In the meantime, I have decided to go ahead and build a couple more shop cabinets. I had gone to the Depot to get what I needed to make my radius dishes, but they had cabinet grade ply on sale for a little over twenty bucks, so I took the opportunity. I will have scraps sufficient to make the router jig, and I did buy the 3/4 MDF that will be the dishes. The shop cabinets are relatively simple affairs. They are basically plywood boxes, joined with a tongue and groove -- that is, I cut a 1/4 groove on the sides of the cabinet, and a tongue on the top and bottom ends to fit the groove. One will be used for my routers, and the other will be used for miscellaneous power tools.
As I was building the lattice jig, I did get a start on the jig to cut the radius dishes. The plan is this: I built what I am calling a Xmas Tree Stand, which is basically just a plywood X with each arm 22 inches long. The MDF dishes will spin on this base. The router jig will be similar to the one used to shape the drum for the thickness sander with a couple of exceptions. My router base happens to be 6 inches wide, so two end pieces will be cut at 6 inches wide by about 8 inches tall. The sides will about 6 inches wide as well (conservation of scrap) and about 25 inches long. One end of the jig will be attached to the Xmas Tree Stand and the other will overhang about three inches or the radius of my router plate.
I plan to profile the sides with the arch on one side for the back using my router and a flush cut bit. The first step is the creation of a template for the arch. I use my metal shop ruler to create the arch. I c-clamp a small block of scrap to the back-side of the rule, then clamp that down at the center of the arch. I then deflect the ends up to create the arch, scribe it, then sand to the line on 1/4 inch MDF. Remember, the low point of the arch should be over the center of the Xmas Tree Stand, and should allow enough clearance to attach the sides of the jig to the ends. To accommodate that, I measure in 3/4 inches from one end of the side (where it will attach to the fixed side) then 11 and 22 inches from that mark. The 11 inch mark is the center, and I deflect the rule up 1/4 inch on each of the other marks. I then double stick the template to the side, and cut with the pattern bit.
The amount of deflection at either end can be easily calculated (though I had to be reminded of high school geometry and algebra to do it). Take the radius of the dish (in my case, 11 inches) and square it (121 inches). Take the radius of the back and square it (in my case, 20' or 240 inches, squared is 57,600). Imagine a line tangent to circle 20' in diameter. Now, imagine a point 11 inches out on that line from the point where it intersects the circle. Using the Pythagorean theorem (a squared + b squared = c squared), you can calculate the distance between the point 11 inches out and the center of the circle (in my case the square root of (121 + 57,600) or the square root of 57,721, or 240.25195, which I rounded to 240.25). The difference between the radius of the back (or the distance to the point where the circle intersects the tangent) and the distance to the point 11 inches out on the tangent line is .25 or 1/4 inch. So each end needs to be deflected up 1/4 inch. For the soundboard, I'm going with 1/8th inch.
When I have the arches correct, I will attach a 7 and 1/2 inch wide strip of thin ply to the arch with screws. I'll clamp the ends to the sides so I can get the width exactly right, and then I will attach it to the Xmas Tree Stand so there is sufficient clearance for the MDF dish. Before I cut the dish, I will cut the slot in the 1/4 ply for the router bit, put the dish in place, and cut up and back to the center mark while spinning the dish slowly.
I finished the shop cabinets, but didn't get as far beyond that as I had imagined -- focus on one thing at a time. So the dishes are a project for next weekend. I will let you know how it really went.
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