Those Rainbow Trajectories

Commentators on the rifle musket have made much of its so-called “rainbow” trajectory that made the rifle ball travel in a much higher arc than than today’s rifles due to its slow muzzle velocity. However, a lot of misunderstandings have also crept in. Most pundits seem to have looked at the illustration in Jack Coggins’ Arms and Equipment of the Civil War, shown below (click on either for a larger view):

Now Jack Coggins knew a lot about arms, and must have known that this was somewhat misleading. It shows a kneeling soldier with a rifle musket, the sight set on 300 yards. The bullet describes a perfect arc and will fly over an enemy’s head except during the first 75 yards or so and another 110 yards centering around 300 yards, where the sight is set.

There are two main problems here. One is that in the real world the bullet does not describe an arc—the muzzle energy drives the bullet forward on a more nearly horizontal path for the first third of its trajectory, which means it does not rise nearly as much as shown here. As the bullet loses energy, however, air resistance begins to take over and once it passes its apogee it begins to drop more and more steeply. The arc, then, is skewed toward the back part of the trajectory, as shown in this comparison of the .45-70 (very similar to the .58 cal. Minie ball) and the modern .308 round.

Even this is a bit misleading, since both rifles are shown being fired at an angle that will send the bullet to its maximum range, which would not be how a soldier on the battlefield would do it. As we saw in a previous post of engagement frequencies, most shots would be at targets 1-300 yards away, and the vast majority at 100 yards and under.

The second problem with the Coggins illustration is that it invites the reader to assume that a soldier set his sights to 300 yards and left them there. Green soldiers may well have done this but a veteran would adjust his sights as his enemy neared. Most used a battle sight setting such as the one shown in the Enfield below.

The sight (withe blade laid down on the ramp) could quickly be set on 100 yards (the default), 200, 300, and 400 yards, but many soldiers seem to have kept the default setting and added “Kentucky windage” (i.e. aiming high) as required. How did this work in practice? Joe Bilby observed:

Civil war soldiers seldom shot at each other at the long range capabilities of their small arms. My estimation of engagement ranges at Gettysburg, using markers and a modern digital range finder, suggests that 200 yards was the usual distance that troops began to shoot at advancing opponents (actually a greater distance than Griffith’s original mid-war estimates), and the available primary sources reinforce that conclusion.  A “center hold” using the 100 yard sight setting on a man sized target with a .58 caliber Springfield rifle-musket will hit it somewhere at a range up to 200 yards.

The greater the range, however, the more problematic the hit probability, as air resistance quickly slowed the bullet leading to a steep drop at longer ranges. Given these constraints and the small basic load (40-60 rounds), commanders often felt it better to let the enemy approach more closely than their weapons were capable of firing. Engagements at 200 yards and under, however, required little in the way of sight adjustment or range estimation, making them more suitable for the bulk of the soldiery.

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4 responses to “Those Rainbow Trajectories”

  1. Dan Avatar

    My big question with this is probably the unanswerable one: what evidence do we have that any considerable percentage of soldiers, outside of sharpshooters, actually adjusted their sights? Are there references in letters or memoirs?

    Just curious.

  2. Bryn Avatar


    I just read this, had a think, managed to acquire the necessary ballistic coefficient and have calculated the drop etc.

    I’ve posted it to my blog:


  3. […] is a Pic Bullet path drawing __________________ "Government is not a solution to our problem, government is the […]

  4. […] If you want a look at the trajectories and the Enfield battle sight (the Springfield was similar) I did a previous post about it. […]

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