Re: [ATM] Crazy simple mirror cell idea

["Nils Olof Carlin" <nilsolof.carlin@telia.com>]

Bob May wrote:

> Lets start with the misconception that larger mirrors need mour
> support points.
> The need for more support points is a function of the thickness
> to diameter ratio.  At around 12:1 ratio, the mirror starts
> becoming glexible enough to where the error budget starts
> affecting the real shape of the mirror to the point where the
> mirror isn't working right.  It's all in how much flex will you
> allow.

For a given mirror thickness, twice the support points will ( to a first
approximation, and assuming the sagitta is negligible, which it isn't in
reality) support twice as much mirror area for a given deformation - hardly
surprising.

But more surprising may be this: PLOP shows that for a given support,
deformation increases about as the 3rd power of mirror diameter (again
neglecting sagitta). For a given support, deformation is again roughly
inversely proportional to the thickness of the glass (it gets stiffer, but
also heavier).

And, to compensate for halving the number of support points, you need to
increase thickness by a factor of 8!

This assumes an "even" support point distribution, which is not nearly true
for all cell styles (compare the classic 9 point cell with a 6 point one).

> Note that I didn't mention any particular size when I mentioned
> the ratio?  That is because the ratio sets the amount of flex in
> the structure, not the actual size of the structure for anything
> of a real size that we'd make.

You should perhaps have.

A 12:1 mirror of some 670 mm (sagitta negligible) in a classic 9 point cell
will have about 10 nm RMS deformation which would certainly noticeable - a
12:1 mirror of 180 mm dia will have, in the analogous cell, 0.7 nm RMS
deformation which as certainly is not detectable.

The 12:1 rule (or 6:1) has no physical significance at all - your best bet
would be to run a finite element analysis - by PLOP, as it is available for
free, or any other available.

Nils Olof


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