I have been seeing comments about radial vs parabolic vs eliptical
facings. For clarinet facings at least there is very, very little
difference between the three. For example, using a typical tip opening
of 110 (that's 1.10 mm = 0.04331 inches) and a facing length of 20mm
(thats a scale reading of 40, or 0.7874 inches), the feeler gage scale
readings would be as follows. This is a facing with a 7.18 inch radius
(for the circular curve).

          <<<<<<<<<<< SCALE READINGS >>>>>>>>>>>> 
Gage      Circle    Parabola  Ellipse(2:1 aspect ratio)
------    ------    --------  -------------------------
0.0015    32.54      32.56       32.55
0.010     20.76      20.78       20.77
0.024     10.20      10.22       10.22
0.034      4.55       4.56        4.55

This shows that the differences mighty small. 

From my experience grinding telescope mirrors, the difference between
circle and parabolic curves is ignored for mirrors with a high f
number (f = focal length divided by diameter). You can see why from
the above table because, in this case, the f number for the circular
curve would be the radius of the circle divided by the length of the
facing, which gives a f number over 9, which is high.

The maximum deviation between the three curves shown above is only
0.02 scale unit which is about 0.0004 inches. I bet that's on the same
order of magnitude as the thermal expansion of the mouthpiece as it
warms up.

Does anyone have a feeling about differences of 4/1000 inch? Do they
actually make a significant difference, as long as the facing is a
smooth arc with no flat spots?

If anyone wants to see the spreadsheet that calculates these facing
readings for each type of curve (circle, parabola and ellipse), let me
know and I'll upload it.

- B Smith -

Good stuff Brent.  It is not significant for clarinet curves since the tip
openings are small and the facing lengths are short.  But I think clarinet
facers exagerate the parabolic curve.  It probably is closer to a higher
power, but they are just guestimating a curve that flattens out near the
tip.

Now for a sax, you can find some elliptical curves but the axis is reversed
from what you calculated.  They are flatter near the table and more curved
near the tip.  The major axis can be 4-5X the minor axis.  I've seen some
8-9X but they play with too much resistance.

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