A Momentum-Based Indicator for Predicting the Peak Opening Load of Supersonic Parachutes

In this paper, a new empirical indicator for predicting the peak opening loads of supersonic parachutes is presented. The proposed indicator is proportional to twice the free-stream dynamic pressure and the projected area of the parachute, which is equivalent to estimating the opening load as a percentage of the free-stream momentum flux through the projected area at the moment of peak inflation. The form of this expression is motivated by a classical control volume analysis of the aerodynamic forces acting on a parachute during inflation, under the simplifying assumptions of quasi-static and one-dimensional flow. For parachute geometries and flight conditions typical of Mars Entry, Descent, and Landing systems, the largest contribution to the total drag is shown to be a momentum flux term that is associated with the entrainment of atmosphere within the inflating parachute volume. Using this new method, empirical constants are calculated from existing flight reconstruction data and are shown to have a smaller standard deviation than similar constants determined using the customary indicator form, which is based on the steady-state subsonic drag and proportional to the parachute reference area. These empirical constants are also compared to an analytic estimate, derived from the control volume analysis, and shown to have excellent agreement across a wide range of Mach numbers and dynamic pressures for several parachute geometries. While opening loads estimated using both methods produce similar results at low supersonic Mach numbers typical of past inflations, the proposed method predicts notably larger loads at higher Mach numbers, those above Mach 2.0, due to the omission of any Mach Efficiency Factor. Several current Mars EDL projects have adopted this new indicator.