Toward a Universal Relationship for the Drag Coefficients and Associated Terminal Velocities of Unmelted through Melting Hailstones: Laboratory and Field Program Measurements

Ice replicas of natural hailstones together with earlier measurements for natural hailstones are used to develop a relationship that characterizes the drag coefficient and terminal velocity of hailstones through their stages of development and melting. The ice replicas were produced based on 3D scans of natural hailstones. These particles were then levitated in the wind tunnel, and their terminal velocity, mass, and dimensions were measured as the particles were melting. Constant temperatures are used to characterize the properties of the hailstones as they melt. A primary goal of this study was to find a relationship that includes the apparent increase in drag coefficient found at relatively high Reynolds numbers (Re) and associated terminal velocities found in the wind tunnel for nonmelting hailstones, which has not been considered in earlier representations of hail terminal velocities. For this reason, several drag coefficient models for regularly and irregularly shaped particles using particle sphericity and shape are tested against the observations. Although several of the sphericity/shape models fit the data reasonably well, the increase in the drag coefficient at the higher Re is overpredicted in most of the models. Models and drag coefficients dependent only on the Re are also tested against the observations. A consistency is found between the observations and a relationship between the Reynolds number and maximum or equivalent diameters fit to the data. SIGNIFICANCE STATEMENT: Earlier studies have largely assumed that hail is spherical with solid ice density and that unmelted and melted hail fall equally fast. This study develops consistent relationships across the range of conditions encountered by unmelted and melting hailstones that can be readily incorporated into models.