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The effect of the bolt driving spring on the bolt velocity can be estimated as follows: The initial compression of the spring at the instant of piston impact is equal to:

F0'2=Foa f DK2=25 + .0207 X10 X 12 = 25 | 2.48=27.5 (lb.)

The force exerted by the spring at a 10-inch deflection is

Therefore, the average force of the spring (taken with respect to time) over the 0.018 second required for completion of the bolt travel may be estimated roughlv as:

(This estimate is not exact because the velocity of the movement will not be constant over the interval, but it is close enough for present purposes.) The velocity loss caused by the action of the driving spring can now be estimated by using the formula:

Favxt 81.2X. 0170X32

It will be recalled that there will still be some blowback action after the bolt impact. As shown in fig. 3-24, the action of blowback after 0.005 second will increase the bolt velocity by approximately 7.5 feet per second. Therefore, the net loss of bolt velocity after impact will be the difference between the loss produced by thé spring and the gain produced by the remaining blowback action or 8.89—7.5=1.4 feet per second. Since the loss is approximately 1.4 feet per second and the desired average velocity is 53.3 feet per second, the velocity after the piston impact should be 53.3+1.4/2=54 feet per second. To allow for the time of action of the backplate, this velocity will be taken as 55 feet per second.

The following data arc now available for determining the conditions of piston impact: Bolt weight, W2=5 (lb.) Initial bolt velocity, V2—25.8 (ft./sec.) Desired final bolt velocity V'2=55 (ft./sec.) Since the parts will be of steel, the coefficient of restitution, e, will be taken as 0.55. Using these data, computations are made by the same methods described in the analysis of gas operation. The equation expressing the relationship between the piston velocity Vi and the piston weight Wi is found as follows :

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