Strongest Cross Section Geometry

The equilateral triangles are stronger. This is why they're used so much in construction... and construction equipment. Consider the crane.

You may be able to use larger triangles, removing more glass and increasing rigidity at the same time.

Try bounding some triangles within a circle on paper and see what your intuition tells you.

Whoa back, greater strength or stiffness?

passingtongreen asked: ". . . . greater strength or stiffness?"

Stiffness to be sure.

These mirror blanks are figured to 1/20th of a wave of light in the visible spectrum. If the substrate is strong but lacks mechanical rigidity, the entire effort is compromised.

L.J.

These mirrors are statically mounted, that is, they're not actively deformed to compensate for sag? Are they relatively large mirrors? (I'd say not, given the cell size vs the mirror diameter in your drawing).

Bees, btw, put stuff in their cells and the cells are hexagonal for maximum packing density (same for pencils - you can ship more in the same space as fewer round pencils).

europium wrote: "These mirrors are statically mounted, that is, they're not actively deformed to compensate for sag?"

That is correct. Everything possible is done to prevent deformation so either the aspect ratio is kept as close as possible to what was once called the "Standard Ratio" (6:1) or, a special multi-point cell is engineered for the express purpose of maintaining uniform pressure under the mirror.

When I saw that how much weight was reduced by the honeycombed pockets, I changed the aspect ratio to something in the order of 10:1, thus reducing the strain on the mirror even further as well as the thermal mass.

I do not like the complexity, the weight nor the fabrication costs of multi-point mirror cells. Everything possible is done to keep the fixturing simple by adjusting the mirror geometry to be self-supporting without excessive outside assistance.

europium asked: Are they relatively large mirrors? (I'd say not, given the cell size vs the mirror diameter in your drawing).

You are correct, no they not large; not if you are comparing them to what is created at the Arizona Mirror Lab!

The mirror image I first displayed for this string includes the mass properties however the image is too crude to read the text. That's a 14" mirror cast from plate glass and the hexagon pockets are about 2.375-inches across the flats. That model was created in SolidWorks Mechanical Design software. Export files were imported into CATIA for meshing and analysis.

My kilns limit the honeycombed apertures I can cast to about 22 inches. My production kilns are computer controlled 17 and 24 inches in diameter.

I've a larger kiln with a 30 inch chamber but that is used primarily for bulk annealing mirrors made in the smaller kilns. Until I master the smaller size mirrors I refuse to entertain blanks that size.

Packing pencils is a great analogy! Thanks

L.J.

Not being an expert at all but wary of possible implications I think the bees are looking for a perfection of space while you are looking for a perfection of strength.

The honeycomb pattern is derived from speres being put together. Triangles in space form the Tetraeder. I believe this form has minimum volume to surface ratio. Nothing the bees would like probably.

Cylinders in a plane, maybe. You're thinking of tetrahedra, which bees do not build.

Yeah, but each hexagon can be divided into 6 equilateral triangles.

...that would form nice clear cut diameters across the lens.....

Usbport wrote: "The Corning engineers who used hexagons for the back of the 200 inch mirror for the Hale Telescope at Mt. Palomar knew what they were doing."

That scope was completed in 1948. That achievement, 60 years ago, was viewed as the equivalent of our placing a man on the moon. What I love about it was not one dime of government subsidy was spent building it!

It's interesting to observe that the famous Mirror Lab at the University of Arizona

http://theketelsens.blogspot.com/2009/05/new-mirror-lab-project.html

is making all those super giant mirrors using honeycombed patterns made with hexagon shaped inserts.

Thanks

L.J.

You're right on. GA!!

I have two on-topic questions, though not directly related to your post.

1. Does your hexagonal pattern take into account the (parabolic) sag of the mirror; i.e., are the central hexagons the shortest, with the heights increasing toward the perimeter?

2. What would the weight be for, say, an 18 inch mirror with a nominal f/4 focal ratio? (In case, you know, someone was interesting in buying such a mirror for his home observatory?) Thanks.

