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Figure 3-18. Graph of Projectile Velocity Versus Time (20 mm Gun).

recoil gun up to the time the accelerator begins its action. There arc certain differences, however, which result from the influence of the gas actuating device. Since these differences make its impractical to refer simply to the applicable portion of the short-recoil analysis, a complete analysis of the entire operating cycle for gas operation will be given here. Because of the close similarity of the two systems at some points in the cycle, a certain amount of repetition of the material covered under short recoil is unavoidable.)

1. Co nditions of free recoil

Before considering the actual motions of the recoiling parts under the restraint of the barrel spring and bolt driving spring, and before analyzing the effect of firing while the gun is still moving forward, it is necessary in the following method to determine first how the recoiling parts would move under the conditions of free recoil. (For determining the free recoil motion, it is assumed that the gun is fired while stationary and is mounted so that it can move to the rear without friction or any other restraint.) Under these conditions, the impulse of the recoil force will impart to the gun a rearward momentum equal to the forward momentum of the projectile and powder gases. Until the instant the projcctilc passes the gas port, this momentum relation is expressed by the equation:

Since the powder gases will be thoroughly mixed by the turbulence created in the propellant explosion, it is reasonable to assume that the center of mass of the gases moves forward at one-half the velocity of the projectile. Actually, this is not quite accurate because the presence of the enlargement at the chamber and the fact that the rifling does not extend the full length of the space occupied by the gases creates a condition in which the volume of the space is not uniformly distributed along its length. Nevertheless, the assumption is close enough for present purposes. Therefore, equation 3-13 may be rewritten as:

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