things simple and really low tech
And most of all - APPROPRIATE. If you are building a solar cooker in a dirt poor village in Africa, all the welders will have left to get gainful employment, and all you are left with are poor people and dirt!
What skills might the people have? How about building with dirt or mud? Probably really skilled at, too!
I am a stone mason and for years, I knew it is easy as pie to draw an elliptical curve for rock planters and so on. Just use 2 sticks hammered into the ground, some string line, and another stick to mark the curve. Perhaps I could use this method to approximate a parabolic dish?
I looked long and hard at the German relief worker's diagrams and saw that if I could stop the T square from cutting through the parabolic curve, I could make a parabolic shape in 3 dimensions! Not just a line in 2 dimensions. This is a HUGE improvement (if it can be done).
It means that your device can be used directly on-site to mark a parabolic dish. One STEP - can it be done?
A little idea was gelling in my mind, so I set to work making a cob parabolic dish. Cob is clay sand and straw mixed together and it drys hard. (I have a self-built cob shed in my backyard). I am not at all technically good, so I used part of an old office chair, string line and some curtain rods to make my first mechanical mathematician! It worked really well! It really surprised me how quickly it all went. You start on the outside and work in. Excess cob is just trowelled down as you work. You find the surface of the dish with the mathematician and trowel to it.
This is not perfect because my form was too narrow at one side (I used scrap wood) and because one of the legs of the chair was wobbly, but it sure looked dishy when the curve was done! I let it dry a bit, stuck kitchen foil to the cob and tipped it onto its side to face the sun, and I had my 40-inch square parabolic dish!
Not too bad. It has taken me nearly 4 months (!) to get this diagram done up. I tried to explain with the cob parabola image, but it just looks like a space alien or a junkyard robot. I think the diagram is good enough to explain the mathematician.
The next stage is informing people in relief agencies and so forth. I have got no feedback from relief people except some positive stuff from one man who is going to work in a hospital in Haiti.
Seriously, this thing means that you could easily make a 3 or 4 meter fixed parabolic dish in-situ for very little cost. (Just point the central post of the mathematician at the midday sun, decide on your focus, and extend the string to make the parabola with minimal material use) and away you go!
I have scavenged the solar cooker to add to my cob shed. While it was in use, I never thought to use it as a MOULD for cardboard solar cookers. DARN!
What you do is make radial cuts in your cardboard and put it in the cooker to fit its shape, cut out as directed and tape it together, and then add and stick on the aluminum foil. Then take it out and tape the back, too!
It should work but I have never done this.
If you have an old satellite dish at home, try it please and send me the results!
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Re: The Mechanical Mathematician: Large Parabolic Reflectors for Solar Cookers
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