A B S T R A C TMany fish swim using body undulations to generate thrust and maneuver in three dimensions. The pattern of body bending during steady rectilinear locomotion has similar general characteristics in many fishes and involves a wave of increasing amplitude passing from the head region toward the tail. While great progress has been made in understanding the mechanics of undulatory propulsion in fishes, the inability to control and precisely alter individual parameters such as oscillation frequency, body shape, and body stiffness, and the difficulty of measuring forces on freely swimming fishes have greatly hampered our ability to understand the fundamental mechanics of the undulatory mode of locomotion in aquatic systems. In this paper, we present the use of a robotic flapping foil apparatus that allows these parameters to be individually altered and forces measured on self-propelling flapping flexible foils that produce a wave-like motion very similar to that of freely swimming fishes. We use this robotic device to explore the effects of changing swimming speed, foil length, and foil-trailing edge shape on locomotor hydrodynamics, the cost of transport, and the shape of the undulating foil during locomotion. We also examine the passive swimming capabilities of a freshly dead fish body. Finally, we model fin-fin interactions in fishes using dual-flapping foils and show that thrust can be enhanced under correct conditions of foil phasing and spacing as a result of the downstream foil making use of vortical energy released by the upstream foil.

An undulatory pattern of body bending in which waves pass along the body from head to tail is a major mechanism of creating thrust in many fish species during steady locomotion. Analyses of live fish swimming have provided the foundation of our current understanding of undulatory locomotion, but our inability to experimentally manipulate key variables such as body length, flexural stiffness and tailbeat frequency in freely swimming fish has limited our ability to investigate a number of important features of undulatory propulsion. In this paper we use a mechanical flapping apparatus to create an undulatory wave in swimming flexible foils driven with a heave motion at their leading edge, and compare this motion with body bending patterns of bluegill sunfish (Lepomis macrochirus) and clown knifefish (Notopterus chitala). We found similar swimming speeds, Reynolds and Strouhal numbers, and patterns of curvature and shape between these fish and foils, suggesting that flexible foils provide a useful model for understanding fish undulatory locomotion. We swam foils with different lengths, stiffnesses and heave frequencies while measuring forces, torques and hydrodynamics. From measured forces and torques we calculated thrust and power coefficients, work and cost of transport for each foil. We found that increasing frequency and stiffness produced faster swimming speeds and more thrust. Increasing length had minimal impact on swimming speed, but had a large impact on Strouhal number, thrust coefficient and cost of transport. Foils that were both stiff and long had the lowest cost of transport (in mJ m −1 g −1 ) at low cycle frequencies, and the ability to reach the highest speed at high cycle frequencies.

Cliff swallows (Petrochelidon pyrrhonota) are highly maneuverable social birds that often forage and fly in large open spaces. Here we used multi-camera videography to measure the three-dimensional kinematics of their natural flight maneuvers in the field. Specifically, we collected data on tandem flights, defined as two birds maneuvering together. These data permit us to evaluate several hypotheses on the high-speed maneuvering flight performance of birds. We found that high-speed turns are roll-based, but that the magnitude of the centripetal force created in typical maneuvers varied only slightly with flight speed, typically reaching a peak of ~2 body weights. Turning maneuvers typically involved active flapping rather than gliding. In tandem flights the following bird copied the flight path and wingbeat frequency (~12.3 Hz) of the lead bird while maintaining position slightly above the leader. The lead bird turned in a direction away from the lateral position of the following bird 65% of the time on average. Tandem flights vary widely in instantaneous speed (1.0 to 15.6 m s −1 ) and duration (0.72 to 4.71 s), and no single tracking strategy appeared to explain the course taken by the following bird.

