II. The Mechanics of Terminal Ballistics

II. A. Mechanics of Lethal Wounding

Since the understanding of what causes effective wounding is prerequisite to any discussion of the desired terminal performance of a bullet, let us first examine the mechanisms of wounding which result in incapacitation and death.

Incapacitation alone is of little interest to the hunter of big game in most circumstances. If a shot is well placed, then it will result in incapacitation leading to rapid death. The circumstances in which rapid incapacitation, as opposed to rapid death, are of paramount importance all relate to scenarios in which the shooter desires to immediately stop the physical acrtivity of the target. These scenarios could be self-defence in the wild or the home, or the stopping of an armed aggressor by a police officer, or even stopping the flight (or charge) of a wounded game animal. Incapacitation is a more complex matter than lethality, so I will deal with lethality first.

All modes of lethality ultimately depend on the collapse of the central nervous system (i.e., brain death). Brain death can be caused directly by damaging the brain or upper spinal tissue, or indirectly by depriving it of oxygen. Damage to the brain or upper spinal tissue may be due to proximal passage of the bullet or in some cases by remote pressure effects (discussed later). Oxygen deprivation is the result of cardiac arrest (induced by whatever mechanism) or of hemorrhaging which reduces blood pressure or else damage that completely shuts off the circulatory function. Thus, rapid death is accomplished by causing the rapid collapse of the central nervous or circulatory systems.

The importance of hit location and shotline cannot be overstated. It is true that sometimes even a direct hit on the brain by a bullet is not instantly incapacitating (read Massad Ayoob's story in The Ayoob Files - Day of the Terminator: The Chaney/Lawrence Incident, American Handgunner, September / October, 1991, pgs. 70 - 82), but generally this is because that portion of the brain struck is the relatively "unimportant" part associated with cognition. Hits against the base of the brain or the upper spine are almost always instantly fatal because these regions control the involuntary vital functions like heartbeat and respiration.

In the case of hemorrhage resulting from damage to the lungs or arteries, central nervous system collapse will likely occur prior to cessation of cardiac function; the time required for brain functions to deteriorate to the point of unconsciousness depending on the rate of hemorrhage. However, when damage is done directly to the heart, the circulatory function may be arrested first, leading to unconsciousness within a few seconds.

There is another mechanism of cardiac arrest that is less well understood but which may account for the nearly instantaneous death of game animals hit with modern weapons and that is induced cardiac fibrillation and arrest. The precise mechanism for the onset of the cardiac arrest is not fully understood, but its effect is well documented. It may involve some type of local neurological or humeral communication between the heart and lungs that gets short-circuited. Alternatively, a violent wound to the lung tissue may create a tiny embolism that interrupts cardio-pulmonary function at a critical moment.

Additionally, there is some evidence to suggest that the sudden pressure resulting from the bullet's passage through the heart, coupled with the coincidence of the ventricular systole peak of the blood pressure cycle, may communicate up the arteries to the brain and produce, in effect, a ruptured cranial aneurysm resulting in an indirect, remote injury to the central nervous system.

Other than hits to the central nervous system (brain and spine) or the unpredictable mechanism of spontaneous cardiac arrest or cranial hemorrhage, the only reliable cause of rapid death is through hemorrhaging produced by cutting a hole through major blood-bearing organs (heart, lungs, liver) or major blood vessels (e.g., aorta). The dimensions and especially the location of the cavity produced by the bullet will determine the rate of hemorrhaging and in turn the rapidity of the onset of death. It is actually more lethal in some cases to sever the arteries directly above the heart, than to penetrate the heart itself. If these arteries are cut, blood pressure instantly drops to zero and death will follow in seconds (this is one reason why an arrow can kill as fast as a bullet). Lethal hemorrhaging does not depend upon how much blood exits the body, but only upon the loss of blood pressure.

Three things are worth noting: 1) hemorrhaging in the thorax is far more severe in the case of pneumothorac injuries (collpased lung) than in vascular tissue such as muscle, due to the relative pressure difference between the pleural space and the cardio-vascular system, 2) the surface area of the wound, not its volume, is most related to the rate of hemorrhage, and 3) the body's natural response to hemorrhage, coagulation, is more pronounced in extremely violent wounds which rupture thrombocytes, releasing fibrin into the blood (in other words very sharp cuts generally bleed more freely and longer than ragged, macerated wounds - although a cleanly severed artery may spasm and close, whereas a torn artery may continue to bleed).

