The 9-point cells described here all use three isosceles triangles. The three triangles are located at 120 degree intervals. Each triangle has three support points that contact the mirrors.
Plop allows designs where the angles between support points and the relative forces on the support points are varied. This differs from "conventional" designs in which the forces on the support points are usually equal. I have used both of these options for many the 9-point cells. One result is that the triangle pivot points are not necessarily located at the "centroid" of each triangle.
The 9-point cells designed with varying angles and/or forces tend to share a common problem. The triangles are very short. That is, the altitude is short compared to the base. This also makes the pivot altitude short. Triangles like these place tight constraints on construction accuracy. Small errors in the placement of the pivot, in particular, can significantly degrade performance. Unless you can construct to tight tolerances, such as using a milling machine to place all the holes, it may be best to avoid these designs. I have begun adding to this page 9-point cells optimized without the variable angles and forces options.
An analysis, not yet presented on this web site, shows that 6-point cells are actually superior in support to 9-point cells without variable angles and forces. The upshot of this paragraph and the preceeding one is that one should consider skipping 9-point cells altogether, in favor either of 6 or 12 point designs.
All of the older 9-point cell designs arranged the triangles as shown in the first image below. Plop also returns this arrangement for thicker mirrors. For thinner mirrors however, Plop indicates that the triangles should be arranged as in the second image. This is a fairly radical change from "conventional" designs, and is an example of how quantitative engineering can sometimes lead to counterintuitive results.
In the tables, r1 always refers to the position of the "middle" three points of the triangles no matter whether they are arranged as in the first or second figure. r3 always refers to the "outer" six points of the triangles no matter whether they are arranged as in the first or second figure. If the triangles are arranged as in Figure 2, r1 may be greater than r3.
Diameter = Mirror Blank Diameter in Inches
Thickness = Mirror Blank Edge Thickness in Inches
f/ = Focal Length in Inches / Diameter
Obs Dia. = Central Obstruction Diameter in Inches (This is usually the diagonal mirror minor axis.)
Figure: Which of the two figures above, this cell resembles.
r1 = Radius of circle on which inner three mirror support points lie as a fraction of mirror blank radius.
r2 = Radius of circle on which the triangle pivot points lie as a fraction of mirror blank radius
r3 = Radius of circle on which the six outer mirror support points lie as a fraction of the mirror radius.
B = Base of each triangle as a fraction of the mirror blank radius.
A1 = Altitude of each triangle.
A2 = Altitude of pivot point on each triangle.
P-V = Peak to Valley Mirror Deformation with this cell in Waves (1 wave = 500nm)
RMS = Root Mean Square Mirror Deformation with this cell in Waves (1 wave = 500nm)
Focus Shift = Change in focal length due to cell induced deformation. (In millimeters)
V.A. = Was
PLOP's Variable Angle feature turned on for this cell? Y= Yes, N = No
V.F. = Was
PLOP's Variable Force feature turned on for this cell? Y= Yes, N = No
See below for correspondence with cell dimensions in The Dobsonian Telescope by Kriege and Berry.
In their book, The Dobsonian Telescope, Kriege and Berry give dimensions for 9 point mirror cells. One should not use the dimensions they give, because they were designed before the use of
PLOP. Their diagrams and detailed mechnical design are however still quite useful. Their diagram and table for 9-point mirror cells is Table 5-3 found on page 121 of the first edition, ©1997. They use different descriptions for the cell dimensions. The following table lists the correspondence between Kriege & Berry's terms and the terms used in this web site.
Note: r = radius of mirror. This is the diameter / 2, not the radius of curvature. The asterix (*) means the arithmetic multiply operation.
|Kriege & Berry||This site|
|Radius of outer support points||r * r3|
|Radius of inner support points||r * r1|
|Base of triangle (isosceles)||r * B|
|Altitude of triangle||r * A1|
|Balance Point from vertex||r * (A1 - A2)|
|Radius to balance point||r * r2|
© 2002 Mark D. Holm