Wednesday, September 23, 2009

The general-purpose rifle - Power

This article is the third in a series about the general-purpose rifle. The first, here, introduces what we mean by general-purpose rifle, and the second, here, discusses trajectory.

Practical ballistics 102: the difficulty of representing power

One would think that the concept of power would be reasonably straightforward, and comparative discussion would be easy. After all, there is a physical definition and units of measure. Crunch numbers, compare one load to another, and you've got an answer, right?

Ha! That's funny.

There are several reasons why measuring this is difficult, starting right up there with what people mean when they use the word power--which probably isn't the best word to use to begin with. What most people really want a measure of is how effective the projectile is at accomplishing its task, out there at the point when it strikes its target. And just what is that task? That is likely to be different for different people, different targets, different circumstances... Is your goal to kill, or to stop an attack? Is the target a living, sentient thing, whose response to being hit can vary almost without limit, or is it a mechanical vehicle which needs temporary or permanent disabling? ...

It becomes obvious pretty quickly that everything that might be useful as a controlling attribute, is in fact highly variable, and you are essentially working within chaos. Welcome to the world of the independent generalist. (There is a liberty lesson in that too, by the way.) In considering general-purpose riflery, what we are interested in are the broad strokes--those things that hold the truest across the most possible scenarios. We make our choices with these considerations in mind and understand that there will be times when we have "power" to spare, and other times when we will really be stretching the limits of what a rifle bullet can do.

Measurable factors

For all the variability, most of us speak in terms of the things we can measure and compare, and useful comparisons can be made from observing the following measurable factors:
  • Impact velocity (which will always be lower than initial velocity)
  • General shape and construction of the bullet
  • Mass of the bullet
People have come up with numerous ways of putting these values together to evaluate one cartridge or load against another, and although they are all too simplistic to predict real life, a few of them do have enough of a documented "actuals" record (a load of known measurables and an accurate description of what happened) to be useful to the generalist. If you'll bear with it, the following may prove helpful:


Certainly the most popular comparative device is to calculate the simple kinetic energy that a bullet of a given weight generates when it hits a target at a given impact velocity. Mathematically, this is expressed as the bullet's mass times the square of its velocity, and typically is represented in the US with "foot-pound" units (loosely, one foot-pound is the amount of work required to move a weight of one pound a distance of one foot, and ten ft-lbs is the amount of work that will move ten pounds a distance of one foot). It is easy to calculate, and there are several widely-known "rules of thumb" that relate a given energy level to the capacity to quickly and humanely kill game animals of different sizes. The most common example is that a bullet that impacts with a kinetic energy of 1,000 ft-lbs or greater is considered suitable for taking deer-sized game animals.

The principal flaw with using energy as a means of comparison is that it weights velocity with two factors in the equation, while mass has only one. Just like the Mercator mapping projection is reasonably accurate at low latitudes and becomes increasingly distorted as latitude approaches 90 degrees, so energy can become deceiving by overstating the abilities of very small bullets at very high velocities, and by understating the abilities of very large bullets at low or moderate velocities. By way of a somewhat hyperbolic example, a simple energy comparison from JBM Ballistics shows that at an impact distance of 100 yards, a 55-grain bullet from a .223 carbine that left its muzzle at 3,300fps, generates 1,049ft-lb of energy, while a 400-grain bullet from a .45/70 rifle that left its muzzle at 1,300fps, generates 1,075ft-lb at the same distance. Energy alone would thus suggest that the .223 bullet is nearly as effective at that distance as the much larger .45/70 bullet. Is this true? Ooh, that depends. Is the target a 30lb coyote, a 200lb human attacker, or a 1,000lb brown bear? In the case of the small animal, the .223 may prove to be far more effective than the larger bore, which will probably poke right through and carry most of its inertia well downrange. For the human, the answer may swing either way, depending on lots of variable circumstances. The one thing that is for sure here is that if you poke a thousand-pound boar with a 55-grain .223 bullet, he will probably get really irritated at you, whereas a solid hit with a 400-grain .45/70 is as likely to stop him as anything you can lift to your shoulder. (The Examiner column actually had a bit of fun with a similar idea recently.)

Energy is useful, but it's not everything.


