Analytical Solution for Optimal Drogue-to-Main Parachute Transition Altitude for Precision Ballistic Airdrops

Abstract

During ballistic airdrops, a single discrete control input can be made during the descent of a bundle to counter the effects of unmodeled physics and disturbances that occur before the control event. This control event is the altitude at which the drogue-to-main parachute transition occurs. The ability to vary the transition altitude of a bundle can significantly reduce the miss distance of a bundle to an intended target. The state-of-the-art method for optimizing the transition altitude is computationally burdensome and nondeterministic in time. In this exposition, an analytical solution for optimizing the transition altitude that minimizes the miss distance of an airdropped bundle from a specified ground target is developed. The solution time is deterministic and small enough that it can be implemented in real time on an embedded computer located on the bundle itself. By pairing this bundle-mounted embedded computer with a Global Positioning System sensor, the optimal transition altitude can be recomputed during the descent based on real-time bundle location measurements. Unlike the state-of-the-art method, the proposed method is guaranteed to find the global optimal solution in deterministic time. Additionally, this method demonstrates over a 5000-time improvement in speed relative to the state of the art for an example scenario.