Usbport asked:

1. "Does your hexagonal pattern take into account the (parabolic) sag of the mirror; i.e., are the central hexagons the shortest, with the heights increasing toward the perimeter?"

For those of you not familiar with mirror jargon, Usb's use of the word "Sag" is not the word sag as in "drooping". Rather, it is a contraction of the word "Sagitta", which is a spherical or parabolic curve ground into the mirror surface, which will eventually be polished, figured as needed and then aluminized in a vacuum deposition chamber.

To answer the question: The depth of the hexagon pattern is a constant and typically designed to produce a "roof" with a minimum of a three-eighths inch thickness at the origin after the sagitta has been ground.

This is critical and is purposefully done to minimize the chance of having the webs of the hex's below printing through the top surface under the pressure of grinding. The width of the webs in the hex structure is also a contributing factor but perhaps the most influential geometry are the generous fillets in the roof of each hex whose radii reduces print-through even more as well as reducing the chance of stress risers.

Efforts to vary the depths of the honeycombed pockets from center to edge were dropped when it aggravated production costs but failed to significantly reduce weight.

2 What would the weight be for, say, an 18 inch mirror with a nominal f/4 focal ratio? (In case, you know, someone was interesting in buying such a mirror for his home observatory?) Thanks.

I do not have an existing 18 inch model I can refer to but can say with some certainty that the weight of a honeycomb blank would be less than half the weight of solid blank of the same aperture, and it would have a radiant surface area about 300% greater when compared to a solid blank.

The speed with which honeycombed blanks reach thermal equilibrium is unmatched except by the meniscus shaped mirrors that are starting to gain in popularity. In fact it is so good, that I believe that there is little to be gained by using more costly materials like Pyrex and borosilicates for their lower C of TE.

These blanks reach equilibrium so much faster than solid blanks that the cost-benefit advantage of materials with low thermal expansion are difficult to justify.

L.J.

A "normal" and low cost CAD soft. Nothing special. The name is TURBOCAD

What is a hex but in fact 6 equilateral triangles with the intervening walls removed? Walls I might add that add weight and thermal mass to little advantage. Hexagons are the most efficient shape for filling a volume with minimum surface area as well. Since we are obviously doing this in a 3d modelling program have you tried doing it both ways in FEA to prove why hexes make for better voids? my guess is that the stiffness will go up some but the weight (and therefore the optical sag) will more than make up for whatever small gains in stiffness you get. also your thermal mass will go up as well.

Rorschach asked: ". . . . . have you tried doing it both ways in FEA to prove why hexes make for better voids?"

No I have not.

After so many years of success with that geometry there was no reason to challenge what appears to work well.

In the face of recent dramatic breakthrough's in materials, perhaps that's not the best logic but I am not using modern materials. I'm using something invented thousands of years ago.

While the chemistry of mirror glass is admittedly more recent, the isotropic properties are not substantially different.

In other words, if it works, why fix it?

Thanks

L.J.

LJ, you interest me strangely, I'm actually curious enough to give it a go just to see what I learn. if you would be kind enough to either post or message me with some representative dimensions I'd like to try an fea run both ways for sh1ts and giggles...

I suspect that no uniformal pattern is exactly "optimum" on it's own, all depends on stress planes of the specific application, so it should have for example less mass near the mirror center, more mass disributed "radially" than "circularly" so you need wall thickness AND cell depth variation in the pattern etc. Without passing it through FEA it's not that easy, and as my first estimation, hexagonal is not a a bad start. S.M.

I wish to thank all who responded for the time and effort expended in supporting this inquiry.

Your generosity is obvious and appreciated.

Thanks

L.J.

By the way, the circles inside the hexagons have contact-points with each other in the form of triangles already, don't they?...

But more importantly, how many lenses have your detractors made with just triangular lense prisms? Any? Even one? Have they shown you the result of their own efforts (how it should be done)?...

If so, what was the comparative cost? Where is their design or their financial documentation, if any?...

