Cited by 994Biomimetic flight and propulsion mechanismsFluid Dynamics and Vibration AnalysisFluid dynamics and aerodynamics studies

The DOI matches its Crossref record; 42 of the 42 references it cites were found in a registry or an index.

Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency

Taylor, Graham K., Nudds, Robert L., Thomas, Adrian L. R.·2003·Nature

DOI 10.1038/nature02000

Open this paper in CoChat — free account

Abstract

Dimensionless numbers are important in biomechanics because their constancy can imply dynamic similarity between systems, despite possible differences in medium or scale. A dimensionless parameter that describes the tail or wing kinematics of swimming and flying animals is the Strouhal number, St = fA/U, which divides stroke frequency (f) and amplitude (A) by forward speed (U). St is known to govern a well-defined series of vortex growth and shedding regimes for airfoils undergoing pitching and heaving motions. Propulsive efficiency is high over a narrow range of St and usually peaks within the interval 0.2 < St < 0.4 (refs 3-8). Because natural selection is likely to tune animals for high propulsive efficiency, we expect it to constrain the range of St that animals use. This seems to be true for dolphins, sharks and bony fish, which swim at 0.2 < St < 0.4. Here we show that birds, bats and insects also converge on the same narrow range of St, but only when cruising. Tuning cruise kinematics to optimize St therefore seems to be a general principle of oscillatory lift-based propulsion.

Integrity signals

Registry

Crossref · 10.1038/nature02000

Cites

42 of 42 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Oscillating foils of high propulsive efficiency
Anderson, J. M., Streitlien, K., Barrett, D. S., & Triantafyllou, M. S. (1998) · Journal of Fluid Mechanics · doi:10.1017/s0022112097008392 · Cited by 1,296
Principles of Animal Locomotion
Alexander, R. M. (2002) · doi:10.1515/9781400849512 · Cited by 1,151
Hydrodynamics of Fishlike Swimming
Triantafyllou, M. S., Triantafyllou, G. S., & Yue, D. K. P. (2000) · Annual Review of Fluid Mechanics · doi:10.1146/annurev.fluid.32.1.33 · Cited by 999
Optimal Thrust Development in Oscillating Foils with Application to Fish Propulsion
Triantafyllou, G. S., Triantafyllou, M. S., & Grosenbaugh, M. A. (1993) · Journal of Fluids and Structures · doi:10.1006/jfls.1993.1012 · Cited by 887
Form and Function in Avian Flight
Rayner, J. (1988) · Springer eBooks · doi:10.1007/978-1-4615-6787-5_1 · Cited by 512
Forces on oscillating foils for propulsion and maneuvering
Read, D. A., Hover, F. S., & Triantafyllou, M. S. (2003) · Journal of Fluids and Structures · doi:10.1016/s0889-9746(02)00115-9 · Cited by 505
Wake mechanics for thrust generation in oscillating foils
Triantafyllou, M. S., Triantafyllou, G. S., & Gopalkrishnan, R. (1991) · Physics of Fluids A Fluid Dynamics · doi:10.1063/1.858173 · Cited by 501
Source–sink balance and carbon allocation below ground in plants exposed to ozone
Andersen, C. P. (2003) · New Phytologist · doi:10.1046/j.1469-8137.2003.00674.x · Cited by 500
Urbanization effects on tree growth in the vicinity of New York City
Gregg, J. W., Jones, C. G., & Dawson, T. E. (2003) · Nature · doi:10.1038/nature01728 · Cited by 472
Growth of Continental-Scale Metro-Agro-Plexes, Regional Ozone Pollution, and World Food Production
Chameides, W. L., Kasibhatla, P. S., Yienger, J. J., & Levy, H., II (1994) · Science · doi:10.1126/science.264.5155.74 · Cited by 443

