I have settled on a size based on the available corrugated board on hand. Using a standard 'wardrobe' box, I cut 4 clean pieces 42" x +-18". From the large systems I looked at, the focus is nested below the level of the parabola's edges, but because I am using flammable paperboard I didn't want the tube too close.
Where p is the distance from the Focus to the Vertex of a parabola, I have settled on p=10". Then we have x^2=4py for the standard equation of an up pointing parabola. This gives me x^2=40y as the equation for my table of points to use in the layout.
This then gives me a 42 " trough 11" deep, leaving the tube 3/4 of the way inside the reflector.
I have in mind to glue some 11x17 1/4" size graph paper on 1/2 of one corrugated sheet to plot my points on, then cut that out & use it for a template on the rest of the partitions.
