I like using curves that are not a portion of a circle, but more akin to a parabolic curve. While I've got lots of old elliptical templates around left from previous projects that I can use a portion of, sometimes I'll need something I can't find anything appropriate for.
Everybody knows how to bend a batten, using nails or weights to hold it while marking the edge with a pencil. Taking that idea further, all one needs to do is make the batten tapered, which allows it to bend more easily on the thin end than on the thick. This gives a nice changing curve when compress end to end, as long as the grain is straight. Adjustments are easily made by thinning one end or the other with a block plane.
Keep in mind that when bending wood, the curve never goes all the way from end to end. I think 8 times the thickness is the general rule for minimum straight on each end, so always try to have some extra length beyond what you need to work with.
I'm pretty good at free-hand drawing what I'm after, but I once really struggled finding a FAIR curve, and this little trick is so easy