Based upon research to estimate the minimum lethality required to cause a game animal to collapse from hemorrhage within 10 seconds (or 100 yds) from a wound caused by an arrow (Jan Friis-Hansen, Mesolithic Cutting Arrows: Functional Analysis of Arrows Used in the Hunting of Large Game, Antiquity, No. 64, 1990, pp. 494 - 504), the minimum lethal wound surface area for ideal performance by a bullet can be similarly estimated. In practice, a bullet will require a somewhat larger area to offset the crushing mechanism of cavitation which promotes coagulation. The formula adapted from this study for minimum wound area is:

Important caveats are necessary here. Only penetration and cavitation in the thoracic cavity through cardio-vascular tissues produces effective hemorrhaging (unless a major artery is cut). In other words, the penetration and cavitation produced in muscle and gut don't count toward this measure of a MWA because it does not bleed as freely or in the volume of heart, lung and liver tissue. This MWA value is based on a shotline transverse through the thorax (hitting heart and/or lungs). The thorax depth assumed here is based on a line passing between the number 4 sternal ribs above the heart. The figures presented are approximate, as animal anatomy varies by species and individual.

On a broadside shot through the shoulder of a typical whitetail you can add two or three inches of muscle and bone to the necessary penetration for your bullet before it can begin its killing work. The same location on a brown bear or buffalo would be quite different. The toughness of muscle and bone on larger game far exceeds that of light game animals and can stop bullets short and cause them to go to pieces. That is not addressed here. This MWA only describes the dimensions of a wound interior to the thoracic cavity.

Assuming that the relationship holds true with varying wound diameter and since the wound area is a linear function of diameter, it is a simple matter to calculate the minimum penetration required if the wound diameter were larger or smaller. However, this assumption may not be true and one should avoid the temptation to believe that any such relationship could hold to the uttermost extrapolation of that idea (a very wide but very shallow wound, for example).

A reasonable minimum wound is one that penetrates at least halfway across the thoracic cavity through the heart and/or lungs, and that is reflected in the suggested minimum wound diameter of 15 mm in the table below. So, for a shallow wound, it should produce a mean wound diameter of at least 15 mm to be effective.

Typically, once a bullet has entered the thoracic cavity, it will at least cross the entire cavity, even if it is captured under the hide on the other side of the body. Consequently, the maximum thoracic depth implies a minimum mean wound diameter of roughly 7.5 mm to be effective. And again, these figures are drawn from data in which wounds did not rapidly coagulate, so the minimum for bullets will be larger in practice.

The minimum wound should lie between these two boundaries. This is illustrated in the following figure:

Approximate Minimum Wound Dimensions as a Function of Game Animal Mass

What emerges is that nearly all big game cartridges are capable of killing essentially any size game animal (short perhaps of pachyderms) under ideal conditions even with solids, which experience has shown to be true. Some years ago now, a friend of Craig Boddington used F. C. Selous' Holland Woodward single shot in .256 Mannlicher to kill a Cape Buffalo with a 156 grain solid bullet - very nearly the least destructive projectile that could be employed - and he killed it with a single shot. (African Legends, Craig Boddington, Guns n' Ammo, 21 February 2012)

It should be understood that this calculation is merely an estimate of what is required to result a rapid incapacitation due to loss of blood pressure. It certainly does not suggest that one millimeter less in depth or diameter represents a non-lethal wound. Nor should it be taken as a recommendation. Almost any bullet wound through the thorax is certainly fatal. The real question is: "How quickly?" As hunters we should strive for 10 seconds or less.

What is not apparent from this assessment is that, owing to physiological operations, causing a more extensive wound than what is sufficient to result in collapse by this definition will not necessarily result in any appreciable reduction in the time for collapse. In other words, given that the circulatory system has been shut down, the animal can still remain on its feet and act for anything up to 10 seconds or so with the oxygen in its blood at the time it lost circulation. Other than by inhibiting locomotion through damage to the limbs or to the central nervous system, more extensive wounding will have little influence on that limitation.

The foregoing remarks should not be taken to suggest that any wound larger than the MWA is superfluous. I certainly do not believe that to be true and in fact I am persuaded that there is a significant advantage to be obtained by much larger and deeper wounds than these minimum figures, for several reasons. For one, these numbers are subject to criticism. The analysis or the data may be flawed, and the extrapolation to high velocity bullet woulds may be far too different to be valid. Additionally, modern weapons can produce wounds that not only cause hemorrhaging, but that destroy large regions of vital tissue. The loss of tissue function (cardiac arrest, rupture of the alveoli in the lungs or damage resulting in pneumothorax) is a more immediate effect than oxygen starvation caused by loss of blood pressure through exsanguination alone. The countdown to brain death starts at once and may proceed more quickly. Additionally, whenever dangerous game is hunted, one will strive to deliver a wound that is as lethal as possible and that will put the animal down immediately. More than the minimum is preferred. Fortunately, most modern weapons will produce wounds that are significantly more extensive than these minimum dimensions; however, bullets that enter from oblique angles and traverse a considerable length of the body, losing most of their energy in muscle or gut, may be making wounds of a size very close to these minimum values. Such wounds approach (and may fall below) the lower threshold for effective lethality and are to be avoided.

