PROJECTILE TRANSVERSE MOTION AND STABILITY IN ELECTROMAGNETIC - INDUCTION LAUNCHERS

The transverse motion of a projectile in an electromagnetic induction launcher is considered, The equations of motion for translation and ro tation are derived assuming a rigid projectile and a flyway restoring force per unit length that is proportional to the local displacement, Linearized transverse forces and torques due to energized coils are de rived for displaced or tilted armature elements based on a first order perturbation method, The resulting equations of motion for a rigid pr ojectile composed of multiple elements in a multi-coil launcher are an alyzed as a coupled oscillator system of equations and a simple linear stability condition is derived, The equations of motion are incorpora ted into the 2-D Slingshot circuit code and numerical solutions for th e transverse motion are obtained, For a launcher with a 10 cm bore rad ius with a 40 cm long solid armature, we find that stability is achiev ed with a restoring force (per unit length) constant of k approximate to 4x10(8) N/m(2). For k = 5.0x10(8) N/m(2) and sample coil misalignme nt modeled as a sine wave of 1 mm amplitude at wavelengths of one or t wo meters, the projectfile displacement grows to a maximum of 1.2 mm, This growth is due to resonance between the natural frequency of the p rojectile transverse motion and the coil displacement wavelength, This resonance does not persist because of the changing axial velocity, Ra ndom coil displacement is also found to cause roughly the same project ile displacement, For the maximum displacement a rough estimate of the transverse pressure is 50 bars. Results for a wound armature with uni form current density throughout show very similar displacements.