[ATM] Re: ATM Digest, Vol 2, Issue 15

[artbianconi at blast.net (artbianconi@blast.net)]

{SEQ CHAPTER \h \r 1}I?d like you to indulge me while I walk us through a brief but necessary trip in 
the birth of a mirror. I?m doing this so that I might better understand my 
bewilderment at some of the preoccupation people exhibit with cell designs 
and their demonstrated attachment to sagging and the multipoint  balance 
scales with which mirrors are supported.	

First we take a wheel of glass. To make things easier for all, I?ll let you define 
it?s material properties using common reflective materials.. 

That piece of glass is now laid horizontally, typically on a wooden table made 
for the purpose and is ground to a curve that approximates an arc segment of 
a sphere. Whether that table be stationary or motorized is not relevant, at least 
not for this discussion.

Then, by various degrees, it?s taken from the rough finish to a smooth finish.

When it?s as smooth as it will ever get, the hunk of glass is lifted from that 
horizontal surface of questionable stiffness, where it was ground and 
polished, and now placed vertically in a stand so it can be ?figured? via 
Foucault Testing. 

Nothing to sneeze at, this or the equally popular ?Raunchy? test appear to 
have humbled many a driven ATM during their passionate pursuit of a 
diffraction limited mirror. We are talking here about the pursuit of  
?Gadzooks!? precision:   ?one millionth of an inch? or in the more popular 
vernacular   ?one-twelfth wave?. 

This test is conducted while the mirror is in a position that it will rarely see 
when in use, vertical, and when the entire weight of the mirror is suspended 
from two points on the perimeter at approximately 4 pm and 8 pm. 

Then it will be placed back on that horizontal table who?s stiffness, or lack 
thereof,  is the same as it was before. The mirror will now be polished with a 
mysterious collection of moves whose consequences are predicable only to a 
handful of souls. For the rest of us mortals, it?s a mad, frustrating chase for 
that elusive diffraction limited mirror. 

I will take out my magic wand at this point, sprinkle some magic dust from 
Tinkerbell and bless this ATM with good fortune. I?ve made it easy! I have 
given him a finished mirror with numbers so perfect that it makes TEX leap 
off the screen and his orthodontist close shop!!

Now he starts to build his telescope.  Maybe he doesn?t stick this one in a 
cardboard tube made for pouring cement! Perhaps be builds a mount out of 
something of less questionable geometric stability: wood! If it?s a large 
aperture, it?s likely to be an open truss with Dobsonian heritage. The truss 
tubes will be anchored to the wood at the bottom and the wood at the top. The 
probability of the tubes being made of aluminum is likely. This material has 
amongst the highest coefficients of thermal expansion of any man made 
material. But that?s ok.

Now we are ready to suspend that divinely precise hunk of glass and 
suddenly, out of now where comes this zealous preoccupation with 
?sagging?!  Why? 

Why wasn?t it considered when it was being polished on a horizontal table 
made of half inch plywood (maybe!)?   

Why wasn?t it considered when the mirror was vertical and the stresses 
concentrated on two points at 4 and 8 o?clock?

The rigidity of any mechanical system, weather static or dynamic, is only as 
good as it?s weakest  link. Here we are with enormously heavy wooden boxes 
which are not even closed but open across what is perhaps it?s largest surface 
(the mirror has to see out, right?). It?s suspended between two trunnions 
which pivot on yet another box open on THREE of it?s six sides and also 
made of wood.  

However, before we get to that part of the project, we must build a 
suspension system of sorts to prevent the mirror from sagging and losing that 
diffraction limited surface.

I am not an astronomer, at least not to the degree that most around me are. 
Me? Enter a ?Messiah? Contest? Forget it! If you asked me I couldn?t find 
2% of the most popular objects without a lot of help.

I am not much as an ATM either. Others will tell I can?t pronounce half those 
damn French words much less explain what they do or why.

BUT! I know a little bit about materials and structures. I am no slouch at 
using some of them having done so for over 45 years in some of the most 
demanding design environments. 

What I simply do NOT understand is that if sagging of any mirror is such a 
concern, why isn?t that preoccupation apparent when it is being polished, 
especially on a dime store bench (or the generic equivalent) which has about 
as much stiffness as a Frisbee? Why isn?t it a concern when the mirror is 
being tested?  It?s vertical,  essentially totally unsupported and subjected to a 
load distribution pattern totally alien to anything it will ever see in actual use 
but this is the way the mirror is evaluated! Whatsamatter? Didn?t it sag then? 

There?s an old joke about someone being told his tire is flat. His response? 
?Oh, that?s OK; it?s only flat on the bottom?.  How is a mirror, ANY mirror 
different? 

Has it ever occurred to anyone that concentrating the weight of the entire 
mirror on two points at the bottom, in a narrow 25 to 30% portion of its 
perimeter, just might cause the glass to bulge some nearby?  Has anyone here 
ever seen someone rotate the mirror 45 or 60 degrees and test it again? 
Probably not. It probably wouldn?t make a difference anyway, the ?flat? 
doesn?t move. 

What?s more appropriate and equally unlikely is to rotate the slit or knife 
edge and do the test at an angle WITHOUT moving the mirror! Wouldn?t 
THAT show some interesting results! Or as I suggested to one highly 
regarded mirror master, put your 500 pound mirror bench in the basement, 
put the Foucault Tester in the peak of the roof in your attic, aim it straight 
down and drill a hole any floor that gets in the way.  Noqw THAT's a knife 
edge tester!

I will build a super stiff cell as planned from properly oriented Carbon Fiber. 
It will be a hundred times stiffer than a mirror of 4 times the thickness and it 
will weigh almost nothing by comparison. We?ll do a star test and see how it 
compares to the Bumble Bee which, by older aerodynamic laws, can?t 
possibly fly.

?Curiouser and Curiouser? spake the Mad Hatter
  
Art Bianconi