Arcs, tangents, degrees, rays, minutes, arctangents, radians. Like Jughead I don’t know anything about this stuff, but that is probably unfair to Jughead. So here’s what I’ve learned so far.
The two main considerations are whether the width of the arch rail will be the same as the stiles, and the degree or diameter or curve of the arch. The minimum curve diameter that is flush with the outside dimension is the width of the gate itself. This also produces the sharpest or steepest angle. A broader curve that is less steep is just a section of a larger diameter circle. More than anyone ever wants to know, but I do not really notice things until I try to design and build them.
There are a couple of techniques to scribe a curve. You can bend a thin piece of material to form a curve or cut a pattern with a tramel or circle jig. I used the bending and pattern/template technique that David Marks used but will probably use a tramel arm on a router to make the actual cut.
I used a Mortise Pal jig (see review) to cut matching 4”x 3/4” mortises to attached the pieces with a loose tenon.
And used the cutoffs to help clamp the pieces. Pictured here with the bottom rail that has been cut to final width.
-- tim hill www.newcalshop.com