I have measured button rifled, TC's at .0015" depth to .004" in just 3 guns - Friend Tom's, Taylor's and mine. Taylor's was .003", mine .004". I would call all of those shallow for around ball gun.
All 3 of them were .50's. Tom's and Taylor's rifles shot best with 370gr. lead bullets, while mine shot just fine with round ball - .495" AND a .022" Denim patch yes. Tom had to paper patch the first couple maxi-balls with cigarette paper so they wouldn't slide out the bore if he tipped the muzzle down while walking. In my rifle and load, the round ball became elongated somewhat but it shot very well - with 80gr. to 100gr. of 2F- groups at 50 yards were usually one, but a fairly large hole - perhaps 1 1/2" on centres most of the time - so, they will shoot most of the time, but require a tight load.
One thing about them, the barrels were made out of something between peanut butter and real steel (real scientific, I know). Taylor and I were at a gun club and a fellow couldn't get the load I suggested he use, started in his .50 TC. He was trying to load a good combination in a factory lathe-cut crown - won't work, too sharp, the corners. I re-cut the muzzle's angles with my pocket knife, then a slip of emery from my possible's bag, I re-crowned the muzzle & the fellow could then load the tight combination. That was in the early 70's. Maybe they make them out of steel now, I don't know, don't care much, either.
My Pedersoli Kodiak .58 had .007" or .008" rifling. I never thought of it being 'shallow'. That DR shot well at 50 yards with 82gr. 2F, each barrel making 1" groups for 5 shots, but they were not very close together, crossing (left shooting right & low, right shooting left & high) by 2 1/2"wide and 5" vertical dispersion. With 100gr. 2F, the rifle would make a round 1 1/2" group for 4 shots, 2 from each barrel. With 110gr. 2F, the groups were parallel, that is, each barrel shot it's group about 1" apart centred from the other barrel's group, thus groups side by side.
The groups would be 2" to 2 1/2" wide on centre to centre. For a DR, that's about perfect regulation, as the barrels shoot "centre" at all ranges, never converging, nor diverging. While I did test with the same patches and a .562" ball, I preferred those patches and the slightly more accurate .574" DEAD SOFT lead ball - I prefer to call it PURE lead, but some meticulous people say it isn't pure as it has up to 1% to 2% foreign metals included, so it isn't "pure" oh well. I also loaded it most of the time with the rifle's little 3/8" hickory rod.
