ATM Blobs [was Mirror cell thoughts]

[Aplanatic@aol.com]

Tom Krajci wrote:

> The only concern I have is if you have rather wide RTV pads, they may not be
>  as compliant as smaller pads, unless you make them a bit thicker.  The
>  compliance problem may rear its head when observing in temperatures very
>  different from that at which the cell was glued/cured to the mirror.  Maybe
>  enough stress will be transmitted to the mirror through the wide RTV pads 
to
>  noticeably distort the mirror's figure in very cold weather.

How big should we make the blobs?  Here's a rough analysis of the 
problem.  

I am building a Schmidt camera that uses a guide scope for guiding.  
I don't want the image at the focal surface to move more than 10 
microns during a 30 minute exposure.  Thus, the combination of 
mirror tip and lateral mirror motion should cause less than 120 
microns of image shift at the focal surface when the scope is 
rotated from the zenith to the horizon.  Call the image shift, zenith 
to horizon, dx inches.

Assume that the mirror is mounted with just two blobs of RTV, one 
at the top of the mirror and one at the bottom.  Each blob has 
area A square inches, is l inches thick, and is located d inches 
from the center of the mirror.  In addition, assume that the mirror 
has weight W pounds and has thickness t inches.  Finally, assume 
that the focal length of the Schmidt camera is F inches, and the 
RTV has a Young's modulus E pounds per square inch.

Then I get:

dx = (l*t*W*F)/(4*d^2*A*E) + (W*l)/(2*E*A)

The first term is due to the rotation of the mirror on its cell and the 
second term is due to the lateral motion of the mirror.  I have 
conveniently ignored Poisson's ratio in the above.  The correct 
analysis would include it.  Nonetheless, the above expression 
should be correct to within a factor of two.

Now, let's evaluate the two terms in the expression for a concrete 
example, namely:

W = 20 pounds (12.5" mirror, 2" thick)
E = 200 PSI (my guess at Young's modulus for RTV
F = 22 inches (the focal length of the Schmidt camera)
t = 2" (the mirror thickness)
l = 0.1" (thickness of the RTV blobs)
d = 5" (the distance of each blob from the center of the mirror)
A = 1 square inch (the area of each blob)

Then the first term evaluates to dx = 0.0044" or 110 microns.  
The second term evaluates to dx = 0.005" or 125 microns.

Clearly, to meet my goal, I need a total of 4 square inches 
of RTV on the 12.5" diameter, full thickness mirror.  To be safe, I 
plan on using 8 square inches in an array of 9 blobs.

This problem of guide-scope guiding a Schmidt camera is about 
as severe as it gets.  For the average visual Newtonian, the blob 
area need only be large enough to prevent miscollimation of the 
telescope when tipped from zenith to horizon.  One can probably 
allow the mirror to tip several arcminutes without seeing a problem, 
even for fast Newtonians and discriminating observers.  For a 12.5" 
f/4 scope, this requirement is met with a total blob area of A = 1 
square inch, including a safety margin of 2.  So, you can see that 
a little RTV goes a long way.  In practice, for a 12.5" mirror, 2" thick, 
I would use 9 blobs that are 0.5" diameter, 0.1" thick.

Dave Rowe.