brackets will be mounted: Take one of the four tank support brackets and center it five inches to the right of the plywood's center line; place another one five inches to the left. Position the brackets so that they're square to the plywood's factory edge, with their inner corners just touching the tank's circle. Mark this location for future reference.
That's it. Now you're ready to put your pencil marks to use.

Cutting The Involutes

Take the sheet of plywood you've been working on, and place it on top of the duplicate piece you cut earlier. Clamp or lightly nail the two sheets together (rough side to rough side), and use a saber saw to cut along the modified involute curve. Because you're cutting through both sheets of plywood at once, you'll end up with two virtually identical involute patterns, and that's just what you want. (Save the pieces of scrap plywood. They can be used later on.) Drill one 3/8-inch hole at each of the support bracket mounting locations, making sure you drill through both sheets of plywood. Then unclamp and separate the involute patterns.
Later on, these patterns and the entire reflector assembly will be covered with a mirrorlike layer of "aluminized Mylar" (a plastic). Cutting the Mylar to fit these complex curves would be very difficult to do when the reflector is completely assembled. Instead, it makes much more sense to cut the Mylar now, and set it aside for later use.
Photo Three shows how: Cover an area of the floor with newspaper and unroll the Mylar so that the side with the aluminized coating is facing up and the clear plastic side is down. (To determine which side is which, take a pencil eraser or a rag covered with a small amount of white toothpaste and rub one side of the Mylar. If the eraser or the cloth turns black, you have rubbed the side that has the thin, shiny coat of aluminum.)
Place one of the involute patterns on the Mylar, kneel on the pattern, and using a utility knife, cut through the Mylar along the perimeter of the plywood. When you're done, use a felt-tipped pen to mark the letter "A" on both the pattern and the Mylar. Next, repeat the entire operation and cut a second piece of Mylar, this time using the second involute pattern as a template. Mark both these second pieces "B," then set the Mylar aside.

Above The cusp's original sharp angle must be altered to 90 degrees so that a square 2 X 2-inch "reflector center support" can be used as the backbone of the assembly. In later steps, aluminum flashing will be added to recreate the initial shape of the cusp.

Building The Reflector

Now (at last) you're ready to begin some actual construction, adding the top cleats, center cleats, and tank support bracket cleats onto the involute patterns.

Photo Four illustrates this step. First, cut out all the cleats to the correct dimensions. Next, using wood glue and one-inch nails, fasten one top cleat to each of the plywood involute patterns. The cleat should be mounted on the rough side of the plywood, flush with the factory edge, and with an equal amount of overhang to either side of the pattern. (Nail in from the plywood.)
Next, cut and mount the two center cleats. (These cleats can be cut from corners of the scrap plywood left over from cutting the involute patterns.) The "point" of the cleat should extend about 2'/4 inches into the space between the involute halves, as shown in Photo Four. (A precise measurement is unnecessary.) Again, use wood glue and nails to secure the cleats.
The tank support bracket cleats are the last to be mounted. They should be positioned flush against the top cleat and spaced so that they fall squarely over the 3/8-inch bracket mounting holes you drilled earlier into the plywood.
Once the bracket cleats are mounted, use the bracket holes as a guide, and drill through the cleats at the same location. (The 3/8-inch bracket holes must extend through both the plywood and the cleat.)
With the addition of the two reflector side boards, the assembly begins to take on a recognizable form. First, cut the side boards to length. Then stand the two involute patterns on their factory ends (as shown in Photo Five) and glue and nail the side boards into the top cleats. Use 8d nails, two per joint.
Photo Five also shows the addition of the reflector center support and two sheets of hardboard reflector backing:

Cut the center support and both sheets of hardboard to length. Because each hardboard sheet will form half of the curved reflector area, the width of each sheet must equal half the perimeter of the involute curve. However, as Illustration D shows, one of the hardboard sheets will overlap the other by 1/8 inch, so one of the sheets must be trimmed by this amount. Use a tape measure or a length of wire to measure the length of one half of the involute curve (the distance along the perimeter between the point of the cusp and the furthest corner of the factory edge). Subtract 1/8 inch from this measurement, and cut one sheet of hardboard to this length. Mark this sheet "C." Then repeat the procedure for the other half of the involute, but don't subtract the 1/8 inch. Instead, cut the hardboard to the full measure, and mark this sheet "D."
Now measure the distance from the point of the cusp to the flashing layout line you marked earlier. Transfer this measurement to both of the hardboard sheets and snap a chalk line across the full length of the hardboard. (The distance between the chalk line and the edge of the hardboard should equal the distance between the point of the cusp and the flashing layout line. See Illustration D.)
Just as with the involute patterns, it's much easier to cut the Mylar for the hardboard sheets now than to try to do it later, when they're mounted. Following the same procedure as before, use each hardboard sheet as a template and cut out pieces of Mylar to fit. Mark the Mylar "C" or "D," to identify which hardboard sheet goes with which piece of Mylar. Set the Mylar aside. Now, using one-inch underlayment nails, nail both sheets of hardboard to the reflector center support so that they form a "V" shape, with the center support at the tip. Refer to Illustration D: The smooth sides of the hardboard should face out, and one hardboard