Use a follow rest to get the barrel to its max diameter, full length. Then set the lathe for the taper. Then, If there is a lot of taper I will the step the barrel to rough diameter from the small to large diameter still using the steady in the center. Like Jim said, you can not use a follow rest on a taper without special equipment. Then start the taper with the steady supporting as needed, usually the center. Last pass is full length, without steady and a light cut. Might sound crazy, but on that last pass lay a piece of wood or just grab the barrel with an oily hand which will change the barrel harmonics and help with chatter.
Just as important as work holding is the tooling. Generally on a manual lathe doing this type of work you can not use carbide insert type tooling. They are not sharp enough and the nose has too much radius. I used brazed carbide tools that are manually sharpened, to very sharp. You do need special grinding wheels to grinding carbide, I use diamond. The idea is to keep the tool load at a minimum so the setup must be rigid, tool holders place properly, rake and cutting angles correct. My word of warning would be to stop immediately once chatter starts. If you continue it just get much harder to correct. I would also setup a test run, 15 inches or so to play with, before starting the barrel. This is not hard, just get the proper setup and take your time. I usually start with barrel blanks and take several hour profiling a barrel. It like watching grass grow!
Bob
