A general method for the electro-thermal design optimisation of non-transitioning solid armatures with resistive contact regions is presented which predicts the maximum velocity at which transition to an arcing contact occurs. Comparison with a wide range of published experimental results supports the validity of the velocity skin-effect (VSE) model used. It is shown that the optimum combination of armature design parameters with copper rails requires a contact region resistivity within the range of molybdenum to titanium and that transition velocities, as limited by the VSE, of > 2.5km/s should be achieved with 90mm bore armatures and these optimum parameters.