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. 2-22).

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

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

3. Integrate under the curve drawn in step 2 to obtain the displacement curve.

4. Assume that the curvc drawn in step 3 represents the actual time-travel curve and use this curve to determine the retardation due to the spring constant. (Use the combined spring constant for the barrel return spring and the bolt driving spring, KiK:ยป.) Ordinarily, it will be found that this retardation is so small thai it will not have anv effect worthy of consideration.

5. In the event that the retardation determined in step 4 is sufficient to affect the velocity, use it to modify the curve drawn in step 2 and then integrate under the new curve to obtain a corrected displacement curve. 6. Steps 4 and 5 can be repeated as often as is necessary until no significant change occurs in the displacement curve. Actually, this proccss of successive approximation should never be necessary and satisfactory results should be obtained in the first three steps or at least in the first five steps.

Fig. 2-23 shows the curves obtained for the gun of the example for the interval before unlocking. The total loss in velocity due to the combined effect of the initial compressions of the springs during this interval (0 to 0.00307 second) is:

v(X<> 1 + ^2)1 _ (250+25).003Q7 X 32.2 Mr ~ 50

The loss due to the combined effect of the spring constants as determined by the method of step 4 is only about 0.115 feet per second. The final curves shown in fig. 2-23 arc the result of performing step 3. Since the velocity loss due to the effect of the

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