A Comprehensive Observational Study of Graupel and Hail Terminal Velocity, Mass Flux, and Kinetic Energy

Abstract

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.

Understanding Hail in the Earth System

“…The models allow for the ratio of the volume of a scanned hailstone to be compared with the volume of a sphere of the same maximum diameter. The pilot results of this approach confirmed as in previous studies that hailstones depart from spherical shapes as they increase in size (Heymsfield et al, ; Heymsfield et al, ; Knight, ).…”

“…Radar hail detection and numerical weather prediction parameterization schemes also have dependencies to these quantities and the underlying hailstone shapes that drive them. The physical measurements of hailstones after impacting the ground such as maximum diameter, mass, density, and basic shapes (e.g., axis ratios) have been well documented in the historical literature; however, the material properties of hailstones such as hardness or strength have been more difficult to quantify (Blair & Leighton, ; Browning, ; Browning, ; Browning & Foote, ; Foote & Knight, ; Giammanco et al, ; Heymsfield et al, ; Heymsfield et al, ; Knight et al, ; Knight & Knight, ; Macklin, ; Ziegler et al, ).…”

“…The large observational data set also allowed for power law curves for different percentile groups providing an estimate of the range of possible terminal velocities and kinetic energies (Table ). Heymsfield et al () built upon this work through the use of a larger catalog of natural hailstones and provided detailed comparisons to historical research on hailstone aerodynamics. In addition, experimental testing was conducted in a vertical wind tunnel using 3‐D printed hailstones from digital models of natural hail (digital models of natural hailstones were captured using a laser scanning system).…”

“…While photogrammetry‐based instrumentation exists, such systems are often not rugged enough to survive repeated exposure to impacts from large hail. New technologies such as 3‐D scanning and printing has fostered new experimental research using printed hailstones placed in a vertical wind tunnel to evaluate the aerodynamics and tumbling of hail in such situations (Heymsfield et al, ).…”

“…The load cells sense impacts anywhere on the surface of the sphere which enable a slightly higher degree of precision than an acoustic‐based sensor and the ability to estimate impact angle. Similar to the IBHS instruments, there is some degree of inherent error due to the reliance on momentum/kinetic energy to hail diameter relationships such as those found in Heymsfield et al () and Heymsfield et al (). Over time, the data collected from these networks may offer a more detailed climatology of the characteristics of hailstorms and provide another data set for comparisons with other hail sensing applications (i.e., radar‐based, satellite, etc.…”