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Article – Missing Targets: Understanding Small Arms Accuracy and Dispersion

Small arms are complex; they are the foundation weapon system of all soldiers and form the cornerstone of land combat. We ask a lot of small arms and they are truly the ‘jack of all trades and master of none’. We’ve previously looked at small arms terminal performance in order to understand that terminal performance is more than increased calibre. ‘Target defeat’ is the last element in the chain and therefore a systems perspective needs to be considered.

This article is going to explore the key factors that affect small arms accuracy and dispersion; examining barrel length, suppression, recoil and projectile trajectory.

Although arguably it is the most important aspect in the kill chain, defeating the target is the last element. As outlined below, a target must be detected, identified, hit and lastly defeated. This then means that the overall system is critical to defeating a target. For example, for a target to be ‘hit’, the weapon system and sights must be correctly aligned with the projectiles trajectory or as we refer to it; the rifle must be ‘zeroed’.

P(detect) x P(identify) x P(hit) x P(defeat) = P(kill)
Note: P = Probability

Figure 1: The small arms ‘kill’ chain

 

Definition and understanding

The definition of accuracy and dispersion differs across the literature; Carlucci, 2008 defines accuracy as the ‘closeness’ to the intended point of impact and dispersion as the spread around the intended point of impact. The accuracy of the projectile can be affected by the firer, weapon and atmospheric conditions, including wind speed and direction.

  • Dispersion.
    • Dispersion group size, also referred to as extreme spread is the generally agreed method to measure projectile dispersion. The distance between the two extreme projectiles of a single group is measured whilst the other projectiles are ignored. Although it might make it prone to chance it is normally suitable for range practices.
    • The measure of error or dispersion used during test and evaluation activities is ‘standard deviation’ (SD). Standard deviation is a means to reliably describe the dispersion of projectiles during NATO standardised Accuracy Test. Dispersion can be expressed as ‘a length as a product of the target distance’ (for example SD=52.2mm@400m). An alternative measurement is angle (for example SD=0.13mil). Utilising an angle is independent of the distance because dispersion grows at the same rate as the distance.
  • Accuracy. Accuracy describes the distance of the mean point of impact from the desired point of impact (which is also the point of aim). Accuracy is one of the fundamental elements in the small arms kill chain. Unless the weapon shoots true, a small group is useless. A pre-condition for accuracy is a ‘zeroed’ weapon although it is difficult to determine the true zero of a weapon as projectile dispersion blurs the true location of the mean point of impact.

Factors affecting accuracy and dispersion 

  • Barrel length and construction. Variations in barrel length and construction will have a substantial impact on accuracy and dispersion. Long barrels that are constructed from thin materials may suffer from barrel whip, which will lead to increased projectile dispersion. Shorter barrels constructed from heavier materials lead to internal ballistic issues causing irregular propellant burning rates which leads to increased projectile dispersion.
  • Suppression and recoil management. 