There is some controversy among experienced hunters regarding the best aimpoint for ideal killing. Townsend Whelen and others favor a low aimpoint for the heart area. Some advocate attempting to hit behind the shoulder into the lungs (to avoid damaging meat), while others recommend smashing the shoulder and/or spine if possible (for maximum trauma). I hate to differ with the esteemed Colonel, but I prefer a slightly higher aimpoint than the heart shot. The heart is very far forward, usually right amongst the legs and there is a possibility of maiming a game animal by shooting off a leg in the event of a poor shot rather than missing cleanly, a wound which will not prove fatal nor slow the animal enough to permit a clean coup de grace.

Aiming deliberately for the spine is also hazardous because in most game the target actually lies well below the hairline and is quite small; a high shot through the heavy muscles and dorsal spinal processes to which these muscles are attached may inflict a nonfatal wound or one leading to crippling infection and possibly a lingering death. There is a prevalent myth that a gap exists between the spine and the lungs, especially in larger game animals. God is not sloppy -- there is no empty space inside the thorax. In a living animal the heart, lungs, esophagus, trachea and major blood vessels fully occupy the thorax. The action of the diaphragm depends on the vacuum tight connection of the lungs to the thoracic cavity walls to make the lungs expand and contract for respiration. After death or after being torn open by the passage of a bullet, the lungs can collapse. A hit above the spine might instantly drop an animal in its tracks for a few seconds, but it will then suddenly recover and run away with a wound that will not bleed or lead to a quick death since no vital organs have been damaged.

Its generally thought best to aim for the center of the thorax and leave a margin of error on all sides which will be highly lethal even if range estimation or wind or steadiness or a sudden movement by the quarry (or all of these) interfere with the shot ­ unless one has ideal shot placement conditions (absolutely known trajectory, still target, no wind, steady rest, etc.). Usually one can find the proper aimpoint on a line centered between the front legs and approximately one-third of the distance from the sternum to the top of the shoulders (ventral to dorsal). On a fully broadside presentation, the aimpoint will lie just behind the front legs at the same height.

In this context I think it appropriate to state my definite advocacy against neck shots. In the first place, there is no call for it. The often heard argument that it saves meat is false; ribs have no meat of consequence while the neck does. There are only two vital targets in the neck, the spine and the carotid artery. They are closely situated so that a hit on one is likely to damage the other. This target is very small in terms of vertical dimension and located in a large mass of muscle. As indicated earlier, a large wound in muscle will not bleed like a wound in the lungs. If the spine is missed on a neck shot the animal will be maimed, its neck muscles macerated, its esophagus perforated or severed entirely. It will die, but death may be agonizing days in coming. Anyone who has observed deer for more than a few moments will know that they frequently and very rapidly move their heads and necks. It would be very easy to have this motion ruin the extremely fine aim that is required to make a neck shot. Since that is completely outside the hunter's control and since the movement of the entire body is required to change the position of the thorax, in which a large lethal target is still presented, allowing for significant errors in aim to still be equally lethal, I regard the neck shot as flatly unsportsmanlike in all but very rare instances. Neck shots are in the way of a trick shot, and that is not what is wanted in the hunting field. I have seen it go wrong often as not and am convinced that it goes wrong far more often than its adherants will admit. It does not lie within the skill of the hunter to make this a reliable shot, and that is the salient issue.

The first hit is the most important, because endorphins that are released into the body as a result of serious injury cause the constriction of the blood vessels, reduce or eliminate most pain, and condition the body to operate with minimal oxygen in the blood. If the first hit is not immediately lethal, then subsequent hits will often be less effective in quickly dropping the target, even if they are lethal wounds. Few people realize this, but it is well documented. It is the same mechanism which makes a startled or alert deer harder to kill than one which is completely surprised, because fear also triggers the release of endorphins.

It is sometimes advised to go for a "mobility kill" (in military parlance) in order to prevent or stop a charge, incapacitate an armed aggressor, or to prevent a wounded animal from escaping. Mobility kills are hits which prevent or limit movement, and on game are usually aimed at the front shoulder. If you read the exploits of African hunters you will find that when the first shot against a dangerous game animal failed to drop it instantly, the second shot was sometimes intended to physically immobilize it (it is worth noting that some very reputable hunters argue against this approach). Once immobilized, it could be dispatched with a precise shot to the brain. Against humans, the hips are the target. According to Louis L'Amour, this was the preferred target for some gunfighters in the Old West, because the hips are the center of movement, therefore easier to hit, and because a bone-breaking hit here would put a man down (incidentally, this is the shot which put the "Terminator" down in the Massad Ayoob article, after the direct hit in the brain failed to stop him). Partly for this reason, the power to smash major bones is also sometimes an important attribute for a bullet load.

Before departing from this subject it is worthwhile to preemptively dismiss one of the most fundamental misunderstandings of wound ballistics. Many people talk of "stopping power", "knockdown power" and "killing power", and while these terms have many interpretations based upon the personal experiences and observations of the speaker they all fundamentally refer to an inherent ability on the part of the bullet, load or weapon to dispatch an animal (or person) post haste, specifically to drop it in its tracks. What I maintain and what I believe the most thoroughly experienced hunters and rigorously accurate students of wound ballistics will readily admit is that no bullet or cartridge, in itself, can reliably provide this effect.

One of the most significant and utterly uncontrollable variables in terminal performance is the target itself; not merely the shot path or point of impact (these can be controlled), but the intrinsic constitution of the animal. I have seen deer with their heart blown quite literally away that ran 100 or even 200 yds on nothing more than the oxygen present in the blood at the instant of impact. Others spring lightly away as if unhurt when hit in an identical manner by a load which has dropped similarly sized game as if struck by a thunderbolt. Some will continue to graze calmly as though unaffected by the passage of the bullet through their vitals or the sound of the rifle's report (clearly in a state of shock). Some appear to be flipped or thrown by the impact while others never twitch a muscle. Some flinch or drop their hind quarters in a spasmodic contraction of agony, but nevertheless run or walk away. The point is this: there is never any certainty of the effect on a game animal even when all of the controllable variables are held constant. Shoot any ten deer, elk, sheep, antelope of identical size and age on a classic broadside shot through the shoulder and lungs; half of them will crumple on the spot but the remainder will exhibit most or all of the various behaviors described above. A research project by the South Carolina Dept. of Natural Resources into the effects on deer shot with high powered rifles demonstrates these assertions.

The phenomenon from which this misunderstanding arises is simply trauma to the central nervous system (typically the upper or thoracic spinal region, but also the brain in special instances) resulting from the violent pressure wave that accompanies a bullet passing nearby. Consider the following exerpt from the abstract to an study by a researcher at the California Institute of Technology, Department of Aerospace:

The focusing effect of thoracic vertebrae on pressure waves impinging on the spine from different directions has been calculated using the theory of geometrical acoustics. The bony tissue lateral to the spinal canal forms a bi-concave lens which owing to the large sound velocity of bone strongly focuses pressure waves into the canal. This effect occurs over a large range of incidence angles, so it is likely to occur any time missile-generated pressure waves impact on the spine. Because of this focusing effect, individuals receiving lateral impulsive impact by gunshot are subject to neurological threat even when the missile does not enter the spinal column.

(Shock Wave Effects in Biomechanics, B. Sturtevant, Sadhana: Surveys in Fluid Mechanics-IV, Vol. 23, Parts 5 & 6, Oct & Dec 1998, pp. 579 - 596)

(Remote spinal injury caused by the focusing of pressure waves induced by missile penetration, B. Carriere, B. Sturtevant, J. S. Kung, S. Wolf, and J. Cates. Prepared for Journal of Trauma, 2001 (Unpublished))

The result is instant incapacitation, not due to loss of blood or oxygen to the brain, but rather to a paralyzing trauma. This effect is typically temporary (ie, non-fatal in itself) but usually attended by severe wound trauma which leads very quickly to fatal hemorrhage. Attributing this effect to certain cartridges or bullets is a mistake. Move the shot path a couple of inches lower and no such effect will be observed, although the animal will expire in the same matter of seconds, remaining on its feet standing, walking or running. The only time this is really important is against dangerous game (when those 5 to 10 seconds might include being trampled, mauled or gored) and from what I've read and witnessed it cannot be depended upon in the case of the Cape buffalo with the largest rifles ever made. I have never seen any Cape buffalo hit in the body which appeared to be affected by "shock" to any degree whatsoever.

However, here is a contrarian view, for what its worth:

...as I idly leafed through the pages my attention was arrested by an article on knockdown effect. It was not the same tired old stuff about ballistics and penetration, but the result of a controlled study carried out by professional veterinarians engaged in a buffalo culling operation.