An even simpler calculation involves one factor each of mass and velocity: pure momentum. Most often this is not even expressed in units (such as pounds-per-second), but rather as a purely arbitrary number with its own assigned "scale" of effectiveness. In competitive shooting events momentum is often evaluated as a "power factor" to classify entrants into different categories, usually so that those firing "major" powered loads may be permitted marginally more peripheral hits than "minor" powered loads. As with energy, it is most accurate in the middle of the scale. The great value of momentum is that it is very easy to measure in the field: if your load knocks down this inelastic steel plate designed to fall to a "major" hit, you have "made major"; if it does not fall, you must compete in "minor" class.

Momentum disregards the magnifying effect of velocity in contributing to a phenomenon in living tissue called "hydrostatic shock", which is little-understood but certainly seems to be observable in some situations. Velocity is not everything, by any means, but there is clearly something to it, and in going from two factors of velocity to one in the equation, pure momentum may understate the real effectiveness, in living tissue, of a smaller, high-velocity bullet of appropriate construction. There are too many documented cases in which smaller bullets performed like bigger ones, to discount the idea that velocity does have some sort of magnifying effect.

Optimum Game Weight

If two factors of velocity and one of mass distorts the result grotesquely for fringe values, and one factor of each seems to completely ignore some sort of observable non-linear phenomenon, what about three factors of velocity and two of mass? This is the idea behind a measure called Optimum Game Weight, and while it too is not perfect, it seems to stack up much more accurately, across most of the spectrum, with the documented action record than either pure energy or pure momentum. Using the previous example of the 3,300fps, 55-grain .223 bullet (still traveling 2,931fps at 100yd) against the 1,300fps, 400-grain .45/70 bullet (retaining 1,100fps at 100yd), we find that the .223 is rated for an optimum target weight of 114lbs; that is probably a bit optimistic for "optimum" but it is now clearly distinct from the .45-caliber bullet, which rates at 320lbs on the scale. Now...hunters who know the .45/70 will note that this is still a gross under-representation of what the .45/70 is capable of; this scale still only considers mass and velocity, and just like velocity seems to have a magnifying effect on hydrostatic shock in targets of a certain size, other attributes such as bullet diameter also have a documentable effect that is completely ignored in simplistic calculations.

"In-between" as it may be, even OGW distorts at the margins and should be taken as a guideline, albeit an informative one. Fortunately for our purposes, it seems to be the most accurate in the middle of the scale, where most of our interest lies.

Other factors of interest

If you're getting the idea that all this is almost so variable as to be completely discounted, take heart. There is value in context, and you will notice that subsequent discussions of cartridge selection focus on the broad agreements that all these considerations seem to have in precisely the area we care about most: intermediate sized targets at intermediate ranges, with variability in both. Remember, we're generalists, not specialists.

That said, one can neatly round out the discussion of practical ballistics with a couple more observations of interest to all of the foregoing. Consider these notes to be "of interest" items to any cartridge, and to any measure of performance.

Velocity is evanescent. Consider the .30-06 Springfield cartridge, which is an outstanding choice for a general-purpose rifle. the "ought-six" can push a 150-grain bullet from its muzzle at about 2,900fps, and a 180-grain bullet at about 2,700fps, or 200fps slower. Assuming both those bullets are of the same basic design, the heavier bullet will have made up the starting gap of 200fps entirely by the time both have traveled 400 yards, and at the same speed, 180 grains will hit noticeably harder than 150 (just ask elk hunters). The reason this happens is both because the longer 180-grain bullet in the same caliber has a better coefficient of drag than the 150, and its increased mass contributes to retarding horizontal velocity loss as well. The point here is that sexy muzzle velocities do not always tell the downrange story, and in general you should think twice about trading bullet weight for muzzle velocity.

Consider the bullet's ability to penetrate. Some cartridges rely excessively on the effect of hydrostatic shock to perform their work, and while they may be dynamite on thin-skinned, small- to medium-sized living targets (which are most likely to respond to this effect), they may be completely unable to penetrate large, dense, thick-skinned animals with huge bones, or to disable a vehicle. Again using a somewhat hyperbolic example, the .223 carbine bullet (typically 55 grains in weight) may or may not have a devastating effect on an unarmored human target at close to moderate range, but it absolutely will not smash the block of a gasoline engine to disable a vehicle, nor will it penetrate reliably to the vitals of a thousand pound animal after hitting a massive shoulder bone it would be lucky to break at all. The .30-06, however, even in its "lightweight" 150-grain guise, can accomplish all of these tasks reliably--given bullets that hold together.

