## Gas Operation

time of unlocking. Since the free recoil velocity curve shows the gain in velocity resulting from the thrust of the powder gases, the difference between the curves will be the net recoil velocity, or in other words the velocity of retarded recoil.

The foregoing method would be very simple if the retarding force were constant or if the variation of this force with respect to time were known. However, when the force varies with recoil travel as it docs with the type of spring assumed for purposes of this analysis, 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 the recoil travel wtih respect to time, and the latter curve is one of those which yet remain to be determined.

This difficulty can be overcome by employing a process of successive approximation. While the powder gas pressures arc acting, the loss in velocity resulting from the retarding effect of the spring will be relatively small and will be almost entirely due to the constant effect of the initial compression. The varying force due to the spring constant during this interval of time will almost certainly be negligible but, if necessary, it can be approximated very closely.

The procedure for plotting the velocity and travel curves for the time before unlocking occurs is as follows:

1. Plot the curve of free recoil velocity versus time (fig. 3-26).

2. The loss in velocity due to the initial compression of the barrel spring is equal to:

Fojt

Determine the velocity loss for various values of t, subtract each from the corresponding ordinate of the free recoil velocity curve and draw a curve through the resulting points. If the effect of the spring constant proves to be negligible, this curve is the retarded velocitv curve.

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