Whereas virtually all of our opinions about knockdown power are based on isolated examples, the data gathered during the culling operation was taken from a number of animals. Even more important, the animals were then examined and dissected in a scientific manner by professionals.

Predictably, some of the buffalo dropped where they were shot and some didn't, even though all received near-identical hits in the vital heart-lung area. When the brains of all the buffalo were removed, the researchers discovered that those that had been knocked down instantly had suffered massive rupturing of blood vessels in the brain. The brains of animals that hadn't fallen instantly showed no such damage. So what is the connection?

Their conclusion was that the bullets that killed instantly had struck just at the moment of the animal's heartbeat! The arteries to the brain, already carrying a full surge of blood pressure, received a mega-dose of additional pressure from the bullet's impact, thus creating a blood pressure overload and rupturing the vessels.

(Knockdown Power: Some calibers always seem to flatten game. Here's why, Jim Carmichael, Outdoor Life, July 31, 2003)

The foregoing case study is a fascinating observation and supports the existence of another incapacitating mechanism besides temporary neurologic paralyzation. This mechanism has been suggested by a pathologist I corresponded with years ago and amounts to an induced cranial aneurysm. I would love to know the details of the study described by Jim Carmichael, in particular the precise shot line through the body and the fraction of kills that exhibited this behavior, but I do not have a reference.

As an example of the downside of this instantaneous incapacitation phenomenon, consider the following account from the experience of Sir Samuel White Baker using the .577 Snider, which drove a 480 grain bullet at approximately 1200 fps:

I never like to see an animal fall apparently stone dead without the slightest struggle, as it is generally paralysed for the moment, but quickly recovers, and escapes;...I had missed the shoulder, and the bullet had struck in the middle of the neck. We were standing together, admiring the massive proportions of this fine waterbuck, when, without the slightest warning or preparatory struggle, it jumped up and started off at a full gallop. ...

This was a curious example of an instantaneous recovery from the stunning effect of a shot in the neck. My rifle was a wonderfully accurate weapon, but it was in the early days of breechloaders, and although .577, it carried the Snider bullet and 2-1/2 drams of powder. This had no penetration and animals were continually escaping, which would not have been the case with a larger charge and a solid bullet. In this instance the bullet had struck the spine, but had not sufficient power to break the bone, after passing through the hard muscles and tough hide of the waterbuck at a distance of about 220 paces.

(Sir Samuel W. Baker, Wild Beasts and Their Ways, Briar Patch Press, 1988, pg. 345)

My brother related an even more astounding story of a deer that was "killed outright" by a single pellet of buckshot on a late morning hunt. It was transported back to camp, but left unbutchered until after the afternoon hunt, whereupon many hours later it suddenly "came back to life", creating no small amount of consternation.

In summary, lethality in terminal ballistics is caused by collapse of the central nervous system, either directly or indirectly by collapse of the circulatory system. Incapacitation may be caused by interruption of the central nervous system, or else by damage to vital systems or skeletal structures. Furthermore, incapacitation and lethality are distinct physiological effects, caused by different mechanisms, and the terminal ballistics attributes and mechanics responsible for the one effect do not necessarily apply to the other.

Having established what constitutes an effective wound, let us consider the kinematics of wounding. The best explanation of actual wounding potential is very simple. It relies upon the 7th grade definition of energy. Remember?

In terms of terminal ballistics, "work" involves all aspects of the bullet-target interaction event; but not all of this kinetic energy is applied to effective work. Some of the energy is lost to heat, some to friction, some is tied up in the rotational velocity of the bullet, some lost to elastic displacement, and some is usually spent on deforming the bullet. The only work which is effective work is that which causes damage to the target, by penetration and cavitation.

The basic elements of the kinetic energy of a bullet are provided by rotational (angular) and axial (linear) velocity. Generally, only the axial velocity is applied to wounding work. Some bullets were designed with cutting surfaces on their expanded edges; examples include the Trophy-Bonded Bear Claw bullet, Barnes X-Bullet, and the Winchester Black Talon and Fail Safe and PMC Starfire pistol bullets. These bullet designs were intended to use rotational velocity to enhance cavitation by cutting tissue as the bullet penetrates. However, it is relevant to observe that the kinetic energy of a bullet due to its angular velocity is only about 0.5 % of its axial kinetic energy, thus any effect realized by this approach is hardly significant.