The ability to penetrate is affected by many things, including a useful property called sectional density that relates a bullet's diameter to its weight and length. Simply put, bullets of greater sectional density penetrate better, and it is generally a good idea to select bullets that are "long" for their caliber when you have a choice. Also, you want bullets that will hold together when they hit a living target. There is a surprising amount of technology that goes into the design of rifle bullets, and much of this effort has gone toward guaranteeing that a given bullet will both expand somewhat on contact (expansion increases the size of the wound channel, which can cause much more rapid incapacitation) and also penetrate adequately (if the bullet fragments, its penetrative ability decreases radically, and big-game hunters consider this a cardinal no-no).

Recoil. None of us yet have managed to subvert Newton's Third Law of Motion, and while much more is made of recoil than necessary, it is still a factor. In an ideal world, we would select a rifle which provided a laser-like trajectory to a half-mile distance and fire quarter-pound projectiles that would impact at 3,000fps at that distance...and that would recoil like a .22 rimfire. (Yeah, I'm full of the jokes today.)

Ain't gonna happen. The point here is that for general-purpose riflery, we will have to deal with at least a little recoil to get any sort of performance that satisfies all the core needs, but there is no need to put up with brutish hammering. There are plenty of suitable cartridges that provide ample "power" while recoiling very moderately, and which provide additional logistical advantages (availability, variety of loadings, compact size, expense) as well.

Going forward...


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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.

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The general-purpose rifle - Introduction

NOTE: This was originally published as an Anchorage Libertarian Examiner article, with the intent that follow-up topics would appear from time to time. During the writing of some of the follow-up topics, it grew reasonably obvious that there was more content there than probably made sense for that venue. As a consequence, full discussions will appear here, and future Examiner articles will link to these pages. The decision is somewhat arbitrary, but this seemed to make more sense given the purpose of this blog and the Examiner column.

Courtesy Oleg Volk, A Human Right
A lot of ink is out there praising the value of the rifle in the hands of sovereign individuals, without any specific reference made as to what kind of rifle that may be. In general, it is good that we stay away from technical discussions that might feed the ridiculous red-herring "this rifle good, that rifle baad" arguments that disarmers latch onto like flies on shite. However, not all liberty-lovers are riflemen, and sometimes questions come up concerning the topic of just what we mean when we discuss the rifle as a tool of the free man. It is a valid topic!

I certainly can't speak for all riflemen, and in fact do not presume to, but in the interest of getting good information out there, the following may prove useful either to someone who simply wants credible information for discussion, or who might actually be looking to become a rifleman.


My strongest influence, by far, is that of the late (and sorely missed) Jeff Cooper, known primarily for his development of the Modern Technique of the Pistol, but who also contributed incalculably to the technique of riflecraft as well. In the early 1980s, Cooper systematically took up this very question of what is a general-purpose rifle, and developed an actual rifle design to support this definition. His classic work The Art of the Rifle should be considered required reading for anyone interested in this topic.

Bear this influence in mind, and make whatever mental adjustments you deem necessary.

What might one call upon a rifle to do?

By general-purpose, we imply that a rifle might be called upon to do different things, and this seems rather obviously true. There are certainly a great many enjoyable sporting games that involve rifles, but as far as "serious purposes", a sovereign individual might employ a rifle to do the following:

  • Defend himself or others against human or animal attack
  • Secure meat for the table
  • Assert his self-sovereignty against outside claims

(Of interest: note that the first and last items do not necessarily even require that shots be fired...although they are rendered meaningless unless that capacity is present.)

A good rifle is uniquely capable of supporting all these tasks, none of which are trivial even on their own. Take the tasks together, and one begins to understand what a remarkable device a rifle really is. The variation in potential target size may be enormous, and the distance to engagement may range from arm's length to as far as an individual human can see.

This is the quintessential value of the rifle--it is a weapon capable of delivering an adequate blow on a suitable target, in time, at any range that the target may happen to be when it requires engagement.

All these terms are somewhat plastic, although the point is the same for any reasonable set of variations. The general purpose rifle is capable of doing anything that a rifle may be called upon to do, even if it may not do it better or even quite as well as a more specialized weapon. And so a fifteen-pound, four-and-a-half-foot long rifle with a thirty-six power riflescope, firing a cartridge that allows for a five hundred yard "point-blank" trajectory, may indeed be easier to hit with at a half-mile than a lightweight sporter...but it may prove completely useless in a whirl-and-fire situation at ten yards, and is certainly a chore to lug around all day. Likewise, an instrument such as the .30 M1 Carbine is just about as light and handy a shoulder weapon as can be had, but its trajectory can be limiting to a competent rifleman, and its power level can be uninspiring if the target is a large animal, or returning fire from a distance. The sort of rifle we discuss here is able to handle both of these situations very nearly as well as the more specialized arm; fortunately, there are a lot of rifles that fit this bill.

