without any loss). At the instant acceleration starts, the velocity of the bolt is 36.7 feet per second. Since the bolt weighs 5 pounds, the kinetic energy possessed by the bolt is:
Assuming that all of the available 250 foot pounds of energy is transferred to the bolt, the kinctic energy of the bolt after acceleration will be:
Having this kinetic energy-, the velocity of the bolt after acceleration would be:
Sincc the bolt velocity before acceleration was 36.7
feet per second, this represents a velocity gain factor of 1.815 times. It should be realized that this velocity gain factor is the theoretical maximum based on a 100 per cent efficiency in transferring the available energy from the barrel to the bolt and therefore the bolt velocity in this particular design could never exceed 66.7 feet per second regardless of what type of accelerating device is used.
In actual practice, an energy transfer efficiency of 100 per cent can not be attained because there will always be unavoidable losses which decrease the amount of energy transferred. One of these losses is due to the fact that it is impractical to attempt a design in which the action of the accelerator alone brings the barrel to a complete stop. Therefore there will always be some energy remaining in the barrel after the accclcrating function is completed. There will also be losses due to friction, impact, and extraction of the cartridge case and some energy will be absorbed by the barrel return spring and bolt driving spring. Without having a definite mechanical design to work with and in the absence of detailed design data, there is no positive way to arrive at accurate specific values for these losses and accordinelv it will be necessary here to v- / t select arbitrarily values which are reasonable practical estimates. Let it be assumed that residual barrel velocity after acceleration is 6 feet per second and that the other inc idental losses amount to 50 foot pounds.
On this basis, the residual kinctic energy in the barrel after acceleration will be:
Subtracting this energy and the incidental losses of 50 foot pounds from the available 250 foot pounds of energy gives the energy actually transferred as 175 foot pounds. Adding this energy to the initial kinetic energy of the bolt (101.5 foot pounds) produces a final kinetic energy of 280 foot pounds in the bolt. With this kinetic energy the final velocity of the bolt after acceleration will be:
The velocity gain factor is now:
The efficiency of energy transfer is:
o^X 100-70 percent 2o0
'This appears to be a value which reasonably could be expected under practical conditions.
Having established the fact the action of the accelerator will speed the bolt up from 36.7 feet per sccond to 60 feet per second (a velocity gain of 24.3 feet per sccond) and will slow the barrel down from 18.5 feet per second to 6 feet per second (a velocity loss of 12.5 feet per sccond), the problem now is to design the accelerator which will produce these changes in velocity. The major consideration in this design is to arrange the accelerator mechanism so that, the required transfer of energy will be accomplished without heavy shock or excessive acceleration forces and the velocities of the barrel and bolt will vary smoothlv.
The basic characteristics of the motions which occur during the action of the accelerator will depend on whether the accelerator is of the catapult spring type or of the lever or cam type. Either type
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