I think neal's suggestion about your sagging 4x's would be your fastest, cheapest route. Personally I would stay away from running the 2x's perpendicular. Only because the 2x4's are just going to follow the the shape of the existing beams ,and depending on how bad they are sagging this could...
Correct me if I'm wrong , but i think what bridge man is referring to is taking a string and attaching it at two points and letting it hang in the center.
Trace the string carefully with a pencil . For example, lets say your arch is to be 6 foot wide, 6 inches high . You would do...