a) Covering the dish
There were several ways to cover the dish with reflective material:
- Using aluminum foil and glue, the cheapest but probably the weakest solution. The reflecting surface would be irregular and in fact would diffuse too much light.
- Using sticky mirror paper, a simple but more expensive solution that we chose because it is still relatively inexpensive.
Our first problem was that this kind of dish is not at all flat, which of course is why it functions. We looked for a way of covering it, minimizing the number of air bubbles.
Looking at the diagram in Fig. 10 below it is obvious that the distance SA is greater than the radius R. We decided to divide the surface of the dish into 16 sectors so as to reduce the formation of air bubbles that would result because the surface is not a flat disk.
In the diagram in Fig. 10 the sector of a circle with a radius R and an angle a is represented by dotted lines. Actually, the sector of a circle that we cut has to have the same length arc, but a radius SA>R. Therefore, this sector needs to have a smaller angle; angle b, is less than angle a, as shown in the diagram.
Therefore, the arc length is: l =R.a=SA.b so with a=2p/16 = p/8.
Fig. 10: Cross-sectional view of the dish and template of a sector of mirror paper to be cut out
When we went to Morocco in January 2016, our friends from the Dar Bellarj foundation had salvaged a satellite dish with a large diameter (140cm). We were surprised to find that the diameter of the dish was not regular, but varied from between 120 and 140cm. However we decided to cover it, choosing the greatest diameter, being 140cm.
b) Location of the support
A parabolic mirror enables the incident rays, which are parallel each other, to be concentrated in one focal point F, but only if the rays are parallel to the optical axis of the dish.
Fig. 11 Reflection of the rays a) parallel to and b) on a slight incline from the optical axis
If incident rays are not parallel to the optical axis, they don't converge in a single point anymore, but we can determine a minimal surface on which all these rays concentrate.
This is that case which had to be chosen because for our device, the support passes through the center of the dish.
For the purchased commercial solar dish, we wanted to determine the location of the focal point F with respect to its vertex Sto see if the manufacturer of the dish had set the support close enough to the focal point.
Fig. 12: Reflection of the rays on the pressure cooker
To determine the focal length f, we used a halogen floodlight we placed 20m from the dish so we could make the assumption that the rays of light arrive parallel to each other on the dish. We made the assumption that these rays were parallel to the optical axis of the dish.
Using a black plate (to minimize the reflection) that was small in size compared to the dish, we searched for the position in which the reflected rays formed the smallest possible spot of light (indeed, the rays did not all converge in a single point)
Results: we obtained a focal length f = (61±1)cm.
We have always supposed the solar dish was a paraboloid.
Fig. 14: Satellite dish covered with mirror paper and concentrating the sunlight under the pressure cooker
This device gave us satisfying results and an output equivalent to that from the purchased dish, being an output of 55%. It enabled us to distill, like the purchased dish did, but it led us to search for another solution because the focal length was much greater, making the support longer and the device unstable.