Ballistics is the scientific study of projectiles. Numerous variables determine initial projectile velocity, characteristics of flight, and the projectile's effects on the target. These can be divided into the fields of internal ballistics, external ballistics, and terminal ballistics. Understanding projectile terminal behavior in human tissues is important to the radiologist when assessing the imaging of shot patients.
The key fundamental principle in ballistics is the transfer of kinetic energy, derived from the equation Ek = 0.5mv2, where m is the projectile's mass and v is its velocity.
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Internal ballistics
Internal ballistics refers to the events before a projectile leaves the firearm. The design of the firearm and ammunition is principally concerned with generating sufficient projectile kinetic energy to cause the desired effect on the target.
Types of firearms
Firearms propel projectiles (ammunition) through a barrel initiated by expanding gas. The barrel provides a linear unidirectional transfer of kinetic energy to the projectile. Barrels are typically made of alloy steel to provide rigidity and to tolerate rapid heating during firearm discharge 1,2 .
There are five basic types of firearms.
Handguns
fire a single projectile (bullet) at low to medium velocity through a rifled barrel
typically held in one or both outstretched hands
include single shot pistols, derringers, revolvers and automatic pistols
Rifles
fire a single projectile (bullet) at high velocity through a rifled barrel
typically held with the stock against a shoulder for stability
include single shot, lever action, bolt action, pump action and autoloading (semiautomatic) varieties
Shotguns
fire either multiple projectiles (pellets or shot) or single projectile (slug) through a non-rifled smooth barrel
pellets will diverge from the muzzle thereby increasing the area of the target
the barrel can be cylindrical or have a taper (choke) at the end
ammunition also include wadding (or piston) between the propellant and the projectiles which is made of plastic, paper or fiber and maximizes transmitted energy to the shot
typically held with the stock against a shoulder for stability
include single shot, over and under, double barrel, bolt action, pump action and autoloading varieties
Submachine guns
fully automatic weapons which fire bullets with large magazine capacities
smaller than machine guns and therefore can be fired by a single user
Machine guns
fully automatic weapons with large magazines or belt-fed cartridges
can be small enough to be handheld and fired by a single user
when large require stabilization such as a tripod or mounting onto a vehicle
Rifling
Rifling is the helical grooves machined along the length of the inner surface of the barrel, which provide gyroscopic spin (rotational kinetic energy) to the projectile upon discharge to stabilize its trajectory during flight. The grooves in a rifled barrel are separated by lands, which leave markings on the projectile. Rifling can vary based on the number, diameter, and width of the lands and groves, the depth of the grooves, and the direction and degree of groove twist. These factors will affect the markings left on the projectile after discharge. They can be of value for projectile and firearm identification (so much so that forensic pathologists use plastic forceps to retrieve projectiles as metallic forceps may scratch them).
Firearm size
The caliber description of a firearm historically refers to the internal diameter of the barrel before the grooves were machined into the barrel, which are typically measured in fractions of an inch in the U.S. and millimeters in Europe. An example is the common 22 caliber representing a barrel diameter of 0.22 inches. However, in reality gun manufacturers use caliber to variably refer to the barrel diameter with or without grooves or the diameter of the bullet.
Shotgun barrel diameter is described by gauge (or bore) rather than caliber and is historically based on the fraction of a pound of a solid lead sphere that would fit into the bore. An example is a 12G shotgun where the barrel will allow a lead ball weighing 1/12th of a pound.
Types of ammunition
The fundamental unit of firearm ammunition is the cartridge or round. It contains a projectile (or projectiles), a propellant and an ignition primer all held together by a case. Projectile velocities vary substantially depending on ammunition and firearm type, and in general velocity is referred to as low if below the speed of sound (340 m/s) 1-4.
