ams@philabs.UUCP (Ali Shaik) (12/09/85)
One way to figure out if a thin circular sheet would deform
to a paraboloid when pressurized is to set up the differential
equations of deformation and solve them. Intuitive analogies
to soap bubbles, etc may not always work.
I looked up "Theory of plates and shells" by Timoshenko and
Woinowsky-Kreiger, and sure enough, they had done all the dirty
work for me! (see eq. 67 on page 57).
The deflection contains the square of the radius multiplied by
a large constant plus radius to the fourth power. The surface
is a paraboloid to within 6% upto half the radius of the sheet.
Thus darkening the area beyond 0.5r looks as if it would give
close approximation to a paraboloid. I don't know how much
this means in terms of image quality. It looks promising for
manufacture of cheap telescopes.
- Ali "Bangalore" Shaik
ihnp4!philabs!amsgwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (12/10/85)
> It looks promising for manufacture of cheap telescopes.
Now we just need cheap space boosters.