From: atm{at}misterg.fsnet.co.uk (Andy Gray)
To: atm{at}shore.net
Reply-To: atm{at}misterg.fsnet.co.uk (Andy Gray)


On Sat, 07 Jun 2003 13:07:33 -0400,  Mark Holm
 wrote:

>Bob May wrote:
>
>> Make sure that you have the autofocusing off
>> for the program or it will refocus to get the best shape and that will be a
>> problem in reality as the focus will then change as the attitude changes.
>
>I can't agree with Bob here, at least not entirely.  [.snip.]
>I think too much has been made of this focus shift due to Plop's refocusing.
The numbers
>typically come out less than 0.05 mm.

For those using silicone sealant in your mirror cells:

consider a 2kg (20N) mirror (200mm x 30mm) mounted by three 20mm diameter
blobs 3mm thick at 50% radius (for the sake of argument).

I have taken the Young's modulus of silicone as 130 N/cm^2 (from
extrapolation of the slope for small strains on a graph in an obscure paper
on silicone used as a road sealant found on the web!)

At zenith, the weight of the mirror rests on the pads, resulting in a
stress in the pads of:

 20N / (3 pads x 3.1cm^2 each) ~ 2N/cm^2

and a consequent compression of the pads by 2 / 130 = 1.5% or 1.5% x 3mm ~0.05mm.

At the horizon, the mirror will pull on an upper pad, and push on a lower
one with a moment roughly equal to its weight x 1/2 thickness: 20N x 1.5cm
= 30Ncm. This will leave the centre of the mirror in approximately its
neutral position, but with a pointing error:

[consider one mounting pad is horizontally in line with the centre of the
mirror. The vertical separation of the other 2 is then mounting radius
(20cm x 50%)/2 x sqrt(3) = 8.6cm. I bet anyone a beer that the results work
out the same for arbitrary pad angles, but the math is easier this way]

Force in upper & lower pads = moment / spacing = 30Ncm / 8.6cm ~3.5N,
over 3.1cm^2 pad area ~ 1N/cm^2. Giving a length change of ~0.75% (half of
previous answer), or a difference in height of 0.05mm over 86mm - about 2'
pointing error.

So, a change in focal length of 0.05mm, and a change in pointing of 2'.
Given that RTV cells work, the "in use" effect of the change in
focal length by allowing PLOP to re-focus has to be minimal. I think there
are other trade-offs, however which aren't factored into PLOP's
optimisation, such as ease of construction, sensitivity to errors, and
support in elevations other than at zenith (not intended as a criticism of
PLOP!) that seem to become more significant as the mounting radius
decreases.

Personally, I would use PLOP "unrestricted" to determine the best
possible design, then draw up a "practical" design, feed it back
into PLOP, and see what compromises I've made. Iterate.

In case anyone is thinking of using this as an argument against silicone,
it would have to be an exceptionally well designed 'mechanical' cell to get
these levels of repeatability (IMO).

Too long, again!

Andy

Andy Gray, N. Wales, UK.

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