Dimensioning of the primary mirror cell with GUI PLOP

WHAT 'GUI PLOP:

Gui plop

GUI PLOP is a powerful program for the project and the qualitative assessment of the primary mirror of the telescope support cell.

Why can be critical the mechanics of the cell supporting the mirror?

Who is the craftman is aware of the fact that the optical precision of an objective reflector telescope for quality “barely acceptable”, It consists in presenting a defect ON THE GLASS of its reflective surface (understood as measurement “peak-to-valley” of its worst bumps on the surface), such as not to exceed 68,75 nanometers high., or millionths of a millimeter, that degrade the’ WAVE REFLECTED of a value that is one quarter of the wavelength (lambda) of 550 nanometers owned by the yellow - green reflected light, to which the human eye is more sensitive: That is the famous “lambda/4.

And this is due to the fact that the wave, It is reflected in, It is damaged twice error on the glass: A first time in incidence and a second emerging from it.   

And this double accident and emerging wave damage shows that to maintain wave a defect of reflection of Lambda / 4 , it is necessary that the glass owns a double accuracy, namely Lambda / 8, since:

Lambda/8 + Lambda/8 = Lambda/4.

obviously, since it is to reach at least the accuracy of 68.75 millionths of a millimeter tolerance, the mirror performance may also be significantly affected by deformations not own optics, but induced a mediocre mirror support, which in its cell can be brought to flex when varies its attitude pointing objects that are at the zenith or others who are on the horizon.

These possible deflections generate an additional error that is added to the right of its surface, potentially degrading instrument performance.

Who is the author of GUI PLOP?

The program is the result of the work of several people. As man's read in the window “About Plop”, those cited for the first importance is the author of the program, and David Lewis, engineer Toshimi Taki.

The latter is Japanese aeronautical engineer with the hobby of astronomy, and it modified for this purpose a specific tool of modern designers, which is the structural calculation method ofFinite element” , in order to apply it to design and verify the cells supporting the mirrors for telescopes, in such a way as to minimize the distortions introduced by their stresses which adversely affect the optical performance.

One of these cells support in fact, It is characterized by supporting the primary mirror in a series of points in the plane, whose arrangement is calculated in order to load on each of them, a portion of the weight of the mirror even varying its trim in the telescope pointing, to generate the minimum distortion of reflective surface(in function of the number of support points chosen), and with such distortion seeing the error of optical reflection expressed in RMS, or in ratio values ​​peak / valley, that will overlap with other surface errors, contributing to the degradation of the performance of the instrument.

What is the “Structural calculation Finite Element”?:

It is the study of the behavior under load of a structural element complex urged from its supports (I our case, the mirror) , which is then divided into a NETWORK of thousands of components of a little size, whose behavior under load is describable with the approximation of algebraic equations, only reachable by with the power of current computers. Equations that describe this behaviour, coming to display in different colors the different degree of deformation of the different stressed zones of the surface under examination.

What is the utility GUI PLOP for the Stargazer?

The program allows in-depth technical evaluations that go far beyond the knowledge of the normal BASE stargazer self telescope making. However, with regard to "do it yourself" astronomical amateur, PLOP GUI is very useful for the design of the cell size of the primary of your own telescope.

But the use of the program is not so "friendly" and immediate. So not younger people like me, that use it very rarely, in time, forget "how to".

This is the reason that often prompts me to write the instruction "a reminder" for the benefit of myself. To fall back in time, in case My of future needs.

This script is then one....

 PSEUDO TUTORIAL FOR USING THE PROGRAM GUI PLOP

…Tutorial here limited to a PRATICAL EXAMPLE of sizing the primary mirror cell Newton Ø300mm with 9 support points (but we will see that at the user is, however, reserved the right to choose A DIFFERENT number of support points desirables, in order to compare their values ​​and choose the optimal one).

1) In PLOP window DESIGNER CELL click AUTOMATIC CELL DESIGN –

1
2-modif

   

If after the window plops AUTOMATIC CELL DESIGNER, where to place the primary diameter 300 mm – 30mm thick – focal length 1500mm – diameter of the secondary mirror 67 mm – leave blank the central hole box –

2) click NEXT –

9 mpunti
4

  

This opens the window for selecting the number of the cell support points

3) Choose the cell to 9 point and click DONE

4) It opens the PLOP RUN CONTROLS window where click START PLOT –

the program processes the calculations and when he finished the communication window opens – PLOT EXECUTION FINISHED –

5) press OK. The following page becomes visible , from which, by clicking on the EDIT AS TEXT tab….

