Wednesday, September 23, 2009

The general-purpose rifle - Trajectory

This article is the second in a series about the general-purpose rifle. The first is here.

The 101 on practical ballistics

In order to have a meaningful discussion on cartridge selection and sighting, one must understand a few things about basic external ballistics. Here, we are going to focus on the things you need to know to make reasonable comparisons about satisfying our two primary criteria, potential target size (on occasion up to 1,000 pounds) and possible engagement distance (up to 300 yards of working range). Those who wish to can get a whole lot more technical than that (a quick peek here gives you an idea), but this quickly moves into the realm of specialty. For the basics, rocket science is definitely not required--just a little attention to detail.


We take as a given that when a shot is fired, the component of the cartridge that we call the bullet is propelled (accelerated) by the powder charge down the barrel, and exits into free air with an initial velocity that we can measure with a chronograph. Once in free flight, the bullet is subject to two major forces that we care about, and a myriad of more minor influences that we essentially ignore for the purposes of relative comparison. (We take as a given that these minor influences are either less significant than our own ability to hold accurately, or that they affect compared scenarios in so identical a fashion as to be considered of negligible comparative value.) The two forces we care about are wind resistance (drag), which is determined by the shape of the bullet, and gravity, which is constant. These, along with the initial velocity of the bullet, can be used to calculate the bullet's trajectory, or flight arc, to a degree of accuracy suitable for general-purpose shooting. This arc has the shape of a vertical parabola, and it is useful to the rifleman because it tells us where that bullet is going to be at given points along its flight path. We use the information in this curve to regulate our sights for a maximum "point-blank" range, within which we can essentially ignore the curve while aiming.

Maximum point-blank range (MPBR)

Visualizing a parabola, it is easy to see how one might just fire the bullet parallel to the ground, and simply measure the amount of drop at various ranges, as the effect of gravity pulls the bullet to the ground. The tricky part is that at longer ranges, the amount of drop for another increment of distance becomes significant: that is, the amount of drop from 25 to 50 yards may be negligible, but the amount of drop between 325 and 350 yards may well be a very big deal. At sufficiently long distances, the problem becomes not so much how much you need to over-hold, but how accurate is your assessment of the distance to the target. For the hunter, misjudging a 350-yard shot as a 325-yard one (and that's easy to do) might make the difference between a good hit in a deer's vital zone after breaking the shoulder, and one that hits below the vital zone, crippling the foreleg. This is not ethically acceptable!

So, we decide for ourselves the maximum distance from our exact point of aim that we are willing to let shots drift due to trajectory, and then regulate our sights so that the shot's arc stays within that tolerance for the maximum possible "point-blank" distance to target. The barrel is actually elevated slightly, such that the shot actually begins under the true line of sight, traveling upwards for a distance to our selected maximum ordinate (this would be the apex of the parabola) and only after that actually begins to drop relative to the line of sight. What we would look for is a trajectory that allows a maximum point-blank range as close as possible to our working maximum range--where only at the outside edge of our ability to place the shot, do we need to worry consciously about over-hold. (This is a compromise that we'll talk about more in a future section about selecting an appropriate cartridge.)

As a very relevant example, consider a 150-grain pointed "spitzer" bullet fired from a .308 Winchester cartridge with an initial velocity of 2,700 feet per second (fps). (This is a splendid choice for a general-purpose rifle.) Using the online ballistic calculator at JBM Ballistics, and having it calculate based upon a maximum ordinate ("Vital Zone Radius" in the form's inputs) of 3 inches (implying a target size of 6 inches), this shot will have a maximum point-blank range of about 225 yards. The numbers come out roughly like this:

The maximum ordinate occurs above the true line of sight at about 128 yards, and again below the line of sight at 226 yards. This means that from the muzzle all the way out to 226 yards, we can hold in the exact center of our target and expect the bullet to hit within three inches of that point of aim, and this frees us up to focus on the nontrivial problem of our ability to hold accurately under varying conditions. In short, MPBR is a practical way to make trajectory considerations as trivial as possible at common engagement ranges. Only at ranges that are way out there, does one need to start consciously compensating for drop.

Incidentally, note the dramatic difference when we change the maximum ordinate to four inches, implying an 8-inch target size. MPBR is recalculated to 297 yards, with the "midrange trajectory" (maximum positive ordinate) at 141 yards. The table recalculates thus:

That is certainly significant--the MPBR with a four-inch ordinate is almost exactly the same as our maximum working distance. Is this then better than using the three-inch ordinate? This will depend on your preferences. The penalty you pay with a larger maximum ordinate is that you may have more occasion to under-hold at common shorter distances for precision shots, and that begins to defeat the purpose of zeroing the rifle at a maximum point-blank range.

Which is a nice segue into the key wrap-up thought about trajectory. Do not let the mathematical, theoretical aspect of all this become it's own raison d'etre. We look at MPBR as a rough comparator of trajectory between different cartridges, or different loadings within the same cartridge. (This will start to make more "real-world" sense as we discuss comparisons between cartridges.) Once you have settled on a cartridge and a loading, and have zeroed your rifle the way you want it, you should shift your focus to confirming for yourself, off a bench rest at known distances, just exactly what your shots are doing at those ranges. Historically, published ballistics for factory-loaded cartridges can vary significantly due to very normal factors like temperature, variances in barrel length and other attributes of your particular rifle, etc. Do not trust the factory's published ballistics, which are often optimistic--see for yourself.

To recap: we care about trajectory because it represents a mapping of how we will aim at various points within our maximum working range (and it will also give us a guideline of what to expect if we must do something beyond that range). The ideal general-purpose rifle will fire a cartridge that gives us a trajectory that we can hit reliably with, out to the limits of our ability to hold accurately. As much as possible, the rifleman would like to make considerations of trajectory trivial enough to ignore--so he can focus all his energies on holding steady and minimizing his own "wobble zone". And so we use the concept of zeroing our sights to achieve a maximized point-blank range for a representative target size.

Next time...

The next article in this series will discuss the other primary use of comparative ballistics: the even less-exact science of assessing whether the bullet has enough power to accomplish its task--not at the muzzle, but out there where it actually hits the target.

Next article
Previous article

No comments: