Experimetal study of a freely falling plate with an inhomogeneous mass distribution

Abstract

A homogeneous thin plate often flutters while falling through a fluid under gravity. The center of gravity of the plate moves back-and-forth horizontally and the plate tilting angle oscillates symmetrically from the horizontal. Here we show that such a scenario is qualitatively changed for a plate with noncoinciding centers of gravity and buoyancy due to an inhomogeneous mass distribution. Mismatch of the centers causes an external torque that breaks the symmetry of rotational motion, shifts the mean tilting position from the horizontal, and leads to a net horizontal plate displacement. In laboratory experiments with a Reynolds number around 1500, we found that the net horizontal displacement scales linearly with the separation between the centers up to a critical value, beyond which the plate falls vertically in an edge-on configuration with the heavier side downward. Experimental results are compared to predictions of a quasi-steady numerical model. Our work demonstrates that motion of freely moving objects in a fluid depends sensitively on external torques, which potentially can be used as an effective control method.