Step 1
Frame the dormer up to the top plates. Cut two arch shapes out of 3/4-inch plywood. The arches should be at least 6 inches wide. Glue and screw together the two arches. Cut a notch at the peak of the completed arch. This will form one rafter for the barrel roof. Make enough rafters to stretch from one end of the barrel roof to the other. Rafters should be laid out 16 inches apart.
Step 2
Install the rafters on the top plates of the dormer. Cut a ridge to the correct length and lay it in the notches at the top of the rafters. Cut a length of wood long enough to run from one of the ridges across three of the rafters. This will be used as a straightedge. Mark the straightedge in 16-inch increments, corresponding to the placement of the rafters. Staple rosin paper to the roof sheathing beside the ridge. This will form a pattern to make valley boards for the rafters.
Step 3
Tape a level to the straightedge. Tape a pencil to one end of the straightedge, making sure that it lies perpendicular to the level. Run the straightedge over the outside of each rafter, letting the pencil trace the shape on the rosin paper. Repeat this procedure on the inside of each rafter.
Step 4
Remove the rosin paper. Place the rosin paper on 3/4-inch plywood, and use it as a pattern to cut curved valley boards. Glue the valley boards to the main roof sheathing and tie down with crews. Place the straightedge on the last rafter. Line up the first mark with the rafter. Slide it down until it contacts the valley board. Measure from the bottom of the straightedge to the top dormer plate. Use this measurement to mark distance on the each leg of the rafters. Draw a straight line between the two marks. Make a pitch cut along each of these lines. Install the rafters. Curved sheathing made of two to three layers of 1/4-inch plywood can now be attached.