## The Machine Gun

ample for the period from t=0 to t=0.010 second. These curves, for the time after t=0.00334 second were obtained by the step-by-step system described under plain blowback and the steps referred to in the figure are those in the procedure described for plain blowback. The velocity loss resulting from the initial compression of the bolt driving spring for the time interval between t~0.00334 and t=0.010 second is equal to 2.81 feet per second, computed as follows:

The loss due to the spring constant K, as determined by the method of step 4 is only about 0.697 foot per second. This loss Is so slight that it is not necessary to continue the process of successive approximation any further than step 5.

The remainder of the bolt displacement curve can be determined analytically by using equation 1-10, modified as necessary to account for the displacement d' during the first 0.010 second. The changed values to be used in equation 1-10 are the following:

F0' = F0 f- Kd' =-120+ 230 X .245 = 176.3 D' = D-d'-D-.245 t' = t —.010

Making the required substitutions as explained for plain blowback gives the final form of the equation to be used after the first 0.010 second as:

This equation is used to complete the bolt displacement curve and gives the result shown in fig. 1 39. The ordinates of the displacement curve are then multiplied by K and increased by Fa to obtain a curve showing the variation of spring force with time (fig. 1—40). (Note that the initial compression used is 130.8 pounds which takes into account the compression resulting from the recoil movement before unlocking.) integrating under this curve and dividing the results by M, in accordance with equation 1 15 will give a graph of the velocity loss due to the spring force. (All computations start at the time of unlocking, 0.00334 sccond.) Subtracting this curve from the free bolt velocity curve of fig. 1 - 37 will give the complete graph for the retarded bolt velocity, which is also shown in fig. 1-39. Fig. 1-41 shows the velocity versus displacement curves for the gun of the example as derived from the curvcs of figs. 1-35 and 1-39.

From fig. 1-39, the time for the complete cyclc is given as 0.0875 second. This gives the rate of fire for the gun of the example as:

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