An investigation of the effect of the muzzle on the motion of the projectile in a recoilless gun

Expressions for the position and velocity of a projectile at any time in a recoilless gun are derived. The one dimensional wave equation is assumed to be valid in describing the motion of the gas. The muzzle velocity of the projectile is calculated, and compared with that obtained for the case in which no waves are reflected back from the muzzle. It is shown that the effect of the reflected waves is to increase the muzzle velocity. In the limiting case, when the ratio of the mass of gas initially in the barrel to the mass of the projectile is infinite, the theoretical muzzle velocity of the projectile is increased to twice the value that would be obtained if the effect of the reflected waves was neglected.