ams@philabs.UUCP (Ali Shaik) (12/09/85)
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!amsgcb1@ukc.UUCP (G.C.Blair) (12/11/85)
> 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
ams@philabs.UUCP (Ali Shaik) (12/13/85)
> > 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
ncx@cheviot.uucp (Lindsay F. Marshall) (12/13/85)
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 UUCP : <UK>!ukc!cheviot!lindsay -------------------------------------------------------------------------------