Flagged first, then by citations

Show all 42 references

Sorted by citations

Items 601–700 of 992

The Effect of Hindwing Trajectories on Wake–Wing Interactions in the Configuration of Two Flapping Wings in Tandem
Xu, H., Wang, C., Jia, P., & Zhong, Z. (2024) · Biomimetics · doi:10.3390/biomimetics9070406 · Cited by 6
Pressure pulsation analysis of a large reactor coolant pump experimental loop based on field test and numerical simulation
Liu, L., Chen, X., Gao, J., Zhou, C., & Liu, L. (2024) · Nuclear Engineering and Design · doi:10.1016/j.nucengdes.2024.113686 · Cited by 6
Upstroke wing clapping in bats and bat-inspired robots offers efficient lift generation
Fan, X., Bortoni, A., Hao, S., Swartz, S. M., & Breuer, K. (2025) · Journal of The Royal Society Interface · doi:10.1098/rsif.2024.0590 · Cited by 6
Aspects of diversity, paleobiology, and morphology of wing-propelled diving birds
Watanabe, J. (2025) · Geobios · doi:10.1016/j.geobios.2024.11.005 · Cited by 6
The roles of body and wing pitching angles in hovering butterflies
Wu, J., Chu, S., Chen, L., & Zhang, Y. (2025) · Physics of Fluids · doi:10.1063/5.0265833 · Cited by 6
Flapping Foil-Based Propulsion and Power Generation: A Comprehensive Review
Kandel, P., Wang, J., & Deng, J. (2026) · Biomimetics · doi:10.3390/biomimetics11020086 · Cited by 6
Flapping-foil energy harvesters: Principles, performance, and prospects
Alam, M., Kim, B., & Shahid, F. (2026) · Applied Ocean Research · doi:10.1016/j.apor.2026.104953 · Cited by 6
Aerodynamic Exploration on Rough Airfoil Based on Overlapping Feathers of a Swift-Wing Structure
Huang, W. Q., Zhang, Q., Xu, J., Wang, J., Zheng, J., & Chen, X. (2023) · Aerospace · doi:10.3390/aerospace10080660 · Cited by 6
Evolution of wake structure with aspect ratio behind a thin pitching panel
De, A. K., & Sarkar, S. (2023) · Journal of Fluids and Structures · doi:10.1016/j.jfluidstructs.2023.104025 · Cited by 6
A bioinspired fish fin webbing for proprioceptive feedback
Bruns, A., Flammang, B. E., Papotti, G., Mastropoll, C., Hansen, T., & Anderson, I. A. (2024) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/ada1bb · Cited by 6
Optimal propulsion of an undulating slender body with anisotropic friction
Texier, B. D., Ibarra, A., & Melo, F. (2017) · Soft Matter · doi:10.1039/c7sm01545c · Cited by 6
On the noise generation and unsteady performance of combined heaving and pitching foils
Wagenhoffer, N., Moored, K. W., & Jaworski, J. (2023) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/acd59d · Cited by 6
Efficiency-Optimal Rigidity Configuration of Passive Torsional Flapping Wings
Zhao, L., & Jiao, Z. (2021) · AIAA Journal · doi:10.2514/1.j060311 · Cited by 6
The Role of Acoustics in the Conservation of the Ivory-Billed Woodpecker (Campephilus principalis)
Collins, M. D. (2021) · Journal of Theoretical and Computational Acoustics · doi:10.1142/s2591728521500201 · Cited by 6
Fully-passive tethered flapping airfoil to harvest high-altitude wind energy
Jiang, W., Yue, Y., Xie, D., & Hou, Y. (2022) · Energy Conversion and Management · doi:10.1016/j.enconman.2022.115940 · Cited by 6
Experimental analysis of the sweepback angle effect on the thrust generation of a robotic penguin wing
Shen, Y., & Tanaka, H. (2023) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/acb521 · Cited by 6
Effects of Flexibility on the Aerodynamics of a Hovering Flexible Airfoil at Reynolds Number of 100 to 1000
Kang, C.-K., & Shyy, W. (2012) · AIAA Aerospace Sciences Meeting · doi:10.2514/6.2012-1206 · Cited by 6
