Trammel is by far the quickest and most accurate method up to about 20'R. I dedicate a long stiff, lightweight board specifically for this use. setting trammels to radius takes only a minute, finding the center takes a couple of minutes, and then you just swing the arc. Dead simple, fast, and perfectly accurate. It really takes two people to hold the trammel arm over about 15', though.
A tape measure can be used as a trammel as well with pretty decent results. Just drive a 16d nail at the center and hook your tape on it, hold the pencil at your radius and swing it. to be honest, that's how I'd do it in this case.
bmike's way is a good alternative if you can use a drafting program.
And if neither of those options are available, here's a tried and true method I've used. You need to be able to calculate the rise of an arc given the radius and the chord length. You can do that with a construction master calculator (the pro version) or alternatively, there are several online circle calculators that will do it. (here's one
http://www.handymath.com/cgi-bin/arc18.cgi?submit=Entry )
Let's assume the finished timber is 10' long (and the curve runs all the way to the end and starts at the very edge of the stick. Using 20' as the raduis, find the rise of the arc in that distance. (7 5/8") So at 5' from each end, square up that distance and mark your centerpoint.
Now, measure between the end point and the center point (5' 9 - 15/32" is what i calculate). use that as your new chord length to calculate a new rise in that distance. I come up with 2-17/32". Snap a line through one of the end points and the centerpoint and find the center of this line. at that point, square over your 2-17/32" and mark a new point. repeat until you have enough points to get the accuracy you need. And then lay it all out on the other end of the stick.
Hope this is clear, I'm out of time.