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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