An explanation of the relationship between mass, metabolic rate and characteristic length for placental mammals
Frasier, C. C. (2015) · PeerJ · doi:10.7717/peerj.1228 · Cited by 6
Comparison of the Average Lift Coefficient CL and Normalized Lift ηL for Evaluating Hovering and Forward Flapping Flight
Burgers, P. (2016) · Aerospace · doi:10.3390/aerospace3030024 · Cited by 6
Dimensionally and Physically Proper Lift, Drag, and Thrust-Related Numbers as Figures of Merit: Normalized Lift, Drag, and Thrust, ηL, ηD, and ηT
Burgers, P. (2016) · Journal of Aerospace Engineering · doi:10.1061/(asce)as.1943-5525.0000689 · Cited by 6
On the autorotation of animal wings
Ortega-Jiménez, V. M., Martín-Alcántara, A., Fernández-Feria, R., & Dudley, R. (2017) · Journal of The Royal Society Interface · doi:10.1098/rsif.2016.0870 · Cited by 6
Underwater thrust performance of tandem flapping fins: Effects of stroke phasing and fin spacing
Geder, J. D., Ramamurti, R., Viswanath, K., & Pruessner, M. (2017) · OCEANS 2017 – Anchorage · Cited by 6
Numerical and experimental studies of hydrodynamics of flapping foils
Zhou, K., Liu, J., & Chen, W. (2018) · Journal of Hydrodynamics · doi:10.1007/s42241-018-0028-3 · Cited by 6
Experimental Study of the Three-Dimensional Wakes Produced by Trapezoidal Panels with Varying Trailing Edge Geometry and Pitching Amplitude
King, J. T., & Green, M. (2019) · AIAA SciTech Forum · doi:10.2514/6.2019-1380 · Cited by 6
Analysis of aerodynamic characteristics of flexible flapping flap with bidirectional fluid–structure interaction
Qin, J., Li, L., Hao, Y., Xu, J., Bai, F., & Ye, J. (2020) · AIP Advances · doi:10.1063/5.0021567 · Cited by 6
A new propulsion concept for high propulsive hydrodynamic efficiency
Caja, A. S., Martio, J., & Viitanen, V. M. (2021) · Ocean Engineering · doi:10.1016/j.oceaneng.2021.110298 · Cited by 6
Numerical validation of simple non-stationary models for self-propelled pitching foils
Fernández-Feria, R., Sanmiguel‐Rojas, E., & Lopez-Tello, P. E. (2022) · Ocean Engineering · doi:10.1016/j.oceaneng.2022.111973 · Cited by 6
Numerical Simulation of the Wake Structure and Thrust/Lift Generation of a Pitching Airfoil at Low Reynolds number via an Immersed Boundary Method
Hosseinjani, A. A., & Ashrafizadeh, A. (2015) · Journal of Aerospace Technology and Management · doi:10.5028/jatm.v7i3.476 · Cited by 6
Two Vision-guided vehicles: temporal coordination using nonlinear dynamical systems
Santos, C. P., & Ferreira, M. J. (2007) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/robot.2007.363758 · Cited by 6
Efficient flight of pterosaurs - an unsteady aerodynamic approach
Sträng, K. A., Kroo, I. M., Gerritsen, M. G., & Delp, S. L. (2009) · AIAA Aerospace Sciences Meeting · doi:10.2514/6.2009-1301 · Cited by 6
A Study on Flapping Motion for MAV Design Using Design Exploration
Oyama, A., Okabe, Y., Shimoyama, K., & Fujii, K. (2007) · AIAA Infotech@Aerospace 2007 Conference and Exhibit · doi:10.2514/6.2007-2878 · Cited by 6
Fluid Dynamics as an Evolutionary Constraint for Flapping Appendages
Gharib, M., & Milano, M. (2006) · AIAA Aerospace Sciences Meeting and Exhibit · doi:10.2514/6.2006-39 · Cited by 6
Modeling inline oscillating foils using periodic conformal mapping
Yen, W.-K., & Paley, D. A. (2025) · Applied Ocean Research · doi:10.1016/j.apor.2025.104459 · Cited by 5
Design and Control of Multi-Rigid Link Pectoral Fins Using Virtual Spring-Damper System for a Manta Ray Robot
Asada, T., Tsujimoto, T., Oki, T., & Furuhashi, H. (2025) · IEEE Access · doi:10.1109/access.2025.3562081 · Cited by 5
