A musket is not an accurate weapon. That’s a well known fact. But, why is it inaccurate and what can we learn from its shortcoming we can apply to studies of the Revolutionary War battlefield.
There are innumerable variables concerning the musket. To keep this analysis simple most of the variables will be ignored (things such as temperature, humidity, elevation above sea level, variances in quality of the gunpowder, uniformity of the roundball itself, the size of the ball vs. size of the interior of the barrel, etc.).
Basically a musket is a smoothbore weapon much like a 12 gauge shotgun. My test weapon is a standard .75 caliber Brown Bess replica (I wouldn’t shoot an original and nobody else should either). I shoot it with a .69 inch roundball which weighs 476 grains, or one ounce, loaded from a paper cartridge. The velocity of the roundball varies depending on the amount of powder used and how much fouling is in the barrel. But, for our purposes we’ll use the average of 1000 feet per second (fps).
The best target rifle in the world is not accurate if it has poor sights. The Brown Bess, Charleville and other muskets of the period have no sights at all. The Brown Bess does have a bayonet lug to secure the bayonet. The bayonet lug is not an ideal sight but it is on the top of the barrel; so we will consider that a front sight.
Normally, the shooter would look down the barrel and align his rear sight (the sight closest to his face) with the front sight and with the target. This cannot be done with the musket since there is no rear sight. Without a rear sight the shooter’s eyeball acts as the rear sight. That would not be a problem if the eyeball could always be placed exactly in the same place each time the musket was fired. But, it cannot be done.
No matter how carefully the shooter places his cheek to the stock his eyeball will not be in the exact place each time. And here small variances make a big difference. All things being equal if the eyeball is placed a mere 1/4 inch above, below, left or right of the ideal sighting position the impact of the roundball will be over 9 inches off the desired point of impact at a target only 50 yards away. In the heat, chaos, and stress of battle, the shooter’s eyeball may be far more than 1/4 inch from the ideal position.
The musket itself is not accurate for a variety of reasons. One reason is the aerodynamics of the big roundball itself. When it leaves the muzzle of the musket at a velocity of 1000 fps it immediately begins to drop due to the force of gravity. At 25 yards it drops only one inch but at 50 yards it drops over 4 inches. At 75 yards it drops 10 inches and at 100 yards it drops over 18 inches. For a target at 125 yards the roundball drops 30 inches. These, of course, would be the figures if the musket could be properly aimed with sights – which as we have seen it is impossible as it has no sights.
Another major problem with accuracy is the soldier himself. To fire at leisure on the target range is one thing. To face an enemy very likely within 100 yards, and perhaps much closer, would be a very different situation. The concussion of the soldier firing on the side of our soldier would certainly interfere with his shooting skills. And, those skills may have been minimal in the first place as live fire practice was not a continuous drill.
Today we think of the infantryman using his rifle, and in a worst case scenario, falling back on his bayonet as a last resort. However, in the 18th century the musket was used to pave the way for the use of the bayonet. It was the bayonet that was the real primary weapon. As it has been said, the musket is a good handle for the bayonet. There’s a lot of truth to that statement.
 To load the musket the soldier would take the paper cartridge consisting of the roundball and powder out of his cartridge box and bite off the powder filled end of the cartridge. He would then put a small amount of powder in the pan where the flint lock, when fired, will cause it to flash and ignite the main charge inside the barrel. The rest of the powder the soldier would pour down the barrel and then push the ball and the paper of the cartridge down the barrel with his ramrod. The paper would keep the ball from rolling out of the barrel and also provide a seal between the ball and the walls of the interior of the barrel.
 The calculation is: the sight radius (eyeball to front sight in inches) X the error (in inches) divided by the distance to target (inches) = the correction, or 48 inches X 9.3 inches divided by 1800 inches = 1/4 inch.