Maximum Projectile Velocity in an Augmented Railgun

The time at which a projectile attains its maximum velocity in an augmented railgun, taking into account the circuit resistance, is derived. The relation reduces to an approximate expression derived previously in the literature as the circuit resistance approaches zero. The exact expression derived here predicts a significantly higher maximum projectile velocity for identical parameters. Increasing the augmenting field for a finite circuit resistance increases the maximum projectile energy.