Bullet deformation is a significant source of energy loss. The energy required to expand or fragment a bullet is not used to penetrate or cavitate. For this reason, most big game bullets are designed not to "shed their cores" or otherwise fragment, though some extremely successful designs have exploited this very mechanism, notably the Nosler Ballistic Tip. Energy, like water, follows the paths of least resistance. If the bullet is not tough enough to accept the stresses encountered at impact, it deforms along with the target. This deformation takes the form of expansion, fragmentation, core-jacket separation, bending, flattening, etc. Soft point bullets are designed to deform in a controlled fashion while remaining in a point forward orientation during penetration. Big-bore solids for heavy dangerous game are designed to (ideally) remain undeformed throughout penetration, thereby using all of their kinetic energy for penetration and cavitation (most of it on penetration). Deformation is not necessarily bad. Most bullets rely upon deformation for their success, and have been designed for a balance of deformation and structural integrity for a specific purpose.

Other exceptions to the rule (besides big game solids) are full metal jacket (FMJ) spitzer military bullets. Because living tissue is roughly 1000 times denser than air, for a non-deforming spitzer bullet in which the center of pressure lies ahead of its center of mass, the angular velocity of a rifled bullet that gives it stability in air will typically not keep it in a stable point forward orientation after impact. Bullets in flight have small pitch and yaw deflections, as well as resultant precession and nutation motions, but these are held within reasonable limits by the angular momentum of the spin. Because of the angular momentum, pitch and yaw motions are coupled. Here is a good, brief description of bullet flight motions. Although bullets in flight do have a true up direction in an inertial frame, ballisticians more often dispense with the classical distinctions of pitch and yaw, instead using the term yaw to describe any angular difference between the axis of the bullet and the direction of travel. I don't remember seeing the term pitch being professionally used in a wound ballistics context either. For this discussion, I will adopt this practice. Non-deforming spitzer bullets yaw and oscillate during penetration at impact velocities greater than 2000 to 2200 fps due to instabilities precipitated by their shape and in spite of their angular momentum (deforming bullets immediately assume a more stable shape). The instability imparted at impact causes the bullet to yaw (or "tumble") as it attempts to reorient itself in a stable position (generally, base forward if it remains intact). All of this yawing causes increased cavitation (from the larger presented area) while the bullet is penetrating, and some recent military bullet designs have been specifically engineered to do this (thereby contravening the intent, if not the letter, of the Hague Convention).

Wounding is caused by the force exerted by a bullet to displace tissue. The exertion of force in displacing tissue requires an expenditure of energy, and translates into damage to the tissue in the form of penetration and cavitation as the elastic limits of the tissue are exceeded by the stresses imparted from this force. According to Cranz' Law, the kinetic energy of a non-deforming projectile is proportional (in a non-elastic medium) to the volume displaced by penetration and cavitation. But the quantity of kinetic energy alone does not tell us enough to predict the dimensions of this cavity. Reality differs. Real bullets generally deform and real tissue is extremely elastic. In understanding the interaction of the bullet with the target, it is helpful to consider the water analogy. The higher the impact velocity of a projectile, the greater the initial resistance. This is what I call the "splash effect", and is true of all solids when the stresses placed upon them overcome their intrinsic rigidity and cause them to behave like a fluid. It is easier to push your hand into water than to slap into it. Pushing slowly, you can penetrate deeper with less effort (energy) than by slapping at a high velocity. However, by slapping you make a bigger splash in the water (cavitation). These are exactly the basic mechanisms which govern terminal ballistics in living tissue. Understanding how the kinetic energy of a bullet contributes to wounding, we can consider the separate components of wounding.

Penetration is simply the depth to which a bullet passes through a target. Factors affecting penetration for modern weapons, in order of importance are: 1) bullet construction, 2) bullet shape, and 3) impact velocity.

Bullet construction is the most important factor because it will determine whether the stresses of impact allow the bullet to overcome the resistivity of the target. In other words, is the bullet tough enough to survive the impact and penetrate, and if so will it deform by ductile flow and erosion or will it shatter, and how far will the residual mass(es) and/or fragments penetrate? Advances in metallurgical processing of bullets have made contemporary designs superior to anything used in the last century, giving small-bore bullets the effectiveness of huge lead balls. The target material will greatly affect the selection of bullet material, but in general, toughness (malleability) is more important than hardness. Other features, such as bonded cores and tapered or partitioned jackets permit greater penetration by controlling the expanded presented area and retaining bullet mass.