Hummingbirds are known to defend food resources such as nectar sources from encroachment by competitors (including conspecifics). These competitive intraspecific interactions provide an opportunity to quantify the biomechanics of hummingbird flight performance during ecologically relevant natural behavior. We recorded the three-dimensional flight trajectories of Ruby-throated Hummingbirds defending, being chased from and freely departing from a feeder. These trajectories allowed us to compare natural flight performance to earlier laboratory measurements of maximum flight speed, aerodynamic force generation and power estimates. During field observation, hummingbirds rarely approached the maximal flight speeds previously reported from wind tunnel tests and never did so during level flight. However, the accelerations and rates of change in kinetic and potential energy we recorded indicate that these hummingbirds likely operated near the maximum of their flight force and metabolic power capabilities during these competitive interactions. Furthermore, although birds departing from the feeder while chased did so faster than freely-departing birds, these speed gains were accomplished by modulating kinetic and potential energy gains (or losses) rather than increasing overall power output, essentially trading altitude for speed during their evasive maneuver. Finally, the trajectories of defending birds were directed toward the position of the encroaching bird rather than the feeder.

Hollow cylindrical muscular organs are widespread in animals and are effective in providing support for locomotion and movement, yet are subject to significant non-uniformities in circumferential muscle strain. During contraction of the mantle of squid, the circular muscle fibers along the inner (lumen) surface of the mantle experience circumferential strains 1.3 to 1.6 times greater than fibers along the outer surface of the mantle. This transmural gradient of strain may require the circular muscle fibers near the inner and outer surfaces of the mantle to operate in different regions of the length-tension curve during a given mantle contraction cycle. We tested the hypothesis that circular muscle contractile properties vary transmurally in the mantle of the Atlantic longfin squid, Doryteuthis pealeii. We found that both the length-twitch force and length-tetanic force relationships of the obliquely striated, central mitochondria-poor (CMP) circular muscle fibers varied with radial position in the mantle wall. CMP circular fibers near the inner surface of the mantle produced higher force relative to maximum isometric tetanic force, P 0 , at all points along the ascending limb of the length-tension curve than CMP circular fibers near the outer surface of the mantle. The mean ± s.d. maximum isometric tetanic stresses at L 0 (the preparation length that produced the maximum isometric tetanic force) of 212±105 and 290±166 kN m −2 for the fibers from the outer and inner surfaces of the mantle, respectively, did not differ significantly (P=0.29). The mean twitch:tetanus ratios for the outer and inner preparations, 0.60±0.085 and 0.58±0.10, respectively, did not differ significantly (P=0.67). The circular fibers did not exhibit length-dependent changes in contraction kinetics when given a twitch stimulus. As the stimulation frequency increased, L 0 was approximately 1.06 times longer than L TW , the mean preparation length that yielded maximum isometric twitch force. Sonomicrometry experiments revealed that the CMP circular muscle fibers operated in vivo primarily along the ascending limb of the length-tension curve. The CMP fibers functioned routinely over muscle lengths at which force output ranged from only 85% to 40% of P 0 , and during escape jets from 100% to 30% of P 0 . Our work shows that the functional diversity of obliquely striated muscles is much greater than previously recognized.

Recent work has shown that contraction of hollow, cylindrical, muscular organs is accompanied by significant non‐uniformities in circumferential strain across the muscular body wall. In squid, circumferential strain along the inner surface of the mantle wall is 1.3 to 1.6 times greater during the mantle contractions used to power jet locomotion than along the outer surface of the mantle. This transmural gradient of strain may result in the circular muscle fibers from near the inner and outer surfaces of the mantle operating over different regions of the length‐tension curve during the same mantle contraction cycle, potentially generating different instantaneous forces. We used sonomicrometry on swimming squid and isometric tests on bundles of circular fibers to test the hypothesis that circular muscle contractile properties vary transmurally in the mantle in the Atlantic longfin squid, Doryteuthis pealeii. We found that the length‐force relationship of the obliquely striated circular muscle fibers varied significantly with radial position in the mantle wall. Sonomicrometry experiments revealed that the circular fibers operated in vivo primarily along the entire ascending limb of the length‐tension curve. Our work shows that the functional diversity of obliquely striated muscles is much greater than previously thought. Supported by NSF grant IOS‐0950827.

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