    • Suppressors and recoil management devices like muzzle brakes and flash hiders have a direct influence on the intermediate ballistics phase and therefore potentially affect the trajectory. Suppressors are designed to reduce noise generated from the expanding super-heated gas pressure wave referred to as the Mach disc. Suppressors also reduce flash and recoil although not to same extent as the dedicated devices.
    • Suppressors lower the energy of the gas by: allowing the gases to expand within a closed container; by increasing the volume the gas flows into; by making the gas do mechanical work; or by reducing the temperature through absorption. Suppressors that are built into the barrel can also reduce the muzzle velocity of the projectile to less than the speed of sound by bleeding off some gas near the muzzle of the weapon, thereby preventing the supersonic boom of firing.
    • Muzzle brakes are designed to direct the muzzle gas sideways rather than in a primary forwards motion. Gas deflection is obtained by placing one or more sets of symmetrical ports along the sides of the muzzle attachment to enable gases to escape. Modern flash hiders are usually the simplest type of muzzle attachment. These devices are primarily designed to reduce intermediate muzzle flash by dispersing the muzzle gas and breaking up the barrel shock and Mach disk while limiting secondary burning. They are usually cone-shaped, a tube with odd-numbered slots, or a bar style.
  • Internal ballistics. Internal ballistics begins when the firing pin strikes the cartridge and ceases when the projectile exits the muzzle. Internal ballistics leverage a range of concepts for example combustion theory, Piobert’s law, and the ideal gas law. Propellant is composed of grains of organic material (based on nitrocellulose) designed to burn at a controlled rate. In modern smokeless propellants, the shape and dimensions of the grains and the presence of moderators and stabilizers within or coated on the grain surface control the burning rate of the propellant. As the grains combust, they produce a large volume of gas (primarily carbon dioxide). Obturation is provided by the cartridge case and chamber of the firearm and the projectile. The temperature and pressure builds inside the cartridge, thereby increasing the burning rate of the propellant and resulting in an exponential rate of combustion. The initial rate of combustion is also determined by the ratio between propellant volume and case volume; a greater volume of unfilled space in the cartridge case will result in a slower combustion rate, as the gas has more space to fill before the pressure can start to rise. When the pressure is high enough in the cartridge it forces the projectile free from the cartridge case; this is known as shot start. A consistent internal ballistics phase ensures consistent muzzle velocities and minimises projectile dispersion.
  • Projectile trajectory. As soon as the projectile exits the muzzle, the energy and force acting on the projectile is in the forwards (horizontal) direction away from the muzzle, therefore the velocity vector has a positive value. Initially this will be the dominant direction of force acting on the projectile. There are a range of forces that affect the trajectory of a projectile which are outlined below:
    • Air resistance and drag.
      • Unless the projectile is fired into a vacuum, there will always be a force acting against the projectile in the opposite direction limiting the forwards progression and reducing the velocity of the projectile over time. These opposing forces are from the interaction with molecules within the atmosphere; this phenomenon is known as drag. The forward movement of the projectile compresses the air molecules in front of it causing areas of higher pressure which act in all directions around the front of the projectile.
      • Minimizing the cross-sectional area of the projectile and making the projectile less angular will reduce drag. The air molecules then flow around the projectile, a small amount of surface friction is created between the air molecules and the sides of the projectile, further reducing the kinetic energy and velocity of the projectile. When the air molecules have passed over the sides of the projectile, they have to fill in the space left by the base of the projectile. This causes high-pressure regions at the back edges of the projectile and leaves a turbulent wake of gas behind the projectile known as base drag. The shape of the nose and base of the projectile are therefore critical to limiting the effect of air resistance on the kinetic energy and velocity of the projectile.
      • A more aerodynamically shaped projectile will exhibit a slower decline in velocity and kinetic energy due to drag. Aerodynamically shaped supersonic projectiles will display a long, sharp and low-angled nose (spitzer) to reduce the cross-sectional surface area initially presented to the air and may even have a slightly angled base (boat-tail) to improve the flow of air particles and reduce turbulence from air molecules behind the projectile. The term ballistic coefficient is used to calculate the decline in projectile velocity due to the air, and takes into account projectile mass and diameter. Typically, the higher the ballistic coefficient, the better a projectile retains its velocity over time.
    • Gravity. Drag is not the only force acting on the projectile. Gravitational pull from the Earth is constantly acting vertically downwards on the unsupported object at 9.81 ms2. As a result, the natural flight path or trajectory will always ultimately curve downwards towards the ground (bullet drop), unless the trajectory is prematurely interrupted by an object.
  • Ammunition. Maximum effective range of projectile trajectories is affected by projectile velocity, mass, shape, construction and cross-sectional area. As velocity is calculated by dividing distance by time, the greater the velocity of the projectile, the further the projectile will travel in a set period of time. To maximize range, the aerodynamic shape and geometry of the projectile are critical depending on projectile muzzle velocity (subsonic or supersonic). Subsonic projectiles are most influenced by base drag, whereas supersonic projectiles are most influenced by wave drag, and therefore the nose of supersonic projectiles needs to be designed to minimize drag.
  • Effect of crosswind. Crosswind can have an inconsistent effect on accuracy and dispersion however can change from shot to shot. The same projectile, when travelling at a slower speed due to a shorter barrel, is more affected by crosswind than a projectile travelling at higher speeds.

We need to continue to clean out small arms theory and improve the general understanding of ballistics so that we can continue to understand performance and modernise the capability. A range of factors impact our ability to hit a target or in some cases enhance the probability that we’ll miss a target. To fully employ our small arms weapon systems, we must understand the trajectory, optics, recoil, training and suppression requirements. Each of these elements are critical in any explanation on how small arms operate and how munitions defeat targets.

 


About the author: Mathew Brooks is a Senior Ammunition Technical Officer and was the Officer Commanding, P&EE Graytown. He holds multiple graduate and post-graduate qualifications. He would like to the acknowledge CAPT Bryan Brown and CAPT Andrew Cassar. You can follow him at his ballistics blog / twitter feed at @shooting_holes.

One thought on “Article – Missing Targets: Understanding Small Arms Accuracy and Dispersion

  1. A good article and a useful summary. If you don’t mind, a few comments.

    “Shot start” should actually be “shot start pressure”. The physical dynamics should also include not only case separation in the case of cased SAA but include the commencement of engraving. Caseless SAA follows a similar convention, although the chamber design may include a forcing cone.

    Muzzle exit is also a funny thing. The gases (air) at the muzzle are not at ambient temperature and pressure. The compression resulting from the forward motion of the projectile exerts an effect. Also, behind the projectile is a volume of gas whose unrestricted acceleration is necessarily impeded by the projectile. At muzzle exit, this can result in a gaseous flow that effectively means that aerodynamically, the projectile is flying backwards. Yet another small increment in uncertainty that affects overall accuracy.

    The one term that I would have liked to see you emphasise more is “system”. Small arms accuracy and dispersion is the result of both actual and probabilistic variations in the performance of subsystems. I was reminded of these variations when discussing this very subject with a person who had just completed their sniper course. To them, reducing variation was critical because of the need to ensure that first round kill.

    Once again, I enjoyed the article. 312

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