Cartridge case
metallic (usually brass) casing which houses the components of the round and functions to expand and seal the chamber from retrograde escape of gas when fired
can be straight (pistols), bottlenecked (rifles) or tapered (uncommon) in shape
once fired, the cartridge is expelled from the rear of the barrel (automatically or manually) and does not travel far
head stamps contain information of the manufacturer and size and type of ammunition (therefore can be used for identification)
Primer
explosive chemical compounds housed in the base of the cartridge case that ignite with contact (percussion) of the firing pin to ignite the propellent
centerfire and rimfire types
primer residue travels through the barrel after firing and may be deposited on materials (such as a close-range target) and therefore can be used for ammunition identification
Propellant
initiated from primer ignition, the propellant combusts and rapidly expands to increase the pressure in the cartridge and propel the projectile out of the cartridge through the barrel
originally termed gunpowder, now most compounds are fast burning and smokeless
Projectiles
There are three main types of projectiles 1,2 :
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bullet
the metal bullet (typically made of lead) is housed in the tip of the cartridge and upon round discharge travels through the barrel and exits the muzzle towards the target
bullets may be designed to deform and fragment on entry of the target (thereby transferring maximal kinetic energy)
bullets may be solid or have a protective outer metallic coating (jacket) which prevents deformity in the barrel of high velocity firearms caused by rifling
jackets can be complete (full metal jacket), partial (semi-jacketed) or absent (non-jacketed)
full metal jacket bullets do not tend to deform within the target and therefore often pass through
bullet tip design (soft-point or hollow-point) allows bullet deformity upon entering the target
the base of the bullet may be crimped with a copper cup (gas check) which prevent the bullet from melting due to high temperatures and pressures
the bullet, jacket and gas check may be detached from each other and enter the target separately
a RIP round (radically invasive projectile) has several grooves machined into the tip of the bullet which is designed to create diverging separation of the components upon entry into the target, thereby causing maximal tissue injury
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shot
consists of multiple small metallic pellets (balls or beads) and most are made of lead or steel
pellet size can be classed as small (birdshot) or large (buckshot)
pellets often deform but seldom fragment
the wadding may enter the target if fired from close-range and can be used for ammunition identification
home-made shot can contain various materials and shrapnel
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slug
single large metallic projectile fired from a shotgun
mainly used for large game hunting
designed for short range and low velocity
Firearm discharge
Firing the firearm is initiated when the trigger is pulled or squeezed which engages a mechanism to hit the firing pin against the cartridge’s primer which ignites. This causes ignition and combustion of the propellant which rapidly converts from solid form to a heated gas. The gas expands to apply a strong positive pressure on the projectile, accelerating it out of the casing, down the barrel and out of the muzzle towards the target. In general, larger volumes of propellant, more explosive propellants and longer barrels accelerate the projectile at higher velocities.
External ballistics
External ballistics is the science of projectiles in flight, that is the time between discharge of the firearm to entry into the target. Drag produced by air (air resistance) significantly affects the flight of the projectile and is primarily dependent on the projectile surface area. Projectile characteristics that reduce surface area will lead to less air resistance and more stable flight trajectory. Effective surface area increases if the projectile long axis deviates from the direction of flight thereby creating trajectory instability. This is termed yaw, which is slow and akin to a sweeping motion. Yaw is analogous to proton precession in a magnetic field B0. Yaw is centered on the projectile center of mass and when extreme enough, the projectile can tumble during flight which greatly increases effective surface area and leads to a suboptimal trajectory profile. Nutation, smaller changes in the axis of rotation akin to nodding also contributes to trajectory instability. By reducing the distance of the muzzle to the target, drag is reduced allowing greater kinetic energy deposition into the target.
Terminal ballistics
Terminal ballistics describes the effects of projectiles on a target. Wound ballistics is a subset of terminal ballistics, referring to the effects of projectiles on living tissues and is of importance to the trauma radiologist assessing medical imaging of patients with projectile injuries. Traumatic injuries are the result of the transfer of kinetic energy from projectiles to human tissue. Injury type and severity are affected by projectile and tissue factors:
projectile mass, composition and construction, entry velocity and trajectory
tissue type (viscoelastic tissue characteristics include elasticity, density and internal cohesiveness) and presence of pre-existing disease
Projectile interactions within tissues
Projectiles traversing biological tissues, just like in air, experience yaw which increases the surface area along the path of travel. When doing so, the projectile transfers greater energy to the tissue (per unit length) which widens the wound cavity. Projectiles designed to deform (mushrooming), expand or fragment upon entering the target exploit this concept to produce maximal tissue damage. Yaw producing tumbling can curve the path of injury.
Most ballistic injuries encountered in radiological practice in the civilian or law enforcement setting is from ammunition that fragments in the target. Each projectile fragment thereby becomes its own individual projectile, albeit with overall lower energy (due to less mass) than its parent projectile. Fragmentation also occurs when projectiles strike bone where further tissue damage can occur from fragments of shattered bone acting as individual projectiles.
