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Figure 1-15. Free Recoil Velocity Versus Time (0-1.0 Sec.).

of the forcc and the time for which it is applied). Solving for dv gives:

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

In accordance with equation 1-15, the retarding effcct of a forcc 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 i~0 and some time ti.

3. Divide the measured area by the mass. This gives the ordinate of the retardation curve for the time ti.

4. Repeat 2 and 3 for other values of t and plot the retardation curve.

When this procedure is applied to the driving spring and bolt, the resulting curve shows the loss in bolt, velocity resulting from the resistance of the spring. Since the free bolt velocity curve shows the gain in bolt velocity resulting from the thrust of the powder gases, the difference between the curves will be the net bolt velocity, or in other words, the velocity of retarded recoil.

If the retarding force were constant or if its varia-

tion with respect to time were known, the application of this method would be very simple. However, when the force varies with bolt displacement as it docs in the ease of the driving spring, a difficulty is encountered. In order to plot a graph showing the variation of the retarding force with respect to time, it is necessary to have a curve showing the variation of bolt displacement with respect to time and it is this very curve that we arc attempting to plot.

This difficulty can be ctrcumventcd by considering the problem in two stages. For the first 0.010 second while the powder gas pressures are acting, the retardation offered by the spring will be small and in any ease will be almost entirely due to the constant effect of the initial compression. The varying force due to the spring rate during this interval will almost certainly be negligible but, if necessary, it can be approximated very closely. These considerations make it possible to obtain accurate results for the first 0.010 second. For the remainder of the cycle of operation, the powder gas pressures arc not acting and the displacement of the bolt can be determined analytically without any trouble.

The procedure for plotting the velocity and displacement curves for the first 0.010 second is as follows:

1. Plot curve of free bolt velocity versus time (fig. 1 H).

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