Jay Pique writes:
Say you need a curved piece of wood 6" wide with an outside radius of
23 feet and it needs to include a cord length of 13 feet. How would
you do it? (No CNC allowed.)

See http://www.delorie.com/wood/chord-radius.html

R = 23
C = 6.5
RC = sqrt(R*R-C*C) = 22.0624
D = R - RC = 0.936

w = acos(RC/R) = 16.416 degrees

See http://www.delorie.com/wood/segturn.html

Say, five pieces, 22.5 to 23 feet (270 to 276 inches) at 33 degrees...

Radii: 270" (22' 6") - 276" (23')
Segments: 5
Width: 6 19/32"
Length: 31 27/32" (2' 7 27/32")
Total Length: 159 3/16" (13' 3 3/16")
Miter: 3.3 deg

To cut a 3.3 degree angle on a 1x8 (7.25" wide), offset one side's
mark by 7.25*tan(3.3) = 0.418 inches.

That gives you a blank the right size and approximate shape.

Now, get a 23 foot long string or wire (wire stretches less)...

You can approximate a circle using a bent batten; get one twice as
long as the "segments" and bend it so that it touches the middle of
each long edge of three adjacent segments, and trace only the middle.
Repeat for each segment.