I use Google sketchup. Draw the arc you want with the right dimensions. Then measure the height from the basr every 3". Transfer that layout to your plywood and connect the dots. I just used that method on a 14' and a 19' eyebrow arch. Much smoother than freehanding or trying to guess at it. You do eyebrows and ellipses by stretching a circle.
The string method works, but not really well on larger arches past 6 feet or so, the string has too much stretch to be consistent in my experience.