On Tumbling of a Two-Dimensional Plate under Free Flight

Abstract

In this study, we experimentally deal with the tumbling, which is a rotating motion of a plate with its axis perpendicular to the falling direction. As the plate, we consider a rectangular-cross-section prism with a depth-to-width ratio λ = 0.3, an aspect ratio AR = 10, and inertia moment ratios I^* = 0.75 - 43, together with a wide range of a non-dimensional control parameter C = 7.2×10¹ - 1.6×10³. As a result, we specify fundamental aerodynamic characteristics in terminal condition, like the reduced rotating rate Ω^*, the lift coefficient C_L, the drag coefficient C_D and the lift-to-drag ratio C_L/C_D as functions of both C and I^*. Moreover, the relation between the actual Reynolds number Re and the Reynolds number Re(V_d) based on V_d can be approximately determined, being independent of C and I^*. Eventually, we successfully propose a series of empirical formulae to predict Ω^*, C_L, C_D and C_L/C_D as functions of Re(V_d) alone, which is available for a wide parameter range except for large C and small I^*.