🚀 go-pugleaf

Keywords:mirror using pressurized sheet


   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!ams