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# How to make Plop triangles equal

13 replies to this topic

### #1 hakann

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Posted 11 May 2019 - 10:02 AM

I had this topics up before and has been try get a solution.

It's no real need to has a equal sided triangle as Plop do the math, but its more easy do them equal ( even in CAD/CNC machine ) and centre is correct located so balance is perfect.

If I take my cell for a example.

457 mm in diameter. ( 18" )

1829 mm FL ( f/4 )

33 mm edge thickness.

Quartz.

18 pt cell.

Automatic cell get's me a nm RMS at 9.2e07.

That gets me the 2 radius at ;

0.804606.

0.399088.

Now I did a even radius to 0.8 and 0.4 and run the program.

The side # 2-3 got me a number.

The #1 side got me a shorter number.

To get this equal one has to add +15.47% on that shorter number, and then the triangles is equal.

In program I let the radius 0.8 be there but I must adjust the radius 0.4 some.

The readings in Plop now show a hair more at 1.15e06 now, so it's a 'price' to pay.

A note here.

One could try adjust the 0.8 radius to get it more equal, so then the nm RMS readings might be little better, or clooser to the automatic number.

.

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Edited by hakann, 11 May 2019 - 01:28 PM.

### #2 MitchAlsup

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Posted 11 May 2019 - 03:22 PM

I see no advantage in equal sided triangles when doing the cutting by hand, let alone CAD/CAM.

### #3 Pinbout

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Posted 11 May 2019 - 04:07 PM

That’s not even the dims for the triangles, just the points of support, you have to make the triangles biggerer to have some meat to support the supports.

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### #4 hakann

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Posted 11 May 2019 - 05:02 PM

-Well as I said, but it's nice to has them equal and the centre exact in the mid.

I did a marginal adjustment here so I made the 0.8 radii less, so I tested 0.795.
Then the 0.4 radii was 0.411522 to match that up.
That way I did hope to come down to under 1 nm, but I was at 1.05e06.
( little 'better' than the 0.8 radii that was at 1.15e06 ;-)

Triangle will be 6 mm bigger and pads at 8 mm. ( 1/2" CF ) riding on a ball and the triangle has a 45 degree chamfered hole in centre.

Cruxis reading on same mirror data is 1.1 nm RMS whit a wiffle tree.

I had a FEM on this cell I planned whit Invar steel triangles.. ( same ppm/C as the Quartz glass )
To make them rigid ( 1/4” thick ) FEM was at the ’golden’ <5 nm ( or as I got it ; twice the diffraction limit ) but as weight was a ’factor’ triangles was made on purpose smaller than ex Plop ( aka higher readings )

/But as I wanted a ’better’ reading’s I do go after Plop now, but instead make the triangles in CF, and now equal 60 degrees as the FEM idea.

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Edited by hakann, 11 May 2019 - 06:22 PM.

### #5 mark cowan

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Posted 11 May 2019 - 06:24 PM

I thought you wanted to see if PLOP would match this outside design you had... Does it do that?

### #6 hakann

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Posted 11 May 2019 - 06:47 PM

Mark,
No, this was made by adjust the program myself and then let the program show the readings.
Even so, now I saw the reading on a equal triangle.
Just some math - but good should be if this was made in the program.
If you find a way, let me know.

### #7 hakann

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Posted 12 May 2019 - 01:06 PM

Even if this is playing whit 'numbers', I did finally get it under 1 nm ( 9.749e07 )

Actually the Plop program made the triangles some mm smaller from the 1.05 readings yesterday.

The numbers of radii went to be 0.785 and 0.40635.

I added 8 mm outside the Plop fix points.

Pads is drawed at 8 mm.

### #8 hakann

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Posted 15 May 2019 - 10:04 AM

I know this idea is not seems as ok or needed, but the ones who like a equal sided triangles and get way better than golden >5 nm RMS.
Here is the easy concept for a 18 pts cell.

Run automatic cell design with the mirror data.
Re-run Plop whit material to be used.
Re-run Plop whit set the new factors.

Use factors ;
0.40635 & 0.785.

I did run a 24" f/4.5 now ( 2" thick Zerodur ) and I got readings at 1.6 nm RMS and triangles get equal.

If you don't can do the math or has CAD, just rotate the triangle and you see its equal.
Centre you see as Y and X in triangle.
Centre hole is at 60 degrees.

The number on triangle ; X of CG is the outer radius of triangle ( factor 0.785 )
The number of the bar ; Y of CG is the inner radius of triangle ( factor 0.40645 )

Wol'a.

Edited by hakann, 15 May 2019 - 10:31 AM.

### #9 mark cowan

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Posted 15 May 2019 - 11:19 PM

You can set the material before you run PLOP and you can set the factors the same way.  Just so you know.

BTW I get 1.43nm RMS and 0.996nm RMS for the Z88 calculation with a 20% obstruction.

If those are the same numbers as your outside design then it's done.

Edited by mark cowan, 15 May 2019 - 11:21 PM.

### #10 hakann

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Posted 16 May 2019 - 04:18 PM

Mark,
What’s really the z88 ?

You should get 0.974e07 whit the numbers.
458
1828
33
FS
101.6
0.785
0.40635

How about tilt at 45 degree ?

Not able to find that / yet.

### #11 mark cowan

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Posted 16 May 2019 - 04:44 PM

The Z88 is 3D FEM instead of the 2D plate analysis used by original PLOP.  Both are accurate but the 3D FEM does a better job of allowing for point-loading force distribution which is important with mirrors.

I did a 20% obstruction for an f/4.5.  You used 22% but didn't specify what it was.

If I take my cell for a example.

457 mm in diameter. ( 18" )

1829 mm FL ( f/4 )

33 mm edge thickness.

Quartz.

18 pt cel

So they are the same for all intents and purposes.

### #12 mark cowan

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Posted 16 May 2019 - 05:01 PM

Yeah I get that number for your example.

Tilt only works for Z88 modeling.  When I run those #s with 45 degree tilt for a 180 degree sling I get 2.8nm RMS for Z88 results.

### #13 hakann

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Posted 16 May 2019 - 05:46 PM

Well Mark, I guess I’ ok ;-)

Is this sling or wiffle vs 45 degree ?

Can you do the same for a 24”.
609
2745
44.5
FS
89
0.785
0.40635

z88 & tilted 45.

Edited by hakann, 17 May 2019 - 01:27 AM.

### #14 mark cowan

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Posted 16 May 2019 - 06:05 PM

That's a sling.  You can do the other yourself once you get the same result as what I showed.

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