Thanks to the work of people like David Lewis, and Richard Schwartz - analysis of mirror support schemes has improved dramatically for the amateur telescope maker. It's great to get output from David's software (PLOP) that helps you decide on an acceptable mirror cell design. Some excellent references on mirror cell designs include the following
1. A great example of other support schemes, with 18 or more points, see: http://www.cs.berkeley.edu/~jonah/18plus/
2. Analysis of PLOP and good/bad ways to use the software, see: http://www.cs.berkeley.edu/~jonah/18plus/p18.html
3. Another good reference on mirror cell designs is from Mark Holm at: http://users.telerama.com/~mdholm/atm/cells/index.html
Many of the cell designs and configurations discussed in the above references make use of triangles as cell components (as opposed to beams). There is good reason for that. As you increase the number of cell components in your 'stack'...use of triangles allows you to devise a mirror cell with many support points, yet few layers of triangles.
However, some cheapskate ATM's (that only have access to bar stock), or those that only need a relatively small number of support points, may be interested in using cells that make exclusive use of beams. (Understand that this approach can be counterproductive if you need many support points. In that case I recommend the use of triangles.)
I will assume the reader is familiar with a 3 point cell, and (if you place a beam at each of the three support points) a six point cell (with all six points at the same radius.) However, if you keep adding layers of beams to double the number of points, you get support schemes that may be unfamiliar to many ATMs: 12, 24 and 48 point supports. Let's look at these less common support schemes.
Here is one layout of a 12 point support. Inner ring of 3 points, outer ring of 9 points. (Note the 3-fold symmetry in the cell components.)
Here is another layout of a 12 point support. Inner ring of 4 points, outer ring of 8 points. (There is no three-fold symmetry in this example, but there is bilateral symmetry.) The differences in support performance between this arrangement and the one above is often very small. Use PLOP to analyze the particular case of your mirror to see what works best for you. Or, choose the arrangement that you may find easier to fabricate.
Here is a 24 point support that uses only two rings (inner 8, outer 16).
Here is a 24 point support that uses three rings (inner 4, middle 8, outer 12). In most cases the arrangement of 24 points in 3 rings is better than 2 rings.
Here is a 48 point support that uses four rings (inner 6, second 9, third 15, outer 18). Note that this example has 3-fold symmetry. Also note that you will need four levels of beams for this cell design.
I do not claim that I have found the absolute optimum layout of 12, 24, and 48 points in the above examples. Be careful when optimizing 3 and 4 rings of supports. Sometimes I have allowed PLOP to optimize all ring radii at once...and seen PLOP 'recommend' an optimum outer ring radius larger than the mirror! (Starting from scratch you may want to let PLOP optimize one ring at a time while holding all others at a fixed radius. After you get some experience with the software this will not be so tedious and frightening.)
A comment about PLOP's use (or non-use) of refocusing while analyzing/optimzing mirror cell designs. Cell performance and support point location can chage a great deal with use/non-use of refocusing, depending on how many rings of support in the cell design. With only one ring of supports, use/non-use of refocusing has the greatest change on performance and point location. With three and four rings of supports, refocusing has very little change in support performance, and only small changes in location of support points. I am not advocating one way or the other, but I want you to be aware of the changes it can make in your design analysis, and I recommend you be consistent in your use (or non-use) of refocusing as you investigate various cell designs with PLOP.
The above is not an exhaustive discussion, but I hope it serves as a good starting point.
Below are the PLOP *.gr files used to generate the above diagrams. Cut and paste the text below into PLOP and adjust parameters to suit your needs. Enjoy!
;12 point cell using only beams...no triangles.
;Inner ring of 3, outer ring of 9...lends itself to 120 degree
symmetry for final three collimation bolts.
;Essentially identical performance to the 12 point cell using 4
inner and 8 outer supports.
diameter 400
thickness 40
focal-length 2400
n-mesh-rings 17
rel-support-radii 0.274129 0.801421
num-support 3 9
support-angle 0 20
basis-ring-size 3
basis-ring-min 0
obstruction-diam 65
optimize rel-support-radii 0 0.01
optimize rel-support-radii 1 0.01
part bar 3 point 0 0 point 1 0
part bar 3 point 1 1 point 1 2
part bar 3 part 0 0 part 1 0
;12 point cell using only beams...no triangles.
