Keepsake Box Step by step
I made this arch top Keepsake Box using about 5 or 6 beveled boards, gluing them together in segments and then in a final glue up. Lot of planing on the "convex" top side and lots of scraping and sanding on the "convex" bottom surface.
I beveled the board on the jointer, setting the fence over at an angle.... pretty much eyeball guessing what it was, no math involved. A table saw would have worked just as well, maybe better. I don't remember if this curve is a true radius or just a pleasing curve which may not be consistent all across creating "math" issues to compensate. If it's a true radius, that makes it a lot easier. If you are dealing with a semi-circular form like a mailbox roof, your chord is also the interior diameter/outside of the box, plus a little extra for clearance.
Layout your semi-circle and strike lines to the center point giving you the angles, depending on the number of segments ...
180 divided by 8 segments is 22.5 degrees, a good place to start. 10 segments is 18 degrees. etc.
The bottom boards do not get beveled and are 90 degrees to connect to the sides.
You might be able to use the mail box itself as a clamping form, using bicycle inner tubes or small strap clamps. Just put a thin layer of strips to space off your wood leaving the gap needed.