Figure 2-7. Free Recoil Velocity While Projectile Is in Bore.

Figure 2-7. Free Recoil Velocity While Projectile Is in Bore.

Therefore, before the projectile leaves the muzzle, the free velocity of the recoiling parts is:

The curve obtained by using this relation is shown in fig. 2-7 and is also shown in fig. 2-8 as the portion between t=0 and t=.00234 second. (In fig. 2-8, the time axis is compressed in order to show how the velocity varies after the projectile leaves the muzzle.)

The manner in which the free recoil velocity varies after the projectile leaves the muzzle can not be determined from equation 2-3 because the projectile is no longer part of the system. Since the effect of the residual pressure can not be expected in simple terms, a special method is used to extend the curve obtained from equation 2-3. This method is based on the fact that the results of experimental firings of various guns show that the maximum velocity of free recoil may be closely approximated as:

This relationship is equivalent to saying that the maximum momentum imparted to the recoiling parts is equal to the sum of the muzzle momentum of the projectile and the momentum of the powder gases, assuming that the powder gases leave the gun at an average velocity of 4700 feet per second. For the gun used as an example:

y M.29X27fl0+4700X.070asBs22 5 / ft. \

A line representing this value of the maximum velocity of free recoil is drawn on the velocity graph (fig. 2-8) and the curve previously drawn from equation 2-3 is extrapolated until it becomes tangent to the line. The point at which the curve becomes tangent represents the time at which the residual pressure becomes zero and therefore imparts no further velocity to the recoiling parts. Although an error in locating the exact point of tangency will not have any serious effect on the accuracy of the results, it may be of some assistance in plotting to determine this point by using Vallier's formula for approximating the duration of the residual pressure:

For the sample cartridge and barrel:

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