## The Machine Gun

a considerable time interval on either side of the instant of bolt impact, the gun velocity is in the order of only one or two feet per second, which is very close to zero when compared to the bolt striking velocity of 54.5 feet per second.)

### 11. Counter-recoil motions of bolt and gun

While the bolt and gun are moving forward, the bolt motion is influenced by the force of the bolt driving spring, but the gun motion is influenced by both the force of the barrel spring and the force of the bolt driving spring. (Since the bolt is free, the force of its spring opposes the gun motion.) The counter-recoil motions are determined by essentially the same method previously employed for analyzing the effects of the springs.

The first step is to draw the free bolt velocity curve which is a horizontal line at minus 32.7 feet per second and the free gun velocity curve which is a horizontal line at zero feet per second (fig. 3-35). The subsequent procedure must be modified slightly because the springs are aiding the motions rather than retarding them. At the start of the counter-recoil movement the barrel spring is compressed 0.125 foot and hcncc, if the spring losses were ignored, the initial compression of the spring for purpose of computing the counter-recoil motion would be:

However, if 10 per cent is allowed to account for the spring losses, the force exerted by the barrel spring at the start of counter-recoil will be 345 pounds. The bolt driving spring is compressed 0.833 feet and, ignoring spring losses, its force would be:

Again allowing 10 per cent for the losses, the force exerted by the bolt driving spring at the start of counter-recoil will be 112.5 pounds,

Sincc the bolt is free of the gun, the force of the bolt spring must be subtracted from the barrel spring force to give the effective force acting on the gun as 345 -112.5=232.5 pounds. The velocity gain due to this force would be:

The cffcct of this gain in velocity is shown in fig. 3-35 by the line designated as step 2 for the gun. The gain in bolt velocity due to the initial force of the bolt driving spring would be:

The effect of this gain in velocity is shown in fig. 3-35 by the line designated as step 2 for the bolt.

The effect of the spring constants is determined by using the curvcs designated as step 2 to obtain a first approximation of the gun and bolt travels (curves designated as steps 3 in fig. 3-32). The first approximation of the relative motion between the gun and bolt is obtained by subtracting the gun travel curve of step 3 from the bolt travel curve of step 3. This relative motion curve is used during recoil to determine the effect on the gun of the spring constant for the bolt driving spring. Combining this effect with the effect of the barrel spring on the gun gives the gun velocity curve designated as step 5 in fig. 3-35. Since the change in the velocity curve is so slight, it is not necessary to modify the gun travel curve obtained in step 3.

NOTE: Since the gun is moving forward, the effects of the spring constants must be applied opposite to the way they were applied during recoil. (Here, the effect of the spring constant for the barrel spring must be subtracted from the curve obtained in step 2 and the effect of the bolt spring constant must be added.) The validity of this procedure can be demonstrated by examining the equation expressing the change in gun velocity due to the cffect of the barrel spring alone.

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