Efficiency and scaling of constant inductance gradient DC electromagnetic launchers

We present efficiency and scaling relationships for dc (i.e., noninduction) constant inductance gradient electromagnetic launchers. We derive expressions for electromagnetic force, efficiency, back-voltage, and kinetic power in terms of electrical circuit parameters. We show that launcher efficiency is a simple function of armature velocity and the launcher's characteristic velocity. The characteristic velocity characterizes the launcher and is the product of two new parameters: the mode constant and launcher constant. Mathematically, the launcher must operate at its characteristic velocity for 50% maximum efficiency. The mode constant reflects the manner in which the launcher is powered and its maximum efficiency. The launcher constant reflects the geometry of the launcher. We consider two modes of operation: constant current and zero exit current operation. We develop the ideal electromagnetic launcher concept and define it as operation at 100% maximum efficiency at all velocities. We also develop the concept of same-scale comparisons, that is, that electromagnetic launcher comparisons should be done with equal bore diameter, launcher length, projectile mass, and velocity. Finally, we present a comparative analysis based on experimental data of same-scale constant gradient electromagnetic launchers for conventional railgun, augmented railgun, and helical gun launchers in terms of the launcher constant, inductance gradient, bore diameter, bore length, system resistance, and armature (i.e., projectile) velocity.