Using a ballistic coefficient of 0.145 for the Burton ball and the calculator here I've calculated the ballistic arcs of the 0.58 Springfield rifle-musket.
Figure 1: Springfield with sights set at 100, 300 and 500 yards. -60 inches is the approximate ground level (edit: as Fred points out below, there was no real "zeroing" of the weapons, and is sloppy nomenclature on my part).
The purple line is 12 inches above the bore and the turcoise line at -60 inches is approximately the ground. When the arc is between these two lines it may hit a target.
The default 100 yard sight setting means that the bullet describes a single dangerous space out to roughly 200 yards (assuming the musket is approximately 5 feet above the ground, i.e. shoulder height, if the shooter is prone the bullet strikes the ground roughly at 120 yards). Set at 300 yards we get the pattern described in Fred Ray's recent blog post. At 500 yards setting the round is out of the dangerous space around 10 yards into flight, and comes down on a step plunging trajectory with a very small dangerous space of about 50 yards. As an aside, these arcs are not symmetrical, the round is accelerating towards the ground in them.
If we make a comparison with the smoothbore musket then we find that if both are zeroed at 100 yards there is no significant difference, both are still in the dangerous space out to about 200 yards. The superior muzzle velocity of the smoothbore beats the superior ballistic coefficient of the rifle.
Figure 2: Comparison of M1861 rifle musket and M1842 smoothbore musket
This of course ignores the fact that the rifle bullet will disperse less and is effected by wind only around a third of the ball. For firing at picked targets on the skirmish line the rifle will be better at 200 yards. If firing at a massed target (i.e. a battleline) there is essentially no difference. At around 100 yards there is little discernable difference in whether or not the target is hit.
Assuming the following minutes of arc, figure 3 shows the chances of hitting a 2 foot circular target (roughly a torso) for various weapons:
M1861 Springfield rifle-musket: 10.5 MOA
M1842 Springfield percussion musket: 24 MOA (edit: this may have been a patched ball)
P1853 Enfield rifle-musket: 7.5 MOA
British Baker Rifle (Napoleonic weapon): 18 MOA
French Charville Musket (Napoleonic weapon): 36 MOA
Figure 3: Chance of hitting a 2 foot target. "Effective range" was reckoned on the 20% hit line.
This shows that, ignoring the problem of rangefinding and wind effects, the Springfield had 3.5x the range of an old flintlock, and twice the range of the percussion musket it replaced. It also shows that the Confederate were right that the Enfield was a far more accurate weapon. In fact this accuracy was never achieved for the Springfield due to concerns over loading; after only a few rounds the barrel would become so clogged that the .58 bullet could not be loaded, the Ordnance bureau started supplying the 0.57 bullet for the Enfield as standard, which increased windage (and ease of loading) at the expense of accuracy.
Figures 1 and 3 must be considered together, and can be summed (which I won't do here as it is a lot of work). Firing at a target 225 yards away with a Springfield is difficult, you must set your sights at 300 yards, then aim below the targets feet, awkward when poorly trained soldiers naturally shoot high. The solution adopted for the line infantry of the US, CS and also most of continental Europe was to set sights at 100 yards, and only shoot at 150 yards or less. Sharpshooters, jaegars, chasseurs and other specialist troops would be trained in the full use of sights and long range shooting. Only the British would stick to training their line infantry to shoot at long ranges.
