Re: [ATM] Plop Flop

[Mark Holm <mdholm@telerama.com>]

Hi Jay,

I have run two 18 point cells for your mirror, assuming that the glass 
type is plate glass.  If the glass is different, I can certainly run the 
numbers again to optimize for that glass.  The changes will be small.

The first cell I ran is the 18-point design for 20 inch diameter given 
in Kriege & Berry Edition 1, 1997, page 123, Table 5.5.  The RMS 
deformation for this cell is 1.05 nM (1/476 wave). The P-V deformation 
is 7.66 nM (1/65 wave).  The focus shift is -0.011 mm.

These are very good numbers, indicating that this cell will give good 
back support built just as K & B specified it.  (Confirming Jeff 
Anderson-Lee's statement.)



I also ran an 18 point design, allowing Plop to optimize the radii of 
the support point rings.  This gives a little lower deformations than 
the K & B cell.
The RMS deformation is 0.96 nM (1/519 wave).  The P-V deformation is 7.5 
nM (1/67 wave).  The focus shift is -0.033 mm.

The dimensions of this cell are (stated in the same terms used in K & B):

Radius of outer support points      7.680"
Radius of inner support points      3.868"
Base of triangle (isosceles)        3.976"
Altitude of triangle                3.551"
Balance point from vertex           2.367"
Length of bar connecting triangles  6.235"
Radius to center point of bar       5.400"

Monte Carlo analysis of these cells using +- 1 mm on the support radii 
and +- 1 degree on the angles gave about 1% increase in deformation, 
quite acceptable.  This isn't a complete Monte Carlo analysis since I 
did not let all the dimensions vary independently.  (That would require 
a much more complicated Plop setup.)  It does indicate that sensitivity 
to building tolerances is not too great.  This is substantiated by the 
similarity in performance between the K & B cell and the Plop optimized 
cell.  The radii differences between these cells are about 3 and 5 
percent, but the deformation performance is similar.

If you will be using hand tools to cut your cell parts, you may find my 
program CellParts helpful   
http://www.atmsite.org/contrib/Holm/cellparts/cellparts.html



That was the conventional and "safe" cell design approach.  Some atm's 
prefer to be unconventional whenever possible.  (I wonder who that might 
be? ;)  )  In order to keep these fellows happy, I must point out that a 
12 point cell would also work quite well.

I have used Jeff Anderson-Lee's 12h layout as shown in the 12-point 
section at http://pong.telerama.com/~mdholm/atm/cells/index.html

Optimized for our mirror, assuming plate glass, this gives:

RMS deformation  1.53 nM  (1/326 wave)
P-V deformation  11.5 nM  (1/43 wave)
Focus Shift -0.041 mm

These are also quite acceptable numbers, indicating very good support.  
The 100 run Monte Carlo analysis gave a maximum error of 2.07 nM, also 
acceptable.  (+- 1 mm on all the radii, +- 1 degree on all the angles)

The dimensions are:

Radii of the 3 inner triangle mirror support points    83.16 mm
Radii of the 6 outer triangle mirror support points   184.92 mm
Radii of the 3 bar mirror support points             179.80 mm

Triangle base (Isosceles)    138.345 mm
Triangle altitude             88.335 mm
Triangle pivot altitude       29.445 mm
Triangle Balance point from vertex   69.89 mm
Radius of triangle pivot      142.052 mm (this is the distance from the 
cell center to the attachment point between the bar and the triangle)

Bar Length                   164.210 mm
Bar Pivot point              123.157 mm
Bar Pivot Radius             142.052 mm  (this is distance from the cell 
center to the attachment point from the cell back structure to the bar)


Mark Holm
mdholm@telerama.com 

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