Tuning of Strouhal number for high propulsive efficiency accurately predicts how wingbeat frequency and stroke amplitude relate and scale with size and flight speed in birds

• Published in: Proceedings of the Royal Society. B, Biological sciences Vol. 271; no. 1552; pp. 2071 - 2076
• Main Authors: Nudds, Robert L., Taylor, Graham K., Thomas, Adrian L. R.
• Format: Journal Article
• Language: English
• Published: England The Royal Society 07.10.2004
• Subjects: Aerial locomotion; Aerodynamics; Animal wings; Animals; Aves; Biomechanical Phenomena; Bird; Birds; Birds - physiology; Flight; Flight mechanics; Flight, Animal - physiology; Kinematics; Modeling; Models, Biological; Propulsive efficiency; Statistical variance; Stroke Amplitude; Strouhal Number; Strouhal numbers; Wingbeat Frequency; Wings, Animal - physiology
• ISSN: 0962-8452; 1471-2954
• DOI: 10.1098/rspb.2004.2838

The wing kinematics of birds vary systematically with body size, but we still, after several decades of research, lack a clear mechanistic understanding of the aerodynamic selection pressures that shape them. Swimming and flying animals have recently been shown to cruise at Strouhal numbers (St) corresponding to a regime of vortex growth and shedding in which the propulsive efficiency of flapping foils peaks (St fA/U, where f is wingbeat frequency, U is cruising speed and A bsin(θ/2) is stroke amplitude, in which b is wingspan and θ is stroke angle). We show that St is a simple and accurate predictor of wingbeat frequency in birds. The Strouhal numbers of cruising birds have converged on the lower end of the range 0.2 < St < 0.4 associated with high propulsive efficiency. Stroke angle scales as θ 67b−0.24, so wingbeat frequency can be predicted as f St. U/bsin(33.5b−0.24), with St = 0.21 and St = 0.25 for direct and intermittent fliers, respectively. This simple aerodynamic model predicts wingbeat frequency better than any other relationship proposed to date, explaining 90% of the observed variance in a sample of 60 bird species. Avian wing kinematics therefore appear to have been tuned by natural selection for high aerodynamic efficiency: physical and physiological constraints upon wing kinematics must be reconsidered in this light.