## Recoil Operation

parts, and the velocity of the recoiling parts. Such curves may be drawn by using the formulas developed under the preceding heading, but it should be realized that all of these formulas are based on the assumption that the initial energy was transferred instantaneously to the recoiling parts. Therefore, curves plotted in this way would not take account of the detailed effects resulting from the conditions which exist during the time of action of the powder gas pressures. This time is so short that it will be relatively negligible when the overall cycle of operation is considered, particularly if the rate of fire is low. However, for higher rates of lire, the time of action of the powder gas pressure may represent a small but significant portion of the time required for recoil and accordingly should be given due consideration in plotting bolt motion curves. In addition, because of the high accelerations which occur during the propellant explosion, it is highly desirable to determine in detail what motion characteristics may be cxpcctcd in the initial portion of the recoil stroke.

The effects of the powder gas pressure can not be expressed by simple equations and therefore a special method is employed to account for these effects in plotting the bolt motion curves. The method consists essentially of first plotting a curve of free recoil velocity and then subtracting from each ordinate of this curvc the velocity loss resulting from the retarding effects of the springs.

The curves showing the velocity of free recoil versus time were developed previously and are shown in figs. 2-7 and 2-8. These curves will be used to illustrate the following description of the method.

To determine the retarding effects of the spring, use Is made of the law expressed by the equation:

This law states that the change in the momentum of a mass is equal to the applied impulse (the product of the force and the time for which it is applied). Solving for dv gives:

To obtain the variation of the change in velocity with rcspcct to time, this expression is integrated.

In accordance with equation 2-1 (S, the retarding effect of a force on a given mass can be determined as follows:

1. Plot a curve showing the variation of the force with respect to time.

2. Measure the area under the curve between t=0 and some time ti.

3. Divide the measured area bv the mass. This

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