;Inner ring of 4, outer ring of 8.
;Essentially identical performance to the 12 point cell using 3
inner and 9 outer supports.
diameter 400
thickness 40
focal-length 2400
n-mesh-rings 17
rel-support-radii 0.372119 0.827988
num-support 4 8
support-angle 0 22.5
basis-ring-size 4
basis-ring-min 0
obstruction-diam 65
optimize rel-support-radii 0 0.01
optimize rel-support-radii 1 0.01
part bar 2 point 0 0 point 1 0
part bar 2 point 0 1 point 1 1
part bar 2 point 1 2 point 1 3
part bar 1 part 0 0 part 1 0
part bar 1 part 2 0 part 0 1
part bar 1 part 1 1 part 2 1
;24 point cell using only beams...no triangles.
;2 rings of 8 and 16 points.
diameter 400
thickness 40
focal-length 2400
n-mesh-rings 15
rel-support-radii 0.37934 0.825132
num-support 8 16
support-angle 0 0
basis-ring-size 8
basis-ring-min 0
obstruction-diam 65
optimize rel-support-radii 0 0.01
optimize rel-support-radii 1 0.01
part bar 4 point 0 0 point 1 0
part bar 4 point 0 1 point 1 1
part bar 4 point 1 2 point 1 3
part bar 2 part 0 0 part 1 0
part bar 2 part 2 0 part 0 1
part bar 2 part 2 1 part 1 1
part bar 1 part 3 0 part 4 0
part bar 1 part 5 0 part 3 1
part bar 1 part 4 1 part 5 1
;24 point support...no triangles, only beams.
;Three rings: 4, 8, and 12 supports
;Slightly better than 2-ring support of 8 and 16 points.
diameter 400
thickness 40
density 2.23e-06
modulus 6400
poisson 0.2
focal-length 2400
n-mesh-rings 25
rel-support-radii 0.270603 0.579416 0.816178
num-support 4 8 12
basis-ring-size 4
basis-ring-min 0
obstruction-diam 65
optimize rel-support-radii 0 0.01
optimize rel-support-radii 1 0.01
optimize rel-support-radii 2 0.01
part bar 4 point 0 0 point 1 0
part bar 4 point 1 1 point 2 1
part bar 4 point 2 2 point 2 3
part bar 2 part 0 0 part 1 0
part bar 2 part 0 1 part 2 0
part bar 2 part 1 1 part 2 1
part bar 1 part 3 0 part 4 0
part bar 1 part 5 0 part 3 1
part bar 1 part 4 1 part 5 1
;48 point support.
;4 rings: 6, 9, 15, 18.
;Has 3-way, 120 degree symmetry.
;Requires 4 levels or generations of beams.
diameter 800
thickness 40
density 2.23e-06
modulus 6400
poisson 0.2
f-ratio 4
n-mesh-rings 30
rel-support-radii 0.254393 0.496836 0.711151 0.92014
num-support 6 9 15 18
support-angle 0 0 0 0
basis-ring-size 3
basis-ring-min 0
obstruction-diam 100
optimize rel-support-radii 0 0.005
optimize rel-support-radii 1 0.005
optimize rel-support-radii 2 0.005
optimize rel-support-radii 3 0.005
part bar 3 point 0 0 point 1 0
part bar 3 point 0 1 point 1 1
part bar 3 point 1 2 point 2 3
part bar 3 point 2 0 point 3 0
part bar 3 point 2 1 point 3 1
part bar 3 point 2 2 point 3 2
part bar 3 point 2 4 point 3 5
part bar 3 point 3 3 point 3 4
part bar 3 part 0 0 part 1 0
part bar 3 part 3 0 part 4 0
part bar 3 part 5 0 part 7 0
part bar 3 part 2 0 part 6 0
part bar 3 part 8 0 part 9 0
part bar 3 part 10 0 part 11 0
part bar 3 part 12 0 part 13 0
All feedback is encouraged!
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Last update: 29 Mar 2002