Compound parabolic dishes have a super advantage over parabolic dishes. You rarely have to reposition them as the sun moves. So you can leave them unattended for long periods!
There are many possible compound parabolic dish configurations and rather than me try to satisfy everyone, I though it would be better to give you a method to make your own petal templates.
Then you can make a 1 hour, 2 hour 3 hour or 4 hour compound parabolic solar cooker.
Whatever you want is within your grasp! You can easily make petal templates for parabolic dishes with this method too.
For 12 petal templates the error in the method (because you are using flat material to make a surface curved in 3 dimensions) is about 1%. I believe that is acceptable.
If you do not want to read the whole instructable, just read the image notes on the first image.
It should suffice for many people.
Step 1: Compound Parabolic Concentrators, What Are They?
The typical compound parabolic concentrator is a fairly old device, They are shaped like a bicycle light or a tulip flower with a hole at the bottom and as long as the sunlight enters within the acceptance angle it gets reflected all the way down the concentrator and gets trapped there at the bottom. They are made by putting the focus for 2 identical parabolas on the curve of the other one. To do this you have to twist each parabola (which gives you the acceptance angle) and the resultant 2 dimensional shape is spun on its axis to get the flower shape of the compound parabola.
Many times the reflectors for box ovens are based loosely on this type of concentration. They are good because if you face the box cooker the right way it stays collecting sunlight well for a long time.
But I wanted something different. I set out to apply the same principle to parabolic dishes.
Parabolic dishes are great because they can focus a lot of energy but they quickly go out of focus and have to be readjusted. There is virtually nothing out there about applying the same principles to parabolic dishes so I had to start from scratch. My first compound parabolic dish was a great success but not many people were interested in copying my construction method. They prefer a template.
Step 2: How to Make the Compound Parabolic Shape
easy way to make a compound parabolic shape. You have a parabolic shape already with its focus.
All you need to do is rotate it as shown and you have the compound parabolic shape!
45 degrees acceptance angle gives a 3 hour solar cooking dish. The axis of the dish will be through the 22.5 degree line. Half of the acceptance angle.
Step 3: 45 Degree Compound Parabolic Petal Template
The first 2 images show the figures to make your own and the shape of the particular template.
Scale up until you get the right size.
Figures that are important for this template scaling are:
6.5 cm from top of the dish to the focus
The height of the dish is 11.7 cm and
the radius of the dish at the bottom is 12.3 cm
The cooking pot should fit in the scaled up 6.5 cm space between the focus and the top of the dish when the solar cooker is in operation.
Step 4: A Little About Compound Parabolic Dishes and Parabolic Dishes
For now I am just leaving an animated gif here to show the differences between parabolas and compound parabolas for dishes. Please note that this is very much a shot in the dark for me. There are likely to be errors (but not substantial ones) in my explanation. Eventually others may confirm or improve on what I explain but I wouldn't hold my breath. Please go with this until something better comes along.
Note. Parapolas are like circles in that there are large and small ones but the fundimental shape is exactly the same. Unlike circles, nobody has ever seen a complete parabola. (the ends go on infinitely).
Compound parabolic dishes can have their curves come in and meet up. I show the MAXIMUM EXTENT for useful curve for a 30 degree (green), 45 degree(blue) and 60 degree(yellow) compound parabolic dish in the animated gif. Note of course that making the maximum extent would be costly and you can just use a cost effective portion nearer the focal point just as people do with parabolic dishes!
For my compound parabolic dishes all I did was twist one half of the parabola round its focal point.
This concentrates the light in the area between the back of the dish and the focal point as long as the incoming light is within the acceptance angle of the dish.
Step 5: How Do We Test a Compound Parabolic Shape for Effectivness?
This is part of my continuing attempts to understand what I am doing!
Below are pictures of a 60 degree compound parabolic model that I made around January 18th 2009
As you can see, depending on the angle at which the picture was taken, the reflection of the apple or little ball was very different. (The apple happened to be closest to the size of the distance between the focus and the bottom of the dish). I think the photos are a clue to how effective the dish can be.
I also used a lazer spot to test its effectiveness.
I have not done anything scientific just yet but it is a start! As you get closer to directly over the dish, you get an increase in the size of the reflection that probably coresponds to how effective the dish will be when the sun is in that posititon.
Step 6: Known Issues
I. When I rotate the parabola around its focus for say a 45 degree compound parabolic dish, I am left with a 45 degree"gap" which I just fill with and arc of a circle. But an arc is probably NOT the best way to fill this space to reflect the light towards the cooking vessel. A line or perhaps a dimple pointing at the focus might be better and will allow for greater concentration of light and a smaller cooking vessel.
A circle is good enough for me for the moment. I am sure someone will find a more accurate solution in the future. This will allow for more concentration of energy and larger reflector to cooking pot ratios while maintaining the long unattended cooktimes.
2. I do not know exactly how the light reflects off the dish as the sun moves across the sky.
Some light may miss the cooking pot when the sun is not directly over the focus.
3. A large (2 square meter) stationary dish (perhaps 60 degree compound parabolic) may be suitable for same time every day cooking all year long if aimed at the equinox sun at its highest point.
but I do not know how it would behave when the sun traverses 23 degrees above the aimed direction (high summer) and 23 degrees below, (mid winter) and the tropical equivalents of these times.
This awaits software modeling or small physical reflector models and laser tests.
Thank you Brian White
Step 7: Other People's Work
Other people have traveled the compound parabolic road.
Anyone who designs a flashlight reflector or lampshade reflector to spread out the light from the bulb is doing something similar, just doing it in reverse!
A guy called Roland Winston had patents for compound parabolic troughs. The patents have now expired and are online. He is a well respected scientist. He did things probably the perfectly mathematically correct way so I will put one of his patent drawings here. I found it online on about the 14th of January 2009. (Pity I did not see it earlier)
Here is a picture of one of them from the patent application itself! As you can see, he has a bump or dimple under the receiver. Once again, I do not know how this will work when we make a dish.
He seems to use 2 parabolas without a combined focus. Please take a look.
I do not know if I am allowed to show the entire patent (I have it in pdf format on my computer) it is easy to search for it, if you just put in the patent number and winston in your search.
As you can see, it is fairly similar to what I came up with but it is a trough not a dish.