In 1976 Swedish mathematician Ambjörn Naeve combined 2 troughs to mimic a parabolic dish with its burning point of light in the 1970's but his work never got the attention it deserved. The kyoto trough is a similar idea.

In this case, the troughs need not be parabolic and the idea is to produce a “ball” of light that is maintained over your cooking pot for several hours. For my first test model, I used a primary trough with parabolic curves inclined inwards and secondary parabolic troughs and it seems to have worked.

I made a “compound parabolic” solar cooking dish september 2008 (hopefully with a longer cooking time than a parabolic dish) and it seemed to do a good job. But I wanted to know for sure where the suns rays were going and how they were leaking out. Winter was approaching and the winter sun does not shine in my back yard on the experiments. So I started asking around on forums for software to model what happens. Pov ray, truespace, blender, sketchup. But I didn't find anything easy to use. Users on their forums were helpful to a point but did not get me anywhere close to where I wanted to go. This year I found art of illusion. It is a free java program and the guy who started it and some of the users helped out big time and got me going. I used it to model various dishes (including my own).

Basically the technique is very simple. You place a camera high in the sky and move it over the scene. The camera takes a suns eye view. Any reflected light from the cooking pot shows up as a red area on the reflective dish. It shows very different properties for different dishes and it helped me see the potential for combining troughs. is the combined troughs from the Swedish mathematician.

For solar cooking, we are not concerned with having a superhot point of light. It is a potential danger! Instead we need a ball of light that stays on the cooking pot for a long time. One property of a parabolic trough that is useful is that if you twist the sides inwards round the focal line, you can get a known time where all the light goes below the focal line. Then, you can use a second smaller trough to focus this light onto the cooking pot. More details can be found on at that shows an art of illusion simulation of the trough and you can find information at too. Just as the swedish guy made 2 troughs to mimic a parabolic dish, perhaps you could reverse engineer (with calculus) this type of trough to see what shape a dish might be! Because it is not a parabolic dish. I think it will be shaped like a flower with 2 petals (in line with the path of the sun) The petals will have upcurled edges.


Brian White
gaiatechician at