An Analytic Expression of Inductance Gradient for Rail-Type Electromagnetic Launcher

Abstract

The rail-type electromagnetic launcher (EML) has good development and applied prospects for military and civilian dual purpose. The inductance gradient is an important parameter to design the EML structure and evaluate the system performance. Based on the Biot-Savart law and current skin-effect behavior, we derive an analytic formula to predict the EML inductance gradient, which expands Batteh's formula by introducing rail thickness <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</i> and skin depth δ. Our expression is more accurate because the geometrical parameters of both rails and armature are considered in this paper. We investigate the inductance gradient change as a function of the ratio of bore width to height <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> , rail thickness <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</i> , and two-rail interval <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</i> . Finally, our results at different scales are compared with those of other formulas of the inductance gradient. This paper could be used directly to design and optimize the rail-type EML.