Semi-empirical prediction of internal pressure distribution and muzzle velocity in the rifled barrel of a light weapon

• Internal ballistics parameters are predicted using a semi-empirical model.
• The model was validated for various barrel lengths using a custom-designed barrel.
• Pressure and velocity were predicted within 90% of confidence.

When a weapon is fired, pressure that dynamically changes behind the projectile/bullet and along the barrel and the projectile velocity are the most important internal ballistic parameters for barrel design. These facts require time consuming and expensive measurements, knowledgeable personnel and additional safety measures to properly study. In this work, shooting tests were conducted extensively for different projectile and gunpowder weights using NATO standard small caliber barrels of 7.62 mm and 5.56 mm in diameter. Internal pressure distributions and projectile velocities were measured as functions of time and displacement experimentally. Using the curve-fitting method, a projectile velocity profile was modeled according to a function defined as v(x)=axk(xk+b) and the barrel internal pressure was derived from the velocity profile. The coefficients a, b and k were determined empirically based on projectile and gunpowder weights. The model was validated for various barrel lengths using a custom-designed barrel. With the velocity function defined in this work, the internal pressure distributions and projectile velocities of 7.62 mm and 5.56 mm small caliber weapons were predicted within 90% of confidence without the need for time consuming and expensive measurements.