Barrel lateral force modeling of a curved EM railgun

The author presents a mathematical model to assess the normal barrel-projectile interaction forces arising from the barrel curvature of an electromagnetic railgun. He shows the significant relationships among the main parameters, such as the Lorentz force, the projectile displacement, velocity, and the barrel curvature. Equations are derived to make quick computations and parametric relations are expressed explicitly. In a sample computation, the results show that a large normal force would be generated by a sufficiently curved barrel. The maximum lateral force computed is 620 kN, while the estimated muzzle lateral force of a given barrel drooping 0.01 m is 3.4 kN. The maximum Lorentz force is 2450 kN and, hence, the maximum lateral force is one quarter of the maximum Lorentz force. In comparison to the maximum balloting force computed for this projectile, 47 kN, this shows that barrel curvature does have a large effect