Alcids-like flapping wing for exploring the role of wing folding in underwater locomotion
Shen, Y., Zhao, Z., Tanaka, H., Chen, B., & Huang, Z. (2025) · Journal of The Royal Society Interface · doi:10.1098/rsif.2024.0830 · Cited by 5
Biomechanics and energetics of swimming
Hawkins, O. H., Santo, V. D., & Tytell, E. D. (2025) · Fish physiology · doi:10.1016/bs.fp.2025.06.003 · Cited by 5
Comments on “New insight into the definitions of the Bejan number”
Trancossi, M., Pascoa, J. C., & Cannistraro, G. (2020) · International Communications in Heat and Mass Transfer · doi:10.1016/j.icheatmasstransfer.2020.104997 · Cited by 5
Plunging Airfoil: Reynolds Number and Angle of Attack Effects
Camacho, E. A., Neves, F. P., Silva, A. R. R., & Barata, J. (2021) · Aerospace · doi:10.3390/aerospace8080216 · Cited by 5
Modeling and Analysis of Eagle Flight Mechanics from Experimental Flight Data
Shepherd, S., & Valasek, J. (2012) · AIAA Aerospace Sciences Meeting · doi:10.2514/6.2012-27 · Cited by 5
Numerical simulation of bionic foils in tandem arrangement
Zhou, K., Liu, J., & Chen, W. (2016) · Advances in Mechanical Engineering · doi:10.1177/1687814016649299 · Cited by 5
Assessing the ecological relevance of swimming performance traits: a case study of bluegill sunfish (Lepomis macrochirus)
Ellerby, D. J., Berlin, C. G., Cathcart, K., Dornon, M. K., Feldman, A., Gee, J. K., & Moran, C. J. (2018) · Aquatic Ecology · doi:10.1007/s10452-018-9665-4 · Cited by 4
A simulation-based approach to modeling component interactions during design of flapping wing aerial vehicles
Gerdes, J., Bruck, H. A., & Gupta, S. K. (2019) · International Journal of Micro Air Vehicles · doi:10.1177/1756829318822325 · Cited by 5
Flow Control by Hydrofoils with Leading-Edge Tubercles
New, T. H., Wei, Z., Cui, Y., Ibrahim, I. H., & Ho, W. H. (2020) · Springer eBooks · doi:10.1007/978-3-030-23792-9_4 · Cited by 5
Hopscotching jellyfish: combining different duty cycle kinematics can lead to enhanced swimming performance
Baldwin, T., & Battista, N. (2021) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/ac2afe · Cited by 5
Exploring the sensitivity in jellyfish locomotion under variations in scale, frequency, and duty cycle
Miles, J. G., & Battista, N. (2021) · Journal of Mathematical Biology · doi:10.1007/s00285-021-01678-z · Cited by 10
Reconstruction of Flight Parameters of a Bat for Flapping Robots
Singh, S. K., Zhang, L., & Zhao, J. (2021) · Journal of Biomechanical Engineering · doi:10.1115/1.4052889 · Cited by 5
Turning-ascending flight of a Hipposideros pratti bat
Rahman, A., Windes, P., & Tafti, D. K. (2022) · Royal Society Open Science · doi:10.1098/rsos.211788 · Cited by 5
A fundamental propulsive mechanism employed by swimmers and flyers throughout the animal kingdom
Costello, J. H., Colin, S. P., Gemmell, B. J., Dabiri, J. O., & Kanso, E. A. (2023) · Journal of Experimental Biology · doi:10.1242/jeb.245346 · Cited by 5
Optimal propulsion efficiency for NACA0012 foils with asymmetries in motion: A hybrid approach using the Taguchi method and artificial neural networks
Chen, K., Chiang, C.-Y., & Lai, Y. (2024) · Energy · doi:10.1016/j.energy.2024.132168 · Cited by 5
Electrostatic and aerodynamic forced vibrations of a thin flexible electrode: Quasi-periodic vs. chaotic oscillations
Madanu, S. B., Barbel, S. I., & Ward, T. (2016) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.4954025 · Cited by 5
EFFECT OF LEADING EDGE PROTUBERANCE ON THRUST PRODUCTION OF A DYNAMICALLY PITCHING AEROFOIL
