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OVERKILL AND UNDERKILL
Dr. Chris Ryan
Why Do Animals Die?
OVERKILL AND UNDERKILL by Dr. Chris Ryan (continued)
HOW BULLETS KILL
The bullet, after traveling from the gun to the animal, now goes from air to the animal, a medium of different density--usually several different densities. Many things can happen at this crucial juncture. With respect to the bullet, it can enter or not. It can fly straight or be deflected. It can be deformed (expand, break up, or bend) or remain intact. Each of these changes can have very important effects on the bulletís killing power.
Obviously, if a bullet doesnít enter, the effect it has on the animal has to do with concussion, much the same as throwing a rock. In general, if a bullet doesnít enter the animal, it canít be effective. Now I know there are exceptions, but realistically, these are stories that are interesting only because theyíre so unusual. The conclusion to draw, therefore, is that the bullet must have sufficient force and structural integrity to penetrate that portion of the animal presented.
Deflection can occur at any point, but generally Newtonís first law of motion applies:
Obviously, any bullet striking an animal already has two major forces changing its uniform motion before impact. Gravity wants to pull it to Earth. The friction of the air wants to slow the bullet down. The bullet is therefore progressively slowing and dropping. But the major velocity- and direction-changing event happens when the bullet hits the animal. The much higher density of flesh will always slow the bullet: the only question is, how much. If the bullet slows enough, it may cause only surface penetration and damage. Often the bigger effect is the change of direction caused by the surface tissue. While the bullet may have been aimed directly at an underlying vital area from outside, when it strikes surface tissue it may angle away and miss the mark entirely.
The classic example of this is the boss of a cape buffalo horn. Bone in general, however, is a special case in terms of bullet performance. Bone and horn are the hardest and most bullet-resistant substances in an animalís body, and, inch-for-inch, will challenge a bulletís structural integrity more than anything else in an animalís body.
Bullet deformation can be beneficial or detrimental. Expansion of the frontal area increases the diameter of both the permanent and temporary wound channels. Other things remaining equal, this results in greater tissue damage. However, this change in the shape of the bullet happens at the expense of energy (which causes the expansion). Remember that this bullet energy comes from the mass of the bullet and its velocity. Bullet deformation, without loss of significant weight, must therefore result in lower velocity. Also, an expanded bullet requires more energy to drive it forward, as the larger frontal area displaces more tissue as it advances, encountering greater frictional resistance. Instead, ever less energy is available, so the bullet slows even more. Eventually, the bullet stops. If it has reached and damaged enough tissue, the bullet has done its job. If not, it has failed.
Bullet expansion can turn into bullet disintegration, meaning that the bulletís structural integrity is insufficient to hold the bullet together under the energy the bullet develops at that velocity. This happens with varmint bullets, and also with light and lightly-constructed bullets in super-zapper magnums. The bullet can separate from its jacket or shatter all together. Bullet breakup usually decreases penetration and frequently changes the direction the projectiles take through the animal, because of loss of both momentum and directional stability. (This, by the way, is the exception to the rule that Linebaugh sites, that the weight of the bullet is a constant. His statement is generally true of a well-constructed solid, and anyone who has read Linebaugh knows that this is basically his assumption; my observation is not criticism of his position.)
Bullet deformation also includes bending and changing the shape of the leading edge. Both of these effects generally will result in deflection of the bullet, and may mean bullet failure. Peter Capstick told some hair-raising stories about solids in his .375 H&H deforming, turning a boring day into a lively one, in short order.
The Mid game
From the standpoint of survival, it doesnít take a rocket scientist to figure out why vital organs donít reside on the surface of animals. The purpose of surface tissue, from plants to humans, is to keep the inside in and the outside out. The surface also contains openings to the inside and outside: sensations, air, food, and water come in, and waste goes out. While no one could reasonably argue that these functions arenít vital, destruction of surface tissues isnít usually lethal. It follows that it takes more than just getting a bullet into the animal to kill it. As Capstick observed, you have to do more than just hit meat and arrange for taxidermy. So, whatís inside that critter you just shot?
