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From: ams@philabs.UUCP (Ali Shaik)
Newsgroups: net.physics,net.space
Subject: Telescopes and parabolic mirrors
Message-ID: <532@philabs.UUCP>
Date: Mon, 9-Dec-85 11:14:12 EST
Article-I.D.: philabs.532
Posted: Mon Dec  9 11:14:12 1985
Date-Received: Wed, 11-Dec-85 04:09:16 EST
Reply-To: ams@philabs.UUCP (Ali Shaik)
Organization: Philips Labs, Briarcliff Manor, NY
Lines: 22
Keywords: mirror using pressurized sheet
Xref: watmath net.physics:3676 net.space:4921



   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