However, since some recoil travel ('d') occurred during the first 0.010 second, the values of F0,

D, and t must be modified to take this motion into account and d' must be added to the resulting values obtained for d. Also note that the values for K, Ft», D, and Mr must be selected to suit the particular portion of the operating cycle under consideration. During recoil, both springs act on the total mass of the recoiling parts but in counter-recoil the barrel is returned to battery first while the bolt remains latched and then the bolt is returned. Thus it is necessary to consider the motions in three phases: recoil motion, barrel counter-recoil, and bolt return.

To account for the recoil movement during the time of action of the powder gases, the following changed values are used in equation 2-10:

F0' = F0+Kd' or F</=F[>l + F02+(K14-K2)d' TV —D —d' t' —t —.010

Also since the barrel and bolt and their springs act as a unit during the recoil stroke, the following substitutions are also made in equation 2-10:

F0-F01+F02

k=k1+k2

Making these substitutions gives the modified form of equation 2-10 as it applies to the recoil stroke as:

Simplifying:

This equation is employed to plot the displacement curve from the time t=0.010 until the bolt is latched at the rear. Since the design used as example allows for only a very slight overtravel, this overtravel will be neglected and it will be considered that the bolt is latched when the counter-recoil movement is equal to D (0.875 foot).

After the bolt is latched and the bolt lock is opened, the barrel continues its forward movement in counter-recoil and is now driven bv the barrel spring alone. The movement of the barrel during this time can be determined by using equation 2-10 in a special way. Since the barrel spring only is acting, the value Ki is substituted for K, F«, is substituted for F<>, and Mri is substituted for M,. In the equation, the time used for determining the barrel counter-recoil curve must be equal to t+ (Ti— T); where T is the time to recoil expressed by equation 11, and Ti is the time required for the barrel alone to complete its counter-rccoil movement. This substitution is necessary because the period of the sine curve expressing the barrel counter-recoil move ment is different from that of the curve expressing the recoil movement of the combined mass of the barrel and bolt. Making the necessary substitutions gives the modified form of equation 2-10 as it applies to the barrel counter-recoil movement as:

KjD-r

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