Wound Ballistics

Until this point we have dealt with the penetration of projectiles into inanimate objects. One of the more tragic aspects of ballistics is the fact that they are used against living creatures. This is not meant to imply that hunting is good or bad, but simply that there are instances when people, intentionally or not, fire weapons at other people or animals and the effects of the bullet impact must be understood. When a projectile is fired at a living creature some amount of incapacitation is desired. If

a projectile is of the nonlethal type, trauma to the target must be minimized and either a fluid must be injected, the victim must be rendered physically immobile, or some other effect must be obtained. If the projectile is of the lethal type, ideally one hit should subdue the victim (through any protection) rendering them incapable of harm. Because the subject of wound ballistics is as complicated as the target’s anatomy, we

shall only conduct a cursory review here, pointing the interested reader to some excellent references for further detail. We shall only treat subjects which affect humans, though these may affect animals in a similar manner. An interesting statistic is that over 58% of combat casualties in the British army during

the First World War were caused by fragments rather than bullets [1]. This is interesting since we all have seen movies (accurate or not) of wild charges into machine gun fire. This is probably the case with most conflicts. In the sections on aeroballistics, we have learned to treat projectile flight through a fluid

medium (air). While these equations still hold in a human body, the simplifications we made do not always hold and we must take steps to include properties such as the elasticity of tissue. The initial conditions such as entrance angle become largely important when dealing with a wound. Additionally, a bullet is usually unstable in a human body, causing it to yaw greatly or even tumble. Thus, bullet geometry, mass properties, and material strength matter a great deal as far as the extent of damage is concerned. Before we discuss the details any further, it must be understood that there are many

people who have diligently studied the field of wound ballistics during their entire careers. These researchers have drawn on their wide experience, some from the engineering viewpoint and some from the medical viewpoint, to reach conclusions and develop theories about wound physics. They are probably all correct even though their viewpoints may be vastly different. The reality is that ‘‘anything’’ can happen when a bullet interacts with a human. It has been these authors’ experience that the experts can be categorized into two broad camps: the medical camp and the engineering camp. The medical camp sees the wounds (even wounds that were caused by an identical bullet at an identical entrance angle into an identical location) as individually different and must be treated through a medical procedure based on the caregivers’ experience, observations, and understanding. The medical camp believes that the psychological and physiological effects of a wound will always be different and that no conclusions can be drawn based on weapon type, etc. The engineering camp believes that wounding can be quantified through physics. They believe

that relationships (potentially very complex) can be drawn based on energy, momentum, material properties, etc., which can be used to quantify the effect of projectiles against persons. The truth is probably a combination of both camps, but to date no one has found the Holy Grail that would bring it all together. The work by Peters [2] states that there are several misconceptions about wounding that

must be addressed. One misconception is that the temporary cavity is the major cause of tissue damage. This has probably grown out of extremely interesting videos that have been published showing massive temporary cavities in projectile firings through gelatin blocks. It is difficult to imagine, as a human, that these cavities would not cause huge amounts of damage. In fact, this topic is rather hotly debated by experts. We shall pass no judgment here, simply state that the work of Peters suggests that less than 20% of all tissue damage is caused by the temporary cavity. Another misconception pointed out by Peters is that tissue damage is proportional

to kinetic energy of the projectile. Peters suggests that there is a relationship but it is nonlinear. It was thought (and possibly still is) that the sizes of the maximum temporary cavity and the permanent cavity were somehow proportional to energy deposited in the target by the projectile. Peters suggests that there is a nonlinear relationship but additionally, over some ranges of the data, it can be linearized which is possibly why the conclusion was drawn. Engineers who look at a person as an engineering structure at some point assume that

the volume of the permanent cavity must, in some way, result from material ejected from the wound. That is, that the permanent cavity volume must equal the volume of material ejected. This is not the case since a permanent cavity remains even when the bullet stops in the target. The cause of this permanent cavity is primarily through inelastic deformation of the tissue. Peters and other researchers have shown that temporary cavities in humans or animals

