## The Machine Gun

Therefore, before the projcctilc passes the gas port, the free velocity of the recoiling parts is:

vrf=.00542 v

If it were not for the presence of the gas port, this same equation would apply until the instant that the projectile leaves the muzzle. However, after the projectile passes the gas port, the pressure in the gas cylinder rapidly rises and starts to drive the piston to the rear. This pressure acts both rearward on the piston and forward on the front projection of the cylinder bore. Sincc the piston at this time does not exert any force on the gun (except perhaps through a relatively weak piston return spring), the rearward pressure on the piston docs not have any effect on the recoiling gun mass. On the other hand, forward pressure on the front cylinder face is transmitted directly to the gun and acts to oppose the recoil motion. In other words, after the projectile passes the gas port, the pressure in the gas cylinder produces a retarding impulse on the gun which is equal to the impulse imparted to the gas piston.

The actual magnitude of the retarding impulse and the manner in which it develops with respcct to time will depend on the operational characteristics of the gas cylinder and on the location of the gas port. At this point in the design, these characteristics are not vet established, so it will be nec-

essarv to make a reasonable estimate which can be corrected later if ncccssary. Experience with weapons of this calibcr indicates that the impulse which must be applied to the piston will vary with time approximately as shown in fig. 3-8. Assuming for the present that this curve is applicable to the gun of the example, the free recoil curve for the interval before the projectile leaves the muzzle can be drawn as follows:

Using equation 3-16, a curve is plotted for the interval from t=0 to t=.00234 sccond as shown in fig. 3-20. This curve is shown dotted after t=.0016 second, at which time the assumed curve of fig. 3-8 indicates that the projectile passes the gas port. For the interval from t-i.0016 to ^.00234 second, the changes in recoil velocity produced by the piston impulse are now computed, dividing the ordinates of the curve in fig. 3-8 by the mass of the recoiling parts (assuming that the weight of the piston is negligible, when compared to the entire weight of the recoiling parts). That is:

AV"=Mrwrir-5201

This calculation is performed for selected ordinates in the interval and the values obtained are subtracted from the corresponding ordinates of the curve plotted from equation 3-16. The resulting curve is shown in fig. 3-20 and is also shown in fig. 3-21. (In fig. 3-21, the time axis is compressed to show how the velocity varies after the projectile leaves the muzzle.)

The manner in which the free recoil velocity varies after the projectile leaves the muzzle can not be determined from equation 3-16 because the projectile

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