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Bending plastic to a concave shape

The most common method of bending plastic into a "big" concave shape is to 
(1) make a "reverse" curved model. (In other words, a big "dish" shaped model)
(2) you connect a weak vacuum pump to a little hole in the underside of the 
model, at the rough center.
(3) you fasten a sheet of the plastic you want to form around the upper rim 
of the model, sealing it and also fastening it securely.
(4) you activate your "weak vacuum pump" and then use a heat gun to soften 
the plastic.  It is kind of a "learn by doing" process, so you may have to 
experiment a bit.  The plastic, as it is softened by the heat gun, is 
"pushed' slowly into the concave model by atmospheric pressure. You control 
the speed of the "bending" of the warm plastic sheet with both the amount of 
vacuum, and how you heat the plastic.

I used to do this in smaller scale, to make clear plastic "canopies' for 
large model airplanes.

Hope this idea is helpful.