Benaissa, M., Ibrahim, I. H., New, T. H., & Ho, W. H. (2017) · Topical Problems of Fluid Mechanics · doi:10.14311/tpfm.2017.004 · Cited by 5
Simple Karman Street model
Tapia-Siles, C., & Chellali, R. (2010) · OCEANS'10 IEEE SYDNEY · doi:10.1109/oceanssyd.2010.5603671 · Cited by 5
Vortex Flow Developed in the Vicinity of a Wall of an Elastic Heaving Airfoils and its Wake Structure
Kurinami, T., FUCHIWAKI, M., & Tanaka, K. (2011) · Journal of Fluid Science and Technology · doi:10.1299/jfst.6.562 · Cited by 5
Effect of flexion on the propulsive performance of a flexible flapping wing
Deng, S., & Xiao, T. (2015) · Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering · doi:10.1177/0954410015623304 · Cited by 5
Nonlinear Vibration Characterization of MAV Flapping Wings
Pai, P. F., Palazotto, A. N., & Chernova, D. K. (2009) · AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference (SDM) · doi:10.2514/6.2009-2415 · Cited by 5
An Experimental Study of Unsteady Vortex Structures in the Wake of a Piezoelectric Flapping Wing
Clemons, L., Igarashi, H., & Hu, H. (2010) · AIAA Aerospace Sciences Meeting · doi:10.2514/6.2010-1025 · Cited by 5
A Novel Large Slosh-or-Spin Low-Speed Underwater Propulsor Bridges the Unsteady and Steady Propulsion Mechanisms of Nature and Engineering
Bandyopadhyay, P. R. (2016) · IEEE Journal of Oceanic Engineering · doi:10.1109/joe.2015.2497879 · Cited by 5
Bioinspired and Biomimetic Microflyers
Sirohi, J. (2013) · Elsevier eBooks · doi:10.1016/b978-0-12-415995-2.00005-2 · Cited by 5
Aerodynamic periodicity of transient aerodynamic forces of flexible plunging airfoils
Zhou, C., Zhang, Y., & Wu, J. (2020) · Chinese Journal of Aeronautics · doi:10.1016/j.cja.2020.09.054 · Cited by 5
Application of guided flexural waves in immersed plates to aquatic propulsion of mono-hull marine vessels
Krylov, V. V., & Porteous, E. (2008) · The Journal of the Acoustical Society of America · doi:10.1121/1.2932805 · Cited by 5
Modeling and Control of Flapping Wing Robots
Murphy, I. P. (2013) · VTechWorks (Virginia Tech) · Cited by 5
Author response: Mapping Spatial Patterns to Energetic Benefits in Groups of Flow-coupled Swimmers
Heydari, S., Hang, H., & Kanso, E. A. (2024) · eLife · doi:10.7554/elife.96129.2.sa0 · Cited by 4
Optimal Strouhal numbers for oscillatory propulsion in density stratified fluids
Wang, J., Kandel, P., & Deng, J. (2025) · Journal of Fluid Mechanics · doi:10.1017/jfm.2025.283 · Cited by 4
Hydrodynamic interactions in tandem flapping wing systems
Flores, Ó., & García‐Villalba, M. (2025) · Physical Review Fluids · doi:10.1103/1ry9-t1rt · Cited by 4
Reynold number scaling of circulation growth on flapping wings
Hajati, Z., Evenden, M. L., & Wong, J. G. (2025) · Physics of Fluids · doi:10.1063/5.0262632 · Cited by 4
Experimental Study of a Periodical Flapping Flag
Bai, Y., Yong-Xia, J., Cun-Biao, L., & Yi-Ding, Z. (2016) · Acta Physica Sinica · doi:10.7498/aps.65.124701 · Cited by 4
Plunging Airfoil Motion: Effects of Unequal Ascending and Descending Velocities
Rodrigues, D., Camacho, E. A., Neves, F. P., Barata, J., & Silva, A. R. R. (2020) · AIAA AVIATION Forum · doi:10.2514/6.2020-3042 · Cited by 4
Optimized flapping flight in Venus surface atmospheric conditions
Terze, Z., Kasalo, M., Pandža, V., & Zlatar, D. (2022) · Acta Astronautica · doi:10.1016/j.actaastro.2022.01.031 · Cited by 4
The Effect of Unsteady Flapping Motion on the Aerodynamic Performance of Bio-Inspired Alula
