Re: ATM Question re: How long a figuring session

["Bill T." <twentiethwave@hotmail.com>]

Ken,

FWIW, I cranked your mirror and tool parameters in the Gort program, 10.5"
tool on a 21" mirror.  After some fiddling around, it appears that a very
simple stroke might be able to figure that mirror neat and sweet.

Here are some diagrams.  The mirror outline is black, the 70% zone is
violet, the tool and its path are white.  The yellow graph is the
"displacement curve" due the current figuring step -- the initial curve is
taken to be a straight line at the top of the graph.

Here's the overall path, with the tool at its lower right excursion.  The
line is "drawn" by the center of the tool.  Note that the path strongly
favors the center of the mirror, and that the end point of travel straddle
the 70% zone:

http://www.kupercontrols.com/misc/lowright.jpg

Here's the mirror at its bottom-most excursion:

http://www.kupercontrols.com/misc/lowcenter.jpg

Here the effective surface coverage:

http://www.kupercontrols.com/misc/coverage.jpg

It is assumed the tool is moving somewhere in the range of 1 to 4 inches per
second, is well pressed, and is tapered something like this:

http://www.kupercontrols.com/misc/figurelap1.jpg

It is also assumed that the pattern W being rotated approximately 5 degrees
during the course of each pattern.

The extreme overhang at the upper and lower center positions risks a turned
edge, although it is safest to do in this location where the lap is coming
straight off the mirror edge.  Note that the "lower right" overhang is much
less.  Initially the overhangs might want to be a less extreme, until the
edge starts to let us know what it really wants to do.

Of course the initial curve on the mirror must be smooth and regular.  The
stroke can be temporarily widened or narrowed as needed to selectively take
down the edges or the center, but persistently getting too far away from the
"ideal" stroke will also create a pan, or a hill, or both in the center of
the mirror.

Based on my experiences with laps around 8 to 10" on 20" mirrors, I have
fair confidence in that beautiful "displacement curve" at the bottom could
be the result -- that kind of curve smells like a parabola, every time.

However, the usual caveat has never applied more:  "Works for me, might not
won't work for you!" ;^)

I any case, I feel this would a better approach that the strict "one side
only" offset linear stroke we talked about earlier.  The result would at
least be a lot smoother, IMHO.

Bill Tondreau