Bullet shape is next in importance because a pointed bullet which does not deform becomes unstable at impact velocities of interest and will not penetrate as deeply as a flat-nosed or round-nosed bullet of the same weight and velocity. Non-deforming round nosed bullets generally penetrate more deeply than flat-nosed bullets, depending on the width of the flat nose and the radius of the round nose. Since nearly all rifle bullets today are pointed designs intended to deform, bullet shape also applies to expanded or fragmented bullets. Sectional density is a quantity often associated with penetration, and is defined as bullet weight divided by the diameter squared. In simplistic theory, it describes the relative ability of a bullet or fragment to penetrate. For a given caliber, the heavier bullet will have a higher sectional density. However, this value does not consider bullet construction, the shape of the nose or the effect of erosion (loss of bullet mass) after impact. At impact, the effective sectional density becomes the retained bullet weight divided by its expanded represented frontal area (which initially is smaller than the nominal caliber). Thus, practically speaking, two bullets having the same sectional density can have very different penetrations after impact, depending upon their shape and toughness. Sectional density is a misleading indicator of performance for bullets of different constructions and materials; sometimes even for apparently similar designs. Varmint bullets have low sectional densities, but even these values suggest better penetration than they are capable of providing when compared to big-game bullets of heavy jacketed, bonded core or monolithic construction. Similarly, the stronger premium bullets (such as the Barnes X-Bullet) are capable of penetrating as deeply as bullets of conventional construction having much higher sectional density.

Finally, impact velocity determines the hydrodynamic pressure, which may be thought of as the resistance to penetration encountered by the bullet. Impact velocity has a significant effect on bullet deformation (involving both bullet construction and shape), but beyond this it also affects the amount of cavitation caused by the bullet in tissue. In theoretical terms, a projectile creates a cavity which is proportional to its kinetic energy (actually, the permanent volume of the cavity may be considerably less than the theoretical expected volume). The cavity extends radially (what I term cavitation) and along the path of the bullet (penetration). The more it cavitates, the less deeply it penetrates. High velocity can have a detrimental effect on penetration in a fluid, due to the "splash effect". It can destroy the bullet or cause it to create an enormous cavity without penetrating (which is not necessarily undesirable in certain tactical situations).

Most rifle bullets are designed to perform reliably within a rather narrow range of velocities, usually 2000 to 3000 fps for most conventional rifle bullets. Below this velocity range, the bullet may not expand; above it, the bullet may shatter on impact. This is a limitation imposed by material properties and design characteristics. For this reason, bullets which are intended for pistol hunting loads would be inappropriate for use in high velocity rifles, since their impact velocities would be very much higher than those they were designed for (although they may perform perfectly for long range shots where the velocity has moderated). Other bullets, referred to as "custom" or "premium" designs, can be successfully used for a wider range of impact velocities, perhaps as low as 1700 fps and as high as 3300 fps (though most designs tend to work better at one end of the velocity spectrum than the other). They are typically designed to expand easily at low velocities but retain their weight (at least most of it) at high impact velocities. Bullets designed for the older low-velocity rifle cartridges and for handguns can be relied upon to expand down to about 1400 fps in the case of rifles and 900 fps in handguns.

Against hard solid targets, such as armor or heavy bones, high impact velocity is the most important factor contributing to maximum penetration (assuming that the bullet remains intact), because this has a shattering effect upon the material. Maximum penetration in a fluid medium, however, is achieved when cavitation is held to a minimum, as in the case of a non-deforming, round-nosed bullet travelling at "moderate" velocity. Heavy big-bore, flat-nosed, hard-cast lead-alloy bullets are favored by handgun hunters for large game because they are more efficient than jacketed soft points. The broad flat nose on the relatively large caliber bullet provides adequate cavitation, so expansion isn't necessary. Since there is no expansion, there is also no energy lost to bullet deformation - all of the remaining kinetic energy of the extra-heavy bullet is directed toward penetration with acceptable cavitation.

Cavitation is caused by two sources: mechanical crushing and hydrodynamic pressure.

Mechanical crushing occurs directly in the path of penetration and is caused by the undeformed bullet nose or the expanded bullet "mushroom". At low velocities, flat or sloping surfaces merely push tissue aside. However, at higher velocities, tissue is macerated. For rigid solid bullets, a flat nose shape with a broad meplat (the flat portion of the bullet nose) will create a larger crushed cavity than a semi-spitzer or round nose shape. For expanding bullets, a broad and nearly flat expanded bullet shape will create a larger crushed cavity than an expanded "mushroom" with a classic round shape with gently sloping edges. Although an expanded bullet may have a diameter of 0.55 to 0.75 inch (14 to 19 mm), the effective meplat diameter is rarely more than the nominal bore diameter.