Nerve tissue is delicate and easy to destroy. Much of it is vital to functioning of the animal, especially the brain. Damage to the spinal cord will instantly incapacitate at least part of the animal, but will not kill the animal outright.
Puncture blood vessels and they bleed; bigger vessels and the heart bleed the most. "Vital organs", such as the liver, kidneys, and lungs, bleed when they are damaged, and so will the other internal organs. Other tissues bleed as well, of course, but bone, muscle, and connective tissue are relatively less vascular. In addition, the contraction of muscle can (at least temporarily) slow or stop the flow of blood. Regardless of the source, unchecked loss of blood will eventually kill the animal.
Some experts talk about "breaking down the animal", and thereís certainly a lot to this. It involves damage to the structures that allow the animal to move, keeping it from running away. In some animals, damage to the hip or shoulder joints may limit mobility. Much more certain is the damage to the spine and spinal cord, which immobilizes the animal by massive nerve damage. J. D. Jones talks quite a bit about shots to the pelvis or the "spine-tail shot". Done right, this shot damages both bones and joints, as well as the big bundles of nerves and blood vessels. However, this shot wonít usually kill the animal; it simply allows the hunter to approach the animal for a killing shot.
"Shock" is controversial, and must sometimes enter the picture, but how is a very complex issue, and one that may take another chapter by itself.
The Function of the Bullet
The bullet must destroy vital structures. I donít like to roll the dice, and donít do so intentionally. Therefore, I define bullet effectiveness as undeviating penetration, and sufficient destruction of vital tissue. Letís take up each one of these in turn.
The bullet may start its flight in the direction of a vital structure, but if it deviates, it wonít strike its target. If it doesnít penetrate sufficiently, it wonít strike its target. Therefore, the two most important attributes of a bullet in this context are momentum and directional stability.
Momentum (or, more properly, linear momentum) has a simple definition from physics:
p = mv
Basically, it is the tendency for the bullet to continue forward, to go straight and to penetrate. Youíll notice it is also part of the Taylor KO formula. Itís easy to see that, at the same velocity, a heavier projectile will tend to carry forward better than a lighter one.
The other motion of the bullet is its rotation, which imparts a gyroscopic stability to the projectile. The bullet spins from its having engaged the rifling, and (ideally) keeps its directional stability as a result.
In addition, this rotation of the bullet creates what is referred to as angular momentum, which classical physics defines as:
L = Iw
Roughly translated, the tendency of the bullet to continue spinning is equal to the weight of the bullet times the speed of the spin.
Now hereís where I really got stumped in understanding the Taylor formula. I could understand how momentum got there, as the product of bullet weight and velocity. And I thought that the diameter of the bullet in the equation represented only the size of the hole. But it has also to do with angular momentum. If the twist of a barrel stays constant, the rotational speed of a bigger caliber bullet will be greater than that of a smaller caliber bullet. If the twist is once in ten inches (for the sake of argument), then ten inches down the trajectory a .45 caliber bullet will have twisted a distance of .45" x 3.14159..., and a .357 caliber bullet will have twisted and distance of .357" x 3.14159.... In other words, all other things being equal, a larger caliber bullet will have a greater speed of spin than a smaller caliber bullet, and therefore will have greater tendency to keep spinning, even with the same bullet weight. Of course, the larger caliber projectiles are also usually heavier, and that tips the balance even further toward the larger caliber bullet. So the bigger caliber slug will have greater tendency to keep spinning, and will tend to retain its gyroscopic stability mores than its smaller caliber counterpart.
The second component of bullet effectiveness is sufficient destruction of vital tissue. Here, too, the larger diameter slug holds the edge. Veral Smith of Lead Bullets Technology has pointed out that the size of the meplat that encounters the tissue of the leading surface is the relevant variable in determining both the permanent and temporary wound channel. In general, the caliber of the bullet will determine the hole in the tissue. But the destruction of the tissue by the forces of concussion and cavitation in the temporary wound channel has to do with the aerodynamics of the bullet. All other things being equal, though, a bigger diameter bullet makes a bigger hole, and destroys more tissue.
