September 23, 2010
The nitty-gritty of what you need to know about a bullet's flight.
For many people, shooters and nonshooters alike, the word "ballistics" evokes all kinds of things technical. And understandably so, for there are actually three aspects of the term: internal, external and terminal, all of which are remarkably different from one another.
Internal ballistics has to do with what happens from the instant of ignition to the bullet's exiting the muzzle. External ballistics deals with the bullet's path from muzzle to target, and terminal ballistics is the study of the bullet's behavior after impact and lethality.
Obviously, internal ballistics, which deals with the burning rates of various powders, time/pressure curves and such, is something a non-handloader needn't concern himself with. Terminal ballistics, on the other hand, can be of interest to the hunter as it relates to his choice of bullet for a given application. This article deals with the bullet's flight, for that's what's important if we're going to hit our target.
A bullet's path or trajectory can be measured using different criteria. The least complicated is measuring the actual drop of the bullet relative to the bore line, the imaginary line that runs down the center of the bore out to infinity.
What complicates this relatively straightforward concept is the fact that we don't aim a firearm by peering down the bore. The sights, whether they be open, aperture, or a scope, are mounted above the bore. Referred to as "line of sight," this too is an imaginary straight line formed by the alignment of the front and rear sight.
If a scope is employed, the line formed by the alignment of a front and rear sight is optically compressed into a single plane, so instead of having to deal with three optical planes--the rear sight, front sight and target--a scope optically merges these three planes into one, greatly simplifying the aiming process.
Nevertheless, regardless of the sighting system, with the line of sight being above the bore line, unless angled downward, it will never intersect the path of the bullet to allow the gun to be zeroed at some point downrange.
Generally speaking, open or iron sights are about 0.8 inch above the bore line, and a typical one-inch tube scope is about 1.5 inches above. That means that unless the sights are angled downward, the bullet will print 0.8 inch or 1.5 inches low, respectively, at the muzzle, and continue to drop as it travels downrange.
However, angling the sights downward introduces another factor into the equation. If, for example, we want our rifle to be printing dead-on at 250 yards, no matter how flat-shooting the cartridge, the sights must be angled downward enough so that the bullet's path actually intersects the line of sight at two points: one at a point some 25 to 35 yards from the muzzle (depending on muzzle velocity, bullet weight and trajectory) and the second at the desired 250-yard range.
On more than one occasion I've read where the bullet always intersects the line of sight at two ranges, but that's not necessarily true. It depends on how flat-shooting the cartridge, the height of the sighting plane above the bore, and the zero range.
Let's say we have a very flat-shooting cartridge--a 7mm Ultra Mag shooting a 140-grain AccuTip bullet at 3,300 fps with a scope mounted 1.5 inches above the bore--and the gun is sighted in to hit dead-on at 100 yards (much too close for that cartridge but used here for illustration). In this particular instance, the trajectory is actually flat enough that the bullet's path doesn't "rise" above the sighting plane before reaching that 100-yard distance.
When it comes to understanding bore line as it relates to muzzle attitude and point of impact, shooting at distances beyond 100 yards is much more revealing than firing at closer ranges.
In other words, the bullet actually drops less than 1.5 inches between the muzzle and a 100-yard target, so that to get the two to intersect (zero) at that range, the scope needn't be angled downward enough that the bullet crosses the line of sight close to the muzzle as it would with realistic zero ranges of 200 or 300 yards; they would intersect only once at the 100-yard range.
Which brings up another issue. In many ballistics charts, particularly in those of days gone by, that part of the bullet's path that courses above the line of sight was often referred to as its "rise," leading some people to believe that a bullet rises after leaving the muzzle. A bullet starts dropping the moment it leaves the barrel, but with the sights angled downward, the bullet spends its time between its first convergence and the zero distance above the line of sight, hence the term "rise."
If we really want to nitpick, a bullet can actually rise above the bore line. This seeming contradiction of Newton's Law is attributable to barrel oscillations. Like a garden hose that's violently shaken up and down at one end, the "wave" that travels down the hose is what happens when a bullet accelerates down a gun barrel. The attitude of the muzzle at the moment the bullets exits is almost always different from the theoretical bore line.
We're talking minute differences, but the fact remains that the line of sight and the bore line are rarely the same. This explains why in a theoretical situation where a bullet did not drop at all from the muzzle to a 100-yard target, and that the rifle could be bore sighted with such precision that the bore line absolutely coincides with a pinpoint on the target, shots fired through that barrel will in all likelihood be left, right, up or down from that projected impact point.
That explains why, when we switch to a lighter or heavier bullet, our point of impact is not necessarily higher or lower, respectively, because the attitude of the muzzle does not generally coincide with the bore line. Different weight bullets accelerate at different speeds, and that changes a barrel's vibrational pattern. This also explains why a different load can impact to the left or right of the previous one, as well as higher or lower. The thinner the barrel, the whippier it is and the more pronounced these effects are likely to be.
Back in the early 1960s when I was first getting into handloading, ballistic charts used "midrange trajectory" to describe the relationship of the bullet's path to the bore line at 100, 200 and 300 yards. For a 7mm Remington Magnum 150-grain load, for
example, the midrange trajectories were 0.5, 1.8 and 4.7 inches, respectively. That meant if you were zeroed to hit dead on at 300 yards, the bullet would be 1.8 inches above the line of sight at 100 yards, and 4.7 inches high at 150 yards.
