Atmospheric effects on projectile acceleration in the rail gun

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Abstract
The manner in which projectile velocity in a rail gun is limited by the presence of atmosphere in the gun tube is studied. In particular, we solve the equation of motion for the acceleration of the armature and projectile, accounting for both the decelerating force exerted by the atmosphere and the time decay of the current profile. From the solution, a characteristic time is derived which indicates quantitatively when the effect of the atmosphere can be expected to be significant. Results of the calculation are then compared qualitatively with results from two recent experiments: one in which atmospheric effects are nearly negligible and one in which they are not.