On the Aerodynamics of Spheroidal Hailstone Models

Abstract

Drag, lift and torques for smooth oblate spheroids, of axis ratio from 0.50 to 0.79, were measured over a range of Reynolds number from 4?104 to 4?105 at various inclination angles of the models to the flow. The data show that the aerodynamic forces and moments do not vary greatly up to the range of the critical Reynolds numbers where the drag decreases, and the lift and torque increase. Assuming that the values measured at steady-state conditions are adequate for calculations, the behavior of freely-failing hailstones was numerically modelled. Data about horizontal motions and periodic variations of rotational and vertical speeds are given in addition to average vertical speeds and oscillating or tumbling motions. The effect of a possible but unknown damping was also considered. Thereby, it could he shown that given a small perturbation from the steady state with the minor axis vertical, either amplification will lead to constant-amplitude oscillation or continuous tumbling, or damping will restore the initial state. The final mode of motion depends on the axis ratio and the size of the spheroid and the damping coefficient of the air.