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curves. A detailed analysis of this type is particularly important because most of the critical actions and high accelerations occur during the progress of the propellant explosion and it is therefore highly desirable to determine what motion characteristics may be expected in the initial portion of the operating cycle.
Since the effects of the powder gases can not be expressed by simple equations, a special method is employed to account for these effects in plotting the bolt motion curves. The method consists esscntiallv j of first plotting a curve of free recoil velocity against time and then subtracting from each ordinate of this curve the velocity loss resulting from the retarding effects of the springs.
The curve showing the velocity of free recoil versus time for the time interval before unlocking was developed previously arid is shown in fig. 3-25. This curve will be used to illustrate the following description of the method.
To determine the retarding effects of the springs, use is made of the law expressed by the equation :
This law states that the change in the momentum of a mass is equal to the applied impulse (the prod uct of the force and the time for which it is applied). Solving for dv gives:
To obtain the variation of the change in velocity with respect to time, this expression is integrated.
In accordance with equation 3-21, the retarding effect of a force on a given mass can be determined as follows:
1. Plot a curve showing the variation of the force with respect to time.
2. Measure the area under the curve between t:=0 and some time ti.
3. Divide the measured area by the mass. This gives the ordinate of the retardation curve for the time ti.
4. Repeat steps 2 and 3 for other values of t and plot the retardation curve.
Applying this procedure using the mass of the recoiling parts and the resistance of the barrel spring produces a curve showing the loss in recoil velocity resulting from the action of the spring up to the
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