Bao, H., Ma, D., Yang, W., Song, B., & Xue, D. (2022) · Journal of Aerospace Engineering · doi:10.1061/(asce)as.1943-5525.0001412 · Cited by 4
Folding angle and wing flexibility influence the flight performance of origami winged fruits
Cai, J.-F., Hsu, Y.-C., Yen, Y.-C., Lee, Y.-C., Peyton, B., Huang, M., Yu, H., & Juang, J. (2024) · Nonlinear Dynamics · doi:10.1007/s11071-024-09618-4 · Cited by 4
Metabolic Allometric Scaling of Multicellular Organisms as a Product of Evolutionary Development and Optimization of Food Chains
Shestopaloff, Y. K. (2024) · Biophysical Reviews and Letters · doi:10.1142/s1793048024500061 · Cited by 4
Hydrodynamic scaling of metachronal swimming
Garayev, K., & Murphy, D. W. (2024) · Physical Review Fluids · doi:10.1103/physrevfluids.9.l111101 · Cited by 4
Metachronal rowing provides robust propulsive performance across four orders of magnitude variation in Reynolds number
Ford, M. P., & Santhanakrishnan, A. (2025) · Journal of The Royal Society Interface · doi:10.1098/rsif.2024.0822 · Cited by 4
Profiling Flight Performance of Young Racing Pigeons (Columba Livia) in Training
Scullion, F. T., & Scullion, F. T. (2018) · Journal of Veterinary Healthcare · doi:10.14302/issn.2575-1212.jvhc-17-1796 · Cited by 4
Effect of Flow Interaction between Median Paired and Caudal Fins on Propulsion
Geder, J. D., Ramamurti, R., Viswanath, K., Pruessner, M., & Koehler, R. (2018) · MTS/IEEE OCEANS Conference (OCEANS) · doi:10.1109/oceans.2018.8604704 · Cited by 4
Central Pattern Generator Based Control of a Wire-driven Robot Fish
Xie, F., Zhong, Y., Kwok, T. M., & Du, R. (2018) · IEEE International Conference on Information and Automation (ICIA) · doi:10.1109/icinfa.2018.8812605 · Cited by 4
Measuring the effect of wing tears on flight in common pipistrelle bats (Pipistrellus pipistrellus)
Khayat, R. O. S., Shaw, K. J., Mead, C., Ryan, H., Dougill, G., Melling, L. M., & Grant, R. A. (2020) · Mammal Communications · doi:10.59922/wlqr5749 · Cited by 4
Trophic guilds of suction-feeding fishes are distinguished by their characteristic hydrodynamics of swimming and feeding
Olsson, K. H., Gurka, R., & Holzman, R. (2022) · Proceedings of the Royal Society B Biological Sciences · doi:10.1098/rspb.2021.1968 · Cited by 4
Numerical Analysis of the Effect of Flexibility on the Propulsive Performance of a Heaving Hydrofoil Undergoing Sinusoidal and Non-Sinusoidal Motions
Li, F., Yu, P., Wang, Q., Li, G., & Wu, X. (2021) · Polish Maritime Research · doi:10.2478/pomr-2021-0045 · Cited by 4
Vorticity preference of the Yangtze finless porpoise (Neophocaena asiaeorientalis) during the dry season at the Wanhe River Estuary confluence
Ding, R. F., Zhang, X., Chen, M., Lian, Y., & Yu, D. (2023) · Ecological Modelling · doi:10.1016/j.ecolmodel.2023.110504 · Cited by 4
Escape performance in the cyclopoid copepod Oithona davisae
Uttieri, M., & Svetlichny, L. S. (2024) · Scientific Reports · doi:10.1038/s41598-024-51288-0 · Cited by 4
Intermittent swimming and muscle power output in brook trout, Salvelinus fontinalis
Coughlin, D. J., & Dutterer, M. D. (2024) · Journal of Experimental Zoology Part A Ecological and Integrative Physiology · doi:10.1002/jez.2844 · Cited by 4
Unsteady Vortex Flows Produced by Trailing Edge Articulation
Huyer, S. A., Beal, D., Macumber, D. L., & Annaswamy, A. M. (2008) · Journal of Fluids Engineering · doi:10.1115/1.2844579 · Cited by 4
Design and investigation of a bio-inspired ventilated flapping wing
Zhang, G., Peyada, N. K., Go, T. H., & Yu, S. C. M. (2014) · Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering · doi:10.1177/0954410014547549 · Cited by 4
