An e-mail by Richard Schwartz :

 

Finite element analysis is available to any amateur who asks me to do it. If you send me the dimensions of your mirror, and the properties of the material (density, young's modulus, and shear modulus), and the peak-to-valley deformation of the mirror surface you require, I will do your analysis. (e-mail to Richard)

In order to select the number of support points, you can use a flat plate model.
For plate glass flat or slightly menicus, the optimized peak-to-valley deformation is   in micro-inches without refocusing , approximately

p-v = k * a^4 / t^2

So solve the above, and determine what k must be. The available values of k depend on the number of support points.

n k configuration
=============== =============== ==========================
1 748e-6 single support at center of mirror
3 200e-6 3 points at 64.5%
4 79.6e-6 4 points at 70%
5 41.6e-6 ?
6 (Richards!) 35.3e-6 ?
6 (hexagonal) 31.5e-6 6 points at 68.1%
7 20.8e-6 centerpoint 11.83% load, 6 points at 73.7%
9 (equal loads ? ) 10.6e-6 3 points at 37.5% and 6 at 82%
11 14.4e-6 ?
12 8.85e-6 ?
more Don't do it;
get thicker glass!
infinity 19.1e-6 continuous ring at 67.85%


I am opposed to more than 12 support points.
I find that mirrors so thin are very sensitive to the location of the support points.
Only .01" error in the location of a support point is too much!

 

Note : take care with these values, this project is still in experimental phase. Contact Richard if you want to know more about it. He's working on an article for the ATMJ about his mirror supports.

back.gif (2055 bytes)