In Long Range Shooting: Ballistics Terms Part 1, we talked about some general ballistics terminology. But, that’s only part of what we’ll need to talk ballistics. Most of what we’ll need to understand about ballistics for long range shooting falls under external ballistics. Here are some of the most common, and important, terms we’ll use.
Muzzle: the projectile exit end of the barrel.
Muzzle velocity: bullet speed the moment it leaves the muzzle, expressed in fps (feet per second) or m/s (meters per second).
Line of departure: also referred to as bore axis or bore centerline, is the extension of the axis of the barrel. It represents the linear trajectory the bullet would have if undisturbed by external forces.
Line of sights: the straight line between the aligned sights (or scope reticle) and point of aim.
Bullet trajectory: the projectile’s parabolic flight path.
Bullet drop: the distance from the line of departure to the bullet trajectory at a given distance. Drop is measured vertically, as with a plumb-bob, irrespective of the line of departure angle.
Bullet path: the distance between the line of sight and the bullet trajectory at a given distance. It is always measured perpendicular to the line of sight. Unlike bullet drop, which is always below line of departure, bullet path can be above or below the line of sight. Effectively, the bullet path is where you would see the bullet at a given distance looking through your aligned sights. Bullet path is marked + when above line of sight and – when it is below.
Line of sight height: the vertical distance between the line of sight and the bore axis, measured at the muzzle. For convenience, it is always measured at the scope’s front lens or at the front sight. This introduces a slight error, but it’s negligible considering that the actual angle between the line of sight and the bore axis is generally <1°.
Initial point: where the trajectory and line of sight first intersect. It generally occurs ~25yds from the muzzle. Between initial point and zero range, bullet path is always above line of sight.
Zero range: the farthest distance at which the bullet trajectory and the line of sight intersect. Initial point and zero range are the only two points you can hit exactly where you’re aiming. Zero range is also the distance used as reference for all compensation and adjustments.
Elevation angle/Depression angle: When shooting uphill/downhill, is the angle between the horizontal plane and the line of departure. In other words, the angle of the barrel relative to the horizon.
Time of flight: Is the time it takes the bullet to cover the distance between the muzzle and the target.
Residual velocity: Is the speed of the bullet, slowed down by drag, at a given distance.
Drag model: Is the mathematical model used to calculate the effect of air resistance, or drag, on the bullet. Every model is optimized for a specific bullet shape and type. The more common model for rifle bullets are G1 (Ingall’s) and G7.
Ballistic coefficient: a value declared by manufacturers, obtained by mathematical calculations and lab tests, which indicates the aerodynamic efficiency of a bullet. The closer the BC value is to 1, the better the bullet performance. BC increases exponentially as bullet velocity increases. The declared BC is related to a specific drag model, and if manufacturers do not indicate at which model it is referred, it’s generally assumed to be the G1 model (for rifle bullets).
Gyroscopic motion: the rotatory motion, on its horizontal axis, of the bullet in flight. This motion, also called spin, is generated by the barrel’s rifling and is essential for the bullet stabilization and to keep it pointed forward during its flight. It is the same principle that keeps a spinning football stable during a long pass.
Atmospheric pressure: also called barometric pressure, because of the instrument (the barometer) used to gauge it. Is the force that the weight of a column of air exerts at ground level. It is dependent on weather, and varies with elevation (it decreases exponentially with increasing altitude). The SI unit of measurement for atmospheric pressure is Pa (Pascal), but you can find it measured in inHg (inches of mercury, more common in the USA), mmHg (millimetres of mercury) and hPa (hectopascal, or millibar in non-SI denomination). Atmospheric pressure data reported by weather services are generally relative to sea-level (called mean sea level pressure or MSLP), regardless of the elevation of the weather station. Pressure measured with barometers can be relative to sea level, or can be absolute if the instrument measures the real pressure at its altitude.
Speed of sound: Is the velocity of propagation of a sound wave in air. It is dependent on air density and its standard value is 343.2 m/s (1,126 ft/s) at sea level and 20° C (68° F) of temperature. The speed of an object, in our case the bullet, relative to the speed of sound is also indicated with Mach number, where Mach 1 is the speed of sound, Mach 2 is twice the speed of sound and so on. Bullets traveling under the speed of sound are called subsonic. Bullets traveling above the speed of sound are called supersonic. Bullets that travel at more than five times the speed of sound (more than Mach 5) are called hypersonic. The range of speed between Mach 0.8 and 1.2 is called transonic region. The speed of the bullet relative to the speed of sound is important because it dramatically changes aerodynamics.
More information about external ballistics can be found in these books:
“Modern Exterior Ballistics: The Launch and Flight Dynamics of Symmetric projectiles” by Robert L. McCoy. It is has a lot of difficult math in it, so it is appropriate only for those who have a solid knowledge of calculus.
“Applied Ballistics for Long-range Shooting, 2nd Edition” by Brian Litz. More friendly than McCoy’s work and, being more recent, includes more modern technologies and solutions.
“Sierra 5th Edition Rifle and Handgun Reloading Manual” it has a well written section dedicated to exterior ballistics.