Key principle of the efficient running, swimming, and flying
Kokshenev, V. B. (2010) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/90/48005 · Cited by 4
Numerical Analysis of the Unsteady Subsonic Flow around a Plunging Airfoil
Lee, K., & Kim, J. (2013) · International Journal of Aeronautical and Space Sciences · doi:10.5139/ijass.2013.14.3.201 · Cited by 4
Performance Analysis of a Self-Propelling Flat Plate Fin with Joint Compliance
Reddy, N. S., Sen, S., Pal, S. K., & Shome, S. N. (2017) · Journal of The Institution of Engineers (India) Series C · doi:10.1007/s40032-017-0417-3 · Cited by 4
Central Pattern Generator Control for a Biomimetic Robot Fish in Maneuvering
Xie, F., & Du, R. (2018) · IEEE International Conference on Robotics and Biomimetics (ROBIO) · doi:10.1109/robio.2018.8665047 · Cited by 5
An Assessment of a Linear Aerodynamic Modeling of a Generic Flapping Wing Ornithopter
Djojodihardjo, H. H., & S., R. A. S. (2018) · International Journal of Astronautics and Aeronautical Engineering · doi:10.35840/2631-5009/7517 · Cited by 4
Primitive and modern swimmers solve the challenges of turning similarly to achieve high maneuverabilityPreprint
Dabiri, J. O., Colin, S. P., Gemmell, B. J., Lucas, K. N., Leftwich, M. C., & Costello, J. H. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/706762 · Cited by 4
Mapping Spatial Patterns to Energetic Benefits in Groups of Flow-coupled Swimmers
Heydari, S., Hang, H., & Kanso, E. (2024) · doi:10.7554/elife.96129.2 · Cited by 3
Accelerated corrosion of low carbon steel by oscillatory acidic streams generated with a bio-inspired claw device
Godínez, F. A., Montoya-Rangel, M., & Montoya, R. (2024) · PLoS ONE · doi:10.1371/journal.pone.0298266 · Cited by 3
Perspectives on low-Reynolds-number aerodynamics: shape, motion and structure
Chen, D., Fu, L., Hefler, C., Ji, T., Noda, R., Pittman, M., Qiu, H., Shyy, W., & Zhang, Q. (2025) · Acta Mechanica Sinica · doi:10.1007/s10409-025-25312-x · Cited by 4
A universal law for predicting the thrust performance of flapping thin airfoils
Xue, D., Liu, J., Zhang, B., & Song, B. (2025) · Physics of Fluids · doi:10.1063/5.0276982 · Cited by 3
Universal vortex formation time of flapping flight
Sun, Y., Palmer, E. H., Dougherty, C., Sbrocco, C., Shih, A., Shields, J., & Roh, C. (2025) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2501511122 · Cited by 3
Hydrodynamic characteristics and performance of the 3-DoF three-phase motion of hydrofoil inspired by sea lion foreflipper
Xue, Y., Yu, Z., Liu, Y., Wang, B., Du, J., & Bai, H. (2025) · Engineering Applications of Computational Fluid Mechanics · doi:10.1080/19942060.2025.2562106 · Cited by 3
Fins in formation: hydrodynamic impact of median fins in in-line fish swimming
Menzer, A., Pan, Y., LAUDER, G. V., & Dong, H. (2026) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/ae3652 · Cited by 4
Flapping dynamics of a compliant membrane in a uniform incoming flow
Zhang, C., Gao, A., & Zhu, X. (2026) · Journal of Fluid Mechanics · doi:10.1017/jfm.2025.11069 · Cited by 3
A coupled framework for modeling fish schooling
Mao, X., Xin, Z., Mao, X., Li, X., Wang, J., & Deng, J. (2026) · Bioinspiration & Biomimetics · doi:10.1088/1748-3190/ae3c72 · Cited by 3
Improved Scaling Law for Bio-inspired Flapping Wing Air Vehicles
Liu, L., Song, B., Liu, X.-R., Xue, D., Xuan, J., & Zhang, Y.-G. (2026) · Journal of Bionic Engineering · doi:10.1007/s42235-026-00854-5 · Cited by 1

