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The tests I wrote of were done with some of the crappiest powder of the late 20th century, but still the velocities were in a 25 fps window with each. I was just hitting the PODR with those powders in that old Dickert. From a prone position, shooting in the early morning calm just after sunrise, I could keep 10 shots in a group about 4-5" high and about 8-9" wide (there's never no wind). And that was with a 200 year old rifle, with sights that I struggled with.I am also building a muzzle loader bullet rifle, a 45 with vernier sights. It is primarily for hunting but since I now have access to a 300 yard range I will sight it in to that range and see what I can do. The one variable no one seems to mention is the quality of the powder 250 years ago. I have in the past shot 5 shot 1 inch groups at 100 yards. but not having access to a range over 100 yards was unable to try longer ranges. I do believe given the powder available today with good sights it is possible to shoot a tight group with a patched round ball at 200 yards. Doubt that a round ball would be very deadly at that range though.
In my .54 flinter, I could get another 100 fps using the first lot of Swiss to hit the US. Using that rifle and load, with sights were set up for my eyes, group sizes shot prone at 200 yards were about 3" high and 7" wide. Significant, but not a major improvement.
Don't bet on a round ball not being deadly at 200 yards, or even 400. At 200 yards, that load in the Dickert would shoot almost through the chest of a buck mule deer. At 400 yards the ball would travel through about 2" of seasoned white pine. (Yes, I literally shot at the broad side of a barn. In my defense, I usually hit it! The barn was slated for destruction, so the owner let me use it for a backstop for some experiments.)