Buckingham Pi Analysis of Railgun Multiphysics

Predicting railgun physics is complicated by the presence of multiple physical phenomena whose coupling is incompletely understood. Because computational models analyzing these effects are numerically expensive, we use the Buckingham Pi technique to derive dimensionless parameters that define a railgun on the rail scale to rapidly assess design changes to maintain railgun performance. Assuming that electromagnetism, thermal physics, structural mechanics, and kinematics play a major role on this length scale, we first derive dimensionless parameters for each individual physics before obtaining parameters for more complicated coupling to maximize their physical relevance. We ultimately define the railgun with 18 physical quantities and 13 dimensionless parameters. We show that the dimensionless parameters may be scaled to maintain railgun performance after modifying a single physical quantity. As an example, we show how changing the length scale (or gun length) affects the remaining 17 physical quantities.