Wouldn't we like to see it?...

Roger Angel's spin-cast mirrors have honeycomb backs mainly to allow them to adjust quickly to changing ambient conditions, according to Angel. I met Dr. Angel at the Steward Observatory's lab where he was casting a 27' mirror for the Magellan telescope (my old boss, who worked for many years at the MMTO, introduced us). Angel pointed out that he does not want his mirrors to be too stiff, as they are dynamically deformed by actuators on the backside of the mirror (so-called whiffle trees) to compensate for variations in how the mirror sags as the telescope's altitude (angle, not height) varies. The Magellan uses seven aspheric mirrors. Corrections are similarly applied to a much smaller, secondary reflector at a much higher rate (>500 Hz) to compensate for atmospheric abberation, itself measured by means of an artificial star.

Jag, I have to agree with BIGG's statement. He gets another GA from me.

IMO, for all intensive purposes the primary reason for the inclusion hexagon backing in large optical primary mirrors is:

1. More effective radial cooling of the blank after it is cast, and hence the lessening of imperfections being induced into the blank.

2. Most efficient weight reduction-to-strength ratio.

3. Most thermally efficient, and thus most inherently stable, design of the mirror whenever there are changes in the ambient air temperature.

[BTW, I'm a telescope builder myself, and have been so for some 38years since I was 15, but not to the advance degree and capabilities of Laughing Jaguar.]

Moosie!

Hi Stranger! It's been a while!

Thanks for the generous comments!

L.J.

Hiya LJ! Yeah, it's been a while hasn't it?! LOL I've been lurking about mostly in CR4 the past few weeks + been terribly busy incorporating (Professional Corporation...S-Corp. that is) my engineering firm with NYS. What a PIA, and costly too! ***BILL THE CAT ACCCKKKKKK ACCCKKKKK!!!***

You're very welcome my friend! Howz the telescope building coming along? I betcha it's a great big mirror, eh? <<<ENVY>>>

LJ, who says you must defend? Did those attacking provide any proof, or just thin arguments?

defense consists of verification by test and independent review.

Can you make small mirrors, I have a future use for some light weight optics? < 20" / 500 cm

On closer investigation, it appears that the proponent of triangles is an arm-chair theorist who designs with CATIA and whose knowledge of the software has gone to his head.

He is beginning to look suspiciously like a college age young man with visions of grandeur.

I won't challenge his logic out of politeness but after repeated absurdities it's obvious he has little experience actually making anything.

I've three computer managed kilns up to 30 inches and concentrating my efforts on conventional honeycombed blanks and meniscus mirrors up to 22 inches. The 30 inch is destined to be used exclusively for bulk annealing.

Continued experimentation is the current effort and I am close to getting consistent repeatable results which is encouraging.

I am NOT a mirror maker actually. That craft requires exceptional hand skills with glass which I do not have the time or inclination to develop even though I have ground and figured some with success.

I'll be content providing the raw blanks to those who can.

I hope to have some on display at NEAF.

Thanks

L.J.

NEAF? And yes, that is often the case with people who have never built anything. That said, sometimes someone who has no vested interests or baggage can see things that the "old hands" have turned a blind eye to as well, so it pays to listen, and then if you can't explain why their idea won't work, investigate, because that is where innovation comes from sometimes. You never know, sometimes you learn something new.

This has been an interesting thread, I have learned much, enough to throw in my two pennyworth or two cents worth, depending.

Maintaining the "shape" of the mirror, the cell roof, is by far, the highest of objectives. It seems logical that the most uniform arrangement would satisfy this requirement. In the hexagonal cell, if the center of the roof is one unit from the corner, it is 0.866 units from the edge, not too much difference. In the equilateral triangle if the distance to the corner is one unit, the distance to the edge is 0.5 units. this would imply uneven support and uneven cooling/heating. The symmetries of the hex cell make additional symmetries across the mirror, what will happen relatively uniformly to the hex cell will happen relatively uniformly across the mirror. It follows that what will happen less uniformly to the triangular cell will also occur less uniformly to the mirror. An additional downside to the triangular arrangement is that six walls would meet at a junction instead of three in the hex arrangement. When you add in six fillets it makes a thick piece of material.