What a general purpose rifle is not

This is probably where I will ruffle the most feathers among the gunnies, but I'll do it anyway: a rifle is not a carbine. The word "carbine" connotes a shoulder arm that may be handier but is certainly less powerful than a full-power rifle, and the ubiquitous .223-caliber (5.56mm) guns such as the M-16/AR-15 or the AK-47 pattern firearms in 7.62x39mm (aka .30 Russian) are not properly general-purpose rifles. Their cartridges do not satisfy the general-purpose need for larger targets at extended ranges.

This is not to denigrate the carbine, okay? Many competent shooters feel the carbine does excel at its specialty (although Jeff Cooper riflemen might just smile quietly at that), and hey: since most carbines are also EBRs (Evil Black Rifles) which will send the disarmers into automatic conniption fits, everybody should own one if at all possible. But they are simply not adequate for reliable results at long distances on large targets, and a general-purpose rifle must be capable of that task.

Some terms to work with going forward

Okay, so we've defined things somewhat vaguely, and this is on purpose: the goal is to define a rifle that can do whatever task a rifleman might be called upon to perform. The more we know about what will be required, the easier it is to start specializing, so it's best to keep things as vague as possible.

However, a little concreteness helps us to visualize, and in this case we can use two reasonably known quantities: 1) typical targets you might expect to engage, and 2) a working distance beyond which the rifleman cannot reliably hit his target, and thus will not ordinarily attempt shots.

In much of the US, animal targets would include small-game animals, deer of various sizes, feral hogs and the like, and on the upper end, elk, moose and bear. In extraordinary circumstances, other live targets such as cattle, horses, and other humans attacking you may end up on the list as well, and in that latter case you may also be called upon to disable vehicles supporting your attackers. Different parts of the country may present somewhat different concentrations of these--for example, here in Alaska, the ubiquitous moose may run well over a thousand pounds live weight. The point is that a general-purpose rifle may be called upon to put down a tiny target at short range, or a 700lb animal three football fields away. For the sake of discussion, we'll settle on an upper limit of 1,000 pounds for a live target, and say that a general purpose rifle must be capable of handling that upper limit--on occasion.

Likewise, there is the matter of the ability to hit at a distance. It is not easy to hit a twelve-inch target at 300 yards range--every time, from improvised field positions, under time pressure. In almost every case, the intrinsic accuracy of even an "ordinary" rifle is better than the ability of the shooter to place his shots, and somewhere between 200 and 400 yards is a practical outer limit for most of us. Jeff Cooper extolled the "sporting limit" of 300 yards, which he quoted from Townsend Whelen, and this seems like as good a working number as any. We train to be capable beyond that--somebody shooting at me from 400 yards away is by no means safe from return fire--but there is a limit to what we can call general-purpose.

The "sporting limit" works very well in this sense, as well: if I am taking a shot at an unwounded game animal to secure meat for the table, I will hold myself to rigid standards out of respect--to wit, I will not shoot beyond that distance at which I can no longer guarantee a quick and sure kill. I've got too much respect for game animals to risk making them suffer needlessly by wounding. On the other hand, if things have got so far out of hand that I actually have to take a shot at another human, then considerations of sportsmanship go right out the window, and my only concern is that my attacker is immediately disabled from further trying to hurt me. And so only in exceptional circumstances have I taken a shot past 300 yards on game animals--and even then I didn't feel entirely right about it (fortunately for my conscience, both of those instances were instant "lights-out" results)...but if another human presents an immediate threat at 500 yards distance (an extraordinary circumstance among extraordinary circumstances), all bets are off.

Until next time...

Very well then: for the purposes of subsequent installments, we'll consider a general-purpose rifle to be capable of handling the occasional 1,000 pound live target at a maximum "working" range of 300 yards, with smaller targets and closer ranges being the norm. Please keep in mind that quibbling about the numbers is not the point--the point is that we are talking about a diverse and demanding set of criteria to meet. And there is much to discuss there!

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