will be of different size than those developed in gelatin blocks. Currently, this is a very active area of research. There are even differences in cavity formation between animals and humans to the extent that no scaling law has been universally established. One of the most interesting aspects of wound ballistics is the inertial effect on a human

body. In many Hollywood action films, we routinely see people being picked up and thrown several feet backward by impacts of small arms projectiles. When the numbers are worked out with a 7.62-mm projectile at point blank range, the

energy exchange (assuming the bullet remains lodged in the target) is such that the rearward velocity is less than 0.2 mil=h. In fact, most human targets usually fall toward the shooter (unless they were running away when hit). We shall next discuss some bullet types that are illustrated in Figure 19.1. A solid slug is

nothing more than a soft metal (usually a lead alloy) projectile that is engraved along its body length by the rifling to impart spin. A full metal jacket (FMJ) projectile is a solid slug

Theory and Design of Guns and

that is coated with a material such as copper to better withstand firing stresses and whose residue can easily be removed from the inside of the gun tube. A semi-jacketed projectile or open-tipped projectile is jacketed up to a small region of the nose. This region, being softer than the jacketed region and unable to withstand the radial stresses upon impact, expands as it enters the target theoretically causing a more extensive wound. A hollow point projectile is similar to a semi-jacketed projectile except that the tip is actually concave, which uses fluid mechanics coupled with the lower radial strength upon penetration, to open larger. Finally, the steel-core projectile has a hard core for penetration of metallic structures or textile armor. There are a huge number of other projectile types such as slit jackets, dum-dums, etc., but usually they fall into one of the aforementioned categories. In the earlier paragraphs, we mentioned some terms such as temporary cavity and

permanent cavity. We will now define some of these terms. A laceration is a cut through tissue. A projectile’s primary means of incapacitation is

through laceration. Because of the complicated nature of the human body, a projectile which penetrates can do anything from causing minor bleeding if no major organ or artery is damaged to rapid death if a vital organ is hit. If a projectile impacts bone tissue or even meets a severe gradient in density, it can be deflected considerably. We learned a great deal about stress waves previously. When a projectile enters a human

being, it sends stress waves through the body. These waves and associated rarefactions can cause damage, but it is generally agreed that, primarily, these waves will damage nerves and can, possibly, collapse organs. The temporary cavity is created through the process of cavitation introduced earlier in

the fluid mechanics section (Figure 19.2). It results from the adherence of the fluid molecules to the surface of the projectile, and when the shear stress drops to zero on the surface, the flow separates. This separation bubble can grow to 40 times the projectile diameter as the projectile passes through the body. Once the projectile has passed by, however, the radial energy that it imparted to the tissue is removed and the elasticity of the tissue causes it to immediately collapse to a much smaller size. The largest extent that this bubble reaches is known as the maximum temporary cavity while the small, equilibrium cavity is known as the permanent cavity. Projectile yaw has a dramatic effect on cavitation. As stated earlier, a projectile is usually

unstable in a human body. This causes it to yaw considerably and possibly tumble. As one can imagine, because of the relatively immense presented area of a projectile flying with a large yaw, the separation and associated cavitation can be huge. In fact, if a projectile rotates 1808, it will usually exit the target base first. This is depicted in Figure 19.3. Analysis of this flight behavior is extremely difficult because projectiles perform differ-

ently depending upon what tissue they happen to be passing through. The following is a short list of just a few of the different types of tissues that affect bullet passage through a living creature:

. Bone

. Skull and brain

. Thorax=ribs

. Lung

. Intestine=stomach=bladder

. Muscle

Each of these tissue types will have a different effect on the projectile. It is even important if an organ is flaccid (empty) or not or whether the target is living or dead. For simplicity, the most general research is carried out on muscle tissue and that is where a great deal of work has been expended to come up with a suitable surrogate material. Assuming we are discussing muscle tissue penetration, the first thing we must recognize