If there were tons of photons beating the mirror down, that is, if structural support was a bigger factor, the hex cell may not be the best configuration, but it is not bad.

Nature doesn't go much on triangles. Maybe you can argue about thermal stress distribution with pictures;

Just for argument sake, is your software robust enough to make a mirror based on triangles, and then compute its regidity?

The design software used and the export files to other analysis software has already been discussed. The evaluations and comparisons made by others make further analysis moot.

I am satisfied that in the context of a telescope mirror, the hexagon is the preferred geometry for patterning, for thermal reasons as well as superiority in the area of strength to weight.

There is nothing left to dispute much less argue.

"If it ain't broke; don't fix it!"

L.J.

It seems to me that you are chasing red herrings. There is nothing inherently wrong with thermal mass. What should concern you is the evenness of the heat flow, which could be helped or hurt by thermal mass. Oddly enough, pistons of heat engines often have shapes similar to telescope mirrors, and designing for proper heat flow to allow controlled clearance tolerances and avoid lubricant breakdown is very important. If your work allows, you should always begin by analyzing the information you already have. If you don't have any, get some, as how much thermal distortion is there in functioning mirrors, relative to the mechanical distortions. Can you model the triangle vs. hexagon stiffening in a different medium that would be easier (and cheaper) to get data? My intuition (based on piston design) is that the best stiffening pattern would reflect the exposure to heat and cold sources as well as the the location of the mechanical mounts. Whether this is economically appropriate is up to you (or your triangulat friends).

"There is nothing inherently wrong with thermal mass."

You obviously have never looked through a telescope adapting to temperatures or you would know empirically that in the context of optics, that assertion is patently wrong!

It was already made clear early on in this discussion, that the reflective parabolic surfaces of these mirrors are figured to a precision greater than 1/20th of a wave of light in the visible spectrum.

Comparing that degree of precision to that of a cam-shaped piston in a Otto Cycle engine is like comparing an electron microscope to a hand held magnifying glass!

L.I.,

No wonder you do not easily understand. Where did the "cam-shaped" , Otto cycle" come from? You added (overlaid) your assumptions onto my suggestions without actually seeing the underlying similarities. You can keep your erroneous assumptions smugly to yourself and just go on with as much error as you want, since you seem to think you are already within " 1/20th of a wave length of light in the visible spectrum".

There are several aspects which have to be analysed:

a- behavior when the glass is poured into the form

b- behavior under own weight at different angles

c- behavior when a temperature change occurs

If an active compensation is not used then the mirror frame has to be VERY stiff in order to deform as low as possible under the load (variable).

In order to avoid internal tensions at cooling the uniformity has to be as good as possible. If the walls are too different as in other cast parts voids can be generated since the poured mass cools at some places faster and does not allow a full filling.

Qualitative similitude has limits when the order of magnitude is too different! This applies especially to the deformation under a heat gradient. The piston has a broad possibility to deform and fulfill its function, a mirror will totally loose its optical quality even at VERY low deformations here is one of the biggest problems.

Do not forget that Hubble had only a very very small error and brought bad pictures, this was easy to notice when same parts of the sky were presented as pictures before and after the correction.

The cam-shaped piston came from the fact that the temperature field was non uniform due to the thermal paths and so that the temperature depending radial expansion was as well non uniform. This was compensated by the cam profile in order to obtain a cylinder after temperature stabilized.

There are some telescopes now build with many small mirror actively controlled as well for the compensation of mechanical influences as for effects of air turbulence which deteriorates the image.

What I personnaly do not like in your reaction is the almost insulting attitude toward LJ because he did not accept your opinion. How do you know his assumptions are erroneous? Elaborate with detailed explanations.

THIS IS NOT CR4 COMPATIBLE! At least this is my opinion.