Re: [ATM] more trouble with figuring...

["Jerry" <wa4guu@verizon.net>]

Hello Norm

The over correction at zone 6 (290%) is your problem. The under correction
at zone 4 is not a problem, it could easily be made larger but you don't
want to worry about that now. You need to reduce the overcorrection in zone
6. More on that after a little set up.

I think something that complicates learning figuring is that there is more
than just the question of how to work a zone, there is the question of
deciding which zone to work. You've taken those knife readings and just how
do you use them to decide what to do? Then after deciding what change you
would like to see happen, how do you make it happen?

You are trying to learn two things at the same time. The success of the
second is somewhat dependent on the first having been done properly.

The first thing is to determine where you can bend the curve and in which
direction to make the shape better. Those zone reading say a lot about what
to do. Each zone has a desired knife position. You know the desired numbers
and you might convert them by some process that makes the knife movements
easier to compare to the desired movements. That is how you determine the
present shape. 


I'll run through the process I use the Foucault test data to decide how to
go.

I'll go step by step in enough detail so that you know what I'm doing and
can correct me if I get something wrong in my understanding your numbers or
my calculations.

After measuring the mirror's radius of curvature, the knife zone readings
boil down to a movement from one zone to another. You desire the movement
calculated from hm^/r or hm^/2r depending on the tester type. For the fixed
source tester it is hm^2/r. When you have calculated the desired knife
position for each zone, subtract each zone's knife position from the
position for the next zone outward to get the desired knife movement from
each zone to the next.



I calculated your desired knife movements from each zone to the next

zone1  
      > .052
zone2 
      > .055
zone3   
      > .054
zone4  
      > .054
zone5  
      > .054
zone6   


I averaged your actual test knife readings resulting in...


zone1  .1943
zone2  .246
zone3  .2897
zone4  .2997
zone5  .3493
zone6  .506

and calculated the actual knife movement from zone to zone to get

zone1  
      > .052
zone2 
      > .044
zone3   
      > .010
zone4  
      > .050
zone5  
      > .157
zone6   


As an example desired knife movement from zone 1 to zone 2 is .052" and the
actual is .052" and that is 100%.  Do that for each zone and you have the
following percentages. I think the percentages have it boiled down to the
numbers that make comparison most easy.

zone1  
      > 100%
zone2 
      >  80%
zone3   
      >  19%
zone4  
      >  93%
zone5  
      > 290%
zone6   


Compare the individual readings, desired reading and actual reading for each
zone. You can just look and see if they are over or under, or you can
calculate the percentage each actual reading is of the desired knife
movement as I did. If you learn to drive these numbers individually in
whichever direction you desire then I'm sure you can see that you should be
able to drive them to the desired numbers. That is what you want to do,
drive them individually. So look at them individually.

In practice you will find that if you change one in most cases another (or
more) will change also. You might find that you can make one change faster
than another one and you might find that frequently when you make one go up
another goes down. Then if you pay attention to what the numbers are doing
you might see that when you make one go up, with a small variation of the
stroke you can control which one goes down. You have a choice of where the
reaction will occur and you put it where it does good. To the extent that
you can't precisely put work on only one zone without a reaction elsewhere,
you can learn develop a strategy that sets up a shape where the final action
and its reaction both improve the shape. I can't tell you exactly how to do
that. I can suggest but you have to do it to learn it. But it might help you
to realize that that is what you should be thinking of. 

You don't have to do this very well to make a good mirror. If you do enough
to learn it well then making them well is easier. If you do it enough,
driving to the parabola is like driving to work in the morning. You know the
way to work and you hardly think about how to steer your way there. You know
the moves, slow down for that bump and go over it just a little to the right
and you won't spill your coffee. 

On the drive to work, there are situations that you know you don't want to
get into no matter how good a driver you are. Maybe on the interstate
highway you know those people coming on that ramp cut way over across all
the other lanes to get to a left exit ahead. You know that and you are
careful not to let them cut you off and run you onto the grass median wet
with dew. If you got over there you might be able to maintain control and
get safely back on the road, but you can't be sure of it and the odds may be
stacked against that. 

Figuring is like that. There are some situations you can handle some of the
times, but your really don't want to be there. You make plans to avoid it.

You can see from the percentages that zone 6 is well over-corrected.
Unfortunately it is much easier to move correction from the center outward
than it is to move it from the edge inward. To reduce that 290% in the last
zone to 100% or less is difficult without changing the others. The good news
is that it is so important to get that number down that you should not worry
what happens inward. It can't be worse, or at least not much worse than so
much over-correction near the edge. You are in the wet grass in the median.
And sideways!

