123D (free CAD software by Autodesk)
123D Make (free slicing software by Autodesk)
CorelDraw or Inkscape
Laser Cutter (a shopbot or waterjet would also work) I used a 120W Epilog Legend 36 EXT with a 36"x24" cutting bed
Hot Glue Gun
Wide Masking Tape
Sandpaper (Coarse & Fine)
Paint (to use as a sealant) like Acrylic base or Polyurethane
Stick-On Mirrored film
Thin copper tubing
1/2 cup of table salt
High-temperature black stove paint
1/2 inch metal conduit pipe
Rubber tubing. Use high-temp stuff if you plan to use it for a long time.
Step 1: Is It Possible?
How big of a mirror is that?
That was a lot bigger than I could make, but it gave me an idea of scale. For example, if I could wait 1 minute instead of 15 seconds for my cup of water, I only needed a 4-foot dish. In the end, I decided to make a 36" dish because that was the biggest I could make on my laser cutter without slicing up my support rings into smaller pieces (which is certainly an option.)
Step 2: Designing the Shape
Another way of thinking about your parabola is to use the equation FD = R2/4 where D is the depth of the dish from the center to the rim and R is the radius of the rim.
Using my equation (I used y= x2/4 and calculating from x=-2 to 2), I calculated about 20 (x,y) points between 0 and 2. (I didn't worry about units, because I was planning on changing the scale later.)
Step 3: Creating the Shape in 123D
In 123D, I created a sketch and entered the coordinates of my points one at a time. Then I connected them with a spline. This is the curve that defines the inner surface of the dish. I added some more lines to complete the cross-section of the dish, then revolved it 360 degrees about the center line.
Step 4: Slicing the Shape in 123D-Make
123D Make lets you turn your 3d shape into a lattice of 2d profiles that you can cut out and fit together. After importing my shape, scaled it to the biggest size I could make on my laser cutter and I chose a radial slicing pattern. I chose the slice direction from the dish's center outwards (like spokes) and upwards like rings. 123D Make automatically calculates the profiles I needed for the lattice and adds slots so that every piece slides into the correct place.
I started by making an 11-inch diameter dish out of cardboard as a prototype, then did a 36" diameter dish out of .25" plywood. 123D Make's nesting algorithm wastes material by putting too few segments on a given sheet. I wanted to lay out the pattern to use the most of my material, so after generating the laser sheets, I consolidated them in CorelDraw. For the 36" dish, I had to cut the biggest rings in separate pieces, so I split them in CorelDraw before cutting. (Looking back, I would have made the pieces of the ring interlock like a puzzle, adding more rigidity.)
Step 5: Laser-Cut and Assemble
Once everything was cut, it was time for assembly. 123D-Make does a neat animation of how your dish can be assembled. For this job, I used a bit of hot glue to hold the first three supports in place, but after that, no glue was needed. There was enough friction that the dish held itself together perfectly.
Step 6: Create the Surface
Once the spackle had the smooth, curved surface that I was looking for, I sealed the surface with three coats of clear acrylic paint. I considered epoxy and polyurethane, but decided on acrylic since it was the least toxic and had the lowest environmental impact.
Step 7: Make It Shiny!
I used a knife and a straight edge to cut strips about 1" wide. Then laid them down, starting with a strip across the center and working up to the left and the right. At the end, I trimmed off the extra around the rim and it was ready for the first test.
Step 8: Test 1: Light Things on Fire!
Next, we tried roasting marshmallows. Unfortunately, they hardly cooked at all. They were so white that they reflected all the light that hit them. When we rubbed some black charcoal on one and it started charring instantly when we put it in the beam.
On a Safety note, always store your mirror covered or out of the sun so it will not burn your house down. Try not to leave your mirror unattended in a sunny spot.
Step 9: Add the Boiler
After completing the coil, I mounted it to a piece of scrap pipe going through the center. The diameter pipe is about 1/2 an inch smaller than the inner diameter of the coil. I filled the empty space with spackle, which will function as insulation for the inside of the coil. Finally, I painted the coil with a coating of black stove-paint. It's paint that's designed to handle high temperatures and it's very important. Without it, the coil would just reflect most of the energy we are beaming at it.
I drilled a whole through the center of the parabola and mounted a piece of pipe that will hold the boiler using some laser-cut disks of wood. Two plastic hoses come up through the center to run water to and from the boiler. There's a needle valve to regulate the water flow.