edit as text

6) showing the following list of variables and relative calculation coefficients appears on the lower half page, than multiplied by the mirror diameter, provide the correct measurements of the inner and outer circumferences, on which they will rise (for our cell with 9 points) the 3 internal support points, ed the 6 external of the support triangles of the mirror in its cell.

graphic plots

  

7) Prepare to draw the cell with a CAD, or other manual drawing method:

8) First draw the primary mirror diameter circle (300mm);

9) It is now necessary to search, among the many rows in columns relating to the displayed variables, the one that will allow us to calculate the radius of the internal support circle, which is the VAR R_INNER 0.331085 – and then multiply the radius of the mirror by that coefficient 0.331085 to get the radius of the inner circle of the cell on which i will stand the 3 internal support points, of our cell at 9 points.

(150×0.331085=) 49.66mm = radius of inner supports

10) Draw this circle to be concentric to the mirror diameter.

11) Then between from the same rows and columns look for the variable of the external radius VAR R_OUTER 0.742219 – and multiply the radius of the mirror by that coefficient to obtain the radius of the circle on which there are other 6 external support points.

(150×0.742219=) 111.33mm = radius of the outer circle supports.

12) Draw this new inner support circle concentric at the preceeding .

13) Go to the MENU ’ of window PLOP CELL DESIGNER, and click GRAPHIC PLOTS, then click CELL PARTS:

cell parts
triangles position

 

You will see the location in respect of the mirror were are the three isosceles triangles of support (due to a chosen cell is 9 points that provides in support of the nine vertex of the three triangles).

 14) At this point, window closed PLOP CELL PART, we are still on the window below that shows the list of data already used. So to continue we must first close the EDIT AS TEXT file, by clicking on another file cabinet. For example on the nearby BASIS, in order to avoid the appearance of a blocking error “invalid floating point operation”l

Error that is due to an inconsistency between the comma sign, used by Windowws as a decimal separator in Italy, instead of the dot, Anglo-Saxon separator required in the calculations of the GUI PLOP program.

Calculations that we have to relaunch without displaying them anymore, to avoid the error resulting from the replacement of the decimal separator.

15) On the PLOP CELL DESIGNER window we click on the AUTOMATIC CELL DESIGN button, confirm with DONE the same data previously introduced in the RUN CONTROL card by launching START PLOP , and pressing OK when completed

16) PLOP RUN CONTROL must then be closed and returned to the PLOP CELL DESIGNER window below, from whose drop-down menu GRAPHIC PLOTS choose PART DIMENSIONS.

graphic plots + part dimensions
coordinate trinagolo

  

The PART NUMBER data sheet appears 1, which is one of three equal triangles, in Cartesian coordinates (in colour black) of the three vertex of support, and centre of gravity (in red) of each triangle,  which will fall on a third circumference still to be drawn, lying between the two already drawn to the support points of the mirror.

Look at the BOX on top right, that indicates the position coordinates of the gravity center (CG = Center of Gravity of the piece displayed), givenin coordinates relative to the center of the mirror with:

X coordinate of the center of gravity = 80.832mm and Y coordinate = 0:

Which means that the vertical center of gravity (Y = 0) the center mirror, at a distance (radius) from 80.832mm center (coord. Y,):

Distance that identifies this third circle which lies, until 120 degrees away from each other, the three centroids of the three mirror support triangles.

17) Then draw the concentric circle of radius 80.332mm base of seat gravity points of the three triangles.

Looking at the triangle shape displayed, We note that both the vertex and the Centre of gravity are indicated in Cartesian coordinates , but this time refered to 2 (the vertex 2 lower left side) of the triangle, which has coordinates X = 0 and Y = 0, indicating the "zero point" of all measurements displayed.

The point 1 (the lower horizontal straight) Have then X-coordinate = 72,696 and Y = 0, which means that is long 72,696 mm i.e.like his abscissa, without variations of ordinate (because Y = zero).

18) We write that value not to forget it.

The window with the triangle displayed, presents the ROTATE function button, with which you can rotate the triangle counterclockwise, and lead from time to time each of its three vertices (The first of these was the number 2; the second will be the n. 3 and the third on n.. 1) in the point at – origin of coordinates X = 0; Y = 0,  that is to the left of the image in video.

In this way, for each rotation that we will request, It will be gradually displayed the length of the side which is located horizontal bottom, indicated by its abscissa X.

19) we must keep notation even for those remaining two values, that with the first will identify the dimensions of each of the three triangles. (Two of these three values ​​will be identical, because it is of isosceles triangles).

