A comprehensive observational study of graupel and hail terminal velocity, mass flux, and kinetic energy

This study uses novel approaches to estimate the fall characteristics of hail, covering a size range from about 0.5 to 7 cm, and the drag coefficients of lump and conical graupel. Three-dimensional (3D) volume scans of 60 hailstones of sizes from 2.5 to 6.7 cm were printed in three dimensions using acrylonitrile butadiene styrene (ABS) plastic, and their terminal velocities were measured in the Mainz, Germany, vertical wind tunnel. To simulate lump graupel, 40 of the hailstones were printed with maximum dimensions of about 0.2, 0.3, and 0.5 cm, and their terminal velocities were measured. Conical graupel, whose three dimensions (maximum dimension 0.1-1 cm) were estimated from an analytical representation and printed, and the terminal velocities of seven groups of particles were measured in the tunnel. From these experiments, with printed particle densities from 0.2 to 0.9 g cm^-3, together with earlier observations, relationships between the drag coefficient and the Reynolds number and between the Reynolds number and the Best number were derived for a wide range of particle sizes and heights (pressures) in the atmosphere. This information, together with the combined total of more than 2800 hailstones for which the mass and the cross-sectional area were measured, has been used to develop size-dependent relationships for the terminal velocity, the mass flux, and the kinetic energy of realistic hailstones.