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Extending the original curve until it is tangent to the maximum free recoil velocity line at this point gives the complete free recoil velocity curve shown in fig. 3-21. Actually only a portion of the curve shown in the figure applies to the recoil conditions in a gas-opcratcd gun because unlocking occurs before the residual pressure has become zero. It also must be remembered that the curve obtained by the preceding method must be checked after the actual piston impulse curve js obtained.

2. Effect of blowback before piston strikes bolt and computation of unlocking time

The next point for consideration is the effect on the bolt velocity of the blowback action which occurs between the time that the bolt is unlocked and the time that the piston strikes the bolt to speed it rearward. As pointed out in the analysis of gas operation, the ideal condition for this portion of the blow-back 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 cffcct, it is only necessary to consider the velocity of the bolt with respect to the gun. For this determination. it is necessary to know the bolt weight. It will be assumed here that the bolt weight, as estimated from the preliminary design layout, is equal to 5 pounds. After the bolt is unlocked, the residual pressure continues to act on the bolt, but since the bolt is now free of the gun, the recoil force exerted on the gun by the residual pressure is reduced to a negligible value. (The gases expanding at the muzzle do exert some force on the muzzle face of the barrel, but in the abscncc of a gas trap, such as exists when a muzzle booster is used, the impulse applied to the muzzle face represents a very small portion of the total impulse resulting from the residual pressure.)

Fig. 3-10, 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. 3-22. This curve is plotted by the same method used for the curve in fig. 3 21 except that the effect of the piston impulse is not included. In other words, this curve represents the free recoil velocity that would be imparted if there were no gas cylinder. If the ordinates of the velocity curve in fig. 3-22 are multiplied by the mass of the recoiling parts, the resulting curve (fig. 3-23) will show the im-

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