MouseOver (touch) the bullet to start the animation. Yaw and precession decrease as the distance of the bullet from the barrel increases.Įxample of yaw. Nutation refers to small circular movement at the bullet tip. Precession refers to rotation of the bullet around the center of mass. Yaw refers to the rotation of the nose of the bullet away from the line of flight. These rotational effects are diagrammed below: Rotational forces are in effect that keep the bullet off a straight axis of flight. Thus, increasing the twist of the rifling from 1 in 7 will impart greater spin than the typical 1 in 12 spiral (one turn in 12 inches of barrel).īullets do not typically follow a straight line to the target. The faster the spin, the less likely a bullet will "yaw" or turn sideways and tumble in its flight path through the air. Since drag (D) is a function of velocity, it can be seen that for a bullet of a given mass (M), the greater the velocity, the greater the retardation. The form factor value I decreases with increasing pointedness of the bullet (a sphere would have the highest I value). Sectional density is calculated from the bullet mass (M) divided by the square of its diameter. SD is the sectional density of the bullet, and I is a form factor for the bullet shape. The degree to which a bullet is slowed by drag is called retardation (r) given by the formula:ĭrag is difficult to measure, so the Ballistic Coefficient (BC) is often used: Thus, greater velocity, greater caliber, or denser tissue gives more drag. p is the density of the medium (tissue density is >800 times that of air), d is the diameter (caliber) of the bullet, and v thevelocity. k is a constant for the shape of the bullet and & is a constant for yaw (deviation from linear flight). This is the bullet's energy as it leaves the muzzle, but the ballistic coefficient (BC) will determine the amount of KE delivered to the target as air resistance is encountered.įorward motion of the bullet is also affected by drag (D), which is calculated as:į(v/a) is a coefficient related to the ratio of the velocity of the bullet to the velocity of sound in the medium through which it travels. Velocity (V) is usually given in feet per second (fps) and mass (M) is given in pounds, derived from the weight (W) of the bullet in grains, divided by 7000 grains per pound times the acceleration of gravity (32 ft/sec) so that: The external ballistics of a bullet's path can be determined by several formulae, the simplest of which is: (Jandial et al, 2008) External ballistics (from gun to target) The effect upon the subsequent flight path of the bullet is usually insignificant. This results from minor (rarely major) imperfections or variations in rifling or tool marks within the barrel. (Volgas, Stannard and Alonso, 2005)Īs the bullet traverses the barrel of the gun, some minor deformation occurs, called setback deformation. Up to a point of diminishing pressure, the longer the barrel, the greater the acceleration of the bullet. Bullet travel through a gun barrel is characterized by increasing acceleration as the expanding gases push on it, but decreasing pressure in the barrel as the gas expands. The last of these factors is a function of barrel length. Therefore, the energy transmitted to the bullet (with a given mass) will depend upon mass times force times the time interval over which the force is applied. The area here is the base of the bullet (equivalent to diameter of barrel) and is a constant. The controlled expansion of gases from burning gunpowder generates pressure (force/area). It is difficult in practice to measure the forces within a gun barrel, but the one easily measured parameter is the velocity with which the bullet exits the barrel (muzzle velocity) and this measurement will be used in examples below. Higher pressures require a bigger gun with more recoil that is slower to load and generates more heat that produces more wear on the metal. More powder can also be used in rifle cartridges because the bullet chambers can be designed to withstand greater pressures (50,000 to 70,000 for rifles psi vs. (Fackler, 1996) Internal, or initial ballistics (within the gun)īullets fired from a rifle will have more energy than similar bullets fired from a handgun. The wounding potential of projectiles is a complex matter. The flight path of a bullet includes: travel down the barrel, path through the air, and path through a target. The term ballistics refers to the science of the travel of a projectile in flight.
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