Authors: Taylor, G. K., Nudds, R. L., & Thomas, A. L. R.
Affiliations: University of Oxford (GB)
University of Leeds (GB)
Corresponding author: Taylor, Graham K.
ORCID: Taylor, Graham K.
Nudds, Robert L.
Thomas, Adrian L. R.
Venue: Nature
Publisher: Springer Science and Business Media LLC
Published: 2003-10
Volume: 425
Issue: 6959
Pages: 707-711
ISSN: 0028-0836 (ISSN-L)
1476-4687
DOI: 10.1038/nature02000
OpenAlex: W2003172346
Cited by: 994
References: 42
Citations by year: 2026: 53 · 2025: 45 · 2024: 71 · 2023: 56 · 2022: 43 · 2021: 70 · 2020: 69 · 2019: 50 · 2018: 50 · 2017: 56 · 2016: 55 · 2015: 51 · 2014: 43 · 2013: 44 · 2012: 32
FWCI: 40.63
Type: journal article
Language: en
Open access: closed
Licence: www.springer.com/tdm (tdm)
Locations: Nature (publishedVersion)
PubMed (publishedVersion)
RePEc: Research Papers in Economics (submittedVersion)
Research Explorer (The University of Manchester) (submittedVersion)
Topics: Physical Sciences › Engineering › Aerospace Engineering › Biomimetic flight and propulsion mechanisms
Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Vibration Analysis
Physical Sciences › Engineering › Computational Mechanics › Fluid dynamics and aerodynamics studies
Keywords: Strouhal number, propulsive efficiency, vortex shedding, birds, bats, insects, flying animals, dynamic similarity, natural selection
MeSH terms: Animals, Biomechanical Phenomena, Birds, Chiroptera, Flight, Animal, Insecta, Models, Biological, Monte Carlo Method, Swimming, Wings, Animal

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency

Abstract

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Citations

Cites

Cited by

Related

Metadata

Record

About these checks