## Recoil Operation

Figure 2-21. Free Recoil Velocity Before Unlocking.

determine this point by using Vallier s formula for approximating the duration of the residual pressure:

For the sample cartridge and barrel:

32.2X J (.790)2X5000

To obtain the total time of action of the powder gases, this value is added to the time at which the projectile leaves the muzzle:

Extending the original curve until it is tangent at this point gives the complete free recoil velocity curve shown in fig. 2 21. Actually, the entire curve shown in the figure does not apply to the actual recoil conditions in a short recoil gun because unlocking occurs before the residual pressure has become zero.

2. Effect of blow back before acceleration and computation of unlocking lime

The next point for consideration is the effect on the bolt velocity of the blowback action which occurs between the time that unlocking occurs and the time that the accelerator starts to operate. As pointed out in the analysis of short recoil, the ideal condition for this portion of the blowback action is that the bolt should move 0.250 inch with respect to the barrel by the time that the residual pressure has dropped to the safe limit of 750 pounds per square inch. (These figures are based on assumed safe values for a typical 20-mm cartridge and should be checked experimentally for any specific cartridge. )

For purposes of determining the blowback effect, it is onlv necessary to consider the velocity of the bolt with respect to the barrel. After the bolt is unlocked, the residual pressure has no further effect on the barrel but merely imparts motion to the bolt with respect to the barrel. It will be assumed here that the bolt weight, as estimated from a preliminary layout of the mechanism is 5 pounds.

Fig. 2-17 which is a graph of the residual pressure versus time for the sample gun, shows that the residual pressure reaches 750 pounds per square inch at 0.005 second. The problem Is to decide how long before this point the bolt should be unlocked so that its motion with respect to the barrel will be 0.250 inch at 0.005 second. This problem can be solved using the data in fig. 2-21. If the ordinate's of the velocity curve in fig. 2-21 are multiplied by the mass of the recoiling parts, the resulting MAXIMUM FREE RECOIL VELOCITY (22.5 FT./SEC.)

POINT OF TANGENCY {.00826 SEC)