Telescopes and parabolic mirrors

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4 total messages Started by Ali Shaik Mon, 09 Dec 1985 15:39

#24

Author: Ali Shaik
Date: Mon, 09 Dec 1985 15:39

23 lines
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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

Re: Telescopes and parabolic mirrors

#27

Author: G.C.Blair
Date: Wed, 11 Dec 1985 13:08

15 lines
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> Keywords:mirror using pressurized sheet
> 
> 
>    ... 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. ......
> 
> 
>     ihnp4!philabs!ams

Thank goodness someone's at last found documented evidence to substantiate
my casual use of the word "parabolic"! Can we now please end this discussion?
			Grant C Blair  (unintentional initiator)

Replies to ....{seismo or your link to Europe}!mcvax!ukc!gcb1

Re: Re: Telescopes and parabolic mirrors

#29

Author: Ali Shaik
Date: Fri, 13 Dec 1985 13:31

27 lines
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> > Keywords:mirror using pressurized sheet
> > 
> > 
> >    ... 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. ......
> > 
> > 
> >     ihnp4!philabs!ams


> 
> Thank goodness someone's at last found documented evidence to substantiate
> my casual use of the word "parabolic"! Can we now please end this discussion?
> 			Grant C Blair  (unintentional initiator)
> 
> Replies to ....{seismo or your link to Europe}!mcvax!ukc!gcb1

*** REPLACE THIS LINE WITH YOUR MESSAGE ***
         Don't be too sure! The shell stuff I looked up, it was
	 pointed out, was valid for small deflections, NORMAL
	 load....

	 Anybody out there got a good book on membranes?! The
	 problem seems interesting enough pursure further.    

	 Ali Shaik, ihnp4!philabs!ams

Re: Telescopes and parabolic mirrors

#30

Author: Lindsay F. Marshall
Date: Fri, 13 Dec 1985 15:27

10 lines
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Work constructing just such telescopes as this has been carried out at
Strathclyde University. They are the pioneers in this field. Perhaps
someone there could give us more details?

------------------------------------------------------------------------------
Lindsay F. Marshall, Computing Lab., U of Newcastle upon Tyne, Tyne & Wear, UK
  ARPA  : lindsay%cheviot.newcastle.ac.uk@ucl-cs.arpa
  JANET : lindsay@uk.ac.newcastle.cheviot
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