Because these calculations were made from the bore line rather than line of sight, they weren't all that useful. Then, too, the maximum ordinate actually occurs slightly beyond midrange--say, around 165 yards rather than 150 for a 300-yard zero. That's because the bullet is always dropping more over the last half of its flight distance than it does over the first half.
Laser rangefinders such as this Leupold RX series not only measure distances but compensate for up- and downhill angles by giving the actual horizontal distance and correct hold-over.
It wasn't until the mid-1980s that the combined ballistic charts of Federal, Hornady, Remington and Winchester, as printed in Gun Digest, started to use "bullet path" instead of midrange trajectory. Even then, bullet path was computed from a line of sight that was 0.9 inch above the bore, so it was a slight compromise in deference to iron sights, even though by then most of us were using scopes.
To illustrate how much that changed things, the bullet path of that same 150-grain load from a 7mm Remington Magnum relative to a line of sight 0.9 inch above the bore and a zero range of 200 yards was 1.6 inches high at 100 yards and 6.2 inches low at 300. These figures were far more useful than midrange trajectory.
Today, our ballistics charts are predicated on a line of sight 1.5 inches above the bore, which doesn't change the aforementioned figures enough to worry about, at least not out to ethical shooting distances.
The terms ballistic coefficient and sectional density are terms that gun weenies love to use to impress the less enlightened, but the fact of the matter is, both are relatively simple yardsticks for measuring a bullet's attributes.
BC is simply a way of expressing a bullet's ability to overcome air resistance or rate of deceleration, while SD is a way of expressing the weight of the bullet relative to caliber.
Common sense tells us that a "pointy" bullet is more aerodynamic than a round- or flat-nosed one. Hornady's 170-grain flat-nose .30 caliber bullet, for example, has a BC of .189, while its 168-grain A-Max spitzer boattail bullet in the same caliber has a BC of .475. Big difference.
How big? Well, if both are launched at 3,000 fps, at 300 yards the A-Max slug is still going 2,410 fps, while the flat-nose job has slowed to 1,470, almost 1,000 fps difference. It also means the latter drops about eight inches more at 300 yards.
In normal game calibers--say, .25 through .338--you can rest assured that a BC approaching .400 is indicative of a very streamlined spitzer bullet, and those approaching BCs of .500 are extremely efficient. But don't think that the 20 percent difference translates proportionately when it comes to flatter shooting.
Again using Hornady bullets as examples (because they happen to have two 7mm bullets of equal weight that differ by almost exactly .100 in BC), the 154-grain flat-base spitzer (BC of .433) will drop just 0.4 inch less at 300 yards, and 1.2 inches less at 400--all other things equal--than the 154-grain SST and InterBond bullets that have a BC of .530.
As for sectional density, you can have a bullet that's streamlined as far as its shape is concerned, but because it's very light for the caliber--a 110-grain .30 caliber bullet for example--it will shed velocity faster than a heavier bullet of the same nose shape. Though it can be launched faster, it slows down more rapidly. Consider: a 100-grain 7mm spitzer bullet exiting at 3,800 fps, and a 162-grain 7mm bullet exiting at 3,300 fps. At 300 yards the heavier bullet will not only have made up for its 500 fps deficit, but will be traveling almost 100 fps faster than the lighter bullet.
Bullets that are light for caliber (low sectional density) can't have a high BC. Take these two 7mm bullets. The 100-grain at left has an SD of .177 and a BC of .225. The 175-grain spitzer boattail is rated at .310 and .533, respectively.
What it boils down to is that BC and SD are interrelated. You can't have a bullet of low SD with a high BC, but you can have a bullet of high SD and low BC. It's a matter of Newton's Law that says objects in motion tend to stay in motion, and the heavier the object, the more it tends to stay in motion, assuming similar shapes.
But again, shape and relative weight are two different things. Unlike BC, sectional density has nothing to do with the shape of the bullet--only its weight relative to its diameter.
A 180-grain .30 caliber bullet has a SD of .271 regardless of how blunt or streamlined its shape. In 6mm, bullets of 90 to 105 grains are heavy for the caliber; in 7mm it's 160 to 175 grains; and in .30 caliber it's 180 to 200. All these bullets will have a high SD, and if of streamlined shape, high ballistic coefficients as well.
Last, we come to the old uphill/ downhill shooting where we're told to hold low in both situations, which seems to fly in the teeth of logic. The explanation is really quite simple. Just imagine you're at the lower left corner of the 7.75x10.5-inch page you're now reading, and that your target is at the upper right hand corner of the page (an extreme uphill shot to be sure but used here to emphasize a point).
As measured diagonally from your position to the target, it's 13 inches away, but measured on the horizontal, it's only 7.75 inches distant. Gravity acts upon the bullet only to the extent of its horizontal travel.
If we convert the aforementioned inch measurements into hundreds of yards, an animal that a laser rangefinder tells us is 1,300 yards away as measured uphill, is only 775 yards as far as gravity is concerned. Therefore, we hold for a 775-yard shot rather than 1,300-yard one. Up or down, there's no difference; we'd hold the same in either case.
Today, of course, we have laser rangefinders that can measure the angled distance on up and downhill shots, translate that into horizontal distance and tell us the correct hold. Amazing.