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Calculating a radius

Q: I’m building a picket fence and want to swoop the tops of the pickets. I’d like to make a pattern so that I can trace the swoop on the pickets and cut them in place with a jigsaw, but I’m not sure how to calculate the radius of the curve. The fence posts are about 5 ft. apart, and I want the pickets at the posts to be 3 in. taller than the pickets in the middle. What’s the easiest way to accomplish this?

A: Assistant editor Daniel S. Morrison replies: The simplest way to create the swoop for your fence is to use a semirigid rod (1-in. PVC pipe works well, but a 1x3 would work, too) to scribe one section; then either make a template based on that section, or continue to use the rod for each section of fence. Make the rod about 1 ft. longer than the planned length of the curve. Drive a nail or screw at each end of the arc to rest the rod on. Tie a piece of string to the center of the rod, pull it down 3 in., then pencil the cutline on the pickets along the arc.

From Fine Homebuilding 165, pp. 106 September 1, 2004