~  -----Original Message-----
~  From: owner-oldtools@l...
~  [mailto:owner-oldtools@l...]On Behalf Of
~  Tom Dugan
~  Sent: Friday, December 03, 1999 2:26 PM
~  To: oldtools@l...
~  Subject: re: maths and planing straight
~
~
~  [Long treatise on calculating the sagitta beneath a chord
~  snipped, sadly.]

Thanks for the word, Tom.

~  Second, the 'stute galoot will observe while planing that his
~  boards become crowned rather more than the calculations show.
~  As the plane approaches the end of the board it begins to
~  overhang, and the apparent length decreases until the mouth
~  reaches the end of the board. At this point, the iron is at the
~  very front of the apparent length and is taking a full depth
~  shaving. The reverse is happenening at the start of a stroke,
~  of course.

This suggests that, assuming that the plane is always trying to plane
a concave curve, that the chord of the arc progressively increases
from the start of the stroke and decreases towards the ends, ie the
radius (proportional to the square of the chord's length) is less at
each end, thus making the curve 'deeper' at each end.

Although the maths relevance is distinctly galoot, there is a
practical value to the information since if one starts planing at the
mid-area of a surface/edge until the plane will not cut any more, one
knows that that section of the the surface is not convex (ie, tha's
taken 't bumps aht). Subsequently, one increases the length of the
stroke until it is working full-length. If the job involves glueing
two surfaces together, concave surfaces can be desirable, of course.

Naturally, if one wants a dead straight/flat surface, one then has to
start snipping the ends a bit.

Jeff