20) It only remains to draw the three triangles at 120 ° away from one another, by placing 6 points of 9 overall, relative to the extremes of their hypotenuses, on the circumference of radius OUTER (VAR = R_OUTER) 111.33mm;

And verify that the three points relating to their heights will lies on the circumference of inner radius (VAR R_INNER =) 49.66mm.

While their center of gravity is located on the intermediate circumference radius of 80.832mm

TAKE NOTE THAT: In this example of a simple cell with 9 points, the CELL PARTS is only one, that is the triangle for mirror support (in this case to be made in three identical copies).

While if you chose a cell having 18 points, the CELL PARTS would be two: That is, as a part 1 there will be the triangle for mirror support, (in this case to be realized in 6 identical specimens) and as part 2 the barbell bar that supports each of the three pairs of triangles (to be made in three copies).

And so also for other cells complicated by greater points of support, the display of data relating to the additional CELL PARTS is obtained by continuing beyond the display of element number one (which is usually one of the mirror support triangles), by making the mouse scroll down the cursor on the right of the window that displays the triangle itself. Any further constructive element will appear, in the usual way, showing all the information of its position, in the box at the top, and of its size in the center of the window , which may possibly be referred to the Cartesian coordinates of the element underlying horizontal the design, rotatable as described in the case of the triangle in this tutorial referring to a cell at 9 points, to identify the data from time to time relating to the side that is in a low horizontal position.

END OF DESIGN OF CELL.

If now we go back to point 13) PLOP CELL DESIGNER, and click on GRAPHIC PLOTS, We have the opportunity to choose to see other graphic representations of the mirror and its deformation when it were mounted in this designed cell .

The first view, You can get by clicking on the dropdown menu GRAPHIC PLOTS at the voice MESH , to see how the mirror surface has been divided into the network of polygons of equal area, identified as the “finite elements” I am taken into account in the calculation.

mesh

The second menu item is pop SUPPORTS, that we had already seen above.

The third item of the menu is stress CONTOUR and will show the "level sollicitation lines" around the support points. A sort of contour lines, lines indicating the homogeneous level changes (albeit infinitesimal) reached by the deformed surface, same stress.

graphic plots contour

The fourth item in the drop-down menu is interesting COLOURPLOT that will display the map with the amount of deformation expressed even in relation RMS like “"Efficace value"” of the entire surface, AND even at local surface level in the various colors of a scale shown at the side, indicating values ​​PEAK / VALLEYfrom the deformations generated.

colour plot

The RMS value 1.88 exponent-06 detectable in column at the upper right of the graph, It indicates the effective value (or mean square) error produced on the entire surface of the mirror by this type of cell, in relation to the wavelength (lambda) of 550 Nanometers of yellow-green light that the human eye is most sensitive;

While the underlying P-V 8,397 Exponent-06 indicates the error expressed as peak / valley, or local minimum and maximum deformation of the surface.

In practice, the areas in blue are those less deformed becuase well supported by the support points for the mirror; while the green areas are intermediate deformation, and the red ones are the most deformed.

How to get an idea of ​​the goodness of the cell?

Even without resorting to mathematics for a techincally precise quntification, we read in the program guide“PloP user.pdf”, the suggestion that an RMS error of 4.2 Exponent-06 mm is corresponding to Lambda / 128, and it is to be considered a limit reasonably good for a cell.

Our cell complaint in the graph an RMS value of 1.88E-06, which is 2.23 times smaller and therefore better, than the limit defined as reasonably good for a cell.

Now that we made an idea of ​​the magnitude of the quality of our cell, we only see what function have the remaining items on the pulldown menu.

We go ahead and end up jumping the fifth and the sixth entry CELL PARTS and PART DIMENSIONS, both already been seen above., and we meet the last entry “Z88” the drop-down menu, which it is not to our direct interest as it relates to the use of a software extension called for Z88 “insiders” of the calculation with the finite element.

Comments (5)

  1. Avatar

    fulvio_

    Excellent explanation. :good:
    GUI PLOP is truly a valuable tool for the design of a floating cell!
    For curiosity, i tried the same specs of mirror diameter (300 mm), mirror thickness (30 mm), focal length (1500 mm) and secondary diameter (67 mm) – but with a cell a 18 points instead of 9 – .
    Well, the cell would be even better, with an RMS of 3.398E-07 mm (≃ λ / 1618) and a P-V value of 2003E-06 mm.
    However, the software provides the radii of the circumferences on which i insist 6 internal points (0,387981 mm to be multiplied by the radius equal to 150 mm), the 12 external points (0,792588 mm to multiply by the radius) and the centers of gravity of the 6 triangles (95.957 mm). But the radius of the circumference on which i insist is not given 3 collimation bolts (center of 3 barre) to be placed at 120 °, nor the length of the 3 barre. How you do it? :scratch:
    sure, KRIEGE tables can be used. But GUI PLOP allows you to set up “accurately” all the constructive parameters and I assume it returns a more accurate project.