Hydrodynamic pressure causes damage from the induced radial velocity extending from the stagnation point at the point of the bullet in its axis of travel to the outer edges of the bullet. The tissue velocity is zero at the infinitessimal point of the bullet nose, where the hydrodynamic pressure has its highest value. The velocity with which the tissue is displaced by this pressure is a function of the angle between the axis of penetration and the bullet nose (see the figure below). If the angle is small, the radial displacement velocity is small. For this reason, a larger diameter, flatter expanded bullet is more effective in producing cavitation from hydrodynamic pressure than a smaller diameter, steeply sloped bullet shape. Because the tissue displacement velocity is also proportional to the penetration velocity, the permanent cavitation can be much larger than the actual diameter of the bullet. This is how a .50 inch (13 mm) diameter expanded bullet can create a 1.5+ inch (39 mm+) permanent hole in game.

In the realm of armor penetration there is a principle known as Cranz' Law, which states that the penetrated cavity volume is proportional to the kinetic energy of the penetrator. There is a corrolary in wound ballistics, which was characterized and described in a seminal study entitled Wound Ballistics, part of a history of the US Army Medical Department during World War II:

Figure illustrating the effect of bullet nose or expanded shape on the cavitation flow field for: solid flat-nose (upper left),
solid round-nose (lower left), monolithic expanding (upper right) and lead-core expanding soft nose (lower right)

The chart below describes the dynamic pressure of a projectile moving through water at ballistic velocities. Now tissue is not exactly the same as water but the densities are similar and so the hydrodynamic pressures created are similar (actually a bit higher since tissue has mechanical strength and fluids do not). Soft lead has a tensile yield strength (flow stress) of roughly 5000 psi (5 ksi). Harder lead alloys have a flow stress of about 7500 psi and heat-treated wheel weight alloy has a flow stress of roughly 11 ksi. Pure soft copper has a flow stress of roughly 17.5 to 20 ksi, while harder copper alloys can have yield strengths approaching that of mild steel, or about 80 ksi. If you examine the chart you will see that these figures correlate reasonably well to experience. Pure lead bullets will deform at velocities down to 800 or 900 fps in impacts with soft tissue. Harder lead alloys will deform at magnum handgun velocities. Monolithic soft copper bullets can be expected to deform at velocities above 1700 or 1800 fps. A brass alloy bullet might retain its shape until extremely high impact velocities were involved. Obviously deformation depends on design as well, so these numbers are merely general bounds. What this also shows is the severity of high velocity impacts. The dynamic pressure at 3000 fps is more than twice that at 2000 fps.

Figure illustrating the dynamic pressure exerted on a bullet moving through water at ballistic speeds of interest

All tissue is elastic and will rebound, up to a point, from the stretch caused by the hydrodynamic force of the bullet's passage (this is termed a temporary cavity). Tissue has varying elasticity and some tissues will be damaged by hydrodynamic pressure which causes only temporary cavitation in other surrounding tissues. In general, however, temporary cavitation is relatively insignificant for the hunter, although it is often very useful in combat situations. Humans are not as psychologically predisposed to struggle to survive as wild animals, and will often collapse or surrender when struck by a bullet which causes violent temporary cavitation, even if they are not physically incapacitated (especially if the bullet passes close by the spine). Game animals will generally recover and run (or charge) within a second or so; aggressors hyped on drugs or anaesthetized by endorphins as a result of a previous injury will behave in the same way.

The figure below illustrates the typical wound cavity created by most conventional lead-alloy cored, copper-alloy jacketed bullets. The dashed line indicates the dimensions of the temporary cavity. Note that there is often a short "upset depth" before the bullet begins to deform, then a violent cavitation as the bullet expands. The deformation of the bullet is complete approximately at the terminus of the large cavity. Thereafter, the bullet penetrates in a rigid form until the termination velocity of the tissue is reached. It then travels a short distance elastically with its residual momentum until rebounding to the end of the permanent cavity at rest.

Figure illustrating a generalized wound track in ballistic gelatin, showing both the permanent cavity
(in white) and temporary cavity (dashed lines)

I will make a general statement which I will defend at length as we go along. Assuming that a bullet creates at least a 3/4 to 1 inch (19 to 25 mm) diameter hole through the vitals (a well placed shot), penetration is the more important of the two functions of a bullet for the big game hunter. A 3/4 inch (19 mm) hole which severs major arteries or passes through blood bearing vital organs will cause a rapid loss of blood pressure and will drop most game within 50 yards. This is not to suggest that extreme cavitation will not cause an animal to succumb more rapidly. It could. However, bullets which cause extreme cavitation generally do not penetrate deeply and may not be suitable for some aspect angles due to the depth of penetration required to reach vital organs or the presence of interposing heavy bones. On the other hand, if only broadside body shots are taken, extreme cavitation may deliver the highest proportion of rapid kills.

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III. Myths, Misconceptions and Miscalculations

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