27 Dec 17

The “Back Curve”

“The Earth is round, so that we never see too far down the road.”

Karen Blixen

Conversations with “precision riflemen” often get into tedious, esoteric mathematical realms, and usually very quickly!

Many factors influence the bullet during the brief fraction of a second (sometimes longer) while it is in free-flight between when it departs the muzzle and the point of ultimate impact (exterior ballistics), but the two main ingredients are (1) air friction, and (2) gravity.

Density of air varies, of course, with elevation above sea-level, humidity, temperature, and dust/smoke content, but gravity relentlessly pulls the bullet toward the center of the Earth. Wind blowing against the flying bullet, from any direction, will push it (to some degree) off its still-air trajectory.

And, there are other things to consider, from the rotation of the Earth, to “ballistic drift”, to the “Coriolis effect,” even the gravitational pull of Jupiter, but all these are of concern mainly to the artillery officer, generally irrelevant for the practical rifleman!

Shape, diameter, and density of the missile itself also significantly affects the way in which it passes through the air. And of course, intermediate impact with grass and brush will greatly influence missile’s trajectory, thus the location of the ultimate impact point.

With modern, autoloading, military rifles, the bore-line/sight-line span is six centimeters (2.5 inches), and we consider any bullet that impacts within a circle with a six-centimeter radius to be sufficiently accurate for most serious purposes.

So, the instant our bullet departs the muzzle, it is already six centimeter low. With sights adjusted correctly, the bullet will then climb until it crosses the sight-line. With 5.56×45 (223) caliber, I recommend this intersection take place at 40m. This is the “initial intersection.”

The bullet then continues to rise until, under the influence of gravity, it starts to fall back toward the sight-line. This highest point in the bullet’s flight, the “maximum ordinate,” is reached at 140m. At this range, the bullet is six centimeters above the sight line, but no more.

As it continues downrange, the bullet then falls back toward the sight-line, crossing it once more (this time on the way down) at 240m. This is the “second intersection.”

The bullet then continues to fall until it is, once again, six centimeters below the sight-line. This takes place at 260m.

So, between point-blank and 260m, the bullet is never more than six centimeters away from the sight-line, “all other things being equal.”

We call this “maximum point-blank range,” or MPBR. Beyond 260m, we are in the “back-curve zone.”
However, the foregoing holds true only when the rifle itself, as it is fired, is perfectly vertical. When a shooting position necessitates the rifle be fired from a “rotated” position, the six-centimeter standard collapses after 150m.

Thus, I tell students that their M4 is basically a 150m gun. Within that range, it is deadly accurate, no matter the shooting position, no matter the wind, no matter most other factors.

The “back-curve zone” is that portion of the trajectory which lies between maximum point-blank range and the ultimate point of bullet impact. Any time a rifleman is working in ranges that involve the “back-curve” of the trajectory, that is, after the bullet has fallen more than six centimeters below the sight line (after the second intersection), the path of the bullet becomes harder and harder to predict.

The rotating bullet is designed to remain stable as it travels through air, but only so long as it remains supersonic.

The speed of sound in dry air, at sea level, at 70 degrees F, is 342 m/s (1,125 f/s). When bullet velocity degrades to the point when it transitions into subsonic velocities, stability progressively suffers. Modern rifle bullets are not designed for stability at subsonic velocities!

Yet, today’s snipers are amazing is their ability to skillfully use the back-curve zone, and they enjoy my admiration! But, the rest of us, under “field conditions,” using generic military rifles, will squander much ammunition trying (mostly in vain) to get reliable hits there.

I suggest therefore, that the “practical/useable effective range” of your defensive rifle excludes the back-curve zone. The “practical/useable effective range” of your rifle is thus confined to MPBR, often a good deal less than that, as noted above. The “academic/theoretical range” of your rifle may extend into the back-curve zone, but with issues described above.

When the rifleman tries to sight-in his rifle for a particular, extended range (beyond MPBR), he must adjust the sighting device so that the second intersection will occur at a range that necessitates a maximum ordinate in excess of six centimeters. That means, when he subsequently attempts a shot at a shorter range (without a sight adjustment), it will probably be high. In fact, the rifle will shoot “dead-on” only at the exact, extended distance for which it has been sighted. Without another, subsequent sight adjustment, “holding over” or “holding under” will be necessary for all other ranges. The shooter will thus find himself with a “single-purpose rifle.”

As you might imagine, I don’t recommend adjusting rifle sights in the middle of a fight!

When you want to get into sniping, a single-purpose, long-range sniper rifle (in appropriate caliber) is just the ticket! But, it requires great devotion, tedious attention to detail, anal maintenance, and an attention-span far in excess of mine!

When training for real fighting and equipping ourselves with an M4, XCR, SCAR, et al, fitted with a red-dot, in 5.56×45 caliber (we can probably include 300Blk also), so long as we stay within MPBR, we’ll enjoy great success, and we won’t squander irreplaceable ammunition on dubious shots!

“A man has to know his limitations”

Harry Callahan (played by Clint Eastwood) in the 1973 feature film, “Magnum Force”