That is really all I need to know to see what I would do, but you won't
always have so clear a view so let me continue interpreting the shape. You
could run the numbers through one of the programs but you don't really have
to do that to see where and which way the slopes are changing. 

You can draw a line 6.125 inches long to represent the half diameter of your
mirror and mark the zone boundaries on it. You can pick a zone (any zone so
start at zone 1) and say that it is right on the reference line you drew.
Then if to the next zone outward is over corrected that is a change in slope
downward, if it is under corrected the slope change is upward. Do each
successive zone and if two or more zones in a row are under corrected the
change toward upward slope increases at each under correction. Same for two
or more over corrections in a row. The down turn increases at each. The
degree of slope change is determined by percentage of correction between
each zone. If the correction to the next zone is 100% the slope continues
unchanged from the last zone. That may be an up slope, a down slope or
level.

Now that all the slopes have been drawn you can rotate the paper to bring
the resulting profile as near level as possible. It will be much the same as
the output from a program. It will have the information you need except you
will not have the height of the profile. After doing this a bit you will see
that you don't need to know the height. What ever the height, you will get
your numbers as close as possible, and you won't be able to make them better
if you know the height. When you get them as good as you can, then you run
the numbers through the program to see how good the finished mirror is. If
you did a good job of getting the numbers right the program has no choice
but to say the mirror is very good.

The reason I recommend doing it this way is that it assures that you will
learn what is important in figuring. Just putting the numbers into a program
and letting it spit out a profile can obscure the fact that you can see that
profile without the program. Easily. I know you are going to use the
program, but do it manually also and you and I think you will see that you
will know better what is going on.

I think I may have already told you how to move the numbers in the desired
direction.

Now the profile. If you drew that profile correctly you will see you have a
raised 90% zone. The slope upward to the crest starts at about the zone 3-4
boundary. That is about the 70% zone. So from 70% it rises to the crest at
90% and turns down from there to the edge. The edge is not really low. Now
if you run the numbers through one of the programs you will see the 90% is
high by about 1/3 wave on the glass surface or about 7 millionths inch. It
can be fixed but it ain't easy to do without uglying up the edge.

To be continued....

Jerry
P. S.

I should say that from your description of trying to increase the under
correction the result is more correction farther out and none where you
wanted it, you have not realized yet (and I think I told you) if you push on
zone 4 you reduce correction from 3 to 4 and increase correction from 4 to
5. Not that you would want to do it now but if you wanted that 19% from zone
3 to 4 to get larger you would push on zone 3. When you do that correction 3
to 4 will increase and 1 to 2 will decrease.

Let me phrase that another way.. To increase the correction of a zone push
on the next zone inward. To decrease correction of a zone push it down, but
keep in mind that that will increase the correction to the next zone outward
from the one you push unless you push that one too.



-----Original Message-----
From: atm-bounces@atmlist.net [mailto:atm-bounces@atmlist.net] On Behalf Of
Norm Prince
Sent: Thursday, October 18, 2007 10:26 AM
To: atm@atmlist.net
Subject: [ATM] more trouble with figuring...

Howdie yall.

I thought I would be able to get along okay after absorbing all the q & a 
from resent discusions on the topic of figuring but i'm nearly at my wits 
end on this 12" project.

let me get some numbers out of the way

12.25" f/5 newt
full size lap w/gugolz #64
fixed source tester

mask as follows
zone1  0-2.155"
zone2  2.155-3.349"
zone3  3.349-4.218"
zone4  4.218-4.936"
zone5  4.936-5.563"
zone6  5.563-6.125"

Okay that said...here is a sample set of readings that is much like the last

many sets of readings i have taken with figuring sessions in between.

zone1  .2,.194,.189
zone2  .234,.245,.259
zone3  .29,.288,.291
zone4  .304,.291,.304
zone5  .351,.341,.356
zone6  .485,.513,.52

The way i see it, the upshot of numbers like that is...the edge zone is 
winding up a bit over corrected and zones 3-5 wind up way undercorrected.  I

was trying to get the undercorrected zones in shape by using short strokes 
with side swing and pressure over the undercorrected zones, but this is 
having little effect and is causing over correction in zone 2(???)...I tried

making the center deeper(the under correction in the 3-5 being relative), 
but that just lead to way too much movement of the knife edge over all 
center to edge, and zones 3-5 were still undercorrected ...uhg... I've been 
able to change this over all shape repeatedly, but whenever i get to trying 
to correct the new shape i wind up right back here with zone 4 and 5 just 
not cooperating....i definitely do not have a good feel for this figuring 
stuff.

So...any suggestions on stroke or course of action?  Short of polishing back

to sphere and starting the figuring proccess all over i got no more ideas.

any advice would be greatly appreciated...

Norm Prince 


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