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Holes stabilize freely falling coins

Published online by Cambridge University Press:  21 July 2016

Lionel Vincent ,
W. Scott Shambaugh  and
Eva Kanso
Lionel Vincent
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
W. Scott Shambaugh
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
Eva Kanso*
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089, USA
*
†Email address for correspondence: [email protected]
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Abstract

The free fall of heavy bodies in a viscous fluid medium is a problem of interest to many engineering and scientific disciplines, including the study of unpowered flight and seed dispersal. The falling behaviour of coins and thin discs in particular has been categorized into one of four distinct modes; steady, fluttering, chaotic or tumbling, depending on the moment of inertia and Reynolds number. This paper investigates, through a carefully designed experiment, the falling dynamics of thin discs with central holes. The effects of the central hole on the disc’s motion is characterized for a range of Reynolds number, moments of inertia and inner to outer diameter ratio. By increasing this ratio, that is, the hole size, the disc is found to transition from tumbling to chaotic then fluttering at values of the moment of inertia not predicted by the falling modes of whole discs. This transition from tumbling to fluttering with increased hole size is viewed as a stabilization process. Flow visualization of the wake behind annular discs shows the presence of a vortex ring at the disc’s outer edge, as in the case of whole discs, and an additional counter-rotating vortex ring at the disc’s inner edge. The inner vortex ring is responsible for stabilizing the disc’s falling motion. These findings have significant implications on the development of design principles for engineered robotic systems in free flight, and may shed light on the stability of gliding animals.

JFM classification

Instability: Instability Biological Fluid Dynamics: Swimming/flying
Type
Papers
Information
Journal of Fluid Mechanics , Volume 801 , 25 August 2016 , pp. 250 - 259
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Copyright
© 2016 Cambridge University Press 

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