Solar Concentrator

A few months ago I got into my car, and it was really hot. (over 100 degrees, I was really interested so I checked it with a thermometer)
This inspired me to build a solar oven, I mean, if my car can get that hot, just imagine if heat was actually the goal.
I built this https://www.instructables.com/id/CERC-Green-Solar-Oven/, which worked incredibly well (325 degrees F) but I feel it's severely limited by the use of tinfoil as a reflective surface.

I decided CDs would be a perfect substitute, they are more reflective, and I happen to have tons of them lying around. But my goal had never really been to create a solar oven, just to create heat from sunlight. So instead of improving my solar oven, I decided to build a parabolic solar concentrator.

-Cardboard
     Corrugated is harder to cut, thin cardboard will make it more difficult to attach the mirrors*
     (I used a thin corrugated cardboard)

-Tape or Glue
     Tape will partially cover parts of the mirrors, cutting down on the actual light reflected, but it allows for the mirrors to be more easily          removed and adjusted

-CDs

-Protractor
-Ruler
-Pen/Pencil/Marker
-Scissors
-Box cutter/X-Acto Knife

*The mirrors are actually just pieces of the CDs, but it's easier to refer to them like this

-Draw two parallel lines with the midpoint of each line touching the slightly raised inner circle of the CD
-Rotate 90 degrees, repeat.
-Connect the endpoints of the pairs of parallel lines

You should end up with 4 squares containing only reflective surface, nothing clear, a square in the middle, and some arc shaped pieces.
Only the first 4 squares are important.

This CD will become your guide for cutting multiple CDs at the same time.

Tape the pattern CD to the top of all the the CDs you are going to cut.
Use at least 8 pieces of tape evenly spaced around the edges of the CDs.

I put the tape on the bottom CD, put all of the CDs on a spindle to make sure they were centered, and then folded the tape over.

-Cut along all of the lines

You can cut them anyway that you think will work, just remember that friction from any sort of saw will create heat. I had to pry mine apart, but it was no big deal. I'm not sure how that would go with a power saw. (if you try, please share your results in the comments)

I put the stack in a bench vice and used a hand saw. Holding it together with clamps as well as using the vice will help prevent cracking.
When cutting on the curved surface, starting with a small hacksaw is much easier than starting with a large saw.
I started with a miter saw, but eventually switched too a hacksaw. The hacksaw had a slightly thinner blade than the miter saw and got stuck less often. It also never cracked a CD.

Measure the sides of your most average CD square, then average them.
If you have a perfect square, Congratulations! 
I did not. My squares were about 1.5 inches per side, you will see that thicker cardboard helps to compensate for slight variations.

Draw a line this length in the middle of your piece of cardboard, parallel with and about an inch above a flat edge of it.

I first drew a center line and then went out half of the mirror length on each side of it.

This center line will be where the first mirror goes. Light strikes from directly above and is reflect straight up.

Decide how high you want the focus of your concentrator to be.
I decided to make mine focus 12 inches above the center mirror for no particular reason.

With the knowledge of the focal length, the distance from the center to the edge of the last mirror "placed" (the last line drawn), and the difference in height between the center mirror and the edge of the last mirror placed, you can determine the angle the next mirror should be placed at.

The focal length will be f, this is constant. 
The distance from the center to the edge of the last mirror placed  will be d.
The difference in height between the center mirror and the edge of the last mirror placed will be h.
The angle of the next mirror will be 
                 90 - arctan ( (f - h) / d )

In the case of the second mirror, which is adjacent to the center mirror, d = half of the side length of the mirrors. h will be 0 (the last mirror placed is the center mirror).

For me this meant 90 - arctan ( 12 / 0.75 ) = 3.6 degrees

Whatever angle you get, starting from the edges of the center mirror, draw a line at that angle and mark it at the length of one of your mirrors, d.

The rest of the mirrors are drawn in the same way. 
You may have realized that you could find the angle of every mirror mathematically, but measuring each time to find the values for h and d is more accurate because your drawing may not be accurate. This way if you accidentally draw a line at the wrong length or angle it won't affect any other lines.

So continue with
Angle = 90 - arctan ( (f - h) / d )

Until you get to the edge, or your desired height or width.

Cut along the line. The bottom piece is now your stencil.
You will need at least two of these pieces for one row of mirrors. Each successive parallel row of mirrors will require one more piece of cardboard in this shape. The maximum number of rows of mirrors is equal to the number of sections on your pattern, each the length of your pattern.

To assemble the frame, slot the cardboard at the edge of each mirror segment. Slot half of your pieces at the top, and half on the bottom.
Place the top pieces onto the bottom pieces, making sure the tops are flush. By doing so you make sure the pieces are angled correctly.

Finally attach the mirrors onto the square sections using either tape or glue.

I thought a hot wire would be the perfect way to cut through these plastic CDs. I tested it with one CD, a piece of guitar string, and two lead acid batteries. Other than the CD catching on fire where it contacted the wire this worked pretty well.
With multiple CDs though, I broke multiple wires.