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Figure 1-10. Graph of Projectile Bore f. Energy equation for holt and driving spring.

g. Formula for determining time to rcroil.

h. Expression for computing rate of fire.

1. Determination of bolt weight

When the propellant charge is exploded, the projectile and powder gases move forward through the bore while the bolt is driven to the rear. Since the bolt is not connected to the barrel, the forces resisting the motion of the projcctilc are not equal to the forces resisting the motion of the bolt. However, bccausc such an extremely small percentage of the explosive impulse is required to overcome friction and account for other losses, it may be assumed with verv little error that the momentum of the bolt

at any time is equal to the combined momentum of the projectile and powder gases. Assuming that the center of mass of the powder gases moves through the bore at one-half the velocity of the projectile, the momentum equality may be expressed as follows:

The subscript, f, in the symbol for the bolt velocity indicates that this is the free or unrctarded bolt velocity. In other words, it is assumed for the present that the bolt motion is not subjected to the retarding effects of the driving spring or friction. This assumption will not introduce any significant inaccuracy for the time during which the powder

res f(ftll)

Symbols Used in Analysis

Area of bore cross-section in.2 Arbitrary constant of integration Toial recoil travel of bolt—ft. Recoil travel of boh for time t—ft. Initial bolt energy—ft. lb. Average spring force over distance ID—lb.

Initial compression of spring—lb.

Acceleration of gravity—32.2 ft./see.2

Mass of powder charge—lb.scc.2/ft.

Mass of projectile—lb.sec.2/ft.

Mass of boll (recoiling parts)—

lb.sec.Vft.

M uzzle pressure— lb ./in .2 Time to recoil—sec. Time—sec.

Time of duration of residual pressure sec. Muzzle velocity of projectile—ft./see. Velocity of projectile in bore at time l—ft./sec.

Vehxitv of retarded recoil at time

Maximum velocity of free recoil— ft./sec.

Yelocitv of free recoil at time t—

Allowable average recoil velocity—ft./ sec.

Weight of powder charge lb. Weight of projectile—lb. Weight of boll (recoiling parts)—lb.

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