Intrinsic equilibrium of stably autorotating samaras

Peixing Niu, Michael D. Atkins, Yanyan Liu, Moxiao Li, Tian Jian Lu, and Tongbeum Kim
Phys. Rev. E 106, 014405 – Published 26 July 2022
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Abstract

During descent, a single-winged maple seed (samara) can naturally reach a delicate equilibrium state, stable autorotation, before landing. This article reveals the intrinsic equilibrium of a particular type of samaras in terms of measurable aerodynamic and geometric parameters. To this end, we conducted a series of in situ measurements for the rate of vertical descent (exclusive of crosswind) of an autorotating samara in a natural range of samara sizes and masses. We then extended the range of size and mass by introducing artificial samaras, with discrete mass elements purposely designed to approximate the asymmetrical and nonuniform distribution of mass found with natural samaras. Based on the widened range, a fundamental nondimensional correlation of dynamic pressure and disc loading was generalized, where all stable autorotation descent profiles collapse to a single descent characteristic curve, irrespective of the size and mass of the natural and artificial samara's specimens. Results reveal that for stably autorotating (both natural and artificial) samaras, their terminal descent velocity (expressed as dynamic pressure) and disc loading attained equilibrium at a value that is inversely proportional to the coefficient of lift.

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  • Received 15 March 2022
  • Accepted 29 June 2022

DOI:https://doi.org/10.1103/PhysRevE.106.014405

©2022 American Physical Society

Physics Subject Headings (PhySH)

Physics of Living Systems

Authors & Affiliations

Peixing Niu1,2, Michael D. Atkins3, Yanyan Liu1,2, Moxiao Li1,2, Tian Jian Lu1,2,4, and Tongbeum Kim1,2,3,4

  • 1State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
  • 2MIIT Key Laboratory of Multifunctional Lightweight Materials and Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
  • 3School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, Johannesburg 2000, South Africa
  • 4State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, China

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Issue

Vol. 106, Iss. 1 — July 2022

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