## Recoil Operation

to determine curves showing the variation with time of the forces exerted by the springs during the various parts of the cycle of operation. To obtain the spring force curves for the recoil stroke, the ordinates of the corresponding portion of the displacement curve are multiplied by the factor K1+K2 and arc increased bv F0,4-Fv. For the barrel counter-

recoil movement, the spring force curve is determined by multiplying each ordinate of the corresponding portion of the displacement curve by Ki and increasing the result by Fot. The spring force curve for the bolt return stroke is determined in the same way using K> and Fo2. Integrating under the first portion of the curve and dividing by Mr, + Mr2 in accordance with equation 2-1 fi gives a graph showing the loss in recoil velocity resulting from the combined force of the barrel and bolt springs. Subtracting this curvc from the free bolt velocity curve produces the graph showing the retarded recoil velocity. The curve showing the

Figure 2-12. Variation of Spring Forces With Time.

tuted for Mr. The time used in the equation must be equal to t+Tj— (T+Ti); where T> is the time required for the bolt alone to complete its return movement. This substitution is necessary for the same reason as explained in the preceding paragraph. Making the indicated substitutions gives the modified form of equation 2-10 as it applies to the bolt return movement as:

This equation is applicable from the time t=T+Ti to the time t—T-j-Ti-f-T-.:, at which time the curve reaches the zero axis.

The three equations described in the preceding paragraph are used to complete the curves showing the recoil and counter-recoil movements of the barrel and bolt. The resulting curves can be used

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