Ballistic Limit Equation Derivation for Thin Tape Tethers

Abstract

Electromagnetic tethers of hundreds or thousands of meters have been proposed for maneuvring spacecraft in Low Earth Orbit, and in particular, for post-mission disposals. The debate on tether survivability to debris impact is still influencing further advances in the implementation of such technology because of the large area they expose to the debris environment; thin tape geometries have been proposed instead of round ones to increase the survivability to hypervelocity impacts. In this context, this paper introduces a new Ballistic Limit Equation (BLE) for thin tape tethers, derived from experimental results, numerical simulations, and literature data. The resulting equation is non-monotonic with respect to impact angle, presenting a minimum depending on the debris velocity and size; for high obliquities, the debris fragmentation triggered by shock waves propagating into the material reduces the damage. This feature allows to set a minimum particle diameter for risk assessment, excluding a significant part of the debris flux. The proposed BLE confirms the performance of thin tape tethers, with respect to round wires, due to their better ballistic response as well as their reduced cross-section at high-obliquity impacts.