Thermal-energy transport from arc to rails in an arc-driven rail gun

A model is developed for examining thermal-energy transfer from the arc to the rails in an arc-driven rail gun. Resistive heating within the rails is also accounted for, though the contribution to the rail temperature from this mechanism is frequently negligible. Melting of the rail surface is allowed in the model, but it is assumed that the melted material is swept away and absorbs no further energy. A set of differential equations is derived which, when solved, yield the temperature, magnetic induction, and current density within the rail, as well as the mass lost from the rail surface. Both numerical and limiting-case analytic solutions to the equations are presented, and approximate expressions are obtained for the time to melting and the steady-state melting velocity of the rail surface. It is found that the governing equations can be written in a form so that they depend only on experimentally measured properties of the arc. The model is then used to analyze rail melting in a recent experiment by Jamison and Burden, for which these properties have been obtained. It is also used to estimate rail damage in other experiments by using arc properties calculated in our previous work. Considerable discussion is given of the probable sources of error in the calculation and recommendations for improvements in future work are made.