Types of wounds
Injuries caused by projectiles can be described as 2:
penetrating injuries: referring to injuries where the projectile remains inside the body
perforating injuries: referring to injuries where the projectile enter and exit the body with minor tissue loss
avulsive injuries: referring to extensive tissue loss
Mechanisms of tissue injury
In basic terms, tissue destruction occurs when the elastic limits of the tissues are exceeded by the kinetic energy deposited by the projectile. Tissue damage can be direct or indirect and there are three main mechanisms of injury 1,2,5,6 :
Laceration and crushing
primary injury produced by the projectile’s leading edge along its path, that is it occurs immediately in front of the projectile
the diameter of the path is proportional to the effective surface area of the projectile
Cavitation
this is the tissue damage produced behind the projectile, and there are two types
a permanent cavity is formed along the path of the projectile, following the initial laceration and crush injury. diameter of the cavity is proportional to the effective surface area of the projectile
a temporary cavity is formed by hydrostatic forces stretching the tissues surrounding the permanent cavity and radiate outwards, perpendicular to the projectile path. Higher velocity projectiles and those with greater yaw increase the size of the temporary cavity. The cavity can be asymmetric and tissue injury in the temporary cavity can be minimal or non-existent with low-velocity projectiles (with exceptions being sensitive tissues such as the brain). The most susceptible tissues to temporary cavitation are those with low elasticity due to water-like tissue density such as brain, liver and spleen and fluid-filled organs including the heart, bladder, bowel and vessels. Highly elastic tissues are the least susceptible to temporary cavitation and include lung and skeletal muscle.
Shock waves
are the mechanical forces that travel in front of and to the side of the projectile that rapidly compress surrounding tissues causing violent pressure changes
these forces can lead to tissue damage especially in higher velocity projectiles which produce greater shock waves
Shotgun pellets collectively possess significant mass and kinetic energy at close range, whereas individually each pellet has a small amount of kinetic energy due to its relatively low mass. At longer range, the pellets lose velocity quickly and therefore reduce kinetic energy substantially. Therefore, shotgun pellets rarely exit the body as their energy is completely deposited into the target.
Entry and exit wounds
Although the realm of the forensic medical examiners and pathologists, radiologists are sometimes asked to determine the likely entry and exit skin wounds. Often these are not obvious on CT images, but the use of 3D volume rendered reformats can help. In general, entry wounds are usually more round or oval and sharper than exit wounds, but this is a very broad generalization. Exit wounds can vary substantially in both size and shape and may have tissue protruding from them. Obviously correlating the number of entry and exit wounds with the number of retained projectiles is paramount. As previously discussed, shotgun pellets rarely exit the body as their energy is completely deposited into the target. However high-powered shotguns fired at close range, along with high-velocity rifles can produce explosive-type exit wounds with significance tissue damage. Some radiologists and trauma physicians advocate the use of markers placed on the skin at the site of the wounds to aid the radiologist reading the CT. These can be useful provided they do no create artefact that can be misinterpreted as foreign body material.
Bone bevelling
Significant energy is imparted to bone by projectiles leading to fracture as bones is very dense. In projectile injuries with minimal or no yaw, a characteristic fracture appearance occurs with a bevelled edge. The projectile initially fractures the first cortex (this could be the inner or outer table of the skull) creating a small entry margin of the bevel (internal bevel). Then traveling along its path, the second cortex is fractured with a wider exit margin (external bevel). The internal bevel may be accentuated in areas of very high dense bone such as the petrous temporal bone. Beyond the bone, osseous fragments and debris can get pulled along the track of the continuing projectile, which therefore can help determine directionality. With high velocity projectiles exerting massive supersonic forces, an explosive pattern of injury may be seen, especially in the skull.
Other biological manifestations of ballistic injury
Bullet embolization
This is uncommon and more likely with shot rather than a single bullet. It occurs most often in the arterial system but has been reported in the portal system and intracranial and pulmonary circulations. The heart and aorta are the most common site of entry. Embolization typically occurs at the time of injury but delayed embolization (up to 4 weeks later) has been observed. Not unsurprisingly, venous emboli typically are found in the right heart chambers or pulmonary arteries and arterial emboli in the extremities. The key to radiological diagnosis is retained projectiles remote to the entry wound or trajectory or changing position of the projectiles over serial imaging. Projectiles can also migrate when initially coming to rest in other body cavities, such as bullets found in the GIT from entry via the mouth or neck.
Secondary infection
Infection can occur as despite the heat generated by firing, projectiles are not sterile. Bacteria can enter the wound with the projectile from the firearm barrel, intermediary materials passed though such as clothes and the skin and mucosal surfaces of the body.
Plumbism
Plumbism refers to systemic lead toxicity and it is extremely rare after projectile injury. Due to the number of shot pellets, it is more commonly seen in patients with retained shot rather than single bullets. Most cases arise from the retained projectile being lodged within a joint, a bone or an intervertebral disk. Intra-articular retention leading to plumbism is classically described in the literature due to the synovial fluid being capable of dissolving lead.
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