Surprising behaviors in flapping locomotion with passive pitching

Saverio E. Spagnolie, Lionel Moret, Michael J. Shelley, Jun Zhang

Research output: Contribution to journalArticlepeer-review


To better understand the role of wing and fin flexibility in flapping locomotion, we study through experiment and numerical simulation a freely moving wing that can "pitch" passively as it is actively heaved in a fluid. We observe a range of flapping frequencies corresponding to large horizontal velocities, a regime of underperformance relative to a clamped (nonpitching) flapping wing, and a surprising, hysteretic regime in which the flapping wing can move horizontally in either direction (despite left/right symmetry being broken by the specific mode of pitching). The horizontal velocity is shown to peak when the flapping frequency is near the immersed system's resonant frequency. Unlike for the clamped wing, we find that locomotion is achieved by vertically flapped symmetric wings with even the slightest pitching flexibility, and the system exhibits a continuous departure from the Stokesian regime. The phase difference between the vertical heaving motion and consequent pitching changes continuously with the flapping frequency, and the direction reversal is found to correspond to a critical phase relationship. Finally, we show a transition from coherent to chaotic motion by increasing the wing's aspect ratio, and then a return to coherence for flapping bodies with circular cross section.

Original languageEnglish (US)
Article number008004PHF
Pages (from-to)1-20
Number of pages20
JournalPhysics of Fluids
Issue number4
StatePublished - Apr 2010

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


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