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Most analyses of electromagnetic (EM) railguns for military applications assume that the current will be supplied to the gun breech and that it will be constant, or as nearly so as the power supply can provide. A constant current provides a constant EM accelerating force and produces the minimum barrel length for a given muzzle energy. However, there are other potential applications, such as launch to very high velocities, where very long barrels may be needed. In such barrels, the rail resistive losses become large and a distributed power feed arrangement becomes necessary. Since the back electromotive force (EMF) of the barrel increases as the projectile velocity increases, high velocity guns that could accelerate large masses may require a back EMF of tens of kilovolts. When combined with a current of MA, the power systems feeding each stage may have to provide power levels of tens to hundreds of gigawatts. One way to mitigate these requirements is to design a system that operates with constant power instead of constant force. A simple description of such a system is provided here and compared with the constant force system for an example where high masses are launched to high velocities. In this way, the power requirements can be substantially reduced compared with the constant force case but this benefit necessitates an increase in launcher length. A simple numerical method of estimating the barrel length increase is provided.