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10" huh?
Okay, have you a router? and if you do do you have a radius arm? If not do you have a jigsaw? Most jigsaws have a position on the base plate where a radius arm can be fitted. If not, free hand with the jig saw would do.
Cut out a disc from 20mm ply to fit the inside of your sonotube. Determine the size of three holes to be cut with a holesaw from the disc at 120° (should be around 2"). This will eliminate around 50% of the discs weight. This becomes your backboard. Then cut out a second disc of 10" diameter to be used as the mirror board. You can lighten it in the same way.
Collimation. At 120° intervals fit three "T"-nuts through the wood with the topo of the "T" on the mirror side. Obtain three heavy duty springs to go between the mirror board and the backing board and using three bolts through the mirror board for collimation screws. OR three more "T"nuts on the backing board to provide push against the pull of the mirror board ones.
Support of the Mirror. You can use Plop if you wish, or the formula given in The Amateur Telescope Makers Handbook by Sidgewick to determine where the weight bearing points are to be located on the mirror board. From here there are a couple of methods of attaching the mirror to the mirror board. 1) you can simply place small blobs of silicon at the bearing points, about the size of a pea. Place three 5 cent pieces or washers of equal thickness around the edge. Put your mirror onto the board and let it cure for 24 hours.
OR take 9 brass thumbtacks and fit them at the nine determined weight bearing points and use three "L" shaped clamps at 120° on the mirror to hold it into place. You can drill three small holes through the clamps and squeeze some silicon into the space between the clamp and the mirror edge to buffer the mirror, alow it to cure for 24 hours.
Does that help?
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