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Figure 2-S. Free Recoil Velocity for First 0.010 Second.

curve shown in fig. 2-8. This curve will be used as the basis for the remainder of the calculations in this analysis.

2. Determination of spring design data

The calculations made for obtaining the free recoil velocity curve give the maximum velocity of free recoil as 22.5 feet per second. Since the total acceleration of the recoiling parts occurs in less than 0.010 second and since the retardation offered during this interval by the barrel spring and bolt driving spring will be very small, it may be assumed for purposes of considering the effect of the springs that an initial recoil velocity equal to the maximum velocity of free recoil is imparted instantaneously to the recoiling mass. On the basis of this assumption, the initial kinetic energy of the recoiling parts is given by the expression:

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Evaluating this expression for the conditions of the example gives the initial bolt energy as:

Since it has been assumed that this kinetic energy is instantaneously transferred to the recoiling parts, the springs must be proportioned to absorb this energy over the entire distance through which the barrel and bolt move in recoil. The energy absorbed by the springs is equal to the distance through which they arc compressed times the average force required to produce this deflection. That is:

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If it is assumed that the bolt in the example must open 10.5 inches to permit feeding of a 20-mm cartridge (including a slight overtravel allowed to account for minor variations in the loading of the cartridges), the total recoil distance is 10.5 inches (0.875 feet). Therefore the average combined force of the barrel spring and bolt driving spring must be:

It should be noted here that the friction between the recoiling parts and the slide will produce ah essentially constant retarding force. If it is expected that the force required to overcome friction will be considerable, this force should be determined and subtracted from the average spring force computed by using equation 2-7. Ordinarily, however, the friction force should be small when compared to the average spring force of 450 pounds and for purposes of the present analysis, the friction force will be neglected.

Having the average combined spring force, it remains to choose spring characteristics such that