  2. Avatar

    fulvio_

    EDIT: by length of 3 barre (as a missing parameter) I meant more correctly the distance of the collimation bolt (center of the bar) from the center of gravity of the two lateral triangles to the bar.

    • Avatar

      Giulio TiberinI

      Hello Fulvio.
      Sorry for the delay in this answer.
      Note that in a cylinder with 9 points, as shown in the tutorial example, there is only one “building element” which are the three identical triangles and their placement.
      While in a cell at 18 points, there are two constructive elements :
      1) The first constructive element is the support triangle of the mirror, of which there is 6 identical parts ;
      2) the second constructive element is precisely the balance bar in three identical examples, which supports each pair of triangles.
      To see this element n°2 which is the bar, when (as you have already done) you are in GRAPHIC PLOT – PART DIMENSION, that allows you to see one of the identical triangles, you have to scroll down the cursor that is on the right side of the window that contains the triangle, and you see it.

      Also for this element “bar” you will find in the box at the top right of the window. the positioning coordinates of its center, which are in X = 71.968 and Y = 41.551, and are at 30° on a circumference with a radius of 83.102mm, (note that the 30 degrees refer to the picture of the whole cell that you see with GRAPHIC PLOT – CELL PARTS). While the figure of the bar is represented by a simple straight line, whose center of gravity is indicated at 47,974 mm of its length which measures 95,947 mm de long.

      Thanks Fulvio for the observation, which allows me to insert a summary of this explanation also in the article.
      Health
      Giulio

  3. Avatar

    fulvio_

    Thanks to you Giulio for the answer, which is always courtesy! :good:
    Vero, it was enough to scroll the window cursor “Part dimensions” to get all the missing info on the three bars!
    With GUI PLOP designing a primary mirror support cell is “relatively” simple. The pitfalls then lie in the many construction details: tailgate type, materials / hardware used, thicknesses, cinghia vs Whiffletree, use of the mobile frame (which seems to me an excellent solution to make the entire cell integral with the mirror)… etc. For some of these “parameters” you basically navigate on sight, empirically.
    For example, the practical methodology intrigued me a lot (tests) with which Mike Lockwood determined the best type of Whiffletree (with roller bearings).
    http://www.loptics.com/articles/mirrorsupport/mirrorsupport.html
    Even in this niche sector, knowledge is obtained in successive steps, giving a blow to the circle (theory) and one to the barrel (experiment). :good:

    • Avatar

      Giulio TiberinI

      Hi Fulvio.
      Is’ vero. The general thought for those who are preparing to have their own (maybe sooner) making a dobson, it can relate to the "best" manufacturing choices resulting from that of the number of support points of the mirror in the cell.

      As a general line it always pays off (according to the weight and diameter of the primary) reach the goal using Occam's razor, addressing simple and functional technological versions, because there is always time to complicate life. Since a self-built Dobsonian usually opens a "Fabbrica del Duomo" which remains continuously active both in maintenance and in any improvements.

      The choice of a floating cell is fundamental, that is mounted on an isosceles triangular structure at whose vertices the three collimation bolts move the whole set independently. Basically it is the type of cell that Lookwood displays on the site at your link.
      It is worth not complicating your life with 18 points of contact when with 9 a lambda of a few cents lower is obtained.

      The lower support that holds the mirror in place, intended as a "whiffletree", perhaps it makes sense to do it with bearings at the ends with primary diameters of 20 ”and up, otherwise visually you see no flaws.
      This is because if the mirror is pointing to the zenith, rests on its contact points, it does not move when pointing the telescope also towards the’ horizon (where, however, there would be a self-defeating vision, ruined by 300 more km of atmosphere to overcome, against 15 surmountable by aiming objects at the zenith).

      With lightened Dobsonians to facilitate their transport, problems and compromises soon become counterproductive to that purpose.
      Of course, your orientation and performance expectation counts in everything. Mine is Spartan. For me, beauty is not aesthetics, but what is experienced shows the greatest simplicity in carrying out its technical task in a satisfactory way.

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