## The Machine Gun Figure 3-30. Assumed Pressure Rise in Gas Cylinder.

The velocity curve shown in fig. 3-31 is the result of performing this operation and adding the velocity changes so obtained to the initial velocity of 6.4 feet per second. The piston travel curve was obtained by integrating under the velocity curve. For convenient reference, the piston travel and bolt travel curves (obtained from fig. 3-27 ) are both drawn on the field of fig. 3-31. Comparing the relative movements shows that the free travel of the piston before actuating the unlocking device must be 0.036 foot or 0.432 inch (distance AB in fig. 3-11). The piston must then have an additional free travel of 0.132 foot or 1.504 inches before it strikes the bolt (distance BC in fig. 3-11). This free travel permits sufficient time for blowback to occur while the residual pressure is decreasing to a safe operating limit.

9. Theoretical tune-travel and time-velocity curves after piston impact

In order to determine the theoretical time-travel and time-velocity curves after the impact of the piston, it is necessary to consider the gun motion and bolt motion simultaneously. As shown in fig. 3-27, the velocity of the gun at 0.005 second is 7.7 feet per second and from this instant on the free recoil velocity may be represented as a horizontal line. (Sec line designated as step 1 in fig. 3-32.) At 0.005 second the travel of the gun is 0.0302 foot and at this displacement the force of the barrel spring is:

F0,-f K,D = 200+ 122.5X 12X.0302 —244.5 (lb.) For purposes of determining the gun motion from 0.005 second on, this force of 244.5 pounds can be