Internal Ballistics

Definition: Internal ballistics is the study of events within the barrel from the firing pin strike to the bullet's exit. Core concerns include propellant pressure, acceleration, muzzle velocity, and recoil.
Forensic & Utility: Notes use include ensuring weapon safety, consistent launches, and forensic performance testing (e.g., investigating modified guns or determining causes of weapon failure).

Gun Efficiency: A gun acts as an engine converting chemical energy into kinetic energy. Typical efficiency is $30\%$ to $33\%$ . * $30\%$ : Kinetic energy of the projectile. * $60\%\text{-}70\%$ : Gas (thermal and pressure). * $10\%$ : Lost to heat, friction, recoil, and flash.
Example (7.62mm NATO rifle): Chemical energy ( $10000\,J$ ) results in projectile kinetic energy of ( $3000\,J$ ).

Internal Pressure: Ignition of propellant creates high-volume gases (typically $\text{CO}_2$ and water vapor). Pressure falls as the bullet moves and volume increases.
Moderation: Moderators (additives) and physical modifications (perforations) are used to increase the burning rate and compensate for the pressure drop.
Piobert’s Law: Grains burn in parallel layers, preserving their shape during the process.
Grain Types: * Progressive Burn: Multiple perforations/star cuts; surface area increases during burning. * Regressive Burn: Solid grains (spheres/cylinders); surface area decreases. * Neutral Burn: Single perforation; surface area remains constant.

Governing Laws: * Newton’s Third Law: Action and reaction are equal and opposite (recoil). * Conservation of Momentum: $M_1 V_1 = M_2 V_2$ (where index 1 is the gun and 2 is the projectile).
Recoil Velocity formula: $V_1 = \frac{M_2 V_2}{M_1}$ .
Muzzle Lift: Caused by the barrel being situated above the wrist's rotational axis, causing the gun to rotate upward.
Recoil Energy: Calculated as Kinetic Energy $KE = \frac{1}{2} M V^2$ .

Core Physics Formulas: * $Force = mass \times acceleration$ ( $F=ma$ ). * $Pressure = \frac{Force}{Area}$ ( $P=\frac{F}{A}$ ). * $Kinetic\ Energy = \frac{1}{2} m v^2$ .
Barrel Residence Time: To approximate the time a bullet stays in the barrel: $t = \frac{1}{2} \times \frac{L}{V}$ , where $L$ is length and $V$ is muzzle velocity.
Velocity Predictions: Idealized formulas often overestimate velocity (e.g., predicting $1343\,ft/sec$ for a $.45"$ calibre when actual velocity is $810\,ft/sec$ ) because internal pressure is not constant throughout the barrel length.