The Machine Gun

counter-rccoil velocity of the barrel is obtained by integrating under the second portion of the spring force curve and dividing by Mr,. (The resulting ordinates are plotted as negative values because the barrel is now moving forward.) A similar method is used to plot the curve showing the velocity at which the bolt returns. The third part of the spring force curve is used and the integrals are divided by Mr,.

Fig. 2-11 shows the displacement and velocity curves obtained by the method described in the prcccding paragraphs, using the data for the gun of the example. After the necessary substitutions arc made, the final forms of the three equations used after the first 0.010 second are:

d —1.14 sin [20.31 + .204] .205 (t from T to T+T,)

d1.162 sin [17.93t I .393|-.287 (t from T + Ti to T + T,+T2)

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