Then we get to something that I donít think Taylor included in his consideration of bullet effectiveness, and certainly didnít include in his formula. I am speaking of sectional density. If a given portion of the bullet has mass behind it, it will tend to carry forward. In general, the frontal surface of an intact solid has the full mass of the bullet behind it. This is not the case with an expanded rifle bullet: the major mass may be contained in the forward surface, which may have mushroomed as much as 50% of the bullet weight. The retained weight of the shank of the bullet is behind only a small percentage of the frontal surface, that in the center. This center portion of the bullet has some retained sectional density, while the rest of the mushroomed frontal surface has the sectional density of a lead potato chip. The tendency of such a projectile to carry must be seriously limited.
So, in summary, a heavier bullet will have a greater tendency to carry forward and penetrate without being deflected from its course than a lighter bullet. The heavier bullet with larger diameter will tend to maintain its rotation, and therefore its directional stability, better than one of smaller diameter. And finally, the larger diameter slug displaces proportionally more tissue. The conclusion from this is that the larger heavier slug should be a more effective bullet.
Force vs. Energy
The usual measure of the power of a bullet is kinetic energy. Recall the energy is equal to the mass of the bullet, times the square of the velocity:
E = mv 2
This means, obviously, that the velocity plays a much greater role in energy than in momentum. So, when the bullet slows down, the effect of this deceleration is much more profound on energy than momentum. If the bulletís velocity slows by half, so does the momentum. The energy drops by 75%!
p 1 = mv (momentum before deceleration)
p 2 = m x 1/2v (momentum after deceleration)
E 1 = m x v x v (energy before deceleration )
E 2 = m x 1/2v x 1/2v, or
E 2 = ľ mv 2 (energy after deceleration)
My conclusion from this is that energy dissipates much more quickly than momentum, meaning that those wonderful huge energy numbers go away very quickly. As I pointed out earlier, there are a couple of things that conspire to decelerate the bullet. One of these is the friction of the tissue on the bullet. Another is the energy needed to deform the bullet. The third is the increased friction on the leading surface of a bullet which has expanded. The conclusion is-- correctly--that an expanding bullet retains less energy in expanding, and loses energy more quickly after expansion.
I know that the rejoinder is that the energy is transferred to the animal, somehow imparting death to the quarry. It ainít that simple. Energy is neither created nor destroyed (at least according to classical physics). Whatís lost from the bullet goes into the animal, all right, but what isnít used up breaking tissue structures turns into heat. Ever wonder why surgeons donít worry much about leaving a bullet behind, rather than doing absolutely everything to remove it? Bullet tracks are sterile, due to the heat generated along the way. Whatís that mean? Heat denatures protein, meaning the structure is changed, and no longer works, either chemically or architecturally: the tissue is destroyed.
Death results from permanent loss of brain function. This can be from direct damage to the brain itself, or from damage to other vital structures, that results in damage to the brain indirectly. We know what those structures are, and where they are. If we can get a bullet to those structures with enough undeviating penetration, and inflict enough damage, our objective will be met.
Energy is fine, but drops off fast. It is not an indicator of penetration potential, and tells us nothing about directional stability. It may give us some indication of the amount of damage around the wound channel, but unless that wound channel blasts through something vital, collateral damage doesnít make much difference.
Momentum does tell us something about penetration, and angular momentum and sectional density tells us about directional stability. This means:
1) Velocity is less important than worshipers of energy figures believe,
2) In the same caliber, heavy bullets will carry farther than light bullets, and stabilize better, and
3) Larger diameter bullets will stabilize better, and destroy more tissue (other things being equal).
This brings us once again the Taylor KO formula:
KO = mvd
where m is the weight of the bullet in grains, divided by 7000 grains per pound; v is the velocity in feet per second ("foot seconds" is an incorrect way to talk about bullet velocity, so donít say it, unless you want to be ignorant intentionally); and d is the diameter of the bullet in inches. The reason we are drawn to this formula, it seems to me, is that it contains all of the elements that are relevant in determining undeviating penetration and the permanent wound channel.
Now, if we could just understand Stopping Power......