Simple Rules for Parachute Inflation Testing at Underscale and Performance Extrapolation to Full-Scale

Abstract

Testing smaller-sized parachutes in the hopes of extrapolating inflation performance to large-scale parachutes () has been a long-sought goal in decelerator systems research and development. Using a new approach based on the momentum-impulse theorem, this paper discusses how the nondimensional and dimensional metrics of peak drag are related to several dimensionless inputs driving the relevant physics at any scale, namely, the mass ratio, the Froude number, and the Reynolds number. This input list is further expanded to probe the size scaling of inflation duration, another important driver of peak drag. The result is the inclusion of the canopy stiffness index to the list, as well as of a new so-called volume-surface-diameter ratio, a parametrization of the filled canopy volume (postinflation) per unit of initial skirt cross-section area and canopy diameter. The dynamical relationships that result yield so-called “underscale” construction dimensions and deployment conditions that inform inflation performance at the larger scale. Interestingly, not all small-scale parachute systems can achieve this, unless dropped at impractical speeds and altitudes. Finally, it is shown how these rules differ, depending on what to match at both scales: that is, matching to get the same nondimensional peak drag or the same (dimensional) peak drag per canopy area.