Sensitivity Analysis for the Inductance Gradient of EMFY-3 Electromagnetic Launcher

ASELSAN Inc. has been working on electromagnetic launch technologies since 2014. The first prototype, EMFY-1, has a 25 mm
$\times25$
mm square bore and 3-m-length rails. The second prototype, EMFY-2, has a 50
$\times50$
mm square bore and 3-m-length. This article presents a recently developed prototype, EMFY-3, with a 50
$\times75$
mm rectangular bore and 6-m length. The input energy of the pulsed-power supply (PPS) is doubled to 8 MJ, and the 2.91 MJ muzzle energy is obtained. Velocity curves are captured with Doppler radar, enabling us to establish propulsive inductance gradient
$L^{\prime }_{\mathrm {pr}}$
transients empirically. The results confirm that
$L^{\prime }_{\mathrm {pr}}$
is constant throughout the launch, as no significant breaking mechanism occurs with the non-magnetic containment. However, a slight variation (2% at maximum) happens with different rails’ current magnitudes from one launch to another. The transition phenomenon is a candidate for the drop in the
$L^{\prime }_{\mathrm {pr}}$
, as it occurs more likely at launches with higher linear current densities. Moreover, a sensitivity analysis is conducted to show the importance of
$L^{\prime }_{\mathrm {pr}}$
calculations. A deviation of 5% from the actual value can cause an error in muzzle velocity up to 6.2%. This fact indicates that simulation models are very susceptible to
$L^{\prime }_{\mathrm {pr}}$
calculations. Although
$L^{\prime }_{\mathrm {pr}}$
is calculated as 0.515
$\mathrm {\mu H/m}$
with 3-D finite element method (FEM), the Kerrisk formula calculates as if
$0.561~\mathrm {\mu H/m}$
; the experimental measurement gives 0.575
$\mathrm {\mu H/m}$
. These methods differ by 8% at maximum, which causes muzzle velocities errors. Regarding empirical findings, the 3-D FEM model calculates
$L^{\prime }_{\mathrm {pr}}$
more precisely than analytical formulas, and the contrast between models have grave importance due to the muzzle velocity errors.