A 9:12 barrel vault truss with a 16' wide barrel:
The design of this type of truss is controlled by the following parameters:
1.) Out-to-out span
2.) Top chord pitch
3.) Barrel vault width
4.) Barrel vault radius
Assuming a typical web configuration as shown above the truss design is really only dependent on these four inputs. Minor details with regards to member depths, overhangs and ply thickness also factor in as well but don't really change much.
I can also see the possibility of running a raised heel variant but I don't know how common that would be.
Has anyone ever seen a gable end version of this truss type? My thinking is that it might make more sense to just use a common gable truss otherwise you would be looking at some very complicated wall framing below the truss.