02 January 2013

Firearm Lethality: Bullet Flight

This post will ignore handgun bullets entirely.  Long range shots with handguns will have all the same considerations, so for the sake of simplicity I will focus on rifle bullets.

In the normal course of ballistic study bullets are shot into gelatin at 90 degrees.  The goal is to find out what the bullet will do under normal conditions at relatively short ranges.  Sometimes loads are reduced to test expansion at lower terminal velocities, to simulate a long range shot.

Shadowgraph of bullet in flight.  Note turbulent drag
There is a bit of an issue with this assumption.  Bullets don't always fly straight.  Generally they fly "straight enough" for government work.

No matter what the construction of an individual bullet is, there will be imperfections in uniformity which lead to "bullet imbalance."  The faster you spin a bullet, the greater the effect of bullet imbalance in terms of group size.  In practical terms for service rifles used for war, this doesn't mean much.  For service rifles designed for competition, it means the world.

Dr. Mann's experiment with bullet flight through screens, 1907
This imbalance will cause the bullet to fly in a decreasing spiral pattern until some optimum stabilization is achieved (where we can't detect it any more) for that projectile.  Looking at the path of a bullet 90 degrees to path of flight shows an irregular wave motion.  Not a smooth sine wave at all.  Dr. Mann's plot is instructive, but it only shows half the picture.

The other half of the picture is how the bullet is flying as observed in line with flight.  Pictured on the right on the bottom, labeled nutation, are two sets of spirals.  The greater the bullet imbalance the larger the spirals.  If there were such a thing as a mathematically perfect bullet it would fly true, and the center dot of the "nutation" column would simply be the path of flight.

Historically one of the ways to minimize bullet imbalance was to use the slowest possible twist rate for a given bullet length.  The faster the rifling twist, the more the imbalance will show, ergo the most accurate rifles all else being equal, use the slowest twist possible.  Consider the standard 1:10 twist for 308 caliber rifles.  As the twist gets slower we see accuracy platforms arise.  The 1:11.25 twist of the Remington M24 sniper weapon system has been cloned to death on the civilian market.  Palma competitors have been known to use a 1:13 twist or 1:14 twist optimized for the 155gr Palma bullet.  For those shooting 30 Benchrest, a 1:16 to 1:18 twist barrel will toss those lightweight benchrest bullets very tightly.

Remember the triad of lethality, Accuracy, Penetration, Tissue Disruption.  By maximizing accuracy with a slow twist and light bullets, we are going to limit penetration.  Twist rate is the compromise point between accuracy and penetration.  In reality, it doesn't matter very much unless you are using a firearm unsuited for the target you are shooting, but from a pure engineering perspective, it matters.  Dan Lilja wrote a very nice article about this over a decade a go, and if you haven't read it now is a good time: http://www.riflebarrels.com/articles/bullets_ballastics/bullet_imbalance_twist.htm

What twist rate you choose should not be determined by anything other than the ranges at which you intend to shoot.  If I were to build a High Power service rifle for 200 yard reduced distance courses I would have no issue at all using a 1:12 or 1:14 twist barrel shooting a 53gr Sierra Match King bullet.  However I would not choose that for a full course rifle, and in fact I chose a 1:7 Colt and 1:7.7 Krieger barrel for my service rifle which handle 80gr A-Max bullets very nicely out to 600 yards. 

And on the subject of service rifles there are a lot of myths about the M16, and the most common is "the bullet tumbles and causes horrendous wounds" which is utter nonsense.  The original M16 had a 1:14 twist which proved too slow for a 55gr bullet in sub zero Arctic conditions, so the twist was tightened to a whopping 1:12.  What is really happening is that the bullets used in the M16A1 (m193, 55gr FMJBT) and M16A2 (M855 FMJBT) were "yaw dependent" to fragment.  That chart showing bullet fragmentation at various velocities a few posts back?  That fragmentation doesn't happen reliably if the bullet has stabilized.

Donald G. Miller, International Journal of Impact Engineering

Going to the first picture in this post you see that the largest period of instability is in the first 100 yards.  By the time the bullet has reached 200 yards it will be "terminally stable" so to speak.

The diagram to the right shows how the spiral effect decreases with time and distance.  As the bullet flies through the air it loses energy relatively quickly due to drag.  This provides a level of stability, which some have theorized explains why some loads measure better at further distances.

Our M193 55gr FMJBT bullet gets stabilized rather quickly, and after about 175 meters becomes really good at poking 22 caliber holes in tissue, flipping around as all boat tail spitzer bullets do, and causing the normal wound channel we expect to see without fragmentation.

Note the smoothing of the path of flight wth distance.
All of this is fascinating, but what does it really matter?  Not much, really, but in an absolute sense, the bullet you are aiming, even if it hits perfectly, is going to impact at a different angle than you are looking at your target. At short ranges, the bullet will be rising up, at long ranges the bullet will be pointing down at an angle that increases with range.  To explain how much of a non issue this is, a 308 Winchester shooting at a mile will have one yard of drop for every seven yards of horizontal travel.  If that bullet impacted an animal, the deflection would be less than 5 inches at 4 feet inside the animal assuming normal penetration.

There you have it folks.  If you have a bullet designed to expand you don't need a yaw dependent bullet.  If you have a bullet designed to penetrate you don't need a yaw dependent bullet.  If you are stuck with what Uncle Sam (or Papa Ivan, or Supreme Leader Ying, whatever) decides to issue you, sometimes it is helpful to know when to call for a different weapon system.


Anonymous said...

What then are the differences in flight charateristics between a 55gr and 75gr at say 600 meters? If you are picking the nits for best accuarcy on paper then the increased energy is nearly moot, right?

AM said...

On a perfectly calm day... The flight difference is actually pretty minimal, to the point where if you are aiming at a human size torso with a 75gr bullet using an ACOG with 55gr ballistic markings will get you on to the torso.

In the wind, forget about it. The 75gr bullet will shoot a lot tighter than the 55gr bullet. Trust me on this one.

And at 100 meters the 53gr SMK will probably shoot tighter than a 75gr HPBT. At 600, in real conditions, the other way.