Laying out a large curve with a cobbled-together, oversize compass is a pain in the neck. Instead I use a bowed slat that can be adjusted to any curve. I used to bend the slat with my hands and draw the curve with a pencil in my mouth. That didn't work very well! The solution came to me in the bathroom when I looked up and saw that little chain hanging from the ceiling light.
Here's what I did.: First I ripped a thin, 1/8" slat, 1-1/2" wide and 36" long. In the middle of each end I cut a 1/2" long slot on the bandsaw. I slipped in the end of a 40" long beaded chain (available at most hardware stores) through one slot. While holding the free end of the slat and pulling on the chain, I create a curve in the slat. Slipping the free end of the chain into the other slot locks the slat into the curve. By shortening or lengthening the chain I can make subtle changes in the curve.
Love it. Simple and cheap. One thing to remember though, is that a wood slat may or may not bend evenly. If you're after a curve, and not necessarily an exact radius, no problem. A variation on this is to create a slat that's tapered, to ensure that it doesn't bend evenly. This way you can create an interesting arc with a radius that becomes tighter or straighter over its length. Technically speaking, I think that's called a Euler spiral.