is that tissue has a nonnegligible tearing stress that must be overcome. This additional stress must be incorporated into our drag model. We cannot emphasize the complexity of the problem enough. Even though, in the discussion that follows, we shall assume a penetration into homogeneous muscle tissue we must always keep in mind that a penetration event is much more complicated. We know that as a projectile enters muscle tissue, what was once relatively simple aeroballistics becomes a more complicated problem of continuum mechanics: in air, there was no yield stress to overcome (this is the major difference); the viscosity and density of muscle are different than air. If the impact angle is low enough, the nose of the projectile will enter first. The usual decrease in shear stress as we progress along the projectile will occur and at some point the shear stress will reach zero and the tissue will separate from the projectile forming a cavitation bubble. Throughout this event, the projectile will slow down due to drag. There will also be a larger overturning moment than in air because of the large force on the small area of the nose (higher density in the dynamic pressure term) and in addition the separation will take place ahead of the CG, increasing the moment arm. The drag force will also include the force required to overcome the cohesive stresses in the tissue (tearing stress) which is not usually included in aerodynamic models. What was once a transonic=supersonic flow field becomes a transonic (at best) or subsonic flow field. This is because the speed of sound in muscle tissue is around 1500 m=s (4920 ft=s). In comparison to the aerodynamic models we have presented earlier, Peters et al. [3]

have developed a drag model that accounts for the tearing of the tissue. The equation of motion is given by

Theory and Design of Guns and

mdV dt ¼ 1 2 rV2ACD þ 12 r(aU)

2ACD (19:1)

or it can be written in terms of distance traveled as

mV dV dx ¼ 1 2 rACD V2 þ (aU)2

(19:2)

In these equations, m is the mass of the projectile, V is its velocity, r is the density of the tissue, A is the presented area* of the projectile, CD is the projectile drag coefficient, x is the distance the projectile has progressed into the tissue, a is a modification to CD, and U is a characteristic velocity of the tissue (more on these last two terms will follow). If we examine Equation 19.2, we see that if we exclude the second term on the RHS, we

get our classic equation for aerodynamic drag (assuming, of course that the area is a crosssectional area, S, of the projectile). The second term accounts for the energy loss associated with the tearing of the tissue and its movement away from the projectile. The characteristic velocity is defined as

U ¼ U6 dd6

These are empirically derived values. In Equation 19.3, d is the diameter of the actual projectile, d6 is the diameter of a 6-mm projectile (in case you want the units of d in a different system), and U6 is a characteristic velocity for different materials determined through experiments with a 6-mm diameter projectile. The parameter a in Equations 19.1 and 19.2 is a function of the projectile type and the angle of attack of the projectile. The stability criteria developed in Part II of this book work fairly well for behavior in the

human body. As stated earlier, the density terms must be increased as well as the effect of Mach number. It is also recommended to add a force term as was included in Equation 19.2, however, that would require a re-derivation of the stability equations which is beyond our scope. If a projectile has features which would cause it to expand upon impact with the more

dense human tissue, it will cause greater trauma. These were mentioned earlier as hollow point and slit-jacketed bullets. The opening of the hollow point or jacket allows more of the projectiles energy to be transferred to the body and the flatter surface directs the flow of the tissue in a more radial direction. If a bullet is unstable in the body and it tumbles, there is more surface area presented for the body to slow the projectile down and thus more energy would be expended on the body. A greater amount of cavitation will occur as well due to greater radial flow of the tissue. Depending on whether this expansion happens at the entrance to the body, the exit, or somewhere in between, the wound would be affected as depicted in Figure 19.4. To defend against projectile impacts, body armor has been developed. Body armor

for humans has been designed since projectiles were first fired. Metallic armors were good against ball ammunition but armor-piercing rounds can go through them easily. Textile=composite armor has met with better success at stopping penetration, but it can still happen. Even with textile armor some depth of penetration or organ damage is still possible. In addition, the same mechanisms that we discussed about non-penetrating

damage are applicable here as well such as shock waves and momentum transfer (which is even greater for a non-penetrating hit than a pass-through). In summary, we have touched upon several aspects of wound ballistics. A more com-

prehensive treatment is provided in Ref. [4]. It is a complicated and hotly debated subject, yet one that is extremely fascinating.