Kevin Miller wrote:
The usual way to do segmented turnings is to cut trapezoids and glue
them up in a ring then stack the rings up to make the vessel.
Typically, one cuts the same angle at both ends of the segment.

When doing reverse segments, one cuts one end to the appropriate angle,
and leaves the other end at 90 degrees. The angled edge of the segment
is oriented outwards rather than inwards. See my facebook post for an
example of a ring being glued up:
https://www.facebook.com/media/set/?...l=f 7a342b1e7

When cutting normal segments, one sizes them for a given outside and
inside diameter. There's lots of segment calculators on the web that
will give you the width of the board to use, and the length of each
segment. However I can't find any calculators that will determine the
dimensions for a reverse segment except I have a spreadsheet that
calculates the width and length for an eight sided ring using the
following formula:

OR = outside radius
IR = inside radius

Width = OR - (.924* IR)
Length = (.541*IR+Width)/.707

The segment length seems to come out a little long but that gives some
fudge factor so that's fine.

What I'm looking for is the formula to enter the number of segments, the
inside and outside diameter and for it to calculate the length of the
long edge of the segment. Any math whiz out there that can clue me in?

Thanks...

No math whizard here. Looks like the setup you show in the picture
would give all end grain showing, if that is any factor.

--
Gerald Ross

Everyone must row with the oars he has.