residual pressure still continues to act until 0.00826 second and imparts an additional free bolt velocity of 7.5 feet per second. (Cf. fig. 3-24.) This increase is shown by the curve designated as step 1 in fig. 3-33. Note that after the residual pressure has decreased to zero, the free recoil curve is a hori-zontal line, indicating that the bolt tends to continue moving of its own momentum at the maximum velocity of 62.5 feet per second.
At the instant of impact, the bolt has moved 0.0208 foot with respect to the gun and at this displacement, the force of the bolt driving spring is:
For developing the bolt motion curves after the impact, this force of 27.5 pounds can be considered to be the initial compression of the spring and the retarding effect of the spring can be determined by methods similar to those used before the impact. The velocity loss due to the initial compression will be:
That is. the effect of the initial compression causes the bolt velocity to decrease at the rate of 177 feet per sccond. This loss is shown in fig. 3-32 by the curve designated as step 2 for the bolt.
To determine the effect of the spring constants, allowance must be made for the time that the bolt is moving. The force exerted on the bolt and gun by the driving spring will therefore depend on the relative movement between the bolt and gun. The first step is to use the curves designated as step 2 to obtain a first approximation of the gun and bolt travels (curves designated as step 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.
The effect of the springs on the gun is obtained by performing step 4 in a special way. First, the method of step 4 is applied using the spring constant for the barrel spring, the gun mass, and the barrel travel curve of step 3. This gives the loss in gun velocity clue to the barrel spring. Second, the procedure is employed again using the spring constant for the bolt driving spring, the gun mass, and the relative travel curve. This gives the gain in gun velocity due to the
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